CONTENTSPreface Thomas .I. Ahrens vii Crystallographic Data for Minerals (2-l) Joseph R. Smyth and Tamsin C. McCormick Thermodynamic Properties of Minerals (2-2) Alexandra Navrotsky 18 Thermal Expansion (2-4) Yingwei Fei 29 Elasticity of Minerals, Glasses, and Melts (2-5) Jay D. Bass 45 Elastic Constants of Mantle Minerals at High Temperature (2-5a) Orson L. Anderson and Donald G. Isaak 64 Static Compression Measurements of Equations of State (2-6a) Elise Knittle 98 Shock Wave Data for Minerals (2-6h) Thomas .I. Ahrens and Mary L. Johnson 143 Electrical Properties of Minerals and Melts (2-8) James A. Tyburczy and Diana K. Fisler 185 Viscosity and Anelasticity of Melts (2-9) Donald B. Dingwell 209 Viscosity of the Outer Core (2-9a) R. A. Secco 218 Models of Mantle Viscosity (2-9h) Scott D. King 227 Plastic Rheology of Crystals (2-10) J. P. Poirier 237 Phase Diagrams of Earth-Forming Minerals (2-11) Dean C. Presnall 248 CONTENTS Diffusion Data for Silicate Minerals, Glasses, and Liquids (2-12) John B. Brady 269 Infrared, Raman, and Optical Spectroscopy of Earth Materials (2-13) Q. Williams 291 Nuclear Magnetic Resonance Spectroscopy of Silicates and Oxides in Geochemistry and Geophysics (2-14) Jonathan F. Stebbins 303 MGssbauer Spectroscopy of Minerals (2-15) Catherine McCammon 332 Index 349 PREFACE The purpose of this Handbook is to provide, in highly accessible form, selected critical data for professional and student solid Earth and planetary geophysicists. Coverage of topics and authors were carefully chosen to fulfill these objectives. These volumes represent the third version of the “Handbook of Physical Constants.” Several generations of solid Earth scientists have found these handbooks’to be the most frequently used item in their personal library. The first version of this Handbook was edited by F. Birch, J. F. Schairer, and H. Cecil Spicer and published in 1942 by the Geological Society of America (GSA) as Special Paper 36. The second edition, edited by Sydney P. Clark, Jr., was also published by GSA as Memoir 92 in 1966. Since 1966, our scientific knowledge of the Earth and planets has grown enormously, spurred by the discovery and verification of plate tectonics and the systematic exploration of the solar system. The present revision was initiated, in part, by a 1989 chance remark by Alexandra Navrotsky asking what the Mineral Physics (now Mineral and Rock Physics) Committee of the American Geophysical Union could produce that would be a tangible useful product. At the time I responded, “update the Handbook of Physical Constants.” As soon as these words were uttered, I realized that I could edit such a revised Handbook. I thank Raymond Jeanloz for his help with initial suggestions of topics, the AGU’s Books Board, especially Ian McGregor, for encouragement and enthusiastic support. Ms. Susan Yamada, my assistant, deserves special thanks for her meticulous stewardship of these volumes. I thank the technical reviewers listed below whose efforts, in all cases, improved the manuscripts. Thomas J. Ahrens, Editor California Institute of Technology Pasadena Carl Agee Thomas J. Ahrens Orson Anderson Don Anderson George H. Brimhall John Brodholt J. Michael Brown Bruce Buffett Robert Butler Clement Chase Robert Creaser Veronique Dehant Alfred G. Duba Larry Finger Michael Gaffey Carey Gazis Michael Gumis William W. Hay Thomas Heaton Thomas Herring Joel ha Andreas K. Kronenberg Robert A. Lange1 John Longhi Guenter W. Lugmair Stephen Ma&well Gerald M. Mavko Walter D. Mooney Herbert Palme Dean Presnall Richard H. Rapp Justin Revenaugh Rich Reynolds Robert Reynolds Yanick Ricard Frank Richter William 1. Rose, Jr. George Rossman John Sass Surendra K. Saxena Ulrich Schmucker Ricardo Schwarz Doug E. Smylie Carol Stein Maureen Steiner Lars Stixrude Edward Stolper Stuart Ross Taylor Jeannot Trampert Marius Vassiliou Richard P. Von Herzen John M. Wahr Yuk Yung Vii ~- ~------- Crystallographic Data For Minerals Joseph R. Smyth and Tamsin C. McCormick With the advent of modern X-ray diffraction instruments and the improving availability of neutron diffraction instrument time, there has been a substantial improvement in the number and quality of structural characterizations of minerals. Also, the past 25 years has seen great advances in high pressure mineral synthesis technology so that many new high pressure silicate and oxide phases of potential geophysical significance have been synthesized in crystals of sufficient size for complete structural characterization by X-ray methods. The object of this work is to compile and present a summary of these data on a selected group of the more abundant, rock-forming minerals in an internally consistent format for use in geophysical and geochemical studies. Using mostly primary references on crystal structure determinations of these minerals, we have compiled basic crystallographic property information for some 300 minerals. These data are presented in Table 1. The minerals were selected to represent the most abundant minerals composing the crust of the Earth as well as high pressure synthetic phases that are believed to compose the bulk of the solid Earth. The data include mineral name, ideal formula, ideal formula weight, crystal system, space group, structure type, Z (number of formula units per cell), unit cell edges, a, b, and c in Angstrom units (lo-lo m) and inter-axial angles cc, p, yin degrees, unit cell volume in A3, molar volume in cm3, calculated density in Mg/m3, and a reference to the complete crystal structure data. To facilitate geochemical and geophysical modeling, data for pure synthetic end mcmbcrs arc presented when available. Otherwise, data arc for near end-member natural samples. For many minerals, structure data (or samples) for pure end members are not available, and in these cases, indicated by an asterisk after the mineral name, data for an impure, natural sample are presented together with an approximate ideal formula and formula weight and density calculated from the ideal formula. In order to conserve space we have omitted the precision given by the original workers in the unit cell parameter determination. However, we have quoted the data such that the stated precision is less than 5 in the last decimal place given. The cell volumes, molar volumes and densities are calculated by us given so that the precision in the last given place is less than 5. The formula weights presented are calculated by us and given to one part in approximately 20,OflO for pure phases and one part in 1000 for impure natural samples. J. R. Smyth, and T. C. McCormick, Department of Geological Sciences, University of Colorado, Boulder, CO 80309-0250 Mineral Physics and Crystallography A Handbook of Physical Constants AGU Reference Shelf 2 Copyright 1995 by the American Geophysical Union. Table 1, Crystallographic Properties of Minerals. Formula Crystal Space structure z a B Y Unit Cell Molar Density Ref. Weight System Group Type (4 (“! (“) Vol (K3) Vol (cm3) (calc)(h4g/m3) Mineral Formula Single Oxides Hemhxkie cuprite cuzo Monoxides Group Periclase NsO h) WUStite Fe0 Lime CaO Bunsenite NiO Munganosite MnO Tenorite cue Montroydite HgO Zincite ZnO Bromellite Be0 sesquioxide Group 143.079 Cub. Pdm Cuprite 2 4.2696 17.833 23.439 6.104 25 40.312 Cub. F&n Halite 4 4.211 71.848 Cub. F&n Halite 4 4.3108 56.079 Cub. F&n Halite 4 4.1684 74.709 Cub. F&m Halite 4 4.446 70.937 Cub. Fm%m Halite 4 4.8105 79.539 Mono.C2lc Tencrite 4 4.6837 3.4226 216.589 Orth. Prima Montroydite 4 6.612 5.20 81.369 Hex. P63mc Wurtzite 2 3.2427 25.012 Hex. P63nu: Wurtzite 2 2.6984 74.67 11.244 3.585 93 80.11 12.062 5.956 61 111.32 16.762. 3.346 235 72.43 10.906 6.850 235 87.88 13.223 5.365 195 99.54 8 1.080 12.209 6.515 11 128.51 19.350 11.193 12 47.306 14.246 5,712 189 26.970 a.122 3.080 189 5.1288 3.531 5.1948 4.2770 254.80 25.517 3.986 157 302.72 30.388 5.255 23 289.92 29.093 5.224 157 297.36 29.850 5.021 157 834.46 31.412 5.027 75 1171.9 44.115 10.353 167 331.8 49.961 3.960 176 1358.19 51.127 3.870 177 1386.9 52.208 5.583 217 331.27 49.881 5.844 216 Corundum Hematite Eskolaite Kureliunite Bixbyite Avicennite Claudetite Arsenolite Senurmontite Valentinite Dioxide Group Brookite Anatase Rutile Cassiterite Stishovite Pyrolusite Baddeleyite Uianinite Thoriunite -41203 Fe203 Cr203 v203 Mnz03 T1203 AS203 AS203 SW3 Sb203 TiO2 79.890 Orth. Ph Brookite 8 9.184 5.447 TiO2 79.890 Ten. Mtlamd Anatase 4 3.7842 Ti02 79.890 Tetr. P42/mnm Rutile 2 4.5845 SnO2 150.69 Tetr. P42/mnm Rutile 2 4.737 SiO2 60.086 Tea P4dmnm Rutile 2 4.1790 MnO2 86.94 Ten. P42/mnm Rutile 2 4.3% m2 123.22 Mono.P;?t/c Baddeleyite 4 5.1454 5.2075 UOZ 270.03 Cub. F&m Fluorite 4 5.4682 Th02 264.04 Cub. F&m Fluorite 4 5.5997 Multiple Oxides Chry~Yl Spin.51G roup Spine1 Hercynite Magnesiofenite BeAl& 126.97 Orth. Prunb Oiivine 4 4.424 9.396 5.471 227.42 34.244 3.708 96 M&Q FeA120.t MgFezQ Mugnesiochromite M&r204 Magnetite FeFe204 Jacobsite MnFe204 Chnnnite FeCr204 101.961 Trig. 159.692 Trig. 151.990 Trig. 149.882 Trig. 157.905 Cub. 456.738 Cub. 197.841 Mono. 197.841 Cub. 291 A98 Cub. 291.498 Chth. R3C R% R% R% la7 1ClS P21ln F&m F&m 6 4.7589 6 5.038 6 4.9607 6 4.952 16 9.4146 16 10.543 4 7.99 4.65 16 11.0744 16 11.1519 4 4.911 12.464 12.9912 13.772 13.599 14.002 Corundum Corundum Corundum Bixbyite Bixbyite Claudetite Arsenolite Arsenolite Vulentinite 9.12 78.3 5.412 5.145 9.5146 2.9533 3.185 2.6651 2.871 5.3107 257.38 19.377 4.123 17 136.25 20.156 3.895 105 62.07 18.693 4.2743 204 71.47 21.523 7.001 15 46.54 14.017 4.287 20 55.48 86.937 5.203 121 140.45 21.149 5.826 208 163.51 24.620 10.968 126 175.59 26.439 9.987 227 99.23 142.27 Cub. F&m Spinet 173.81 Cub. F&m Spinet 200.00 Cub. F&-m Spine1 8 8.0832 8 8.1558 8 8.360 8 8.333 8 8.394 8 8.5110 8 8.3794 528.14 39.762 3.578 61 542.50 40.843 4.256 99 584.28 43.989 4.547 100 578.63 43.564 4.414 100 591.43 44.528 5.200 100 616.51 46.416 4.969 100 588.31 44.293 5.054 100 62 1.96 46.826 4.775 106 192.30 Cub. F&m Spine1 231.54 Cub. Fcdm Spine1 230.63 Cub. k’&m Spine1 223.84 Cub. F&-m Spine1 Ulvwspinel TiFe204 223.59 Cub. F&m Spinet 8 8.536 Table 1. Crystallographic Properties of Minerals (continued). Mineral Formula Fotmula Crystal Space StNCtUE z 0 Y Unit Cell Molar Density Ref. Weight System Group ‘be (A) (“) Vol (A3) Vol (cm3) (calc)(Mg/m3) Tilanale Group Ihnenite FeTiOs Pyrophanite MnTiO3 Perovskite CaTi Armalcolite Mg.@esTiS% Pseudobrookite FeaTi Tungstates and Molybdnks 151.75 Trig. R? Ilmenite 6 5.0884 14.0855 315.84 3 1.705 4.786 229 150.84 Trig. Rs Ilmenite 6 5.137 14.283 326.41 32.766 4.603 235 135.98 Orth. Pbnm Perovskite 4 5.3670 5.4439 7.6438 223.33 33.63 4.044 113 215.88 Otth. Bbmm Pseudobrookite 4 9.7762 10.0214 3.7485 367.25 55.298 3.904 230 239.59 Orth. Bbmm Pscudobrookite 4 9.747 9.947 3.717 361.12 54.375 4.406 3 Ferberite FeW04 Huebnerite MnW04 Scheelite CaWO4 Powellitc CaMoO4 Stolzite Pbwo4 Wulfenite PbMoO4 303.70 Mono. PZ/c Fe&rite 2 4.730 5.703 4.952 90.0 133.58 40.228 7.549 225 302.79 Mono.P2/c Ferberite 2 4.8238 5.7504 4.9901 91.18 138.39 4 1.676 7.265 231 287.93 Tetr. 141/a Scheelite 4 5.243 11.376 312.72 47.087 6.115 114 200.02 Tetr. 141/a Scheelite 4 5.23 11.44 301.07 45.333 4.412 101 455.04 Tetr. 141/a Scheelite 4 5.46 12.05 359.23 54.091 8.412 101 367.12 Tctr. 141/a Scheelite 4 5.435 12.11 357.72 53.864 6.816 101 Hydroxides Gibbsite Diaspore Bochmite Brucitc Goethite Lepidoehrosite WW3 AID APOW MgWh FeO(OH) FeO(OH) 78.00 Mono.P2t/n 59.99 Orth. Pbnm 59.99 Orth. Amam 58.33 Trig. !%I 88.85 Or&. Pbnm 88.85 orth. cmczt Gibbsite 8 8.684 5.078 9.736 4 4.401 9.421 2.845 4 3.693 12.221 2.865 1 3.124 4.766 4 4.587 9.937 3.015 4 3.08 12.50 3.87 9454 Boehmite Brucite Gocthite Boehmite 427.98 32.222 2.421 188 117.96 17.862 3.377 34 129.30 19.507 3.075 98 40.75 24.524 2.377 243 137.43 20.693 4.294 65 148.99 22.435 3.961 43 Carhonotes Magnesite Smithsonite Siderite Rhodochrositc Otavite Calcite Vaterite Dolomite Ankerite Aragonite Strontianite Cerussite Witherite Amrite Malachite M&03 84.32 Trig. R% zatco3 125.38 Trig. R% FeCQ 115.86 Trig. R% MnCOs 114.95 Trig. R% CdCOj 172.41 Trig. R% CaC03 100.09 Trig. R?c CaC03 100.09 Hex. P63hmc CaMgKQh 184.41 Trig. d c*dco3)2 215.95 Trig. RT CaC03 100.09 orth. Pmcn SrC03 147.63 Orth. Pmcn Pbco3 267.20 Orth. Pmcn BaC03 197.39 orth. Pmcn Cu3@H)2(C03)2 344.65 Mon0.P2~/c Cuz@H)zC% 221.10 Mono.P2t/a Calcite Calcite Calcite Calcite Calcite Calcite Vaterite Dolomite Dolomite Aragonite Aranonite Araaonite Aragonite Amrite Malachite 6 4.6328 15.0129 6 4.6526 15.0257 6 4.6916 15.3796 6 4.7682 15.6354 6 4.923 16.287 6 4.9896 17.0610 12 7.151 16.937 3 4.8069 16.0034 3 4.830 16.167 4 4.9614 7.9671 5.7404 4 5.090 8.358 5.997 4 5.180 8.492 6.134 4 5.3126 8.8958 6.4284 2 5.0109 5.8485 10.345 4 9.502 11.974 3.240 92.43 98.75 279.05 28.012 3.010 54 281.68 28.276 4.434 54 293.17 29.429 3.937 54 307.86 30.904 3.720 54 341.85 34.316 5.024 26 367.85 36.9257 2.7106 54 750.07 37.647 2.659 146 320.24 64.293 2.868 182 326.63 65.516 3.293 21 226.91 34.166 2.930 51 255.13 38.416 3.843 51 269.83 40.629 6.577 191 303.81 45.745 4.314 51 302.90 91.219 3.778 245 364.35 54.862 4.030 244 Nitrates Soda Niter Niter Berates Borax Nd% 85.00 Trig. R% Calcite 6 5.0708 16.818 374.51 37.594 2.261 198 KNOs 101.11 or&l. Pmcn Aragonite 4 5.4119 9.1567 6.5189 323.05 48.643 2.079 159 Na2B40s(OH)4.8HaO 381.37 Mono. C2/c 11.885 10.654 12.206 106.62 1480.97 223.00 1.710 128 Y Table 1. Crystallographic Properties of Minerals (continued). P Mineral Formula FormulaCrystal Space StNCtUE % a (A) Y Unit Cell Molar Density Ref. Weight System Group TYPe (“) Vol (A3) Vol (cm3) (calc)(Mg/m3) b2 Kernite Na2B406(0tI)2.31~20 Colemanite CZ~B~O~(OH)~.H~O 273.28 Mono. P21k Kernitc 4 7.0172 9.1582 15.6114 108.86 953.41 143.560 205.55 Mono. P2,la Colemanitc 4 8.74” 1 I.264 6.102 110.12 564.30 84.869 1.904 48 F 2.419 42 E; Q BaS04 233.40 Orth. Pbnm Baritc 4 7.157 8.884 5.457 346.91 52.245 SrS04 183.68 Orth. Pbnm I&rite 4 6.870 8.371 5.355 307.96 46.371 PbS04 303.25 Oh. Pbnm Barite 4 6.959 8.482 5.398 318.62 47.911 CaS04 136.14 Orth. Amma Anhydrite 4 7.006 6.998 6.245 306.18 46.103 CaS042H20 KAk@0dz(0Hki KFes(S0dz(‘W6 CU3(S04)(OW4 NqSO4 K2SG4 MgS047HzO 172.17 Mono.lZ/a GypSlUll 4 5.670 15.201 414.21 Trig. RTm Alunite 3 7.020 500.81 Trig. RTm Alunite 3 7.304 354.71 orth. Prima Antlerite 4 8.244 142.04 Orth. F&ii Thenardite 8 9.829 114.21 Orb. Pmcn Arcanite 4 5.763 246.48 orth. P212121 Epsomite 4 11.846 118.60 6.043 12.302 10.071 12.002 6.533 17.223 17.268 11.987 5.868 7.476 6.859 494.37 74.440 735.04 147.572 797.80 160.172 597.19 89.920 709.54 53.419 433.90 65.335 975.18 146.838 Cag(PO&OH WPWsF Ca#O&CI ccPo4 ym4 W~~~dWQh LiFcPOq LiMnP0.j LiAI(F,OH)POd AMOW3W Am4 502.32 Hex. P63lm Apatite 504.31 Hex. P63/m Apatite 520.77 Hex. P63im Apatite 235.09 Mono.P2t/n Monazite 183.88 Tetr. I4tlomd Ziicon 7.04 2133. Trig. R3c Wbitlockite 157.76 Grth. Pmnb Olivine 156.85 Orth. Pmnb Olivine 146.9 Tric. Pi Amblygonite 199.9 Mono.C2/m Augelitc 121.95 Trig. P3t21 Qu== 2 9.424 2 9.361 2 9.628 4 6.71 4 6.878 3 10.330 4 10.334 4 6.05 2 5.18 4 13.124 3 4.943 6.879 529.09 159.334 3.153 214 6.884 523.09 157.527 3.201 215 6.764 543.01 163.527 3.185 137 6.46 104.0 298.7 44.98 5.23 76 6.036 285.54 43.00 4.277 123 37.103 3428.8 688.386 3.099 38 4.693 291.47 43.888 3.595 237 4.71 294.07 44.280 3.542 101 5.04 112.11 97.78 67.88 160.20 48.242 3.045 16 5.066 112.42 490.95 73.924 2.705 101 10.974 232.21 46.620 2.616 206 6.010 10.32 7.15 7.988 Garnet 8 11.452 1501.9 113.08 3.565 8 Garnet 8 11.531 1533.2 115.43 4.312 8 Garnet 8 11.612 1565.7 117.88 4.199 161 Garnet 8 11.845 1661.9 125.12 3.600 161 Garnet 8 12.058 1753.2 13 1.99 3.850 161 Garnet 8 11.988 1722.8 129.71 3.859 161 MgzSiQ FqSiO4 MnzSi04 Ni2Si04 Ca2Si04 CqSiO4 CaMgSiOd CaFeSi 403.15 Cub. l&d 497.16 Cub. I&d 495.03 Cub. In% 403.15 Cub. IaTd 508.19 Cub. IaTd 500.48 Cub. IaTd 140.70 orth. Pbw?z 203.77 Orth. Pbnm 201.96 Orth. Pbnm 209.50 Ortb. Ptnm 172.24 Orth. Phm 209.95 Orth. Pbmn 156.48 orth. Pbnm 188.01 Orth. Pbnm Olivine 4 4.7534 10.1902 5.9783 289.58 43.603 3.221 69 Olivine 4 4.8195 10.4788 6.0873 307.42 46.290 4.402 69 Olivine 4 4.9023 10.5964 6.2567 325.02 48.939 4.121 69 Olivine 4 4.726 10.118 5.913 282.75 42.574 4.921 124 Olivine 4 5.078 11.225 6.760 385.32 58.020 2.969 50 Olivine 4 4.7811 10.2998 6.0004 295.49 44.493 4.719 32 Olivine 4 4.822 11.108 6.382 341 .x4 51.412 3.040 165 Olivine 4 4.844 10.577 6.146 314.89 47.415 3.965 32 Sulfates Barite Celestite Anglesite Anhydrite Gypsum Alunite* Jamsite* Antleritc Thenarditc Arcanite Epsomite Phosphates Hydroxyspatite Fluorapatite Chlorapatite Monazitc Xenotime Whitlockite Triphylite Lithiophyllite Amblygonite* AugeIite* Berlinite Orthosillcates Garner Group Almandine Spessartine Grossular Andradite Uvarovite Olivine Group Forsterite Fayalite Tephroitc Liebenbergite Ca-olivine Co-olivine Monticellite Kirschsteinite 2.953 118 u 2.313 46 2.807 145 3.127 112 2.959 91 $ 2.659 90 z 2.661 142 m 1.678 36 F v1 Table 1. Crystallographic Properties of Minerals (continued). Mineral Fonnula Formula Crystal Space Stlucture z a (A) 8, Y Unit Cell Molar Density Ref. Weight System Group Type (“1 Vol (A3) Vol (cm3) (calc)(Mg/m3) Zircon Group Zircon ZrSiO4 Hafnon HfSi04 Thorite* ThSiO4 Coffinhe’ USi Wilhife Group Phenacite BezSi04 Willemite ZnzSiO4 Eucryptite LiAlSIO4 Ahminosilicate Group Andalusite Al2SiOS Sillimanite AlzSi05 Kyanite A12SiO5 Topaz Al$i04(OH,E)2 Humite Group Norbergite* Mg3Si04F2 Chondrodite* MgstSiOdzF2 Humite* MmMW3Fz Clinohumite* MgdSQhFz Staurolite* Ee.+ALtaSixO&OH)2 Other Ortbosilicotes Titanite CaBSi Datolite CaBSiOd(OH) Gadolinite* BE$eB2SizOto Chloritoid* FeA12Si05(OH)z Sapphirine* MgwWit.502o Prehnite* Ca2Ai(Al,Si3)0to(OH)2 183.30 Tetr. Irlllumd Zircon 4 6.6042 5.9796 260.80 39.270 4.668 95 210.51 Tetr. 14~lumd Zircon 4 6.5125 5.9632 257.60 38.787 6.916 212 324.1 Tetr. 14tlumd Zircon 4 7.1328 6.3188 321.48 48.401 6.696 222 330.2 Tetr. 14@zd Zircon 4 6.995 6.236 305.13 45.945 7.185 115 110.10 Trig. R7 Wiilemite 18 12.472 8.252 1111.6 37.197 2.960 241 222.82 Trig. RI Willemite 18 13.971 9.334 1577.8 52.195 4.221 207 126.00 Trig. Rj Willemite 18 13.473 9.001 1415.0 41.341 2.661 97 162.05 Orth. Pnnm Andalusite 4 7.7980 7.9031 5.5566 162.05 Orth. Pbam Sillimanite 4 1.4883 1.6808 5.7774 162.05 Tric. PI Kyanite 4 1.1262 7.8520 5.5741 89.99 182.0 Orth. Pbnm Topaz 4 4.6651 8.8381 8.3984 342.44 51.564 3.1426 233 332.29 50.035 3.2386 233 106.03 293.72 44.221 3.6640 233 346.21 52.140 3.492 242 101.11 203.0 Orth. fhm 343 .I Monof2tlb 484.4 Oh. fhm 624.1 Mono. f&lb 1704. Mono. c2/m Norbergite 4 4.7104 10.2718 8.7476 Chondrodite 2 4.7284 10.2539 7.8404 Hurnite 4 4.7408 10.2580 20.8526 Clinohumite 2 4.7441 10.2501 13.6635 Staurolite 1 7.8713 16.6204 5.6560 423.25 63.13 3.186 13 359.30 108.20 3.158 74 1014.09 152.70 3.159 183 652.68 196.55 3.259 186 139.94 445.67 3.823 209 109.06 100.786 90.0 196.06 Mo~o.~?$/Q Titanite 4 7.069 8.122 6.566 159.94 Mono.f&lc Datolite 4 4.832 7.608 9.636 604.5 Mono f&/a Datolite 2 lO.ooo 7.565 4.786 Pi 251.9 Tric. Chioritoid 4 9.46 5.50 9.15 97.05 690.0 Mono.fZ& Sapphirine 4 11.266 14.401 9.929 412.391 Orth. fxm Prehnite 2 4.646 5.483 18.486 90.40 90.31 101.56 125.46 C~(Mg~eAl)AlaSi~~O~42(0H)r~l915.1 Mono.CZlm fi HFeCa&BSbOra 570.12 Tric. Pumpelieyite 1 8.831 5.894 19.10 97.53 Axinite 2 1.151 9.199 8.959 91.8 98.14 370.23 55.748 3.517 213 354.23 53.338 2.999 63 360.69 108.62 5.565 148 90.10 462.72 69.674 3.616 88 1312.11 197.57 3.493 149 470.91 141.82 2.908 170 985.6 593.6 3.226 172 77.30 569.61 171.54 3.324 220 Pumpelleyite Axinite Sorosiiicates & Cyciosiiicates Epidote Group Zoisite Cafil&Otz(OH) Clinozoisite Ca2Al$Si3012(OH) Hancockite* Ca(Rh,Sr)FeAl2Si30r~(OH) Allanite* CaBE(Al,Fe)$i30t2(0H) Epidote* Ca~FeAl#i30t2(0H) Melilite Group Melilite* CaNaAlSizq Gehlenite* Ca;?AlAiSi@ Akerrnanite Ca2MgSi207 Olher Sorosilicates and Cyclosilictaes Lawsonite CaAizSiz07(OH)$I20 BUYi Be3Ai2SieOtx Cordierite’ MgzA4SisOts 454.36 ortb. funa Zoisite 4 16.212 5.559 10.036 454.36 Mono. Pztlm Epidote 2 8.819 5.583 10.155 590.6 Mono.f21/m Epidote 2 8.96 5.67 10.30 565.2 Mono.f2t/m Epidote 2 8.927 5.761 10.150 454.4 Mono.f 2t/m Epidote 2 8.8877 5.6275 10.1517 904.41 136.19 3.336 52 454.36 136.83 3.321 52 416.5 143.5 4.12 53 413.97 142.74 3.96 53 458.73 138.15 3.465 70 115.50 114.4 114.77 115.383 258.2 Ten. fa21rn Meiilite 2 7.6344 5.0513 294.41 88.662 2.912 134 214.2 Tetr. fZ21m Melilite 2 7.7113 5.0860 302.91 91.220 3.006 135 212.64 Tetr. fZ2lrn Meiiiite 2 7.835 5.010 307.55 92.6 19 2.944 116 314.24 orth. ccmm Lawsonite 4 8.795 537.51 Hex. P6lmmc Beryl 2 9.2086 584.97 orth. ccmm Betyl 4 17.079 5.841 9.730 13.142 615.82 101 .I6 3.088 19 9.1900 614.89 203.24 2.645 152 9.356 1554.77 234.11 2.499 45 Table 1. Crystallographic Properties of Minerals (continued). Mineral Fotmula Formula Crystal Space structure 2 a Unit Cell Molar Weight System Group Type (A) (S, Y Density Ref. (“) Vol (A3) Vol (cm3) (calc)(Mg/m3) Tourmaline* NaFe~Al&S~0~7(0H)~ 1043.3 Trig. R3m Vesuvianite* CatgFezMgAltoSitsqo(OH,F)s2935. Tetr. P4/nnc Chain Sillfates EnstotifelFerrosilite Group EIlStatik f+ww6 200.79 Oh. Pbca Ferrosilite Fe#i& 263.86 Orth. Pbca Clinoenstatite MgzSizOs 200.79 Mono. P2tlc Clinoferrosilite Pe2Si206 263.86 Mono.P&lc m 20 115.005 33 Clincpymxene 4 9.C2/m Sheet Slllctaes Talc and Pyrophyllite Talc &s%OldOH)z 379.94 orth.737 5.21 3.3 Mono.218 110.994 10.531 17.51 18. C2lm Tremolite* ~a.312 105.7 3.0872 5.56 401.579 8.701 92.721 7.CZlc Spodumene LiAlSi206 186.14 Mono. Pi Pyroxmangite Mn7Si70a 917.048 Amphibole 2 9.49 62.116 163 2 7.054 7.341 39 Clinopyroxene 4 9.93 96.541 17.630 112.66 2.94 Mono.60 65.37 419.980 7.263 66 Vesuvianite 2 15.33 101.171 7.795 5.926 104.67 579.71 128.CZ/m Glaucophane* Naz(FeMaAlrSisOn~OH~~ 789.62 3.652 5.36 62. Ii Rho&mite MqSisOts 655.08 Mono.~C@WWzz(OH)z 823.867 3.85 65.jO22(OH)2 853.87 125.06 421.9 3.9 Mono.2 Mono.09 389.227 8.CVc Jade& Ntilsi206 202.23 Orth.013 Amphibole 2 9.15 58.90 Mono Calm Pargas&* NaCa2FeMg.78 .43 437.27 94.190 1592.395 5.70 450.888 163 2 11.285 104.15 Mono.596 3.423 8.461 8.845 9.104 11.92 5.899 5.741 Onhoamphibole 4 18.s(Mg$ez)A12Si.85 60.30 115.204 197 Orthopyroxene 8 18. Ci Trioclohedral Mica Group An&e* KFe3(AlSi@t0(OH)2 511.4 Tric.429 6 Orthopyroxene 8 18.813 8.994 3.06 64.851 6.018 90.606 3.30 100.188 108.20 Mono.09 Mono.13 812.52 224.44 788.72 67.09 3.819 5.560 18.79 5.dSi309 358.176 39 Clinopyroxene 4 9.022 Amphibole 2 9.223 107.002 197 Clinoenstatite 4 9.11 Tric.239 3.C2/m Lepidolite* KAlLi2AISi30t0(OH)2 385.231 99.42 429.63 3.53 100.2284 108. (X/m Phlogopite* KMgfi&OldOH)2 417.1 Mono.2 Mono. Pi Aenigmatite’ Na@5TiTiSkOzo 867.740 5.318 219 Orthoamphibole 4 18.406 10.31 Tric.455 113.249 5.279 39 Clinopyroxene 4 9. Ci Bustamite* GaPe.44 Mono.55 382. Pi Pectolitc’ HNaCa&Q 332. Ci Pyrophyllite A12Who@H)2 360.910 18.616 11.PUa Amphibole Group Gedrite* Na.592 39 Clinopymxene 4 9.C2lm Ziiwaldite* K(AlFeLi)AlSi3Otu(OH)2 434. CL/c Pyroxenoid Group Wollastonite CajSi3Og 348.54 95.19 Amphibole 2 9.863 18.188 150 Clinoenstatitc 4 9.49 Tric. C2Ic Hedenbergitc CaPeSi 248.63 438.656 39 Clinopyroxene 4 9.5 Tric.039 3.16 Tric.72 Mono.18 82.752 155 2 6.274 106.749 155 2 10.438 164 Bustantite Rhodonite Pyroxmangite Aenigmatite Pectolite Petalite 4 10.C2/c Lepidolite* KAU&AISi30tdOH)2 385.946 7.992 7.179 832.305 99.609 8.2 Mono.8 421.251 105.825 5.80 2.58 66.56 Mono.261 107.892 4.658 8. Pm Cummingtonite* ~MgsFez)SisOzz(OH)2 843.6 Tric.04 118. C2lc Acmite NaFeSizOs 23 1.564 5.508 3.533 11.56 83.445 3.98 63.26 Mono.54 427.29 764.5 319.076 5.722 5.35 63.65 Tric.33 418. n/c Cosmochlnr NaCrsi206 227.626 8.024 5.56 83.778 2841.31 244.603 17.10 2.CUc Ca-Tschennaks CaAlAlSiOs 218.84 174.CZ/m Tounnaline 3 15.Clinopyroxme Group Diopside CaMgSi& 216.237 875.941 4.746 8.869 40 2 7.7085 9.245 104.10 Mono.2818 5. Prima Anthophyltite* C%sFez)Sis022(OH)2 843. C2Ic LepidolW KAlLifiISi3Oto(OH)2 385.32 744.294 107.516 44 Clinopyroxene 4 9.tAl#i&22(OH)2 864. Pi Petalite LiAlS&Ote 306.55 94.427 9.14 102.023 7.35 105.937 163 4 9.676 3. 98 3.324 10.308 9.39 843.124 192 4 9.155 100.32 126.9 912. Weight System Group Type (4 (“) VoI (A3) Vol (cm3) (calc)(Mg/m3) Mineral Formula Dioctahedral Mica Group Muscovite* Paragonite* Margarite” Bityite* Chlorite Group Chlorite* Chlorite* clay Group NWXite Dickite Kaoiinite Amesite* Lizardite* Tektosiiicates Silica Group Qu- Coesite Tridymite Cristobaiite Stisbovite Feldspar Group Sanidine orthoclase Micro&e High Aibite Low Aibite Anorthite Ceisian KAi~ISi30tc(OH)2 398.3 Mono. FomntlaCrystal Space structure z a Y Unit Ceii Molar Density Ref.57 Chlorite-IIW 2 5.63 506.234 14.14 271.173 9.69 146.67 1725.814 125 1M IM =41 2M2 1M 1M 2 5.295 103.125 939.01 92 3.14 60 3.636 108 2.1038 8.290 9.588 22 .602 24 2.04 5.111 58 3.89 129.38 141.3 Mono.8 265.0 144.834 187 341 4 5.% 274.966 9.09 99.872 94 4 5.14 210.898 19.327 9.85 2.111 95.68 90.0457 95.46 89.57 2.82 141.049 130 Chlorite-IIb2 2 5.1918 9.209 9.0153 20.28 466.909 129 2M2 4 5.2 3.01 10.160 8.058 8.6 140.296 9.74 933.81 699.87 2.986 82 Table 1.825 194 2 5.347 91.C2/c 2Mt 4 5. Crystallographic Properties of Minerals (continued).165 185 3.227 14.776 175 Talc 2 5.5 2.58 940.386 9.358 90.9 902.21 99.51 132.65 259.053 20.287 94.640 109 2.63 3.C2/c Ca(LiAi)z(AIBeSiz)Ote(OH)2 387.20 9.08 487.16 128.184 169 3.13 2.096 100.18 100.C2/c CaAifilSi30tu(OH)2 399.5.268 100.46 858.22 20. C2/c NaAi~AiSi~Oto(OH)~ 384.77 136.7 909.60 273.140 10.763 19.46 98.56 140.60 2.460 90.55 2.128 8.036 2.190 10.9 870.52 2.215 94 2 5.654 2.327 96.061 83 2M1 4 5.185 99.8 262.33 97.09 453.8287 19.135 168 Talc 2 5.82 152.148 95.8 1765.83 480.2 Mono.33 3.35 877.00 700.38 90.64 425.24 210.791 193 2 5.325 9.3 Mono. 159 94.142 12.25 Tetr.Cc 258.47 Mono.16 Mono.0 Mono.8 Mono.173 12.332 7.1934 5.69 200.48 loo.621 178 584.2 1698.01 22.07 108.0 2097.75 2356.599 22 2.C2/m Heuiandite 1 17.869 14.48 108.70 658.627 13.233 178.4cm 158 Fekispathoid Group Leucite KAiSizOe Kaisilite KAiSi04 Nepheiine KNa@J&tOts Meionite* Ct&&jSi&&@ Marialitef NaqAI.8 Chth Pncn Thomsonite 4 13.047 13.%4 7.C2/m 555. CZm Heuiandite 1 17.221 Dickite 4 5.571 47 KAiSisOs 278.94 722.679 64 932.4 2487.400 2827.017 4.408 115.1 1263 .11 115.374 724.269 ill 4 4.9448 7.89 99.697 113.27 99.70 720. Cmcm Mordenite 1 18.610 234 NaAiSi& 262.941 7.34 2.110 93.028 7.700 104.218 116.085 Mono.53 116.625 144 555.478 2.1554 8.085 Tetr.16 Mono.01 90.1464 12.4052 113.085 Trig.657 2.452 2.161 12. I4tla Leucite lb 13.2.Cc 258.91 91.95 99.17 25.90 110.54 14.61 103.17 Hex. P42ln Scapoiite 2 12.82 662.208 14.O 2132.648 127 16 7.8 Tric.832 117.4 Ortb.1 Trig.165 228 BaAi2Si2Os 375. Ci 258.33 Tric.4048 91. Ci Sanidine 4 8.561 31 NaAiSigOs 262.075 3620.46 90.633 17.318 173 2 4.22 1466.778 86 2.93 2585.909 210 48 18.3 332.9 Trig.993 8.721 13.925 2.822 329.13 108. PI 278.347 Amesite 4 5.26 2.738 103.045 14.?/c Anorthite 8 8.16 Tric.jSi.09 13.688 2.875 7. Ci Albite 4 8.3 .494 4.7 Tric.24 667.2 499.26 SiO2 SiO2 SiO2 SiO2 SiO2 60.CZm Sanidine 4 8.283 548.978 6.319 9.558 199 KAISi30s 278.69 2.3796 7.440 3.33 Hex.2 26.991 25.937 14.39 115.CZlm Sanidine 4 8. P31m Nacrite 4 8.68 664.61 87.085 Tar.215 90.167 20.788 2. P63 Nepheiine 2 9.085 Mono.69 Lizardite IT 1 5.715 17.5 Ten.560 l2.156 15.561 12. Ci Albite 4 8.059 7.09 2.831 7.996 7.461 139 158.430 Thomsonite* NaCa2AisSis02cbH20 671.4 60.1790 2.27 89.178 8.287 20 KAISi& 278.2 1284.75 2110.060 90.611 7.785 7.1829 120.803 15.621 89 CaAI&Os 278. f322l 60.948 172.65 115. f4t2t2 Coesite Tridymite Cristobalite 60. P42/n Scapolite 2 12.33 Mono. Pi Anorthite 8 8.01 719.I.7 Mono.721 Kaolinite 2 5. W&nm Rutiie 3 4.089 13.96 688.735 1030.19 116.40 2.8 1557.83 87.261 1336.557 1123.862 89. P63 NepheIine 2 5.599 132 3526.425 2.09 107.Cc 60.C2/c 60.194 7.jO~Cl Zeolite Group AnaIcime* NatsAIt&20g~i 6H2O Chabazite’ Ca$i&sOw i3HzO Mordenite* KsAi&~Oga24H20 CIinoptiioIite* KNa$J+Ai&+&~24H20 Heulandite’ Ca4Kdh%&n26H20 218.587 1103.529 2750.054 2.36 Tric.1 Tetr. Cl 277.757 131 863.6651 46. I4llacd Analcime 1 13.283 2.23 Tric.4 2819.76 20.610 2.192 116.9 Tetr.7 338.19 218.23 Tric. 88.12 100.165 93.35 100.16 8.595 13. R%I Chabazite 1 13.33 Mono.909 5.179 115. 16 2210.3 Orth.273 107 2.41 910. 2292.1 2050.177 211 2.6C02 1008.072~34H~02968.2 2256.4 1356.336 141 P 2.6 203. 00 Mineral Formula Formula Ctystal Space structure z a (A) Y Unit Cell Molar Density Ref. Fdd2 Natrolite 8 18.326 Sodalite* NqA13Si301~CI 484.9 Cub.05 2561. Pii3n Sodahte 2 8.12 2.34 Mono Fd Natrolite 8 18.065 37 2.2 90.3 339.4 423.87 697.62 1155.48 1982.17 Mono.8 1205.682 Brewsterite* SrAlfiis01~5H20 656.@~~l.2 96.7 Mono.886 Fetrierite+ NaKMgfil7Si2gQzlBH20 2590.24 611.06 Cub. P21lm Brewsterite 2 6.gAlgSit0032.8 124.. Mono.44 Mono Am Laumontite 4 7.09 Mono.3 169.443 184 22.8 172.146 9 m 2.116 Ferrierite* NgKMgAl$%3t@Zl8H20 2614.21 1015.22 Tetr.601 124. 996.5 Hex.~Na&leSi.652 6.06 360.300 8. P21/m Phillipsite 1 9.5 1011.236 Faujasite.3 630. hi2d Natrolite 1 13.508 Gonnardite* Na&qAlgSitt0~12H~O 1626. F&n Sodalite 16 24.221 4 2.879 Phillipsite* K2. Crystallographic Properties of Minerals (continued).668 14. 1331. P21/m Phillipsite 1 9.~AIleSi2C.072 90.2 274. P63lmmc Erionite I 13.1 111.870 StiIbite* Nal.373 5 Table 1.581 Gismondine* Ca&IsSia032.P2rla Fenierite 1 18.549 Natrolite* NazA12Si30te2H20 380.23 71 ii 2. B Weight System Group ‘be (“) Vol (A3) Vol (cm3) (calc)(Mg/m3) 4 Harmotome* Ba$a.64 ScoIecite* CaAl~Si30te~3H20 392.6 Cub.12H20 1291.0 15142.23 Orth.jSireG3~13H~O 1312.024 Garronite* NaCa&I.21 Edingtonite* Ba2A14SisO2e8H20 997.74 Ericnite* MgNaKZCa2AlgSi~707~18H202683.740 13.9 2.131205 120824 z1 2. NqCaAl.3 609. 570.306 133 X 2.252 Cancrinite* Car.16Hfl 1401. C2lm Stilbite 1 13.9266 Merlinoite+ K&afilgSi~0~24H20 2620.5 Mono.9 600.590 Pollucite* CsAISi#s 312.3Ca4.195 72 3 .86 210.5Al$itt03~12H20 1466. 18.00 599.238 174 E 2.865 Laumontite* CaA1$%401~4H~O 470.02 2252.9 1349.132 153 2. Immm Merlinoite 1 14. la?d Analcime 16 13.139 8.1 Hex.12 Tetr. P63 Cancrinite I 12.764 140 2 2.223 226 8 2.6 696.81 olth.5Cal. lzm2 Gismondine 1 9. PTi2lm Edingtonite 1 9.&0~16H20 1090.28 1193. P21la Gismondine 1 10.767 14.92 2000.5 1235.04 Tetr.2257.2 Mono.6 702.264 138 2. lmmm Ferrierite I 19.693 14.81 1024. 61 10.166 235 1.832 10.0 90.169 79 2 2.40 High Pressure Silicates Phase B Group Phase B Ww-%%KW2 Anhydrous B MmSidh Superhydrous B bmWhdOW4 MgSiO+roup MgSiOg-perovskite MgSi03 MgSiO+lmenite MgSiO3 MgSiOs-garnet MgSi03 Wadsleyiie Group Wadsleyite MgzSiO4 I%-Co$SiO 4 CqSiO4 Silicate Spine1 Group rM8zSQ Mg#iO.4729 104 5.978 201 rA 2.383 81 3.909 210 4. y-Fez%04 FezSiO4 y-Ni2SiO4 NizSi04 *02SiO4 CqSiO4 Silica Group Coesite SiO2 Stishovite SiO2 Halides Halite N&l Sylvite KCI Villiaumite NtiF .513 7 3.27 6.24 18.107 103 3.174 236 5.470 7.117 17.287 20 2.810 102 3.044 151 3.162 90.527 128.563 196 4.40 14.455 7.526 9.182 14.626 92.327 166 4.810 5.839 235 18.237 156 2.0 90.3031 9.346 151 2.981 11.380 59 3.729 94.622 6.394 10 3.2.914 18 F I .527 6.0 14.848 236 5.229 14.097 80 In 1.435 59 3.946 7.989 235 2. 0449 524.490 98.4 219.23 14.40 Tetr.96 25 1.044 520.40 Chth.54 14.445 100.09 Mono. Pmcb AnhB 2 5.56 39.78 Orth.138 538.96 40.1464 12.581 140.53 235 Table 1.22 26.10 1458.7284 13.4380 8.048 619. RJ Ilmenite 6 4. Weight System Group Type (A) (“1 Vol (K3) Vol (cm3) (calc)(h4g/m3) Fluorite Frankdicksonite Sellaite CdOIllel Cryolite Neighbceite Chlorargyrite Iodyrite Nantokite Sulfides Pyrrhotite Pyrite Cattierhe Vaesite Marcasite Troilite Smythite Chalcopyrite Cubanite Covelllite Chalcocite Tetrahedrite Bon& Enargite Niccolite Cobaltite Sphalerite Wurtzite(2H) Greenockite Pentlandite Alabandite Galena Clausthalite Altaite CaFz BaF2 MtPz HszCh Na3AIFs .085 Tetr.49 39.588 14.3796 7.40 Grth.1790 2.95 Cub. Fmh Halite 4 5.h Spine1 8 8.791 152.614 58.017 58. Pnnm PhsB 2 5.480 1518.501 11.340 552.187 60.085 Mono.749 618.5591 262.657 46.988 Cub.6956 104.14 40.968 8.8969 162.291 41.511 209.100 Cub.985 248.71 orth.638 74.5 28.6983 11.567 835.443 Cub. Crystallographic Properties of Minerals (continued).515 209.71 Cub. F&m Spine1 8 8.93 2. fmma Wadsleyite 8 5.3 22.1829 60. Fa.555 Cub.868 14. P21/c PhsB 4 10. Mineral Formula Formula Crystal Space Structure Z a Y Unit Cell Molar Density Ref.98 37.159 100.40 Trig.78 Cub.95 Ortb.628 140. C2lc Coesite 16 7.753 11.54 26.Carobbiite KF 741.2566 538. Fdm Halite 4 4. F&m Spine1 8 8.524 8. F&n Halite 4 6.0894 13. 141/a Garnet 32 11. Pbnm Perovskite 4 4.16 186.76 20.493 203. f%%n Spine1 8 8.178 10.92 41.073 864.50 Cub.35 24.030 209.097 10. Far% Halite 4 5. P4dmnm Kutile 2 4.7754 4.26 42.34 179.354 100.6651 120.9292 6.283 548. Imma Wadsleyite 8 5.234 558. 51 Tetr.556 234.862 393.5 Cub.467 11.950 21.40 5.02 Cub.884 1660.364 501.9315 .434 Hex P6pc Wurtzite 2 3. Ia33m Tetmhedrite 2 10.NaMgF3 AgCl AsI CUCI Fe7% FeSz Cd2 NiSz Fe& FeS (kWgS11 CuFeS2 CuFezS3 cus cu2s Cut2FeZnSb& CusFeS4 Cu3AsS4 Ni4s CoAsS zns zns CdS NisFe& MnS PbS PbSe PbTe MolyMenite(2H) Md2 Tungstenite ws2 Acantbite h.i3m Sphalerite 4 5.09 Tetr.436 5.214 239.98 orth.619 165.99 Cub. lji2d Chalcopyrite 4 5.460 175. Pnnm Marcasite 2 4.077 Cub.309 Tetr. Fz3m 4 5.80 Orth.4053 97.60 104.06 Cub.84 Cub.464 Hex P63mc Wurtzite 2 4.PZt/c Chaicccite 48 15.289 271. F.660 472.58 98.117 95. P21/n Cryolite 2 5. Pcmn Cubanite 4 6.418 647.80 Orth.45 209. Ptqlmmc NiAs 2 3.17 Hex.44 Trig. P63mc Wurtzite 2 4.963 855.60 Hex. Pd Pyrite 4 5.1964 62. Pcmn Perovskite 4 5.s Argentite AgzS Proustite AgsAsSj Pyrargyritc has% Cinnabar HgS Metacinnabar H@ Coloradoitc HgTe Stibnite SW3 Orpiment As2S3 78.63 Hex.8613 119.418 123.95 Mono. F&m Halite 4 5.676 143.246 11.582 91.5 Cub.434 Cub. Fm%r Fluorite 4 6. Pa3 Pyrite 4 5.3 Trig RTm Smythite 1 3.4651 183. PcaZl Cobaltite 4 5. Pd Pyrite 4 5. F&m Halite 4 5. Pmt12~ Enargite 2 7.414 89. P42/mnm Rut& 2 4.407 6.43 Orth. F&m Halite 4 5.044 87. Fdm Fluorite 4 5. Pbglmmc Covellite 6 3.1348 773.911 Hex.582 5.5385 122.822-l 144.92 Onh.34 Cub.363 7. 14/mmm Calomel 2 4. Pbca Bomite 16 10. P3t Pyrrhotite 3 6.30 orth.25 Cub.32 Cub.436 133.6865 119.14 Mono.98 Cub. F&-m IT&e 4 10.7938 159. PT2c Troilite 12 5. 582 4.89 1.18 226.199 7.167 4.97 67.77 31.72 Trig.010 29 169.65 90.344 4.447 4.676 5.84 139.34 10.93 23.078 10.3 98.20 24.49 17.571 4.437 162 81.024 218 203.853 7.785 203 125.65 Cub.08 215.676 56 116.021 4.06 159.145 9.482 8.86 494.494 10.537 8.84 215.688 4.302 3.26 152.423 7.906 30 361.93 30.076 224 208.23 23.154 5.2 335. Fq3m Sphalerite 4 5.85 40.453 4.780 4.770 240 173.80 Mono.294 247.168 41 .63 89. lm3m Argentite 2 4. P21/n orpiment 4 11.72 232. F.189 6.8717 328.93 26.82 8.323 247.903 4.335 71 157.526 247.930 9.65 Trig. R3c Proustite 6 10.55 Trig.614 160 229.860 4.01 8.45 34.571 5.381 11.222 246. Prima Stibnite 4 11.180 84 447.341 13.25 4.475 9. R3c Proustite 6 Il.069 87 141 .04 23.69 Orth.084 119 99.69 31.11 17.085 122 296.977 221 291.78 5.79 Cub.88 27.248 7.950 6.68 20.I5 21.035 5.062 3.07 3.04 696.754 34.7490 12.286.15 Cub.097 239 79.4541 160.440 339.33 32.408 2 57.19 Cub.801 235 1013.PZl/c Acanthite 4 4.-2H2 3.35 2190.582 6.231 16.999 28 105.54 171.92 Hex P63/mmc Molybdenite.48 227.04 Mono.1602 3.51 136.57 43.953 179 2521.89 25. Fdm I talite 4 6.423 6.496 232.811 162 183.i3m Sphalerite 4 6.80 Cub.2607 6.503 7.093 4.77 237.45 4.1532 12.285 160 268. P&‘l Cinnabar 3 4.91 66.491 5.90 4.231 6.8341 11.1213 334.07 Hex P63lmmc Molybdenite 2 3.69 541.789 51 1113.628 62 159.95 5.37 34.329 4.95 18.79 34.839 117 357.569 7.256 162.236 190 114.9 27. F&m Halite 4 6.270 160 106. 730 101 4.161 223 486.129 64.06 88.096 101 1.80 Cub.69 orth.06 Cub.456 6. R3m Milkrite Linneaite t&s4 305.16 12.482 7.10 Cub.68 70.15 Tetr. Y Unit CeII Molar Density Ref.15 Orth.134 101 Table 1.639 143 90.202 14 202.058 2.217 8.09 40.361 x.633 13 267.881.39 Cub.44 5.1 288.29 28. Fdh Dimmnd 8 3.824 20.26 Trig.42 92.11 25.422 3.28 73.281 Si 28.77 Trig.509 35.52 Cub.222 4. R32 Hazelwoodite COOperitc PtS 227. Pbj/mmc Graphite 4 2.494 154 24.43070 160. P42/m Cooperite Millerhe NiS 90. Fdh Diamond 8 5. F&m Spine1 Da&reel&e FeCrts.98 23.95 3.011 Hex.058 101 5. F&m Spine1 Greigite Fe& 295.086 Cub.329 .186 232 4. n P) Vol (A3) Vol (cm3) (calc)(Mg/m3) Re&ar AsS 106.83 Mono.99 Mono. P4~mmc Cooperite Vysotskite PdS 138. Fd%n Spine1 Violarite FeNi$$ 301.550 101 5.39 5.011 Cub.594 55 920.C2l/d Arsenopyrite Native Elements Diamond Graphite Silicon Sulfur(a) SUWP) Kamacite Taenite Nickel Copper Arsenic Tin Ruthenium Rhodium Palladium Silver Antimony Tellurium Iridium Osmium Platinum Gold Lead C 12.894 180 3.4163 3.68 467.46 Tetr.83 40. Pnnm Loellingite Arsenopjrite FeAsS 162.269 101 101 3.861 55 14i.261 2.PZl/n Realgar Bismuthinite Bi$$ 514.5158 C 12.94 34.98 5.44 30. F&m Spine1 Loellingite FeAs2 205.56679 45.696 34.38 3. F&n Spine1 Polydymite Ni& 304. Crystallographic Properties of Minerals (continued). Pmcn Stibnite Hazelwoodite Ni& 240. E MiIlemI Formula Formula Crystal Space StNCtUR z iJ Weight System Group 5~ (4 8. 649 799.29 22.451 5.864 8.329 Ru 101.080 998. P2t Sulfur 48 10.6190 9.2743 180.50 75.25 20.539 6.8898 60.50 40.465 6.932 AS 14.7056 4.557 Cub Ft&n Taenite 32 7.875 9. P3t21 Selenium 3 4.5 15. R%n Arsenic 6 4.321 17.8665 23.20 Hex.38 9.441 6.522 22.98 8. F&m FCC 4 4.870 24.995 5.458 AU 196.285 Fb 207.076 S 32.368 Rb 102.8197 3.263 Ni 58.113 8.312 6.443 2.52387 43.07825 67.214 19.23 10.60 8.9505 121.710 Cub.16 9. Fn&n FCC 4 3.489 9.723 %2.76 6. P63/mmc HCP 2 2.839 4.587 106.54 16.194 7.268 11.32 18.493 3299.175 3. F&n FCC 4 3. Fd&i Sulfur 128 10.273 17.292 273.41 16.980 Trig.521 7.790 95.910 CU 63.38 11.459 6.9838 2.731 252.92 1276.456 5.4 16.325 3.459 89.571 6.746 43 107.554 501.17488 107.305 89.075 6.070 Hex.427 22.83 10.869 854.311 9.20 Cub.570 Pt 195.55 7.540 Cub.572 6.2803 27.2 62.064 Orth.61496 41.374 832.172 12.652 4.926 10.29 13.12 4.132 847.429 9.29 21. Rsrn Arsenic 18 3. P63/mmc HCP 2 2.7352 4.921 101.424 Pd 106.093 7.7598 10.092 21.S 32.54590 11.86225 212.070 10.499 4.465 9.5475 129. Fm% FCC 4 4.546 13. F&m FCC 4 3.8394 56.500 Sb 121.09 Cub.064 Mono. RTm Arsenic 6 4.168 368.412 89.690 Tetr.93 63.847 Cub /m& a-hm 2 2.806 16 4 2 8 9 8 8 8 8 8 2 8 9.4 64.283 12.14 8.147 11.340 Stl 118.655 5.97 72.590 8.891 5.3083 Il.467 12.873 FeNi 114.342 Bi 208.967 Cub.0862 68. f4tlamd Tin 4 5.242 Ir 192. F&m FCC 4 3.40 Cub.48 26.1499 5.611 3.885 10.905 Cub.8821 9.06 18.94 349.8031 55.82 20.0718 3.190 Cub.75 Trig.15 30.87 Cub. F&m FCC 4 4.01 8. F&m FCC 4 3.981 4.406 9.922 Trig.016 2.326 4. 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Strukturbestimmung eines OH-reichen topases. durch Neutronenbeugung. and from magnetic. 2. Schuster. 1985.. 1161-1166. 244. F. useful data for anhydrous phases of geophysical importance. Te) and its dependence on the chemical-bond characters. T. Department of Geological . Wissenschajien. 241.1971. is the temperature derivative of the enthalpy. H. Cv = (aE/aT)V. The relation between heat capacity at constant pressure. 56. Neutronenbeugungsmessungen am brucit. Cp is virtually independent of pressure but a strong function of temperature (see Fig. 1961. Navrotsky. G. 145-147. H. Neues J. estimates of uncertainty are given..9. and H. CU~(OH)~(CO-&. R. Cp = (dH/aT)p. For solids.. Phase relations in the system Ni-As.. HEAT CAPACITIES The isobaric heat capacity. and that at constant volume. E. Heger.. where T = absolute temperature. and S. 1273-1296. Refined crystal structure of phenacite. 10.D.. 416436. Zigan. The values selected are. 1971. 1). Econ. A number of compendia of thermochemical data [4. in short form. Verfeinerung der Struktur von Malachit. and bulk composition. V = molar volume. The purpose of this summary is to give. 137-143. and R.. 239.311 contain detailed data. 13. Verfeinerung der struktur von azurit. Tokonami. INTRODUCTION Thermochemical properties of minerals can be used to calculate the thermodynamic stability of phases as functions of temperature. Thermodynamic Properties of Minerals Alexandra Navrotsky 1.Cv = TVa2/13. is given by Cp . electronic.5. When possible. 245.. 145. a = thermal expansivity = (l/V) (aV/aT). 240. Mason. Zigan. 15.5. At intermediate temperatures. Cp increases sharply. The magnetic contributions. 1). Heat capacity of Mg2SiO4 (forsterite) from 0 to 1800 K. Cp --> 0 (see Fig. Electronic transitions are usually unimportant in silicates but may become significant in iron oxides and iron silicates at high T and P. Order-disorder is an important complication in framework silicates (Al-Si disorder on tetrahedral sites). Guyot Hall. data from [311. Any “zero point” entropy. @V/aP)T. and increases with temperature. These factors must be considered for specific minerals but detailed discussion is beyond the scope of this review. and micas (cation disorder over several inequivalent octahedral sites).Cv is on the order of a few percent of C. 1. . irrespective of structural detail. Cp . The vibrational heat capacity can be calculated using statistical mechanics from the density of states. As T--> 0 K. the harmonic contribution to C v approaches the Dulong and Petit limit of 3nR (R the gas constant. At high temperature. Cp at 1500 K = 191 J/K*mol. The values at high temperature may be compared with the 3nR limit as follows: Mg2Si04 (forsterite) 3nR = 175 Jmmol. important for transition metals. must be added to this calorimetric entropy. s. namely 3R per gram atom.and GeophysicaSl ciencesa nd Princeton Materials Institute. which in turn can be modeled at various degrees of approximation [20]. arising from “frozen in” configurational disorder.. n the number of atoms per formula unit). Entropies of some common phases are also shown in Table 1. Cp at 1500 K = 188 J/K*mol. play a major role in iron-bearing minerals [321. 1). amphiboles. The Debye temperature is typically 800-1200 K for oxides and silicates. pyroxenes. For solids. = &C. MgA1204 (spinel) 3nR = 188 Jfimol. / TNT (1) 18 NAVROTSKY 19 T(K) T(K) Fig. NJ 08544 Mineral Physics and Crystallography A Handbook of Physical Constants AGU ReferenceS helf2 Copyright 1995 by the American Geophysical Union. Cp is then 510% larger than 3nR and varies slowly and roughly linearly with temperature (see Fig. Thus the Dulong and Petit limit gives a useful first order estimate of the high temperature heat capacity of a solid. Table 1 lists heat capacities for some common minerals. The entropy. Princeton. in spinels (M2+-M3+ disorder over octahedral and tetrahedral sites) and in olivines. 2 82.2 “FeO” (wustite) 48.3 339.3 Fb2TiO4 (titanomagnetite) 142.3 533.0 471.2 Ti02 @utile) 55. Heat Capacities and Entropies of Minerals (J/(K*mol)) 298 K 1OOOK 1500K CP S” Q S” Q S” MgO (periclase) 37.7 Mg2Al2Si5018 (cordierite) 452.3 63.3 277.1 50. a tabulation of coefficients is not given here but the reader is referred to Robie et al.6 CaCO 3 (calcite) 83.0 123.1500 K.4 148.2 MgSi03 (enstatite) 82.9 95.8 .0 248.5 190.5 375.5 CaMg(C03)2 (dolomite) 157.5 187.6 310.9 180.9 197. At 298 .9 121.6 178.1 207.2 MgC03 (magnesite) 76.2 310. 13 11 Cp = A + BT + CT-O5 + DT-2 (2) gives a reasonable fit but must be extrapolated with care.5 155.3 530.8 26.4 214.5 220.5 122.5 105.0 730.2 253.5 201.4 243.1 103.4 312.0 474.2 175.5 222. an expression of the Maier-Kelley form.7 249.1 206.7 350. [3 11.1 MgAJ 204 (spinel) 115.2 FeTi03 (ilmenite) 99.7 773.6 145.1 KAtSi308 (microcline) 202.2 129.The sharp dependence of Cp on T at intermediate temperature makes it difficult to fit Cp by algebraic equations which extrapolate properly to high temperature and such empirical equations almost never show proper low temperature behavior.8 146.9 401.7 124.7 Fe 304 (magnetite) 150.4 191.0 307.6 CaMgSi206 (diopside) 166.2 463.3 144.3 192.0 390.3 82.5 Mg2SiO4 (forsterite) 117.5 79.9 133.9 124.3 73.1 232. Holland and Powell [ 15 Table 1.2 698.8 Ca3Al2Si3012 (grossular) 330.3 217.1 255.1 65.3 264.8 Mg3~2si3012 @yrope) 325.5 87.9 87.3 1126.4 213.5 160.5 252.1 131.4 CaSiO 3 (pseudowollastonite) 86.9 NaAlSi308 (low albite) 205.1 67.4 Fe 203 (hematite) 103.1 155.2 Al 203 (corundum) 79.5 132.8 121.5 143. recommended by Fei and Saxena [8] is Cp=3nR[1+klT-1+k2T-2+k3T-31+ A + BT + C p (disordering) (3) Because different authors fit Cp data to a variety of equations and over different temperature ranges.9 80. A form which ensures proper high temperature behavior.6 55.1 406.5 91.3 168.3 407.5 491.0 50.9 51.12 57.0 53.0 CaSiO 3 (wollastonite) 85. 291 K2Si205 ----. Enthalpy and heat capacity in CaMgSi206.291 338128~291 CaA12Si208 21 I[311
[email protected] 243. Berman [5].5 132. Cl. JANAF [18]. heat capacities of liquids depend only weakly on temperature.291 1160~w91 LQL@W’I MS 2SiO4 _____ -----. At Tg.291 1118 928[28.291 703/28>291 263/28. the heat capacity of the glass from room temperature to the glass transition is not very different from that of the crystalline phase.7 506. the viscosity decreases. 256 J/mol=K at 1000 K.291 1096W. 2.from higher temperalure data andfrom comparison with crystalline phases. 2. In glass-forming systems.1 269.127. [9j for such equations.291 aEstimated.6 1420.291 347128. 20 THERMODYNAh4ICS 500 400 G 300 E + 200 0 0" 100 0 L liquid Tm t 4 0 400 600 1200 1600 2000 600 900 1200 1500 1800 Temperature (K) Temperature (K) 300 Fig. For CaMgSi206 Cp.291 KAlSi 308 209[311 3 161XW 122 1128. a glass-forming system. 311.291 259/X291 CaSiO 3 871301 13 1 P&29301 1065 167/28.3 269. reflecting the onset of configurational rearrangements in the liquid [27].291 NaAlSi 308 2 10[311 32 1128.291 Mg3A2Si3012 33ou 5 16/m91 1020 67@8>291 Mg2A4Si5018 460a 731128.291 CaMgSi206 17w 256128.291 1~7128291 8p.9 Dalafronl [S. For multicomponent glasses and liquids with . NAVROTSKY 21 161.. The heat capacity of the liquid is generally larger than that of the glass (see Table 2) and. glass = 170 J/mol*K at 298 K. and Fei et al. crystal = 167 J/mobK at 298 K._ _ _ _ _ _ _ _ 268/11d21 Na2Si205 --___ 217128. 249 J/mol*K at 1000 K [213.291 1~5PU91 y&8.226/28. Table 2. data from [21].3 753.291 770128. Heat Capacities of Glasses and Liquids and Glass Transition Temperatures Composition Cp glass Cp glass Tg Cp liquid 298 K (at Tg> 6) J/mol*K J/mol*K J/mol=K SiO 2 381311 74 128. and the volume and heat capacity increase. see Fig. except for cases with strong structural rearrangements (such as coordination number changes). where A.28 MO 35. are given in Table 3.compositions relevant to magmatic processes..04 78.00 45. be given as a sum of terms depending on the mole fractions of oxide components.45 62. B.28. Then Cp = CXi Cp i (4) where i is taken over the oxide components of the glass or liquid [22.98 R203 94. heat capacities can.43 82. The free energy of formation is then given by Table 3. partial molar heat capacities are relatively independent of composition. and reference states are the most stable form of the elements or oxides at the temperature in question.60 CaO 43.09 96.89 115.65 Fe0 43. to a useful approximation.6 109.5 ----__--- .8 94.3 240.76 84.96 H20 46.39 70.67 57.g.64 K20 75. 331.22 B203 62. 3.40 A1203 79.09 42. Al.e.04 52. C are different elements (e. i.17 70. Si).56 Ti02 44. ENTROPY.2 89. The partial molar heat capacities of the oxide components in glasses and melts.24 124.89 56. These refer to the reaction aA + bB + CC + “/2 02 = AaBbCcOn (3 and do] + bBOm +cCOn=AaBbCcOn (6) respectively. Ca. Partial Molar Heat Capacities of Oxide Components in Glasses and Melts (J/K*mol) 298 K Glass/291 LiquidL22.8 97.63 79.20 79.92 58.81 77.66 Na20 74.74 143. 0 is oxygen.43 84. ENTHALPY OF FORMATION Table 4 lists enthalpies and entropies of formation of selected minerals from the elements and the oxides at several temperatures.22 96.2 170.6 98. CpV.67 120. MOLAR VOLUME.9 78.33I 400K IOOOK 1500 K SiO2 44.23 47. 3 (311 -9. This reflects the large negative .9[3311 -43.0pi1 337.4[181 -332.0(31] -1211. These curves (see Fig. + y O2 = AO.8 I51 -180.3[311 -321.6f51 -905.5151 -1176.9B11 39.7 (51 2.6L5j -12.2pI1 -67.3 i51 -70.1(311 -85.5f51 -286.3t311 -l42.9 prl 12.4[311 -278.5 I51 -1630.7 f51 -313.5 t51 -585. 3) are the basis for various “buffers” used in geochemistry.1 151 -106. The free energies of formation from the elements become less negative with increasing temperature.7 (51 -2182. QFM (quartz-fayabte-magnetite).4151 -6649.2f51 -3209.9[181 SiO2 (cristobalite) -907.+.g.0L51 -9200.6151 6.9 [311 0. NNO (nickel-nickel oxide) and IW (iron-wurstite).313’1 -1750..6[51 -5.0 I51 -1624.0 (311 23. and more reduced species are generally favored as temperature increases.61311 -3925. (8) as a function of temperature.6151 CaSi03 (pseudowollastonite) -1627. e.3[181 -63.31311 -146.41311 -3J9.9[181 Mg2SiO4 (forsterite) -2174.0[311 36.4 (311 24.7 151 Mg 3N 2Si30 12 (pyrope) -6286.5[181 -115.7 I51 -756.3(311 -74.1 [I@ -174.1 1311 -208.5151 -634.3[181 -103.4[331/ -335.6(311 -60.1 [lsl “FeO” (wustite) -266.7 151 -182.7151 -1702.9(311 -79.2[311 -l9.51(181 CaO (lime) -635.61311 -96.9 (3il -296.3 (311 -155.1 I51 CaMgSi206 (diopside) -3200.4(311 -4.0L31] -81.TAS’.6L51 -903.2L311 -28.8[311 -33.4[311 -24.4151 MgSi03 (enstatite) -1545.9 (311 -19. 3 shows the equilibrium oxygen fugacity for a series of oxidation reactions A+.6J311 -737.1(311 4.4f51 400.2(181 -173.4f51 -283.9151 -293.0151 KAlSi 308 (sanidine) -3959.0[31] 222.1 f51 CaA12Si2Og (anorthite) -4228.4(331] -764.7 IsI -1.71311 -50.01311 NAVROTSKY 23 AGo = AH’ .1552.315] -6317.Table 4.6[31] -156.7 (51 -2.8 [311 55.9 I51 -263.1 1311 -744. Fig.7[31] -91.7 pll -274.0f1@ SiO 2 (quartz) -910.9 (311 4.61311 -579.1m NaAlSi 308 (high albite) -3924.7151 CaSi03 (wollastonite) -1631.5L311 -3962. (7) and AO.4[51 -608.5(3Jll -1472.Oz=AO. Enthalpies and Entropies of Formation of Selected Compounds from Elements and From Oxides Compound Formation from Elements Formation from Oxides 298 K lOOOK 298 K 1000 K AH Es AH AS AH AS AH AS kJ/mol J/m01 K kJ/mol J/m01 K kJ/mol J/m01 K kJ/mol J/mol K MgO (periclase) -601.9[51 Mg2AlqSi5Olg (cordierite) -915g.2[51 Ca3Al2Si3012 (grossular) -6632.8L51 -J693.9 (311 -2.5 1311 -33.3 1311 21.2L311 -730.lPl Fe2SiO4 (fayalite) -1479.6[18~ Al203 (corundum) -1675.1 L311 410.3L51 -X2(311 -38.7 I51 -4239.7L311 -J214.5~5~ -108.21311 -85.0151 .8[311 -735.9 t311 -lOO.5 prl 28.9151 -1214. 4 kJ/mol.2NlO (3) 2co f 02 .bFc203 (2) 2NI * 02 .T)=O=AH. Thus the equilibrium oxygen fugacity for a given oxidation-reduction equilibrium increases with increasing temperature.2CO2 (7) 3/2Fe .TAS.2Fe304 (6) 2C0 . (9) At constant temperature. Thus for A12SiO5. data from [4. 02 .2ceo (4) 2H2 * 02 .: ox. 02 . entropy. 3. vaporization. for MgSi03 (enstatite) A%.04 .-TAS.Fe0 02 cop (9) c f 800 1300 1800 Temperature (K) Fig. 298 = -1. 18.1 kJ/mol.6 kJ/mol. and the following balance of enthalpy. 298 = -35. per mole of 02. 4. 02 . 298 = -89.entropy of incorporation of oxygen gas in the crystalline phase. 02 . solidstate transitions) in either the reactants (elements) or products (oxides). ENTHALPY AND ENTROPY OF PHASE TRANSFORMATION AND MELTING At constant (atmospheric) pressure.+ sP AV(P. a thermodynamically reversible phase transition occurs with increasing pressure if the high pressure phase is denser than the low pressure phase (0 4Fe. Entropies of formation of ternary oxides from binary components are generally small in magnitude (-10 to +lO J/mol*K) unless major order-disorder occurs.Clapeyron equation (@‘/dT)equil= ASIAV (11) Thus the phase boundary is a straight line if AS and . T) dP 1 atm (10) 3) :6) :41 An equilibrium phase boundary has its slope defined by the Clausius . and volume terms is reached AG(P. 02‘ 112Fe304 (8) 2Fe . ox. and for CaSi03 (wollastonite) AH. ox. .2&O (5) 6FeO . at the transformation temperature AG. Gibbs free energy for oxidation-reduction equilibria. 3 reflect phase changes (melting. = 0 = AH. The enthalpies of formation of ternary oxides from binary oxides are generally in the range +lO to -250 kJ/mol and become more exothermic with greater difference in “basicity” (or ionic potential = charge/radius) of the components. Changes in slope (kinks) in the curves in Fig. a thermodynamically reversible first order phase transition occurs with increasing temperature if both the enthalpy and entropy of the high temperature polymorph are higher than those of the low temperature polymorph and.311. (andalusite) A@. 16a 12] -4.d91 MgSi03 (il = pv) 51. st = stishovite Table 6.3L21 I%2Si04(a=y) 3. Enthalpy.9 AZ0 .1 + 6. [21 -15.8 f 2. a = olivine.0[3J -2. q = quartz.912J -15.0 f 1 .20[21 -4.89[171 -3.1 f 2.0 f 2.5[11 SiO 2 (co = st) 49.14[21 -3.4L21 -10. Melting curves tend to show decreasing (dT/dP) with increasing pressure because silicate liquids are often 24 THERh4ODYNAhIICS Table 5.24 L2J -4.7 f 3. pv = perovskite.7 *19a.d21 Fe2Si04(a=P) 9. y = spinel. il = ilmenite.0 + 0. Entropy and Volume Changes for High Pressure Phase Transitions AH’ (kJ/mol) AS” (J/m01 K) AV“ (cm3/mol) Mg2Si04(a= P> 30. px = pyrox-ene.19[17J -2.4[1J -4.94 131 -2.l[lJ -7.1 f 4. as is a reasonable first approximation for solid-solid transitions over moderate P-T intervals at high T.0 * 0.83 [9J -1.4L2J MgSi03 (px = il) 59.63 [II a AH and AS are values at I atm near 1000 K.2 f l.8a f2] Mg2SiO4(a=Y) 39. ThermodynamicP arametersfo r Other PhaseT ransitions Transition AH” AS” AV” (Wmol) (J/K*mol) (cm 3/mol> SiO 2 ( o-quartz = p-quartz) Si02 ( fi-quartz = cristobalite) GeO2 (Wile = quartz) CaSiO3 (wollastonite = pseudowollastonite) Al2SiO5 (andalusite = sillimanite) Al2SiO5 (sillimanite = kyanite) MgSi03 (ortho = clino) .5 f 2. gt = garnet.6 + 1 .l[IJ -3.8/l 71 SiO 2 (q = co) 2.1+ 0. /I = spinelloid or wadsleyite.d171 Ws 2siWYk MgSiWpv)+MgO 96. AV is AV”298.8 + 5. for all listings in table.5 L91 +5 + 4[171 +4 f 41171 -5.0 t 2.0 f 1.05 [I] -6.8[21 -14. co = coesite. A negative P-T slope implies that AS and AV have opposite signs.3131 MgSi03 (px = gt) 35.AV are independent (or only weakly dependent) of P and T. 88[251 -2.06 -0.109 -0.25 Lz5J MnSi03 (pyroxmangite = pyroxene) NaAlSi308 (low albite = high albite) 13. Compound M@ CaO Al203 SiO 2 (quartz) SiO 2 (cristabalite) “FeO” (wustite) Mg2SiO4 (forsterite) MgSi03 (enstatite) R2SiO4 (fayatite) CaSiO3 (wollastonite) CaSiO3 (pseudowollastonite) CaMgSi206 (diopside) NaAlSi 308 (high albite) KAlSi3Og (sanidine) CaA12Si2Og (anorthite) K2SiO 3 Mg3~2si3012 W-w.03 -1.11~2~~ -0.101 0.8815j 4.16 1.40 0.21 -0.0 3.50 -8.0 0.59[51 1.66 14.39 0.51 0.164 -0.b 0.40 11.3 0.35 2.93 561231 5:0[311 4.94151 1.511 -0. AV is AV ‘298 for all listings in table.1[51 15. though a strong higher order component bAH and AY are values near 1000 K.47a.03 -0.002 0.5 -0.027 a Treated as though allfirst order.39 -0.51311 KAlSi 309 (microcline = sanidine) 0.MgSi03 (ortho = proto) FeSi03 (ortho = clino) MnSi03 (rhodonite = pyroxmangite) 0.12 -0.0 0.37[51 0.6 3.) .13L51 -13.318 11. I 1473 K0.3 + 0.6 Fe/(Fe+Mg) 15 P (GPa) -I 373 K 14 I 1 1 I 0. 600 1000 1400 T(K) Fig.5 f 0.1817 57 f 3[281 85. 4.2323 107.8[241 1830 134+ 4[281 9 + 11281 1249 20f 4[28J -_-_--------.4[261 17706 62 !I 4[28j ------------. Enthalpies of Vitrification and Fusion Vitrification Fusion AH (kJ/mol) Melting Point AH(T) T(K) (kJ/mol) ------------------------------------. Schematic diagram showing phase transitions observed in analogue systems of silicates. and titanates.9 zk 1.2163 114f 20a 42 + 1[28l 1834a 77 f 5[281 ------------.17oob 9.2 0. Phase relations in M2Si04 systems at high pressure and temperatures [25].0[287 ------------. Numbers refer to pressure in GPa. bMelting of metastable phase.5 rt 54281 ------------.8[241 1665 138f 2[281 51.8 + 0.2 0.4 f 1.h’&2&si5018 (COIdiCIite) Table 7. 5.1999 8.8 f 0.6 1. germanates.15@W 243 + 8[281 209 f 2161 1740 346 + 10[281 aEstinlated metastable congruent melting.4 PYROXENOID OLIVINE + QUARTZ Fig.0[281 _____________ 1652 31. 15 P (GPa) 11 11.1490 89 k 10~28~ 25. PEROVSKITE M”S03.8 f 08[24] 1373 63 f 20[281 1473a 56f 4[281 77. / [ .7 CaGe03.0 Fe/(Fe+Mg) 19 \ SP(y) 11 a+y lk OL(a) 7 P (GPa)&.2[2@ _-__--------. E. and volumes of fusion at the equilibrium melting point at one atmosphere. Table 6 lists parameters for some other phase transitions. New York. Equilibrium phase relations in H20. Miner.. function of pressure [lo]. Thermochemical properties of inorganic substances. Navrotsky. E. 8. Navrotsky. Inter.. J. Earth Planet. 7. and geophysical application. Berman. (a) Mg2SiOq composition. 1988. 1. 94. The quartz-coesite-stishovite transformations: New calorimetric measurements and calculation of phase diagrams. Res. I. 1973.. For reactions involving volatiles (e. and enthalpy of transformation. T.. thermal expansivity. Ashida. Geophys. Chem. (b) MgSi03 composition. pp. thermochemical calculation. entropies. 921. S. Phys. Navrotsky. enthalpy. R. Phase relations in MgO-Si02 at high P and T. phase boundaries are strongly curved in P-T space because the volume of the volatile (gas or fluid) phase depends very strongly on P and T. [9]. 16. 124-134. and 0. M. Table 7 presents enthalpies of vitrification (crystal + glass. G. MgSi03 ilmenite: heat capacity. germanates. Ito.g. and volume change for high pressure transitions of geophysical significance.671-15686. Table 5 lists entropy. Akaogi. 36. Akaogi. The section by Presnall gives examples of such behavior.. 6. Knacke.. 15. Olivine-modified spinelspine1 transitions in the system Mg2SiO4-Fe2SiO4: Calorimetric measurements. not an equilibrium process) and enthalpies. Barin. Phys. Springer-Verlag. Compiled from various sources [ 141. Internally-consistent thermodynamic data for minerals in the system Na20-K20-CaO-MgOFeOFe203-Al2O3-SiO2-TiO2 substantially more compressible than the corresponding crystals. Ito. and A. PV PX 10 I I 1 I 1000 1500 2000 2500 3000 3500 Temperature W) 30 PV + PER i”o’o0 15’00 20’00 25’00 30’00 35’00 Temperature W) NAVROTSKY 27 200 300 400 TEMPERATURE (K) Fig. A number of silicates. Kume.239-245.18 Fe/(Fe+Mg) Fig. Hz0 and CQ). 1984. Phase relations in Mg2SiO&Fe#i04 as a Fig. and A. 1989. M. and A. and other materials . Res. REFERENCES H2O-CO2. Res. Phys. 13. J. 4. I thank Rebecca Lange and Elena Petrovicova for help with tables and figures. 5-7. C. 445-522. 1983. Chem. Desmond C. S. spinel. Summary and critique of the thermodynamic . 323-342. Geophys. .251-254. A. 6915-6928. 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Heat capacities and entropies of silicate liquids and glasses.475-485. S. 24. High pressure transitions in silicates. Moret. A.. 1984. Thermodynamic properties of wollastonite. Bottinga.. Geochim. 1987. 1989. 463-469. Europ. Finch. Thermochemical properties of silicate glasses and liquids: A review. Amer. Robie. Rev.modifications of Ge02. Prog. . S. U. Stebbins. Geol. Robie.. 3. Robie. I. Cosmochim. D. 456 pp. Mineral. R. 32. 1980. and Y. Petrol. Nucl. Ziegler.1982.. R. B. pseudowollastonite and CaSiO3 glass and liquid. J. Oestrike. 122-130.. 33. Henry. Navrotsky. Inorg. Fisher. and B.. Heat capacity and entropy of fayalite (Fe2SiO4) between 5. Chem.1 and 383 K. 67. Carmichael. Hemingway. A.. Maniar. S. 1986. Mineral. E. Petrol. 1971. 17. Richet. 1991. 44. J. Hemingway.52. A. Mineral. P. 1984. C. 31. Navrotsky. Richet.471-483. Calorimetry of silicate melts at 1773 K: Measurement of enthalpies of fusion and of mixing in the systems diopside-anorthite-albite and anorthite-forsterite. 30. A. Mineral. Chem. 1978. 53-86. Hemingway. Richet.. 86. R. Chenr. and J.. Si02 CaAl2Si208NaAlSi308 and Si02 . Acta. Hon. J. 111-124. D. F. R. R.. K. and B. Viscosity and configurational entropy of silicate 28. and D. 19. measurements on heat capacity and bulk modulus can provide additional constraints on the . silicate spine& silicate ilmenite and silicate perovskite were collected by x-ray diffraction methods [e. many efforts have recently been made to obtain the pressure effect on thermal expansivity [e. 68. four parameters. 54. 22. DC 20015-1305 Mineral Physics and Crystallography A Handbook of Physical Constants AGU Reference Shelf 2 V(T) = 31 + 2k . Fci. the four parameters may be uniquely defined by fitting the experimental data to the model. and the Griineisen parameter (y) by Q. While the data set for l-bar thermal expansion is expanding. 0. 77.) and bulk modulus (K.44. or. 42. 36. dilatometry. 97.g. In a microscopic sense. 14. and silicates have been made by x-ray diffraction.. 16.4M/Qo)‘” ] (1) where E is the energy of the lattice vibrations.. 39.. In the Debye model of solids with a characteristic temperature. Y. When the thermal expansion is accurately measured over a wide temperature range. Geophysical Laboratory. are required to describe the thermal expansion of a solid. olivine.Thermal Expansion Yingwei Fei Since Skinner [75] compiled the thermal expansion data of substances of geological interest. a systematic approach is taken to obtain density and its temperature dependence of natural liquids [e. Q.(1 . 21. With the development of high-temperature x-ray diffraction techniques in the seventies. The thermal expansion coefficient a. the thermal expansion is caused by the anharmonic nature of the vibrations in a potential-well model [103].46. the energy E can be calculated by @D/T E= 9nRT I x3 (f%/T)3 o eX .89]. = K.9. thermal parameters of many rock-forming minerals were measured [e. 45. The Grtineisen theory of thermal expansion leads to a useful relation between volume and temperature [90]. 511. Carnegie Institution of Washington.86.g. wadsleyite. Washington.. k.g.i. defined by a = ~/V(I~V/C~T)?.) at zero Kelvin.g. Considerable thermal expansion data for important mantle-related minerals such as periclase. 4. is related to volume (V. In study of liquid density. 991.1 (2) where n and R are the number of atoms in the chemical formula and the gas constant. and interferometry. 5251 Broad Branch Road. In this model.g.. 711 and by dilatometric and interferometric techniques [e. Furthermore. carbonates. 12... 11. respectively. The constant k is obtained by fitting to the experimental data..VJy.s used to express the volume change of a substance due to a temperature change. and V.88.48]. stishovite... The constant Q. 28. NW. many new measurements on oxides. (T . is the volume at reference temperature (T. When the thermal expansion coefficient is independent of temperature over the measured temperature range. respectively.. recommended.model. [l +a(T . P=3fil+2j)5/2KT and v(r) = vTr exp[%(T . especially when extrapolation of data is involved. For the purpose of fitting experimental data over a specific temperature range.. usually room temperature.). for some mantle-related minerals. (5 0) are constants determined by fitting the experimental data. f=i(gJ- ll where K. i. 29 30 THERMAL EXPANSION thermal expansion coefficient may be used 931 are also recommended as data sources. a(T) = a0 + a. a polynomial expression for the Copyright 1995 by the American Geophysical Union.T. The coefficients for most substances were obtained by fitting the experimental data to equations (3) and (4). either because the accuracy of thermal expansion measurement is not sufficiently high or because the temperature range of measurement is limited. bulk modulus.TAI (5) The commonly used mean thermal expansion coefficient (Z) can be related to equation (5) by truncating the exponential series of exp[a.. and S. where V. can be converted to a~. and a. Table 2 lists the values of K.. and heat capacity through a self-consistent model such as the Debye model [e. The measured volume above room temperature can be well reproduced by The pressure effect on the thermal expansion coefficient may be described by the Anderson-Griineisen parameter (4)9 T v(Tj = vT.T. Kr’.g.)] at its second order.e.T + azT-* (3) where a.k?Xp I1 4WT TI (4) a(C T)/a(T) = ME WVf (7) The thermal expansion coefficient as a function of pressure can be calculated from equation (7) and the third order Birch-Murnaghan equation of state. 811 is. In many cases the above model cannot be uniquely defined. listed in the literature.)] (6) The liquid molar volume of a multioxide liquid can be calculated by Table 1 lists thermal expansion coefficients of solids.. according to equations (5) and (6). a. The mean coefficient @). therefore. v(T) = v. and Kr’ are the bulk modulus and its pressure derivative. . A simultaneous evaluation of thermal expansion. where Xi and Zi are the mole fraction and mean thermal expansion coefficient of oxide component i.3569 0.0000 b 298-963 K 8. normal spine1 MgA1204. Recent measurements on density and thermal expansion coefficient of silicate liquid are summarized in Tables 3a-3d.0250 1.0 0.1743 0. chrysoberyl Be0 CaO 3Ca0*A1203 17Ca0*7A120s Ca0*A1203 Co304. LiF. spine1 MgO. magnesioferrite MgGeOs. hercynite FeCrzOd. ilmenit Hf02 MgA1204. picrochromite MgFe20a.0000 .0000 c 298-963 K 7. KCl. manganosite Th02. wiistite Fe203.1191 -0.0000 V 298-963 K 23..0000 PI I’ 293-2298 K 23. disordered spine1 MgCr204. magnetite FeTiO.5227 0..7315 0.6 0.4198 -0.0758 0. uraninite Zr02. boehmite a 298-963 K 6. olivine MgZGe04. Volumes 12 and 13 of Thermophysical Properties of Matter 192.7 0. rutile U02. BeA1204.03.3 0.0490 1.&iq(T) = 2 Xi I$.~~ is the partial molar volume of component i in the liquid at a reference temperature. and p is the excess volume term.Tr) ] + V ” (10) Thermal expansion coefficients of elements and halides (e. (continued) Names T range sow-3 =o W-9 a1 w-“1 a2 ref. 6. normal spine1 Cr203. Thermal Expansion Coefficients of Solids Names Oxides aA120a. ilmenite Mg2Ge04.0773 0. thorianite TiO Ti02.8 0. we a0 (lo-‘? a1 (10-p a2 ref. and KBr) are not included in this compilation because the data are available in the American Institute of Physics Handbook [41].2777 0.T~[ 1 + Ei(T .0897 PI FBI 31 TABLE 1.2276 0. eskolaite FeA1204.. T.g.6 0. NaCl. a 293-2298 K 7. periclase MnO. baddeleyite Hydrous minerals AlOOH.0540 0. (8) (9) TABLE 1. hematite Fes04. respectively.3 0. corundum T range a.1320 3.0603 PI c 293-2298 K 8. chromite FeO. 6 0.0000 V 298-1883 K 28.0000 a loo-530 K 9.2555 0.0000 0.0000 0.0000 v 293-1273 K 9.6 -0.0000 b loo-530 K 25.2639 0.3 0.6 0.3032 1.2180 1.1264 1.1 0.7404 -0.2689 0.9 0.0591 0.0463 0.1154 -0.1238 3.5 0.0259 -1.0350 1.0000 v 993-1933 K 29.8 0.0000 u 297-1323 K 10.7 -0.0000 V 297-1323 K 27.0000 V 293-843 K 20.6 0.2146 0.0275 12.5 0.v 292-1272 K 17.0000 0.9 0.2118 -1.0000 [301 WI [301 r301 [93.2853 0.0000 0.4 0.8000 0.1063 v 293-1473 K 20.0000 V 303-1273 K 31. [951 [951 .0232 9.0513 1.0000 V 293-1473 K 19.0000 v 293-673 K 23.0000 V 293-1473 K 16.0000 c 297-1323 K 7.0 0.0368 0.0559 0.9392 0.2940 0.1230 0.3210 0.2000 0.1191 -0.5 0.2 0.1006 0.0000 V 298-1273 K 41.7490 V 298-1073 K 12.8160 0.3 0.4031 0.3108 1.0000 0.6293 0.6 0.2490 0.0048 3.1 0. 291 1931 r751a r151 [751 1491 [751 r751 [751 1751 1751 r751 [751 1751 :zz.0000 V 293-873 K 24.1 0.5 0.1110 0.7564 -0.0000 V 293-1473 K 18.0000 V 293-1273 K 24.0000 V 843-1273 K 50.5 0.4 0.9 0.0000 c loo-530 K 0.0000 V 293-1073 K 22.0977 1.0000 V 293-873 K 33.3236 0.0920 V 293-1273 K 21.1832 1.8014 0.2232 0.0000 0.4836 0.2773 V 299-1023 K 22.5013 0.0000 c 293-673 K 8.0890 0.7446 V 293-1123 K 34.2244 0.4000 0.8 0.3933 -0.5 0.0000 c 298-1883 K 11.2042 0.1 0.1820 1.1 0.0000 0.0000 V 298.3482 0.0000 0.2904 v 293-1273 K 15.0000 V loo-530 K 35.9 0.5936 0.0000 0.3317 1.9 0.0000 V 293-1273 K 15.0005 0.1273 K 32.0000 a 293-673 K 7.2000 0.5 0.2446 -0.2094 V 293-1273 K 28.7 -0.0000 0.0638 0.9 0.7 0.0000 a 298-1883 K 8.4110 0.3 -0.0000 v 293-1473 K 10.7904 0.0000 0.0000 0.9 0.0631 2.0353 8. cf.8 0.5 0.3203 0.0687 v 301-995 K 14.3768 0.2055 -0.8 0.1430 1.4122 v 293-2400 K 33.2890 0. . (continued) Names T range a0 w-3 a0 w-7 a1 (10-y a2 ref. siderite SrCOa. 961 1751 r71 [71 [71 [71 32 THERMAL EXPANSION TABLE 1.). aragonite CaCOa . brucite Carbonates BaCO. cf. dolomite MgCOa. C~~M&%Ozz(OHh tremolite QW~%W(OH)2 muscovite Mg(OH)2. rhodochrosite FeCOa..VI PO21 WI [751 1751 [31 r74 [721 WI [901 [75. strontianite a 297-973 K b 297-973 K c 297-973 K /cI 297-973 K v 297-973 K a 293-1073 K b 293-1073 K c 293-1073 K do01 293-1073 K v 293-1073 K a 300-650 K c 300-650 K V 300-650 K a 1093-1233 K c 1093-1233 K v 1093-1233 K a 293-673 K b 293-673 K c 293-673 K v 293-673 K a 297-1173 K c 297-1173 K v 297-1173 K .. cf. 961 [751 [851 1851 P51 [75. calcit CdCO. otavite CaMg(CO. magnesite MnCOa. (hexagonal) CaCO. 2 0.2 0.0 0.0000 0.0000 35.0000 13.1379 0.0000 0.1 0.0 2.0000 0.9 0.0000 0.3941 -1.0583 0.0000 19.2 -0.9 0.0000 35.0560 0.0000 22.1152 15.5 0.0180 0.0000 26.1 0.0000 13.0508 0.0266 0.0 0.0000 0.5809 13.1703 -0.0000 5.0000 18.0000 18.1110 0.6 0.2140 3.7 -0.0000 0.0000 -2.0 0.1 0.1920 0.0 0.0000 9.8 0.1107 0.0000 93.0000 62.8 0.0000 0.1 0.0000 0.2140 -5.3362 0.0000 0.4982 3.0 0.0000 0.0000 31.6630 0.1233 2.0000 0.0000 0.0000 16.0000 0.7429 -1.4137 0.3131 0.7 0.0000 0.0000 22.6 -0.1111 0.0000 80.6 0.0 -1.0271 0.1610 0.2629 3.0000 0.0000 0.0000 -3.2 0.0000 8.6221 0.0037 4.0315 0.1686 4.0833 0.0000 11.0000 297.9300 0.8 0.2 0.0200 0.0000 0.8 0.2 0.0000 -102.0000 0.1367 0.7 0.2280 0.0000 59.0000 5.1922 2.0000 3.2711 0.0000 0.5183 -1.0000 0.0000 12.2 0.7 0.0000 13.0775 0.2286 -0.3089 22.5393 2.3537 0.8 0.3520 0.0540 0.5 0.1167 0.0000 P31 F31 .1150 0.0000 0.3 0.2 0.a 293-593 K c 293-593 K v 293-593 K a 297-973 K c 297-973 K v 297-973 K a 297-773 K c 297-773 K v 297-773 K n 297-773 K c 297-773 K v 297-773 K a 297-773 K c 297-773 K V 297-773 K a 293-1073 K b 293-1073 K c 293-1073 K V 293-1073 K 12.0000 0.0000 0.4 0.3 0.0713 3.0000 0.0000 0.2 0.6045 -0.1100 0.0000 11.0000 0.1862 0.5900 0.0000 0.0000 0.0994 0.2690 0.1618 1.0000 7.0000 11.8000 0.4 0.3 0.0000 0.8 0.0000 0.1928 3.0000 59.0000 36.1202 0.2270 0.0000 11.2934 -0.9700 0. :. LiAlSi04 Feldspars Celsian. wurtzite BaS04. Be.SiOs Cancrinite Cordierite Mg2At4SisO18 (hexagonal) f%Eucryptite. BaAi2Si208 High Albite..A12Sib0. r751 [751 1751 FE1 33 TABLE 1. sphalerite ZnS. (continued) Names T range a0 (10 % WV al (10-q a2 ref. 1751 [751 1751 1531 1531 [. Ca2MgSi20T Andalusite.I [51 151 [701 [701 . P91 P91 [431 [431 t:.8 Calcium silicates Ca3Si207.1831 F31 t. NaAlSi$18 . WI PI WI t:.. Sulfides and Sulfates FeS2. A12SiOs Beryl. galena ZnS. pyrite PbS. rankinite p-Ca2Si04 Ca. barite K2S04 Silicates Akermanite. r531 [531 [691 1691 1691 1641 rw :Gt.:i. 0000 -0.2550 0.0000 [731 V 298-1158 K 63.0963 8.0260 0.0 0.0000 [751 a 293-693 K c 293-693 K V 293-693 K a 298-1273 K b 298-1273 K c 298-1273 K V 298-1273 K a 298-1073 K c 298-1073 K V 298-1073 K V 293-1473 K V 293-1473 K V 293-1273 K a 298-673 K c 298-673 K V 298-673 K a 298-873 K c 298-873 K V 298-873 K a 296-920 K c 296-920 K V 296-920 K V 293-673 K u 297-1378 K b 297-1378 K c 297-1378 K 10.1 0.4106 31.2136 1.0364 8.8280 27.5 -0.0000 33.0860 0.0230 0.5027 2.9 0.0000 0.6 0.0000 .0000 22.1852 2.4601 0.7589 2.1720 0.5061 1751 a 298-1158 K 20.7 0.0000 0.0000 0.0220 0.v 293-673 K 25.3252 19.1223 0.0000 -2.3 0.3815 -0.5 0.7 0.1 0.0233 0.2629 29.8 0.4073 7.2 0.0000 0.0000 [731 b 298-1158 K 25.0000 2.7701 0.2453 0.8700 12.1713 10.4 0.1256 4.0000 1751 c 293-673 K 42.0938 -0.1065 0.9 0.2181 0.0158 25.0260 0.1885 1751 c 293-1273 K 6.0290 0.6 0.5 0.7 0.7 0.3873 0.4 0.1274 1751 v 293-1273 K 19.0 0.7 0.9 -0.8705 0.0000 1731 c 298-1158 K 17.6 0.0000 8.4 0.8 0.2 0.1628 8.1 0.0763 0.7 0.0000 [751 b 293-673 K 33.0346 0.1918 2.0000 2.2883 1.0000 0.0762 0.3 0.8 -0.1 0.0000 5.1134 -0.2836 0.6406 0.0000 1751 v 293-673 K 91.0753 0.6125 0.0328 4.5 0.0000 -1.0034 2.1 0.0000 1751 V 293-873 K 58.2070 0.3337 0.0180 0.3261 2.0000 r751 v 293-1273 K 17.0000 [731 a 293-673 K 15.6370 0.9537 [751 a 293-1273 K 6.6 0.2150 16. 0000 0.0605 0.0000 0.0000 0.6 0.0000 0.8114 6.0000 0.2 0.0000 0.0000 -1.0000 0.0000 -1.8692 9.1840 0.0000 0.2 -0.0000 1311 [311 1311 [971 [971 1971 [971 [581 [581 [581 [751 1751 r751 1751 1751 1751 [351 1351 [35.0000 5. cf.0000 0.0716 0.0000 0.0000 0.6 0.-18.0656 0.7 0.0000 0.0000 0.3157 0.0000 0.0000 8.4 -0.0000 o.oooo 0.0120 0.0000 0. 671b rw [Ml WI [751 WI WI 0.0523 0.0000 0.0000 0.0000 0.0000 0.0000 PI 34 THERMAL EXPANSION .0000 0.0000 0. Oa Adularia. WwWi3012 Spessartite. Ab+n.0%)Si02(2a. Ab5&nU Plagioclase. Low Albite.dl\b32.446)Cr a 297-1378 K /3 297-1378 K y 297-1378 K v 297-1378 K a 298-1243 K b 298-1243 K c 298-1243 K a 298-1243 K j? 298-1243 K y ’ 298-1243 K V ‘298-1243 K V 293-1273 K v 293-1273 K V 293-1273 K V 293-1273 K v 293-1273 K V 293-1273 K V 293-1273 K V 294-1044 K V 294-963 K V 300-10OOK v 292-980 K v 283-1031 K v 292-973 K V 298-1000 K V 293-1473 K V 293-1273 K (I 298-1073 K b 298-1073 K c 298-1073 K V 298-1073 Y v 293-1473 I. Mn3A12Si3012 Natural garnet (pyrope-rich) Gehlenite.5Ab16.5 Orthoclase. Plagioclase.4 Microcline. Ca2A12Si07 Hornblende Kyanite. A12SiOs Merwinite. Ora3. Ca. Fe3A12Si3012 Audradite. Ab7+nU Plagioclase. CaJMg(Si04)2 Mullite.-l 73K . a 57 17’> K b F-. Oraa&b9.TABLE 1.2%)Si02(x646) A1203(60. A1203(71. NaAlSi.Fe2Si3012 Cacium-rich garnet Grossularite. Ca&Si3C11.6 Plagioclase. (continued) Names T range a0 <lo-Y 4 w-9 02 ref.&. Or66. AbSAngS Garnets Almandite.&n2. Pyrope. 0000 0.5 0.0097 3.0000 11.2103 0.9 0.2 0.oooo -0.0061 -0.0000 3.5719 -0.0197 -0.2245 20.1560 23.3080 -0.0000 15.6 0.0000 o.1297 0.2505 o.7 0.4538 17.0580 0.6 -0.1490 0.6617 16.oooo -2.8603 10.3641 0.5038 -0.8714 8.6 0.0661 0.5071 20.0620 0.2880 0. cf.oooo 0.0000 6.0000 5.0390 0.9479 o.0263 -1.1 0.0000 0.0 0.8 0.4 0.8 0.4972 19.9 0.0284 o.1095 o.8089 -0.0000 11.oooo 26.oooo 0.0000 3.1524 0.oooo 9.1 0.6 0.oooo 0.6 0.6839 -0.1394 0.0749 0.2199 1.2 -0.0000 3.0371 0.0000 WI WI WI [68.0000 7.4618 0.0000 -2.5285 0.0560 0.7 0.0882 0.7927 0.oooo 7.5490 0.6 0.4 0.0113 0.0000 o.oooo 6.0000 0.1737 1.5550 14.1951 0. 991 .0000 23.0000 o.0 0.0000 0.oooo 5.8 0.oooo -2.2075 1.2455 0.6 0.1 0.0597 0.2311 0.oooo 25.1670 0.9 0.oooo 4.1846 0.2140 -0.0252 -0.0252 o.oooo 5.0 0.9 0.9 0.0270 o.7 0.0000 o.9 0.1603 -6.5 0.2320 0.0000 10.8683 o.8 0.1776 1.0000 14.2726 -1.2679 0.0000 0.7 0.0000 0.3400 o.5521 24.2787 -0.0700 0.oooo 16.2 0.0987 o.7 -0.c >73-1173 K v 5%1173 K 573-1173 K b 573-1173 K c 573-1173 K v 573-1173 K II 573-1173 K b 573-1173 K c 573-1173 K v 573-1173 K -2.0000 15.7276 0.2647 0.0000 7.0000 22.oooo o.1 0.6 0.0000 15.0000 29.2927 0.5956 -0.8 0.0000 0.oooo 0.0000 -5.7683 -0.3 -0.2 0.0560 0.3 0.0271 -0.7621 0.0330 o.0700 0.2 0.0000 0.6 0.1612 0.8088 15.1120 o.0547 0.0310 o.1590 0.3 -0.2521 1. diO4 monticellite CaMn(MgZn)Si04 glaucochroite Mg2Si04.. Ni-olivine Fe. forsterite Mg2Si04.SiO.P81 WI PI P81 PI [981 . tephroite Ni2Si04. 1741 [741 [741 FE1 35 TABLE 1. forsterite Mn2Si04. fayalite @kde&SiO4 hortonolite Mgo. forsterite Mg2Si04. [751 1751 [751 [751 [751 [75.7&. ii.l&no. (10 a0 (10-4) a1 (10-y a2 ref.:.z. 1971 1971 [971 [751 1741 [741 1741 [741 r741 1741 r741 t. 247 r751 [751 t381 1751 1751 1751 [E. forsterite Mg2Si04. (continued) Names T range a.dh.. Nephelines PkdGd~SiQ Olivines CaMgo.diO~ hortnolite Perovskite . cf. 0000 [751 6.1055 0.0665 0.8133 6.1 0.1428 0.1889 4.2091 -0.2891 24.5 0.2071 0.0000 [751 58.0976 0.5 0.0000 1751 8.3605 6.3 0.2575 10.0000 [751 19.2783 -0.3 0.1235 0.0855 0.4236 -0.4 0.6733 -0.0965 0.0000 [751 31.2627 -2.3114 0.2233 -0.7192 -1.1806 -0.0000 [751 19.6515 -2.3 0.0512 1.3007 0.1498 0.5 0.0953 0.5544 0.4 0.3852 20.8 0.2331 7.0211 0.1308 -0.MgSiOs a 293-1073 K c 293-1073 K v 293-1073 K a 293-1073 K c 293-1073 K v 293-1073 K a 298-1068 K b 298-1068 K c 298-1068 K v 298-1068 K n 298-1073 K b 2981073 K c 298-1073 K v 298-1073 K (I 303-1173 K b 303-1173 K c 303-1173 K v 303-1173 K v 296-1293 K v 298-1273 K v 300-1300 K a 298-1123 K b 298-1123 K c 298-1123 K v 298-1123 K n 298-1173 K b 298-1173 K c 298-1173 K v 298-1173 K a 298-1123 K b 298-1123 K c 298-1123 K V 298-1123 K a 297-983 K b 297-983 K c 297-983 K v 297-983 K (I 296-1173 K b 296-1173 K c 296-1173 K V 296-1173 K a 77-298 K b 77-298 K 11.2 0.3536 7.3 0.9931 0.1952 -0.1080 .4 0.2 0. 0000 11.0518 6.1 0.2696 9.76.1217 -0.4594 26.0621 8.7 0.0916 0.5249 0.0000 35.0000 14.1746 -0.5 0.2635 1.6 0.3 0.7545 27.1172 0.0975 0.6 0.1629 -0.3504 0.0000 9.0602 -0.2744 -0.4036 0.0000 9.1929 26.0740 -0.3898 -0.0000 0.2386 1.3407 0.9 0.0663 0.1526 -0.1050 0.9 0.7422 -0.0960 0.0000 0.3842 5.0990 0.0000 0.6 0.1201 0.0000 9.0080 -0.6 0.1409 8.5 0.0000 WI 1451 1451 r451 1451 r451 1451 [451 WI WI F361 E.0610 0.2854 1.6 0.5381 30.0853 22.0918 9.6.0807 0.1396 27.0 0.3034 0.1109 0.4958 7.4 0.0397 0.9 0.2882 -0.1456 0.0000 28.0000 0.1004 0.0000 0.1 0.0 0.2898 9.8 0.1 0.3 0.8674 -0.2 0.0000 0.1049 0.5598 -0. [541 1401 1611 WI 1611 WI [451 [451 r451 [451 WI WI WI [91.8 0.5 0.0649 -0.1042 0.0819 0.27] P31 .0000 0.1530 -0.2188 8.2307 1.0000 25.3370 -0.3036 0.2 0.0 0.9 0.2557 0.1827 -0.8 0.2093 -0.4204 5.0694 9.0000 0.1387 9. 2050 0.0000 0. cf.1040 0.0840 0.0000 [781 V 293-1123 K 43.0000 WI V 298-1473 K 27.3330 0.0888 0.~Si03 ferrohypersthene Cao.2780 0.0000 0. Be2Si04 Pseudowollastonite.3o~Feo. CaSiO.4 0.8 0.0000 WI c 298-1473 K 8.0000 1141 c 297-1273 K 6.0606 0.ol5M~.0000 WI a 297-1273 K 7.ol~Mgo. EXPANSION TABLE 1.0000 [771 c 293-973 K 13.0000 1781 a 293-973 K 16.0000 [781 c 293-1123 K 15. hedenbergite %d-+u. C 77-298 K v 77-298 K v 298-381 K a loo-250 K b loo-250 K c loo-250 K v loo-250 K a 250-373 K b 250-373 K c 250-373 K v 250-373 K v HO-373 K v 298-840 K a 298-963 K c 298-963 K v 298-963 K v 293-1473 K Pyroxenes CaA12SiOs.1 0.&i03~ FsWo a 298-1473 K 8. cf.1380 0.1204 0.2 0.0000 0.1540 0.1350 0.0000 r771 .0000 0.0000 0.8 0.0779 0.0882 0.0000 0.9 0.0000 [14.0000 0.0000 0.~SiO.0000 0.0000 [771 b 293-973 K 10.0000 0.4380 0.0000 1711 [711 36 THERMAL.l)SiO3 Phenakite.5 0.1620 0.0646 0.P31 [I31 1131 ]271 1271 1271 [27.0000 1141 V 297-1273 K 33.0 o.0000 0. CaTs CaMgSi20b. diopside Cao.8 0.1450 0.5 0. UW@%.3 0. P-9 a0 w-9 a1 (10-y a2 ref.0000 [781 b 293-1123 K 14.4 0.0000 0.0000 1141 b 297-1273 K 20. 791 8.0 0.oooo 0.8 0. (continued) Names T range a.3o~Feo.0000 0.lFW Wsd%.4 0.0000 [I41 dlO0 297-1273 K 6.0000 0.0000 0.0000 0.0000 0. 221 a 293-1123 K 13.5 0.0000 PI b 298-1473 K 12.8 0.0000 0.5 0.0000 0. clinohypersthene CaFeSi20b. 0000 o.6 0.2 0.2 0.0520 0.7 0.0000 [771 a 297-1273 K 7.0000 1141 a 297-773 K 18.2474 1.0810 0.0000 0.6 0. pyroxmangite NaAlSi20b.0000 rw 5.3 0.0000 16.0000 0.8 0.1680 0.0000 0.1890 0.1760 0.0000 o.oooo 5.9 0. spodumene Mga8Feo.0000 0.0000 P41 c 297-1273 K 6.0597 0.0830 0.0000 30.0000 P41 v 297-1273 K 29.3156 0.9 0.0096 0.0000 0.1890 0.oooo [al V 297-773 K 37.0000 0.0 0. orthoferrosilite LiAlSi.0000 8.0893 0..1450 0.8 0. FeSiOs. acmite .0450 0.0 0. enstatite MgSiOs. protoenstatite MnSiO.0000 0.0000 5. bronzite MgSiO. jadeite NaCrSi20h.0000 6.8 0.4 0.0000 4.9421 -0..0000 0.2200 0.5 0.0000 22.0000 27.0000 14.5 0.0000 19.0000 5.3760 0.0000 1141 dlO0 297-1273 K 4.0640 0.0000 WI c 297-773 K 15.0000 0. ureyite NaFeSi.0000 WI 1711 1711 WI 1621 WI WI WI WI WI F21 [ii.1330 0.0000 0.5 0.0724 0.0520 0.O.0000 0.0 0.1520 0.O.3270 0.8 0.0483 0.0000 0.0000 0.2 0..0000 0.0000 0.1550 0.1 0.0000 15.0000 o.0000 18.2SiOs.dlO0 293-973K 8.0000 0..0000 0.4 0.0540 0.0000 0.2980 0. (continued) Names T range a0 w-7 a0 (10”‘) al (10-q a2 ref.0000 WI b 297-773 K 13.0000 P41 b 297-1273 K 17.7 0.4 0.8 0.0000 0.0000 0.3271 5.0000 ~0.0000 0.0590 0.1900 0.9 0.0580 0.0000 5.0000 0.oooo WI dlO0 297-773 K 8.0540 0.3 0.9 0.0000 0. 1301 1301 1301 1751 FE1 37 TABLE 1.0000 1771 v 293-973 K 32.2 0. 0000 P41 3.1090 0.1110 0.Silicate ilmenite.0380 0.0000 0. y-Fe2SiOd Sillimanite.1120 0.0000 0.3930 0.0000 P41 11.0000 0.SiO.2 0.8 0. MgSiOs Silicate spine1 y-Mg2Si04 y-Ni2Si04 y-Fe. A12SiOs a 297-1253 K b 297-1253 K c 297-1253 K v 297-1253 K a 297-1033 K b 297-1033 K c 297-1033 K dlO0 297-1033 K v 297-1033 K a 298-1273 K b 298-1273 K c 298-1273 K v 298-1273 K v 293-1073 K V 1353-1633 K a 297-1073 K b 297-1073 K c 297-1073 K v 297-1073 K a 297-1073 K b 297-1073 K c 297-1073 K dlO0 297-1073 K v 297-1073 K a 297-873 K b 297-873 K c 297-873 K dlO0 297-873 K v 297-873 K u 297-1073 K b 297-1073 K c 297-1073 K dlO0 297-1073 K v 297-1073 K a 298-876 K c 298-876 K V 298-876 K v 297-1023 K v 298-973 K v 298-673 K v 298-673 K a 298-1273 K b 298-1273 K c 298-1273 K V 298-1273 K 11.1680 0.0000 0.8 0.0000 0.0000 r141 .0000 [841 10.3 0.0000 P41 39.1 0.9 0.0000 If341 16.0000 0. 0000 WI 13.3 0.0670 0.5 0.1 0.0000 0.oooo 1971 4.0000 F51 6.2810 0. low Cristobalite.8 0.0000 1141 12.0000 1141 3.4 0.4770 0.0000 0.9 0.0450 0.0000 1141 20.0000 1231 14.5 0.0000 0.1380 0.0000 0.0000 0.2470 0.0092 -0.2470 0.0000 0.0000 0.0000 1141 8.0000 0.1670 0.2947 0.0000 0.8 0.0000 0.5588 [751 16.1200 0.0 0.063 1 0.2314 0.2 0.1260 0.5 0.0000 0.0000 0.0000 0.2694 -0.1450 0.0000 P41 7.0000 P41 10.4 0.0000 1141 7. Si02 group Coesite Crisfobalite.2680 0.0 0.0231 0.0000 [651 28.0000 0.0000 0.0996 0.0000 0.0691 0.0000 0.0000 0.0000 F51 8.0000 0.0000 0.0850 0.0 0.0000 0.4 0.0000 P41 16.0000 0.0000 1521 1.0000 r41 18.3639 -0.0 0.0946 0.0H)2 .0817 0.0 0.7 0.0000 P41 24.0000 [1011 27.0000 1141 6.2 0.0000 1141 6.7 0.6531 PI 26.7 0.7 0.9 0.0000 [591 7.0 0.3 0.0000 0. high a-Quartz B-Quartz Stishovite Stishovite Spodumene.1000 0.1 0.0727 0.0000 [651 13.0000 0.0000 0. A12Si04(F.0000 P71 38 THERMAL EXPANSION TABLE 1.0727 0.1 0.4 0.9 0.1051 0.0000 0.7 0.0000 0.0000 1141 4. (continued) Names T range a0 w-3 q(lo-8) a2 ref.2 0.2040 0.0390 0.0000 1231 47.0000 P31 16.0000 0.0000 /41 10.0000 P41 9.5 0.8 0.1680 0.0000 0.0 0.0 0.0000 P41 22.0804 0.0000 0.0000 0. a-LiAlSi20h Topaz.0000 iI41 6.0000 0.0000 0.2497 0.0000 P41 8.2300 0.0475 0.0000 P41 24.0600 0.0707 0.0760 0.6 0.8 0.1185 1971 7.0000 WI 23.0000 P41 5.0585 0.0386 0.2697 0.0000 ~231 24.2220 0.4.3 0.1640 0.9 0.0000 E41 24.0470 o.2440 0. 0000 o.0000 0.0440 0.2487 PI c 293-1073 K 9.0000 PI a 291-873 K 7.0758 1.1574 0.0656 0.4040 0.oooo a 298-873 K 40.3 0.0000 o.6553 -0.0000 Fl V 293-1293 K 12.oooo 0.0000 o.0000 0.0 0.0000 0.3 0.6 0.3110 o.0000 o.2060 0.0600 0.3795 0.1500 [391 v 291-873 K 16.9490 0.0000 0.0000 1751 b 293-1273 K 3. perovskite NaMgOs.oooo 0.1050 0.1000 0.1417 9.0000 0.0000 [751 a 293-1073 K 6.0000 0.8800 0.0340 0.5 0.9 0.1 0.Wadsleyite (p-phase) Mg2Si0.0000 v 295-520 K 31.0000 V 288-873 K 88.2700 0.0000 0.4 -0.0000 0.0000 0.0000 1391 c 291-873 K 0.0791 0.0000 0.3884 -0.1 0.1231 1751 a 301-491 K 19.oooo 0.0000 E751d V 298-773 K 24.0758 0.0000 a 295-520 K 13.8 0.0000 c 293-973 K 10.8903 WI a 293-1293 K 3.0000 F31 V 673-1473 K 6.5772 -0.9 0.0 0.1210 0.0245 0.0000 w41 [501 r501 1501 WI 1501 .0000 b 293-973 K 7.9170 0. 821 V 293-873 K 20.0485 0. perovskite NaMgO. ZrSi04 Perovskites BaZrO.0000 0.0 0.1542 0.7697 -0.0000 0.1 0.4 0.0000 c 298-873 K 30.oooo u 293-973 K 10.0000 PI V 1473-1673 K -4.8 0.1500 1391 a 300-693 K 7.0 0.0 0.7 0.0000 a 520-673 K 12.1860 0.6 0. cf.0597 0.0680 0.8 0.1230 0.6973 [lle V 848-1373 K 0.5270 o.0000 PI c 300-693 K 3.6 0.4 0.4698 0.0000 o.3500 o.6581 -1.oooo o.8 0.0000 1631 V 301-491 K 91.5 0. cubic ScAlOs.1388 -0.6 0.0000 V 520-673 K 35.7886 -0.0000 0.2893 0.3 0.0000 b 520-673 K 12.0000 b 295-520 K 6.3412 P91 V 293-1073 K 20.0000 1751 a 293-1273 K 4.0000 1751 v 293-1273 K 14. Zircon.0000 0.oooo 1631 c 301-491 K 52.0316 0..oooo 0. perovskite CaGeOs.0000 0.0700 0.0000 0.6 0. perovskite V 293-1273 K 6.0 0.7 0.0000 c 520-673 K 10.0000 0.3 0.1196 0.0000 0.0750 0..0 0.0000 PI V 300-693 K 18.4 0.1380 0.2662 WI b 293-1073 K 5.1050 0.085 1 0.0000 161 c 293-1293 K 5.9 0.0 0.0000 c 295520 K 10.0000 [6.5 0.6 0.oooo b 298-873 K 15.0560 0.9 0.0000 0.1000 0.1165 -0.8 0.0000 E751 c 293-1273 K 6.0 0.3060 0.15300 o.6 0.4924 0.1098 1.0000 0.0000 P81 v 293-1073 K 11.oooo V 1038-1173 K 94.0380 0.1210 0.5 0.0060 0.3 0.1950 0. 0000 0.0970 0.oooo 0.5 r341 .0000 PO41 0.. magnesiowiistite WW-02 Mg2Si04. and ~bh’%o~l~ dInversion at 491 K.1240 0.0000 DO41 0.r501 [501 [501 PO51 w51 r 1051 11051 PO51 [321 1321 r321 FE1 39 TABLE 1. Ab%l. Pressure Effect on Thermal Expansion Coefficient of Selected Substances Phases KT. bSee [.0000 0.. ‘See [24] for plagioclases. spine1 (Mge9Fe.r)Si0a.8 V 1123-1443 K 37.1610 o. periclase (Mga~e0.0000 r 1041 0.0000 0.0820 0.3750 0.4)0.0000 0.0000 0.9 c 1123-1443 K 6.0000 DO41 0.~F%.5 c 293-973 K 9.0000 [321 0.0000 PO41 0. perovskite 165.0000 0.0 a 293-973 K 12.6 b 973-1123 K 16.la)2sio4 Mg2Si04. Also see [75] for data on tridymite.0760 0. Ed.3240 0.2700 0.and Fe-cordierites.1 c 973-1123 K 8. SrZrO.2 v 973-1123 K 32.4 b 293-973 K 7.8 II 973-1123 K 7. GPa KT' s.and b-quartz transition at 846 K.0750 0.0000 0.30 6.0000 0.5 0. see [75] for original data sources.0000 0.0000 PO41 0. %@‘%0~1~ AWhOr2. olivine
[email protected] II 1123-1443 K 14. AhbP3.0000 PO41 0. Antoo. (continued) Names T range a0 W6) %I w-9 a1 (lo-s) a2 ref.0000 PO41 0.0000 PO41 “For data cited from [75].0000 PO41 0. see [l] for discussion on thermal expansion near the transition. TABLE 2.2980 0. references Fe@cc) WW Fe(fcc) NaCl LiF MgO.0680 0. Abdw.56] for orthorhombic cordierite and [33] for hydrous Mg.0000 0.7 v 293-973 K 29.0 5.1490 0. perovskite V 283-1373 K 27.0000 0.0000 PO41 0. 5 22.30 5.33 ’ Data were derived from density measurements of melts in ironfree system [8.57.5 r341 167.5 1371 174.61 26.7 33.8 PW 65. b Data were derived from density measurements of 64 melts in the system Na2@-K~0-Ca0-Mg0-Fe0-Fe203-A1203-Ti02-Si02 [8.75 Ti02 22.7 [361 157.43 32.0 36.0 4.3 4.00 5.4 WI 160.80 7.80].24 23.l573 K ‘i (X10’) SiOz TiOz M2O3 Fe203 Fe0 MN CaO Na20 K2O Liz0 Na20-TiO. Units are in cc/mole and l/K.01 5.00 6.4 16.27 17.70 4.3 4.8 r551 261.8 44. EXPANSION TABLE 3~.10 -1.10 17. TABLE 3b.7 11.98 37.1 16.3 2.80].53 47.37 5.212.8 28.0 4. Partial Molar Volume and Mean Thermal Expansion Coefficient of Oxide Components [46] iron-free silicate liquida 64 liquidsb Oxides vi.00 6.0 5.46.9 13.0 4. Partial Molar Volume and Mean Thermal Expansion Coefficient of Oxide Components in Al-Free Melts [ 1 l] Oxides vi.00 4.4 20.4 72.88 23. 1673 'i(X105) Si02 26.9 26.9 : 0.2 26.10 5.5 r511 40 THERMAL.40 .0 4.0 5.0 4.0 4.00 6.84 29.46.3 1201 54.85 16.52 11.44 21.35 21.19 32.02 26.5 rw 129.92 0 36. 26.3 5.13 4.45 Fe203 44.5 PI 24.1 [211 183.3 25.1 41.42 20.l773 K ‘i (X10’) vi. 5 Si02-CaO 0 -11. a Data were derived from density measurements of 12 melts in the system Na.1 21.042 a Data were derived from density measurements of Al free melts.1 61.64 SrO 20.31 MnO 14. 1673 ‘i (X10’) Si02 25.59 Na20 29.4 17.13 NiO 12.770 13.-CaO > 20 wt% silican low silica Oxides vi. Units are in cc/mole and l/K.1 24.9 35.2 35.1 32. FE1 41 1.22 cs20 68.94 W$’ 12. Partial Molar Volume and ltiean Thermal Expansion Coeffkient of Oxide Components in CaO-FeO-Fe203-SiO2 Melts 1’ i] Vliq(T) = x Xi E.20 PbO 25.Tr[ 1 + Ei(T .4 16.71 Rb20 54.39 12.30 Liz0 17.0 13.. 2.2 a Data were derived from density measurements of 30 melts in the system CaO-FeO-Fe203-SiO.388 12.60 0.727 0 27.7 25.1 37.57].801 0 Fe203 37.45 BaO 26.7 Na20 28.4 CaO 18.3 71.O-FeO-Fe203-Si02 [ 171 and ferric-ferrous relations (471.087 19. 1573 Si02 26.0 15.0 15.61 18.626 21.9 Fe0 13. TABLE 3d Partial Molar Volume and Mean Thermal Expansion Coefficient of Oxide Components in Na20-FeO-FezOx-Si02 Melts [47] vi.7 12. [16.1 34.501 9.9 22.3 Fe0 14. See [ll] for data sources.48 23.2 16.9 43.Tr)] + XSiOryCaO V&O. . Units are in cc/mole and l/K.48 ZnO 13.1673 K OLi(X105) vi.Fe0 13. Units are in cc/mole and l/K.33 0.03 K2O 46.4 TABLE 3~.3 Fe203 41.32 CaO 16.460 10. I. 7. 5. 95. 1984. Phys. Weigel. 45. Rex. 1974.. P. 1984. Melting. Bull. and S. 129-131. and D. 16. A. Z.3. High TemperaCryst.239-245.. compounds with zircon and scheelite structures. J.. and A. Weill. G. thermal expansion. White.736. and phase transitions of iron at high pressures. 133.. Revised method for aluminosilicate . 147-150. 1971. 106. 10. Bockris. ilmenite: heat capacity. Minerals.. Thermal expansion of LiF at high pressures. thermal expansivity. J. and C. and enthalpy of tramsformation. Y. W. Miyamoto. 129-138. Mineral. Ito. Calculation of the density and thermal expansion coefficient of silicate liquids. Less-Common Met. L. and J. Traverse.. 12.1972.. 1956.. Solids. E. Ackermann. Kennedy. REFERENCES Density calculations for silicate liquids.1988. von Bargen.. Chem. Thermal expansion and the high-low transformation in quartz. 85-90. 16.: A high-temperature thermal expansion standard. T. Solids. Chem. temperature X-ray studies. Sorrell. 1980. G. and A Chopelas. G... 40. 11. Weill. O. R. Minerals. Phys. 8. Ashida. P. Boehler. F. Thermal expansion of boehmite. J. J.. 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Thermal expansion of modified spine]. Stein. 90. 305-313. J. 1990. 88. of rutile as a function of temperature up to 1600 “C. Suzuki. Suzuki. Anderson. Phys.273-280.. M. Kirby. I. T. Subbarao. C. R. Thermal expansion of compounds of zircon structure.198O.. D. Stixrude. Geophys.. 69.SiO. Amer. 89. I. Suzuki. L. 649664. 1973. Amer. 85. R.1975..125138. Z. Prewitt. E. Smyth. 27.325.. Thermal expansion of single-crystal manganosite. Fundamental thermodynamic relations and silicate melting with implications for the constitution of D”. and I. Soot. and Y. The crystal structures of forsterite and hortonolite at several temperatures up to 9OO”C. Phys. Smyth. Kristallogr. H. Mineral.080 K. Kumazawa. 1979. Suzuki.. Mineral. Kumazawa. 1976. 87. Seya. E. Takei.. and M. Sallese.. The high temperature crystal chemistry of tremolite.. R.. R.1974.. Orthoferrosilite: Hightemperature crystal chemistry. 1246-1252. Bukowinski. J. 1973. . 83.. Phys. S.. K. The crystal structure. J. S. Ceram. E. J. @-Mg. 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A. Touloukian.. Crystal structure of ilmenite (FeTiO. Ho.. S. 176 pp. J. J. Miner.. Thermal expansion: Metallic elements and alloys. S. R.. In Thermophysical Properties of Matter. Yamanaka. 103.. 99. J. Mineral. 1983. A high-temperature study of the thermal expansion and the anisotropy of the sodium atom in low albite. 98... S. and F. 165. Chetn. Taylor. 69. Akimoto and M. Winter.O. Chem. T. Kristallogr. Crystal structures of Ni. 13. I. and Fe. and C. Thermal expansion of SrZrO. 102. B. 1982. Amer. Plenum Press. 64. S.. Winter. Zhao. edited by Y. S. 101. New York. High temperature elasticity of sodium chloride. spine1 at high temperatures up to 1700 “C. and D.. Anderson. 1977. L. Cent. We use the standard Voigt notation [80]. Interiors. cij . Chem. D. in the Landolt-Bornstein tables. 471. and Melts Jay D. Glasses. and D. 1301 West Green Street. Earth Planet. which are stiffness coefficients in the linear stress-strain relationship [80]: flij = cijklfkl (1) where Uij and ckr are the stress and strain tensors. The main content of the tables consists of elastic moduli. Parise. The discipline of elasticity is a mature one. to represent the moduli as components of a 6 x 6 matrix cij where the indices i and i range from 1 to 6. the results from many older studies are not individually listed. In cases where a . and of Bansal and Doremus [6] (for glasses). there are several excellent compilations of elastic moduli available. J. are included as separate entries. E. Laboratory measurements of elasticity have been actively investigated for a number of years for a wide variety of materials. D. we have cited the average moduli computed by Hearmon [46. 471. and by Bansal and Doremus [6]. Minerals. J.material has been the subject of several studies. and Sumino and Anderson [118] (f or crystalline materials). 1991. Also listed for each material are the adiabatic bulk modulus and shear modulus for an equivalent isotropic polycrysJ. Thermal expansion and structure distortion of perovskite: Data for NaMgO. in press. Here are summarized elastic moduli of most direct geologic importance. Bass.. Urbana. However. Elasticity of Minerals. Thus. especially where they have been superceded by experiments using more modern techniques. perovskites. University of Illinois. where available. only results from single-crystal studies . This has made the present summary far more compact than it would otherwise be. 105. the moduli can be used to calculate acoustic velocities using standard relations WI* This chapter is not meant to be either historically complete nor encyclopedic in scope. Weidner. IL 61801 Mineral Physics and Crystallography A Handbook of Physical Constants AGU Reference Shelf 2 talline aggregate. Except in a few important cases. In conjunction with the density. respectively. notably those of Hearmon [46. B. Phys.BaZrO. Cox. Bass INTRODUCTION In this chapter I present a compilation of the elastic moduli of minerals and related substances which may be of use in geophysical or geochemical calculations. elastic properties reported after the compilations of Hearmon [46. Zhao. Included are many important results published in the last few years which are not available in other summaries. 1993. Y. The isotropic moduli listed are are Hill averages of the Voigt and Reuss bounds [135]. 471. Department of Geology. Phys. 18. perovskites. Consequently. 294-301. although some .are reported. 45 46 ELAsTlClTY The number of independent elastic constants appropriate to a material depends on the symmetry of that material [80]. Results from experiments on polycrystalline samples were uniformly excluded unless no single-crystal data were available.) grouped together. we have cited the zero frequency. complimentary results on the equation of state of minerals from static compression data are found in the chapter by Knittle. elements. Tables are therefore organized on the basis of crystallographic symmetry. In cases where the dispersive properties of liquids were investigated. Since the earlier compilation by Birch [16]. or relaxed. The results in this chapter derive from a variety of techniques which have a broad range of precision. Most of the entries are for minerals. with materials of a similar nature (e. Likewise. Copyright 1995 by the American Geophysical Union. The notation used throughout the tables is as follows: Symbol Units Description Cij Ii’s ICs. to three for an cubic (isometric) crystal.g. to twenty one for a triclinic crystal. We have not made any attempt to assess the relative accuracy of results from different laboratories on a given material.o G VP T GPa Single-crystal elastic stiffness moduli GPa Adiabatic bulk modulus GPa Adiabatic bulk modulus at zero frequency GPa Shear modulus m/s Longitudinal wave velocity Kelvins Temperature P P E D GPa Pressure m/m3 Density Superscripts Indicates constant electric field Indicates constant electric displacement Note that for melts. the quantity of data related to the equation of state of rocks and minerals has grown considerably. garnets. It is not possible within the framework of this review to summarize the frequency dependence of the elastic properties of melts or glasses at high temperature. ranging from two for a noncrystalline substance. we have listed the results obtained at the lowest frequency. bulk modulus where possible. For many materials. etc. with which there is a degree of overlap. the chapter by Anderson and Isaak present considerably more detail on the high temperature elasticity of minerals. 5 217 46 227 78 223.5 78. Copper Fe.920.8 155. the compositions of solid solutions are given in terms of mole percentages of the end-members.8 297. Bunsenit e Elements.874 7.684 7. In all of the tables.4 45.o~ Feo.6 220.283 10.675 7.9430 Feo. Silver C.1 226. indicated by the subscripts. Elastic Moduli of Cubic Crystals at Room P & T Material P Subscript ij in modulus cij (GPa) KS G ReferMg/m3 11 44 12 GPa GPa ences Au. cr-Iron Feo.7 44.3 230 117 221*0 122.932 7. Diamond Cu.3 222.3 123 216.0 294 155 296.chemically and structurally related compounds of interest are included. Gold Ag.8 155.7 218.4 124.512 8.6 Binary Oxides 122 34*4 224 80.5 80. Manganosite MgO.5 1079 578 169 75.os Feo.6 40 5. Table 1.4 79.601 191 42.glSio.500 3.94sio.&o.950 MnO.os BaO CaO.4 245. Periclase NiO. Lime coo Fec.992 .4 122 45.8 344. Wugtite Feo.03 260 82. Me2allic Compounds 19. except where specifically noted. 708 5.8 15 116 153.578 3.584 3.63 .584 3.3 47 149.7 81.7 77 I22 137.368 5.2.5AlzOs 5.2 47 124 443.365 5.0 80.730 5. Magnetite FeCr204.1 162.1 72 134 161.0 47.7 36.3.7 80.3 46.0 68.1 163.3 89 114.8 149.7 81.346 3.1 72 45 70.4 80.09 3.5 164.349 6.009 170 55.1 152 141 205 58.3 71.438 5.584 6.6 47 92 102.206 5.3 46 95.1 68.1 47 111.6 10.59 81 145 183. Chromi te M&04.7 27.9 46 135 166.346 3.8 46.7 112.1 120 123.578 3.3 181.8 134 BASS 41 Table 1.0 535. (continued) Material MgTm” Subscript ij in modulus cij (GPa) ITS G Refer11 44 12 GPa GPa ences SrO UOz. 326 60 114. Spine1 Mg0.0 68.828 162 171.97 389 59.0 46.7 138 93 160.3 162.4 46.7 131.0 130. Uraninite 5.7 Spine1 Structured Oxides Fe&.8 57 95.2 46.0 29.5 130.5 47 135.9 152.619 3.681 5.40 103 135. 111 57.0 154.3.6AlaOs Mg0.4 81.4 56 121 153. 0 114.13 3.826 4.741 4.2 47 322 117 144 203.3 198.160 3. Halite 2.987 Pyrope PY). Pleonaste FeA1204.8 155.0 91.9 108.602 3.7 46 269.088 BaFz. Sphalerite 4.74(H404)1. Pyrite 5.0 91.6 157.8 46 303 156 158 206.3 106 300.4 197.836 3.775 3.5 143. Hercyni te 7-MgaSiOd.4 47 270 98.597 ZnS.131 4.5 152 298.886 CaFz.7 97 130 .7 108 162.5 163.351 4.3 46. Ringwoodite Ni$SiOd MgAMh 3.389 Fe&.6 116.563 3.6 153.9 47 282 154 154 196.28 Andradite (Anss) CasFet3SisOra AwoGmAlmd’y3 ~mJ’y2&m23Sp~ Ah&dhSpllA& Ahd’mGr&h PyrsAlmrsAnd4Uvs PYdhdh 3.839 275 95.(Gres) CasAlsSisOr2 Uvarovite (Uv) Ca3CrzSi3012 Spessartite (Spsa) MnsAlaSiaOr2 Hibschite Ca3A12(Si04)1. Sylvite 1.3 104.9o04.4 126 312 157 168 216.280 3. Frankdicksonite 4.9 154.75Feo.850 4.7 202.5 104 161.7 108.567 3.0 115.195 3.163 KCl.5 158. Galena 7.3 114. Fluorite 3.705 3.016 PbS.Mgo.3sA11. 24 282.559 5.7 202.181 NaCl. ~gdWMh2 Grossular.6 153. 6 Binary Halides 90.7 47 24.1 46 47 86.1 9.0 173.9 47 64.1 12.8 95.9 289 85 281.3 84.5 6.266.3 58.1 31.9 176.3 113.4 108.4 147.7 25.0 57.6 121 110.5 95.2 99.2 92.2 87.8 96.9 306.5 177.8 40.3 42.0 94.2 92.6 304 84 182.2 187 63.7 108 -44 104.5 171.3 165 33.1 46.7 46 6.8 24.7 104.3 86 92 157 90 10 80.9 14.3 111 108.4 94.6 84 111.9 49.5 210.4 46 111.7 296.0 133.9 11 91 162 92 10 309. (continued) Material Subscript ij in modulus cij (GPa) MgTm3 11 44 12 .4 58.3 92.2 168.2 402 114 127 23 102 44.4 101.7 149.9 136 46 87.9 310.6 31.6 301.2 91.5 130 112 184 119 144 155 226 106 13 118 179 110 140 33.6 91.5 306.4 46 12.0 85 117 177 89 67 91.6 77.5 327 126 366 106 300 126 Sulphides 361 105.4 170.6 142.5 47 41.8 92.8 25. 116 119 209 83 35 48 ELA!377CITY Table 1.27 Garnets 296.7 94.6 295 90 321.7 125.1 172.3 11 57 100 64.9 5 112.9 18.5 178.6 94.7 5 100. Zincite 5. Bromellite MgTm3 11 Subscript ij in modulus cij (GPa) Ii. Gr. Sp.6 (NazCa)4(Al.824 CD CE HzO.26 Calo(P04)s(OH)2. 3.6 277.200 Fluorapatite Cancrinite 2. majorite (Si-rich and Al-poor garnet).5 1060 140 141 79 86.4 66.675 CE CD 304.555 164 89 12 MjdYtx 3.i66pY34 3.527 172 92 Nal. Ice-I (257K) Ice-I (270K) 0. Uv.0 209.nHzO CdS.94012 3. Greenockite 4. pyrope.5 .1 132 Majorite (Mj) .6 65. 3.8 112.146 Hydroxyapatite Calo(P04)sFz. Mj.lsSi4. andradite.1 36.5 13.Its G ReferGPa GPa ences 4.s7Mgl. uvarovite.698 C.70 79 117 209 207. Graphite 2.G arnet Solid Solutions 3.5 83.9 G Refer33 44 12 13 GPa GPa ences 3. almandite.249 308. Alm.2 . spessartite.545 170 92 M. grossular.9175 NasKAl&Cis. An. 2.1 13.01 470 494 153 168 119 251 162 14 Beryl 2.724 Bea&SisGis 2. 150 150 90 Table 2.Si04)sCOs.5 94.2 308.3 177.571 Nepheline /3-SiO2 (873K) ZnO. Elastic Moduli of Hexagonal Crystals (5 Moduli) at Room P & T Material BeO.8 83.3 283.606 329 114 96 174 115 Abbreviations: Py.3 180 36.7 96. 1 209. ZnS 4.8 87.3 101.8 (Na)(Mg.7 120.5 Cr203.0 47.5 44.0 85.9 30.009 259 156 54. Elastic Moduli of Trigonal Crystals (6 Moduli) at Room P & T Mineral Mgym3 11 Subscript ij in modulus cij (GPa) K’s G Refer33 44 12 13 14 GPa GPa ences A1203. a-Quartz 2.F)~ 160 115 . 3.3 46 BASS 49 Table 3.Li)sA1s(B0s)s(Sis0~s)(OH.2 61 Wurtzite.63 8.2 Berlinite.47 107.2 94.3 61 101.712 144 84.648 86.8 47 38 21 48.7 47 16 120 117.6 34.4 15.9 11.7 46 54.0 Tourmaline.4 41.8 NaNOs.1 45.620 64.5 61 50. Magnesite 3.7 42 74.3 18 13 69 80.96 125 37.3 14.2 58.72 3.0 46.3 62.21 374 362 159 FeaOs. 5.1 123.0 109.084 122 138 28.7 16.1 142.8 46 106.5 39.1 42.48 46 6.4 46.5 5.2 153 180 15 161.100 305.3 142.8 AIP04.982 497 501 146.59 59.7 17.A1.97 5.7 17. 3.648 86.9 3.8 114.9 30.8 221.2 CaCOz.Fe+2.5 15.0 96.1 61 6.260 54.8 15.8 94.97 Proustite SiOn.8 cE 2.2 57.3 125 37.4 58 33 56.6 106.999 495 497 146 Corundum 3.6 47 46 56 212.8 153 128.254 MgCOs. Hematite 5.4 64.5 176 78.3 Ag&%.Fe+3.2 60. (cE) 2.0 33.9 8.8 43.4 47 104 143.4 45. Sapphire.74 107.8 9. (cD) 69. Eskolaite 5. Nitratine 2.70 2.5 181 79.9 47 51.09 14.9 118.1 57.6 46.0 33.9 CD 2.73 3.0 60.5 46.648 86.177 44.0 176.2 110 36 218 44.9 48.40 37 38 21 48. Calcite 2. 5 46 -21.5 13.2 9.960 BezSiOa MgSiOs 3.335 6.5 46 108 51 -6 127.6 -17.4 46 6.9 -18.0 0.1 37.4 -19.25 11.9 51.795 CaMg(CO3)a Phenacite 2.4 29.6 58.1 3. Elastic Moduli of Tetragonal Crystals (6 Moduh) at Room P & T Material MgTm3 11 Subscript ij in modulus cij (GPa) KS G Refer33 44 66 12 13 GPa GPa ences SiO2. Cassiterite TeOz.7 12.6 10.02 5.4 148. Stishovite SiOz.7 29.6 91.8 98.0 136.7 46.0 46. 50 7.9 -17. Paratellurite Ti02.9 32.2 12.9 148 472 382 106 168 70 -27 24 212 132 141 50 ELA!XIClTY Table 5. a-Cristobalite SnO2.7 32 -20.3 46 6. 3.9 37.6 14.99 4.8 18.279 .8 11.5 73.290 2.3 31.2 1.9 253.5 28.0 123.1 148 175 75. Elastic Moduli of Trigonal Crystals (7 Moduli) at Room P & T Material MgTm3 Subscript ij in modulus (GPa) IC.4 33.8 44.0 69 -19.5 212.8 71.260 6.0 68.0 47 Table 4.0 25 13.9 19.0 91.5 87 -23 251.7 162. Rutile GeO2 4. 50 341.0 46 -19 234.8 37.2 81.0 57.9 45.9 53.162 116 7.3 32.0 114.2 83 -12.975 6. 46 206.5 163.8 44.3 33.7 94.5 44.18 36.795 Ilmenite structure 205 113 39.0 46 0.9 391.6 6.7 G References 11 33 44 12 c1ij3 14 15 GPa GPa Dolomite.98 11. 4 47 258.6 21.3 65.3 29.9 51.3 29.CO3) Vesuvianite CaloMg2A4(SiO4)5(Si207)2(0H)4 ZrSiOa”.K)4Als(AI. Table 6.2 269 337.9 43.3 101.6 150.4 16.8 65.3 65.2 187.3 69.8 65 47 -13.6 103.7 261.0 122 192 177 146 215.4 38.70 256 372 73.9 35.4 161.8 22 55. Elastic Moduli of Tetragonal Crystals (7 Moduli) at Room P & T 88 47 Material MgTm3 11 Subscript ij in modulus cij (GPa) KS G Refer33 44 66 12 13 16 GPa GPa ences CaMo04. 4.4 177.5 108.6 ’ nonmetamict.0 39.2 140 166 99 102 102 153 424.3 489.1 47 30.4 58.4 257.4 42.2 25.Si)s SkO24(CGO4.4 39.4 93 55.1 151 105.9 46 Powellite .4 188.9 109.5 212.2 48.1 35.3 131.9 43.Ca.7 449.BazSizTiOs.5 81.7 149 227.5 24.5 112.4 67.255 144 127 36.2 155.0 Rutile-Structured 776 252 302 211 3.0 166 55.7 53.6 140 23.6 55.8 45.2 21.4 58 44 77.3 46 22. (Na.1 48.0 48 44 82. Presnoite (cE) Scapolite.0 23.7 113 15.7 19.6 43.0 20.0 140 23.4 38.5 47 Zircon 4.9 66.9 42.1 207.1 47 30.1 47 54.8 131 59 36 24 56.8 45.1 46 69.2 43. 4.5 Other Minerals 83 33 100 31.8 26.4 480 124 599.8 203 316 220 143 -4.675 453 59.5 116 175 214 223. 4 24.4 205.0 193.6 72.8 3.129 258.335 229.4 63 51 -15. Monticellite.299 319 192 238 4.7 3.5 210. MgSiOs Ferrosilite (Fsrcc).119 141 125 33. FeSiOs Ends6 Emdh5. CaMgSi04 Ni2Si04 CozSiO4 MgzGe04 3.1 3.4 46 Scheelite PbMo04.6 206.9 165.108 NaMgF3 3.4 165.7 61 41 -17 76.373 231.5 46 Wulfenite 108 95 26.7 197.8 25. MgSiOa 3.5 37.8 215.4 35.7 40.2 .8 194.7 68 53 -13.38 266 168 232 3.325 320.0 169.0 46 Material Table 7.058 Enstatite (Enloo).2 hd’s2o 3.221 328 200 235 4. Mg2Si04 Fayalite (Faloo).9 233.002 198 136 175 Protoenstatite.198 4.272 229.3 167.CaW04. FeaSiO4 Fog 1 Fag Fodb hxd’aa.7 234.4 3.316 324 196 232 3.816 109 92 26.354 228.116 216 150 184 4.052 213 152 246 Forsterite (Force).2 195.7 33. Elastic Constants of Orthorhombic Crystals at Room P & T MgTm3 Subscript ij in modulus cij (GPa) KS G Refer11 22 33 44 55 66 12 13 23 GPa GPa ences MgSiOs 4. 6.933 340 238 253 4.1 Fo9dh Mn2Si04.311 323.6 160.9 3. 6.6 235.7 3.706 307.8 70.8 3. 3 142.9 59 58 79.6 49 77.5 76.2 78 64.6 50.5 81 44 Olivines 66.5 71 87 46.1 109.7 147.8 75.1 52.0 78.9 64.1 81.5 64 71.1 43.6 102.4 54.7 149 155 72.8 78.8 59.9 57.5 45.5 74.0 54.6 77.9 77.7 76.4.9 31 78.9 213.9 63.4 184.1 63.8 117 117 139 246.0 75.6 56.7 81.3 46.1 79.4 49.4 81.9 57 78.8 Pyroxenes 224.5 82.9 31 70.7 57.8 79.7 44.7 177.5 77.8 75.8 46.8 46.1 76.4 75.3 32.1 67 80.2 66.1 57.1 83.7 78.8 76.3 55.2 49.1 75.3 73.5 63.7 142 84 72 55 101 52 9 73.7 107.0 103.029 312 187 217 Perovskites 515 525 435 179 202 125.6 49.2 137 .7 63.7 46.9 61.5 46.6 75.1 78.6 78.3 49.6 105.3 45. (continued) Material P Mg/m3 11 22 Subscript ij in modulus cij (GPa) 33 44 55 66 12 13 23 KS G HeferGPa GPa ences 383 Other Silicates Wadsleyite. .3 Sulphur 2.76 59 70 112 63 123 69 69 73 129.6 75.4 71.5 71.5 66. Celestite Na2S04.7 78. Anhydrite SrS04.6 71.1 68.4 79.5 129.1 92 134 50.8 128. Barite CaS04.474 360 3.145 233.5 77.065 BaS04.5 81.1 78.9 70.7 79.0 92 128 54 77 106 55.6 129. 273 112 118 98 @-MgzSiOd AlzSiOs Andalusite Sillimanite 3.241 287.7 72 126.2 113 165 80 103 148 62 46 92 55 67.5 59 76 87 95 59 71 136 65 82 82 117 92 110 105 13 117 71 60 65 66 120 72 140 Table 7.4 3. 7 170.Fe3+)OsSiOs(0.6 16.1 41.3 8.7 111 15.7 46 3.4 105 67.4 80.2 65. 2.2 5.6 29.99 131 198 211 64.8 43.4 14.3 78.2 31.6 32.6 25.4 122.0 22. Carbonates 20.5 44 50 41 80.6 36.0 23.5 9.3 125 1.4 81.3 33.930 160 Chrysoberyl.7 116.9 388.5 26.0 28.4 94.1 26.6 12.3 4.9 38.8 55.7 54.1 6.4 114.05 215 155 110 37.5 87.1 99. 3.0 59.0 7.7 138 19.3 46 37.6 42.7 2.9 29.7 185 112 32. CaBzSizOa Datolite.9 19.9 48.1 93.3 231.8 46 51.2 3.2 45 16.Mg)2(A1.3 17.3 2.OH)2Si04 Natrolite.8 Alz(F.7 29.5 15.3 46 47.79 343 185 147 46 70 92 67 61 128 128.5 27.7 89.0H)2 Topaz 3. Aragonite 4.4 53.0 27.0 95.6 3.3 4.7 7.8 87.1 29.8 112.0 380.25 72.Thenardite CaC03.6 11. Al2 Be04 Danburite.4 162 99.2 23.6 83.9 50 64 34 91.4 22.9 31.3 8.8 58.8 21.563 281 349 294 108 132 131 125 84 88 167. CaBS&040H Staurolite.0 3.3 24 14.8 91.8 74. Sulphides.9 26.0 107 12.5 2.1 8.8 29.6 77 60 62 81.27 4.663 80.5 48.3 Sulphates.963 3.5 126 13.2 57.7 .8 25.7 64.9 83.8 18.7 24.2 81.7 110.5 128 240 160 (Fe.1 50.3 25.473 2.972 104 106 129 13.2 89.4 46 46 46 133 46 46 46 46 47 289.8 41.72 527.5 75 110 105 174 114 105 97.7 18.7 46.1 126 158.9 27.1 15.2 84. 3 26.6 24. ferrosilite.8 73.3 114 64.0 (Ca.8 63.5 49. Fo.7 -14.9 45.7 58.7 37.6 150.9 16.0 33.4 30.9 37.3 Plagioclase Solid Solution&’ 17.6 14.4 21.4 7.4 26.3 -18.4 161 124 13.2 -19.7 51. 3.9 67. (Ba.4 39.8 70.6 14.2 52.9 32. Hyalophane.7 62.31 204 175 238 67. Elastic Constants of Monoclinic Crystals at Room P & T Material MgTm3 11 22 33 Subscript ij in modulus cii (GPa) KS G Refer44 55 66 12 13 23 15 25 35 46 GPa GPa ences Pyroxenes Acmite.0 68.7 -19.7 34.7 27.A1)20s AcmiteAugite Diopside.1 55.9 38.6 25.8 181.Na)(Mg.0 30.6 -12.1 123.3 35.3 18.2 3.7 465.4 68.9 52.Fe.9 62.6 3 .3 48.5 58. Fs.9 62.4 158 150 21.4 -6.3 26.3 113 67 3.5 14.6 151.6 85 61.8 69.2 -7.8 Abbreviations: En.1 -30. fayalite.Other Minerals 438.7 -23.4 25.5 84.4 88.7 -15.8 -1.7 112 58.8 3.1 18.5 -9.5 33.1 50.7 -1.7 -8.4 62.4 30.1 62.0 -0. Fa.6 -15.1 35.2 39.8 144.3 95 59.42 155.3 234.8 151.0 -2.4 41.5 40.0 169 118 80.32 181.5 39.9 149.9 -8.3 56.657 222 176 249 55 63 60 69 79 86 12 13 26 -10 120 61 3.3 29.8 29.289 223 171 235 74 67 66 77 81 57 17 7 43 7.4 -0. CaAl$i20s.7 88 64 69 -40 -26.4 74. NaAlSisOs Anorthite.7 67. LiAlSilOs 3.0 62.0 46. Table 8. enstatite.8 41.8 99.0 19.6 9.6 210.30 153.8 163 124 An9 74.0 Feldspars 17.4 -5.3 23.4 42.9 3.5 66 50 42 -19 -7 -18 -1 84.1 25.5 72. 3.5 56.4 72.5 37.0 29.2 -12.9 19.8 9.8 137 129 Am4 82 145 133 88 65 94 94 71 82 4 14 28 13 143 85 70.9 55.2 31.0 47.8 -7.1 21.4 33.8 216.5 20.2 4.9 51.8 36.1 66.4 31.6 32.7 -6.8 48.4 28.7 -12.33 274 253 282 3.4 45. NaAISiaOs Spodumene.K)AlzSizOs Labradorite”?’ KAlSisOs Microcline Oligoclase” 74 131 128 124 205 156 23.19 245 199 287 Albite.1 102 46.3 -19.8 -20.5 -10.6 -12.0 -6.2 -2.8 70.2 11.7 NaFeSizOs Augite.6 -11.Al)(Si. CaFeSi Jadeite. CaMgSizOs Diallage Hedenbergite.1 40.6 4.9 28.8 28.7 217.0 36.5 70.7 -2.2 81.0 -1.6 -33. forsterite.1 62.3 -15.50 185.0 33.7 26.1 31.4 145. 2 61.1 36.5 10.3 178.3 -3.4 46 CaS04 94.9 1.+a .8 21.5 15.56 62.4 34.4 42.3 23.1 -2.2 2.6 0.58 63.0 -11.7 -4.2 -10.1 163 141 20.8 73.5 -18. ’ Labradorite is a plagioclase feldspar with composition in the range 50-70% anorthite and 30-50% albite.4 36.8 36.4 -14.1 43.3 -12.4 231.0 -6.1 24.1 16.4 106.8 -1.6 67.8 24.7 61.4 10.2 42.0 43.5 4.1 102.2 47 0mAbz7Am 2.8 -5.Fe)sSia012(0H) Hornblende.3 49.7 37.7 46 Abbreviations: Ab.3 3 3 68 3 59 60 46 46 47 47 47 47 47 47 47 Table 8. 2.0 43.9 -1.3 -13.1 40.4 65.6 57.5 47 Na-K Feldspar Solid Solutions Ovb Or79Ab 19 2.1 20.5 -6.3 37.57 61.0 48.9 113. b Subscripts indicate weight percentages of components.3 37.6 9.8 230.8 35.7 18.4 -18.3 34.7 33.844 184.4 61.1 -17.4 -1.0 39.3 9.6 72.3 47 Omaha 2.0 -1.0 21.0 28.3 -11.0 61.9 47 Or67Ab 2.9 47 Silicates SiO2.2 8.5 66.0 159.3 22.4 9.4 48.2 -7.0 36.5 -1.7 -12.8 173 141 20.317 78.3 53.2 -14.0 36.5 172 124 14.0 26.2 0.0 2.40 211.7 202.3 33.1 -2.7 191.7 198.0 6.6 47 An56 98.9 20.6 35.6 51.5 47.6 62. orthoclase.9 28.4 31. ’ Triclinic.4 147 99 12.8 37.12 116.1 -11.8 52.aJ VP Frequency References K GPa m/s loss. BASS 55 Table 9.7 45.4 151 132 18.54 58.2 47 Ovdbz2 2.5 58.9 31.9 61.3 124 KAlaSia01o(OH)2 Sulphides.8 82.6 -0.1 38.8 -10.6 32.4 47 Ana3 97.* Fe CaAl$!&Os (An) An” Ad& h36Di6.8 -15.9 -2.7 47 Ordb35 2.9 43. albite.9 44.0 32.1 26.0 152 118 10. An.4 25.0 -1.4 18.7 -2.1 -12. 47 3.5 65.0 -3.9 -40.0 23. anorthite.15 130.3 32.7 27.8 21.9 -7.6 42.4 -9.0 3.0 15.4 10.8 53.57 59.4 59. 3.2 104 Caz(Al.3 -2.1 51.3 2.2 32. Or.2 61.4 41.0 35.8 24.3 45.5 -6.2 -2.1 187. Sulphates Gypsum.2 -8.1 42.Si)sO&OH)2 3.1 33. Elastic Moduli and Velocities in Melts Composition T kg/m3 fL.1 -15.0 -1.9 158 100 14.0 17.2 87.8 44.2 -7.9 32.2 148 103 13.5 34.6 -36.8 35.8 -9. (Ca.8 -18.5 -11.9 93.8 33.6 -10.9 34.2 36.4 -6.2 50.0 3.0 31.8 -12.9 49.0 -8.6 139 Epidote. 47 Muscovite.3 71.54 57.6 57.6 158 105 13.8 238. 2.1 63.7 72.Al)5(A1.5 -2. Coesite 2.4 59.6 -39.1 26.5 34.3 19.2 77.2 45.9 35.4 24. quasi monoclinic.3 58. (continued) Material MgTm3 11 22 33 Subscript ij in modulus cij (GPa) KS G Refer44 55 66 12 13 23 15 25 35 46 GPa GPa ences An29 84.911 160.Fe.2 35.Na)2-3(Mg.4 70.3 36.0 23.3 36. Awdh hdbo AhDko Abdh. Ab33An33DiB BaSi205 CaSiOa CaTiSiOs CszSiz05 caMgsi&& (Di)” Di Fe&i04 KzSi205 KzSiOs Liz!%205 LisSiOs MgSiOa NaCl (Naz0)~(A1203)s(Si02)61 (Na20)32(A1203)15(Si02)52 N&$05 NazSiOs 2490 3950 1833 1893 1923 1677 1673 1673 1573 1753 1698 1598 1753 1648 1698 1583 1793 1693 1836 1753 1653 1693 1208 1773 1758 1698 1693 1598 1653 1503 1693 1408 1698 1498 1693 1411 1543 . 12 2.1 .01 3.61 2.0 24.50 3.17 2.45 2.48 3.26 2.08 2.65 2.61 2.8 52.22 2.14 3.6 20.49 2.10 2.46 2.22 2.39 2.61 2.1913 1094 1322 1684 1599 1690 1693 1408 1573 1458 6.61 3.60 2.51 3.60 2.4 17.4 20.54 2.6 22.47 2.54 5.71 3.20 2.16 2.96 3.55 2.25 94.76 2.56 2.44 3.34 2.40 2.52 2.2 21.17 2.44 2.9 23. 635 2910 3.3 16.83 2345 3.5 15.0 6.922 2850 3.1 19.8 19.529 3.0 16.4a 18.7 20.0 16.842 3020 3.5 8.565 3400 3.803 2880 3.3 20.4 22.6 10.3 11.8” 16.023 3040 3.944 2390 3.6 21.4 8.665 .7 17.9 20.906 2410 3.2 15.5 20.484 2590 4.1 19.2 24.833 2805 3.2 20.2 27.9 7.4 16.8 22.17.0 3808 3075 2850 3.013 1450 3.854 2345 4.6 15.2 19.014 2580 4.6” 14.943 2800 3.7 19.0 2885 3.652 3120 3.8 18.858 2735 3.5 19.662 2830 3.4 24. 909 1970 5.2450 3.712 2860 4.040 1727 8.955 2600 3.934 2680 3.707 2695 3.951 1890 4.1 2752 8.4 48 48 100 107 99 107 98 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 99 100 100 100 100 100 100 100 100 100 100 100 100 100 100 .680 2400 7.65 2450 8.100 2740 3.67 2190 3.558 2525 3.61 2653 3.852 3160 3.764 2835 5.61 1540 8.242 2670 4.990 2663 10. 974 100 1758 3.6 3850 3.63 63 63 63 63 100 100 100 100 56 ELASTICITY Composition Table 9.909 100 1803 2.836 100 1598 2.790 100 1503 2.833 100 1708 2.1 5200 3.723 106 Abbreviations: An.31 13.8 4300 3.9 2600 3. G kg/qn3 GPa 6K/6P 6G/6P 6K/6T 6G/6T References GPa MPa K-’ MPa K-l SiO2 MgSiOs CaSiO3 caMgsizo6 CaAlaSizOs Na2Si20s (Nazo)3s(SiOz)ss” NaAlSisOs Na2AlzSizOs (Naz0)30(Ti0z)zo(Si0z)soa (Kz0)z5(Si0z)75a .1 2570 3.40 16.02 19. KAlSisOs.889 100 1803 2.46 16. Di.78 7.04 20.0 2795 3.6 2700 3.656 100 1578 2.88 9. Table 10.945 100 1408 2.6 2550 3.38 16.1 2775 3. NaAlSisOs.0 4350 3. Or.5 3470 3.68 18.8 1678 3.664 100 1553 2.3 2610 3. CaMgSi2Os. Ab.827 100 1553 2.65 17.44 16.59 19.33 13.9 2130 3. CaAlzSinOs.55 18. (continued) T kgTm3 I&X2 VP Frequency References K GPa m/s loss-’ OmAm or61 Dk9 Rb$SizOs SrSi205 Tholeitic Basalt Basalt-Andesite Andesite Ryolite 1783 2.863 100 1783 2. ’ From shock wave experiments.29 13.839 100 1505 2.35 14.4 2980 3.923 100 1768 2.690 100 1653 3.5 5280 3.673 100 1693 2. Elastic Moduli of Glasses Composition I(. 495 41. Wiistite Feo. (bee) A1203.2 36. P and T derivatives of Isotropic Elastic Moduli Material 6&/&P 6G/6P GKs/ST &G/ST AT References MPa/K MPa/K K Ag.761 78.1 -0.42 30 21 2.880 69. Hematite .2 2.23 1.8 -1.920. BASS 51 Table 11.7 75 129 -9 44 -7.7 2.3 BaO 5.5 -6 -3.2 2. 79 129 129 129 113 129 129 -10.331 37.4 -0.4 -1.369 39.3 2.494 41.7 0.7 .2 2. Lime 5.35 -7 4.5 31. Corundum 4.749 50.5 33.1 2.1 38.5 -8.8 2.571 52.8 2.8 30.777 62.847 74.2 38. 36 79 79 79 ’ Composition given as mole percentages of oxide components.9430.9 36. Gold C.490 45.1 29.693 69.4 16 4.6 0.8 41.9 39.7 coo Feo. Silver Au.4 75.0 30.863 76.9 24.9 0.1 30.1 74 -3.6 -0.12 CaO.0 1.64 6. Wiistite FezOs.1 -4to+4 -1 -2.2 2.2 2.0 2.12.0 23.52 1. Diamond a-Fe.204 36.8 2.Obsidian Andesite Basalt 2.3 4 38.6 2.7 2.1 2. 0 5.7 1. Wadsleyite 4.8 MgA1204.18 6.28 1.29 5.61 0.89 Mg0.6A1203 4.7 -15. Rutile UO2.18 6.0 5.16 -51 3.50 6.68 -21.4 6.91 -43 2.73 6.46 0.71 4.G&t.83 1.97 5.13 4.82 -31 1.55 4.5 2.5 1.7 -9.5 4. (rutile structure) MnO. Metallic Compounds .42 Spine1 Structured Oxides 1.3 1.2 3. Periclase SrO Sn02.69 P-Mg2Si04.2.4 Elements.85 4.09 6.78 1.27 2.5 1.13 4. Cassiterite SiO2.7 1.1 0. Uraninite 5.5 0. Manganosite MgO.0 2.4 -43 -18 -19 -33 Simple Oxides 4.61 0. Spine1 5.27 -31.3 -8. Quartz TiO2.2 1.5 2.2 5.78 5.13 4.66 %Wh 4.76 4. 298 17 -8.1200 281 .8 20 -20 -27 -24 -24 -12.500 29.1 -11.7 -21.6 281.298 103 -30 298 .7 298 .7 -14.1 -12.8 @293 -48.9 112 12.900 29.-15 -23 -19 -23.900 103 .3 -21 @180011’ -17.5 -26 @1200K -21.700 29.4 79 .373 -8.373 -20.3 -11 14.0 -14. 128 -43 800 . 49 -14 77 .303 @I298 -36 -12 293 .8 -15.583 -12.303 195 .298 17 -5.300 29.298 -7.2 -14.9 -7 -14.473 @298 300 .323 77 -27 25 .4 @296 @lOOO @1825 281.298 195 . 42 -33 300 .293 300 .0 298 .8 -12.5 -24 @30011 -22.5 -0.293 -19 -6.6 273 .7 79 .3 -21 -15.9 195 .800 -14.300 71 -17 80 .298 293 . 102 -47 500 .3 -19.0 -13.7 223 .293 283 . 114 22 78. 40 40 40 2G 127 112 8. 76 35 293 .37 Olivine. Galena 6. 4. Sylvite 5.28 ZnS.36A11.9004. Fluorite NaCI.29 130 PbS.423 43 70. Frankdicksonite CaF2. 52 52 26 8. 114 81 26 120 120 56 69 131 138 89 120 115 4 52. FesSi Orthopyroxene . Wurtzite 4. (continued) GGISP 6Ks/6T &G/&T AT References MPa/K MPa/K K Mgo. Pleonaste 4. Fogs Fo9&7 Fog1 Fag Fodalo FogzFaa Fayalite (Fa). 110.75Feo.118 34.37 BaF2.92 0.152 24 106 58 ELASTICITY Material iX’s/bP Table 11. 73.39.0 Forsterite (Fo). Halite KCl. 57 23.97 MgsSiOa 5. NasKAl&Ors Zircon.5 -15.38 -26.6 1.71 1.05 4.43 10.56 Binary Halides -14.0 -7.5 Svlphides -39.90 4.00 -9.92 5. BesAl2SisCrs Calcite”.27 5.0 0.8 1.9 -14.44 1.9 -24 2.14 -10.5 2.256 4.95 5.8 -11.2)SiO3 AlPOd.80 -15.(Mg.56 -18.13 -10.7 Garnets -19.6 5.79 -15.1 -14.2 2.7 1.5 1.8 9.7 Other Minerals 1. ZrSi04 4.6 1.06 2.8 -7 -3.13 4.83 6.56 5.d%.0 -16. CaCOs Nepheline.5 -17.93 4.0 -16.74 4.2 -8. Berlinite Beryl.82 -17.7 0.78 -21 .0 -15.9 -18.6 3.40 -20. 5 300 . 30 146 298 .1500 -13.800 294 .353 137 33 .8 300 .94 298 .5 -3.30 298 .338 745 .373 21 195 .700 -13.1350 -12.865 298 .298 195 .1250 121 137 20 132 111 54 54 -13.673 -13.2 -5.298 1.0.295 300 . 28.623 -2 180 .298 145 -9.300 91.1700 -1.0 298 .5 293 .5 300 .2 -9.2 195 .1000 294 .306 -13.6 300 .306 -13.9 -8.6 298 .6 288 .766 300 .6 -10.1500 -13 300 .5 300 .313 -12.1000 145 7 116 147 147 7.00 77 .6 300 .9 298 .338 -10.500 41 65 119 53 154 65 136 51 51 55 -11. 6 53 53 136 154 57 56 0. Mater. 2. Lime Orthopyroxene. and T. The elastic properties of rock-forming minerals: pyroxenes and amphiboles. (Mg. Alm. And. C. Gr.9 -1. Alexandrov. USSR Acad.25 153 58 19 -9. .08 -1. Andradite Ca3Fe2Si3012. K.28 -0.5 24 38 -1. Fa. Boeyens.12 -1.07 -5. 1. V. S. The elastic constants and distance dependence of the magnetic interactions of Cr203. Almandite Mg3A12Si3012. Periclase Fee. J. A. (Mg.3 81 137 0. L.1 54 Acknowledgments: This work was supported in part by the NSF under grant no.8 -1. Albers. Spessartite Mn3A12Si3012. H. Uvarovite Ca3Cr2Si3012. BASS 59 Table 12.05 -0.2 -0. Grossular Ca3A12Si3012.03 -0.Fe)SiOs MgA1204.10 -1.gdsO. Pyrope Mg3AlZSi3012. Fayalite FeaSiO4..4 -2. Magnetism Mag. Wiistite CaO. Sp. IN. 2. The review of O.8 -0.1 136 -0.06 -0. a Pressure derivative of KT is given.573 88 Abbreviations: Py.. 1976.4 298 .6 -0. Ryzhova.L. Higher Order Pressure and Temperature Derivatives Composition 62 Ii’/6P2 S2G/6P2 b2 Ii’/6T2 b2G/bT2 GPa-’ GPa-’ kPa Kw2 kPa Km2 References SiO2 Glass Grossular Garnet CasA12Sis012 Pyrope Garnet WwWkOl2 Forsterite.Fe)2SiO4 MgO.15 -0. EAR-90-18676.7 -0. Spine1 2.11 -0. Forsterite MgzSi04. Fo. T < 760 MgzSiOa T > 760 Olivine. 327-333. Anderson is appreciated.. and J. Uv. 7. Res.. in Handbook of Physical Constants. elastic constants. Phys. 14.O single crystals. Elastic constants of Fel-. Ceramic Sot. 1964. Orlando. I. 1991-1992. Jr. K. V. D. Res. 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Elastic properties of the olivine and spine1 polymorphs of MgzGe04. Chem. 275-283. Yamamoto. Phys. D. Wang. J. Weidner. 1993. J. 45. L. Elastic properties of the pyrope-majorite solid solution series. Monogr. D. Weidner. 2453-2456. 153. ABSTRACT Data on elastic constants and associated thermoelastic constants at high temperatures for 14 solids of significance to geophysics are presented and discussed. Single-crystal elastic moduli of magnesium metasilicate perovskite. A. Weidner. and R. elastic constant data have been taken above the Debye temperature of mantle minerals. Newham. Yeganeh-Haeri. 1993.149. Science. Anderson and Donald G. Using the techniques of resonant ultrasound spectroscopy (RUS) [6. and J. 260.. Phys. M. 13-25. UCLA. Yoneda. A. and D.. Ito. Geophys.. Geophys. 19-55. CA 90024 Mineral Physics and Crystallography A Handbook of Physical Constants . 71. J. Isaak. The single crystal elastic moduli of neighborite. 152. 151.. A. Ser. Science. Isaak 1. Institute of Geophysics and Planetary Physics. Chem. 591. pp. D. 1992. INTRODUCTION Though compendiums of elastic constant data for minerals exist [ll. Res. J. vol. and E. Yeganeh-Haeri. 1989. Center for Chemistry and Physics of Earth and Planets. Pressure derivatives of elastic constants of single crystal MgO and MgAl204. 20. Elastic Constants of Mantle Minerals at High Temperature Orson L.29. Yoon. Current problems in mantle geophysics and geochemistry often require values of elastic constants at temperatures found in the lower crust and mantle (1000 to 1900 K). Anderson and D. Zhao. 50. which is of the order of T = 20. 38. 17. 155. in Perouskite: A Structure of Great Interest to Geophysics and Materials Science.. J. J.. M. Equations for extrapolating the bulk and shear moduli to temperatures beyond the limit of experimental measurement are given and evaluated. Elasticity of cY-cristobalite: A silicon dioxide with a negative Poisson’s ratio. 1990. E. G. A. 1990. 2. Ito. often as high as 1825 K. Yeganeh-Haeri. D. 507-509. Slutsky. where 0 is the Debye temperature [13]. Phys. 0. and L. Brown. Minerals. E.. J. J. Acta Cryst. Y. Zaug. 1973. Earth.. B. H. Parise. Los Angeles. H. Abramson. and E. 154. Lett. S. 257. Sound velocities in olivine at Earth mantle’pressures.. 419-424. J. 650-652f. 1487-1489. they are restricted to temperatures at or near room temperature. Weidner. 150. A synopsis of quasiharmonic theory in the high temperature limit shows that anharmonic corrections to the quasiharmonic determination of thermal pressure are not needed in the equation of state throughout conditions of the lower mantle.. The elastic properties of beryl. A. which is the change of thermal pressure relative to the pressure at 300 K. to be computed from KS and G. thus defining several important dimensionless thermoelastic parameters that are presented in Tables 2942. measured value of T/O: 1.6 f0.3 274.5 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500 1600 1700 1800 299.3 88. up and v. In Tables 15-28. included are silicates.AGU Reference Shelf 2 Copyright 1995 by the American Geophysical Union.0 296.6 98.0 155.. v.6 280.6 154. 0.7 f0. 64 ANDERSON AND ISAAK 65 Table 1.2 292. We also list the Debye temperature. From the values of properties in Tables 15-28 the temperature derivatives are calculated.1 101.0 96. allow the computation of the Griineisen ratio y and then values for the isothermal bulk modulus KT (computed from KS) and the specific heat at constant V Cv (computed from Cp).8 91.22) 1000 K (max. determined from sound velocities.8 98. a. I?.4 151.0 .. Poisson’s ratio. measured value of T/O: 2. and the measure of the rate of change of shear sound velocity with the longitudinal velocity. which allows the respective isotropic longitudinal and shear sound velocities. oxides. and two alkali halides. including the adiabatic bulk modulus KS and the shear modulus G obtained by appropriate averaging schemes (See Section 4). 6s and 6~.4 157. we present isotropic thermoelastic properties. the dimensionless ratio of change of G with T. The techniques of RUS do not lend themselves to pressure measurement. the predominant technique used to obtain the data here is the rectangular parallelepiped technique (RPR) pioneered by Ohno [44] and Sumino et al. Values of thermal expansivity CY and specific heat (at constant P) Cp. We present the elastic constants. MgO: Measured single-crystal Table 3.0 152.9 97.9 97. at high T for fourteen solids listed in Tables 1-14. We note that of the several RUS techniques. and (YKT and its integrated value APT. Cij versus T.3 94.62) T (K) Cl1 Cl2 c44 c. coupled with the elasticity data.3 f0. [60] (see Shankland and Bass [49] for a review of techniques). We list the Anderson-Griineisen parameters.5 98.9 T (K) Cl1 Cl2 c44 c. The density p is computed from (Y.3 f0. Pyrope-rich garnet: Measured singleelastic modulit (GPa) from 300 to 1800 K crystal elastic modulit (GPa) from 300 to (max. 1 285. 300 350 400 450 500 550 600 650 700 750 800 850 900 950 1000 296.9 90.52 187.O 294. Grossular garnet: Measured singleelastic modulit (GPa) from 300 to 1200 K crystal elastic modulit (GPa) from 300 to (max.3 289.1 141.2 95.0 91.5 91.Gz). measured value of T/O: 1.94 73.6 58.2 89.02 f0.7 57.13 182.2 f0.5 90.7 134. [43].96 79.18 71.1 137.6 91.2 93.3 213.70 76.3 ho.l f0.2 98.6 94.4 95.67 80.08 f0.3 98.7 98.1 56. tFrom Oda et al.35 78.5 .0 58.6 91.2 105.46 68.72 66.9 208.09 cs = (l/q(cll.6 f1.0 f1.9 90.1 90.99 73.7 255.2 98.268.4 136.6 231.2 61.4 92.9 58.72 201.4 f0.9 219.92 64.0 106.5 57.7 58.6 139.23 78.6 107.7 106.5 292.4 143.0 97.5 66.5 104.6 108. CaO: Measured single-crystal Table 4.2 58.2 fl.03 81. t From Isaak et al.0 96.7 84.66 77. measured value of T/O: 1.98 74.9 63.Cl2).9 98.5 243.28 196.8 92.24 f0.0 133.85 210.25 205.7 146.5 98. [34].9 291.04 215.3 105.98 75.3 69.89) T W) Cl1 Cl2 c44 CS 300 400 500 600 700 800 900 1000 1100 1200 220.5 f0.5 149.5 249.5 237.2 cs = (1/2)(G1.1 81.44 77.56 f0.2 Al.61) 1350 K (max.8 75.5 Al.6 148.6 89.96 74.1 58.09 f0.43 fO.9 97.17 61.8 _ 261.88 192.2 58.7 287. Table 2.81 76.7 224.48 59.7 58.6 144.7 58.5 78.1 72.89 178. 8 91.283.1 86.3 290.4 f0.2 99.2 f0.2 155.8 f0.8 154.5 98.7 284.7 58.8 162.3 101.9 58.0 276.3 103.20) (max. 66 HIGH T ELASTICITY OF MANTLE MINERALS Table 5.3 158.7 89.4 f1.9 60.2 95.2 159.5 86.3 89.5 102.1 93.7 156.0 86.4 60.2 f0.2 57.4 1100 289.2 f5.2 59.8 96.1 89. tAfter Isaak et al.7 88.G2).0 1350 278.9 92.2 87.6 297.8 101.8 149.4 163. measured value of T/O: 1.3 155.2 100.8 w Cl1 Cl2 G4 c.4 88.8 90.7 f0.0 f1.6 278.2 f1.2 280.3 282.3 85.7 91.5 88.5 100.2 102.2 164.4 111. [36].8 152.3 f0.5 85.7 275.1 160.2 90. MgAlz04: Measured single-crystal Table 7.8 282.9 900 296.3 400 315.5 288.1 167.7 91.2 fl.8 104.1 101.8 108.4 cs = (W)(C11.7 273.8 89.1 103.7 102.7 500 311.8 1300 280.6 104.3 61.8 55.4 cs = (1/2)(Gl-.9 152.3 274.5 90.1 286.0 61.42) T (K) Cl1 Cl2 c44 G T 300 350 400 450 500 550 600 650 700 750 800 850 900 950 1000 292.6 87.9 95.5 59.2 1000 292.6 166.3 157.0 97.6 60.5 103.8 150.5 300 318.9 f0. KCl: Measured single-crystal elastic modulit (GPa) from 300 to 1000 K elastic modulit (GPa) from 300 to 850 K (max.5 61.7 106.7 153.2 88.6 800 300.8 101.7 89.2 273.6 91.1 277.C12).0 f1.9 87.7 1200 284.4 700 303. tAfter Suzuki & Anderson [65].2 96.1 161.0 281. measured value of T/O: 4.8 151.7 149.0 86. T w Cl1 Cl2 c44 c.O f0.8 88.8 88.2 91.5 f2.4 97.9 113.2 168.1 99.8 94.5 .1 271.4 110.1 600 307.5 86. 4 13.21 15.3 12.62 17.7 850 23.5 147.0 700 28.7 12.5 5.3 6.7 76.3 51.02 f0.1 156.09 14.7 5. measured value of T/O: 0.69 9.6 12.31 11.15 14.1 54.7 350 220.9 35.7 77.0 13.2 111.1 56.4 6.5 13.84) 300 40.9 267.28 15.79 18.5 f3. t After Pa&o & Graham [47].57 7.271.8 52.3 47.5 57.3 400 217. 300 350 400 450 500 550 600 650 700 750 49. measured value of T/Cl: 2.7 5.1 6.1 6.2 155.8 400 36.05 12.2 12. Table 6.6 f4.7 f0.43 16.6 6.2 750 26. T (K) Cl1 Cl2 c 44 CS T w Cl1 Cl2 G4 cs 300 223.26 15.02 f0.02 f0.2 11.9 f0.5 f1.5 600 31.1 55.8 6.5 f0.96) (max.1 f0. t After Yamamoto & Anderson [76].4 f0.5 f3.02 f0.1 13.3 550 32.7 5.0 146.7 cs = (W)(Gl .1 45.2 7.4 f0.2 500 210.9 56.3 350 38.5 800 25.9 11.1 500 33.4 40.4 146.0 154.6 7.0 6.4 f0. MnO: Measured single-crystal Table 8. t After Cynn [19].4 13.5 7. NaCl: Measured single-crystal elastic modulit (GPa) from 300 to 500 K elastic modulit (GPa) from 300 to 750 K (max.7 5.5 f6.2 7.1 111.5 111.0 450 35.4 f0.35 16.90 13.3 42.8 650 29.9 7.8 78.2 44.8 78.96 11.9 f2.4 cs = (W)(G1.87 11.5 f0.5 13.8 13.7 56.8 77.5 f0.3 f0.5 38.4 7.7 13.3 7.2 33.0 f6.2 6.52 11.3 .5 12.7 450 214.10 10.1 7.4 266.3 269.8 7.9 111.79 10.4 cs = (1/2)(G1-G2).4 f0.8 5.Gz).1 f0.7 37.9 f2.1 11.Gz).9 f4.4 111.3 154.1 11.11 13.57 8.6 13.5 148.4 12.7 7.5 11.5 49.4 f0.1 f0.71 12. 6 fO.5 f0.4 62.5 59.4 272.3 168.8 f0.0 71.4 54.2 f0.6 78.5 57.91 69.9 67.2 202.1 59.9 700 314.4 175.3 66.29 74.0 67.3 213.0 65.1 231.ll f0.0 49.7 78.7 69.8 155.6 75.2 59.1 32.0 60.97 73.3 60.3 69.5 62.3 197.8 194.57 62.8 72.7 f0.1 234.8 56.2 65.2 316.3 61.4 280.9 166.2 233.1 63.1 209.3 f0.2 76.2 195.0 184.3 76.8 165.4 59. MgzSi04: Measured single-crystal elastic modulit (GPa) from 300 to 1700 K (max.1 65.6 313.6 67.9 f0.2 69.07 70.0 300.4 f0.8 52.73 73.33 73.5 285.4 zto.0 77.6 191.4 70.1 65.68 68.l f0.2 60.1 175.0 f0.8 71.6 197.05 74.7 900 306.3 f0.45 72.2 66. [77].4 159.7 224.0 600 318.9 65.8 192.Cl2).4 56.6 71.4 58.6 61. ANDERSON AND ISAAK 67 Table 9.0 69.9 65.6 66. measured value of T/O: 1.3 67.2 226.4 65.5 188.3 1200 292. measured value of T/O: 2.8 56.6 56.3 71.5 55.4 194.5 f0.06 64.3 181.41) T w Cl1 c22 c33 c44 c55 (766 c23 (731 Cl2 300 266.6 54.9 74.2 61.0 236.4 64.7 68.6 62.4 46.1 74.28 65.9 64.1 199. tAfter Yamamoto et al.3 62.0 178.6 66.2 57.6 67.6 59.2 f0.61 74.3 70.6 220.4 63. measured value of T/O: 2.5 216.5 239.17 71.9 67.1 f0.4 1000 302.cs = (1/2)(C11.8 289.3 67.4 1100 297.7 f0.6 49.2 57.2 66.8 61.0 fl.5 67.4 309.0 70.0 178.7 57.8 61.8 171.1 162.2 305.1 68.1 48.1 350 400 .4 63.6 61.3 206.0 62.0 159.0 62.0 192.5 217.7 95. Fe#iOa: Measured single-crystal elastic modulit (GPa) from 300 to 700 K (max.6 163. 68 HIGH T ELASTICITY OF MANTLE MINERALS Table 11.5 400 326. [35].4 78.4 60.8 71.2 f0.72 77.0 61.1 1700 269.3 73.1 64.3 68.0 187.5 59.9 227.2 63.2 t From Isaak [32].53 69.9 98.1 62.0 223.2 81.73 72.3 1300 288.47 67.5 58.3 62.3 214.7 53.0 172.8 293.5 57.9 68.8 Al.2 72.3 66.0 195.9 52.7 f0.05 fO.3 60.0 200.1 64.3 184.2 f0.6 73.9 80.2 48.83 63.3 1400 283.2 fO.2 51.7 202.2 f0.5 81.2 f0.0 58.0 66.0 68.0 58.6 69.8 206.1 169.7 53.6 64.3 97.3 55.52 66.2 276. Olivine FogoFalo: Measured elastic modulit (GPa) from 300 to 1500 K (max.9 58.1) T (K) Cl1 c22 c 33 (744 css C66 c23 c31 Cl2 300 330.1 54.l f0.08 f0.4 f0.07 f0.5 57.6 188.4 f0.1 66.01 68.4 59.7 181.0 61.9 51.1 79.4 f0.3 f0.0 190.1 69.37 76.8 63.59 71.26) T (K) Cl1 c22 c33 c44 cs5 C66 c23 c31 Cl2 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500 320.51 67.5 f0.8 220.23 71. Table 10.8 64.5 f0.3 68.3 51.3 64.2 230.3 54.7 61.2 1600 274.9 64.5 zto.0 55.1 63.8 f From Isaak et al.6 58.6 297.9 173.8 74.1 199.7 64.3 210.2 500 322.4 71.8 800 310.6 53.3 66.02 67.2 1500 279.5 50. 3 400 254.9 f1.0 220.6 57.9 251.5 88.2 f0.2 97.6 Al.1 700 294. AlsOs: Measured single-crystal elastic modulit (GPa) from 300 to 1800 K ( max.5 186.3 c44 Cl2 Cl3 Cl4 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500 1600 .8 91.2 51.6 51.5 92.8 94.9 600 297.6 230.7 95.7 194.9 31. measured value of T/O: 1.5 206.5 31.5 500 251.8 61.4 232.4 95.3 41.5 96.1 f0.4 87.5 51.8 400 304.4 45.4 f1.9 62.8 166.9 96.1 190.7 168.2 220.0 159.5 45.6 95.3 97.4 260.7 f0.8 43.450 500 550 600 650 700 f1.95) T WI Cl1 G4.8 52.8 54.4 54.3 97.8 97. Co2SiO4: Measured single-crystal elastic modulit (GPa) from 300 to 700 K (max.0 f1.7 t After Sumino [58].2 62.2 105.2 700 244. measured value of T/O: 1.0 252.6 45.1 f1.4 56.4 31.5 31.l f0.5 45.7 45.2 f1.2 fl.4 45.2 87.2 89.8 97.5 52.1 fO.9 46.5 92.l f0.4 fO.8 162.9 82.9 44.9 fl.9 227.3 f1.1 fO.9 f1.4 80.0 91.1 600 247.9 257.9 63.2 fl.7 31.8 100.8 99.8 f1.8 500 301.3 97.7 98.4 97.8 160.5 97.25) T w Cl1 c22 c33 (7-44 c5s C66 c23 c31 Cl2 300 307.5 264.4 53.7 f0.7 fl.8 258.7 63.0 53.8 60.0 96. ANDERSON AND ISAAK 69 Table 14.6 f2.3 159.5 171.7 96.9 96. MnzSi04: Measured single-crystal elastic modulit (GPa) from 300 to 700 K (max.O f1.9 fO.3 96.0 55. Table 13.0 164.6 f0.1 f0.5 227.1 234.6 229.8 101.1 31.6 94.3 f1.l f0.0 45.0 101.3 tAfter Sumino [58].2 60.0 89.0 31.3 fO.3 90.0 162.28) T m Cl1 c22 c33 (744 C55 (766 c23 c31 Cl2 300 258.7 93. Table 12.3 165.2 f0.8 201.1 90.l f0.2 f1.3 f1.2 94.9 64.0 94.3 f1.6 f1.2 f1.8 225.O f0.0 255.2 195.7 46.2 56.1 f0.7 52.9 87.3 f1.4 45.0 198.7 f1.7 234.4 45.6 99.7 59.9 222.6 52.6 t After Sumino [58].3 55.8 188.2 55.1 100.1 51.4 50.8 85.6 44. measured value of T/O: 1.5 102.0 192.2 170.8 237.8 99.8 157.8 103.3 262.5 51.6 93.7 f2.l f1.7 46.7 31.7 61.3 f1.6 91.3 154.1 f1.5 Al.2 42.8 53.4 90.8 103.1 fO.3 83.1 46.7 88.7 203.8 224.2 f0.l f0.2 f1. 4 3.2 f2.7 114.1 f 0.14 157.0 3.5 .2 144.3 112.7 159.9 136.2 446.63 165.2 -24.6 432.9 131.573 3.9 f2.4 107.602 0.2 494.5 tFrom Goto et al.1 123.5 107.9 f1.2 500.1 f0.8 161.2 128.8 3.3 451.8 116.5 -24.3 129.0 -23.4 109.5 427.9 456.0 100.6 -23.8 163.4 446.9 3.2 441.38 153.1 113.4 158.4 99.12 163.1 119.4 163.9 111.3 476.531 4.3 461.4 471.4 -24.26 155. isotropic elastic constantst and velocitiesf T g/A at 10-‘/K [ia Gta ciJ* Y cv IcT K J/W) J/(gK) GPa lcr$s kr$s 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500 1600 1700 1800 3. Table 15.6 493.4 -24.8 108.7 450.8 f0.9 111.6 141.47 151.5 162.516 4. [26].6 161.9 467.3 3.9 -23.5 110.5 102.2 432.4 115.7 132.7 497.0 486.8 f0.8 115.0 99.02 158.2 3.501 4.559 3.1 159.5 3.5 466.6 f0. specific heat.2 120.3 481.57 162.06 f0.0 158.0 131.1 3.7 472.1 -24.2 163.1 116.2 160.O f 0. MgO: Thermal expansivity.3 -22.2 f2.6 -23.5 442.9 124.8 117.5 159.5 51.2 457.4 125.3 436.1 462.5 f1.1 -24.8 480.1700 1800 497.4 101.8 146.597 2.4 133.0 489.4 160.585 3.2 f1.2 437.2 162.486 4.005 f0.1 114.7 126.4 110.4 476.9 162.5 490.4 -24.0 104.56 148.6 130.7 105.1 121.7 fl.2 139.545 4.1 -24.7 162.470 4.7 3.5 484.84 160.4 3.0 -21.4 -23.6 -24.24 164. 50 1.52 1.4 106.371 5.173 1.65 146.53 1.10 fl.334 1.130 1.346 1.323 1.7 94.55 1.185 1.276 1.194 0.153 1.53 1.54 1.9 96.246 1.098 1.3 3.0 103.53 1.5 f0.181 1.662 0.131 1.54 1.54 1.915 1.53 1.166 1.3 99.227 1.358 1.658 0.422 4.928 1.4 3.03 0.405 4.6 0.52 1.98 137.53 1.80 142.89 139.438 4.7 101.312 1.03 1.007 fO.8 3.354 5.1 f1.7 3.7 109.190 .188 1.289 1.3.53 1.204 1.262 1.52 1.0 3.048 1.061 1.54 f0.59 1.0 3.388 4.50 f0.175 1.301 1.71 144.04 134.13 132.454 4.194 0.51 1. 975 1.7 f2.193 1.62 253.36 116.6 9.10 161.6 154. AlsOs: Thermal expansivity.8 3.82 144.78 6.4 9.46 122.13 163.09 228.80 6.5 8.9 133.6 3.937 2.06 f0.916 2. tS uzuki [64].59 244.51 246.72 138.7 3.872 3.860 3.2 3.57 5.0 147.78 5.0 137.03 f1.6 161.3 9. 70 HIGH T ELASTICITY OF MANTLE MINERALS Table 16.77 141.5 3.883 2.848 3.73 240.97 153.23 250.1.56 128.5 9.4 9.6 3.26 5.8 3.8 144.193 165.957 2.03 230.982 1.96 232.62 132.1 3. specific heat. [25].85 5.1 3.6 156.2 3.191 1.4 149.2 0.92 5.39 5. isotropic mod& and velocities1 T P fft KS G Cp* 7 Cv KT vp u.19 5.6 9.2 3.1 9.88 235.009 f0.0 f0.4 9.02 156.05 5.9 9.6 163.8 3.63 5.51 125.15 225.1 134.191 1.92 150. ‘Garvin et al.1 9.98 5.7 8.1 9.3 9.33 5.01 dLo.947 2.41 119.6 8.45 5.73 6.66 242.9 3.80 237.31 fl. 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500 1600 1700 1800 3.6 f0.894 2.99 252.40 248.906 2.927 2.9 158.1 9.5 .6 139.1 f0.01 158.6 8.05 $Computed from Table 1.2 142.68 6.04 f0.4 151.191 1.966 2.87 147.13 5.67 135.51 5. 43 f0.257 1.40 1.244 1.37 1.42 1.8 10.024 1.70 6.8 131.009 f0.75 6.082 1.40 f1.040 1.148 1.33 243.3.36 1.38 1.5 f0.43 1.194 1.36 1.37 1.9 10.80 6.933 1.306 1.36 1.209 1.207 1.103 1.205 1.20 224.25 .296 1.318 1.2 3.835 3.3 f4.43 1.212 1.167 1.8 127.84 6.25 221.121 1.37 1.88 6.286 1.7 f0.06 249.0 10.03 1.148 1.943 1.8 0.32 f0.277 1.36 1.179 1.267 1.216 252.199 1.37 247.34 1.205 1.8 10.180 1.823 3.41 1.06 f2.29 240.05 f0.203 1.1 10.223 1.03 0.774 0.779 0. 899 0.33 5.2 107.06 f6.115 1.576 2.2 f2.009 fO.28 5.39 6.63 199.78 f2.4 3.2 3.5 3.00 217.38 203.2 102.ll $Computed from Table 14.95 214.12 5. 300 350 400 450 500 550 600 650 700 750 800 850 900 950 1000 3.9 108.13 228.014 1.04 f5.3 99.65 6.7 101.179 1.0 10.5 f2.51 201. MgA1204: Thermal expansivity.518 2.005 f0.04 220. specific heat.537 2.8 105.18 208. t White t Roberts [75].2 f0.7 103..61 6.6 104.0 3.7 3.4 10.11 209.572 2.7 10.819 0.160 1.213 .57 200.25 207.21 234.74 196.1 3.5 3.3 104.5 10.528 2.17 5.6 3.5 10.3 106.7 10.50 6.23 5.8 10.45 202. *F urukawa et al.551 2. isotropic modulit and velocities* T P at KS G C$ 7 Cv KT up v.4 101.9 106.6 3.8 10.8 f0.90 192.0 3.560 2.512 2.55 6.94 191.564 2. [24].86 207.85 193.088 1.237.44 6.2 10. Dimensions as in Table 15.005 f0.7 10.547 2.2 f0.0 103.82 204.7 0.180 1.80 194.09 224.0 100.69 197.532 2.17 231.5 3.523 2.139 1.91 210.542 2.555 2.055 1.9 3.3 3.1 10.1 107. Table 17.8 3.963 1.32 205.568 2. 952 1.45 197.039 1.889 0.09 f0.87 5.91 5.ll f0.1.81 5.68 5.27 1. +Touloukian et al.2 f0.4 9.115 1.27 1.9 9.27 1.201 1.3 fO.46 199.34 184.28 1.8 9.05 0.28 1.7 9.243 1.9 9.149 1.95 5. ANDERSON AND ISAAK 71 Table 18.28 1.0 9.253 1.51 f0.42 194.49 204.92 5.28 f0. MgzSiOa: Thermal expansivity. *Robie et al.47 200. Dimensions as in Table 15.41 192.094 1.t and velocities 3 T P KS 400 500 600 .83 5.069 1.45 196.65 5.1 9.38 189.85 5.61 5.30 1.37 187.27 1.27 1.133 1.63 5.32 1.27 1. [69].5 9.8 9.33 f6.229 1.164 1. specific heat.41 1.50 f5.9 9.73 5.40 190.3 9.36 185.36 1. [48].208 207.811 0.6 9.4 9.76 5.06 205.4 9.178 1.78 5.5 9.71 5.48 202.07 $Computed from Table 5.05 1. isotropic moduh .190 1.001 1. 2 f0.18 1.22 125.29 0.7 61.6 81.181 3.15 1.068 1.6 f0.235 1.3 G CP* Y cv 0.5 64.211 1.334 1.2 65.096 4.4 f0.315 1.7 3.9 76.21 1.05 f0.192 3.39 107.9 3.109 4.05 112.296 1.222 2.6 3.156 1.50 105.055 4.14 1.700 800 900 1000 1100 1200 1300 1400 1500 1600 1700 3.8 70.007 f0.62 103.27 109.14 1.840 1.3 3.17 1.2 74.7 77.02 1.277 1.72 128.122 4.186 1.15 .1 3.16 111.15 1.6 62.15 1.16 1.4 3.135 3.3 3.15 1.1 3.3 73.6 3.370 f0.81 116.990 1.083 4.15 1.59 120.069 4.159 3.1 80.170 3.1 3.36 123.5 3.48 121.03 127.008 f0.203 3.70 118.92 114.6 3.147 3.0 3.1 3.256 1.213 3.6 71.119 1.831 0.15 1.1 67.352 1.9 68.08 f0.5 f0.4 78. 5 f0.240 1.21 125.09 4.2 7.9 1.12 3.3 1.21 4.13 3.333 3.03 4.73 106.0 8. Olivine FoseFals: Thermal expansivity.58 5. isotropic mod& and velocities 3 T P CN~ KS G Cp' 7 Cv KT up V.35 124.353 2.3 f0.7 76.032 1.2 7.O1 Ito.1.93 118.00 123.148 1.99 127.14 f0.81 111.16 3.2 f0.004 f0.6 8.52 95.02 0.257 KT ‘UP V.05 f0.8 8.17 3.11 .38 4.60 99.7 8.816 1.9 75.124 1.287 3.6 7.85 114.01 $Computed from Table 9.976 1.19 3.54 5.112 1.1 0.167 1. specific heat.957 1.9 69.171 1.3 8.03 f0.183 1.322 3.6 8.4 8.15 4.275 3.9 7.3 8.2 72.5 1. Table 19.8 1.2 1.2 8.093 1.4 fO.3 71.64 118.8 0.85 4.048 1.249 1. 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500 3.197 1.46 122.48 4.0 68.27 4.1 8.96 120. 125. 127.69 104.77 109.311 3.02 3.231 1.65 102.9 8.71 117.66 129.14 3.79 4.145 1.89 116.1 73.32 4.43 4.343 2.3 78.55 120.91 4.02 f0.25 f0.210 1.97 4. t K ajiyoshi [38].299 3.5 1.48 f0.220 1.080 1.194 1.56 97. Dimensions as in Table 15. *Barin & Knacke [15]. 634 f0.256 1.4 0.831 118.5 0.225 4.3 f0.009 f0.79 115.77 125.5 f0.1 6.61 138.79 3.084 3.89 3. *Watanabe [72].22 129.251 3.29 4.03 f0.9 f0.08 f0.5 fO.65 f0.6 6.05 f0.O1 f0.7 8.8 0. isotropic modulil and velocitiest T P at I& G c.803 120.07 0.03 f0.30 f0.666 1.0 0.4 0.8 f0.4 1.32 3.3 f0.19 4.79 123.6 63.781 1.0 6.06 f0.2 8.212 4.65 114.00 109.08 0.57 127.375 3. *Barin & Knacke [15]. isotropic modulit and velocities4 T P fft KS G C.02 3.97 4.79 500 4.055 1.81 4.9 49.8 f0.34 3.03 121.6 fO.16 0.119 2.08 3.096 2.0 0.1 7. FezSi04: Thermal expansivity.362 3.793 1.013 1.7 6.94 3.99 3.0 8.6 8. [67].1 1.129 1.+ y Cv KT up 300 4.667 136.7 1.808 0.02 f0.3 47. t Ok ajima et al.84 f0.543 700 4.850 1.83 f0.7 6.746 1.1 1.8 48.50 105.07 3.07 107.93 111.0 52.2 8.842 126.22 101.009 400 4. .191 1.5 f0. 300 4.6 7.74 135.11 0.75 121.216 128.3.6 f0.294 1.177 1.74 600 4.236 1. tS uzuki et al.91 123.92 4.770 123.7 0.54 107.13 0.004 f0.8 f0.38 f0.02 Table 21.1 50.400 2.011 $Computed from Table 12.05 f0. Dimensions as in Table 15.12 131. specific heat. 7 cv 1-T up V.6 8.68 116.3 fO.512 f0.8 61.163 1.10 3.O1 125.02 0.1 67.736 134.108 2.009 f0. tS uzuki [64].06 f0. 3.60 103.37 3.4 7.604 500 4.86 4.9 8.4 6.06 0.84 3.40 f0.813 129.3 f0.9 54.5 0.21 0.3 7.203 1.109 1.4 64.08 0.673 1.27 128.830 1.0 6.18 0.863 1.06 0.348 3.01 $Computed from Table 10. specific heat.61 112.0 7.34 4.8 6.388 2. Dimensions as in Table 15.57 110.4 0.02 400 4.2 65.O1 fO.1 6.02 $Computed from Table 11.661 128.263 3.O1 f0.13 4.03 f0. Dimensions as in Table 15.8 f0.129 2.0 53.0 51.573 600 4.728 125..147 1.0 51.03 f0.69 4.4 f0.06 f0.24 4.72 118.238 3.005 f0.00 134.1 6.8 1.005 1tO.09 3.07 4.0 48.216 1. Table 20.8 f0.944 1.736 1.86 113.70 700 4.75 4. [46]. *Barin & Knacke [15].275 1.8 7.5 0. MnsSiOe: Thermal expansivity.086 1.818 1.03 4.779 131. 9 0.706 2.5 f0.46 149.06 fO.53 450 5.653 1.575 700 4.9 66.009 f0.752 0.77 145.636 147.739 144.840 1.3 59.359 3.2 61.673 140.67 109.743 .339 3.621 f0.90 3.40 3. specific heat.99 3.03 1.37 1.921 0.009 f0.7 0.37 1.08 0.002 f0.2 68.06 f0.33 3. *B arin & Knacke [15].60 3.8 65.0 68.05 f0.747 1.665 142. Dimensions as in Table 15.92 106.5 fO.6 f1.1 77. MnO: Thermal expansivity.04 350 5.338 3.Table 22.07 f2.56 f0.35 1.275 4.51 0.3 6.20 100.04 f2.26 98. *Watanabe [72].7 6.01 fO.3 71.81 107.t and velocities $ T P at I& G cp* 7 cv I-T VP V.68 146.314 3.849 137.594 600 4.35 zto.6 50. [66].27 148. Table 23.l f0.15 3.5 f0.682 1.369 3.904 0.3 f0.51 0.7 67.03 0.7 73.632 1. CaO: Thermal expansivity. 300 5.965 1.04 f2.63 3.85 144. isotropic moduh .00 3.959 0.04 SComputed from Table 6.5 79.3 0.02 3.O1 zto.35 f0.6 0.262 4.36 1.378 3.880 0.55 400 5.08 103.36 1.6 f1.89 3.7 70.655 3.952 0.OO1 *to.08 f2.14 101.8 64.47 fO.349 3.7 f0.05 f0.76 3.2 6.09 f0.1 0.288 4.37 1.834 0.57 146.868 1.943 0.68 3.4 0.692 1.97 3.57 3.623 146.6 6.93 3. 300 4.327 3.51 0.06 0.3 60.655 143.6 0.5 f0.009 400 4.669 2.12 0.2 6.04 112.03 140.2 62.2 6.01 104.695 2. tSuzuki et al.349 3.611 500 4.4 0.933 0.OO1 f0.71 3.301 3. Table.5 f0.05 f0.07 0.50 500 5.O1O IComputed from Table 13.4 59.557 f0.37 1.06 0.47 110.2 74. t ( assume MnsSiOa).03 f0. isotropic modulit and velocitiest 300 400 500 600 700 800 900 1000 1100 1200 3.77 144.0 67. Dimensions as in Table 15.803 1.641 145.05 0.0 80.7 6.640 1.234 4.58 148.OO1 ho.1 7.0 0. specific heat.3 f0.2 f0. isotropic modulit and velocitiesz T P CY~ KS G Cp* 7 Cv KT I+ V.66 3. specific heat.7 6.91 142.248 4.36 1. CosSiOa: Thermal expansivity.57 fO.7 0.682 2.86 3.791 142.825 139.51 0.51 0.6 f0.59 fO.02 f0.22 3.8 6. 24.669 1.6 76. Grossular garnet: Thermal expansivity.003 IComputed from Table 2.640 4.7 f0.07 f1.3 7.92 167.9 1300 3.0.946 4.945 0.2 105.7 500 3.8 800 3.5 97.905 50.6 93.8 106.12 *0.646 94.901 0.571 f0.597 1. Dimensions as in Table 15.1 700 3.006 f0.609 92.3 7.581 2.2 96.3 7.9 104.894 0.028 1.6 8.49 164.22 1.21 1.61 163.92 156.686 96.865 0.4 7.1 1000 3.571 2.5 8.903 110.931 0.9 zlzO.855 0.995 1.00 152.006 .094 4. [43].006 f0.03 0.1 *to.19 1.2 f0. specific heat. 300 3.858 0.072 1.6 101.20 1.996 4.22 f0.19 1.9 99.501 3.736 .113 1.542 2.092 1. [25].05 f0.170 1. t Oda et al.28 166.7 1100 3.002 fO.3 100.522 2.819 0. ‘G arvin et al.898 0.848 4.723 98.4 1200 3.745 4.2 400 3.897 4.2 0.052 1.589 2.3 7.71 161.903 0.512 2. Table 25.730 0.OO1 108.3 103.83 158.877 0.006 f0. isotropic modulit and velocitiesf T P cryi KS G Cp* y Cv KT vp v.5 900 3.552 2.799 4.693 4.97 154.14 1.977 1.834 104.869 106.0.4 7.3 7.796 102.19 1.562 2.88 157.532 2.888 0.4 f0.4 94.3 f0.759 100.18 1.045 4.03 1.139 1.5 600 3.78 160.3 7.16 1. 7 800 3.8 &to.6 900 3.373 158.025 1.01 166.92 5.6 zto.718 0.2 9.03 5.664 2.50 f0.4 9.04 f0.06 fl. Pyrope-rich garnet: Thermal expansivity.010 1.318 154.6 600 3.02 0.10 5. [39].057 1.2 8.2 92.095 1.902 0.02 zto.11 157.032 1.3 9.4 8.005 f0.07 159.3 87.0 8.21 f0.116 1.104 1.653 3.040 1.056 1.4 400 3.18 5.97 163.1 8.22 5.121 166.5 AO.073 1.5 8.6 8.24 1.6 0.427 162. [36].80 167.289 152.06 5.008 $Computed from Table 4.03 1.84 4.165 f1.686 2.3 9.94 159.0 90.22 1.O1 f0.29 5.29 1.705 2.076 169.5 9.76 4.1.088 1.87 4.99 5.26 1.6 500 3.00 f0.23 1.726 0.34 1.8 f0.72 4.90 5.005 50.90 164.90 . Dimensions as in Table 15.7 700 3. t1 saak et al.02 f0.6 9.675 2. isotropic modulij and velocities1 T P at KS G Cp* y CV KT vp v.96 161. 300 3.889 0.230 148.25 5.642 3.5 1000 3.964 1. Table 26.041 1.259 150.067 1.9 89.453 f0. specific heat.198 146.696 2.1 9.36 171.9 91.2 f0.80 4.3 85.7 fO.3 86.14 5.64 168.4 8.94 5.92 156.6 8.03 161.006 164.631 3.2 88.1 f0.98 164. *Krupka et al.068 1.401 160.3 8.981 1.346 156.3 9. 828 17.4 4.3 14.7 14.132 12.63 0.6 4.382 700 2.006 f0.971 11.059 15.68 4.1 8.91 1.8 25.7 23.806 0.63 0.43 2.04 f0.883 1.64 0.81 0.02 $Computed from Table 3.6 6.0 8.04 1.27 0.3 17.4 f1.68 0.982 11.840 16.9 4.4 7.96 0.2 4.745 0.53 0.1 40. specific heat. NaCl: Thermal expansivity.005 f0.8 21.610 f0.17 2.159 11.701 0.6 8.883 14.416 650 2. V.154.346 750 2.7 13.61 0.2 f0.64 0.29 1. Table 28.074 14.7 17.2 14.756 0.22 2.910 13.935 12.3 f0.7 12.724 0. specific heat.0 4.959 11.44 0.830 19.713 0.2 24.8 4.767 0. * idem.39 2.822 24.59 0.3 4.11 0.868 1.33 2. isotropic elastic modulit and velocities3 T P at KS G Cg 7 Cv KT up v.2 13. tEnck & Dommel [22].02 f0. 74 HIGH T ELA!JTICITY OF MANTLE MINERALS Table 27.8 10.997 1.63 0.85 Al.3 9.964 1.855 15.87 151.923 1.85 1.657 17.829 18.92 2.948 12.8 14.829 16.579 400 2.1 4.2 12.0 6.64 4.41 0.03 f0. KCI: Thermal expansivity.897 14.71 0.1 16.2 12.ll f0.118 13.791 0.80 0.39 1. isotropic elastic modulit and velocitiesl T P CX~ KS G Cp* 7 Cv KT I+.57 1.1 11. Dimensions as in Table 15.5 12.937 1.60 0.08 f0.146 12.27 2.62 0.104 13.830 20.7 8.979 1.005 f0. tb uzuki & Anderson [65].0 3.826 23.735 0.778 0.829 22.7 15.7 13.6 19.13 1.98 1.5 7.7 24.449 600 2.8 9.25 0.482 550 2.830 21.64 1.012 $Computed from Table 8.950 1.19 350 400 450 500 550 600 650 700 750 800 850 f0. Dimensions as in Table 15.42 .008 350 2.0 20.897 1.47 0.309 f0.1 8.3 22.18 1.3 50.3 f0.6 16. *St&l AZ Prophet [57].0 6.3 f0.2 23.689 1. 300 1.923 13.3 fO.02 &0.2 f0.67 1.56 2.2 15.514 500 2.089 14.5 11. 300 2.823 f0.0 17.4 21.47 2.0 7.6 8.0 4.026 16.39 0.043 16.52 2.63 0.5 4.830 19.910 1.2 15.04 f0.11 2.03 1.869 15.545 450 2. 80 2.672 0.62 5.246 3.52 6.44 1.87 f0.676 0.9 3.60 4.239 3.255 3.669 0.64 8.676 0.91 1700 932 0.08 1.35 1.29 6.43 1.6 3.0 3. A120s: Dimensionless parameters.04 f0.02 ANDERSON AND ISAAK 75 Table 29.05 1.2 3.93 1.09 1.09 1.07 1.240 3.47 6.29 1.674 0.03 6.2 f0.237 3.44 1. Table 30.58 6.27 1.235 3.257 2.40 6.42 5.42 1.52 5.93 1300 963 0.39 6.82 1.24 Calculated from Tables 14 & 16.03 $Computed from Table 7.259 2.29 1.13 f0.253 3.71 2.43 5.24 1. [23].03 13.4 3.40 4.251 3.03 1.42 1.24 5.45 1.51 5.75 2.37 6.43 1000 986 0.29 1.250 3.247 3. tEnck et al.29 1.36 6.06 1.98 600 1015 0.30 5.85 4.93 11.32 1.55 700 1008 0.241 3.3 f0.28 1.42 6.248 3.92 5.45 5.74 1.45 500 1022 0.66 1.39 0.08 5.00 400 1029 0.08 0.08 6.30 1.43 1.09 f0.52 4. Dimensions as in Table 15.59 1500 947 0.98 0. MgO: Dimensionless parameters.691 f0.46 5.46 1.7 3.84 2.677 0.48 1.62 7.28 1.06 4.1.53 1.22 5.97 12.20 5.16 15.53 0. f0.85 1.39 5.679 0.50 5.36 6.71 5.64 1200 971 0.42 6.675 0.11 14.55 5.37 6.5 3.93 1400 955 0.60 5.38 6.08 14. Debye temperature and thermal .16 1.46 1.005 f0.38 6.66 9. Debye temperature and thermal pressure T 0 u 6s 6T r (bT--6s) Y 7 ~KT APTH K K MPa/K GPa 300 1034 0.16 5.13 15.243 3.40 6.4 f0.64 2.68 2.3 f0.683 0.32 5.59 1.65 5.9 3.49 1.17 6.76 900 994 0.43 6.2 3.32 1.12 16.30 4.28 1.4 3.30 1.16 5.88 2.80 1.60 4.664 0. *Stull & Prophet [57].15 2.36 6.98 1.30 1.90 10.64 7.73 5.01 1100 979 0.30 1.57 1800 924 0.06 13.87 1.57 6.244 3.71 1.31 5.00 12.42 1.7 3.03 2.24 1600 939 0.66 5.15 800 1001 0. 04 0.92 1.86 4.271 4.90 0.34 650 765 0.00 400 820 0.00 350 777 0.40 0.09 1.56 1.35 800 902 0.90 4.194 2.40 1000 791 0.12 600 920 0.96 1.24 6.07 4.04 800 759 0.03 1.204 3.07 1.13 1.98 900 796 0.02 4.24 1100 875 0.22 1.69 1300 715 0.34 6.218 3.29 3.270 4. Dimensions as in Table 29.03 1.12 4.60 5.75 .22 3.21 6.55 3.12 1.216 3.270 3.50 5.96 4.86 1.208 3.30 6.75 600 811 0.26 4. r (b-i-k.27 5.00 0.94 4.98 5.33 1.185 2.30 4.239 3.40 Calculated from Tables 4 & 25.88 1.270 4.11 1.86 1.50 1300 857 0.21 0.18 1.21 4.92 4.246 3.83 5.13 7.211 3.11 1.31 4.54 5.12 1400 847 0.90 1.239 3.200 3.36 0.97 1.98 4.46 3.25 1200 780 0.00 5.38 5.15 1.18 1.32 4.41 5.08 5.06 1.10 600 767 0.07 4. Debye temperatures and thermal pressure 300 671 0.24 3.241 3.23 3.05 1.240 3.10 1.206 3.27 4.25 4.52 5.37 6. Debye temperatures and thermal pressure T 0 t7 6s 6.42 450 773 0.16 7.00 400 937 0.65 500 771 0.221 3.51 0.270 4.) 7 v QKT APTH 300 945 0.12 1.08 1.22 4.70 4.94 1.35 4.88 4.270 4.40 3.12 5.00 9.01 2.00 0.36 5.03 8.04 0.07 5.34 1000 631 0.13 1200 619 0.05 5.69 1.13 700 649 0.14 5.68 1.00 1.78 5.40 5.57 1.36 5. Debye temperatures and thermal pressure 300 824 0. Grossular garnet: Dimensionless parameters.19 6.19 6.08 1.00 4.270 4.24 3.73 1.23 3.10 1.09 1.16 5.94 1.238 3.73 700 911 0.02 0.31 6.29 4.01 4.01 4.74 0.01 5.73 0.06 1.270 4.57 800 801 0.08 1.72 1.03 4.87 1.26 5.34 900 637 0.90 1.32 3.08 1.98 1.27 4.25 4.97 4.03 1.54 5.64 4.03 0.62 5.13 1.70 5.244 3.08 1.99 1. Dimensions as in Table 29.05 1.34 3. CaO: Dimensionless parameters. Pyrope-rich garnet: Dimensionless parameters.36 500 660 0.04 0.22 3.89 4. 300 779 0.13 1.93 5.31 1.10 1.198 3.34 1.212 3.29 3.00 0.213 3.98 4.97 0.81 6.23 4.99 1.05 1.74 5.86 1.81 750 761 0.09 1.98 5.49 4.36 1.11 1.270 3.74 600 654 0.28 2.210 4.04 4.20 Calculated from Tables 1 dc 15.192 2.92 1.54 500 928 0.41 4.23 3.00 0.73 2.13 4.57 5.57 700 764 0.270 4.270 3.59 0.28 6.74 1500 838 0.93 3.30 3.36 1600 828 0.86 1.23 2.08 1.83 5.29 0.93 4.87 550 769 0.74 2.00 400 666 0.242 3.75 5.09 1.75 1.34 1. Table 33.01 1.22 6.03 1.32 6.23 6.38 1.53 Calculated from Tables 2 & 24.20 6.36 2.96 3.98 1.93 1.21 400 775 0.28 5.31 4.58 1800 811 0.215 3.01 4.188 2.17 1.95 4.237 4.211 3.22 3.30 4.04 1. Table 32.99 2.202 3.S 6T r lb -6.80 4.57 5.60 4.30 4.65 5.69 5.74 2.15 1.89 1.02 1.09 1.16 1.) -i Y ~KT APT.95 1.00 1.11 5.07 1. Table 31.55 5.02 1.27 1.58 4.pressure T 0 Is 6.22 3.40 5.98 4.190 2.84 1.70 3.32 4.07 1.98 900 894 0.92 4.54 1100 625 0.96 1.30 6.36 4.38 2.61 1000 885 0.58 5.22 6.98 5.27 4.74 2.07 1.79 4.25 0.04 4.96 1.01 1.270 4.87 1200 806 0.29 4.35 3.24 5.99 5.64 4.52 900 755 0.05 1.51 1.12 4.36 500 816 0.58 5.84 5.97 1700 820 0.28 4.17 1.183 2.47 5.04 0.243 3.245 3.64 1.53 5.41 3.26 6.16 700 806 0.28 850 757 0.83 1100 786 0.17 1.66 4.64 6.31 4.26 4.23 4.81 4.35 6.34 1.00 4.02 2.28 1.90 4.16 1.01 4.67 5.15 6.23 1. Dimensions as in Table 29.209 3.46 5.00 0.18 1.07 1.01 1.24 4.53 800 643 0.271 4.38 6.11 1.67 0.212 3.92 5.20 1.220 3.219 3.196 3.28 3.52 5.41 3. 18 2.18 4.59 6.54 1.07 1.256 4.16 3.19 4.14 4.23 4.63 1300 669 0.41 1.06 4.16 5. Olivine FosoFalo: Dimensionless parameters.13 1400 689 0.17 1.36 4.02 1.316 5.45 1.23 Calculated from Tables 3 & 26.07 1.47 5. Dimensions as in Table 29.64 600 520 0.44 1.38 1000 688 0.18 4.90 0.97 0.338 5.257 4.97 1.92 5.45 3.14 1.19 4.26 2.09 3.35 1.10 1.46 1.249 3.69 1.20 3.46 5.93 5. Dimensions as in Table 29.28 1.19 2.39 5.13 1.97 5. Table 35.24 6.44 5.39 5.05 1.28 1.25 1. Mg2Si04: Dimensionless parameters.02 1.15 5.03 1.20 4.33 3.255 4.23 0.90 5.22 1.61 6.21 3.49 5.35 7.97 5.99 700 515 0.336 5.25 1.37 5.66 1.96 5.56 6.14 0.37 5.99 7.22 1200 675 0.75 600 744 0.54 3.30 1.40 5.12 5.315 6.06 1.40 5.37 500 501 0.48 5.15 4.00 400 530 0.16 700 494 0.05 4.43 1.56 800 700 0.51 5.16 700 738 0.17 3.16 1.26 1.20 4.92 1.21 4.24 6.07 1.18 1.255 4.13 4.253 4.19 8.338 5.246 4.28 1.43 1.52 0.73 2.13 1.75 600 713 0.248 4.31 6. Dimensions as in Table 29.76 0.95 5.95 0.82 0.10 5.34 Calculated from Tables 12 & 21.44 5. 300 763 0.20 4.57 800 731 0.71 3.02 1.50 4.97 0.18 4.21 5.43 1.42 5.16 5.07 1600 674 0.85 7.12 1.22 2. ANDERSON AND ISAAK 77 Table 34.11 0.49 5. Dimensions as in Table 29.258 4.21 4.19 1.18 4.35 6.315 5.00 5.65 5.17 1.40 1000 718 0.07 1.00 400 757 0.43 1700 668 0.20 1.252 4.38 5.43 6.241 4.239 4.260 4.35 1.238 4.56 1.04 1.56 0.88 Calculated from Tables 10 & 19.31 3.251 3.31 500 525 0.33 5.270 3.56 Calculated from Tables 11 & 20.70 5.338 5.252 3.18 4.97 5.18 6.45 5.69 1300 697 0.17 2.36 1.18 1.17 3.32 4.24 1.00 400 725 0.11 1. MnsSiOa: Dimensionless parameters.80 1100 681 0.95 7.244 4. Debye temperature and thermal pressure T 0 u 6s ST r (6T-6s) u 7 ~KT APT.252 4.36 1.15 5.337 5.24 1.249 5.28 1.25 1.317 5.25 5.94 6.14 1.28 1.270 3.02 1.46 5.76 6.50 1500 682 0.46 0.02 5.63 6.14 1.20 3. .32 1.30 4.317 5.19 3.16 1.33 3.10 5.09 1.245 4.10 1.20 5.17 3.09 1. Dimensions as in Table 29.18 4.32 1.14 1. FezSiOd: Dimensionless parameters.39 1.20 3.63 1.45 1.16 1.50 1.05 5.62 6.87 Calculated from Tables 9 & 18.250 3.07 5.27 1.18 4.25 1200 704 0.76 600 497 0.66 8.11 1.46 5.37 0.05 1400 662 0.22 4.42 1.43 5.251 4.36 5.06 1.50 1.38 1.36 500 751 0.20 4. Debye temperatures and thermal pressure T 0 u 6s ST r (h-b)7 v QKT APTH 300 511 0.20 4.41 5.19 3.20 4.13 5.80 0.98 900 724 0.15 1.49 5.36 500 719 0.254 3.84 1.00 400 506 0.85 4.14 5.35 5.47 5.28 1.08 5.49 1. Debye temperatures and thermal pressure T 0 u 6s 6T r (6T-6S) -7 u Cd--T APTH 300 731 0.250 4.13 5.259 4.58 5.10 1.99 1000 751 0.18 4.83 1100 711 0.19 3.37 4.34 1.15 700 706 0.34 9.96 7.38 1.57 1.242 4.60 4.38 5. Debye temperatures and thermal pressure 300 535 0.44 1.19 4.950 753 0.23 1. TabIe 37.17 3.243 4.46 1500 665 0.06 1.41 0.18 4.97 900 699 0. 78 HIGH T ELASTICITY OF MANTLE MINERALS Table 36.36 5.40 5.240 4.59 1. 65 5.57 5.36 0. Debye temperature and thermal pressure 300 230 0.90 4.72 0.18 2.14 1.86 0.11 2. Debye temperature and thermal pressure T 0 tT 6s ST r (6.60 0.46 1.17 1.279 5.11 1.32 1.16 1.00 350 227 0.19 1.78 0.05 Calculated from Tables 6 & 23.34 0.277 4.72 7.29 0.95 1.278 4.76 1.91 5.07 0.26 2. MgA1204: Dimensionless parameters.56 5.58 5.274 3.44 1.94 5.22 0.95 4.24 2.13 2.30 1.58 7.62 4.85 6.36 5.25 1.37 550 214 0.64 7.82 4.34 1.03 6.23 2.01 1.77 1.21 Calculated from Tables 13 dc 22.88 4.88 4.69 4.38 0.86 1.71 6.91 800 840 0.90 4. Table 41.81 7.21 0.18 5.47 4.13 750 264 0.90 5.316 4.14 0.35 1.97 1.18 1.282 4.00 350 531 0. Debye temperature and thermal pressure T 0 I7 6s 6T r (6T-b) 7 v ~KT APTH 300 304 0.86 5.86 0. Dimensions as in Table 29.55 Table 39.33 1.49 7.280 6.17 1.256 3.83 1.84 4.20 0.83 5.05 1.20 2.88 4.17 1.83 5.83 0.19 0.24 4.84 .27 5.47 600 211 0.62 5.27 Calculated from Tables 8 & 27.35 1.35 400 548 0.60 5.10 1.86 0.32 5.278 5.02 5.27 6.82 0.45 500 854 0.28 450 291 0.56 5. Debye temperatures and thermal pressure 300 534 0.06 5.12 0.29 2.-b) v 7 ~KT A~TH 300 862 0.31 1.86 0.87 0.41 1.84 0.84 0.96 4.302 4.278 4.65 700 204 0.94 0.03 7.268 4.90 4.303 3.57 550 283 0.96 3.03 5.23 600 541 0.01 1.285 4.258 3.84 5.87 0.17 1.17 1.279 4.16 1.96 8.73 1.92 600 850 0.266 4.88 5.30 1.96 1000 830 0.82 8.90 5.53 4.97 1.317 5.96 4.20 1.79 0.49 Calculated from Tables 5 & 17.51 1.90 5.286 4.43 1.97 5.07 4.307 3.305 3.18 1.74 0.17 1.57 5.76 1.27 1.32 1.77 1.62 1.95 1.96 3.35 0.66 1.270 4.10 6.27 500 545 0.77 5.78 1. ANDERSON AND ISAAK 79 Table 40.14 6.01 4.18 1.79 500 519 0.25 1.19 450 221 0.56 5.81 0.278 3.94 1.19 6.56 4.74 6.43 900 835 0.93 1.22 700 538 0.18 0.43 3.91 1.00 400 858 0.284 4.28 1.56 650 208 0.316 4.00 1. CogSiOd: Dimensionless parameters.09 5.71 8.43 500 287 0.275 3.316 4.59 1.260 3.82 4.265 4. KCl: Dimensionless parameters.29 1.75 750 200 0.262 3.24 1.87 5.05 5.71 600 278 0.41 700 845 0.86 0.29 1.88 0.79 1.83 0.26 1.Table 38.316 5.21 1.35 4.279 5.90 1.90 4.20 0.72 5. Dimensions as in Table 29.02 1.18 1. Debye temperatures and thermal pressure 300 551 0.24 4.301 4.265 3.17 0.20 0.96 6.57 5.98 5.77 1.17 1.96 3.34 6.86 0. 0.07 1.28 500 218 0.23 6. Table 42.16 2.278 5. NaCl: Dimensionless parameters.88 4.85 650 274 0. Dimensions as in Table 29.09 400 224 0.19 4.90 5.25 1.277 3.88 6.74 4.73 5.47 5.20 1.10 4.264 3.27 1.23 1.86 0.34 1.92 5.16 1.30 1.11 1.99 700 269 0.33 2.90 5.18 1. Dimensions as in Table 29.80 5.23 1.278 4.30 1. MnO: Dimensionless parameters.00 0.14 400 296 0.88 4.10 2.26 400 527 0.52 450 523 0.00 350 300 0.86 1.08 2.88 0.37 4.14 5. AlzOs. giving PTH(T) . Using (6) for an isochore.289 4. (7) which is equivalent to the statement that PTH = If CYKT is independent of T at constant V and also independent of volume. A well-known thermodynamic identity is that the temperature derivative of the pressure at constant V is exactly equal to CYKT by means of calculus definitions.0). so that where l+~ is the thermal pressure. and v. PTH = J (Y KT dT.288 4.34 6. Since the value of 0 for most mantle minerals is 600900 K.76 1.= (g$f).81 0. Such high T data permit the verification of classical equations.19 1. then (YKT comes out of the integral shown by (7). decrease with increasing T. Theory appropriate to the high temperature trends of the data is presented in Section 5. the four dimensionless thermoelastic parameters at each T are computed [7] using the following nomenclature: CXKS (Y IiT -/x-zPCP PCV (1) 6+&-) (Z). which are in the neighborhood of T/O = 2.3)-1/3. (8) .27 1. The definition of 0 used is e= (k) (z!F)1’3(v.02 Calculated from Tables 7 & 28.33 1. MgzSiOa.93 850 192 0. one can test whether CV is independent of T (as in the Dulong-Petit limit) and whether 7 at constant V is independent of T (as required in the derivation of the Mie-Griineisen equation of state). measurements have to be taken up to the 1300 to 1800 K range so that the high-temperature trends are clearly discernible. 80 HIGH T ELASTICITY OF MANTLE MINERALS The appropriate equations used in preparing the tables are presented in Section 2. KCl. (2) 61 = . For example.(&) (g)p = (a. Dimensions as in Table 29. 8 also decreases with increasing T.3 [4].800 196 0. Since vr. EQUATIONS USED IN TABLED VALUES OF PHYSICAL PROPERTIES Once the elastic constants have been determined over a wide range in T.50 6. The parameters 6~ and 6s are often called the AndersonGriineisen parameters [17].19 5.3+2v.T)p c3) r=-(h) (sgp=(3EJp* The parameter y is known as the Griineisen ratio. The various correlations between the thermoelsstic constants are presented in Anderson et al.77 1. The mineral data are set forth in Section 4.PTN(O) = CXKT(T . Thus (YI<T is the slope for the PTH versus T curve at constant V..19 1. NaCl) either exceed or are close to those of the lower mantle. The dimensionless temperatures reached by some of these data (MgO. [13] and reviewed in Section 3.61 1. The measurements must be done at sufficiently high temperature so that one is justified in speaking of observations in the hightemperature region.04 5. Extrapolation equations are reviewed in Section 6.. 3. (14 Equation (14) is seldom a good approximation below T = 8. . We also list values of the adiabatic Poisson’s ratio u given by 3Ks . p’ ( > (11) which is of interest in seismic tomography calculations [l.2G IY= 6Ks+2G’ (12) 4. however. we show the variation of (6~ . especially for AlsOs. ( lob) In isobaric high-temperature calculations the thermoelastic parameters given by (2) and (3) are useful for many thermodynamic applications relating sound speed or bulk modulus to temperature. then we may expect that 6~ .6s and 7 is [lo]: sT-a =7{l+K%L+G%]) s (1+ a7TbT) . usually near and above 0. APTH is linear in T down to much lower temperatures than 0. v= afhv. 6-Q The measured Cp data can be used to find CV from (lOa) once y has been determined. we see that ST -6s = 7 may be an approximation valid only over a limited range of temperatures. that even in some hightemperature regions. the value of (dy/dT).6s is close in value to 7. is close to zero at high T. the adiabatic case arising from adiabatic elastic constants and the isothermal case arising from isothermal elastic constants. We note.6s) /7 with T/O for our fourteen minerals. the approximation 6T-6s = 7 is useful. (13) If the relative increase in (Y with T nearly compensates for the relative decrease of 7 with T taking into account the change in the denominator of (13). but for CaO. 7 decreases with T at high T. and we usually find empirically that the data satisfy A&H = CYKT(T . it appears that (87/aT).6s = 7. The variation of 7 with T for all fourteen minerals is listed in Tables 29-42. AlsOs. and MgzSiOd. For some solids. Since the rate of change of 7 with T is seldom the same as the rate of change of (Y with T. (14) is in error. The equation showing the relationship between ST . In some thermodynamics manipulations. While the value of (87/aT). at high T is close to zero for many minerals. SOME CORRELATIONS FOUND FOR PROPERTIES IN THE TABLES This section deals with relationships between the thermoelastic dimensionless parameters.As an empirical finding. is less and is always a negative number not close to zero (because . 371. Thus an empirically determined approximation where actual high-temperature data are lacking is 6. In Tables 29-42.300). 20. Similarly. We list our experimental values for the dimensionless parameter v defined by ANDERSON AND ISAAK 81 8 Cn 21. O. The A is data for 0 (acoustic) for perovskite at room temperature. [78].. with T for perovskite is shown in Figure 1. for perovskite will be high.. and 34. Debye Temperature (four minerals) 1200 1 I 1100 ~ perovskite ---- El P= O 1 600 ' 200 600 1000 1400 1800 Temperature (K) Fig. yielding a value near 900 at 1900 K.. and pc suggests that the measured thermal pressure of corundum could be used as a guide for that of perovskite at mantle temperatures and pressures. 1. 82 HIGH T ELA!XICITY OF MANTLE MINERALS Another significant correlation found for most minerals is r=bT. 30. This similarity in values of 8.JTO cryq dT. The expected variation of O.94 km/s. of perovskite is compared to that of forsterite and periclase. for perovskite at ambient conditions calculated by (5) is 1094 K. for corundum is 1033 K.. the value of 8. in the neighborhood of that found for AlzOs.. We know that when the average mass is constant from material to material.. Thus the listed uncertainties reflect how consistent the frequency data are in providing . v. (15) which allows one to calculate G for KT in high temperature ranges where G is not known. This behavior of (87/8T). Solid lines show data on 8 from Tables 29.. It immediately follows from (15) that. because G is less than KS. = 6. shows that minerals with higher density have higher values of 0. The values vr.. We would therefore expect that O.. and all values in the integrand are positive). The Cij data for thirteen of the fourteen minerals in Tables 1-14 were retrieved by the already defined RUS method (either rectangular parallelepipeds or resonant spheres). has an important effect on the validity of the Mie-Griineisen formulation of the thermal pressure. = 10.69 km/s.108 g/cm3 used in the calculation are given by Yeganeh-Haeri et al. The errors indicated at selected temperatures in Tables l-14 are those listed in the original references. The value of O.981. and pc = 3. Plots of 0 (acoustic) versus T. The tabulated errors in the Cij from these thirteen minerals are the standard deviations determined from the difference of each measured modal frequency with that modal frequency value calculated from the final set of Cij. 5. The dashed line shows the expected variation of 0 (acoustic) with T.the correction involves . 8.. rises as the 4/3 power of the density [2]. I@WT) p 1 must be smaller than I(dKs/aT)pI. The acoustic version of 0. and ps = 4. where O. PRESENTATION OF MINERAL DATA We tabulate the adiabatic single-crystal elastic moduli (Cij) for 14 minerals in Tables 1 to 14 starting at 300 K and proceeding in intervals of either 50’ or lOOoK. CaO. and v should be taken as 5% or more. I?. the HS scheme usually provides significantly narrower bounds and is preferred. MgO Prior to the work of Isaak et al.Cij values for a particular specimen. 5a. Spetzler [55] used an ultrasonic pulseecho method to obtain ambient P data at 300 and 800 K and provides a table listing T derivatives of elasticity at these two temperatures. extended the T range for which data were . We use the VRH scheme to determine the isotropic G for KC1 because of difficulties in interpreting the HS upper and lower bounds (see Section g. The values in the tables are the averages of the upper and lower bounds found with the HS scheme. up. The errors indicated in Tables 15-28 for KS and G are propagated by standard error techniques in which two sources of error are considered. Mn. and NaCl) and both KS and G for minerals with orthorhombic symmetry ([Mg. since the values of these parameters can depend somewhat on the order of polynomial fit used when determining the T derivatives. which are based on the VRH scheme.+).30. MgAlzOd. We use the Hashin-Shtrikman (HS) [29. MnO. below). The uncertainty in the dimensionless quantities 6s) 6T. Sumino et al.1 GPa) between our tabulated values of I<s and G for the orthorhombit minerals and the values found in the original references are due to the differences in KS (or G) that result when using the HS and Voigt-Reuss-Hill (VRH) schemes. Co]zSiO. For minerals with cubic crystal symmetry. I<s is given by (1/3)(Cii + 2Crz). high T data on the elastic moduli of single-crystal MgO were available up to 1300 K. We couple thermal expansion CY and heat capacity Cp (at constant P) data with KS and G and calculate the values for several other thermoelsstic quantities given in Tables 15-42. [34]. The MnO Cij data and their uncertainties are not from RUS measurements. using the rectangular parallelepiped resonance (RPR) method. Very small variations (typically 5 0. For corundum (AlzOs) we use the KS and G values tabulated by Goto et al. Cv. Fe. garnet. but are those recommended by Pacalo and Graham [47] from a weighted linear regression analyses together with the Pacalo and Graham [47] temperature derivatives. The isotropic adiabatic bulk KS and shear G moduli computed from the Cij in Tables l-14 are included in Tables 15-28. [26]. and vI at high and low temperatures in Tables 15-28.73] scheme to compute G for cubic minerals (MgO. KT. These errors include both the uncertainty with which the midpoints of the upper and lower bounds of KS and G are known and the difference between the midpoints and the upper bounds. However. [63]. We assume LY is accurate to 2% (unless specified otherwise in the original reference from which the a! data are obtained) and rigorously propagate errors to p. Sumino et al. We extrapolate (linear in ii’s and Cir. when a lower order of fit. up. The high T (i. &(T). [34] (RPR) and Zouboulis and Grimsditch [80] (Brillouin scattering) report Cij data for MgO UP to 1800 and 1900 K.1. 0. The dimensionless parameters 6s and ST (Table 33) are found by a linear fit of the KS and KT values in Table 26. We find very little difference in the value of these dimensionless parameters. and Isaak et al. We list the Cij values as reported by Isaak et al. and the combined moduli (Crr + Crz + 2644)/2 and (Cir . [34]. 4. KT. The values of the dimensionless parameters. 5c. Crr. 6. and v# results as done by Isaak et al. Oda et al. almandine. We find excellent agreement in (dC~/dT)p values when comparing the results of Spetzler [55]. and v. G.e.&)/2 versus T.. 72. errors for KS. Zouboulis and Grimsditch [80] report (711(T). 24.3%. and CJ~ values given by Suzuki and Anderson [65] (see their Table 1) as the primary data source and interpolate to obtain these moduli given in Table 3 at 100°K increments of T. I’.7%. in Table 30 are found using sixth order polyANDERSON AND ISAAK 83 nomial fits to the KS. respectively. androdite.) or are propagated from the errors in KS. [34] in their T range of overlap. and grossular. [34]. up. [43] used the resonant sphere technique (RST) to reach 1200 K. CaO The appropriate thermoelastic quantities for CaO [43] are listed in Tables 2.e. and Cd4 (i. Cr1. quadratic in C&a) the Suzuki and Anderson [65] Cij data over seven degrees to include the 1000 K values in Table 3. is used. Isaak et al. errors in Ciz and Cs). [43] in our Table 24. All errors in Table 3 are either those given by Suzuki and Anderson [65] (i.. We use the KS. [43]. 15. have noticeable curvature.. [34] in Table 1 and note that an alternative source for high T data can be found in Zouboulis and Grimsditch [80]. so .6%. 5b. However. such as 3.7%. The dimensionless parameters in Table 31 are obtained from a second order polynomial fit of the I<s. In their Table 2. uvarovite. [34] data up to 1800 K. Pyrope-Rich Garnet Suzuki and Anderson [65] provide Cij for pyroperich garnet over the temperature range 298-993 K at irregular intervals of T. spessartine. there is more scatter (especially in the Cd4 modulus) in the data of Zouboulis and Grimsditch [80] than in the data of Isaak et al. 6s. [63]. C.e:. KT.6%. We include the o data of Okajima [45] as tabulated by Oda et al. The specimen used by Suzuki and Anderson [65] is a single-crystal natural garnet with composition: pyrope. G.available up to 1300 K. We find that G and v. T > 1400 K) Zouboulis and Grimsditch [80] data have T dependence nearly identical to that of the Isaak et al. ST. The C’44 value at 638 K given by Suzuki and Anderson [65] seems unusually low and is excluded in our fit for interpolating. Cir. and 31. and Y. other than a slightly less rapid decrease when T > 1500 K. 0. thus we present the dimensionless parameters in Table 40 based on linear fits of KS.2%. Second order fits were applied to the G data to obtain I’ and to the I+. v is constant with a value of 0. Cs. We use the KS. We construct Table 6 using the Cij and (X’ij/dT)p values recommended by Pacalo and Graham [47] (see their Table 10) for MnO. vr. There are data [19] up to 1060 K. The recommended first temperature derivatives are based on both ultrasonic pulse-echo [47] and resonant [62] measurements. 1. The uncertainties in the Cij for MgA1204 are large relative to most other resonance data. KT. For C44 we use a second order polynomial to interpolate at inter vals of 50°K where the nonzero value of (8”Cij/dT2)p is found in Table 6 of Pacalo and Graham [47]. [36] also provide new cx data for grossular-rich garnet and point out the possibility that the Skinner [51] thermal expansion values for garnets may be low. We follow Isaak et al. 5f. C’s. and Ciz.06 over the 300-1000 K range when second order fits to v. The parameters bs and & are found using first order fits to the KS and KT data. and Ciz in Table 10 of Pacalo and Graham [47] are not selfconsistent. G. The uncertainty in p at 300 K (Table 17) is assumed since it is not reported by Cynn [19]. Table 4 is constructed using the KS. and vr versus T are used. Cir. For minerals of cubic symmetry there are only two independent moduli among KS. [36] as primary data. 96. Isaak et al. 5d. and C44 values from 298-999 K given by Cynn [19] as the primary data source and interpolate to obtain the Cij in Table 5 at regular 50°K increments of T. and v.5% almandine or spessartine) to 1350 K. andradite.97 over the 300-1000 K range in T. Cs. and v6 with T. It is worth noting that v tends to increase gradually from about 0. and Cd4 of Isaak et al. pyrope.that second order fits are preferred when calculating F and V. We take Cl1 and Cl2 from Pacalo and Graham [47] as the primary data and use these to . [36]. less than 0. values to obtain V. Errors in Table 5 are either those given by Cynn [19] or are propagated from the errors in KS. 5e. 1. Grossular Garnet Isaak et al..88 to 1. The Cij values in Table 4 are plotted by Isaak et al. [36] provide elasticity data for near endmember grossular (grossular. but not explicitly tabulated in their presentation. If first order fits are assumed. Cir and Crz and their errors are calculated from these primary data. but a sudden change in the slope of the data near 1000 K is attributed to the effect of cation disordering. MnO Pacalo and Graham [47] present new data on MnO from 273-473 K. Spine1 (MgAl~O4) Cynn [19] provides Cij for single-crystal MgAlz04 over the range 298-999 K at irregular intervals of T. [36] in the order of fit used to calculate the T derivatives for the dimensionless parameters.5%. The recommended values for KS. &I. and C44. Thermal expansion cx data on pyrope-rich garnet are also provided in the Suzuki and Anderson [65] paper.6%. but are below the Nkel temperature (522 K for MnO). KT. In determining the isotropic shear modulus G we used the VRH rather than the HS scheme. and Cd4 [76] are taken as the primary data from which C’s and KS (Table 28) and their errors are derived. 5h. up. To find accurate Cij results with the composite oscillator requires that the resonant frequencies of quartz and silica rods that are coupled to the NaCl specimen be known in order to reduce the NaCl data. Ciz. For instance.5 GPa). are done with a linear fit in T when calculating the dimensionless parameters in Table 39.). The Yamamoto et al. from 300-700 K the average value of (aKs/BT)p from Hunter and Siegel [31] is -0.compute KS for Table 23. In any case we must defer to the VRH scheme for this material and note that there are relatively wide bounds on G (thus also on up and v. is warranted when determining the T derivatives. KC1 Table 7 shows Cij for KC1 where we use the Yamamoto and Anderson [76] data to interpolate at even intervals of 100°K. Thus a small difference appears between the 300 K value for KS in our Table 23 84 HIGH T ELASTICITY OF MANTLE MINERALS (149.0 f 2. [77] report elasticity data from 294766 K for NaCl. and v. G. we found that the resulting upper bound for G is less than the lower bound for temperatures in the range of 300-450 K. There are relatively small but measurable differences in the T dependence of the elastic moduli between these two data sets where they overlap.011 GPa/K from 300-800 K. whereas that found by Yamamoto et al.015 GPa/K. [77]. NaCl Yamamoto et al.6f 2. When attempting to use the HS scheme [30]. up. The Yamamoto et al. We also note that the experimental arrangement of Hunter and Siegel [31] requires a large volume to be heated when increasing temperature. Spetzler et al.012 GPa/K. [77]. especially so at lower temperatures. The values at 500 K in our Table 6 require an extrapolation of 27°K beyond the maximum T measured. who obtained elasticity data to 800 K for NaCl. but emphasize that Hunter and Siegel [31] report data 300’K higher in T than do Yamamoto et al. Statistical analysis indicates that a second order polynomial fit of KS. [56]. [56] find (i?Ks/aT)p to be -0. For these reasons we prefer the data of Yamamoto et al.6 GPa) and that given by Pacalo and Graham [47] (150. [77] is -0. This seemingly contradictory result is likely related to the fact that the shear modulus C’s is very near to the value of the bulk modulus KS at the lower temperatures. The Crr. 5g. Elasticity data up to the melting temperature of 1077 K for NaCl [31] were obtained with the composite oscillator method. whereas a linear fit of KT with T is adequate. [77] data are out to a slightly lower maximum temperature than Spetzler . C. Temperature derivatives of KS. [77] results tend to favor those of Spetzler et al. We are unable to resolve this difficulty. and v. 1 to 6. v~. The thermal expansion results of Kajiyoshi [38] are used (see our Table 18) to calculate the thermoelastic properties of MgsSiOd (see Isaak et al.3 as indicated by Yamamoto et al. Isaak et al. [68] to 1200 K. respectively. Isaak et al. The present approach produces smoother variations in 6s. the MgzSiOd (forsterite) data of Isaak et al. and v with T. The uncertainty in the density of the specimen used by Yamamoto et al. [61] to 670 K and Suzuki et al. [35] to 1700 K extend the T limit for which elasticity data are available. but contain a much denser set of tabulated Cij values. and v. G. Yamamoto et al.5. MgaSiO4 Following the work of Sumino et al. Thus we use third ANDERSON AND ISAAK 85 order fits for all T derivatives required to determine dimensionless parameters in Table 34. [35] show that fits of the KS. These differences are due to the difference in method used to calculate the T derivatives. Prior to bhese studies the available data were limited to T near ambient [27. [35] (See Figures 3 and 5). 401. I. [35]. and note that this results in 6T at 300 K having a value near 5. Olivine (F~Fa~o) Isaak [32] reports data to 1400 and 1500 K. values in Table 27. [77]. Isaak et al. [35] used the interval between the two neighboring points to calculate the derivative at a particular T. [77] is assumed to be 0. and C’44 found in Table 2 of Yamamoto et al. We calculate the dimensionless parameters in Table 41 using a second order fit in T to the KS. 6~. here we apply polynomial fits over the whole temperature range from which the derivatives are obtained.et al. KT. We fit the data over the T range of measurement to a polynomial. There are some small differences in the 6s. since this is not provided by Yamamoto et al. [61] provide schemes for extrapolating that are generally confirmed by the higher temperature measurements of Suzuki et al. We interpolate the Crr. We also find that above 600 K. and us data with T imply that third order polynomials are appropriate to describe the data. There is only a small difference (5 0.1 GPa) between the two approaches. up. Sumino et al.8-5. on two natural olivine samples with compositions . and I between our Table 34 and Table 5 of Isaak et al. [68] and Isaak et al. ST increases gradually from 6.9 in this temperature range. [77] find T derivatives by taking a finite difference between two adjacent data points. G. Clz. 5j. rather than having a value nearer 5.005 gm/cm3 at 300 K (Table 27). We construct Table 9 from the Cij reported by Isaak et al. I<T. [56]. [35] due to different methods used in calculating the T derivatives. [77] to regular intervals of 50°K for our primary elasticity data source in Table 8. 5i. 6~. whereas Table 18 lists KS and G obtained from the HS averaging scheme. [35] used the VRH scheme to calculate isotropic KS and G moduli. [35] for a comparison of the Kajiyoshi [38] values of a with other values in the literature).6 rather than 5. There is general agreement between the data where they overlap. . We start our olivine tables by interpolating the T = 296 and 350 K data of Isaak [32] to 300 K. CosSiOd Sumino [58] presents T data from 25’-4OO’C (398673 K) on the elasticity of single-crystal FezSiOa (fayalite). As an example of the effect of uncertainties in the derivative values. We interpolate the Sumino [58] fayalite data (see his Table 3. we defer to the data of Sumino [58] since they involve a significantly wider range in T (up to 673 K) than the maximum temperature of 313 K used by Graham et al. add the squares.r and Fos0.sFas. A small extrapolation over 27’K is required to extend the values represented in Table 3 to 700 K. KT. and Wang et al. I’. 6~. Mn#iO~. This shift in starting T causes minor differences in the T derivatives. G. but caution should be used when interpolating between specimens with small differences in chemistry. Isaak [32] estimated the uncertainty by simply adding the uncertainty with which the HS average value is known to the distance between the average value and the HS high value. whereas Sumino [58] reports -0. even though this transition occurs at a much lower temperature (65 K). and v.0205 GPa/K. From Figure 2 of Sumino [58] it is clear that KS is linear in T. Sumino [58] a 1s o reports elasticity data on singlecrystal Mn$SiOa and CosSiO4 at 300 and 673 K. whereas G requires a higher order T dependence (at least a fourth order polynomial). up. [28] report (llKs/dT)p = -0. Previously available T data on the elasticity of iron-bearing minerals were limited to temperatures near ambient [40]. There are some differences between the Cij of the two olivines reported by Isaak [32] that do not appear to be due to fayalite content.a. [28]. Isaak and Anderson [33].j from 300-700 K in regular 50’K intervals in Table 11. The reasons for these types of discrepancies are under investigation. Here we square both the uncertainty of the HS average and the distance from the HS average to the HS high value. Sumino [58] indicates that all the Cij of Mn#iOr and Co2SiO4 are linearly dependent on T with the exception of Cad for Co$jiO4. which show values of Cij at incremental temperatures . However. We use linear fits in T to the KS.. and v. 6~. In calculating the dimensionless parameters for fayalite in Table 36 we use linear fits in T for KS and KT and fourth order fits for G. and take the root.030 GPa/K. data when obtaining the dimensionless parameters 6s. Graham et al. The differences are small. vr. and I in Table 35 and in Table 6b of Isaak [32]. 5k. Fe#iO. It should be noted that there are questions regarding the values of some of the Cij and some of the T derivatives of fayalite (see Graham et al. specimen TA) so as to provide C.. [71]). and v.iFar. [28].s (referred to here as olivine FoaeFais) in Table 10. We construct Tables 12 and 13.of Fos2. [28].sFas. Sumino [58] attributes the strong nonlinear behavior of the shear modulus to influences of the antiferromagnetic to paramagnetic transition. no compelling reasons exist to suggest that the Sumino [58] fayalite data should be preferred over those of Graham et al. hence the slight differences between 65. At present. The uncertainties in KS and G (and in all properties that depend on KS and G) are somewhat smaller in Table 19 than found in Isaak [32] for these quantities. We include the Cij for Foss. an F. and v. When calculating the dimensionless parameters all T derivatives are assumed linear in T (see Figure 2 in Sumino [58]). and u found in our Table 29 for AlsOs may differ somewhat at a particular T from those given by Goto et al. The KS and G given by Goto et al. I<s. 6. THEORETICAL BASIS FOR OBSERVED PROPERTIES AT HIGH TEMPERATURE Most. and dvrB is the vibrational energy due to motion of the . but do not consider the difference from the Hill average to the upper (or lower) bound. and other isotropic quantities derived from them. We use a third order polynomial fit to determine the T derivatives for each of KS. where electronic and magnetic effects are ignored. As with FesSiOh. test [18]. [26] 6s and ST values than in Table 29.b.e. [26] 6s. we must perform a small extrapolation outside of the maximum T measured in order to include the T = 700 K values in the tables for Mn$SiOa and Co$SiO4. and G (Table 16) for AlaOs are those found in Goto et al. the SS . Appar86 HIGH T ELASTICITY OF MANTLE MINERALS ently Goto et al. i. ST. The Helmholtz Free Energy The expression for the Helmboltz energy for an insulator is [41] A = EST +-km. 6a. we find considerably more scatter in the Goto et al. EST is the potential of a static lattice at absolute zero. [26] assigned errors in G that include only the uncertainty in the Hill average itself. 6T. [26]. of the high temperature properties of the solids reported here are consistent with the high temperature limit of the quasiharmonic approximation of the statistical formulation of the free energy. We assume a linear T dependence of the Co$SiOh Cd4 modulus in constructing Table 13 since the presence of nonlinearity in this modulus is asserted by Sumino [58] but no quantitative result is provided. Thus.. i. 51.. Thus. and p provided at 296 and 350 K to start our Tables 14 and 16 at 300 K. (Table 14). those from Wachtman et al. [26] are found by the the VoigtReuss-Hill averaging scheme. [26]. G. required for the dimensionless parameters shown in Table 29. but not quite all. This accounts for larger errors being assigned to the G values in our Table 14 than are found in Table 2 of Goto et al. Full account is made of the difference between the Hill (averaged VRH) values for KS and G and the Voigt (upper bound) values when assigning errors to KS. We use (Y from White and Roberts [75] rather than the cu preferred by Goto et al. This order of fit seems appropriate from a statistical consideration. [26] in their Tables 4 and 5. using the Cij and the (dCij/aT)p given by Sumino [58] in his Tables 4a. and v values are calculated from derivatives found by using a finite interval from the two nearest data points. G. [26]. KS. We interpolate the Cij. vP.of lOOoK for MnzSi04 and CozSi04. Corundum (AlaOs) The C. G. [70]. The Goto et al.e. KT. When wj are different. N is Avogadro’s A = EST +dvzB. and p is the number of atoms in each cell (or molecule). the dimensionless frequency. The temperature behavior of the thermodynamic properties is indirect. We replace w with y. . unlike the last term in (16). then yi are also different. we define ANDERSON AND ISAAK 87 where AVrB is given by (16). number. j=l (17) Note that. Thus dTH --$ 0 as T --+ 0. (21) We need to divide (21) into temperature-dependent and nontemperature-dependent parts. w is assumed to be dependent upon V but not upon T. so that (18) Thus (16) can be given in terms of the thermal energy dvzB = Ezv + dmz. and EZV is a nonzero number.atoms as each is constrained to vibrate around a lattice point.emyj) = kT c dTHj. This makes all the thermodynamic properties directly dependent on V. and the sum above becomes T-dependent. Ezv is sufficiently small that for most numerical evaluations it could be dropped. Ezv is not affected by T. This term arose by summing the allowed quantum state levels to find the energy of each normal mode. but it is useful to keep this term in dvrB for algebraic manipulations done lat>:r on. The Quasiharmonic Approximation Before we can find thermodynamic properties such as P and CV from (20). called the thermal energy. dvzs -+ EZV as T + 0. there is no T in EZV. the sum C en (1 . However. we must make decisions on the volume and temperature behavior of wj. (22) where ET=o=EsT+Ezv. (23) Dividing (21) into its vibrational and nonvibrational parts. as shown in (17). 6b. so we use A = ET=O + dTH. The first term on the right is the zero point vibrational energy EZV given by E zv = :EhWj. (16) j=l j=l where wj is the jth modal frequency.e-y”) depends upon T. it comes from the fact that while wi is not dependent upon T. The statistical mechanical definition of the vibrational contribution to the Helmholtz energy arising from 3pN independent oscillators is dvrB = i3EhWj +kT3E!n(l-e-‘ui”T). In the quasiharmonic approximation. The expression for the Helmholtz energy for an insulator is thus A = EST + Ezv + dTH. (20) j=l j=l dTH is the energy arising from temperature excitation. W-9 where 3pN 3pN dTH = kT c en (1 . according to the Hamiltonian [42]. ) (32) The expression for (YKT is found by applying a2/8T8V to (22). is Comparing (29) with (20). yielding ’ = ET=o +kT c -& = ET=O + kTx ETHje j=l j=l (25) The pressure P is found by applying . yi is small. and using P given by (26).especially at low T. 6c. we take advantage of the expansion [79]. yielding where (26) d en Wj ^lj = 8 en V (27) and where yj are called the mode gammas. . called the thermal pressure. to A. we see that PTH= $cYjdTHj. yielding Cv = kc ‘jeyj j (eyj .(d/W). Using (30).1)2 = c C. yielding (YI(T = zCY. en (1 . to (25). obtaining S=kCYi(&) -kx en(l-e-y.(a/aT). and equating this to (33). that is.” + .Z "/j (33) To get cu we divide [YKT (given by (33)) by KT. . the expression for &H can be simplified due to the convergence of certain series expansions. j (31) Entropy is found by applying the operator (h’/c?T). we find that [16] (34) The bar over y indicates that this result is an approximation of y = (YKTV/CV resulting from invoking the quasiharmonic approximation to the Helmholtz energy. we find that . 3 (29) (30) The specific heat is formed by applying . to (21). The argument in (16) becomes small since tiwj << kT. The High-Temperature Limit of the Quasiharmonic Approximation At sufficiently high temperatures.. (35) By replacing the last logarithmic term above with its argument. The internal energy 24 is found by applying the formula U = -T2 ((ad/T)/aT) [41].) = &nyj+ en (1-kyj). Thus P=Po+fiH. which is valid for low values of yj. (28) where the thermal energy (20) effect on the pressure.eeyj) = en Yj ( iy. At high temperatures. we find that (YI<T = yCv/V. . defining KT = -V(aP/cW) T . j=l (39) This can be simplified by defining an average frequency a. Ci + k. 3pN A& = kT CC j By using (21) and (34)) the high T Helmholtz energy for insulators at high T is Aht=Es~+Ezv+kT(Cenyj-~Cyj).4 includes only the static potential and the thermal energy in the quasiharmonic approximation. . This is true for MgO. but not for olivine. we must conclude that the quasiharmanic approximation is not adequate for this property. or KCl. we find the high temperature internal energy to be Uht = EST -I. The data on y is found in Tables 15-28. given by en v = -J-C hwj.. If at high T the experimentally determined CV is not parallel to the T axis. For these solids when dy/dT is not zero. Taking the temperature derivative of U to find specific heat. kN. and considering that as T -+ 00. so that 3pN Aht = EST + kT c (en hwj . CaO. 3pN in which case (20) becomes ATH = 3pNT ( en IiiZ . Thermodynamic Properties in the High T Limit of the Quasiharmonic Approximation At high T.en kT) . the quasiharmonic approximation is not adequate for some solids up to T = 20. From Figures 14-26. We see that there is an approximate trend for y to be independent of T at high T. Equations (41) and (42) are important results for the high temperature limit in the quasiharmonic approximation. we see that for several solids of interest to geophysicists (dCv/8T)~ = 0 at high T. The high temperature Griineisen parameter is found from (34). We must conclude that insofar as specific heat is concerned. Cc” = 3pR. where the data for specific heat versus T are listed.eWyj) 2: en . and A1203 and NaCl. garnets. Using the equation U = -l/T’ ((BA/T)/aT). and anharmonic terms must be added to A. (42) where R is the gas constant. it is also true that CV does not .en kT). (38) jj We see that the last term above just cancels the zero temperature energy given by (17). (43) Equation (43) is known as the Dulong and Petit limit.SpRT. ‘?‘ht = Y(T+m) = - (44 which is independent of T. but is adequate for other solids up to T z 20. spinel. (41) 6d.f (36) Thus the high-temperature representation of (20) is 88 HIGH T ELASTICITY OF MANTLE MINERALS yj yj. Thus the high temperature quasiharmonic approximation leads to the classical limit in specific heats.en (1 . Thus departures from quasiharmonic theory in CV create a departure from the quasiharmonic theory of 7. and that is borne out by the experimental results shown in Figure 2. for nine minerals showing: 1) APT. 00 is the acoustic 0 at T = 300 K.178.PTH (6 b) . (See also Figure 2).obey the Dulong and Petit limit.aT term is often obscured. This range covers values of T/O0 for the mantle of the earth. The slope of the APTH .176. then we can define an average value of CXKT. V is a function of T. 6e.0. 0.119. the qua&harmonic approximation appears quite adequate up to relative temperatures of T/C& x 2. and 0. which by using (44) becomes Pht(T. fi) . 0. 0. M/p varies little from mineral to mineral and is near the value 21 [74]. though close to it.053. CYKT. versus T/O. on (45). such that = (yI(T= f$$ po (l-oT) = const. 0. as shown in Figure 2. we find the high T pressure. This means that for the thermal pressure property. 0. ANDERSON AND ISAAK 89 Fig. the departure from (dy/dT). The linearity of PTH with T is not unique to silicates and alkali halides. the mineral with the highest value of po/(M/p) will have the highest slope. as we shall see. Pht . Thus from (48) for M/p = constant the slope increases from mineral to mineral as the ambient density increases. Applying the operator -(a/W). Since PTH = s CYKT dT. we find . exactly independent of T. so that the above is P 3R-m TH = m~o(l. For non iron-bearing silicate minerals. Thus to a very good approximation PTH is proportional to T under the quasiharmonic approximation. 0. 0 = const p413 [2].. we see that APTH is indeed linear with T (for T/O0 > 1).T curve from (47) is empirically a constant. The data in Tables 27-30 bear this out. = 0 is slight. (45) Thus the thermal pressure is PTH = -3 pR v -f’ht T. however. But 7ht is not. Also 7hi does not vary greatly from mineral to mineral. 2.T/O0 line decreases as pc/(M/p) decreases. Thus there are counter effects in T. Since to a good approximation for silicates of constant M/p.160. is linear in T/00. Values of pc/(M/p) in ascending order (l-9) are: 0. and the 1 .151.aT)T. (47) As shown in Tables 15-28. 0. The Bulk Modulus at High T Using the operator -V(a/aV). to (38). and 2) the slope of the APTH . aT II 0. APT. we see that (aP~~/llT)p should increase as 03i4: In general. We see that the quasiharmonic theory allows for PTH to be virtually linear in T: at the highest measured T. according to (48). V) + y7ht T. it is also found for gold (see Figure 10 of Anderson et al.05. The thermal pressure relative to T = 8 for T > 0 is given by APTH = PTH (T. (48) where M/p is the mean atomic weight (per atom). good for T above 0.160. and it is also equal to M/p where it4 is the molecular weight. Above T = 8. V) = P(0. [12]).073.195. Applying the operator (d/aT). KTH. CV is independent of T in this approximation at high T. The average value of QKT is found from the values of APTH between 1000 K and 1800 K listed in Table 30. we have for isochores. This result agrees well with the measurements found in Table 16 showing (c?Ks/dT).. we find that CYKT is independent of T (or approximately so) only at T above 0. then (t3P/BT)v is independent of T. Entropy and CV& Applying the operator (a/X!‘). 90 HIGH T ELASTICITY OF MANTLE MINERALS 6f. aa shown by (43). In contrast. We note that if P is linear in T. as . V) . Thus we find from (53) that a predicted value of (dl(~/aT).$-$pt (1 . (aK~/tlT)v vanishes. = 0. (+7)h’ = -3 PR-h = -@ Yht V (M.0064 GPa/K. (54) The entropy increases with en T in the quasiharmonic approximation at high T. to the pressure given by (45). to be 0. however. the entropy is found Sht = -3pR( Cn kT .= (s)v-&-T(=$)T. The actual measured (YKT will have more structure than (YKT determined from PTH.Qhl).031 GPa/K.1). For q ht = 1. To obtain the isobaric derivative. T Letting ffI(T = (YIcT in the above = -CYKT (Ii’ + qih . V) = KT(O.T (52) The term on the far right of (49) is the thermal bulk modulus. along an isobar. the isochoric bulk modulus is decreasing with T according to the slope ( a r-4 ) - fw v (50) = -$$7& . KTH. c 1o se to actual measured values of ~KT at high T.t(l-qht)-(Yli.p) PO (1 . (53) We thus see that the thermal bulk modulus. From experiments. The high T value of K’ = 4. Using (48) in (52). we use the calculus expression: (fi!$). we have (qth . to (38). In this table CYKT is shown to be 0. = -3 -f. We evaluate (53) for the case of MgO from the data as an example.that the bulk modulus IcT along an isochore is Kp(T. contributes a minor amount to (aK/dT)p.cm (55) Equation (55) is to be compared to (48). (aK~/aT)p.en Foss + 1). (49) where qh’ = (a en 7ht/a en V). so the determination of (50) ordinarily yields a small quantity.03 GPa/K in the high T range. Nevertheless to a fair approximation CYKT is parallel to the T axis for T > 8.d(T . and qht = 1. The functional form of (YKT resembles a Cv curve.1) .5 [8].4 [8].qh’) T. Thus at high T. (51) Thus at high T. for the P = 0 isobar and where a = (13Kp/dT). and using (51). The above equation can be expressed as Q ht =6T-I<. Thus (aP/aT)v should be essentially independent of anharmonicity. We also note that if (BKTI ~P)T = Kh is virtually independent of T. arising as it does from the high temperature limit of the quasiharmonic approximation. we take the logarithmic . (41). and the experimental evidence is in favor of this. It arises because the denominator in (57) has a term that decreases with T even in the qua&harmonic approximation. 6~ at high T should be slightly higher than Kh. (59) reduces to (58) because Cv is independent of V above the Debye temperature.. and the expression for crI<~ given by (48). We derived a relationship between three important dimensionless thermoelastic constants at high T. This steady increase of (Y with T at high T does not necessarily require the assumption of additional anharmonic terms in A beyond the quasiharmonic high T approximation. We saw some evidence of anharmonicity 6i. Further. which show that roughly speaking. (58) Equation (58) is appropriate for high T only. (Y. & and q From the Quasiharmonic Theory From the definition of 6T. KT. This means that equations of state should not be corrected for anharmonic effects for pressures and temperatures corresponding to mantle conditions. Examination of (57) shows that at high T we may expect IY to increase with T at high T even under the quasiharmonic approximation. This is demonstrated in Tables 29-43. const ff = KT. (52) and (53). we find ST = (qht . we have (56) which is close to. and for some solids exactly equal to. this effect does not appear in properties that are controlled by the volume derivatives of A as described above. but even so. (49). is independent of T. . 6h. For an explanain Cv .QT (57) At high T and P = 0. For the low temperature equation corresponding to (59). then (Y is controlled by (57). CYKT. Summary of the Quasiharmonic Approximation Effects Upon Physical Properties The data presented here strongly suggest that the quasiharmonic approximation is valid for the following properties at least up to T = 20: P. providing q > 1.+l. a strictly quasiharmonic equation. is parallel to the T axis. If (BP/BT). (3). LY Versus T at High T Along Isobars Using the expression for Kp versus T. 6g. and all the respective volume derivatives of these four properties. We note that (57) results from the quasiharmonic approximation.Tables 29-42 show. given by (53).1) + . 6. They also suggest that the quasiharmanic approximation may or may not be valid for Cv and entropy for temperatures up to T = 28. T The above equation tells us that 6T should be virtually independent of T at high T. we also showed that there is no evidence of anharmonic effects in PTH because it is linear in T. and Vo all refer to values of these quantities at some reference T beyond which 7 is approximately constant. then the following formula. Extrapolations for KS Using 6s Constant With T Anderson and Nafe [9] pointed out that if bs is independent of T along isobars. for in this case ambient values of 6s and 7 are measured at temperatures much lower than 8. (~0. HIGH TEMPERATURE EXTRAPOLATION FORMULAS 7a. respectively. [63]. as in the case of MgO. Sumino et al. [61] and Sumino et al. see Anderson et nient form.(59) ANDERSON AND ISAAK 91 tion of why P. T. By assuming that 7 and 6s are exactly independent of T. T.L. Extrapolations for KS Using 7 Constant With T If 7 is independent of T. used (60) to extrapolate KS from 700 to 2100 K (forsterite) and 1300 to 3100 K (MgO). This is true especially for minerals. Along isobars.L. [13]. and if cr(T) and Cp(T) data are available at high T. 7. good estimates of KS are found using the definitions of 7 and 8~. and MgzSiOd at high T. Cp. 7c. Anderson [21] present a general formula for extrapolating elastic constants. in which (62) is a special case. CaO. Using (1) Ks=(TKy S0q) [ C -P$(T)r1. q where Ksc. as defined by (1)) yielding =bT-K’+l. Sumino et al. (YKT and Q do not require anhar. 7 and 6s are virtually independent of T for some minerals. and nearly so for others. Introductory Comments Knowledge of the high temperature thermoelastic properties permits one to generate extrapolation formulas for estimating KS and G at temperatures higher than measured. Since the values of bs and 7 are often not steady for T < 0.derivative of 7. Duffy and D. while at the same time Cv and S tion of T. then (62) Using (62) he estimated I<s for MgO up to 2OOO’C (see Figure 1 and Equation (21) of Anderson [3]). KT. 7b. We have seen that at high temperature (above O).. is useful.could be used to find KS vs. which follows when 6s is independent of al. [61] used (62) to extrapolate values of KS for forsterite from 700 K to 2000 K. We emphasize that reliable extrapolations using (60) require that CY be known at high T and the assumption that 7 is constant. Duffy and D. determined from (l). Anderson’s equation for G(T) in terms of the nomenclature used in this paper is G(T) = Go [dT)l~o] ‘a (63) Knowledge of Cp(T) is not required for (62) and (60) . because V is a funcmanic correction. it is not safe to use the extrapolation formulas described below when only low T data for 6s and 7 are available. Anderson [3] used (61) in a more convemay require anharmonic correction. used for one extrapolation and an equation involving linearity in Poisson’s ratio is also used (T . (6% Both extrapolation equations give reasonably good reSumno et al. 119771 -. Isaak et al. at least for forsterite. Equation (67) is very useful because a(T) is not needed to find KS(T). Anderson [5] used (67) t o extrapolate the velocities of sound from 0 to the melting point. (65) Assuming now that the product 6~7 is independent of T at high T. [61] measured the elastic constants of forsterite between -190°C and 4OO’C. [54]. Exlrapolauon (Eq 60) __ Exlraplation (Eq fiZj 7d. and taking V = Vc(l+ aT).To). This was proven experimentally for three minerals for 300 < T < 1200 K by Soga et al. The extrapolation to 2000 K is shown in Figure 3. we have c -1 aK s aT p = -6s aKs = !p. The term a(T . and there is much enthalpy data published listing H to temperatures about or greater than 2500 K.To)/2 is of little consequence in the calculation and can be ignored. and their values are also plotted in Figure 3. Extrapolations of KS by Sumino et al. [61] Sumino et al. The appropriate equation relating p and (Y is p(T) = PO exp [ . but some knowledge of a(T) at high T is required to get p(T) at high T. since the actual measured values are quite close to the extrapolated ones. (62).~+w]. and (67) assuming y and 6s constant in the high temperature regime. [35] reported measured values of KS up to 1700 K. They then extrapolated the values of KS up to 2200 K using (60). Equations (62) and (63) gave good results for extrapolations. Figure 3 illustrates the point that (60) is not a good extrapolation formula.H(To)] en KS = -SS en V + constant (61) 92 HIGH T ELASTICITY OF MANTLE MINERALS where H(T) = s Cp dT is the enthalpy.(63)./ F dT. p(T) at high T may not be known. Equation (67) s h ows that KS(T) should be linear in H(T). and for the same three minerals for 300 < T < 1800 K by Anderson [5]. Integrating (65) with respect to T KS(T) .Ks(To) = . Combining (1) and (2). (64 For some solids. we find to a very good approximation [54] KS(T) .Ks(To) = -e [H(T) . I Mg2Si04 loo\ 0 400 800 1200 1600 2000 . However there is another method that minimizes the dependence of KS upon a(T) and p(T). However. [61] measured G for forsterite up to Fig. Sumino et al. Extrapolation of G to High T Soga and Anderson [52] measured Ii’ and G for MgO and Alz03 up to 1200 K and found that G was linear in T above 800 K. 3. Extrapolations by Sumino et al. et al.dT (>I (T . 170. 60- _ Mg2Si04 50 ” ” ” ” ” ” ” ” ” 1 0 400 800 1200 1600 2000 T (K) Fig. 4. S umino et al. Observed and extrapolated values of G versus T for forsterite. They used equation (60) to extrapolate values of KS above the maximum measurement (1300 K) up to 3000 K. Equation (68) is et al. I 7e. Experimental (plotted symbols): Isaak et al. Experimental (plotted symbols): Isaak to 2200 K. It is clear that the extrapolation formula given by (60) is reasonably successful in the case of MgO. Two extrapolations made by Sumino et al. Observed and extrapolated values of I<s versus T for forsterite. They used the empirical formula 1 21 (3 -1 60 50 40 30 dG G(T) = Go . This is shown in Figure 4. [35] measured G up to 1700 K. 100' ' ' ' ' ' ' 0 500 1000 1500 2000 2500 3000 T (K) Sumino et al. [63] using Equation (60). [34]. Extrapolation by Sumino These results are plotted in Figure 5. [61]: (s) using Equation (60) where 600 K is the reference T. Fig. [61]. Observed and extrapolated values of ICs ver400°C and reported extrapolated values from 700 K sus T for MgO. 5. [61] are confirmed to within 2% out to 1700 K by the measurements of Isaak et al. [35]. and (c) using Equation (67). (b) using Equation (62). Isaak et al.-r (K) Sumino et al. They [53] later measured G and KS up to 1100 K for MgaSiO4 and MgSiOs and also found linearity for G and I(s. [63]. in which the measured values of KS [35] up to 1800 K are also plotted. Experimental (plotted symbols): . [63] measured the elastic constants of MgO from 80 to 1300 K. [35].To) (68) P To ‘::::M gO_ \__I to estimate shear velocities up to 2500 K. :oy 4. Extrapolations by’ Sumino et al. [61] up to 700 K. and up to High T If I( and G are successfully extrapolated.5% out to 1700 K by the measurements of Isaak et al. [35]. and vP by Isaak et al. Experimental points shown with symbols [36]..c3_ 150 xm 140 130 6. These are shown in Figure 6. Extrapolations: TSl refers to first order Taylor expansion using lower temperature data. [61] gave values for the extrapolated values of v. Experimental (plotted symbols): Sumino et al. (b) using Equation (70). [61]. Extrapolations for u. at low T \ \ \ \ 200 600 1000 1400 Temperature (K) 1800 Fig. [61] were quite successful. Comparison with the actual measurements of v. versus T for forsterite. 7. then v. are extrapolated.Isaak et al. [61] are confirmed to within 1. 94 HIGH T ELASTICITY OF MANTLE MINERALS 110 . It is clear that the extrapolations by Sumino et al.". ANDERSON AND ISAAK 93 sults when compared with the later measurements of Isaak et al.. Observed and extrapolated values of vP and v..2 4-. [35] The equation of G is G(T) = 3 Cl .Extrapolated (Sumino et al. The extrapolations made by Sumino et al.'.'. and vr. S umino et al. Observed and extrapolated values of I<s vs. [35]. [35]. Extrapolations by Sumino et al.5% at 1700 K by the measurements of Isaak et al.2a(T)) I&(T) 2 (l+u(T)) ’ (70) 7f. 6. short dashed line using Equation (62) with high temperature values of 6~. [1977]) $:‘."" 0 500 1000 1500 2000 T (K) Fig. [61]: (a) using Equation (68).. Sumino et al. pzisjiq . [35] up to 1700 K. and vr for forsterite up to 2200 K using their 100 K to 200 K measurements. T for grossular garnet. 170 160 2 . [35] and presented in Table 15 are also plotted. long dashed line using Equation (62) with low temperature value of 6s. [61] are from 700 to 2200 K and are confirmed to within 1. Isaak et al."". D. Earth Planet. I. Graham. Extrapolations: TSl and TS2 refer to first and second order Taylor expansions using low T data. measuring 6s and F over a wide T range. vol. H. including M. N. Observed and extrapolated values of G (GPa) versus T for grossular garnet. Suzuki. Anderson. 2. Experimental points shown with symbols [36]. If enthalpy data are available. Weidner. R. pp.. long dashed lines using Equation (63) with low T values of F. The Importance of Using High 6sandI’ T Values of Isaak et al. provided that values of 6s and F measured above 8 are used in the equations. Spetzler. Bass.. Kumazawa. in Physical Acoustics. 6~ and I?. Figures 7 and 8 show the extrapolations presented by them up to 2000 K. Y. Ota. Support for Mr. and M. Shear properties and thermodynamics of the lower mantle. H. L. Jackson. Saga. J. Sumino. and H. Yamamoto. Liebermann. Acknowledgements. L. T. 0. D. Cynn. Mason. The authors thank former members of the mineral physics laboratory who contributed to the data bank published here. The fits were marginally successful. Kim was provided by the . 43- 7g. 45. Oda. 1. P. 1987. edited by W. 8. S. K. 307-327. Phys. are the average high temperature values. and not the low temperature values of I’ (T < 0). Determination and some uses of isotropic elastic constants of polycrystalline aggregates using single-crystal data. Ohno. We acknowledge with thanks the works of E. Sung Kim of Azusa Pacific University provided much help in the statistical analysis required to arrive at values for the various dimensionless parameters.105 100 2 95 4% u 90 a5 a0 75 Gfossular (GGD) 200 600 1000 1400 1800 Temperature (K) Fig. L. I. Inter. Therefore we recommend Equation (62) for extrapolations of KS and Equation (63) f or extrapolations of G. A seismic equation of state. Goto. 3. Manghnani that affected our research programs. as shown in Figures 7 and 8. S. with 4 methods. [36] reported ICS and G for grossular garnet up to 1350 K. Anderson.. I. we recommend (67) for extrapolations of KS. short dashed lines using Equation (63) with high temperature value of I’. The salary of one of us was provided by grants from the LLNL-IGPP branch under the auspices of the Department of Energy under contract W7405-ENG 48. They tried both a first order polynomial and a second order polynomial. II. They also found Equations (62) and (63) t o b e a much better representation of G(T) provided that the exponents. Chem. Rea. J. Geophys. L. Inter.. 1989. 0.. 0. Chem. 70. and H. and J. Goto. 1965. 65. 0.. Appl. 0. L. 6. 241-253.. 39. 12. 0. The dependence of the AndersonGriineisen parameter 6~ upon compression at extreme conditions. Anderson. Res. J. L. 91. and T. 1989. L.. Soga. 3951-3963. Anderson. Rectangular parallelepiped resonance-a technique of resonant ultrasound and its applications to the determination of elasticity at high pressures. L. and D. Anderson. 486 pp. 1968.C. Yamamoto. 1965. 3849. J. Anderson. 54. J. 1992. Earth Planet. Geophys. 1989. Nafe. 3. SOL. G. 10. 491-524.. Rev. 55. Measurement of elastic constants of mantle-related minerals at temperatures up to 1800 K. A proposed law of corresponding state for oxide compounds. 16. AGU. Miner. 559-562. The interrelationship of thermodynamic properties obtained by the piston-cylinder high pressure experiments and RPR high temperature experiments for NaCl. 1993... Geephya. L. Yamamoto. Geophya. and N. Anderson. H. 0. IGPP contribution no. The relationship between adiabatic bulk modulus and enthalpy for mantle minerals. 221-227.. D. 4963-4971. L. 11.. J. Solids. 3537-3542. E. L.. Isaak. G. Phya. 0. Phya. Academic Press. Phya. Oda.Office of Naval Research through Grant no. 1966. Res. 13. Some elastic constant data on minerals relevant to geophysics. Evidence supporting the approximation yp for the Griineisen constant of the earth’s lower mantle. 5... 1987. 0. The bulk modulus-volume relationship for oxide compounds and related geophysical problems. L.. 289-298. Phys.. and S. Anderson. N90014-9310544. Syono. 71. F. D. Monogr. in High Pressure Research in Mineral Phyaica. 4. pp. edited by M. 1979. Liebermann. L.. 6. Anderson. Geophys. Isaak. Anderson. Manghnani and Y. J. Anderson. D. Schreiber. 0. Isaak. 0.. New York. 0. Anharmonicity and the equation of state for gold. Anderson. Ser. and S. Anderson. 22452253. REFERENCES 95. Acoust.. 1534-1543. High temperature elastic ... R. 84. vol. Washington. L. Barron. (Eds. Thermochemical Propertiea of Inorganic Substancea. H. Isaak. D. 2070-2072. The Griineisen parameter for the equation of state of solids. T. Rea. Anderson. R.. 17. B. Phya.). I. 1. 19. 36. 1993.. 21.. 1965. Appl. T. 1993. Bevington. 1989. F. New York. Ann. L155-L159. 16. Natl.. V. Anderson. Jr. Effects of cation disordering in MgA1204 spine1 on the rectangular parallelepiped resonance and Raman measurements of vibrational spectra. in High Preaaure Research: Application to Earth and Planetary Sciences. Manghnani. 77-89. 1973. 328 pp. 839844. A note on the Anderson-Griineisen functions. 369-380. L. Enck. 15. Douglas.. H. T. New York. November 1992. Robinson. 1895-1912. Thermal properties of aluminum oxide from 0’ to 1209 K. 24. Ahrens. 1957. D. 20. 25. 1968. Part l..D. H. Oda. J. Duffy. Furukawa. C. McCoskey. J. 57-90. Phya. 94. K. Geophya. L. 18.. 921 pp. D. Phya. 1962. T. Knacke. D.. McGraw-Hill. the sis. and J. E. Phya.. Marks. KU131.. D. Ph.. Los Angeles.. 1992. White. D. T. and ANDERSON AND ISAAK 95 H. C. Phya. and 0... K. &data Thermodynamic Tables: Selections for Some Compounda of Calcium and Related Mizturea: A . B. 22. and K. Stand. Syono and M. and D. Chopelas. 23.constant data on minerals relevant to geophysics. Duffy. I.. Engle. H. 30. 57. Rea. S. G. K.. Data Reduction and Error Analysis for the Phyaicnl Sciences. and D. H. Washington. Chem.. Minemla.. Behavior of the thermal expansion of NaCl at elevated temperature. J. J. 2nd Edition. Lateral variations in lower mantle seismic velocity. 0. Bur.C. Ginning. A thermodynamic theory of the Griineisen ratio at extreme conditions: MgO as an example. Dommel. Thermal expansion of KC1 at elevated temperatures. SpringerVerlag. 36. 1979. J. 12. Enck. S.. R.. Geophya. 14. F. 19.. Appl. A. G. Garvin. and D. T.. in press. Rev. edited by Y. Terra. P. Parker... 1992. Cynn. and T. Barin. J. Sound velocities in mantle minerals and the mineralogy of the upper mantle. UCLA. Barron. J. and D. 169 pp. 34. J. Rea. 1871-1885. Goto. Elastic constants of single-crystal forsterite as a function of temperature and pressure. J. Z. 1962a. 94. 74. Miner. Elastic constants of corundum up to 1825 K. J. 0. J. 37. 106-120. 29. Phya.. G. 5949-5960. Isaak.. and S. 35.. 343-352... 27. G. Isaak. Anderson. 1989. D. Elasticity of singlecrystal forsterite measured to 1700 K. Elasticity of single-crystal fayalite (abstract). 0. Rev. Miner. Solids. On some variational principles in anisotropic and nonhomogeneous elasticity. 1989R 36. 94... L. Isaak. 186-198. 1987. Rea. Anderson. and G. 1992. K. S. Phya. Solids. 16. Isaak. 1962b. Cohen. 30.. Shtrikman. E. The variation with temperature of the principal elastic moduli of NaCl near the melting point.. Anderson. Washington. Thermal expansion and high temperature elasticity of calcium-rich garnets. Mech. Phys. 16. 0.. Geophya. 0. Takei.. and S. Isaak. and 0. J. Goto. Geoph ys. 1418. Miner. and 0. Mech. Phys. and H.. Geophys.. E. 1988. Schwab.. J. 7588-7602. 1989. and S.. and R. The relationship between shear and compressional velocities at high pressure: Reconciliation of seismic tomography and mineral physics. G. Graham. A. and H. Goto. Chem. Oda. Yamamoto. T. D. 26. 1942. and T. L. Isaak. L. G. Anderson. 1989a. 58955906. Sopkin.. Siegel. 1969. 10. and T. K. L. Geophya. Anderson. J. Ohno. Eoa Trans. Z. G. 19. Chem. Res. I. Hunter. Graham. 335-342. Chem.... G. D... 97. A variational approach to the theory of the elastic behavior of polycrystals. L. AGU. 1992a. Hashin. 28. 31. Jr. L. 70. Hashin. D. 10. 32. The pressure and temperature dependence of the elastic properties of single-crystal fayalite FezSiO4. D. Anderson. 33. Res. D. 356 pp. High temperature elasticity of iron-bearing olivines.. Phys. M. L. Barsch. 61. Measured elastic modulus of single-crystal MgO up to 96 HIGH T ELASTICITY OF MANTLE MINERALS 1800 K. .Prototype Set of Tablea. S. Phya.C. Geophya. D. Hemisphere Publishing Corporation. R. Shtrikman. 703-704. and NaAISiBOs glass. 1992. Chem. Lifshitz. K. 40. grossular. Thermal expansion of single-crystal tephroite. 3. MA. D. Thermal Physics. 1969.52. Jpn. CaAl#zOa glass.Res. A. Okayama. Free vibration of rectangular parallelepiped crystal and its application to determination of elastic constants of orthorhombic crystals.. Elastic Properties and Equations of State.. Phys. DC. 19. K. A... Hemingway.. Suzuki.. Seya. Phys. 568 pp.. 39. S. Isaak. AGU. 46. Kumazawa.. L. Ohno. R. M. 48. J. and Y. from Russian). W. 1978.. M. Okayama Univ. 1978. R. (trans.of minerals and related substances at 298. 741-744.. Chem. 38. 1991.. H. Measurement of elastic properties of single crystal CaO up to 1200 K. pressure derivatives. Graham. 1978. GeoJ. L. Hemingway. Okayama... 41.. Washington. A. 44. Landau. Miner. Geophys. Elastic moduli. Shankland. 14.... Krupka. 42.. Pressure and temperature dependence of the elastic properties of synthetic MnO. and E. Bull. Res. Benjamin. I. Oda. 5961-5972. Phys. J. AddisonWesley Publishing Co. and E. 1992b. and J. 53 pp.15 K and 1 bar (lo5 Pascals) pressure and at higher temperatures. Mineral Physics Reprint. J.. Okajima. 69-80. A. Am. periclase.. Anderson.. Robie. thesis. Inc.. B. Okayama Univ. M. Okajima. Statistical Physics. Study of thermal properties of rock-forming minerals. and temperature derivatives of single-crystal olivine and single-crystal forsterite. K. K. Morse. 43. anorthite. Anderson. Kajiyoshi. D. 1986. Lett. and D. MS. 410 pp. 19. Miner. Fisher. L. Jpn. Sumino. S.. KAlSi308 glass. 30 pp. 1964. Robie. thesis. 45. 86-101.456. I. Reading.l. and 0.. 24... 0. S. pyrophyllite. 1958. 74. New York. S. High temperature equation of state for mantle minerals and their anharmonic properties. R. S. 18. Hightemperature heat capacities of corundum. lll115. 1976. and J. G. Pacalo. Earth. E. M. 49. Mineral. and B. 96-105. Phys. 355379.. R. T. Bass. . 483 pp. 64. muscovite. Thermodynamic properties.. Chem. 1979. Inc.. Minerals. Suru. P. 47.. U. Boca Raton. 1971. Elastic constants of minerals. Equation of state of NaCl: Ultrasonic measurements to 8 kbar and 8OO’C and static lattice theory. N. SO. M. J. Geophys. Simmons. S. 1727-1750. Y. Sumino. 55. pp. VIII. 53. edited by R.). Single Crystal Elastic Constants and Calculated Aggregate Properties. Am. 54. Anderson. 52. 1984. Sammis. Anderson. Ceramic Sot. Nishizawa. I. 1966. 1956. and 0. O’Connell. Ceram. J. 57. and 0. (2nd ed.. 2073-2087. 75. Sumino. H. Spetzler.. 5315-5320. Anderson. Y.. Equation of state of polycrystalline and single-crystal MgO to 8 kilobars and 800°K. Res. 24. Physical properties of end-members of the garnet group. Fl. B. FeaSiOd. N. 56. Prophet (Eds. Skinner. L. Kumazawa. Stull. E. 58. 33. Washington. Phys. 39-137. Earth. 61. 41. 1970. Y. Earth.. J. High temperature elastic properties of polycrystalline MgO and A1203. Estimation of bulk modulus and sound velocities at very high temperatures. 310 pp.. Y.. Soga.. 239-242. DC. 428-436. Department of Commerce. CRC. Schreiber. and 0. 1967. 60... L. Res. H.. Ohno. Am.. Chem. G.1988. T. J. Mineral. Saga. MA. T. 51. S. and M. 355-359. 1971. Solids..). Measurement of elastic constants and internal friction on single-crystal MgO by rectangular parallelepiped resonance. 49.. High temperature elasticity and expansivity of forsterite and steatite. J. J. 1979. L. in Handbook of Physical Properties of Rocks. 1966. 263-273. J.. and H. MIT Press.. C. Temperature variation of elastic constants of single-crystal . Ohno. 59. Ozima. Carmichael. L. Spetzler. and 0. Goto. and R. 1972. 209-238. D. and H. 1141 pp.. Wang. 71. Sumino. J. I. The elastic constants of MnaSiOa.. 50. 1976. Soga. Cambridge. N. R. Phys. Anderson. 0. JANAF Thermochemical Tables. Am. Sot. Sumino. Phys. National Bureau of Standards. and CO$!jiO4 and the elastic properties of olivine group minerals at high temperatures. Goto. 27. Geophys. G.... 65. Seya. Phys. Pluschkell. MnO and CaO and the elasticity of stoichiometric ANDERSON AND ISAAK 97 magnesiowiistite. Y. and their anharmonic properties. 475-495. The elastic constants of single crystal Fel-x.. 1983. I.. Okajima. 64. T. Elastic properties of Fe-bearing pyroxenes and olivines (abstract). 1658 pp. J. Bass. 0. Thermal expansion of single-crystal manganosite. 1979. L. Phys. AGU. 1975. M. New York-Washington. 319-323. Y. 38-46. Chem. edited by S.. Wachtman. 0.. 1982. Phys. S. Earth. L. H. 377392. Phys.. Phys.. Jr.200 K. Lee. Taylor.. R. Suzuki.. 62. Advances in Earth and Planetary Sciences. Nonmetallic Solids: Thermophysical Properties of Matter. K.forsterite. K. 1977. W. Thermal expansion of fayalite.. i981. 38-47. 23. Sumino.. and Y. and 0. Thermal expansion of periclase and olivine. 67. 70. Earth. H. Elastic properties of a single-crystal forsterite Mg#Oa up to 1. Kirby. Earth. 10. Suzuki. 68. S. Sumino. Linear thermal expansion of aluminum oxide and thorium oxide from 100’ to 1. J. Sot.. E. . 63-69. Suzuki. Sumino. Earth. Phys. between -190°C and 9OO”c. R. 31. Elasticity and thermal expansion of a natural garnet up to 1000 K. G. 66. Phys. 60-63. Plenum. pp. 63. Thermal Expansion. 1962. I. Earth. Chem. in High Pressure Research in Geophysics. J. 1. 474. Wang. 13. 72. J. 1983. Seya. Anderson. 1980.. I. B. Scuderi. Eos Trans. Suzuki. D. J. vol. lOOoK. Watt. Rossman.. Suzuki.5. S. Anderson. Center for Academic PubIications. Cleek. Temperature coefficients of single crystal MgO between 80 and 1300 K. Takai. 73. and G. 145-159. L. Hashin-Shtrikman . Am. 9.. Phys. 1989. Miner. and K.. Tokyo. and Y. Kumazawa. Akimoto and M. 1977. and W. 69. Y. 45. Nishizawa. H. 1983. 28.. 0. Sumino. 125-138. Touloukian. P. and G. Suzuki. vol. I. R. Watanabe. I. Chem.7. J. H. Manghnani. Ceram. 441464.. Anderson. 71. R. and Y.. 70. and T. Miner. Miner. 12. J. Y. 27. Thermochemical properties of synthetic highpressure compounds relevant to earth’s mantle. J. in order to determine the isothermal bulk modulus (Km = . Chem.1983. D. White. S. pp.. 3. 91-99. Yamamoto. Equations of state for solids at high pressures and temperatures.. in Perouskite. 1979. and 0. 75. Geophys. 76. Phys. Ito. Solids. High Temp. . 14. Zouboulis. Weidner. Yeganeh-Haeri. 1975. Monogr. elements and related materials. J. P.. vol. translated from Russian by A. Phys. 77. 13-26. Single crystal elastic moduli of magnesium metasilicate perovskite. I. 48. Anderson. Consultants Bureau. Thermal expansion of reference materials: Tungsten and CYAlzOg. G.bounds on the effective elastic moduli of polycrystals with orthorhombic symmetry. Tybulewicz. High temperature elasticity of sodium chloride. phase transitions and the equations of state of deep Earth constituents. Weidner. 80. Shankland. 257 pp.. Anderson. AGU. and R. 332-340. New York. KaIinin. Roberts. 1971. High Pressures. 50.. Minerals. Chem. the vast majority of static compression experiments have focused on measuring isothermal equations of state (P-V measurements at constant temperature). D.. 1991. A. as well as the geochemical behavior of materials at depth in the planet have been derived from experiments involving static compression. Res. Elasticity and anharmonicity of potassium chloride at high temperature. 1987. Appl. 1987. and E..I. S. and M. Geology. and N. E. C. Refractive index and elastic properties of MgO up to 1900 K. Geophys.. To date. 78. Yamamoto... 15. 79. 74. the primary insights into magma genesis. Static Compression Measurements of Equations of State Elise Knittle 1. Indeed. J. 143-151. Zharkov. the emphasisi s on static-compressionm easurementso f the equations of state of minerals. Washington. Phys. 96. In this chapter. V. Watt. 4167-4170. 321-328. Uniformity of mantle composition. J. and 0. L.l/v(dp/dv)T) and its pressure derivative . L. edited by A. T. N. B. and V. K. Ohno. Mao. Grimsditch. 45. Navrotsky and D. S. J. INTRODUCTION Generation of high pressures and temperatures in the laboratory is essential in exploring the behavior of solids and liquids at the pressure and temperature conditions of the Earth’s interior. J.. A. 1989.. Ser. 6290-6295. 2. and thus no details of its operation are presented here. or E. I tabulate bulk moduli data for a variety of minerals and related materials. these diamond cells are used for pressures below about 10 GPa.2151.it is necessaryt o maintain the sample in a hydrostatic environment. University of California. it is possible to extrapolate the density of a material to any pressure condition. With the bulk modulus and its pressure derivative.97. is optimal for obtaining x-ray diffraction data to pressures up to 300 GPa.(dKoT/dP = KOT’) as well as characterizing the pressure conditions of structural phase transitions. 98 KN1l’TL. EXPERIMENTAL TECHNIQUES There are a number of different experimental techniques and apparatuses for achieving high pressures statically. a Mao-Bell or “megabar”-type diamond cell. Diamond-Anvil Cell The most widely used high-pressure apparatus for measuring static equations of state is the diamond-anvil cell coupled with x-ray diffraction. the sample is a powder and the xray diffraction data collected is directly analogous to a Debye-Scherrer powder pattern. The second type of diamond cell. high pressure apparatuses are optimized for either: 1) allowing optical access to the sample while held at high pressures (diamond-anvil cells). A typical sample configuration in the diamond-cell is shown in Figure 2. CA 95064 Mineral Physics and Crystallography A Handbook of Physical Constants AGU Reference Shelf 2 pressures maintainable for long periods of time. In general. Copyright 1995 by the American Geophysical Union. Mineral Physics Laboratory. The bulk moduli data have been collected using primarily either x-ray diffraction or piston displacement in conjunction with a high-pressure apparatus to measure the change in volume of a material as a function of pressure. However. Santa CNZ. the pressure limitation of the diamond cell is not a limiting factor for the experiment. There are several excellent recent reviews on the use of the diamond cell [88.E 99 Optic Access Sample . Here. Since liquid pressure media (such as 4:l methanol:ethanol mixtures) are only hydrostatic to -12 GPa. Usually. Santa CNZ. In general.1. Knittle. For equation-of-state measurements. Institute of Tectonics. 2. two basic diamond cell designs are used (see Figure 1). The Merrill-Bassett-type diamond cells are commonly used for single-crystal x-ray diffraction measurements. in this type of diamond cell. as their small size makes them convenient for mounting on a goniometer to obtain singlecrystal x-ray patterns. for single-crystal measurements. or 2) maintaining large sample volumes (large-volume presses). la. The diamonds are glued onto half-cylinders of tungsten carbide which are mounted in a piston and cylinder made of hardened tool steel (shown here in a cutaway view at the top). A schematic diagram of the geometry of an x-ray diffraction experiment in shown in Figure 3. either Laue spots for single crystal samples or diffracted cones of radiation for powdered samples. The diamonds can be translationally aligned by means of set screws and tilted with respect to each other by rocking the WC halfcylinders. the RI and R2 fluorescence bands of ruby.24 nm and 692. Usually. 361.92 nm.g. The Mao-Bell-type diamond cell capable of generating pressures up to 550 GPa. 28 is the angle between the diffracted x-ray beam and the transmitted beam. The set of dspacings for a crystal is used to determine the lattice parameters and thus the volume of the crystallographic unit cell as a function of pressure. These fluorescence bands have a strong wavelength shift as a function of pressure. MoKa x-rays are passed through the diamonds and sample along the axis of force of the diamond cell. The relationship between dspacings and lattice parameters for the various lattice symmetries are given in most standard texts on x-ray diffraction [e. Pressure in the diamond cell is usually measured using the ruby fluorescence technique [20. are detected by a solid state detector or on film. 1291. The diffracted x-rays. at zero-pressure wavelengths of 694. and d is the d-spacing or the distance between the diffracting set of atomic planes in the crystal. are excited with blue or green laser light (typically He:Cd or Ar-ion lasers are used). The piston and cylinder are placed in a lever arm assembly (bottom) designed to advance the piston within the cylinder. X-ray diffraction from a crystal occurs when the Bragg equation is Satisfied: A= 2dsintI (1) where A is the wavelength of the incoming x-ray. 128.zl Cylinder L Sample fl 2cm 0 Lever Arm Fig. Here. apply force uniformly to the sample held between the diamonds. This shift has been calibrated using simultaneous x-ray diffraction . and exert a minimum amount of torque on the piston.. high-pressure apparatuses: piston-cylinder devices.2. Large-Volume Presses Equation of state measurementsh avea lso beenc arried out using a variety of large-volume. Alignment pins ensure that the the top and bottom halves of the cell are correctly oriented.30 GPa. The backing plates are held in place in recessesin larger steel or inconel plates by means of set screws. 100 STATIC COMPRESSION FWD Plate ff 1 cm Hole to DiamondB ack Boltsf or pressure and Optic Access Application Fig. In addition to average pressure measurements. thus enabling pressure gradients to be accurately determined within diamond cell samples. The single-crystal diamonds are glued on flat. 2. Because diamonds are transparent and allow optical access to the sample. circular backing plates typically made of hardened steel. For example.. which is contained between the diamonds in a metal gasket. Drickamer .. This device can be used to generate pressures of . the changes in the volume of the sample chamber as a function of pressure can be directly measured [cf. and also allow the diamonds to be translationally aligned relative to one another. Holes or slits in the backing plates provide optical access to the sample. or changes in the sample dimensions with pressure may be directly measured [cf. lb. accurate adiabatic moduli and their derivatives may be obtained using Brillouin spectroscopy in conjunction with the diamond cell (see the chapter on Elasticity). Therefore. the accuracy of the pressure measured in the diamond cell is ultimately determined by the accuracy of measurementso f shock-wavee quationso f state. 1393. Merrill-Bassett-type diamond-anvil cell shown in schematic from both side (top) and top views (bottom). Bridgman-anvil presses. 1431. ruby can be finely dispersedi n the sample (fluorescencem easurementsc an be obtained for ruby grains less than 1 pm in diameter). Pressure is applied by sequentially turning the three bolts which compress the top and bottom plates together.measurementso n metals whose equationso f state (pressurevolume relation) are independently known from shock-wave measurements( seeC hapter on Shock-waveM easurements). other methods for measuring equations of state are possible. tungsten carbide or copper-beryllium alloy. Additionally. Such instruments are more difficult to use than a piston-cylinder. however. two tungsten carbide anvils are driven together to uniaxially compress a sample contained within a large retaining ring which acts as a gasket. as their names imply. and by careful measurement of the resulting piston displacement as a function of pressure. The sample assembly. For recent reviews of the design and use of large-volume presses see Graham [59] and Holloway and Wood [85]. In these devices. as the anvils must be carefully aligned and synchronized to compress the sample uniformly and thus prevent failure of the anvils. large-volume devices for equation of state measurements is the pistoncylinder (Figure 4a). In tetrahedral and cubic-anvil presses. As the sample is compressed its volume decreases.presses. A second family of large-volume apparatuses is the multi-anvil press. The routine pressure limit of the pistoncylinder at room temperature is between about 3 and 5 GPa. these devices compress simultaneously from several directions. A number of designs exist for multi-anvil presses of which the ones most commonly used for equation of state measurements are the tetrahedral-anvil and cubic-anvil presses (Figure 4b). the samples are typically contained within either a tetrahedron or a cube composed of oxides. The pressure limit of the Bridgman-anvil press is about lo-12 GPa at room temperature. One of the most widely used high-pressure. Other types of high-pressure. the P-V equation of state can be determined. and the limit of the Drickamer press is about 30-35 GPa. diffraction measurementsc an be madeo n a sample held at high pressures. where the pressure is applied uniaxially by a piston on a sample embedded in a pressure medium and contained by the cylinder. in-situ x-ray diffraction KNITTLE 101 y Pressure Medium I c / Ruby Grains . cubic and tetrahedral-anvil presses and multianvil presses (Figure 4). If all or a portion of the retaining ring is made of a material transparent to x-rays (such as B or Be). is compressed by four hydraulic rams in the case of the tetrahedral press. large-volume devices utilizing opposed anvils for equation of state measurements are Bridgman anvils and the Drickamer press. and multiple-stage systems. much higher pressures can be attained in multi-anvil devices. with the sample occupying a cylindrical cavity inside the cube or tetrahedron. As illustrated in Figure 4c for a cubic-anvil press. Rather than uniaxially compressing the sample. which varies in complexity depending on the experiment. or six hydraulic rams for the cubic press. Specific disadvantages of x-ray diffraction measurementsin large volume pressesi nclude: 1) indirect pressure calibration.( Lower Diamond) Fig. To achieve higher pressures. The pressure inside a large-volume device is determined either by including an internal stress monitor within the sample. x-ray diffraction patterns can be obtained at high pressure along the axis of force of the diamond cell for either single-crystals or powders. Equation of state measurementsh ave typically been madet o pressures of about 12 GPa in the cubic-anvil press. 3. pressureintensifying stage.7 GPa). In the latter case. which necessitates both careful experimental design and a high intensity x-ray source. with wellcharacterized phase transformations. For equation of state measurements. or a noble gas such as argon) and small ruby chips for pressure calibration. The transparent diamonds allow for a wide range of different in situ experiments to be performed on the samples. 2. Furthermore.30 mm). A hole is drilled in a metal gasket (here a typical diameter of 0. where KOT is the isothermal bulk modulus. the oil pressure of the press is calibrated against a series of materials or fixed points. producing few redundanciesin the measuremenot f lattice parameters. I summarize the most common methods for data reduction. and the gasket is centered between the diamond anvils (shown with a typical culet diameter of 0. and . or by calibration of the external load on the sample. the diffraction angles available through the apparatus may be limited. Schematic view of the sample configuration in the diamond cell. and 3) the small volume of the sample relative to the containing material. This analysis implies that KOT' = 0. (From [2151). The sample is placed in the hole in the gasket along with a pressure medium (generally either an alcohol mixture.5 GPa and V-VI transition at 7. such as those occuring in Bi (the I-II transition at 2. The bulk modulus is calculated from the thermodynamic definition: KOT = -l/V(dP/dV)T. measurements can be made through these presses if the sample is contained in an x-ray-transparent material. V is the volume and P is the pressure. an equation of state formalism must be used. A linear fit to pressure-volume data is often used for static compression data limited to low pressures (small compressions). 2) an inability to accurately characterize pressure gradients.10 mm is shown). the sample assembly in a cubicanvil press can be replaced by a second. Here. which represents the most common method for estimating the pressure in all largevolume devices. Such a multi-anvil design can reach typical pressures of about 25 GPa. ANALYSIS OF THE DATA To determine the values of Km and Km from pressurevolume data. x-ray diffraction.thus is at best approximate. Note that Km = 4 reduces equation (3) to a second order equation in strain.) (3) whemfis the Eulerian strain variable defined as f = 1/2[(V/V&‘3 -11 and the coefficients in (3) are: xl = 3/2(K()f . In general. and is most appropriate for rigid materials over narmw pressure ranges (preferably less than 5 GPa). KOT’ is close to 4 for many materials. Pressureis expresseda s a Taylor seriesi n strain: P = 3f(1+2j)5/2Ko~(1 + xrf + x2f2 + . therefore. mineral analogues and chemical elements studied using static compression techniques (i. the x2 term is usually dropped from the equation.! = 312 [KmKm” + Kof(Kof-7) + 143191. and referred to as the BirchMurnaghan equation 1251.e. minerals are seldom compressible enough for KOT” to be significant. Here: P = 3 KOT (VO/V)~~[~-(VIV~)~/~ exp(3/2(KoT’-1) [~-(V/VO)~‘~I). 4. All the data reported is from the literature from 1966 to the present: static compression data from before 1966 can be found in the previous Handbook of . This equation has been empirically shown to describe the behavior of a wide variety of materialso ver a large range of compressions. in which: p = KoT/&$((VO/~~OT’ -1 j (2) The Mumaghan equation is derived from finite strain theory with the assumption that the bulk modulus is a linear function of pressure. EXPLANATION OF THE TABLE The Table lists the isothermal bulk moduli (KoT) and pressure derivatives (dKo~/dl’=K& for minerals. [205] and is known as the Universal equation of state. Recently. In addition.4) x. At modest compressions.. . because KOT' is usually positive. this analysis method will tend to overestimate Km. is often assumed to equal 4. this 102 STATlC COMPRESSION assumption is sufficiently accurate that the Murnaghan equation accurately fits static compression data. (4) This equation is successful in describing the equation of state of a material at extremely high compressions and is being used with increasing frequency in static compression studies. and in the reduction of pressure-volume data. An equation of state formalism used extensively prior to 1980 and sporadically since is the Mumaghan equation [ 1533. One of the most widely used equations of state in reducing static compression data is the Eulerian finite-strain formalism proposed by Birch. another equation of state formalism has been proposed by Vinet et al. piston displacementm easurementso r direct volume measurements at high pressures). Indeed. MOK~ x-rays are passed through the sample and the diffracted x-rays are recorded either on film (shown here) or by a solid-state detector. 4a. Howie and Zussman’s An Introduction to the RockKNllTLE 103 Feedthrough l-l I l-l edium V 2% X-Rays 5cm Assembly Fig. A piston-cylinder apparatus shown in crosssection. except where noted. the structures of the high pressure phases are explicitly given. The silicate minerals are categorized following Deer. halides and hydrides were included which are useful as mineral analogues. Not every entry in the Table is a State Detector Sample P Direct X-ray Beam Fig. atmospheric-pressure phase. or to provide the systematics of the behavior of a given structural type. Here the schematic x-ray pattern is that of a powder diffraction experiment. Oxides. where the film intersects diffracted cones of radiation. In particular. Here. Schematic of an x-ray diffraction experiment through the diamond cell. compressing a pressure medium and thus applying hydrostatic or quasi-hydrostatic pressure to a . It should be noted that entries with no errors simply reflect that error bars were not reported in the original references. The maximum distance between the corresponding x-ray line on either side of the transmitted xray beam is 40. mineral or native element. sulfides. which is used in the Bragg equation to determine the set of d-spacings of the crystal at each pressure. either due to structural similarities to minerals. a uniaxial force is used to advance a piston into a cylinder. All the KOT and KOT’ data listed are for the structure of the common room-temperature. Specifically not included are data for nonmineral III-V compounds and other non-naturally occurring semiconductors. 3.Physical Constants. as are the specific structure for solids with more than one polymorph at ambient conditions. Electrical leads can be brought in between the rams of the press to heat the sample. to a sample contained in a second. and measure pressure-induced changes in electrical conductivity. electrical leads can be introduced into the sample to measure temperature or as a pressure gauge. ultrasonic data or Brillouin spectroscopic results. The sample geometries can vary from relatively simple. The piston and cylinder are usually made of tungsten carbide and the maximum routine pressure limit of this device is 5 GPa at room temperature. synchronized rams are used to compress a cubic sample. The data for high-pressure phases are given in the same category as for the low-pressure phase. iron hydride. based on comparison with other static compression measurements. Fet-. Also.( From [215]). iron sulfides. iron-nickel and iron-cobalt alloys are found in this portion of the Table. For example. with the sample assembly embedded in a cube of pressure medium which is directly compressed by the rams.O. 46 A cubic-anvil press in which six. Therefore. The feedthrough into the cylinder gives a way of monitoring the sample environment. Forming Minerals [38]. cubic. Equation of state measurements can be made in this device by determining the piston displacement as a function of pressure. and iron-silicon. The data for the iron polymorphs and iron alloys which are important as possible core constituents are listed in a separate category (“Iron and Iron Alloys”). (From 12151). For example. Such studies often do not report either bulk moduli or the numerical static compression data. and are accordingly not included in the Table (an example of this type of study are several static compression rest&s for Ge). . The rams are usually made of steel with tungsten carbide or sintered diamond tips. (Fez@) and magnetite (Fe304) are listed with the oxides. pressure-intensifying set of anvils (a multi-anvil press). Another use of the feedthrough is to provide current to a resistance heater surrounding the sample (not shown). In addition. by using a low-atomic weight pressure medium such as B or Be. x-ray diffraction measurements can be obtained on samples held at high pressures. under the “Chain Silicates” category. which have the same stoichiometry. Finally. while more oxidized iron minerals such as hematite Fig.sample contained within the medium. the bulk moduli for perovskitestructured silicates are given with the data for the pyroxenes. I note that a range of materials have been statically compressed with the primary motivation being to characterize the pressure at which phase transitions occur. measurements are not given which clearly seemed to be incorrect. monitor temperature and pressure. 62 2.29 2.65 2. @kh3) Modulus dKoTldP3 Technique and Notes4 (GPa)2 Framework Silicates: SiO2 QUUHZ Si02 Quartz Si02 Quartz Si02 Coesite Si02 Stishovite Si02 Stishovite Si02 Stishovite Si02 Stishovite NaAlSi3Og Low Albite KAlSi30g IIigh Sania!zke caA12si2og Anorthite (low-pressure phase) caA12si2og Anorthite (high-pressure phase) BeAlSi040H Euclase BeqSi2WW. 2.76 3.2 .76 2.56 2.1 f 0.2 (fixed from ultrasonic data) 36. Bulk Moduli from Static Compression Data Chemical Formula1 Density Isothermal Bulk Ref.0 96 + 3 313 f 4 306 (fixed from Brillouin data) .92 4.4 AZ 0.65 2.29 4.61 37.29 4.29 4.5 38.12 2.65 2.104 STATIC COMPRESSION Table 1. ND. B-M EOS PC. P I 5 GPa. 1inPVfit DAC. XRD.4 f 1. scXRD. P I 8. P 5 2.9 1. 1inPVfit DAC.4 8.6 2. B-M EOS DAC. M EOS BA. P I 12 GPa. P < 16 GPa. scXRD. P 5 5 GPa.5 DAC.3ooIt30 288 rk 13 281 70 67 94 106 159 f 3 70 r/I 3 6.5 GPa.3 l!Y 1.8 + 0.4 5. B-M EOS 115 98 157 113 176 21 158 . scXRD. P I 5 GPa. XRD.XRD. 1inPVfit DAC. 1inPVfit DAC. scXRD. P 2 5 GPa.2 _6 5 --__4 (assumed) 5. P I 5. O-H method CAP. P 5 5 GPa. scXRD. P < 5 GPa. 1inPVfit BA.P112 GPa. scXRD. B-M EOS TAP.2 AZ 1 6. scXRD. O-H method DAC. B-M EOS DAC. P I 5 GPa.5 GPa. P 2 12 GPa. scXRD.3 rk 0. scXRD. B-M EOS DAC. XRD.7 + 0.2 GPa. l2(NaqA13 Si9024Cl) Scapolite Chain silicates: CaMgSi206 Diopside caMgsi206 Diopside CaMgSi206 Diopside CaFeSi Heaknbergite Ca(MgO.44 21.8 (in water) 4 (assumed) 2.68(CaqAlgSi6024 C03) * 0.71 86 .66 2.6) Si206 Heafenbergite ~Ca. Bulk Moduli from Static Compression Data (continued) Chemical Formula1 Density Isothermal Bulk @Wm3) Modulus cwYrl@3 (Gl?i~2 Technique and Notes4 Ref.32(NaqA13 SigO24Cl) Scapolite O.83(NaqAl3 Si9024Cl) Scapolite O.4WI.24 40 I!I 1 -2.0.54 60 -2.17(c&jAl(jsi&‘4 C03) . 12NaAlSiO4 -27H20 Zeolite 4A NaAlSi206.30 52 f 8 4 (assumed) 2.179 14 14 14 14 77 63 KNI'lTLE 105 Table 1.7 (in glycerol) 142.O.88(CaqAlgSQjO24 C03) .Fe.Na)Wg.~) Si206 Omphacite (vacancy-rich) 2.H20 Analcite Na4A13Si30l2Cl Sodalite o. B-M EOS DAC. B-M EOS DAC. P I 6 GPa. scXRD. P I 5 76 GPa. B-M EOS DAC. P I 5. 1inPVfit 73 69 76 33 33 90 f 12 4 (assumed) DAC. P c 3 GPa. scXRD. P I 4 GPa. P < 3 GPa.3 GPa. P I 10 GPa. P 5 5.8 3.5 + 1. B-M EOS 3. B-M EOS 112 116 142 228 228 142 106 STATIC COMPRESSION Table 1. pXRD.7 3. scXRD. B-M EOS DAC. scXRD.7 f 1 4 (assumed) 3.Fe. P I 5 GPa. P I 4 GPa. scXRD.DAC.22 114f4 4.22 1131k2 4. 1inPVfit DAC.A~) Si206 Omphacite (va=y-poor) MgSi03 Enstatite MgSi03 (high-pressure . B-M EOS DAC. pXRD.8 f 0. scXRD. Bulk Moduli from Static Compression Data (continued) Chemical Formula1 Density Isothermal Bulk oMg/m3) dKoT/dp3 Modulus Techniquea nd Notes4 Ref- VXWMg. scXRD.3 GPa. P I 10 GPa. scXRD.22 122 f 2 4 (assumed) 3. P I 6 GPa.26 129 k 3 4 (assumd) DAC. scXRD. scXRD.56 119f2 4 (assumed) 3. B-M EOS DAC.42 82. 1inPVfit DAC. B-M EOS DAC. 8 4.25 281 f4 4 (assumed) 4 (assumed) 4 (assumed) 3.22 125 5 (assumed) 3.6 + 1.55 159.10 247 4.8 Majorite Mgo.26 266+6 4.8 + 0.74 221 + 15 4.WwaSiO3 Majorite MgSiO3 (high-pressure perovskite structure) MgSi03 (high-pressure perovskite structure) MgSiOg (high-pressure perovskite structure) Mgo.10 4.10 258 + 20 4.6 WgW2Si3On)o.4 4 (assumed) 4 (assumed) .4 Majorite (Fe4SWi2h.9 ?I 0.29 139f4 4 (assumed) 3.10 254 zk 4 4.sFeo-0.6 4.33 261+4 4.1 4 (assumed) 4 (assumed) 3.4 + 4.2 O.e3&?si3012)0.tetragonal-garnet structure) (Mf%Si4012)0.52 161 4 (assumed) 3.o-o.2 SiO3 (high-pressure perovskite structure) CaSiOg (high-pressure perovskite structure) 3.41 164.nSi03 (high-pressure perovskite structure) Mgl.88Feo. P < ?. B-M EOS DAC.25 275 f 15 4 (assumed) ZnSiOg (ilmenite structure) . XRD. B-M EOS DAC. P I 13 GPa. B-M EOS dKm/dT = -6.5) x 1O-2 GPa/K DAC. scXRD.DAC. P < 6 GPa. B-M EOS DAC. scXRD. P I 6. P < 30 GPa. CaSiO3 (high-pressure perovskite structure) 4. P I8 GPa. P I 6 GPa. B-M EOS CAP. B-M EOS BA. B-M EOS CAP.2 GPa. Bulk Moduli from Static Compression Data (continued) Chemical Formula1 Density fsothe~~~u~ dKoT/dp3 @Wm3) Technique and Notes4 Ref. B-M EOS DAC. B-M EOS 142 159 223 224 224 90 106 173 220 102 138 133 KNI’ITLE 107 Table 1. P I 10 GPa.P16 GPa. B-M EOS DAC. pXRD. scXRD. pXRD.3 (k0. pXRD. pXRD. P I 7 GPa. P I 134 GPa. XRD. B-M EOS DAC. P I 112 GPa. O-H method DAC. XRD.XRD.25 325 + 10 4 (assumed) CaSiO3 (high-pressure perovskite structure) 4. pXRD. B-M EOS DAC.10 NaCa2MgqAlSigA12 022WU2 Pargasite 3.2. scXRD.22 122.39 216 f 2 4 (assumed) 85 -% 97 50 + 1 --13 f 1 123. scXRD.22 120 5.50 Ortho.5 GPa.1 GPa.1 Mg2SiO4 Forsterite 3.3 Fe2SiO4 Fayalite Fe2S i04 Fayalite 4. P I 5.WwW (Si. XRD.98 r!z 0.C1)2 Grunerite 3.9 + 4.96 ca2mssi8022 O-02 Tremolite 2. B-M EOS CAP.39 4. B-M EOS DAC.A1)8022 (OH. pXRD. pXRD.F. 1inPVfit DAC.6 5. B-M EOS .99 Na2MgsA12Si8022 w-02 Glaucophane 3. P I 4 GPa. P I 10 GPa. 1inPVfit DAC. P I 4 GPa.0 5 0.and Ring micates: Mg2SiO4 Forsterite 3.KFe. P I 4 GPa.6 4.0 3. scXRD. scXRD.6 Mg2SiO4 Forsterite 3. 1inPVfit DAC.22 135. P I 31. P I 85 GPa.10 (Na.7 + 1.8 119 * 10 7+4 124 f 2 5 (assumed) DAC. 16)2 Si04 Wadsleyite or PPhase 3. XRD. pXRD.sd+o. P < 15 GPa.75 Wadsleyite or PPhase Mg2SiO4 Wadsleyite or /I-P/use Mg2SiO4 Ringwoodite or FPhase . P I 10 GPa.DAC. O-H method DAC. scXRD. i 612 Si04 Wadsleyite or PPhase 3. Fe2S i04 Fayalite Fe2SiO4 Fayalite Fe2S i04 Fayalite CaMgSiO4 Monticellite ZrSiO4 Zircon (Mgo. M EOS BA. XRD. P < 7 GPa.wFeo. P I 30 GPa. B-M EOS 199 200 184 35 35 35 229 214 159 105 216 222 108 STATIC COMPRESSION Table 1. Bulk Moduli from Static Compression Data (continued) Chemical Formula1 Density Isothe~~u~u~ dKoT/dp3 @Wm3) (GPa)2 Technique and Notes4 Ref. B-M EOS CAP. pXRD.47 1002Mg/(Mg+Fe)2 3.53 (Mgo. P c 38 GPa. B-M EOS DAC.53 (MgW2siQ 3.78 0. P < 27 GPa. dK/dT= -5.55 4.85 124 + 2 134 103. pXRD. dK0T/dT = -2. B-M EOS DAC. P < 14 GPa. B-M EOS DAC.8 (at 400 “C) 113 rf: 3 227 ?z 2 174 f.39 4. scXRD. pXRD. P I 5 GPa. P I30 GPa. B-M EOS.47 3. P < 8.38 f 0.(spine1 structure) (Mgo.7 * 0.7 (fixed from ultrasonic data) 4 (assumed) 4 (assumed) -_5.3 .39 4. P < 6.0 GPa at 400 “C.2 GPa. scXRD.05 4. 3 168 f 4 164*2 171 + 0.39 3.24 _DAC.65 3. B-M EOS DAC.4 x 1O-2 GPa/K DAC. scXRD.09 4. pXRD.6Feo&SiO4 Ringwoodite or YPhase (spine1 structure) Fe2SiO4 (spine1 structure) 4. 1inPVfit DAC.6 166*40 213 + 10 183 f 2 196 Ifr 6 4 (assumed) 4 (assumed) (at 4% “C) 4 (assumed) -4 (assumed) 4. P I 10 GPa. pXRD. 1inPVfit DAC. Fe2SiO4 (spine1 structure) Fe2SiO4 (spine1 structure) Ni2SiO4 (spine1 structure) Ni2SiO4 (spine1s tructure) Ni2SiO4 (spine1s tructure) Co*SiO4 (spine1 structure) Co*SiO4 (spine1 structure) Ca3A2(04Hq)3 Katoite or Hydrogrossular Ca3A12Si3012 Gross&r Ca3Al2Si3012 Grossular Mn3A12Si3012 Spessartine . B-M EOS Re-analysis of [78] MAP. B-M EOS DAC. 1inPVfit MAP. P 5 4 GPa. P I 10 GPa. scXRD. 1inPVfit 131 104 168 186 67 52 78 92 151 151 227 56 KNI’ITLE 109 Table 1. P d 5 GPa. Bulk Moduli from Static Compression Data (continued) Chemical Formula1 Density Isothermal Bulk (Mg/m3) Modulus dKoT/dp3 (GPa)* Techniquea nd Notes4 Ref. scXRD. XRD. P I 50 GPa. XRD.x 1O-2 GPa/K DAC. P18 GPa.P58 GPa.17 206+2 4 (assumed) 2. 1inPVfit CAP.8 7.2 (fixed from ultrasonic data) 175 f 1 7. pXRD.1 f 0.35 214 4 (assumed) 5.0 f 0.17 210 f 6 4.5 + 0.85 197 f 2 4 (assumed) 4. P I 4 GPa. P I 26 GPa.35 227 f 4 4 (assumed) 5. B-M EOS DAC. B-M EOS DAC.58 4.59 -4.XRD. pXRD.35 227 f 4 -5. P I 30 GPa.58 212 + 8 3. B-M EOS DAC.19 171.xRD. B-M EOS DAC.5 3. B-M EOS DAC. B-M EOS CAP.6 5.XRD.5 3.5 2 0.0 3.8 zk 0. B-M EOS 178 131 56 178 127 123 178 . P < 30 GPa.1 f 1. pXRD.WwWWOn Pyrope MS3Al2Si3012 Pyrope WwWSi3012 Pyrope 4.59 168 f 25 6. P 5 43 GPa.5 3.52 66 f 4 4.58 171 f 3 1.6 CAP.2 + 4 168. scXRD.0 5 1. pXRD.85 212 4 (assumed) 5.4 (fixed from Brillouin data) 139 Ifr 5 6.7 3.P18 GPa.4 f 1 174. C02. pXRD.83 162 3. B-M EOS DAC. Fe3A12Si3012 Almandine Fe3A12Si3012 Almandine Ca3Cr2Si3012 Uvarovite Ca3Fe2Si3012 Andradire A12Si05 Andalusite Mg1. B-M EOS DAC.7A@i2 Olo(OH)4 Magnesiochloritoid Be3Al2Si6018 Beryl WgJW2A4Si5018 n(H20.XRD.58 175 f 0.32 175 + 7 4.3 172.58 179 f 3 3.32 190 rt 5 3.86 159 + 2 3. P I 5 114 GPa. K+) Cordietite Be2SiO4 Phenakite Sheet silicates: KMg3AlSi3010 (FDW Phlogopite 3. scXRD. B-M EOS CAP.15 135+ 10 3. B-M EOS 110 STATIC COMPRESSION Table 1.68 148 + 5 GPa 2. pXRD. XRD. 1inPVfit DAC. scXRD. P I 6 66 GPa.156 DAC.66 . P I 19 156 GPa.8 (fixed from Brillouin data) 4. B-M EOS DAC. P I 30 195 GPa.3Feo. Na+. Bulk Moduli from Static Compression Data (continued) Chemical Formula1 Density Isothermal Bulk @kh3) Modulus dKoT/dp3 (GPa)* Technique and Notes4 Ref. P I 25 108 GPa.P<S 183 GPa. 7 4 (assumed) 4 (assumed) --4 (assume4I) 2+4 -DAC.4 f 4. XRD 150 and PD. scXRD. B-M EOS DAC.65 55. scXRD. scXRD.5 4. scXRD.7 65 GPa. P I 5 63 GPa. B-M EOS BaFeSi4010 Gillespite I (low-pressure .3 f 1 3. B-M EOS CAP.XRD. 1inPVfit Chlorite KAWi3OloO-02 Muscovite 2. P I 4.63 170 + 5 110 2.2. scXRD. B-M EOS DAC. P I 4. IinPVfit KNITTLE 111 Table 1. B-M EOS DAC. PkFe. P I 25 108 GPa.0 f 10 -. B-M EOS DAC and PC.4 DAC.80 61.2 34 GPa. B-M EOS DAC. P I 5 75 GPa. P I 30 195 GPa. B-M EOS DAC. P I 3.96 201 + 8 2. pXRD.7 * 0.DAC.7 169 GPa.0 6.Ah 2. P < 18 49 GPa. P < 5 77 GPa. 1inPVfit DAC.9 I!I 1. P I 3 GPa. P I 25 108 GPa.75 58.5 f 1. scXRD. scXRD. Bulk Moduli from Static Compression Data (continued) Chemical Formula1 Density Isothermal Bulk (Mg/m3) Modulus dKOTfdP3 Technique and Notes4 Ref. pXRD. B-M EOS DAC.5 f 2 4 (assumed) 3. pXRD.P18 183 GPa.A1k(Si. P I 4.6 3 f 0. P I 6 75 GPa.7 65 010 (Fm-02 GPa. B-M EOS DAC. pXRD. scXRD.8 + 1 1. B-M EOS DAC. 55<P<135 GPa.2 + 0.79 130 + 20 3. pXRD.38 111* 1 4.9cPc4. 0 < 71 Pc1. 71 1. T I 800 K.54 157 CaO Lime CaO Lime CaO (high-pressure B2 structure) 4 (assumed) DAC.2 3. B-M EOS DAC. M EOS DAC. dKT/dT)p = 2. P I 95 GPa. M EOS DAC. B-M EOS. B-M EOS DP. B-M EOS BaFeSi4010 Gillespite II (high-pressure ortborhombic stlucture) 3.9 GPa.5 f 0. B-M EOS 74 126 41 . P I 55 GPa.01 212 f 3 MgO Pericke 3. M EOS DP.5 DAC. scXRD. scXRD. pXRD.tetragonal structure) 3.56 178 Wgo. BM EOS 4 (assumed) 4. XRD.38 112 3.7 f 3 x 1O-2 GPa/K DAC.7 * 2 4.0 4 (assumed) 3.6 GPa. pXRD.6Fe0.9 3. P I 30 GPa.56 156 f 9 MgO Per&se 3. scXRD. P < 30 GPa.76 66f3 Oxides and Hydroxides: Bromellite 3.72 62 + 3 4 (assumed) DAC. P I 30 GPa. P I 5 GPa. XRD.40 Magnesiowiistite 4. pXRD. 2 f 0.9 8.6 .0 9.7 (fixed from ultrasonics) 6.? (quartz structure) Gee. B-M EOS 120 112 STATIC COMPRESSION Table 1.4 4.02 zk 0.72 66.8 + 1.45 199 190 (fixed from ultrasonics) 190. Bulk Moduli from Static Compression Data (continued) Chemical Formula1 Density Isothermal Bulk (M8fm3) Modulus WTldP3 (GPa)2 Technique and Notes4 Ref.0 cu20 Cuprite GeO.8 6.3 DAC.3 5.46 144 3.9 5.1 5.46 162 31 17 4.6 It 2.63 22.51 170 41 170 SIO 4.2 17. P I 34 GPa.09 33.5 4.7 + 6.1 5.14 160 f 19 4 (assumed) 5.3 6.15 108.25 97. SKI (high-pressure B2 structure) (high-pm%e PlQI structure) MnO Manganosite MnO Manganosite NiO Bunsem’te coo Cd0 Monteponite PbO Massicot EuO 8.0 3.67 6.4 f 0.? (quartz structure) GeO.0 9.8 + 1.70 90.? (quartz structure) 6. pXRD.2 AI 1. 7 GPa.23 63. P I 13 GPa.8 34.5. P I 30 GPa. XRD. pXRD.23 26. P I 5 GPa.2 AI 0.7 4 (assumed) 2. M EOS DP.91 131 4. pXRD. P 5 30 GPa. M EOS DP. P I60 GPa. scXRD. fit to Hooke’s Law DAC.1 f 0.5 16. M EOS BCAC. P 2 30 GPa.5 GPa. B-M EOS PC. pXRD. M EOS 182 211 211 93 41 32 41 41 2 231 208 225 98 86 KNITTLE 113 Table 1. P $30 GPa. pXRD. EXAFS. XRD. P I 6 GPa.4 4.7 4.5 GPa. B-M EOS DAC. B-M EOS DAC. P I 10 GPa. pXRD.5 4 (assumed) 5. ND. 18<pc60. B-M EOS DAC.23 39. P I 10 GPa. P I 5.9 f 0. B-M EOS DP. pXRD. pXRD. B-M EOS DAC.3 DAC. M EOS DAC. XRD. M EOS DP. 36<P<59 GPa. XRD. P I 2. M EOS DAC. Bulk Moduli from Static Compression Data (continued) Chemical Formula1 Density Isothermal Bulk (Mg/m3) Modulus . 4 f 1. Paratellw-ite (tetragonal structure) 6.24 187 7 (assumed) 4 (assumed) 7 (assumed) 4 (assumed) 4 (assumed) 6.8 (fixed from ultrasonics) 4 (assumed) Sn02 Cassiterite 7.5 WI Uranhite 10.00 TeoZ.myrm3 (GWG Techniquea nd Notes4 Ref.24 Ti02 Rutile 4.96 207 7.8 f 0.26 218 f 2 224 f 2 44.2 4 (assumed) 6.24 258 f 5 265 f 5 216 IL 5 222 k 5 203 197 Ti02 Rutile 4.24 4.6 7 (assumed) 4 (assumed) 5.24 394.! Argutite (rutile structure) Ti02 Ruble 6.2 CeQ2 Cerianite . GeQz Argutite (rutile structure) GeO.9 f 0. B-M EOS DAC.17 220 5 (assumed) DAC. P I 5 GPa. pXRD. B-M EOS DAC.84 304 f 25 GPa 4 (assumed) 4 (assumed) Ru02 6. B-M EOS DAC. B-M EOS DAC. scXRD. B-M EOS DAC. B-M EOS DAC. scXRD. B-M EOS DAC. B-M EOS DAC. 3 lcPc70 GPa. P I 25 GPa. scXRD. scXRD. P I 5 GPa.lfkP<25 GPa.7. pXRD. XRD. B-M EOS CAP. scXRD. P c 9 GPa. B-M EOS DAC.97 270 If: 6 4 (assumed) zfl2 Baahkleyite 5.81 95 f 8 4-5 (assumed) zfi2 (high-pressure orthorhombic-I pha. B-M EOS DAC. pXRD. P I 12 GPa. B-M EOS DAC. P I ? GPa. XRD.13 230 f 10 Ceo2 (high-pressure a-PbC12-type structure) 7. P I 9.6 GPa.M 6. O<P<lO GPa. P I 31 GPa. B-M EOS 225 70 70 178 104 70 119 . pXRD. pXRD. P I 5 GPa. P I 5 GPa. pXRD. 73 269 + 3 5.d (high-pressure marokite-type .20 Fe304 Magnetite 5.39 I75 + 11 AlPG4 Berlinite 2. Hf% 9.68 HfO.14 HfoZ (high-pressure orthorhombic-III Phase) 10.98 HfO.0 + 3.! (high-pressure orthorhombic-II ph=) 10.88 v305 v305 (high pressure phase) 4.20 183 31 10 Mn304 Hausmannite 4.83 137.57 36 4 (assumed) WAW4 Spine1 3.55 Fe304 Magnetite 5.8 Mn3O. Bulk Moduli from Static Compression Data (continued) Chemical Formula1 Density Isothermal Bulk (Mdm3) Modulus dQT/c+ (GPa)2 Technique and Notes4 Ref.? (high-pressure tetragonal phase) 11.20 181 zk 2 Fe304 Magnetite 5.24 45 45 70 110 110 114 STATIC COMPRESSION Table 1.20 155 f 12 Fe304 Magnetite 5. pXRD. B-M EOS KNITI’LE 115 Table 1. pXRD. P 5 4. P 5 ? 212 GPa.5 GPa. scXRD. scXRD.3 183 -+ 5 166. B-M EOS DAC. pXRD.O<P< 16 5. P I 4 55 GPa.5 190 GPa. pXRD. P 5 4 55 GPa. 1 OcP<26 3 09 GPa.42<P<50 109 GPa.7 5 (assumed) 5 (assumed) 5 (assumed) 5 (assumed) --4 (assumed) 4 (assumed) 5.3<P< 16 7.6 + 2.structure) 5. pXRD. Bulk Moduli from Static Compression Data (continued) Chemical Formula1 Density Isothermal Bulk @Wm3) Modulus dQlTldP3 (GPzI)~ .5 154 GPa. B-M EOS DAC. B-M EOS DAC. B-M EOS DAC. B-M EOS DAC. pXRD. B-M EOS DAC. B-M EOS DAC. 1inPVfit DAC. lO<P 163 ~39 GPa.OcP<lO 109 GPa. O<P<lO 163 GPa. P < 32 130 GPa. B-M EOS DAC.33 145 210 475 550 194 III 6 186. scXRD.6. pXRD. B-M EOS DAC. B-M EOS DAC.5 * 15 4 (assumed) 4 (assumed) 4 (assumed) 4 (assumed) DAC. scXRD.5 GPa. 1inPVfit DAC.6 (from ultrasonics) 5. scXRD. B-M EOS DAC. scXRD. P I 8.26cP<42 109 GPa. pXRD. 8 -DAC.4 FeTi03 Iimenite 4. scXRD.97 5. B-M EOS see ref.68 158 f 9 4 (assumed) MnTiOg-III (perovskite structure) 4. pXRD.12 4. P c 0.3 SrTi03 Tausonite 5. P I 10. 1inPVfit DAC.2 (fuced from ultrasonic value) 176 5.. P I 13 GPa.6 (assumed) SrTi03 Tausonite 5.44 170+ 7 8f4 177 + 3 4 (assumed) 168 * 13 5fl MnTi03-I Pyrophanite 4.12 196 f 20 4 (assumed) MgGe03 (ilmenite structure) 187 f 2 4 (assumed) MgGe03 (ilmenite structure) 195 3.5 GPa.3 GPa.9 I!I 0.11 67.63 134 IfI 3 2. B-M EOS . Al2Be04 Chrysoberyl Re03 3.4 GPa.97 4. XRD.88 227 + 4 4 (assumed) MnSn03 (perovskite structure) 6.72 OWQ9TiO3 Ilmenite 4.5 CaTiO3 Perovskite 3.9 2OOf4 -LiNbOg 4. B-M EOS DAC.Technique and Notes4 Ref.54 70 I!I 9 4 (assumed) MnTi03-II (LiNbo3 structure) 4.70 242 f 5 4 (assumed) 6.12 174. P I 6.6 CuGe03 4.98 210 r!z 7 5. DAC. P I 7. P 5 3 GPa.XRD. scXRD.44 Nao. B-M EOS DAC. B-M EOS DAC.25 5.s#‘% (perovskite structure) Nao. pXRD. P 4 20 GPa. B-M EOS DAC. P I 20 GPa. P I 22. P c 28 GPa. B-M EOS DAC.25 . pXRD. M EOS DAC. B-M EOS DAC. pXRD. B-M EOS DAC. Bulk Moduli from Static Compression Data (continued) Chemical Formula1 Density fsotheziufulk dKoT/dp3 @Wm3> (GPa)2 Technique and Notes4 Ref. 1inPVfit 62 23 37 218 57 47 207 123 175 175 175 111 184 17 1 116 STATIC COMPRESSION Table 1. B-M EOS DAC. scXRD. 2. scXRD. 7<P<20 GPa. B-M EOS DAC.61 5.62W03 (perovskite structure) 7.Pl8 GPa. Nao.7oWO3 (perovskite structure) Fe203 Hematite Fe203 Hematite 7. B-M EOS CAP.4 <Pc5 GPa. scXRD.3 GPa.5 GPa. pXRD. pXRD. P I 5 GPa. pXRD. P 5 5 GPa.23 7. 4 4 (assumed) .4 + 2.21 Cr203 Eskolaite 5.98 A1203 Ruby 3.98 A1203 Corundum 3.25 A1203 Ruby A1203 Corundum 3.0 171 + 1 175 f 3 195 f 6 222 f 2 231+5 238 f 4 __-4 (assumed) 4 (assumed) 4 (assumed) 4 (assumed) 5.98 3.98 v203 Karelianite 4.0 f 0.87 Cr203 Eskolaite 5.87 v203 Karelianite 4.21 105 119 91 225 199 f 6 228 + 15 178+4 253 ck 1 226 f 2 239 f 4 257 f 6 254.Fe203 5.25 Hematite Fe203 Hematite 5. B-M EOS DAC. P < 12 GPa. scXRD. scXRD. scXRD.1 4 (assumed) DAC. P I 30 GPa. pXRD. B-M EOS CAP. scXRD. XRD. Bulk Moduli from Static Compression Data (continued) Chemical Formula1 Density Isothermal Bulk Wdm3) Modulus dK0TldP3 Technique and Notes4 Ref. P 2 5 GPa. XRD. B-M EOS CAP. P I 10 GPa. B-M EOS DAC. P 5 5 GPa.8 4 (assumed) 4.3 GPa. B-M EOS DAC. P 5 5 GPa.1 f 0. XRD. P I 12 GPa. B-M EOS 72 72 72 54 212 22 181 171 181 53 40 181 54 181 54 KNITTLE 117 Table 1. scXRD. 1inPVfit DAC. XRD.3 GPa. P I 12 GPa.0.006 4 (assumed) 3. scXRD.3 GPa. 1inPVfit DAC. P < 5. P I 65 GPa. B-M EOS DAC. XRD. scXRD.0 f 1. B-M EOS DAC. P I 30 GPa. B-M EOS CAP.7 4 (assumed) 4 (assumed) 2. P < 5. . pXRD. B-M EOS CAP. B-M EOS DAC. P I 12 GPa. scXRD.9 f 0. B-M EOS DAC.275 IL 0. P < 5. P 5 5 GPa. 1inPVfit DAC. 1inPVfit DAC.6 68 GPa. P I 5 3 GPa.26 25. pXRD.8 + 1. 1inPVfit DAC.6 Ik 1.Feo.3 k 0.86 3. P I 2.9 -? 62.1 DAC.3 f 1.7 (CO312 Ankerite BaC03 Witherite srco3 Strontianite M&03 Rhodocrosite CaC03 Calcite ? 84.(GPa)” KV03 RbV03 csvo3 NaN03 Nitratine MgKW2 Brucite CaWO2 Portlandiie Carbon-Bearing Minerals: Sic Moissonite C~~(CO3)2 Dolomite CaMgo.6 6.2 2.39 54.30 3.67 2. scXRD. P 5 5 3 GPa. B-M EOS 227 f 3 4.5 2. scXRD.5 4.2 31 0.8 5.17 21.8 f 0.6 68 GPa. scXRD.1 f 0. scXRD. B-M EOS dKT/dP= -0.24 37. pXRD. P I 5 3 GPa.018~0003 GPa/K DAC.8 2. P I43 5 GPa .22 2. XRD. scXRD. B-M EOS DAC.7 f 0.73 3.2 4.71 DAC. P I 11 144 GPa.7 -? 42.9 -2.9 AI 0. 1inPVfit DAC. B-M EOS DAC.05 4.7 3. P < 35 50 GPa. P < 2. 7 174 GPa. scXRD.9 4.15 PC. DVM. 2. scXRD.7 4.0 3.85 2.82 94. 189 polyPVfit 118 STATIC COMPRESSION Table 1. l<P 6.5 139 GPa. P 24.13 19.5 139 GPa.5<P 139 4.4 f 0.5 GPa.4 f 0.50 56.82 86. l<P 6. B-M EOS 91 4 (assumed) DAC.0 f 0. P I4.0 7.1 8.1 .1 4.94 4 (assumed) DAC. DVM. B-M EOS 50 * 3 4 (assumed) DAC.5 11. B-M EOS 58 f 5 4 (assumed) DAC.85 Sulfides and Tellurides: HgS Cinnabar HgTe Coloraabite CaS Oldhamite CdS Greenockite CdS Greenockite MnS Alabandite MnS Alabandite NiS (NiAs-type structure) BaS (high pz%re B2smlcture) ZnS Sphalerite ZnS (high-pressure phase) 8. CaC03 Calcite II CaC03 Calcite III CaC03 Cal&e III 2.36 4.7 4.3 2.0 174 GPa.6 3.3 3. PD. P I 1. B-M EOS 71.09 16.3 5. DVM. B-M EOS 95 lk 9 4 (assumed) DAC.99 81.50 156 2~ 10 4.99 72 f 2 4.71 2. Bulk Moduli from Static Compression Data (continued) Chemical Formula1 Density Isothermal Bulk (Mg/m3) Modulus wTm3 Technique and Notes4 Ref.2 + 1.5 7.5 GPa. PD.67 21.3 7.1 4. B-M EOS ---DAC. polyPVfit PC. B-M EOS DAC.5<Pc89 GPa.5 4.7 189 GPa. pXRD. XRD. polyPVfit 189 DAC.8 4 (assumed) 32. pXRD.7<P<4 GPa. XRD. P I 30 GPa. B-M EOS DP. P I 24 GPa. P I 24 GPa. B-M EOS DAC. M EOS DAC.4. M EOS DAC.8 f 0. pXRD.02 76. DVM. 6.4 5.2 (at 1. P I 6.1 + 1. P c 45 GPa.4 GPa) 75. XRD. 1. P I 55 GPa. pXRD. P I 30 GPa. B-M EOS DAC.7 GPa) 84. B-M EOS DAC.0 IL 3.49 4. B-M EOS DAC.72 85.4<P< 1.7 (at 1. pXRD. pXRD.25 55. B-M EOS 210 210 41 192 41 41 140 27 211 211 230 KNI’ITLE 119 Table 1.4 + 0. Bulk Moduli from Static Compression Data (continued) Chemical Formula1 Density Isothehed$dk c-uQTl@3 @Wm3) (GPa)* . 3cP< 5 139 GPa. P I21 GPa. pXRD. P I 30 GPa.l lcPc45 GPa.0 + 8 (at l?GPa) ? 4 (assumed) PC. 1. M EOS DP. PD.5 GPa.5 (assumed) 4. pXRD. B-M EOS DP. 4 * 0.3 29 17.0 145 & 6 92 ck 9 109 3~ 6 141 f 11 76.50 As4S3 Dimorphite 3.Technique and Notes4 Ref.36 AgGaS2 4.11 CuGaS:! Gallite 4.58 CuFe2S3 Cubanite 4.0 55.91 MnS2 Hal&d? 3.4 + 0.46 MnS2 (high-pressure orthorhombic marcasite-type structure) 4. YbS 7.8 118.0 213.2 -- .45 NiS2 (high-pressure metallic phase) 4.7 96+ 10 60 IL 8 4 (assumed) 2.27 SnS* Berrdtite 4.3 + 1.38 CeS 5.02 cos* ‘Cattierite 4.87 NiS2 Vaesite 4.56 us 10.1 9.2 5.1 f 0.5 + 1.93 ErS 8.38 ThS 9.2 5.70 6Of3 82 101. -5.5 4 (assumed) 6. M EOS DAC. pXRD. 10 30 cPc35 GPa.64 LiCl 2. P I 3. P I 8 194 GPa.4 5.46 LiI 4. pXRD. M EOS BA.37 La6NiSi2S 14 4. pXRD. B-M EOS DAC. scXRD. 4<P<ll GPa. 1inPVfit BA. PI 3.6 58 GPa. scXRD. XRD. M EOS DAC. B-M EOS DAC.7 141 GPa. M EOS 120 STATIC COMPRESSION Table 1. B-M eqn DAC. Bulk Moduli from Static Compression Data (continued) Chemical Formula1 Density Isothermal Bulk (Wm3) Modulus dKoT/dp3 (GPa)2 Technique and Notes4 Ref. P I 4 GPa. 1sqPV fit 89 DAC. P I25 204 GPa. 48 1inPVfit BA. pXRD. M EOS 31 DAC.07 LiBr 3. XRD. XRD.64 LiF 2.0 --5. LagCoSi2S 14 4.08 NaF .5 6 DAC.64 LiF 2. P < 5 209 GPa. XRD.37 Halides: LiF 2. o<P<lO 30 GPa. P I 5 64 GPa. B-M EOS see ref. pXRD. P I45 160 GPa. pXRD. P I45 160 GPa. P < 12 GPa. P < 16 209 GPa. 1inPVfit 48 DAC. IinPVtit DAC. XRD. B-M EOS DAC. scXRD.. P < 3 GPa. 0 31.2 46. scXRD.7 65.8 f 7.5 6. P < 5 GPa. 1inPVfit .56 NFIF Villiaumite 2.4 3.9 4.5 4.3 16.4 75.7 3.4 23.56 NaF Villiaumite 2.3 4.7 4 (assumed) 3.16 NaCl Halite 2.7 45. 1inPVfit DAC.5 66. P I 5 GPa.9 f 1.17 79.17 NaCl Halite 2.Villiaumite 2.2 5.9 DAC.4 4.4 + 6.17 NaCl Halite 2.2 23.56 (high-pz%rre.8 4.2 AZ 0.2 5.9 46.6 103 f 19 26.8 45. scXRD.56 NZIF Villiaumite 2.9 4.5 62.5 f 0.9 24. B2 structure) 3.0 Ik 3.5 -_3. P I 4.4 5.0 4. P 5 4.5 GPa. pXRD. P 5 4.2 f 4. XRD.2 NaBr 3. M EOS DP.7 f 1.67 14. B-M EOS PC. P I 9 GPa. M EOS PC. P I 4. B-M EOS 145 145 219 202 41 202 202 202 219 180 202 41 180 41 202 180 KNI’ITLE 121 Table 1. M EOS DP. P I 23 GPa. M EOS DAC. 23<P<60 GPa. PD.CAP. pXRD.5 GPa. P I 4. P I 29 GPa.34 36. B-M EOS DAC.5 GPa.5 GPa.5 f 3. M EOS PC.2 4 (assumed) 3. XRD.8 + 1. M EOS PC. B-M EOS PC. P 5 30 GPa. P I 4. PD. pXRD. NaCl (high-pressure B2 structure) NaBr 2.1 5.20 18.1 NaI 3.5 . PD. XRD. PD. P I 30 GPa. P I 9 GPa. PD.5 GPa.67 15. P 2 30 GPa. XRD. Bulk Moduli from Static Compression Data (continued) Chemical Formula1 Density lsothe.7 f 0. M EOS DAC.3 4. M EOS CAP. B-M EOS DP.1 Nd 3.20 20. M EOS PC. XRD.5 GPa. PD.ilIlulk dqrrm3 @Wm3) Technique and Notes4 Ref. M EOS DAC.1 5.1 * 0.6 4 (assumed) 18. PD.67 15.1 5.5 GPa. P I 4. M EOS CAP.5 GPa.0 5.99 3. PD.3 5. B-M EOS PC. XRD. pXRD. P I 4.P< 9 GPa.Pl 9 GPa.87 37.3 f 2. pXRD. P I 30 GPa.4 2.9 CSI 3. B-M EOS . XRD.2 CsCl 17.99 4.XRD.4 1.51 14. M EOS DAC.3 5.3 5.XRD. P I 56 GPa. B-M EOS CAP. B-M EOS DP.0 4.44 4. P I 39 GPa. 25cP<70 GPa.48 29. M EOS CAP. pXRD.9 DAC. XRD.98 37. P I 30 GPa.1 4. B-M EOS DP.34 28.1 5. B2 structure) KC1 Sylvite KC1 (high-pressure B2 structure) CsCl 2. P I 30 GPa. pXRD.0 f 0.44 4.9 ?I 0.4 13.7 31 0. M EOS DAC.XRD. P I 36 GPa.8 CsCl 18.0 5. B-M EOS FC.99 3.0 2.1 CsBr CsBr 19.Nd 3.2 KF Carobbiite (high-prl:urc.P19 GPa. B-M EOS DP. PC. Bulk Moduli from Static Compression Data (continued) Chemical Formula1 Density Isothermal BuIk @Wm3) Modulus dKoT/dp3 (GPa)2 Technique and Notes4 Ref. B-M EOS DAC. PD.5 GPa. pXRD.088 H2 0. pXRD. P I 4.5 Ik 0.20 12.5 13. P < 53 GPa.088 (4 W D2 0.98 MnF2 3.51 Cd 4.24 BaC12 3.56 6. B-M EOS 80 202 180 41 180 202 219 219 41 26 41 219 202 202 103 101 122 STATIC COMPRESSION Table 1.98 (32 Fluorite SrF2 3.51 AgCl Cerargyrite AgBr Bromyrite CuBr 5. CSI 4. M EOS PC. M EOS DAC.2 . P I 4.73 Group I Elements: H2 0.87 BaC12 (high pressure hexagonal phase) 4.18 4. P < 61 GPa. PD.47 4.5 GPa. PD.6 f 0. P I 5 GPa. P < 9 GPa. pXRD. V EOS PC. PD.06 6.9 4 (assumed) 5. lO<P<50 107 GPa.05 8.45 _+ 0. P 5 4. P I 4. scXRD. B-M EOS DAC.40 I!I 0. P I 2 GPa.172 f 0.8 IL 0. PD.2 + 0.2 36. P I 4 GPa.19 f 0.5 GPa.9 2.0 f 1. XRD. XRD. 202 M EOS DAC.362 AZ 0. 202 M EOS DAC. O<P<lO 107 GPa. B-M 136 EOS V EOS PC. scXRD.2 94 f 3 81.166 (4 K> 0. P I 4. 83 5. P _< 100 137 GPa.71 f 0.0 5.1 69. 1sqPVfit .3 f 2 0. scXRD. PD.2 PC.05 4.2 1. 202 M EOS PC.1 4.5 GPa.5 GPa.4cPc26.41.003 (4 K) 0. PD. B-M EOS 13 PC.5 GPa.46 + 0.35 5.5 69.5 5. 149 M EOS DAC. PD.03 (4 K) 7. B-M EOS DAC.04 (4 K) (4’2) 5.5 GPa. 202 M EOS PC.22 I! 0.004 (4 K) 0.5 38. B-M EOS 70 DAC.2 69. P I 4. 033 3.05 PC. P I 2 GPa.93 f 0.5 17.6 4. P 5 11 GPa. 1sqPVfit see ref. 1sqPVfit DAC.53 Na 0.6 i 0.51 f 0.1 2. PD.003 4.76 IL 0.02 33.90 Group II Elements: Mg 1.79 * 0. .53 Rb 1. B-M EOS KNI'ITLE 123 Table 1.1 8.02 4.50 Ba 3. P I 12 GPa.2 GPa.6 2.006 3.5 11.15 x!z 0. PD. 83 6.86 K 0.54 Ca 1.1 3.10 f 0.301 * 0.. P < 0.07 9.83 If: 0.7 GPa.13 f 0.003 3.53 cs 1.01 3.001 4.4 k 0.86 K 0.15 f 0. P I 2 GPa. P I 2 GPa.50 0.61 3.06 + 0.2 V EOS 11.556 + 0.04 2.963 f 0.7 f 0.99 + 0. 1sqPVfit DAC. XRD. pXRD. 1sqPVfit PC.91 f 0. P I 2 GPa. M EOS PC.03 6. Li 0.47 + 0.35 Lb 0.10 2.01 2. P I 2 GPa. Bulk Moduli from Static Compression Data (continued) Chemical Formula1 Density Isothermal Bulk (Mg/m3) Modulus dQT/cP3 (GPa)2 Technique and Notes4 Ref.54 Sr 2.5cPc14.698 ? 0. PD.4 2.62 1.208 f 0.8 DAC.8 18.1 2.7 2.07 2. scXRD.97 K 0.1 12.60 Ba 3. PD.74 Ca 1.60 Sr 2. B-M EOS PC.86 Rb 1.02 4. B-M EOS PC. PD.06 6. 90 8. P I 4. PD. 12 1sqPVfit PC. 12 1sqPVfit 124 STATIC COMPRESSION Table 1.92 8. 12 1sqPVfit PC.43 8. Bulk Moduli from Static Compression Data (continued) Chemical Formula1 Density fsotheretllfulk dKoTldP3 @Wm3) (GPa>2 Technique and Notes4 Ref.19 7. 201 M EOS PC. P 5 4. P I 4. Transition Metals: Ti V V V Cr Cr Mn co Ni cu cu Zn Y zr zr 4.1sqPVfit 11 10 118 10 99 10 197 11 PC. P I 2 GPa. P I 4. P I 2 GPa. 203 M EOS PC.96 8.5 GPa.10 6.46 .19 7. PD. P 5 2 GPa. PD.46 4.10 7.10 6. 201 M EOS PC. PD.14 4. PD.5 GPa. 203 M EOS PC.5 GPa.5 GPa. PD.96 7.51 6. PD. XRD. P I 4. XRD.0 4.5 GPa. B-M EOS DAC. PD.5 GPa.5 GPa.0 139. XRD.89 (fixed from ultrasonics) 6.4 253. M EOS DAC. PD.5 GPa.5 GPa. PD. P < 42 GPa. M EOS DAC. M EOS pPC. P I 4. B-M EOS PC.05 3.4 2.4 If: 3.8 3.6.0 + 11.49 109.0 193 rt 6 131+ 6 167. M EOS PC. B-M EOS PC. PD. P I 10 GPa.4 154 AZ 5 176 . B-M EOS PC.27 (fixed from ultrasonics) 4 18. P I 4. B-M EOS DAC. M EOS . B-M EOS DAC.2 8. M EOS DAC.9 104 102. P < 4.52 4. P 5 60 GPa. P I 4. P I 40 GPa.5 162.9 4.2 2. PD.4 4.3 4.5 GPa. P I 10 GPa. XRD. P 2 4. XRD. PD. XRD.6 + 7 17.1 PC.5 137.4 59.24 5.8 44.1 190. P I 10 GPa. 50 106.9 La 6.8 4.1 4.6 Ta 205.50 120.1 307 f 11 19.6 f 0.0 f 5.32 (fixed from .20 266.60 16. PD.40 171 f 7 4.PC.7 cd 8. P I 30 GPa.03 Nb 8.1 4.7 f 2.2 14.7 f 0.00 128. Bulk Moduli from Static Compression Data (continued) Chemical Formula1 Density Isothermal Bulk @Wm3) Modulus dQTidP3 Technique and Notes4 Ref.8 & 10.41 144.0 4. (GPajL Nh 8.5 MO 10.65 44.5 GPa.2 Ag 10.4 As 10. B-M EOS PC.0 3.7 3.30 194 + 7 300.50 103 f 5 5.17 24. XRD.60 19.30 19. P I 4.7 4 MO 10. M EOS 203 147 19 203 19 147 198 203 201 201 124 201 203 217 203 KNITTLE 125 Table 1.50 116. PD. M EOS DAC.7 Ta 3. P I 4.5 1.20 267 f 11 Pd 12.7 3.46 (fixed from ultrasonics) 5 Ag 10.40 175.5 GPa.5 Nb 8.80 (fixed from ultrasonics) w W 16.9 5. tllulk dQT/m3 @Wm3) (GPa)2 Technique and Notes4 Ref.5 GPa.3 4. B-M EOS PC.5 + 8. P I 4. P I 10 147 GPa.8 DAC. B-M EOS Group III Elements: Al 2. XRD. P I 20 148 (fixed from GPa.30 166. XRD.31-6.85 . P I 10 147 GPa. XRD. P I 10 124 GPa. P I 20 148 (fixed from GPa.5 GPa.70 71.70 77. XRD. XRD. B-M EOS 126 STATIC COMPRESSION Table 1.30 166.9 4.3 DAC. P 14. XRD. B-M EOS DAC. 203 M EOS DAC.6 7. 201 M EOS TCOA. Au 19. XRD. PD. B-M EOS ultrasonics) Al 2. XRD. P I 4. B-M EOS Au 19. PD.5 GPa.5 GPa. B-M EOS PC.5 GPa.8 5.30 163.1 5. 201 M EOS PC.2 C. P I60 19 GPa. 203 M EOS DAC. B-M EOS Tl 11. PD.31 39.5 GPa.70 72. 201 M EOS DAC. B-M EOS ultrasonics) Au 19.5 GPa. P I 4.6 5.31 38 f 2 5.5 GPa. P 5 4. P c 67 185 GPa. P 5 4. XRD. XRD. B-M EOS DAC.3 DAC. PD. P I 12 193 GPa. B-M EOS DAC. PD. PD. XRD. XRD.5 GPa.16 DAC. Bulk Moduli from Static Compression Data (continued) Chemical Formula1 Density Isothe. B-M EOS In 7. P I25 60 GPa.5 zk 0.5 rf: 0.4 + 2. XRD. 201 M EOS DAC.6 PC.42-5. 201 M EOS In 7. PD.7 4. XRD.3 TCOA. P I 10 147 GPa.43 DAC. PD. XRD. P I 60 19 GPa. 201 M EOS PC. P I 4. P I 10 124 GPa. P I 10 147 GPa. 201 M EOS Al 2. B-M EOS PC. P I 12 193 GPa.ultrasonics) PC. PD. P I 70 81 GPa. P I 4. B-M EOS PC.6 f 10. B-M EOS DAC. P < 4.7 f 3. 1 I!C 1. bOdj-Zltered tetragonal structure) (high-~&sure body-centered cubic strllcture) Pb Pb 2.6 DAC.9 f 0.Group IV Elements: C 3. PD.49 7. XRD.30 7.67 36.25 C60 Fullerite 1. Si Si 2.30 7.8 4 (assumed) DAC. XRD.8 5. scXRD.6 3.0 PC.33 100. M EOS 30.40 .49 7. XRD.09 72 312 3.16 Si (high-pressure hcp phase) (high-~&sure fee phase) Sn Sn Sn Sn (high-pressure. P I 20 44 GPa.7 f 0.0 DAC.30 7. 201 M EOS 444 f 3 1.8 4. Bulk Moduli from Static Compression Data (continued) Chemical Formula1 Density Isothermal Bulk dQ-rm3 @Wm3> Modulus Technique and Notes4 Ref.07 3.9 + 1. B-M EOS KNITI-LE 127 Table 1.25 82 f 2 4. M EOS 33.51 Diamona’ C Graphite 2. P I 14 61 GPa. P I42 6 GPa. body-centered tetragonal structure) (high-~&wrc.22 & 0.91 f 0.33 97.3 DAC. P I 4.49 11.25 C Graphite 2. V EOS 18.7 3.8 f 3 8.9 4.5 GPa. P I 11 226 GPa.05 7. PD. XRD. PD. B-M EOS DAC.87 PC. 9.19 2.40 54.11. P I 4. 79<P<248 GPa.5<P< 121 53. P I 4. Pb (combined hcp and bee high pressure ph=s) 11.5 4.13) x 1O-2 GPa/K DAC. 42<P<79 43 GPa. B-M EOS dK/dT = -4. P I 15 191 GPa. XRD.0 5. P I 9. XRD.4 4. 201 M EOS DAC. 201 M EOS DAC.5 GPa.38 (k 0.5 28 GPa.9 56. B-M EOS DAC. Bulk Moduli from Static Compression Data (continued) Chemical Formula1 Density IsotheGiufulk dKoT/dp3 OWm3) (GPa)2 Technique and Notes4 Ref. 9<P<17 167 GPa.24) x 1O-2 GPa/K DAC.81 76. XRD.2 f 0.3 f 0. PD. XRD.4 GPa.8 43. B-M EOS 43 PC. B-M EOS 128 STATIC COMPRESSION Table 1.5 GPa. B-M EOS DAC. P 5 10. XRD. P I 4.65 f 9. B-M EOS PC. B-M EOS DAC.82 f 2.5 GPa) (at 9?GPa) 56.63 (& 1.0 f 1.04 40. XRD. P I 10 206 GPa. XRD. XRD.9 4.53 31 0.2 4. 39 45cP<120 GPa.8 82. 203 M EOS DAC.04 4.8 50.62 Pb (high-pressureh cp ph=J Pb .2 (at 9. B-M EOS dK/dT = -1.3 121 GPa.5 GPa. 03 N2 1. XRD.08 3.02 39.9+ 0.2 6.23 DAC.98 36 f 2 46 + 4 95 f 5 114 40.08 6.93 3. lO<P< 206 100 GPa. XRD.66 Group V Elements: N2 (cubic &phase) 1.16 DAC.69 2. XRD.57 11.78 .70 (high-Lessme rhombohcdml structure) 2. B-M EOS 2.5 3.97 (high-pres:ure simple cubic structure) (high-presfure simple cubic structure) Sb 3. lOO<P< 206 272 GPa.80 Group VI Elements: 02 (high-pressureE phase indexed as monoclinic) 1. B-M EOS 7.4 29.7 37.10 DAC.(high-pressureb ee phase) 11.21 (hexagonal E-phase) P (orthorhombic) 2.13 2~ 0. 15<P< 134 238 GPa. V EOS 5.32 46.63 29.62 Bi 9. XRD. pXRD.79 Te 6.1 f 0. llcP<60 GPa. 10 <P<32 GPa. M EOS DAC.3 2. 02 (high-pressure Ephase indexed as orthorhombic) S 2.79 Se 4.31 DAC. lO<P<62 177 GPa. O-H method DAC. 16<P<44 GPa.4 DAC. P I 4.5 GPa.8 -- 4.24 1. B-M EOS KNITTLE 129 Table 1.72 4.32 Group VII Elements: .5 GPa.24 Te 6. pXRD. XRD. O<P<5.4. O-H method DAC. XRD. B-M EOS PC. PD.07 (high-preszure phase) Se 2. PD. M EOS DAC. 5. P I 4. XRD.07 S 2.5 GPa.0 f 0.5 lk 0.5 <P<lO GPa. M EOS 155 155 98a 98a 98a 187 203 201 3. 5<P<16 GPa. Bulk Moduli from Static Compression Data (continued) Chemical Formula1 Density Isothermal Bulk (Mg/m3) Modulus dKoTldP3 (GPa)2 Technique and Notes4 Ref.5 3. pXRD. M EOS PC. M EOS DAC.6 2. 2 0. XRD. B-M EOS DAC.2 (assumed) 5. O<P<12 165 GPa.? 4. XRD. O<P<4 164 GPa.94 I2 4. lOcPc62 177 GPa.7 GPa) 7.2 24 + 2 (at 2 GPa) 11.6 f 0.18 GPa: 0. P I 4.5 GPa.8 14.2 (assumed) 6.4 13.3 31 0.7 f 0. 203 M EOS DAC.09 6.5 GPa. P I 4. 203 M EOS PC. M EOS . XRD.0 5.94 Noble Gases: He o-o. P I 4.5 GPa. PD. PD.3 48.3 f 0. PD. 5<P<24 125 GPa.8 8.33 * 0.4 2.5 17. M EOS PC.04 (at 7.2 (assumed) -DAC.23 >0.082 4.7 8.21 16.2 (at 7. XRD.43 (solid) GPa: 0.1 k 0. XRD. 203 M EOS DAC.7 GPa) 5.9 13.085 0. B-M EOS PC.7 8.2 (at 2 GPa) 5. B-M EOS DAC.5 7 5 4. OcPc5 125 GPa.10 I2 4.Cl2 2.9 18.09 Br. 09 3. B-M EOS DAC.23 P-V data tabulated DAC.48 (159 K) (at 159 K) 9. XRD. XRD.23 + 0. B-M EOS PC. P < 24 (0 K) only GPa 1.63 (solid) (4 K) (at 4 K) 3.73 2.18 + 0. B-M EOS see reference 42 130 STATIC COMPRESSION Table 1.86 (4 K) (at 4 K) 1. P I 4. 203 M EOS DAC. PD.5 GPa.34 (4 K) (at 4 K) 2.3 IfI 0. P I 45 46 GPa. P < 45 46 GPa.317 1.41 1.097 1. Bulk Moduli from Static Compression Data (continued) Chemical Formula1 Density Isothermal Bulk (M8Jm3) Modulus dKOT/dP3 (GPa)2 Technique and Notes4 Ref.32 GPa (solid) (0 K) (0 K) Xe 3. XRD.1 (at742K) :i”o (at K) 5.82 1. He (solid) Ne (solid) Ar (solid) 0.65 1.41 3. XRD.48 f 0.78 3.K) 4.24 (0 K) .73 P-V data tabulated DAC.78 5. P I 45 46 GPa. P < 80 (0 K) only GPa 2.03 (at74K. (at 8.58 (110 K) (at 110 K) Xe 3.41 (77 W (at 77 K) Ar (solid) Kr (solid) Kr (solid) 1. XRD.DAC.. 51 (4 K) 1. XRD.2 wt. P I 4.2 1.78 40.5 GPa. XRD. P I 106 7 GPa. 203 M EOS KNITTLE 131 Table 1. PD.8 PC.23 35. 203 M EOS Gd 8. PD. P 5 4. P I 2 GPa.6 3.40 Iron and Iron Alloys: Fe a (lxx) phase Fe a @cc) phase Fe a @cc) phase Fe-5.5 GPa.5 GPa. PD. 1sqPVfit 135 84 9 172 166 9 15 9 Lantbanides: Pr 6.37 Th Pa 11. B-M EOS PC.7<P< 110 GPa. Er Actinides: 9.71 + 2. P I 4. XRD.07 4. P I 32 GPa. P I 32 GPa.23 22. 1sqPVfit DAC.5 4.1 PC. XRD. % Ni a (bee) phase .: K) DAC. PD.(at7i2K) (at 1”.70 15. PD. 1sqPVfit DAC. M EOS PC. P I 2 GPa. Bulk Moduli from Static Compression Data (continued) Chemical Formula1 Density Isothermal Bulk (M8h3) dKoT/dp3 Modulus (GPaj2 Technique and Notes4 Ref.6 PC. PD.31 zk 0.77 30. 203 M EOS Gd 8.5 GPa. P I 4. B-M EOS PC.4. 203 M EOS Nl 7.3 5.0 PC. P I 2 GPa. PD.29 DAC.00 32. B-M EOS DY 8. B-M EOS DAC.3 wt. B-M EOS DAC.36 8.6 5. % Ni a (bed ph= Fe-7.7 f 0.3 + 1.88 156 f7 4.86 175. B-M EOS DP. P I 30 .30 208 + 10 4 (assumed) 8.2 Y!Z0 . PD. XRD. B-M EOS DP.6 6. M EOS DAC.Fe-lo.0 -2.5 f 0. XRD.8 7. XRD.7 7. % Si a @cc) phase Fe-25 wt. P I 30 GPa. P < 4.2 wt. B-M EOS DAC.8 3. M EOS DAC. P I 23 GPa.86 162.30 164.0 157 3. PD.8 f 3.39 175 f 8 4.8 7.9 54.8 6.33 f 0. XRD. B-M EOS PC.58 250. XRD.0 7.5 f 0.5 PC. % Si a (bed ph= Fe-8 wt.5 GPa. XRD. XRD. B-M EOS DAC. P I 23 GPa.5 4. P I 30 GPa. XRD.5 GPa.88 153 f 7 5. % Si a (bed ph= Fe3Si Suessite Fe E (hcp) ph= Fe E (hcp) phase Fe E VW ph= 7.5 GPa.5 + 5 5.7 + 9. XRD.30 192.09 44.35 174. XRD.9 1. P I 4. M EOS DAC. P I 30 GPa.8 7.29 + 0.0 4. PD. P I 4. M EOS PC.86 164f7 4 (assumed) 7.0 4. P I 16 GPa. M EOS DAC.0 8.77 214 +9 3. P 5 30 GPa. P I 38 GPa. P I 30 GPa. 87 (ideal) 5. % Co 8. P I 78 GPa.42 7. % Ni E (hcp) phase Fe-7. % Ni E (hcp) phase Fe-IO. % Co 8.9450 Wiistite Fe0 Wiistite Fe0 Wiistite FelmxO x = 0.76 7. B-M EOS 203 203 24 212 201 196 196 196 188 41 188 41 196 96 132 132 STATIC COMPRESSION Table 1.93 Fe-20 wt. B-M EOS DAC. 0.87 . % Si E (hcp) phase Fe-10 wt. XRD.08 Fe0.41 8.GPa.980 Wiistite Feo. % Co 7.2 wt. 0.98 Fe-40 wt.8Nio.10 Wiistite 5. XRD.055. Feo.3 wt. B-M EOS DAC.07. P < 300 GPa. Bulk Moduli from Static Compression Data (continued) Chemical Formula1 Density Isothermal Bulk (Wm3> Modulus dKoTldP3 (GPa)2 Technique and Notes4 Ref.2 E (hcp) phase Fe-5.2 wt.37 8. P I 23 . XRD. XRD.87 (ideal) 5. P < 260 GPa.87 (ideal) 13.19 FeS Troilite 4.0 154 + 5 239 82 f 7 4. B-M EOS DAC. XRD.09 4 (assumed) 4 (assumed) 4 (assumed) 4 (assumed) 4 (assumed) 4 (assumed) 4 (assumed) 4 (assumed) 4 (assumed) 3. P I 30 GPa. B-M EOS DAC.87 (ideal) 5.9410 Wiistite Fe2U 5. P 5 30 GPa.8 _3.74 171.(ideal) 5.4 4 (assumed) 3 -5 f 4 DAC.2 212 f 15 215 k 25 188 + 14 171 + 6 169+ 6 166 f 6 169 f 10 157 f 10 142 f 10 150 * 3 155 + 5 154.87 (ideal) Fe0 Wiistite Feo. XRD.87 (ideal) 5.95 + 0. B-M EOS DAC.8 zk 2. P 5 3. scXRD. XRD.XRD. B-M EOS DAC. B-M EOS DAC. B-M EOS DAC.5 DP. M EOS DAC. P I 20 GPa. XRD. pXRD. P 5 30 GPa. P I 45 GPa.4 GPa. XRD. XRD. B-M EOS FeS2 Pyrite 4. P I 30 GPa. B-M EOS DAC. 100 (high-pressure MnP.95 148 5.95 143 4 (assumed) DAC. M EOS .3 GPa.77 35 f 4 5+2 DAC. XRD. P I 8.6ec6. B-M type structure) EOS FeS2 Pyrite 4. (GPajL FeS 4. 1inPVfit DP. P I 5 GPa. P < 30 GPa. XRD. B-M EOS 132 196 196 188 162 162 162 221 94 131 122 91 41 213 87 100 KNI’ITLE 133 Table 1. P I 26 GPa. B-M EOS DAC.4 GPa. P I 70 95 GPa.3. XRD. B-M EOS DAC.GPa. Bulk Moduli from Static Compression Data (continued) Chemical Formula1 Density IsothehetuIUlk dQT/dP~ Wtim3) Technique and Notes4 Ref. P I 12 GPa. B-M EOS DAC.PI30 41 GPa. XRD. XRD. XRD. scXRD. P < 30 GPa. scXRD. B-M EOS DAC. B-M EOS DAC. P I 14 GPa. M EOS DAC. XRD.3 -t 3.9 GPa) 1.9 4.0 f 1.46 7.2 58 GPa.40 2.5 NbH0.3cP<36 GPa.6 4. XRD.3 f 1.3 GPa) 4 DAC.29 + 0. P I 4. scXRD.DAC.60 202.46 23.75 6. XRD. 3<P<56 161 GPa.0 5. B-M EOS DAC.3 GPa) 1. P I 34 29 GPa.FeS2 Pyrite 4.86 1.03 4. 152 2. XRD. XRD 82 2. P <50 117 GPa. V EOS Ices: CO2 1.3<Pc36 GPa. B-M EOS 134 STATIC COMPRESSION . XRD.21 121 f 19 5.4 + 0.73 193. of several EOS DAC. B-M EOS DAC.15 f 0. XRD. XRD.5 + 0.2 5. P I 35 19 GPa.56 + 0.9 GPa) (PO = 2. 152 2.3<P<128.87 146. P < 35 19 GPa.1 7. Avg. B-M EOS DAC.1kO.9f0. B-M EOS DAC.5 * 4.48 30.5 4.0 4 0. XRD. Avg.9 DAC. B-M EOS FeH 3.95 157 -.95 215.5 4. P I 34 29 GPa. P < 62 18 GPa.31 f 0.06 22.8 NH3 H2G (cubic phase VII) D2G (cubic phase VII) H2G (cubic phase VII) Hydrides: VHo. of several EOS DAC. XRD.07 -5.9 DAC. B-M EOS DAC.93 + 0.7 (PO = 2.7 f 0. IinPVfit FeS2 Pyrite FeS2 Marcarite 4.5 (PO = 2.0 (PO = 2. 0 f 5.21 Ca-Mg-Na glass ? 130. B-M EOS DAC. B-M EOS DAC. PdH -10.0 f 5. length-change .9 It 1 30. l.5 f 3.0 3. XRD.0 135.28 CuH 6.3 10.2 3. B-M EOS DAC. P I 35 GPa.5 + 2 22. XRD.4 (1773 K) 37.9 f. XRD.3 3.5 GPa.1 DAC.3 47.1 (1773 K) -5. P I 35 GPa. B-M EOS DAC. sink/float measurements.4 2.3 f 0. P I 35 GPa.6 + 6.0 lk 5.38 HOW -5. 4. B-M EOS DAC. XRD.0 248. XRD.Table 1.23 AlH3 -1. P I 35 GPa.9 + 2 72.42 Amorphous Materials: Fe2SiO4 3.7 4. B-M EOS PC.2 -2. XRD. P I 35 GPa.O<Pc5. P I 35 GPa.2 PdD -10.2 CrH -6. B-M EOS DAC.2 f 0. P 5 35 GPa.50 WAW -1. Bulk Moduli from Static Compression Data (continued) Chemical Formula1 Density Isothe~~~u~ wJIw3 @Wm3) (GPa)2 Technique and Notes4 Ref.6 f 0.747 liquid (1773 K) Si02 glass 2. B-M EOS DAC.5 35.0 + 9.8 4.7 f 0.2 f 2 24.7 11. XRD. length-change measurements. 7. I’m sure references were missed.J. Rev. 46. V EOS = Vinet et al. P = pressure in GPa.G. Christy. CAP = cubic-anvil press. DV = direct volume measurement. 1inPVfit = linear fit to the pressure volume data. Clark. TAP = tetrahedral-anvil press. 1. Haines and S. Phys. B-M EOS 19 19 19 19 19 19 19 4 143 143 1 Mineral names are given in italics where applicable. Leonard. 2. This work was supported by NSF and the W. E. A high-pressure x-ray powder diffraction and infrared study of copper germanate. 1991. Secondorder phase transition in PbG and SnO at high pressures: Implications for the lithargemassicot phase transformation. 5183-5 190. Ahrens and an anonymous reviewer for helpful comments. M EOS = Mumgahan equation of state. O-H method = Olinger-Halleck method of reducing P-V data (see reference). TCOA = tungsten carbide opposed anvils. scXRD = single-crystal XRD. BA = Bridgman anvil press. Adams. 3. a high-Tc model. BCAC = boron carbide anvil cell.M. XRD = x-ray diifraction. D. P 110 GPa. 4.M.measurements. J. 1992. 5. PD = piston displacement. for which I apologize in advance. Keck Foundation. J. 1sqPVfit = least sqares fit to the pressure volume data. 6. Leonard.G. D. Christy. EXAFS = extended x-ray absorption fine structure. DP = Drickamer press. 2 All values are at ambient pressure and room temperature except where noted. Institute of Tectonics (Mineral Physics Lab) contribution number 208. Haines and S. Key: DAC = diamond-anvil cell. J.: Condens. 11358-11367.M. Matter. P 110 GPa. A. 3. KlUI’ITLE 135 Acknowledgements. Phys. ND = neutron diffraction. B-M EOS = Birch-Mumgahan equation of state (includes a variety of Birch equations).M. Adams. Adams. A. D. I thank T. 3 A dash implies a linear tit to the pressure-volume data (implies that Km’ = 0) or an unstated Kor’. (“universal”) equation of state. pXRD = powder XRD. MAP = mulianvil press. 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Fischer, Insulator-metal transition and valence instablity in EuO near 130 kbar. Phys. Rev., B., 29, 2350-2352, 1984. Shock Wave Data for Minerals Thomas J. Ahrens and Mary L. Johnson 1. INTRODUCTION Shock compression of the materials of planetary interiors yields data, which upon comparison with density-pressure and density-sound velocity profiles of both terrestrial planetary mantles and cores [4,5,94], as well as density profiles for the interior of the major planets [ 1481, constrain internal composition and temperature. Other important applications of shock wave data and related properties are found in the impact mechanics of terrestrial planets and the solid satellites of the terrestrial and major planets. Significant processes which can, or have been, studied using shock wave data include: (1) the formation of planetary metallic cores during accretion [ 169,192], and (2) the production of a shock-melted “magma ocean” and concurrent impact volatilization versus retention of volatiles during accretion [l]. Also of interest are the shock-induced chemical reactions between meteoritic components (e.g. H20 and Fe: [ 1111). The formation of primitive atmospheres, for example, containing a large fraction of H20 and CO2 is also addressable using shock wave and other thermodynamic data for volatile-bearing minerals (e.g. [110,112]). A related application of both shock compression and isentropic release data for minerals T. J. Ahrens and M. L. Johnson, Seismological Laboratory, 252-21. California Institute of Technology, Pasadena, CA 91125 Present Address: M. L. Johnson, Gemological Institute of America, 1639 Stewart Street, Santa Monica, CA 90404 Mineral Physics and Crystallography A Handbook of Physical Constants AGU Reference Shelf 2 Copyright 1995 by the American Geophysical Union. [ 13,141 is in the mechanics of both the continued bombardment and hence cratering on planetary objects through geologic time [ 1701, as well as the effects of giant impacts on the Earth [183,185]. Finally, recovery and characterization of shock-compressed materials have provided important insights into the nature of shock deformation mechanisms and, in some cases, provided physical data on the nature of either shock-induced phase changes or phase changes which occur upon isentropic release from the high-pressure shock state (e.g., melting) [193,194]. As indicated for the data summary of Table 1, a very large data set exists describing the Hugoniot equation of state of minerals. Whereas some earlier summaries have provided raw shock data [47,121,213], the present summary provides fits to shock wave data. Earlier summaries providing fits to data are given by Al’tshuler et al. [24] and Trunin [203]. Hugoniot data specify the locus of pressure-density (or specific volume) states which can be achieved by a mineral from some initial state with a specified initial density. An analogous summary for rocks, usually described as a mixture of minerals are given in Chapter 34. Three pressure units are commonly in use in the shock wave literature: kilobar (kbar), gigapascal (GPa), and megabar (Mbar). These are equal to 109, lOlo, and 1012 dyne/cm2 respectively, pascals in SI uniis. or 108, 109, and lo1 1 2. SHOCK WAVE EQUATION OF STATE The propagation of a shock wave from a detonating explosive or the shock wave induced upon impact of a flyer plate accelerated,v ia explosiveso r with a gun, result 143 TABLE 1. Shock Wave Equation of State of Minerals and Related Materials of the Solar System E Mineral Formula Sample error Density Co ACo (Mg/m3) (kmhec) (kmhec) lower upper References / S E error AS VP UP Phase* NO. of Temp. Refs. (kndsec) (kmhec) Data 8 x s Gases: AirC Nitrogen plus OxygenC Nitric Oxidee Ammonia’ Argon k Argonf Argon’ ArgonC ArgonC Carbon Dioxide’ Carbon Dioxideh Carbon MonoxideC (mixture) 0.884 1: 1 N2+02 0.945 2.28 __ 1.20 __ 4.317 5.788 4.25 __ 0.85 -_ 5.788 7.379 1.83 0.11 1.26 0.03 2.235 3.785 NO 1.263 3.76 0.06 0.98 0.02 2.01 3.245 NH3 0.715 2.45 0.19 1.34 0.04 1.01 7.566 Ar Ar Ar Ar Ar co2 CO? co 0.0013 0.919 1.026 1.401 0.71 1.04 1.1 1.01 1.28 3.04 0.10 1.041 0.018 0.06 1.36 0.02 0.2 1.45 0.07 0.10 1.79 0.08 0.06 1.58 0.02 0.14 1.09 0.03 1.73 7.81 1.59 4.04 1.42 4.10 0.301 1.35 1.32 3.758 3.65 6.451 1.65 0.88 0.15 2.00 1.9 0.3 1.46 2.5 0.3 1.29 0.56 1.85 1.85 3.60 3.60 4.60 1.173 1.541 0.807 1.54 3.3 0.09 0.4 1.44 1.01 1.585 3.765 4.549 6.264 1.99 0.08 1.56 3.27 -_ 1.21 0.11 0.10 0.07 0.03 0.07 0.03 __ __ 0.010 1.03 3.68 3.68 4.79 1.54 __ 2.59 0.04 1.3 0.3 1.40 0.974 1.692 2.471 2.471 5.608 1.21 0.04 5.608 7.92 2 4 2 2 2 2 2 2 2 3 4 2 3 4 2 4 2 4 2 3 4 7 12 25 6 7 9 24 10 8 7 3 16 3 [1471 Cl791 [I791 [83,121,140]/ u591 [58,71,84] [2141 [2131 [80,121,146,180, 2141 / [80,221] [64,109,121, 1891 [147,178] [233] t1501 TABLE 1. Shock Wave Equation of State of Minerals and Related Materials of the Solar System (continued) Mineral Formula Sample error lower upper References / Density Co ACo S error UP UP Phase* NO. of (Mglm3) (km/set) Udsec) Temp. Refs. AS (kmhec) (kmhec) Data Deuteriumb D2 0.167 Heliuma He 0.123 Hydrogenb H2 0.071 Hydrogena H2 0.089 Methaned W 0.423 Nitrogen k N2 0.0013 Nitrogen c N2 0.811 OxygenC Xenonk Xenong Xe Xe 1.202 0.012 3.006 1.7 0.6 1.29 0.12 3.678 6.263 2.4 0.3 1.17 0.03 6.263 9.014 0.674 0.011 1.366 0.002 2.47 9.39 1.128 1.49 2.38 0.006 0.08 0.19 0.12 1.829 0.013 0 1.105 1.51 0.03 1.105 3.080 1.23 0.03 3.080 9.962 1.80 1.89 0.09 0.801 1.525 2.19 -- 1.35 __ 2.222 3.568 2.87 0.09 1.166 0.014 3.568 8.341 0.38 0.02 1.038 0.004 3.80 8.99 0.94 0.10 1.83 0.09 0 1.57 1.14 0.18 1.59 0.08 1.51 3.26 2.1 0.3 1.26 0.06 3.26 5.23 4.0 0.2 0.88 0.04 5.2 8.63 1.60 0.16 2.35 0.10 0.06 2.06 2.98 0.02 2.91 6.766 0.2 1.5 0.04 1.8 0.4 0.5 i:; 1.58 3.33 3.13 4.11 4.11 7.69 7.69 11.1 1.33 1.7 1.49 1.94 0.16 0.15 0.14 1.45 1.22 1.15 0.74 1.14 0.93 1.33 1.1 1.21 1.09 0.13 0.13 0.05 0.05 0.09 d.05 0.03 1.185 2.51 2.51 2.7 2.7 3.82 3.82 5.502 2 3 2 1 2 4 2 2 4 2 1 2 3 4 2 4 1 3 2 4 1 3 2 4 8 4 [63,1W 3 [ 1451 5 3 10 [63,144,215] 4 [lo91 2 4 10 9 15 24 12 9 16 u501 [571 [60,61,62,121, 146,149,179, 213,233] I [ 149,160,221] [121,146,2231 [71,81,216] [151,212,213] /[161,212] TABLE 1. Shock Wave Equation of State of Minerals and Related Materials of the Solar System (continued) E Sample error lower upper References / 2 Mineral Formula Density Co ACo S error @Q/m3) (kmhec) (krrdsec) AS UP UP Phase* NO. of Temp. Refs. is (krdsec) (kndsec) Data ?? e Elements: Antimony Sb 6.695 3.2 2.62 2.03 -0.8 0.95 1.61 0 0.311 0.311 0.997 0.989 2.699 1 2 4 1 2 4 2 2 2 2 3 4 1 2 3 4 2 2 2 2 2 6 13 Bismuth Bi 9.817 Carbon: Graphite Graphite Graphite Graphite Graphite C 2.205 Diamond Diamond DiamondCl Glassy Carbon 2.17 0.06 -1.0 0.5 0 0.32 1.08 0.06 2.20 0.07 0.32 1.183 2.01 0.04 1.358 0.019 1.183 4.45 0.4665 0.4 1 .ooo 0.79 1.611 1.75 1.794 2.04 4.2 1.9 3.11 4.19 7.5 3.92 1.90 1.2 3.191 7.74 3.51 12.16 1.507 2.72 0.02 0.07 0.3 0.12 0.09 0.14 0.5 0.3 0.07 0.05 0.3 0.06 0.2 0.05 _0.11 0.03 0.04 1.14 0.06 2.114 6.147 1.30 0.03 0.772 5.617 I .42 0105 0.911 4.22 1.66 0.08 0 2.563 0.71 0.18 2.372 3.08 1.49 0.07 3.069 5.42 4.7 0.2 0.012 0.41 1.83 0.04 0.404 1.9 0.21 0.11 1.89 3.316 1.331 0.008 3.119 28.38 1.73 0.05 2 6.5 1.456 0.019 1.364 3.133 1 _- 2 8.5 1.12 0.03 0 5.8 17 30 21 6 36 60 30 19 41 12 77 24 22 5 3 -45 [121,126,217, 2271 [30,68,89,113, 121,131,166, 217,226] [I211 [121] [82,121,133,213, 217) [82,121,133,213, 2171 [58,65,82,121, 126,133,162, 2171 u531 w11 11531 [82,121,1811 TABLE 1. Shock Wave Equation of State of Minerals and Related Materials of the Solar System (continued) Mineral Formula Sample error lower upper References / Density Co ACo S error VP VP Phase* NO. of Temp. Refs. (Mg/m3) (kmhec) (kmhec) AS (kmhec) (kmhec) Data Carbon Foam Carbon Fibers Cobalt Cobalt Cobalt Cobalt Copper Copper Copper Copper Copper Copper C C co co co co cu cu cu cu cu cu 0.435 1.519 2.594 4.15 5.533 8.82 1.909 2.887 3.57 4.475 6.144 7.315 0.85 -0.35 1.18 2.52 -0.15 0.05 0.42 1.38 4.53 4.77 3.98 0.03 0.37 0.03 1.35 0.15 1.9 2.73 0.87 3.2 3.15 1.73 0.09 0.12 0.09 0.10 0.06 0.03 0.04 0.08 -0.02 0.13 0.08 0.08 0.02 __ 0.05 0.3 0.11 0.07 0.4 0.14 0.07 0.88 1.34 1.73 1.14 1.602 0.05 0.02 0.06 0.03 0.017 0.014 0.02 0.02 0.815 2.301 2.119 6.734 0.924 2.361 2.361 5.041 0.651 6.39 1.863 2.11 1.76 1.77 1.285 315 0.315 2.03 0.297 2.33 0.669 0.63 3.04 0 0.96 0 0.56 -1.534 1.04 0.014 0.482 0.63 0.661 26.293 2.05 0.97 0.2 0.482 2.063 2 4 2 4 2 2 2 4 1 2 4 2 2 2 1 2 4 1 2 4 1 .009 0.89 5.615 3.1.87 1.406 1.66 -_ 0.8 0 0.008 6.94 0.02 1.89 2.701 3.2 0 0.25 0.07 3.289 4.327 8.15 17.32 1.361 1.675 -2.944 9.015 0.1 1.77 -0.7 0.4 1.944 2.365 1.534 3.04 0.27 0. 90 3. 134. 136.126. of (Mg/m3) (kmhec) (kmhec) Temp.06 -0.226] [24. AS (kmhec) (kndsec) Data 8 $ Copper cu 7. 209.03 0 0.172.121.136.209] [2091 [56.08 0.136l TABLE 1.90 0.121. Refs.131.209] [24.646 .134.204.29 0.217] [56.06 1.39 2.126. Shock Wave Equation of State of Minerals and Related Materials of the Solar System (continued) ii Sample error lower upper References / Mineral Formula Density Cc ACo S !z error UP UP Phase* NO.209] [56.134. 204.128.121.2 ii 5 15 11 8 10 4 2 17 4 27 28 6 2 14 8 14 39 5 3 18 11211 WI W-Y PO93 PO91 [24.04 0.121. 166.627 0.121.217.128. 2.644 5.933 1.04 0. K 139.08 2.9 1.982 0.328 5.143.8 0.629 3.546 0.90.05 0.10 0.47 -.014 1.217.03 0.49 0.25.121. 166.67 0.09 1.172.27 3.24.76 4.931 3.226 1.04 1.646 3.04 0.07 0 0.08 1.98 0.71 3.03 0.3 1.188 Gold Au 19.126.10 1.27 21.71 3.121.02 0. 30.04 1. 205.100.126.932 5.217.07 1.59 0.2.263 2.73 Iridium Ir 22.460 0. F 2261 v1 17 46 [79.65 4. z 166.2 0.37 0.3 1.359 0.0775 1.121.52 1 2 2 1 2 1 2 2 4 1 2 4 1 3 4 2 4 2 3 18 [56.54 0.62 0.04 1.54 3.93 0.03 1.66 2.19 -1.969 Copper cu 8. s 1361 z 315 [22.633 -0.17 0. 131.04 i. 2131 5 11 [24.006 0 12.127.09 Iron Fe 2.019 0.87 Iodine I2 4.184.81 0.09 1.81 0.28.2261 15 .131.1 Germanium Ge 5.629 0.05 1.54 Iron Fe 3.34 0.03 1.36 0.141.932 4.04 0.52 Indium In 7.29.63 0.15 3.902 1.136.04 0.76 0.0.28 0.134.25 0.56 2.134.4 0.226 3.08 0.9 2.63 1.213.48 -.49 0.05 1.281 2.933 1.95 0.121.8 0.23 0.136. 15 0.217.2 1.85 1.58 9.433 1.10 -1.57 0.08 0.05 3.04 0.03 1.209] 24 [121.166.61 0.783 0. Shock Wave Equation of State of Minerals and Related Materials of the Solar System (continued) Mineral Formula Sample error lower upper References I Density Co ACo S error UP DP Phase* NO.6 0 0.04 1.121.537 1 12 1.569 0.17 0.763 1.04 0.98 0.427 3.569 1. Refs. 2041 TABLE 1.05 3.591 3.213] 6 4 3 [24.07 -1.95 4 IO Iron Fe 6.85 0. (Mg/m3) (kmhec) (kmlsec) AS (kmhec) (kmhec) Data Iron Fe 4.941 1.941 2 4 0.1 -2.25 0.013 1.3 2.249 3 3 2.85 2.7 0.5 0 0.413 4.537 0. 2261 5 38 13 [ 125.972 4.2 0.131 -1.2 [24.134.94 0.38 0.12 3.09 1. of Temp.584 0.03 5.121.88 0.136] 6 8 [204.03 1.08 5. W .7 0.3 0.01 0.36 0.91 0.8 0 0.453 1.4 0.50 21.853 16 42 97 18 Iron-Nickel (see Taenite) (Fe.05 0.59 2 33 2.55 1.2 0.008 4.3 1.48 0.77 0.09 1.1 4 6 3.4 0.3 0.73 1 2 3 4 1 2 4a 4b 2 5 4 15 Iron Fe 7.22 0.573 1.565 4.136.71 0.8 0.302 0.547 Iron Fe 5.09 3. 217.198 Ni 5. of Temp.291 2 2 37 3 [121.17 0. 226]/[6. 172.121.55 1.136.134.01 0.202 Nickel Nickel Nickel Ni 6.209] [31.94 0. Refs.641 3.49 4.016 1. 204.31 __ 1.12 1.04 1.29.05 0. 33. 4. (Mg/m3) (km/set) (km/set) AS (ludsec) (kmkec) Data Lead Pb 4.213] [121.36 -.984 3.51 Lead Pb 11.24 4.15 0.79 Lead Pb 8.71 1.05 0.555 0.162.77 0.213.71 Lead Pb 6.83 0.04 0.67 0.15 1.37 0.54 Nickel Ni 1.33 __ 3.03 1.87 0.644 Nickel Ni 3.43.40 Lead Pb 9.016 2.02 1.08 0.44 0.607 1.126.44 3.136.85 0.03 2.24 1.121] Wll Iron-Silicon (see Suessite) Fe3Si TABLE 1.975 2.172.568 Iron-Silicon Fe7Si 7. 206.275 Ni 4.132.07 0.84 0.71 0.07 0.42 __ 0.25.108.06 1.20.78 0.018 1.134.134.014 .59 0.06 0.05 1.134.462 0. 136. Shock Wave Equation of State of Minerals and Related Materials of the Solar System (continued) Sample error lower upper References I Mineral Formula Density Co ACo S error UP UP Phase* NO.345 Mercury Hg 13.016 0.83 5.Iron-Silicon FelTSi 7.726 0.202.136] [24.015 0. 131.121.30.31.138.1. 166.41 [42. 88 .15 1.31 0.006 0 2.16 1.56 0.32 0.10 __ 1.991 -0.0 0.7 1.73 1.3 0.09 0.14 0.02 0.012 0.4 -0.91 1.73 0.009 0.08 0.213 0.45 1.04 -0.67 3.0.40 0.752 2.46 4.992 2.73 2.26 0.18 4.335 19.06 2.13 __ 0.511 1.23 1.71 1.56 1.16 2.36 2.02 0.09 0.02 0.09 0.07 0.87 __ 0.26 -.46 1.007 0.20 1.47 0.70 1.02 2.58 1.016 0.10 1.05 0.05 0.86 5.15 1.51 0.18 2.306 0.04 2.12 1.045 10.87 1.59 1.73 1.724 0.17 0. 1.05 -0.98 1.02 0.13 0.28 4.91 0.23 1.98 8.03 1.02 0.79 2.05 __ 1.80 0.61 3.019 0.64 0.86 1.62 2 3 4 2 3 4 2 3 4 2 3 2 4 2 4 1 2 2 4 2 2 4 1 2 4 2 5 3 4 3 2 3 6 5 3 3 93 42 .54 0.045 0.80 3.53 4.9 1.606 2.28 3. 16 0.870 Sulfur Taenite (also Kamacite) 3.33.206.00 3.09 0.008 0.63 0. of Temp.40 0.984 12.08 0.825 4.7 0.043 0.346 2.896 Palladium Pd 11.04 0.556 0.83 0.00 1.56 0.49 0.014 1.32 0. Shock Wave Equation of State of Minerals and Related Materials of the Solar System (continued) Mineral Formula Sample error lower upper References / Density Co ACo S error UP UP Phase” NO.441 4.00 0.4 0. Refs.04 0.225] G'W PO91 LW [209] [209] TABLE 1.372 1.18 0.426 4.41 0.369 2.444 Re 20.372 3.018 1.006 2.03 0.04 0.996 Platinum Rhenium Rhenium Re Rhodium Rb Silver Suessite (Fe.2 1.Ni)$i 6.12 2.08 1.53 4.028 20.445 3.30.131.217.28.422 4.8 Ag S (Fe.004 3.28 0.05 -0.587 0. 213.00 0.317 Pt 21. (Mg/m3) (kmlsec) (kmlsec) AS (kmhec) (kmhec) Data Nickel Ni 8. 163.12 1. 121.04 1.2 3 16 19 6 3 15 2 7 3 9 2 [209] ~2091 m91 [2091 [25.76 0.141.83 0.12 0.713 0.0 0.02 1.Ni) .226] [121.05 1.004 4.166.127 4.00 0.803 2.06 0.05 1. 3 0.41 0.897 1.349 0.29 0.5 0.05 0.933 4.63 4a 52 5.56 1.046 3 6 4.635 2 28 4.17 1.17 0 0.04 0.015 2.8 0.17 2.633 2.20 0.21 5.10.495 3.49 2.06 0.354 1 4 3.53 2.31 0.48 0.59 1.83 0.627 2 32 3.5 4b 18 7 13 29 3 7 6 7 4 14 3 3.013 0.57 0.606 1.03 0.635 2.08 1.05 1 0.00 2.25 1.41 3.01 1.149 2.04 -_ .23 0.04 0.18 0.63 7.03 0.02 7.23 3.495 0.63 0.79 4.12 4.32 16 9 5.13 -0.431 2.65 1.300 0.04 I .3 0.470 1.00 0.46 0. 121.166.166.02 0.166.010 0.019 2. 217.90.777 2. i AS UP UP (kndsec) (kmhec) Data R .30. 217.0.121.166. 213.15 0.121.25.132.136.136. 131.09 1.217. 2261 [24.03 0.121.226] [121.59 2 4 2 1 2 4 2 1 2 4 2 4 1 2 2 4 1 2 4 11 41 11 [24. 131.56.166.121.00 1.209.136.723 4. Refs. of Temp.1361 [24.217. Shock Wave Equation of State of Minerals and Related Materials of the Solar System (continued) Mineral Formula Sample error Density Co ACo CJv&/m3) (kndsec) (kmhec) lower upper References / S error Phase* NO. 2171 TABLE 1. 2261 [42.05 0.226] [86.136.136] [121.121] Wll [36.226] [56.05 0.121. 03 2.008 2.05 0.38 1.10 0.00 0.003 4.15 8 4.15 3.9 0.08 3.48 0.00 3.08 5.02 -0.85 8 2.4 5.3 0.29 7.04 3.60 0.0 10.70 0.3 0.03 1.78 0.69 0.3 1.299 Wairauite CoFe 8.029 Moissanite SIC 3.048 3.5 2.3 8.2 0.33 0.98 4.304 0.62 6.013 0.647 5.14 0.07 -0.10 0.5 2.333 Sic 3.35 0.05 0.205 0.122 Tantalum Carbide TaC 12.15 1.038 2.84 0.37 0.15 2.69 0.037 3.11 0.49 0.3 4.08 1.01 3.444 .04 0.s Tin Sn 7.05 0.03 1.43 0.54 2.04 2.64 0.09 0.32 0.14 0.51 Zinc Zn 7.12 0.663 1.15 0.0 -0.02 0.05 1.34 i.304 3.98 0.110 2.05 2.303 0.00 0.02 1.04 1.84 3.138 Carbides: Moissanite Moissanite Sic 2.03 1.6 8.801 3.586 0.13 0.17 0.15 1.00 0.12 0.04 1.62 0.091 Zinc Zn 6.02 1.85 4.57 0.03 0.08 0.63 0.626 Tantalum Carbide TaC 14.6 0. 127.136] . 126.842 0.131.112 2.30.127.535 2.464 0.121. 2261 Wll PI [24.166.887 2. 2261 [121.912 0. 126. 213.76 1 3 2 4 2 3 4 2 4 2 3 4 4 3 4 1 3 4 2 2 3 6 66 33 12 5 10 3 4 39 10 9 10 3 4 2 9 10 20 21 [24.00 0.674 1.112 2.131.1.25.224.678 2.435 3.121.136] Cl211 [ 121.619 1.217.678 1.25.36 0. 217.166.30. (Mglmj) (kmiiec) (kmLec) Data Tungsten Carbidep Tungsten Carbide Sulfides: Sphalerite Pyrrhotite Pyrite Potassium Iron Sulfide Halides: Griceite Griceite Villiaumite Halite WC 15.06 0.74 5.83 NaCl 0.32 8.952 5.25 LiF 1.31 3. Refs.10 NaF 2.14 .03 -0.926 ZnS 3.07 -0.08 0.08 6.23 FeS2 4.11 0.70 3.70 3 3 0.17 0.10 0.Cl211 [121.2.152] TABLE 1.15 7.52 2.97 5.10 0.014 0.10 1.66 4.52 2 3 3.09 0.22 0.933 8.2 0.0 0.868 -0. Shock Wave Equation of State of Minerals and Related Materials of the Solar System (continued) Sample error lower upper References / Mineral Formula Density Co ACo S error uD Utl Phase* No Of Temp.0 -0.792 4.8 5.605 5.638 0.09 0.013 4.S 4.2 0.9 -.59 2.27 LiF 2.8 2.03 0.0 __ 2.63 1.04 1.56 4 2 w361 Fel-.03 0.21 WC 15.10 1.3 KFeS2 2.7 2.4 0. 3 3.14 0.45 3.9 -.989 Halite NaCl 1.5 0.02 0.6 6.47 0.62 2a -0.013 2.027 3.79 4.235 0.6 -.7 4 2 1.66 5.133 5 2 11 [10.635 0.6 3 2 -17.39 1 7 1.19 1.007 0.027 3 1.2131 u 3 4z 3 2 I1211 P 5 TABLE 1.28 0.223 2.552 2b 68 [23183.72 4 3 [191.29 5.58 -.2301 1.942 3.2.00 0.819 2 12 [121.181 3 1.1 __ 6.35 0.56 0.3 __ 2.09 1.66 2 4 [1521 -4.05 0.5.496 5.599 2 10 1. Shock Wave Equation of State of Minerals and Related Materials of the Solar System (continued) E Sample error lower upper References I E Mineral Formula Density Co ACo S error Phase* NO.79 Sylvite KC1 1.0 -.74 0.05 2.1 0.79 3 2 1.15 0.531 -1.2 0.41 Sylvite KC1 1.6 6.54 2. of Temp.4 0.15 4/.427 Halite NaCl 2.2.04 0.02 6.912 0.54 2 -0.017 2.72 0.0.547 1 3 2.03 1.16 1.7 0.49 0.03 2.9 -.5 1.159 Sylvite KC1 0.06 1.6.982 4 1.53 6.01 2 1. tz B 8 4i 8 [54.3 0.62 4.4.08 0.369 1.4 1.361 4 14 [3.0.119 5.986 Potassium Bromide KBr 2.452 10.97 0.018 2.0 0.11 .470 0.02 2 5 3.04 1.127.66 6 -5.163 0.225 1.181 5.186] 1.494 1.13 0.[1 12717.5 -.51 0.05 2 11 -1.0 __ 2.4 6.12 1.59 2 2 [lo61 1.1361 1. (Mg/m3) (kmhec) (kmhec) AS DP UP (kmkec) (kndsec) Data B L Halite NaCl 0.369 1 4 1.8 _.49 0.0.1 -. Refs.42 0.03 0.5 __ 4.747 Cesium Iodide CSI 2. 7 2.6 4b 6 0.05 -0.356 3b 43 1.37 0.42 1.1 11.4 3.17 0.2 1.22 ___ 0.52 4b 8 -1 __ 6.3 0.5 2 2 3.12 1.09 4a 12 5.2 1.12 1.3 i.5 0.50 2.05 4c 3 0.63 0.24 .03 0.02 2.1 1.09 14 -.35 2.71 7.7 2a 113 0.04 0.03 0.38 4 3 0.5 3.57 2.03 0.18 0.05 1.09 0.88 0.3 0.04 1.5 3a 109 1.02 6.9 -.66 7.75 4a 95 1.8 0.25 2.27 0.3 2.66 0.19 2 2 [lo61 1.61 1 4 0.83 0.9 2 13 2.26 4.0 0.3 0.07 0.86 0.5 19 3.862 5.09 10.2 6.88 0.08 3.646 1.43 4.09 1.42 0.60 3.66 0.03 0.00 0.8 11.647 1 28 1.71 2 9 6.09 0.1 3 2 7.16 -0.09 0.09 1.41 4.-0.11 0.18 0.02 2.1.05 4.249 2.04 0.4 2.1.33 0.52 6.56 2 2 ma 2.8 3c 2 1.73 4.02 0.9 -.3 6.4 1.2 1 33 2.324 6. 8 __ 1.32 2 7 3.5 __ 0.3 1. Icei Water.75 4 4 [lo61 [lo61 [32.40 0.69 0. 103.3.05 -1.019 1.045 0.3 4a 13 2. Icei Hz0 0.71 0.67 0.661 8.53 2.8 1.64 0.03 2.18 1.454 3.64 0.70 0.96 5.16 4.3 2.4 0.07 0.22 3. (Mg/m3) (kmhec) (kmhec) AS (krnhec) (kmhec) Data Cesium Iodide CSI 4.05 0.2 __ 0. Ice” H20 0.97 1.17 1.35 H20 0.51 1.11 1.70 0.03 0.71 1.42 Seawater (mixture) 1.56 1.479 32.56 4. 176.66 0.66 0.76 6.03 1.13 1.56 3 2 1.3 9. of Temp.-1.10 0.03 0.09 0.8 __ 0.67 1.95 0.106. 121.67 5.270 0.23 6.04 1.141 0.080 0.19 0.38.1 2.302 0.17 0.19 1.16 1. Shock Wave Equation of State of Minerals and Related Materials of the Solar System (continued) Mineral Formula Sample error lower upper References I Density Co ACo S error VP UP Phase* NO.27 0.6 0.89 0.47 0.5 0.07 1.18 Cryolite Na3 AlFg 2.07 3.43 0.93 0.89 0.38 3.915 Water.008 2.04 4.57 0.019 4.48 0.28 4b 3 Fluorite c*2 3. 1771 [38.85.73 2.04 1.16 1.12 1. 107. 213]/[48.84.57 3.03 2.92 Bromellite Be0 2.60 H20 0.213] /[48. 213]/[48] u541 TABLE 1.2 4.57 6.12 -- .121. Icei Water.03 0.57 3.83 0.75 0.106.9 2.16 0.8 Oxides: Water.23 0.06 1.2 5.4 0.10 0.5 -.05 1.11 1.38 8.858 5.107.858 1.06 0. Refs.06 2.76 0.23 2 6 4.1 __ 1.38 Bromellite Be0 2.44 0.32 1. 1771 [34.22 4.08 1.999 0.73.09 1.106.40 0.00 0.14 __ 3. 116. 2251 / [87. 8 (kn-dsec) (kmkec) Data 75 s Bromellite Be0 2. 2131 /[199.76 1.75. Shock Wave Equation of State of Minerals and Related Materials of the Solar System (continued) 5 Sample error lower upper References / 2 Mineral Formula Density Co ACo S error (Mg/m3) (km/se4 (km/=) AS UP DP Phase* NO.46 1 2 3 4 2 4 2 2 1 2 1 2 4 2 4 2 1 2 5 5 7 9 14 58 25 3 4 6 2 3 [38.11 4.209] [351 U861 [411 [411 [41. of Temp.121.119] & H [2101 [120.25 1.167. 2131217.121] [120.0.797 . 140.356 0. Refs.157.121.799 3.213] TABLE 1.25 3.31 1.577 1.29.4 0.154.11 1.121.1141 [19. 121] 2.2 0.2 0.013 2.71 2 5 [120.49 0.259 3.51 0.05 2.10 0.74 5.56 0.11 1.939 1. 127.332 0.13 0.5 1.84 0.28 2.04 1. 2131 10.7 0.Bromellite Be0 2.3 1.825 2 4 7.11 1.2 .509 2.6 0.042 0.5 0.801 3.967 2 25 6.06 1.12 1.6 0. of @Q/m+ (kmlsec) (kmlsec) Temp.06 1.3 3.213] 7.8 0.761 Corundum A1203 3.17 3.16 0.332 1 2 6.12 1.77 2.0 0.6Fe0.3 0.09 0.92 4.094 3.3 1.62 4 11 [37.285 4.77 0.88 0.7 0.11 -0.13 0.00 0.56.47.3 0.094 1 4 6.652 2b 9 5.10 1.083 3.91 0.67 0.324 Wiistite Fet-.886 Bromellite Be0 2.84 0.843 Corundum A1203 3.7 0.558 4 5 [1211 TABLE 1.989 Periclase MU 2.317 0.842 Periclase MgO 3.583 Magnesiowiistite Mgo.10 0.397 Magnesiowiistite Mm.4 0.2 1.06 2.705 1.74 2 12 8.01 3 3 2.63 0.14 1.75 0.40 4.362 2 13 [56.29 4 4 P191 4.628 4.42 0.33 3b 4 4.00 Periclase MgO 3.44 4 16 [2.08 -0.822 4 4 [120.121.1 0.90 5. Refs.02 1.16 1.22 0.662 Corundum A1203 3.28 2 3 5.882 2.3 0.169 2.13 1.528 2 6 [56.79 0.33 6.121.9 -.14 1.92 Corundum A1203 3.1271 3.05 0.53 0.218] /[197] 4.07 0.8 0.00 5.14 0.10 1.29 0.12 1.285 4.121.07 1.75 Ilmenite Fe+2Ti03 4.07 1.18 -1.56 0.Peo.78 0.127] 3.05 3.979 Corundum Hematite A1203 a-Fe203 4.O 5.2 1.217. Shock Wave Equation of State of Minerals and Related Materials of the Solar System (continued) Mineral Formula Sample error lower upper References / Density Co ACo S error UP UP Phase* NO.749 3.83 0.619 5.33 4.16 0.3 __ 5.629 1.939 1 4 9.127] 6.557 2a 8 4.152.705 3a 3 4.721 4 3 [121] 3.96 0.2 1.50 0.980 9. AS (kmlsec) tkmlsec) Data Lime CaO 3.65 0.825 2.7 __ 0.36 0:03 2.27 0.10 0.04 1.76.55 2.08 1.3 2.121.80 0.81 0.56.10 1.368 1.548 Wiistite FetmxO 5.49 0.53 0.08 0.0.78 0.047 Ihnenite Fe+2Ti03 4.191 Lime CaO 2.01 3.07 0.2 2.169 3b 4 4.3 3.083 2 6 6.07 0.355 Periclase W@ 3.626 1.78 4 3 [120.7 1.5 0.5 0.3 2 3 6.32 0.06 1.121.121.61 0.787 7.76 0.18 1. 408 0.05 0.009 4.85 1.61 0.18 0.15 1.39 0.92 3.555 3.08 0.009 3.3 0.294 3.37 5.706 6.04 2.18 0.11 1.05 0.43 5.85 7.15 0.46 0.02 0.20 0.12 1.17 0.0 0.16 1.008 1.56 1.04 0.621 8.125 -1.04 0.1.07 0.08 __ 1.83 0.8 __ 2.73 2.12 1.28 0.18 5.06 0.35 0.5 0.17 0.72 0.07 2.46 0.73 6.282 10.082 3 4 2 3 4 2 3 4 1 2 1 2 2 0 1 2 2 2 3 4 2 3 4 2 3 4 5 9 [971 I[501 .4 -_ 2.00 1.064 9.03 0.03 7.5 11.2 0.8 1.52 0.055 3.011 0.28 6.51 3.18 -4.40 0.46 17.034 2.51 2.71 0.92 1.07 0.6 -14 3 0.04 1.06 0.86 0.626 2.766 1.02 8.07 1.04 0.3.294 4.3 -.07 0.1 0.22 1.13 1.00 0.07 -- __ 0.017 0.33 0.033 0.11 1.84 0.18 1.706 3.652 6.36 0.4 -.9 0.59 0.54 0.09 6.3 0.1.716 0.898 2.035 0.007 1.93 0.3 0.097 2.766 2.955 0.414 4.62 11.05 0.011 1.38 1.18 0.37 0.38 1.898 7.979 8.435 0. 200. 0 Mineral Formula Sample error Density Co ACo (Mg/m3) Odsec) Ndsec) lower upper References I is S error Phase* NO.1 -4.59 2.121.33 3.46 2.127.121. 2171 3 2 2 w361 3 5 12 [121.016 0.3 2 4 [971 2 3 2 [2321 [9.10 0.117 Ru tile TiO2 4.318 3. 127.86 Barium Titanate Spine1 Spine1 BaTi 5.11 1.127.655 2.533 1.334 .121.35 3. Refs.35 6. 122.447 Spine1 Mg&Q 3.127] 7 15 5 10 [47.0 _. 2171 6 [I521 41 6 52 [9.93 0.991 3.121.48 0. Shock Wave Equation of State of Minerals and Related Materials of the Solar System (continued) t0.07 Magnetite Fe+2Fe+32 04 5.3 0.217] 4 [I521 6 4 10 [47.7 -.1.63 0.127] TABLE 1.21 Rutile TiO2 4.417 5.245 Pyrolusite Mnf402 4.10 2.78.77 0.24 4.47.07 0.24 5.5 0.0 0. of Temp.3 0.122. AS DP DP (kmhec) (kmhec) Data H a Perovskite CaTi 3.25 0.26 2.14 1.514 Magnetite Fe+2Fe+3204 5.3.42 6. 05 0.05 1.07 1.72 4.676 0.0 0.8 1.36 0.07 1.27 0.08 2.3 7.1.3 0.311 5.0.42 0.43 0.06 -0.1.5 1.14 2.9 -.987 2.44 2.96 0.16 2.16 1.11 1.04 0.2 0.68 0.2 10.63 7.23 0.6 1.858 2.2 __ -0.146 5.1 0.0 1.24 0.07 0.06 0.06 0.4 1.191 0.48 0.688 8.07 0.05 0.03 1.1 _.00 0.468 2.52 5.786 4.14 1.975 6.15 0.3 2.3 0.09 0.07 0.03 0.21 3.263 2 3 4 1 2 4 4 2 3 4 2 3 4 3 4 2 3 4 3 4 1 3 4 2 5 3 2 [WI 23 55 .07 0.08 0.1.507 7.00 0.17 0.348 7.1 0.13 -_ 0.04 0.03 0.5 -4.14 0.987 8.60 0.4 2.12 1.2 0.00 0.61 6.858 3.321 2.769 3.06 2.3 _.688 2.23 0.8 0.479 4.134 3.61 1.26 0.35 0.44 5.2 -_ 1.311 3.5 3.11 0.757 2.19 1.727 3.10 0.56 0. 127. of (Mg/m3) (kmhec) (kmhec) Temp.121.121.9 9 [66. 2171 3 5 8 [121.47.127] 2 3 [ml 2 10 15 [47. 127. AS (kn-dsec) (kmlsec) Data Cassiterite Argutite Baddeleyite Baddeleyite Cerianite Uraninite Uraninite Uraninite Uraninite Hydroxides: Brucite Brucite Goethite SnO2 GeO.127. Refs.694 .Th)02 uo2 uo2 uo2 uo2 W&W2 Mg@Hh a-Fe+30(0H) 6.127] 2 10 13 [47. Shock Wave Equation of State of Minerals and Related Materials of the Solar System (continued) Sample error lower References I Mineral upper Formula Density Co ACo S error UP UP Phase* NO. 2171 3 5 [351 11 8 8 [11.213] r z [ 121.? 302 m2 (Ce+4.217] TABLE 1.121.217] 16 [47.121.123.130.121. 383 5.12 0.11 5.77 2.509 1.4 0.75 0.4 1.2 9.99 3.35 1.06 1.7 0.6 1.22 2.43 0.91 .12 -0.277 4.133 10.02 1.96 2.2 -0.04 0.9 -.833 2.2.9 5.4 5.51 0.0 4.866 2.03 2.20 0.3.111 4.347 4.41 3.866 2.20 0.26 0.501 0.57 0.512 6.9 -0.05 5.4 0.7 0.06 0.11 0.6 0.6.37 4.4 -.02 1.07 0.814 1.68 0.25 3.22 0.501 2.29 0.06 0.59 1.05 -0.11 -0.07 0.10 0.42 0.337 6.41 0.0 4.82 0.27 1.15 1.2 3.08 0.17 4.306 3.88 1.15 0.3 0. 34 0.983 2.493 1.47 __ 0.88 3.04 0.8 1.22 0.41 2.07 0.6 -_ 1.34 2.03 0.52 1.8 -.11 0.256 1.571 0.05 0.17 0.13 0.61 0.983 1.886 3.1.622 1.70 0.03 0.025 3.17 2.16 0.568 1.994 0.99 1.2.622 2.286 1.17 2.355 4.925 5.855 1.03 0.02 1.51 1 2 4 2 2 4 2 4 2 1 2 4 4 4 4 2 4 2 2 3 4 7 4 3 6 2 8 4 4 .51 1.03 0.437 0.06 1.079 1.00 0.00 1.52 3. 08 6.28 Borates: Sassolite HNh 1.828 Aragonite Sulfates: Mascagnite CaCO3 2.217] W’l w11 ~241 w11 w11 11211 Wll WI w361 [@I WI TABLE 1.701 Magnesite MgCOs 2.30 5. Refs. Shock Wave Equation of State of Minerals and Related Materials of the Solar System (continued) E Sample error lower upper References I 2 Mineral Formula Density Co ACo S error Phase* NO. of Temp.9 3. (Mg/m3) kdsec) (kmhec) AS UP VP (kndsec) (kmhec) Data $ s Carbonates: Calcite CaCO3 2.7 3 12 6 18 15 15 6 2 13 2 3 2 [47.375 GYPSY CaSO4 l 2H20 2.471 6.975 Dolomite C~g(CO3)2 2.71 6.82 0.73 Anhydrite CaS04 2.77 .3 Mascagnite (NHdSh 1.928 (w4)2so4 1.2 5.97 Barite BaS04 4.121.6 Mascagnite WLh‘Q 1. 05 ii.12 0.72 .2 0.4 0.11 _-2.14 0.3 2.12 0.4 0.32 1.12 0.6 0.495 1.1.5 1.78 0.06 __ 0.8 1.15 0.1 1.83 1.12 0.09 0.49 2.87 1.80 5.2 1.167 0.15 2.11 0.5 0.03 0.013 0.7 2.12 0.0 0.81 1.54 2.16 0.60 4.10 0.04 0.09 0.96 3.03 0.81 3.2 2.21 1.09 1.34 0.2 0.3 4.10 0.081 0.26 0.24 3.11 3.61 1.435 0.03 0.11 _0.83 2.17 -0.15 5.5 0.75 1.2 0.71 3.6 3.36 1.28 1.8 1.28 1.845 1.10 0.14 0. 254 1.15 4.86 __ 0.08 1.06 1.03 1.42 3.73 1.29 1.5 1.79 0.102] / .55 1.71 1.69 1.03 1.114 1 2 2 2 4 2 2 4 2 2 2 3 4 2 3 4 2 3 4 2 4 24 6 6 5 19 12 8 11 8 5 3 2 4 2 3 5 3 2 5 3 2 [11.85 __ 1.0.639 2.9 0.95 0.16 0.85 2.15 0.27 0.13 __ 0.639 1.55 1.72 1.69 3.54 1.72 2.64 1.21.85 1.15 2.04 0. 10 1.651 Porous Quartz Porous Quartz Porous Quartz Porous Quartz Porous Quartz Silicic Acid Silicic Acid Silicic Acid SiO2 1.86 0.80 6.61 0.877 SiO2 2.07 0.5 0.75 0.48 0.15 SiO2 1.13 3.66 Ob 29 8.48 3a 6 1.40 0.52 5.62 2.4 1.07 -0.03 1.849 3.55 HaSi 0.11 -1.863 2 2 2 3 4 .55 9.08 0. Refs.55 0.018 4.43 0.9 0.815 lb 12 5.2 0.27 0.65 0.04 1.508 1.43 SiO2 1.6 0.20 0.82 0.81 Oa 16 5.03 2.32 0.356 0.28 1.02 0.33 0.0 2.46 4.10 3.0 0.2 1.295 0.2 0.589 0.25 0.42 0.44 0.766 SiO2 1.12 4.285 0.151 H4Si04 0.19 0.76 4 10 0.019 0.12 0.14 0.51 4.48 1.34 0. Shock Wave Equation of State of Minerals and Related Materials of the Solar System (continued) Mineral Formula Sample error lower upper References / Density Co ACo S error UP UP Phase* NO.13 2.41 0.03 1.55 2 24 8.12 1.803 2. (Mg/m3) (kndsec) (kmlsec) AS (kmhec) (kndsec) Data Silica Polymorphs: Quartz SiO2 2.213] WOI [991 [991 [991 11861 [W [1861 / [1031 Wll TABLE 1.03 0.374 -0.184.13 0.08 0.815 la 16 6.84 3b 3 4.05 2.09 0.09 1.84 26.HO31 uo21 [102.65 H4Si04 0.283 0.80 0.05 1.374 4.29 0. of Temp.011 2. 2 4 2 4 4 4 2 4 15 0.87 0.09 1.38 0.03 0.65 5.08 30 4 3 9 11 15 3.02 0.7 -0.09 0.16 0.84 0.2 1.67 0.11 0.03 0.03 0.04 1.27 0.08 0.799 3.199 0.06 3.199 6.52 0.02 3.51 6.59 11 16 5 -0.01 1.275 0.006 2.94 5.93 6 0.78 0.33 I.05 0.02 0.68 1.98 1.261 0.009 1.98 5.71 3 7 [11,17,27,37,47, 72,118,121,127, 129,155,162, 208,217, 2221 / [118,165] [188,2071 [ 188,207] [188,2071 Wll [121,207] w31 Cl881 [1881 TABLE 1. Shock Wave Equation of State of Minerals and Related Materials of the Solar System (continued) 5 Sample error lower upper References I E Mineral Formula Density Co ACo S error Pha.se* NO. of (Mg/m3) (krnhec) (km/set) UP UP Temp. Refs. AS (kmhec) (km/set) Data i * Aerogel SiO2’ 0.172 Aerogel Aerogel Aerogel SiO2’ 0.55 CristobaLite Coesite SiO2 1.15 Coesite SiO2 2.40 Coesite SiO2 2.92 Silicates: Forsterite MgzSiO4 3.059 Forsterite Mg2SiO4 3.212 SiO2’ 0.295 SiO2’ 0.40 SiO2 2.13 0.21 0.07 1.01 0.02 1.494 4.01 2 6 -0.44 0.10 1.164 0.018 4.01 7.401 4 8 0.21 0.03 1.11 0.05 0.302 0.765 2 3 0.29 0.03 1.089 0.010 1.456 3.63 2 4 -0.214 0.013 1.224 0.003 3.63 6.37 4 4 0.590 0.15 0.006 0.04 0.09 0.05 0.945 0.006 0.335 1.43 2 3 1.219 0.008 1.43 6.1 4 7 2.29 1.23 1.01 1.545 0.96 1.99 2 3 1.99 4.66 4 6 0.44 1.44 0.06 0.014 0.02 1.2 4.59 2 5 WI 3.4 4.3 1.42 0.19 1.33 2.05 2 3 0.97 _- 2.05 4.16 3 2 5.833 6.92 2.6 5.71 3.0 10.5 6.8 7.21 4.6 0.07 0.3 _0.010 0.02 0.4 0.07 0.3 0.2 0.3 0.10 0.3 0.902 0.009 0.66 1.48 2 3 0.168 0.011 1.48 2.86 3 3 1.68 0.12 2.86 4.05 4 3 0.64 0.03 0.825 2.771 2 6 1.65 0.10 2.771 3.626 4 6 -3.8 0.4 0.18 0.797 la 16 1.4 0.6 0.00 0.795 lb 12 0.55 0.06 0.749 2.449 2 20 1.51 0.08 2.433 4.61 4 20 i*s [88,188] u [1581 5 B 3 mm z F [1881 v) W61 W61 W61 [47,121,127, 2171 [91,121,127,201, 229]/ [ 1651 TABLE 1. Shock Wave Equation of State of Minerals and Related Materials of the Solar System (continued) Mineral Formula Sample error lower upper References / Density Co ACo S error UP DP Phase* NO. of (Mg/m+ (kmkec) (kmhec) Temp. Refs. AS (kmhec) (kndsec) Data Olivine (MgFehSiO4; (Wow FeO.o8hsio4 FezSiO4 3.264 Fayalite 4.245 Zircon ZrSiO4 4.549 Almandine Grossular Mullite Mullite (Feo.79Mgo.14 @x04Mwod3 M2Si3012 Ca3A12Si3012 A6Si2013 M6Si2013 4.181 3.45 2.668 3.154 Kyanite A12SiOs 2.921 Kyanite A12Si05 Andalusite A12Si05 3.645 3.074 8.84 0.13 -0.99 0.18 0.272 1.43 5.6 _- 1.3 -_ 1.43 2.19 8.1 -- 0.15 _- 2.19 2.8 6.0 0.3 0.88 0.08 2.8 4.81 6.17 0.09 0.23 0.06 0.702 1.967 3.78 0.13 1.42 0.05 1.967 3.483 8.58 0.18 -1.3 0.4 0.11 1.07 7.14 0.05 0.02 0.03 1.07 2.52 -1.6 0.9 3.5 0.3 2.52 2.84 -10 -- 50 -- 0.29 0.32 5.92 0.07 1.39 0.08 0.45 1.14 3.0 -- 3.6 _- 1.29 1.46 6.4 0.3 1.33 0.16 1.46 1.8 8.3 0.17 0.47 0.10 0.18 3.04 2.30 0.13 1.65 0.04 1.935 4.077 8.732 0.016 -0.394 0.015 0.717 1.479 8.29 0.04 -0.09 0.02 1.479 2.003 6.5 -- 0.78 -_ 2.003 3.311 7.45 0.06 -0.58 0.07 0.608 1.157 7.02 0.09 -0.19 0.05 1.157 2.359 2.2 0.3 1.85 0.10 2.359 3.383 7.8 3.9 -1.7 __ 0.15 0.4 0.6 _- 1.537 2.745 2.0 0.6 2.745 3.22 5.3 6.92 2.9 1.9 -- 0.00 1.1 0.31 0.07 1.1 2.817 1.80 0.13 2.817 3.73 1 2 3 4 2 4 1 3 2 1 2 3 4 2 2 1 3 4 1 3 4 2 4 2 3 4 [15,121] 10 10 [47,121,127, 2171 7 4 4 w41 1771 16 WI 13 [121,127] 3 3 2 r1211 3 5 5 2 3 WI WI 2 12 8 [47,121,217] TABLE 1. Shock Wave Equation of State of Minerals and Related Materials of the Solar System (continued) !i Sample error lower upper References I z Mineral Formula Density Co ACo S error Phase* NO. of Temp. Refs. (Mg/m3> (kmlsec) (km/s@ AS UP UP (kmhec) (kmisec) Data 8 s Sillimanite Topaz Tourmaline Muscovite Serpentine Pyroxenes: Enstatite Enstatite Enstatite A12Si05 3.127 6.97 7.8 3.8 0.15 0.2 0.2 0.09 0.4 0.68 -0.10 1.57 Al2SiO4- (F,OHh Ca(Al,Fe,Mg)s& (B%hSi6018 WV94 KAlz(Si+l)010 @KF)2 3.53 8.10 5.3 0.054 1.722 3.179 6.2 -- 1.2 8.1 0.4 0.05 3.6 1.62 2.835 MggSi205 (OH)4 2.621 3.3 6.2 4.5 5.30 6.5 3.8 0.5 0.3 _0.2 0.15 0.4 0.5 1.95 0.7 1.29 0.90 0.20 1.34 Ma- 2.714 2.70 0.11 1.31 &06 Mgz- 2.814 si206 2.74 0.14 2.04 6.8 __ -0.1 3.64 0.16 1.43 Ma- 3.067 &06 8.11 0.18 -1.5 4.98 0.13 1.18 7.4 0.4 -0.1 3.7 0.3 1.54 0.16 0.11 0.08 0.08 0.15 F.15 0.16 0.16 __ 0.06 0.11 0.18 0.12 0.04 0.09 -- 0.05 0.4 0.09 0.2 0.07 0.00 1.262 1.068 2.461 2.461 3.611 0.052 1.75 1.75 3.59 0.824 1.555 1.555 2.888 2.888 3.695 1.27 2.44 2.44 3.18 3.18 4.74 0.43 1 2.025 1.719 2.561 2.658 5.427 1.901 3.258 0.746 1.956 1.956 2.128 2.128 3.946 0.224 0.60 0.456 2.126 1.817 2.349 2.349 4.54 1 3 4 1 2 1 3 4 2 3 4 2 3 4 2 2 3 4 1 2 3 4 5 3 is 8 10 [47,121,217] ? 2 4 6 M51 2 7 8 r1211 10 10 16 [47,121,211, 2171 5 [47,121,217] 5 2 9 [121,127] 6 19 6 22 [8,121,127,231] I [117,165] TABLE 1. Shock Wave Equation of State of Minerals and Related Materials of the Solar System (continued) Mineral Formula Sample error lower upper References I Density Co ACo S error UP UP Phase* No. of Temp. Refs. (Mg/m3) (kmkec) (kmhec) AS (kndsec) (kmhec) Data Diopside caMgsi206 3.264 4.9 -- 8.4 _- 0.201 0.289 1 2 7.14 0.03 0.626 0.018 0.289 1.85 2 4 6.1 0.2 1.16 0.06 1.85 4.7 4 4 Molten Diopside” Hedenbergite cmgsi206 2.61 3.30 0.12 1.44 0.08 0.73 2.24 2 5 CaFe+2Si206 3.42 1.41 2 2 2.42 3 2 3.62 4 3 Augite, also Salite 3.435 2.8 __ 2.8 __ 1.1 6.1 __ 0.47 __ 1.41 3.30 0.05 1.620 0.018 2.42 6.25 0.11 0.85 0.08 0.935 6.6 0.8 0.6 0.4 1.87 4.6 1.0 1.4 0.3 2.44 1.87 2 5 2.48 3 8 3.82 4 5 Jadeite 00.80Nwd(M&m%.29 Tio.dWO.ZOsil. 85)06 , cmgO.82%. 18si206 Na(A1 Fe+3)f&6 3.335 6.41 0.06 1.30 0.08 0.00 1.005 2a 3 6.57 0.10 1.09 0.07 0.986 1.94 2b 8 7.44 0.12 0.64 0.04 1.94 3.434 4 8 Spodumene LiAlSiz@j 3.14 7.123 6.4 4.0 0.007 0.51 1.56 0.43 1.45 2 3 1.45 2.37 3 2 2.37 3.76 4 3 Wollastonite CaSiOg 2.82 Wollastonite CaSiO3 2.822 2.4 1.65 0.018 6.09 0.08 4.06 4 6 6.3 4.1 -0.15 1.07 1.799 3 5 2.778 4 4 Wollastonite CaSiO3 2.89 5.3 6.826 4.52 0.019 u.3 0.3 0.2 0.2 -0.004 0.15 1.14 -0.156 0.15 0.09 _0.003 1.34 0.94 1.799 0.00 1.195 1.933 1.195 2 2 1.933 3 3 3.282 4 5 [18,196,213] / U981 w331 w51 [18,196,213] [47,121,135, 2171 W'l W'l Wll 1.03 0.06 [I211 TABLE 1. Shock Wave Equation of State of Minerals and Related Materials of me Solar System (continued) Mineral Formula Sample error lower upper References I Density Co ACo S error UP VP Phase* NO. of Temp. Refs. @Q/m3) (kmlsec) (krdsec) AS (kmhec) (kmhec) Data Tremolite Beryl Feldspars: Orthoclase, Microcline Oligoclase Anorthite Molten AnorthiteO (NaAlSi308)75(c~12Si208h9.5 - (KAlSi308h.5 h&%208 CaAl2Si208 2.769 3.17 0.16 1.45 0.04 2.911 4.338 2.55 2.85 0.14 1.27 0.09 0.91 2.37 Nepheline (Na,K)AlSi04 2.63 Glasses: Argutite Glass Quartz Glass (fused quartz) Quartz Glass Cad%Fe+2)5%022(OHh Be3Al&G18 KAlSi308 Ge02 SiO2 SiO2 2.901 2.68 2.561 2.635 3.655 0.145 1.15 5.20 0.14 0.91 0.07 1.15 2.82 3.2 0.8 1.6 0.2 2.78 3.94 8.83 0.10 0.05 0.04 1.4 4.12 2.7 __ 1.6 .- 4.12 6.1 7.70 0.11 -1.1 0.2 0.188 1.21 6.14 0.19 0.21 0.11 1.21 2.41 3.1 0.2 1.39 0.05 2.41 6.27 7.6 0.3 -1.5 1.2 0.195 0.3 4.76 5.7 2.22 0.08 iO8 0.88 0.09 0.52 1.25 0.1 -- 1.25 1.62 1.67 0.02 2.57 3.94 3.6 -- -0.3 -- 0.32 1.35 0.80 0.06 1.79 0.02 1.35 4.46 1.8 -1.2 -0.3 0.2 0.36 -- 1.789 2.309 1.67 0.05 2.309 6.507 0.09 1.51 0.06 3.07 5.21 2 4 2 4 1 2 4 1 2 2 2 3 4 1 2 2 4 4 9 5 4 2 14 4 4 13 3 6 3 2 4 2 7 2 10 4 [1871 [I871 [12,16,186] Cl61 [96] / [173,174] WI 11871 WI Wll UW TABLE 1. Shock Wave Equation of State of Minerals and Related Materials of the Solar System (continued) Sample error lower upper References / Mineral Formula Density Co ACo S error UP DP Phase* NO. of Temp. Refs. C&@/n& (kmhec) (kmhec) AS (kn-hec) (kndsec) Data Quartz Glass SiO2 2.2 0.4 0.5 1.73 0.12 3.61 4.84 4 6 [911 Quartz Glass SiO2 2.204 5.83 0.03 -2.33 0.17 0.00 0.306 1 7 5.264 0.019 -0.114 0.014 0.306 2.106 3 32 3.40 0.08 0.78 0.03 2.063 2.742 2 20 0.80 0.08 1.70 0.02 2.703 5.175 4a 61 3.1 0.2 1.196 0.014 5.175 23.64 4b 3 [101,118,121, 127,129,163, 217,222] / [104,117,118, 175, 1771 Anorthite Glass CaA12Si2Og Pyrex (and soda-lime glass) (SiO2h@203)12(A1203)2.5KW0.4 (WDo.3(Na20)4&20)1(As203)0.6' Soda-Copper Silicate Glass WO2)72.2(cuoh2.4FW3 14(A1203)0.5W3)0.45@W)o.l(Fe203)0.08S 2.692 6.1 6.43 1.8 2.307 5.26 3.96 0.6 2.48 3.10 0.04 1.28 0.08 0.37 0.71 2 3 3.623 0.012 0.531 0.009 0.71 1.55 3 3 1.5 0.2 1.95 0.11 1.51 2.57 4 5 [671 0.3 -0.2 0.4 0.45 0.14 0.01 0.07 1.179 0.3 1.77 0.07 2.731 0.14 -0.37 0.15 0.4 0.12 0.57 0.06 1.444 0.3 1.92 0.09 2.397 1.179 2.731 4.698 1.444 2.397 4.43 15 33 4 15 WI 1 [511 15 24 4 11 [95,121,122, 1361 TABLE 1. Shock Wave Equation of State of Minerals and Related Materials of the Solar System (continued) i Sample error lower upper References I 3 Mineral Formula Density (Mg/m3) (2ec) (ki2C) S error UP UP Phase* No. of Temp. Refs. g 07 6.661 1.3 0.04 0.44 6.19 1.AS (kdsec) (kndsec) Data 7z Q Lunar Glass Other Standards: Aluminum: 1100.985 1.03 0.13 2.10 .825 4 6 [71 : 2 3 .09 0.15 0.10 0.8 0. Russian alloys Aluminum: 1100.955 0.707 Aluminum Al’ 2024 Aluminum Al’ 2024 s 1.18 2.09 0.11 0.02 2 4 s -1.09 5.62 0.8 3.00 2.d K 3 cF 1. Russian alloys Aluminum: 1100.885 Al’ 2.0 2.2 0.8 0.345 Al’ 1.11 0.20 0.39 0.3 0.19 0.2 0.682 1. Russian alloys GiO2)40(TQh(A1203)l l(FeOhOW) lo(CaO>l ls Al’ 1.12 0.4 0.71 2.01 0.0 2. 2 1.0.197 2. 2131 [24.155.162. 163.15 0. 1361 TABLE 1.5 __ 0.739 4.983 2.1 0.0.20 0.4 0.08 0.012 0. Shock Wave Equation of State of Minerals and Related Materials of the Solar System (continued) Mineral Formula Sample error lower upper References I Density Co ACo S error UP UP Phase* NO.28.26.012 2. of Temp.142.00 0.94 30.00 1.6 1.77 1.1 -. 2281 [56.559 4.567 0.224 3.566 4.921 2.142.105.27.38 0. 139.03 2.0 -.849 1 2 1.121.39 0.323 3.2 1.134.54 0.9 __ 0. (Mg/m3) (km/set) (km/set) AS (kmlsec) (kmlsec) Data Aluminum 2024 Al’ 2.3 2.19 0.04 3.324 0.981 4.0 0.14 0.181 0.0 1.190.134.00 0.16 1.70 6.988 0.213.76 2.19 0. Refs.51 0.121.019 5.06 2.064 4 17 Aluminum 2024 Al’ 2.11 0.22 0. 1361 [56.926 2.06 0.361 2 4 2 4 1 2 4 1 2 4 1 2 4 10 4 12 6 10 59 27 3 9 15 3 9 15 [105.124 2 7 3.566 1.2131 [39.724 1 2 .01 0.30 0.526 1.05 1.739 1.121.27 -0.0.849 2. 105.012 1.3 0.07 2.24 0.45.2 0.58 0.428 6.115.6 6.47 0.00 0. 3.678 4.07 0.03 0.005 0.10 2.217.166.914 Molybdenum MO 4.62 5.02 0. Shock Wave Equation of State of Minerals and Related Materials of the Solar System (continued) Sample error lower upper References / Mineral Formula Density Co ACo S error DP UP Phase* NO.05 2 5 -0.013 0.41 Tantalum Ta 6.16 0.18 0.247 0.90 0.761 2 5 4.93 Tungsten W 18.12 0.04 1.54 0.131.73 0.473 0.6 1.19 Tantalum Ta 10.39 0.134.13 2 4 1.02 1. 1361 [56. 217.538 0.761 3.86 Tungsten W 19.40 0.06 1.51 2 10 -0.414 2 5 [I371 [56.10 1.15 0.121.240 4.141.91 2 61 Molybdenum* MO 10.6 19. 163.03 3.82 Tantalum Ta 5.91 0.538 1.59 Molybdenum MO 8.13 Tungsten W 13.67 2. 2261 TABLE 1.66 2 8 0.79 0.649 Tungsten Tungsten Tungsten W 6.56.209] [24.05 . 136.25 2 13 0.65 6.012 0.00 5.74.208 4.788 5.98 0.04 0.24 0.224. (Mg/m3) (krn/sec) (km/set) AS (kndsec) (kmhec) Data Tantalum Ta 2.06 0.18 1.108.121.435 Molybdenum MO 5.07 1.5 0.99 4b 3 5.03 0.01 2 4 -0.121.208 -0.04 0.04 0.92 Tantalum Ta 16.226] I [1651 I2091 GO91 PO91 12091 PO91 [2091 [ 162.72 Molybdenum MO 2.20 Tantalum Ta 8.064 W 4.00 20.25 0.14 0.8 1.3 5.817 4 17 Aluminum 2024 Al’ 2.162.126.213.005 0. 1361 [56.008 0. of Temp. 121.134.36 0.45 0.55 Molybdenum MO 2.47 1. Refs.02 5.6 4a 6 3.3 2 10 0.30 0.06 1.305 0.724 1.277 Molybdenum MO 1. 136.166.735 0.18 2.05 1.87 0.6 W 5.03 1.011 1.134.04 2.13 2.962 2 325 Molybdenum MO 1.09 1.90.356 0.57 Tungsten W 8.163.03 1.94 0.146 Molybdenum MO 10.654 6.10 1. 5 0.451 0.49 0.08 0.4 -3.52 1.010 0.86 2 4 1.54 0.17 -0.09 0.013 -0.05 1.07 6.09 0.07 -1.654 2.03 0.03 0.04 1.15 1.66 1.-0.010 1.649 1.8 3.14 0.06 4.018 0.05 0.64 0.08 0.04 1.23 1.03 0.028 0.23 0.07 0.37 0.17 3.8 0.37 1.04 0.49 2.03 0.10 0.10 0.61 2.02 0.31 -0.601 2.06 0.43 0.19 0.94 -0.04 0.25 -0.33 -0.010 2.00 5.7 1.01 0.26 1.012 1.7 0.14 0.011 1.04 2.306 4 3 3 .012 0.891 1.43 3. 04 0.0. 136.003 0. AS (kndsec) (krdsec) Data Lexan (polycarbon.05 0.4 2.584 1.08 0.12 1.63 3 2 3.007 -ii04 0.68 3 2 2. of Temp.04 1.91 1.84 2.131.2.685 16.121. Shock Wave Equation of State of Minerals and Related Materials of the Solar System (continued) Mineral Formula Sample error Density Co ACo (Mg/m3) (km/set) (km/set) lower upper References/ S error DP UP Phase* NO.9 -.75 0.209] ~091 G'O91 [Qll [100.226] PO91 [204.139.121.35 2 3 2. Refs.295 2.63 3.54 1.04 0.53 0.5 3 6 3 5 31 1.17 2 6 1. 163.1 2 40 [209] PO91 PO91 m91 PO91 [24.56 3.35 2.00 0.193 1.21 1.1.76 3.97 0.204 0.38 2.45 4.108.02 0.685 4a 4 3.721 2 4 1.54 2 6 2.217] TABLE 1.885 4 3 1.4 -.57 1.03 _0.86. 136.302 0.68 3.00 15.421 1 2 .76 2 4 2. 217.166.095 2 8 PO91 1.06 0.51 4b 3 1. momentum. In Table 1.27 0.Eo = 0’1 + Po>(l/po-l/p 1)/2 = l/2 (ul . and us given in the Table are for the final (highest pressure) shock state. P.64 6. compressed gas m Starting temperature 1673K n Starting temperature 1773K O Starting temperature 1923 K P 5% cobalt q raw data not provided r with impurities s composition in weight percent oxides 172 SHOCK WAVE DATA FOR MINERALS FIG.121] Notes: *Phases: 1) Elastic shock. stress in the wave propagation direction is specified by Eq.70 0.421 2. as indicated in Fig. In actuality. and (3) is given in Duvall and Fowles [70]. . into material that is at rest at density p. a Starting temperature5 K b Starting temperature 20K c Starting temperature7 5-86K d Starting temperature 1llK e Starting temperature 122K f Starting temperature1 48K.. A detailed derivation of Eqs. and internal energy per unit mass and. in nearly steady waves in materials. u. Profile of a steady shock wave. In the case of multiple shocks.12 0. 4) High pressure phase. For steady waves a shock velocity Us with respect to the laboratory frame can be defined. and E are density. It should be understood that in this section pressure is used in place of stress in the indicated wave propagation direction. rise time Q. (2). 1.38 0. and internal energy density EI.05 3. compressedg as g Starting temperature 165K h Starting temperature 196K i Starting temperature 203-230K j Starting temperature 258-263K k Starting temperature2 73-298K t Starting temperature 3OOK.92 4 19 [55. Equation (3) also indicates that the material achieves an increase in internal energy (per unit mass) which is exactly equal to the kinetic energy per unit mass.551 0.04 2. and energy across a shock front can then be expressed as P 1 = PO (Us-uo)/(Us-u1) (1) Pl . Conservation of mass. propagating with velocity IJ. the values of U. the subscripts o and 1 refer to the state in front of and behind the shock front. shock pressure. particle velocity. Equations (l)-(3) are often called the Rankine-Hugoniot equations.6 0.ud2 (3) where p. (2). 1.019 0. 2) Low pressure phase.53 2 32 4.379 3. imparting a particle velocity uI pressure Pl. 3) Mixed region.a@ 2. shock velocity and particle velocity are designated as Us and ul. respectively.PO = Po(Ul-uo)Q-Js-uo) (2) El . Thus for a single shock UP = u 1.651 3 21 2. and internal energy density E.2 1.101. (l).03 1.47 0. version 3. The initial and final states are connected by a straight line called a Rayleigh line (Fig. which is the locus of shock states. usually Us. 1).136]. 6-21. it is possible to follow.V 1) is achieved via a a shock front. FIG. The analogous bulk modulus along the Hugoniot is: KH = -V @P/?lv)~. by a shock process. the actual isothermal or isentropic curve to achieve a state on the isotherm or isentrope. The key assumption underpinning the validity of Eqs. Pressure-volume compression curves. A shock. 114 for errors in slopes. = l/p0 and V = l/p. The Hugoniot state (Pl . For isentrope and isotherm. In the case of the isotherm and isentrope.q. (l)-(3). WA 1993) program and the least-square fits to the shock wave data with standard errors were derived by using the LINEST function. however. (I)(3) is that the shock wave is steady.] W) The Us-Up data for a wide range of minerals are given in Table 1. Thus successive states along the Hugoniot curve cannot be achieved. The Hugoniot curve itself then just represents the locus of final shock states corresponding to a given initial state. the Rankine-Hugoniot equations involve six variables (Us. Here Co is the shock velocity at infinitesimally small particle velocity. are constant (see Fig. the thermodynamic path is a straight line to point PI. thus. as a thermodynamic path. etc. 6-22. ~1. (Redmond. uI. The equations employed for line slopes and intercepts are identical to those given in Bevington [46] (Eq.Vl. the thermodynamic path coincides with the locus of states. in relation to other thermodynamic paths. measuring three.Eo. or the ambient pressure bulk sound velocity which is given by . (11) The isentrope and the Hugoniot and isentropic bulk modulus arc related via: KS = KH + KH 77 / (I. El . one from another. AHRENS AND JOHNSON 173 Hugoniot data for minerals and other condensed media may be described over varying ranges of pressure and density in terms of a linear relation of shock and particle velocity in Table 1. in the pressure-volume plant. whereas for shock. is short compared to the characteristic time for which the high pressure. and po. Here V.In the simplest case.59. 2. Upon driving a shock of pressure Pl into a material. ul. This table was assembled using the Microsoft Excel. and Pl. po. so that the rise time zs. p. 2). and a recent book [40]. and Eq.. a final shock state is achieved which is described by Eqs. or Hugoniot.0. on the Hugoniot curve. It has long been recognized that the kinematic parameters measured in shock wave experiments Us and Up can empirically be described in regions where a substantial phase change in the material does not occur as: us=co+sup As further discussed in several review articles on shock compression [22. p. density. p. state is different. 2. when a single shock state is achieved via a shock front. determines the shock state variables p 1. This shock state is shown in Fig. 114 for errors in intercepts). 104. and Pl). Eq. 6-9. El-E. jP. (9) which upon differentiation yield the isentropic bulk modulus Because the Grtineisen ratio relates the isentropic pressure. PH . Co2 (1 + (4S-1) 17 + . 1 to yield: Yo = a KT V&v = a KsVo/Cp. from the form of Eq.[PH-ps] [Y+l-q. V [93. this is given by: Y= V (JPlJE)v = yo (V/Vo)q. is the Griineisen parameter under standard pressure and temperatures and is given by Thus. Upon substituting Eq. Ps. KT is the isothermal bulk modulus and Cp and Cv are the specific heat at constant pressure and volume.) (10) The shock-velocity particle relation of Table 1 can be used to calculate the shock pressure when two objects impact. vo Ps = po co2 (11 + 2sTl2 + . KS = p. based on the data of Table 1.17l])by an expression analogous to Eq. PH = PO co2 “‘1 /(1-sqj2 where (7) where a is the the thermal expansion coefficient. . If (A) the flyer plate and (B) the target are known and expressed in the form of Eq. A pressure-volume relation can be obtained by combining Eq. 7 is often called the “shock wave equation of state” since it defines a curve in the pressure-volume plane. 3). KS = -V (dP/dV)s in the absence of strength effect (see Sect. 2. We note that the Ps and PH can be related by assuming the MieGriineisen relation Tl=l -v/vo=up/LJs.PS = + @H-E& if y is independent of temperature. 4 into Eq. PH.98. where q=dLnyld!nVandq’=denqJtin PH = PoUp (Co + S Up) (6) y. 3 and Es is given by The isentropic pressure can be written (e. (8) Eq. where EH = El-E0 is given by Eq... o-Gl+-*)I Here we assume a volume dependence of the Gruneisen parameter co=dGG (5) where KS is the isentropic bulk modulus.g. and Hugoniot bulk modulus.. (7). 6. 7 as a series Es = . to the Hugoniot pressure. 6 with Eq.*.dV. the particle velocity (13) V (14) (15) (16) (17) 174 SHOCK WAVE DATA FOR MINERALS ul and pressure Pl of the shock state produced upon impact of a flyer plate at velocity ufp on a stationary . KS. and bulk modulus. shock pressure is given as the sum of a linear and quadratic term in particle velocity. it is a key equation of state parameter. and denoting the shock pressure as PH. KH.). ul = (-b . Sketch of shock velocity-particle relation (a) and corresponding pressure-volume Hugoniot curves (b) for a mineral which undergoes dynamic yielding and a phase change.4ac)/2a. Viscoelastic polymeric media generally do not display the HEL phenomenon.o--b . Virtually all nonporous minerals and rocks in which dynamic compression has beens tudied demonstratep henomenonr elated to dynamic yielding.PoB SB.target may be calculated from the solution of the equation equatingt he shock pressuresin the flyer and driver plate: PoA (“fp . SHOCK-INDUCED DYNAMIC YIELDING’ AND PHASE TRANSITIONS Both dynamic yielding and phase transitions give rise to multiple shock wave profiles when pressure or particle velocity versus time is recorded. massive. elements.“l)(CoA + SA (qp . 0: compression up to the Hugoniot Elastic Limit mm 1: transition via dynamic yielding to a quasihydrostatic state 2: low pressure state 3: mixed region . for reasons such as crystallographic control of compression at low pressures Particle Velocity Volume FIG. Moreover. microscopic rearrangement taking place at the shock front. As shown in Fig. (19 where a = s A PoA . (la That is. 3. (20) b = CoA PoA . 3a.ul)) = PoB ul (COB + SB ul). the Hugoniot elastic limit.PoB COB> (21) and C= “fp (GoA PoA + SA PoA “fp). the shock velocity of the HEL state remains nearly constant and for non-porous media is usually equal to the longitudinal elastic wave velocity. (22) 3. is defined as the maximum shock pressure a material may be subjected to without permanent.2SA PoA “fp . 3 for the case of dynamic yielding and phase transition and the available shock wave data are separately fit to linear relations in these regimes in Table 1. The dynamic yield point under shock compression. and organic materials demonstrate shock-induced phase changes. For some minerals there are more than four regimes indicated. in which materials transform from finite elastic strain states to states in which irreversible deformation has occurred. or HEL. most minerals and a large number of compounds. We denote five regimes in Fig. 90.. T. The second term is obtained by using the definition of the Gruneisen parameter (Eq. the Mie-Gruneisen equation of state. ‘X45-C559. can be used to describe shock and postshock temperatures. High-pressure electrical behavior and equation REFERENCES initial volume. Va = Vo. 1 Abe. ionization and debonding in non-metallic Pluids. 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Akimoto.. and L. 463-476. Funtikov. A. I. pp. edited by M... Sevast’yanov.. F. 34. M. J. Dynamic . R. Izv. 203 Trunin. Compression of porous quartz by strong shock waves. Medvedev.. 1963. Phys. Eurrh Phys. and their equation of state in the terapascal pressure range. Takei. H..6943-6953. Popov. Shock compression of porous iron. C. Sov. 208 Trunin. Syono. B. 35. M. V. H. W. Goto. A. and L. Popov. Earth Phys. Shaner. 356-361. Res.-I.199O. G. Moiseyev. V. 202 Taylor. v. M. 68. R. 550-552. Podurets. N. 1972.. Compressibility of various substances at high shock pressures: an overview. . 364-311. Hugoniot overtake sound-velocity measurements on CsI. 204 Tnmin. G. and J. G. Swenson. Podurets. L. 1986. B. 2. Y. A. Sov. JETP. and B. F. Appl. Shock compression measurements of single-crystal forsterite in the pressure range 15-93 GPa. Brown. 205 Trunin. J. 201 Syono. JETP.7924-7935.102-106. Phys.. Simakov. N. B. Izv. AHRENS AND JOHNSON 183 1977. Moiseev. Relative compressibility of copper. 34. Sato. A. Podurets. B. Manghnani and S. R. and Y. R. 22. N. 1971. F. and A. and tungsten.. W. R. G. V. New York. Simakov. 206 Trunin. J. A. Podurets. Dynamic compressibility of acqueous solutions of salts. V.. H. Van Thiel. Urlin. M. 69. Mol. 18011-18027. Compressibility of porous metals in shock waves. Shock compression of deuterium to 900 kbar. E. G. UCRL-50801. A. M. D. G. M. Medvedev. Geophys. Int. J.1966. 1991. V. Mikhailova. F. JETP. J. C. Shock compression of argon. 9. R. J. Res. Zhernokleto. N. L. A. M. S.595- 605. Machalov. Ahrens. 19. A.. J.compressibility of quartz and quartzite at high pressure. and B. F... Mitchell. 210 211 212 213 214 215 216 217 218 219 Trunin. Alder. 1966. UCRL- . Shock wave equation of state of serpentine to 150 GPa: Implications of the occurrence of water in the Earth’s lower mantle. High Pressure Research. Izv. Phys. Chern. 755 pp. 44. and 0. (editor). T. Tyburczy. Phys. Earth Planet.. 427435. 8. Vol.. Kuznetsov.. Sov. M. V. Simakov. Shutov. R.. Lawrence Radiation Laboratory (Livermore). Mitchell. T.. Compendium of Shock Wave Data. and Y. and B.. V. Rev. 1. E. Simakov. A. 1. and V. 1974. Rogozkin.. Alder. B. 96. Liquid xenon study under shock and quasi-isentropic compression. M. University of California. M. 8-12. Van Thiel. Izv. Phys. Duffy. Kusubov. 51-77. Earth Phys. B. M. A. Shock compression of liquid hydrogen. 1971. Phys. and M. W. Earth Physics. Compendium of Shock Wave Data. 23. B. K. L. 209 Trunin. V.580-588. van Thiel. Hord. Fedorov. 1987. Wilbarger.992-995. S. B. Lawrence Livermore Laboratory. A. I. D’Addario. 1977. F. Lange. van Thiel. and B. J. Gust.. and A.. 1056-1065. C. D.. Barrett.1989.. van Thiel.1992. Y. N. J. Sutulov. Phys. Len. Gogulya. 24.. 87.. Walsh. Rice. L. J. pp. 8. The equation of state of Mg0. M. 220 221 222 223 224 225 226 227 228 229 230 Geophys. Doklady. J. McQueen. I. S. Ahrens. Res. Geophys. Geophys.. A.40 to 200 GPa. 26. September 1967. 97. Shock wave .. Res. H. Sov. Vizgirda. J. 1982.. 1544-1556.1967.922-937. J. 9. 1967. 33.. 1962. Rev. Wackerle. J. Dolgoborodov.50108. 1957. 4629.. Hugoniot equation of state of periclase to 200 GPa. Wackerle.. J. Warnes. and T. H.. Appl. J. Yarger. Dynamic compression of liquids from measurements of strong shock waves.I. and Y. L. Phys. C. and F. Phys. Rev. 1981. J. Walsh. M. 127-130. H.6 Feo. M. 729-732. G. W. Investigation of a shock-induced phase transition in antimony. M. and M. 1957. New York.. Voskoboinikov.. Chem. Shock-wave equation of state for high-density oxygen in.. Walsh. Paris. J. Vassiliou. 1980. R. M. and T. Gordon and Breach. Lett. 196-216. Vassiliou. 375-376. . Equation of state of metals from shock wave measurements. 1955. Res.. and T.. Phys. R. Phys. 38. and J.. in Behavior of Dense Media under High Dynamic Pressures Symposium. S. M. 1968. Temperatures of shock compression of liquid nitrogen and argon. 85. Shock-wave compression of quartz.. F. Christian. Shock compression of aragonite and implications for the equation of state of carbonates. M.. H. J.. and R. M. Warnes. J. Appl. Jamieson. Equation of state of metals. Seitz. H. 1982. R. 815-823. J. 4747-4758. Phys. 108.4631.. Rice.. Ahrens. Shock-wave compressions of twenty-seven metals. Ahrens. Ahrens.. P. Geophys. 7. J. Section 1-12). . J. and T. Watt. electronic and ionic transport processes. etc. P. 1988. Tyburczy and D. Ahrens.. Res. 53. Res. Res. inclusions. 233 Zubarev. 7836-7844. and Y. Tyburczy and Diana K. 34-36. defect chemistry. Department of Geology. Geophys. Electrical properties of materials can be very sensitive to minor chemical impurities and variations. Geophys. twins.. Watt. Fisler Electrical properties of minerals and melts aid in the interpretation of geophysical probes of the Earth’s internal electrical structure (see Hermance. J. Because minor element content and experimental conditions are known to strongly affect electrical properties. rather than as a source of absolute values. We have striven to provide reliable data for each material listed. This article contains data and references to electrical properties of minerals and related materials at elevated temperature and 1 bar pressure. in specimens can complicate the achievement of reliable measurements. J. Electrical Properties of Minerals and Melts James A.. K. electrical conductivities and dielectric constants of minerals are used in studies of mineral structure. Phys. 816-819. A. 421. Sov. Res. V. Arizona State University. Shock compression of singlecrystal forsterite. Telegin. In addition. wiistite. 91. 89. The data and tables presented here may best be used as a guide to the literature or as a source of references from J. 1088. Fukuoka. 1983. for a given electrical property of a mineral. Cracks and other macroscopic defects. 88.. we have attempted. Shock-wave equation of state of 15.compression of three polynuclear aromatic compounds. T. 7495-7503.. and T.. Fisler. As a result. Shock compression of 231 Watt. J. Syono. Geophys. and T. J. Shock wave equations of state using mixed-phase regime data. and microscopic defects such as voids. 184 SHOCK WAVE DATA FOR MINERALS J. 1984.. to tabulate both chemical composition and experimental conditions for each measurement. P. where possible. Tempe. there are often a wide range of reported values. Let. Ahrens. J. and other mineral physical properties. J. Doklady. AZ 85287-1404 Mineral Physics and Crystallography A Handbook of Physical Constants AGU Reference Shelf 2 which to start a search.. enstatite. J. 1962. J.9500-9512. The impact compressibility of liquid nitrogen and solid carbon dioxide. Phys.. Certain previous compendia of mineral electrical properties have preferred to give only ranges of values for a given mineral [ 17-191. and G. Recent previous compilations of data on electrical properties of rocks are given in references [17-19. and at elevated temperature and elevated pressure. Chem. 1970. S. 232 Yagi. 1986. N. sometimes differing by as much as several orders of magnitude. K. 22. and the loss tangent 6 is defined as Copyright 1995 by the American Geophysical Union. Materials are classified on the basis of whether they are metallic conductors. 185 186 ELECTRICAL PROPERTIES OF MINERALS tan 6 = E”/E’ (5) The complex resistivity is defined as the reciprocal of the complex total conductivity p’ . In linear systems it can be shown that JT = GE + r&L’& (1) where JT is the total current density. At room temperature. Electrical parameters. In addition to metals. Above the Debye temperature. E is the electric field gradient. Semiconductors are materials with a relatively small difference in energy Eg between the . and t is time. and rocks at room temperature and 1 bar pressure. + i&)-l (6) The SI unit of electrical conductivity is Siemens/meter (S equivalent to l/n). the Fermi level (the highest filled energy level) lies within the conduction band. or insulators. For a time varying electrical field of the form E = E. the conductivity decreases with increasing T. semiconductors. minerals. A total complex conductivity may be defined as 1 crT=oT+i<=o+i6. exp (icut) (2) in which i = J-1 and o = angular frequency. and of aqueous fluids are treated by Olhoeft in Section 3-8 of this series and in [42]. and the conduction electrons are not localized or bound to any particular atom. 441. The electrical conductivity cr and the dielectric permittivity E relate an electrical stimulus and response through Maxwell’s relations.66]. materials such as graphite exhibit metallic conduction.854185 x lo-l2 F/m. Metallic conductors. Even at temperatures approaching 0 K metallic conductivity is very high. The SI unit of dielectric permittivity is Farad/meter (F/m) and is often expressed as the relative dielectric permittivity K K=E/k (7) where &o is the dielectric permittivity of a vacuum = 8.ip” = (0.Electrical properties of elements. In metallic conductors. The first term on the right hand side of equation (1) is called the conduction current and the second term is the displacement current. Types of conductors. For general references see references [ZO.42. metallic conductors have conductivities of lo6 S/m or more.i&” (4) e” is also called the loss factor. Semiconductors. generally decreasing as l/T [37.xz (3) and the permittivity may also be defined as a complex value & = &’ . exp (iot) equation (1) becomes JT = (a + ime) E. In geological materials the distinction between ‘pure’ materials and ‘impure’ or minorelement containing materials is not always clear-cut or useful. k is Boltzmann’s constant. Effects of temperature and pressure. Impurity atoms in low concentrations may have large effects on the magnitude and mechanisms of conductivity in insulators. the l/T factor in the pre exponential term on the right hand side of equation (9a) is not always . and T is temperature.g.bottom of the empty conduction band and the top of the filled valence band (the band gap). In practice. E is often expressed in electron volts eV. Thermal promotion of electrons from the valence to the conduction band can occur. the band gap is large (often 5 eV or more) and prevents thermal elevation of electrons into the valence band. Diffusion is a thermally activated process so that D = Do exp(-E/kT). resulting in ntype semiconduction. In insulators. The NernstEinstein relation links the electrical conductivity to the diffusion coefficient of the charge-carrying species cr = Dz2e2n/(kT) (8) in which D is the diffusion coefficient. n is the concentration of the conducting species. Some solid-solution impurity atoms can donate electrons to the conduction band.. In an impurity-containing insulator. z is the valence of the conducting species. e is the charge of the electron. low temperature conductivity is often dominated by the impurity-controlled mechanisms and is termed extrinsic conductivity. which is termed intrinsic conduction.618 x 10m5 eV/deg. are insulators. Boltzmann’s constant k is equal to 8. therefore the temperature dependenceo f the conductivity will be of the form CT= ?f exp(-E&T) (94 or CTT= A exp(-E/kT) (9b) in which bo and A are pre-exponential constants and E is the activation energy. leaving positively charged holes in the valence band. Many earth materials. halides. Insulators. At high temperatures the conductivity may become dominated by the fundamental ionic conductivity of the pure crystal. many silicates and oxides fall into this category. others can accept electrons causing electron holes in the valence band. Charge transport is by ionic movement from site to site by thermally activated transport (ionic conduction) or by electronic charge transfer between ions of different valence (hopping conduction). resulting in p-type semiconduction. At elevated temperatures. Typical energy gaps for semiconductors are on the order of 1 eV. Conductivity values for insulators are generally lower than about lo-l3 S/m at room temperature. Semiconductors have conductivities in the range 10v3 to lo5 S/m. e. but care should be taken when making this interpretation. both types of expressions are used. However. each defect is given a symbol of the form A B . exp(-F) in which U is the activation internal energy. When available. and mechanistically more meaningful parameters are derived if the entire data set is simultaneously fit to a single expression of the form d = bol exp(-El/kT) + cro2 exp(-E2/kT) (11) In the data tables that follow. Point Defects and Conductivity. We expect that many of these values will be revised as experimental methods improve.24] was developed to describe the type of defect and its effective charge relative to a normal lattice site. The activation volume is often interpreted as indicating the volume of the mobile species.used. exp(-E&T) (10) are employed instead. experimental data that have been fit simultaneously to multiple linear segments are indicated by braces. Plots of the logarithm of electrical conductivity versus l/T that cover an extended range of temperature frequently show two or more linear regions. The effect of pressure on conductivity can be characterized by the inclusion of an activation volume term Vo so that u+ PVo d = b. The values in Table 5 and 6 are the best currently available. The variations in slope can be caused by transition from one dominant conducting species to another or by a TYBURCZY AND FISLER 187 transition from extrinsic (impurity dominated) to intrinsic conductivity. Point defects are imperfections in the crystal lattice and the types of point defects possible are substitutions. vacancies. Each region is then described by an expression of the form of equation (10). In the tables that follow. interstitial ions. and the reader should be careful to employ the proper form of the equation for the constants given. Kroger-Vink notation [23. more precise. The electrical conductivity of materials is determined by the point defect chemistry. electrons. and expressions of the form 0 = b. and electron holes (electron deficiencies in the valence band commonly termed ‘holes’). Incthis notation. activation volumes are given in the tables. In experiments at high pressure it is difficult to control all thermodynamic parameters. in which the main symbol A indicates the species o the . but more commonly measurements at elevated pressures are parameterized isobarically as functions of temperature using equation (10) or (11). In general. In MgO. leaving an oxygen vacancy and two electrons behind. For example. or vacancy).1 in which K is the equilibrium constant and square brackets indicate site fractions. Note how defects caused by aliovalent ions in different valence states are written using this notation. Tables 1 and 2 give these definitions and show as an example the defect species in nonstoichiometric (Mg. = l/2 02(g) + VG + 2e’ describes the reaction of oxygen on a normal lattice site to release an oxygen molecule to the environment. the reaction 02. (14) For such a reaction. the subscript B indicates the type of site (normal lattice site of a particular atom type or an interstitial site).+A. qi is its effective charge. all defects are present in some amount in every crystal and each contributes to the total conductivity. electron.g + 2h’ + 0. the Gibbs free energy AGO for this reaction is given by AGo = -RT ln K (16) in which R is the gas constant and T is temperature. slashes indicate negative charges). Reactions involving oxygen from the surroundings are of particular importance in oxide materials. The electrical conductivity of a material is the sum of the conduction of each charge carrier (or defect) type acting in parallel 0 = Z Oi = Z Ciqjpi (13) in which ci is the concentration of the ith type of charge carrier. the reaction which incorporates oxygen from the surroundings and forms a magnesium vacancy is written l/2 02 = v. and the superscript c indicates the net effective charge of the defect relative to the normally occupancy of that lattice (dots indicate positive relative charge. Thus the mineral stoichiometry depends on the chemical potential of oxygen (or the oxygen fugacity fo2) in the surrounding atmosphere. we can write equations for chemical equilibrium constants in the usual manner K= rvk I rqi (15) [A. For example. and pi is its mobility (in m2 V-l see-l). . Usually only one or two types of defects dominate under a given set of thermodynamic conditions.defect (atom. The concentrations of the defect species are governed by chemical reactions that lead to the production or consumption of each defect type.Fe)O. the removal of a positively-charged ion from its normal site resulting in the formation of a vacancy plus an interstitial ion (formation of a Frenkel defect) can be written as A.=V. hole. Thus. For a three-component system such as (Mg.11. This extreme sensitivity of defect concentration to minor and trace element concentrations makes it very difficult to establish absolute values for the conductivities of ‘pure’ minerals. The results are then combined with defect reactions such as (17) and (18) above and defect conservation laws such as conservation of mass. Thus. For a four-component system such as olivine (Mg. . oxygen fugacity. (20) in which p is also a constant.Fe)$iOq an additional constraint must be specified. . The general practice has been to try to determine which defect dominates conduction under a given set of conditions by determining conductivity under varying conditions of temperature. this constraint means that the temperature. so that the most general conductivity relation would have the form Oi = 00 exp(-E/kT) (F&g)m fGzn aSi& .59. and conservation of lattice sites to determine the particular defect reaction that controls the concentration of the dominant defect and predicts the correct dependence on other environmental conditions (fez in particular). the concentrations of defects (and hence the conductivity) may vary widely. Definitions of defect species (Kroger-Vink) notation. References such as [23-251 describe this process for many materials. the pressure. the exponents n for the dependence of conductivity on oxygen fugacity have been included in the tables that follow. and trace element concentration (or some subset of these conditions). In the presence of even relatively small amounts of impurity ions. in principle.60] describe defect equilibria in some important Earth materials. Where available. the oxygen fugacity. but the parameters in full expressions of the form of equation . and the Mg:Fe ratio in the solid must all be specified. the conductivity will have the general form Oi = (To exp(-E/kT) (F&g)m fG2n (19) in which F& is the fraction of Fe on Mg sites and n and m are cons Pa nts arising from the defect reaction stoichiometries. (positive) in even pure MgO depends on f02 (at constant temperature).Fe)O. charge neutrality. and more recent references such as [9. the magnesium vacancy concentration 188 ELECTRICAL PROPERTIES OF MINERALS Table 1 . To properly and completely specify the thermodynamic state of a defectcontaining crystal. Symbol Meaning Main symbol Element or Atomic symbol species of defect e (electron) h (hole) V (vacancy) Subscript Site Normal Lattice Site (Atomic symbol) I (Interstitial) Superscript Charge relative x (zero) to normal lattice ’ (negative) site . the Gibbs phase rule must be satisfied. especially at low temperatures. . . in olivine the most frequently specified constraint is the silica activity aSlo2 (or equivalently the enstatite activity aEn). High temperature electrical conductivities of minerals given in the format (T = Al exp (-El/kT) f&l or crT = A1 exp (-El/kT) fozni. Note that Fe can be in +2 or +3 valence state.91 1 .1 DC. nl and the bottom line is A2.00 3. PC-J* = 4 MPa [361 773-998 998-1073 1073-1258 1258-1473 0. single crystal.15 -4.15 0.Fe)O. Table 2.2 1. Values surrounded by braces are tits to the 2-term expression (3 = A1 exp (-El/kT) fmnl + A2 exp (-E2/kT) f&! where the top line is Al.11. Oxygen activity buffer QFM refers to the quartz-fayalite-magnetite assemblage.9 0. etc. Species Symbols Normal Lattice Sites Substitutional Defects Lattice Vacancies V” Mg V. See [23-251 for general discussions of defect equilibria and [8. Examples of defect species for (Mg. (F& -V.5 2. synthetic AgBr KBr NaBr RbBr TlBr Chlorides. WM refers to the wustite-magnetite assemblage. CaC03 in K -6.58-601 for discussions applied to Earth materials. Interstitial Ions Electronic Defects e’ h’ Defect Dimers Defect Trimers..48 0. single crystal.05 > II c CJ 120-723 IC Halides: Bromides. T atm Calcite. synthetic .22 1. Pressures are 1 bar total unless otherwise stated.(20) are still not commonly determined. El. Material Form Temperature 1% Ai EI nl Comments References of range 0 in eV fo2 in equation K S/m.15 -1.Oll 1. -F& )’ Table 3.0 0. E2 and n2. and pressure dependences are referenced to 1 atmosphere. 76 1.9 1.23 0.84 723-973 10.79 100 . continued: Fluorides single crystal.AgCl KC1 LiCl NaCl 0 tJT RbCl TIC1 120-723 1 -7.2.25 .04 248-695 5.78 600-723 4.90 823-1041 8.90 625-823 4.35 DC P81 9.54 0.89 823-990 8.48 2.25 2.80 373-728 7.48 2.04 1 7. synthetic KF LiF NaF Form Temperature of range equation K (3 973-l 119 993-1115 1123-1265 log A1 EI “1 Comments References u in eV fo2 in S/m.70 1. T atm in K 9.83 823-1000 10.40 0.30 2.18 2.20 8.97 823-1008 8.32 1.0 1.02 0. (continued) Material Halides.03 323-730 5.7 1.80 0.4 x lOlo Hz AC [461 P81 [331 WI [281 [331 LW Table 3.18 1.0 1.12 293-700 5.66 773-1001 8.65 723-1073 8.68 873-954 8.06 793-879 9.60 2.0 0. 1 Pa fo2 .92 7.96 2.18 1.62 1898-1998 11.5912 1 I 51..10-4Pa fez.68 2.48 3.01 2.51 DC [411 Iodides single crystal.NaMgFg .14 3.. DC fez= 16 Pa fo2= 1 Pa fa=lPa fm = 10m5 Pa fo2 = 10m5 Pa [431 DC fez .5213 61.1773 1473-1773 1473-1773 1473-1773 1473-1773 1.26 1.71 5.60 2.11 6.8 1000-1400 10.83 3. 40 ppm Al 320 ppm Fe u u u 773-953 7..94 3. 1.10S3 .59 kHz AC [611 1473.10 .6962 2.68 1 2.5 1573-1873 5.08 DC WI 10 kHz AC.48 1.77 573-934 7. CaO single crystal Magnesium oxide. MgO single crystal.1 MPa r54.84 1898-1998 13..97 1573-1873 3.49 1 2.1W3.68 2.23 1..01 5.42 1573-1998 5.68 2.lo.11 5. perovskite structure u 833-l 173 6.551 fm.57 3. synthetic KI Nd Oxides: Aluminum oxide.81 { 61.1 Pa fo2 .8273 31.1 MPa Table 3. Al203 single crystal (sapphire) Calcium oxide.11 7. High temperature electrical conductivities of minerals (continued) Material Form Temperature .5 DC.lo4 Pa fo. 86 0.97 2.36 1.s3+A11504 Feo. continued: 400 ppm Al Magnesiowustite. single crystal Spinel.23 873-1673 7.53+A10.2g2%xx7sFtz3% Feg 5 +Mgg 5Fez3+04 Feo’7s2+Mgo 25Fez3+04 Feo:2a2+Mgo:7sPeo. single crystal polycrystalline Scheelite.84 fm = Ni/NiO 1173-1573 8.! = 0.77 0.1O-3 .74 0.1 MPa 1273-1773 2.5 +Mgo.39 873-1673 7.15 873.of range equation K 1% Ai El ni Comments References 0 in eV fo2 in S/m.752+Mgo.40 4.84 0.15 co:coz = 0.05 fo2 = NiINiO 973-1273 4.1’ to ‘QFM-2 873-1673 8.00 DC PHzdpH2 = 1.1246 fez .00 0..&+AQ Fe0.1673 7.47 2.16 8.DC fm=QFM fez = ‘QFM.44 0.25 873.07 > fm .94 1173-1573 9.1673 7.39 873.52 0. CaWO4.41 0. Mgog3Feg.28 873-1673 7.22 co:co.1967 23.74 0.. Fe304 Nickel oxide.52 0.30 0.003 .504 OT 1473-1773 1473.18 873-1673 7.1 873-1673 6. T atm in K Oxides.42 3OO-5x104HzAC.18 873.79 0. NiO.0 pH2dpH2=0.1673 7.1773 2.75 0.59 2.1673 6.t 70 Magnetite.003 973-1273 6.48 1273-1773 3.25 3.104 Pa 25.68 in air 973-1273 5.25Fe1. Fe-Mg-Al Fe2+Feg 53+Al 1504 Fe2+Fe 1’03+Al 1’04 Fe2+Fe1’53+A1204 Feo. 0593 fiO.1095 x=0.0817 x=0. polycrystalline Albite. 0 0 d tST CJ 873-1673 7.77 0.0706 .0. polycrystalline.j Albite.85%1501.30 873.79 0. CaAl&Og.52 0.26 873-1673 7. France.78 0.19 co:co2 = 0. synthetic.0494. synthetic Wustite.oiA13.0967 x=0. Fel-x0 x = 0. Spinel. fluorite structure Silicates: Cordierite.47 873-1673 7. polycrytalline.84 0.873.25 873-1673 7. Mewry.1673 7. z Form Temperature logA1 El nl Comments References F of range 0 in eV fo2 in $: equation K S/m. SrG.48 873-1673 7.giFe0.85. Fe-Mg-G-Al. France Ndlsi$$.48 .0.003 [701 1391 [631 [471 [391 [381 Table 3.69 0.o8Mno.68 0. Albite. synthetic (disordered) NaAlSi3 Og Anorthite.38 873-1673 7.97 0.0.19 873-1673 7.0.1039 .0.1673 7. Mgi.oi 1 VW Feldspar. T atm in K ii! F continued: Strontium oxide.21 0.95Si5.26 873-1673 7. (continued) Material Oxides.41 873-1673 7.0706 x=0.20 873-1673 7. Grisons.0884.77 0.59 0.0566 . ko2Nao 98AlSi308.82 0. natural.71 0. polycrystalline. AZ (Fo9()) (Mgo.168 1173-1573 7. T atm in K Silicates. AZ (Fogg) (Mgo.18 1.873-1673 7.1 0.08 0.003 [381 860.1050 5.1173 3.olivine.025 0.20 0.70 2. [ lOO] orientation [OlO] orientation [OOl] orientation Co. (continued) Material Form Temperature of range equation K log Ai El “1 Comments References 0 in eV fo2 in S/m.161 1173-1573 8. continued: Olivine.967 0.182 Constant thermoelectric potential 161 1000-2025 5.167 1173-1573
[email protected] [ 1001 orientation San Carlos.9Fe0. synthetic Co2SiO4 Olivine. single crystal San Carlos.1473 .75 Impedance spectroscopy 1491 473-l 173 -0.0 DC Fell 1173-1573 8.whSi04.1173 0.869 0.899 0.72 0 673-l 173 -0.10kHzACinair 134. h Si% [ 1001 orientation San Carlos.15 0.26 0 fo2 = 10m5 to 16 Pa WI 0 473. synthetic (Fol& WSQ.od2Si049 [ 1001 orientation [OlO] orientation [OOl] orientation Forsterite.87 TYBURCZY AND FISLER 193 0 3 Table 3.351 0 673.~d%.25 co:co2 = 0.85 1.23 0. (Fogl) 1373.86 673-1173 0.35 0.86 673-l 173 0.163 1173-1573 7. AZ (Fo91) (Mgo.062 0.gFeg1. San Carlos olivine (Mgo. ----.03 1.18 O.41 1.lC@ Pa.77 2.45 12. Pyroxene-buffered.10-“.97 6.17 4.49 2.1773 0.37 1.30 3.52 22.l.63 -0.25 -0.1373-1473 1373-1773 1373-1773 1373-1773 1473.l.66 1.11 6. O.87 10 kHz AC co2:co =157.10 kHz AC co2:co = 10: 1 1681 .10kHzAC co2:co = 10: 1.1 .30 0 fo2 .75 0.18 1.5.63 1.10kHzAC 1.l.10kHzAC co2:co = 30:1.65 4.0 2. -0.77 O.7/l co2:co =157.77 1 0.7/l (332 iP Orientationally-averaged grain interior conductivity from impedance spectroscopy on polycrystalline olivine.40 1.34 0.l.99 1.1. W-M buffer 2.36 0.17 O.5.08 > 1 2.2 2.25 for self-buffered case.18 fo2 .86 4.18 1.10kHzAC 2.75 5.31 0.55 0.1523 1473-1523 1473-1523 1323-1498 1523-2083 1573-2083 1063-1673 998.10-“.36 0. 0.10mP6 a. 0.60 Isotropic parametric model 9. 94 0. I mineral fabric Synthetic II mineral fabric I mineral fabric Pyroxene.02 473-773 5.67 1. Impedance spectroscopy Measurementsm adep arallel . Australia.90 Isotropic parametric model for self-buffered case.i isi% (En891 [ 1001 orientation [OlO] orientation (T cfr cf 0 0 1373. (continued) Material Silicates.03 Air. single crystal Diopside.10kHzAC co2:co = lO:l. continued: Form Temperature of range equation K logA1 El nl Comments References 0 in eV fo2 in S/m.e3A12Si2000600 [ lOO] orientation [OIO] orientation [OOl] orientation Diopside.91 473-773 5. North Wales.[681 1561 [511 181 [481 PI Table 3. 473-773 4.8gfeO.l.30 1. UK Mgo. O.70 3. T atm in K Opal. Brazil Na3Cag~g8sFe12~2sizooO6oo [ 1001 orientation [OlO] orientation Ortbopyroxene.1773 1. NY NagCaggMggd.32 1.38 8. amorphous SiO2 Natural. 15 -0.92 -0.20 1.11 .60 1010-1099 0.72:1 1561 1711 1151 Cl51 [41 Table 3.03 1273-1473 0.00: 1 C02:H2 = 29.54 1020-1163 0.13 CO2:H2 = 29.25 12351316 2.72: 1 1020-l 163 0.20 -0. T atm in K ii! F 1087-1282 0.and perpendiculart o mineral fabric 1273-1473 1.20 1042-l 124 1.64 1.23 1.569: 1 CO2:H2 = 0.72: 1 CO2:H2 = 3.36 1.43 2.643:1 CO2:H2 = 3.15 1190-1282 1.19 1111-1235 2.88 2.57 1149-1282 3.01 1.92 1.0733: 1 CO2:H2 = 0. and lOa to 1e7 Pa at 1473 K 1190-1282 0.0733: 1 C02:H2 = 0. and 10e3 to 1(r7 Pa at 1473 K 1273-1473 -0.36 1031-1099 0. continued: WI orientation s Form Temperature 1% Ai EI nl Comments References 9 of range 0 in eV fo2 in $: equation K S/m.643:1 C02:H2 = 0.11 1.42 CO2:H2 = 29.02 -0.15 fo2 = 104 tolOmgP a at 1273 K.58 2.89 0.67 1.26 1136-1298 0.30 1163-1282 1.02 fo2 = 104 to ltJg Pa at 1273 K.1473 1.5691 CO2:H2 = 0.17 1.0420: 1 1190-1282 1.43 1. (continued) Material Silicates.25 1.64 1592 Hz AC CO2:H2 = 99.18 1273-1473 0.05 -0.12 1273.84 1. 1136-1282 3.8Mg16l.39 1020-l 136 0.0733: 1 Air Air Orthopyroxene.8Mno.36 450-700 8. SiO2.72: 1 C02:H2 = 3.66 1190-1282 1.8 Cri.12 1.13 1.36 1. z-cut Synthetic.4Fe2A. [loo1 .87 1.569: 1 CO2:H2 = 0.76 1. Grade S4.oWh (Ew) [OlO] orientation Orthopyroxene.25 1.8 1.4Sii95.07 1.1473 1098-1449 1111-1449 0T 370-454 6.2Mno.18 1. WOI.5Ai7.2Sii97.4 1.50 1111-1282 2.6Mgi72.82 450-700 8.93Fe0.4A12.28 1. z-cut 0 1176-1282 2. Grade EG. z-cut Synthetic.73 1.569: 1 C02:H2 = 0.76 1.2 Cr0sh9. z-cut Synthetic.7Mg160. Cag.72: 1 CO2:H2 = 0.75 1136-1282 2. New Guinea Mgo.0%0 Quartz.569: 1 CO2:H2 = 0.03 1. Arkansas.80 1176-1282 2.3 0. single crystal Natural. Grade PQ.9Fe34.2Mno.40 450-700 8.21 1. Papua.72 1136-1282 3.20 1592 Hz AC CO2:H2 = 29.33 0.31 1.4%00 Ca0.qFe31.0733: 1 CO2 Air 1kHzAC co2:co = 1999: 1 Mean of 3 orientations: WI.5~5.643: 1 CO2:H2 = 0.71 1149-1282 2.24 1.99 1.4 Cro.6%00 Ca0.67 1.0 1.62 0 973.15 CO2:H2 = 29. 45 0. impedance spectroscopy [ 161 200-300 x 10s6 Al/Si 200 x 10q6 Al&i 15 x 10e6 Al&i 1 x low6 Al/Si Table 4.9lFe0.zFo. Values given for the constants in the expression cYT = A 1 xn exp(-EikT) in which x is mole fraction
[email protected] 0. external heating 1321 .02 E eV 1.66 I x IO.37 Diamond cell.94220 90-250 FeO.79 1.220 400-700 Mgo.26 0.[41 1141 Air.81 f0. Material Temperature Pressure cro E Remarks References range K GPa S/m eV Magnesiowustite (wustite) (Mg.Mg)2SiO4 olivine.58 0 0.lS Fx in mole fraction Fe) 1.92 [ 121.33 1. Oxygen fugacity is that of a CO2:CO 5: 1 mixture.54ko.36 1. Measurements made in the [ 1001 direction at temperatures between 1423 .00 1.Fe)O Mgo.1573 K at 1 bar total pressure. Al S/m ~()6.g9gsG go-250 15 30 32 0 0.58 0 0.35 f 0.92160 90-250 Fe0.04 Table 5.mO FeO. Valid in the composition range 0.oQ 333-2000 Mgo.33 1.45 0.73 1.27 0.02 1.75 1.01 1. exp (-E/kT). Iron content dependence of the electrical conductivity of single crystal (Fe. High pressure electrical conductivity of minerals given in the form o = o. 0 973-1473 3.0 4.0960 0.0978 0.0980 0.5 x 10-l 623-923 2.0955 0.0970 0.0980 Piston-cylinder 1621 0.0.6 x lo2 F 0.0993 Piston-cylinder [621 0.0 973-1473 3.5 1.2 x 103 293-623 5.0 8. guard ring [501 3 0.5 1.4) Temperature Pressure o.FehSiOp natural.0 3.0945 0.22 E A 0.0 x 10-2 623-923 5. (continued) Material Olivine. laser heating 1 kHz AC [29] 0.8 x 1O-2 623-923 3. polj&y&lline Dreiser Weiher.0 1.0905 0.7 x 10-l 973-1473 5.0945 Piston-cylinder 0.42 E .098 1 0.5 2.70 $ 0.0897 [621 Table 5.102 0. (Fo93.0986 0. NiiNiO buffer.29 0.5 5. Germany. (Mg.0918 0.38 Diamond cell.0960 0.52 0.0925 0.0995 0.0 2.33 DC.0982 0. range K GPa S/m Li E Remarks References P E eV ici l 293-623 2.5 x 101 293-623 3. Germany.83 !i Dreiser Weiher.37 3 2 0.8) Olivine.0 1.0 1.1223 1223-1348 847-1331 875-1160 800-1212 823. Leura.1223 866-1212 636-1217 574-1091 615-1273 1.0 1.953 . Australia.1429 953.96 0.0 1.0 1.21 % 0. polycrystalline Fo 1 t)o Forsterite Fotio Fog0 Wo WI (Fal t-x-1F1a Wh Foe Fayalite 900-1093 915-1236 945-1189 953.33 0.0 1.0 2.0 5. synthetic.0 1.0 1.0 1.0 5. (Fo92) San cub & (FOg1.0 1.0 1.0 1.6) Mt.0.0 1.1429 923-1223 795. PQ38. 683 1.54 0.21 x 102 0.75 x lo1 0. 1. guard ring MgO buffer MgO buffer QFM buffer QFM buffer IW buffer QFM buffer IW buffer QM buffer QI buffer [511 [311 [71 Piston-cylinder. polycrystalline.76 0.00 2. (continued) Material Olivine. guard ring [71 natural paragenesis QFM buffer IW buffer 1592 Hz AC.6 kHz AC guard ring [@I QFM buffer QFI buffer Table 5.64 x 106 2.85 2. 2 electrode. 2 electrode.523 1.18 x lo2 0.6 kHz AC.17 0.92 x 101 0. range K GPa S/m . Al203 insulator Piston-cylinder. continued: Fog Fayalite Temperature Pressure cr.6.52 Piston cylinder. 1.984 2.582 7. 1.04 0.622 1.04 0. synthetic.976 2.71 1.777 7.461 1.41 0.941 5.479 9.38 1.14 x lo1 1.383 6.17 8.69 0.6 kHz AC.43 x 101 0.77 0. 10 6.89FeO.31 x lo2 0.0 5. natural polycrystalline Dreiser Weiher.00 940-1283 1.2 293-673 40 295-3200 46 295-3200 55 550-1000 550-1000 550-1000 550-1000 550-1050 500-1020 510-1020 510-1010 520-950 . synthetic.82 0.05 423-l 173 3.0 1323-1518 1.0 3.05 293-673 1.o Bamle.Fe)SiO3 Enlm (Enstatite) %oWo EwoWo End%o En’LOFs8o Fs 1~ (Ferrosilite) Fs 1~ (Ferrosilite) Fs 1~ (Ferrosilite) Qrthopyroxene. polycrystalline (Mg.ii SiO3 Mg0.89Fq.08 1.1W o2.gFolo .E eV Remarks References 799-1500 1. Germany En87.0 1.35 x 100 1.05 1568-1673 2.0 4. 11 SiOg Pyroxene. Norway En86 773-l 100 1 loo-1273 1. Orthoyroxene.51 buffered MgSi03 (SiO2-sat) buffered MgSiO3 (stoichiometric) buffered MgO Fog Fayalite Ni2SiO4 a-Mg2GeO4 Perovskite (silicate) Mgo.843 9151236 1. 24 7.10 x 101 1.80 1.30 x lo2 1.73 x 101 1.78 Piston-cylinder.6 kHz AC guard 7.0 2.0 2.18 1.42 7.24 5.0 2.08 4.98 5.0 2.51 0.0 1. 1.08 0.41 x 102 0.15 X lo2 0. 2 electrode.500-900 500-970 544-831 536842 1070-1323 1323-1673 1.71 ring.0 1.49 9.42 1.78 x lo3 1.0 2.70 6. pyrophyllite insulator 1.13 x 102 1.40 6.0 0. Impedance spectroscopy.76 x lo7 2.8 x lo1 0.92 x lo6 2. Ni/NiO buffer 6.38 x 10-l 0. ERGAN buffered Diamond cell.5 0. external heating U = 0.0 2.12 x 102 0.26 cm3/mole .48 eV.48 7.74 x 102 1. Vo = -.94 x 2.0 1.0 x 100 0.0 2.42 1.0 2.59 1.17 x 102 0.37 2.0 x 100 0.55 1.97 1.0 2.79 x 103 1.37 2.95 x 102 1.24 1.25 x lo2 0.13 1.5 DC.56 108 Piston-cylinder.5 x 101 0. 7 Clinopyroxene. Germany hm7Fv.6 kHz AC.43 1.0 1. natural paragenesis $ 9 .24 x lo5 1. guard ring Quartz buffered Quartz buffered For&rite buffered Forsterite buffered Si02/CCO-buffered SiO2/CCO buffered SiO2/CCO buffered SiO2/CCO buffered SiO2/CCO buffered QFsI buffered QFsM buffer Piston-cylinder. 1. 1.Diamond cell.24 x lo2 1. guard [71 i ring. CO2:CO =ll:l [II [691 i4.98 Piston-cylinder.6 kHz AC. ?I-MmGeQ 1122-1518 1.6 kHz AC guard-ring Natural paragenesis QFM buffer Argon gas medium vessel.24 x 10-l 0.05 7. 1592 Hz AC. 1. polycrystalline Dreiser Weiher. polycrystalline Diopside. CaMgSi206 640847 746-1064 Spinel. laser heating Piston-cylinder.w 1571 [301 1531 171 [51 Table 5. natural.6Wo3o.0 6. synthetic. continued: Clinopyroxene. (continued) Material Temperature Pressure cro range K GPa S/m E eV Remarks References Pyroxene.28 2. 25 Olivine tholeiite (C-2 14) 0.Mg)zSiOq olivine and spine1 (y-form) at room temperature (295 K) and pressures to 20 GPa.59 0.42 0.91 1.15 1.21 1.92 Andesite (VC-4W) 0.87 0.93 0.12 1.195) 0.77 0.84 1.58 0.85 0.64.04 Rhyodacite (HR.30 0.11 1.35 1.15 1.25 Tholeiite (C-8) 0.48 0.91 Trachyte (C.20 x 104 spine1 -5.39 0.76 0.24 1.16 1. where Q is in S/m.16) 0.64 0.69 0.77 0.46 0.E Piston-cylinder.57 0.47 0.36 0. Electrical conductivity of anhydrous naturally-occurring silicate melts at temperatures between 1200 and 1550°C.85 0.96 1.48 0. P is pressure in GPa [26.67 0.76 0.81 0.83 0.4.1) 0.20 x 1O-4 Table 7.02 1.65 0. Electrical conductivity of (Fe.86 0.81 0.97 f 0.56 0. where x is mole per cent Fe.95 1.15) 0.96 1.58 0.43 1.27 Tholeiite (PG.82 0.79 0.22 Alkali olivine basalt (BCR-2) 0.72 0.6 kHz AC.21 1.0651x lo.78 0.06 1. o.58 0. Temperature.I olivine .23 Alkali olivine basalt (C-70) 0.1) 0.42 0.26 Quartz tholeiite (HT.00 1.39 0. Electrical conductivity of naturally occurring silicate melts at elevated pressures over the . in (x in GPa-1 (x in mole S/m mole % % Fe Fe) GPa.48 0.92 1.46 0.22&0.48 0. ‘C Melt type 1200 1250 1300 1350 1400 1450 1500 1550 Nephelinite (C.49 Tholeiitic olivine basalt (C-50) 042 0. m Bo b.16 0.66 0.77 0.41 0.15 Tholeiite (70.59 0.40 0. guard [71 % ring E Piston-cylinder WI z Impedance spectroscopy ERGAN buffered Fc d For oxygen buffer assemblagesF: s = ferrosilite F = fayalite I=iron M = magnetite Q=qmrtz W = wtistite Table 6.74 Table 9.76 0.75 0.45 1.12 x 1O-4 (001) 7.82 0.20 1.27 Alkali olivine basalt (C-222) 0. Mineral log (z.60 0.83 0.03 1.71 0.11 1.17 1.56 0. 1. Expressed as log <r. Data from [45.71 0.93 1.14x lOti (010) 7.95 1.128) 0.07 Mugearite (C-2 10) 0.20 1.53 0.53 0.41 0.00 Andesite (HA) 0.04 1.50 0. Real relative dielectric permittivity K’ (1 MHz) and temperature derivatives for for&rite Mg2SiO4 over the range 293 K to 1273 K [3].62 0.81 Rhyolite obsidian (YRO) 0.48 Basanite (C-90) 0.7 1 f 0. + bx)P].41 0.66 0.00 1.21 1.71 0. Values are given for the constants in the expression axp = rso exp[mx + (B.07 1.27 1.153 1.24 f 0.73 0.64 0.16 1.75 0.88 1.95 1.27].65.65 0.02 1.00 1.52 0.62 0.49 0. Valid in the range 50 5 x 5 100.69 0.91 1.34 0.59 0.2 x 10-l TYBURCZY AND FISLER 201 Table 8.71 Latite (V-3 1) 0.36 1.06 1.11 f 0.97 1.05 1.90 1.10.27 1.69 f 0.67]. Crystallographic lc’ l/K’ (&cXlT) Orientation 293 K K-l (loco 6.60 0.125 2.71 0.73 1.88 0.01 Hawaiite (C-42) 0.67 0. .. Solid lines are total conductivity. Calculated point defect model.5 .4 5.82 1.25..8 1 d/T (K-l) Figure 3.2 Hawaiian Rhyodacite. parameters for tits to the equation log 0 = log o.10m3t o 10m4b. Solid line is total conductivity.6 6. in S/m eV cm B/ mol Yellowstone Rhyolite Obsidian.6 5..9 17 .. dashed lines are ionic conductivity [54.5 -3 -3.5 5.5 2.05 1. HR. for Fog0 olivine at 1473 K [l 11. PO. -2 -2.l.74 5....36 0. Log conductivity versus log fm for MgO containing 40 ppm Al.2 5.5 -3 -3.3 Hawaiin Tholeiite 0 . Melt Type P range 1% Qo Ea AV kb b.9 12.5 -4 -4. in MPa -1 1 Figure 2.5 -6 18 ~‘l~~~l~“.25.4.53 -0.76 3.78 17. which is the sum of ionic conductivity (dashed-dot line) and the electronic conductivity (dashed line) [54.00 0.I I I I -16 -12 -8 -4 0 Log(fO. 551. YRO 0 .5 3.3 5.(Ea + PAVo)/2.25.2 6.8 2..l..33 1.6 8..5 2.temperature range 1200-14OO“C.8 .8 6 6.8 . -I -??O I I I 1 .3kT 16% 651.55]..8.I. Vertical dotted lines represent stability range of olivine.25.5 ... MgO: 40 ppm Al 1300.50 7.77 0. °C & -1300% -7 Log PO.l..12.1 12.. - -2.19 0.55 11. MPa) Figure 1.- 5.1 0 .“~l’~~l~‘~l~ I’_ : MgO: 400 ppm Al f 02= 1 Om3-1 Ow4 Pa II I1l. ar for MgO containing 400 ppm Al. VC-4W 0 .5 3. Log conductivity versus T-1 for f& .l..5 -5 -5.75 0.5 2.30 4. plotted as log of the defect concentration versus log of oxygen fugacity.1 .-A .3 Crater lake Andesite.17 3.4 6.8. ( . . . .) -5 : -8 6 IIIIIIII . . Data from [28.#. . 331. . 2 . ’ >: . . . Solid buffer assemblages controlling fo2 are given in parentheses. Conductivities for KC1 and RbCl coincide. I I I I I I I I I I I. 1 I @ 8 ‘I’ 8 1 I’ r ’ . . 1 -8 -7 -6 -5 -4 -3 -2 -1 0 Log fo2 (Pa) Figure 4. 691.. II -’ : Feldspar and Feldspathoid IIII : Electrical Conductivity -2 : NaAlSiO -3 : NaAISi3G8 : NaAISi308 (nat.5 2 2. ./. Log conductivity versus T-l at 1 GPa for olivines of different compositions. dashed lines at IW. . The low temperature conductivity of NaCl and NaBr is impurity controlled.> -4 .. .5 s -6 -12 0. Data are from [7. .5 3 3.5 1 1. 8 ’ 8 Olivine Electrical Conductivity -5 -6 6 8 10 12 14 16 18 104/T (K-l) Figure 5. .. San Carlos olivine at 1 bar (self-buffered at QFM) is shown for comparison. . . . . l ( .5 San T= Carlos Olivine Electrical Conductivity 1473 K . l . . .5 103/T (K-l) Figure 6.. [68]. . .) -4 : CaAlzSiz08 . l . . / I . solid lines are QFM. . ..-4 -4. e / . . . Log conductivity versus log fo2 for San Carlos olivine @go) illustrating that total conductivity is given by the sum of the two mechanisms (dashed lines) with differing oxygen fugacity dependences [68]. d / . 8 ’ ’ .3. . Log conductivity versus T1 for some halides. . ( l .Adularia (nat... . . Electrical conductivity of REFERENCES orthopyroxene to 1400°C and the resulting selenotherm. Schock. Log conductivity versus T1 for some binary oxides..17 0 (QFW -2 1 -4 -6 1 -8 5 6 7 8 9 10 11 12 104/T (K-l) Figure 8. S.0 1. J. This work was supported by Shankland.61..1973. Shankland and A. 5. All lines refer to intrinsic regime. Journal of Geophysical Research. and A. 727-735. 10 I’ 1 I ’ I ’ * @ r II 8 8 8 1. Acknowledgements. The electrical conductivity of pyroxene. 70. 3397 3404. Data from [6. 3. Fujisawa. Duba. H.5 Density (g cm-a) Figure 9. The electrical conductivity of an isotropic olivine mantle. American Mineralogist. 1965. Duba. Oxygen buffers are shown in parentheses where appropriate. We thank Lee Hirsch. Cygan. T. The responsibility the National Science Foundation. those labeled ‘nat’ are natural samples. J. E. 81. Boland and A. Duba. Demonstration of the electrical conductivity jump produced by the olivine-spine1 transition.Feo. N. A.. N. A. C. Ringwood. 158-766. Log conductivity versus T-l for feldspars and feldpathoids.. T. Constable. Lines labeled by formula only are synthetic samples. Data from [34.9s0 420 . G.bMgo.5 1. and Al Duba for helpful reviews.7 8 9 10 11 12 13 14 15 104/T (K-l) Figure 7. Tom for errors rests with the authors. 4. 71. 443449. Proceedings of . 97.63. 1. and H. 1986.Fe 0. Dielectric and polarization behavior of forsterite at elevated temperatures.70]. 351. 2. Jeff Roberts. R. 8 8 * II 2 I’. Heard and R.’ 11 ’ 8 -: Conductivity of Some Binary Oxides 6 .1992. Lasaga. High pressure electrical conductivity of supercritical H20 versus density [13]. S. C. Journal of Geology. Journal of Geophysical Research. Akimoto. 206 ELECTRICAL PROPERTIES OF MINERALS 1 O-6 Saturation Line I I I I I IIIIIIIII 0. Effect of pressure and temperature on the conductivity and ionic dissociation of water up to 100 kbar and lOOO”C. E. 7. J. Gartstein. 9. Equilibrium point defect concentrations in MgO: Understanding the mechanisms of conduction and diffusion and the role of Fe impurities. M. L.377-384. Electrical conductivity measurements on synthetic olivines and on olivine. and diopside from Dreiser Weiher. Hirsch. 0. 12. and T. Quantitative olivine point defect chemical model: Insights on electric1 conduction. B. 114. M. 1993.199O.. Hirsch. 10. %. 1969. Electrical conduction of Co. Shankland. J. Physics and Chemistry of Minerals. and T.1979. and D. M. B. Huebner. G. G.the 7th Lunar Science Conference.. T. 50. . A. Electrical conductivity of pyroxene which contains trivalent cations: Laboratory measurements and the lunar temperature profile.. Reanalysis of wustite electrical properties. M.36-44. Electrical conduction and polaron mobility in Fe-bearing olivine. Journal of the American Ceramic Society. Duba and L. 1991. L. Shankland and A.245254. 15. L. E. Duba. diffusion. Physics of the Earth and Planetary Interiors. S.SiO. Geophysical Journal International. Eifel (Germany) under defined thermodynamic activities as a function of temperature and pressure. Mason.21-35. 25.C-26. M. 385-403. W. and the role of Fe impurities. J. 17. 44244428. Wiggins. 96. 1991.. 1993. 3173-3181. 1982. 187-190. TYBURCZY AND FISLER 207 13. L. 84. Journal of Geophysical Research. 14. Journal of Geophysical Research. C-24 .. 6. Journal of Chemical Physics. 4652- 4656. Geophysical Journal International. Huebner. J. Shankland. Journal of Geophysical Research.1976. and T. Cemic. Holzapfel. Hirsch. Determination of defect equilibria in minerals. Hirsch. Hirsch. Shankland. and T. Electrical conductivity of diopside: Evidence for oxygen vacancies. S. 1981. 114. enstatite. Hinze. 65. Will and L. Voigt. 8. J. L. E. 11. J.. Introduction to Ceramics. S.s0. H. V. Relations between the concentrations of imperfections in crystalline solids. C. DC. F...1988.. F. 20.American Mineralogist.17. P. Schock. Academic Press. 23. Pappis. edited by S. New York. W.. Kroger. Carmichael. 24. Electrical conductivity of synthetic and natural quartz crystals. Kingery. Inc. 22. H. A. New York. Oxygen ion mobility in cubic Zro. D. Washington. Electrical Properties of Rocks and Minerals.. F. and thermodynamics.. Electrical properties. 42. 1966. E. Inc. V. 1982.477484. Hill. Chemistry of Impedect Crystals. 1956. 25. Sietz and D. 1985. Boca Raton. Geological Society of America. 73. 53. Lacam. G. Geological Society of America.. Amsterdam. Bowen and D. American Geophysical Union. 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Discussion des resultats. 4. M.267-278. pp.Fe).. A. 1933. R. 29. 28. Mao. Li.. Uber die elektrische Leitfahigkeit von Einkristallen. 72. 5067- 5078. The Theory of the Properties of Metals and Alloys. 717-726. Jeanloz. 1991. 91.. Geophysical Laboratory. 96. 37. P. 35. Physics and Chemistry of Minerals. Maurer. Li. Methode et resultats experimentaux. Mapother. W. Lehfeldt. Manko. Bulletin de la Societe Francaise de Mineralogie et Cristallographie. 34. 2Teitschrijt fur Physik. Conductibilite electrique des tectosilicates.6113-6120. 31. 33. D. Effect of iron content on the electrical conductivity of perovskite and magnesiowustite assemblages at lower mantle conditions. Tiefenforsch. Dover Publications. The electrical conductivity of calcite between 300 and 1200 C at CO2 pressure of 40 bars. New York. Lacam.. Effects of composition and high pressures on the electrical conductivity of Fe-rich (Mg. Homilius. Maury. edited by V. Inc. 1985. N. 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Grace. as determined by frequency dependent complex electrical resistivity measurements. Rigdon. McGraw-Hill. Journal of the American Ceramic Society. Metals Park. 1989. E. Touloukian. G. Rai. OR. High-temperature cation distributions in Fe.1958. American Society for Metals. K. Solid electrolyte behavior of NaMgF3: Geophysical implications. B. 0.. 41.-MgAl. M. W. 0. S. Oregon Department of Geology and Mineral Industries. D. Hightemperature electrical measurements and thermodynamic properties of Fe?04-FeCr204-MgCr~O4-FeAl~O4 spmels. pp. Portland. 76. 405426. A. Science. 42. Bovin.. J. Wood and T. 40. D. J. . 46. American Mineralogist. 43. 56. 1985. Judd and R. A. Kingery. 1981.. Wood.FeAl. Electrical conductivity of basalts to 1550°C. edited by Y.1973. and K. 257-329. H. in Magma Genesis: Bulletin 96. Physics. spinels from thermopower and conductivity measurements. Dielectric dispersion and its temperature variation in calcite single crystals. Oregon Department of Geology and Mineral Industries. M. 45.459~464. R. Roy. J. B. Olhoeft. OH. 216. New York. and M. 206.O. O’Keeffe. and W. 1993. C. Stuttgart. E. R. Ionic conductivity and magnesium vacancy mobility in magnesium oxide.. L. 1977. Sempolinski. J. Electrical conductivity of the earth’s lower mantle. Peyronneau and J. 53. in HighPressure researches in Geoscience. Schweizerbart’sche Verlagsbuchhandlung. M. Academic Press. . H. and W. Journal of Geophysical Research. Poirier. Journal of the American Ceramic Society. Voigt. Stocker. Schmidbauer. The electrical conductivity of polycrystalline olivine and pyroxene under pressure. 201214.Frequency dependent electrical properties of polycrystalline olivine compacts. 1980. 1620516222. Journal of Geophysical Research. pp. Standard electrical conductivity of isotropic. Duba.. 63. Akimoto. Heard and H. 58. Kingery and H. G. 48. T. D. Will and R. G. Stromberg. Kingery. Schober. D. 51. W. and P. Sempolinski. The electrical conductivity of some samples of natural olivine at high temperatures and pressures. A. Geophysical Journal International.. L.-P. 49. Smyth. G.198O. Duba and T. 669- 675. Mirwald. 50. M.-F. 664- 669. Shankland. Seifert. J. and R. 94. 1982. 56. D. Applications in Geophysics. pp. R. 1989. at high pressures and temperatures under defined thermodynamic conditions. Tuller. R. Electronic conductivity of single crystalline magnesium oxide. R.199l.25-31.. N. D.5829-5839. edited by M..1993. N. K. Nature. Shankland. Schreyer. edited by W.197l. 344. T. D.FeSiO. Schock. 57. 453-455. Shankland. 63. homogeneous olivine in the temperature range 1200-15OO”C. 1990. 55. 419-432. Duba. New York. 52. Electrical conductivity measurements on synthetic pyroxenes MgSiO. Electrical conductivity of cordierite. Journal of the American Ceramic Society.. Electrical conduction in olivine. W. Zeitschrift fur Geophysik. G. Mineralogy and Petrology. 39-51. 103. Schock. %.283-292. 37. J. and A. A. 54. H. in High Pressure Research. E. J. D. Manghnani and S. 1975. British Journal of Applied Physics. Cambridge. in Point Defects in Minerals. 1978. 175 . H. 54. 145-156. Earth and Planetary Science Letters. R. 68. and D. Duba. 88. A. 64. Wagner. N. Washington. Physics of the Earth and Planetary Interiors. Weill. 1966. oxygen fugacity. MIT Press. Electrical conductivity of San Carlos olivine along [ 1001 under oxygen. L. edited by R. R. Waff. Schock. Tare. A. Stocker. The electrical conductivity of calcium and strontium oxides.Point defects and non-stoichiometry in forsterite. Dielectric Materials and Applications.6462. L. and H. 16. Journal of Applied Physics. S.254-260. Electrical conductivity of magmatic liquids: Effects of temperature. 62. Journal of Geophysical Research.6459 . G. MA. von Hippel. 61. Waff. 60. S. Physics of the Earth and Planetary Interiors.. 10.1983. Influence of oxygen pressure on defect concentrations in olivine with a fixed cationic ratio. 63. Electrical conductivity of molten basalt and andesite to 25 kilobars pressure: Geophysical implications and significance for charge transport. D. 399-403. editor. F. .. Tamura. and J.180. 65. 28. M. 1978. 17. and H. Electrical conductivity in two phase nickel-nickel oxide mixtures and at the nickel-nickel oxide phase boundary.. 22. J. S. Waff. A. J. and composition. 1985. N. J. Geophysical Monograph 31. B. B.and pyroxene-buffered conditions and implications for defect equilibria. A.199o. 66.. 67. 118-129. Tybumzy. Smyth. R. 1954. High Temperatures-High Pressures. pp.1983. Effect of enstatite activity and oxygen partial pressure on the point-defect chemistry of olivine. Pressure dependence of the Neel temperature and the resistivity of FetmyO to 2 GPa. 17. Stocker. Tyburczy. 183-192. 59. 2413~2430. Physics of the Earth and Planetary Interiors. B.. and A. S. Wanamaker. Surplice. and D. C. American Geophysical Union. V.1975. 78-87. High pressure electrical conductivity in naturally occurring silicate liquids. E. Postfach 101251. for an isotropic medium like a silicate melt. B. The ratio of Newtonian D. 1991. Electrical conductivity measurements on olivines and pyroxenes under defined thermodynamic activities as a function of temperature and pressure. a volume (qv) and a shear (qs) component. Cemic. Dingwell 1. K. University Bayreuth. Will. Wood. 1989. we can. the change from liquid to glassy behavior does not occur as a sharp transition but rather describes a region of mixed . regardless of their rheology. 351.Journal of Geophysical Research. M. J. H. The viscosity of a Newtonian material is defined as the ratio of stress to strain rate In contrast.. Voigt. Y. The term silicate melt is used to describe molten silicates quite generally. 821-825. 70. L. American Mineralogist. speak of two components of viscosity. G. the elastic modulus of a Hookean elastic material is defined as the ratio of stress to strain (2) As is the case for elastic moduli. The purely viscous response of a silicate melt is termed “liquid” behavior whereas the purely elastic response is termed “glassy” behavior.-F. D 8580 Bayreuth.. 71. Electrical properties of opal. Donald B. 1993. Bayerisches Geoint. Nell. Notis. B. The combination of volume and shear viscosity yields a longitudinal viscosity. DEFINITIONS A Newtonian fluid is one for which a linear relation exists between stress and the spatial variation of velocity. (qs) q1=qv+ $rls (3) A comparison of longitudinal and shear viscosities illustrates that volume and shear viscosities are subequal at very low strains [9] (see Figure 1).1979. 74. This relaxation time is a convenient approximation to the timescale of deformation where the transition from purely viscous behavior to purely elastic behavior occurs. 4. This ratio T=rl M (4) is the Maxwell relaxation time [24]. Hinze. Nature. Seifert and R.. Hightemperature electrical conductivity of the lower-mantle phase (Mg. XII. and J. Germany Mineral Physics and Crystallography A Handbook of Physical Constants AGU Reference Shelf 2 viscosity to elastic modulus yields a quantity in units of time. Jain and M. Physics and Chemistry of Minerals.Fe)O. Even for the simple case of a Maxwell body. 69. 189197. Viscosity and Anelasticity of Melts. Dingwell. 98.309-311. R. foams and partial melts. Viscosity experiments can be subdivided in several ways. distinguish between those in which the strain rate is controlled and the resultant stress is measured (e. It can be mechanically represented as a series combination of viscous dashpot and elastic spring (a Maxwell element.g. For more complex materials such as crystal suspensions. bubble deformation. phases (e.).. for example. fiber elongation).. We can. Inherent in the experimental study of magma rheology then. the term anelasticity refers to the instantaneous plus the delayed recoverable deformation and the entire deformation behavior falls under the heading of viscoelasticity [26]. CLASSES OF EXPERIMENTS In principle. We can also separate those methods that involve only shear stresses (e. concentric cylinder) from those which involve a combination of shear and volume (compressive or dilational) stress (e.a region of viscoelasticity. Figure 2 illustrates these components for a creep experiment. Structural relaxation in silicate melts is but one example of a relaxation mode.O SHEAR VISCOSITY Figure 1...g. The relationship between longitudinal and shear viscosities in silicate melts. Deformation experiments performed in the viscoelastic region contain three distinct time-resolved components of deformation. 2. the experimental timescale. Redrawn from Dingwell and Webb (1989).. involving additional viscoelastic elements in the linear regime and non-linear effects as well. For any given geometry that employs controlled strain we can further distinguish between the application of a step function of strain and the continuous application of strain (e. The dashed line is the best lit to the data and lies within la of the theoretical line. It is this experimental timescale which must most closely match the natural process in order to make secure applications of the rheological results.e. matrix compaction.. concentric cylinder) and those in which the stress is controlled and the resultant strain rate is measured (e. crystal-crystal interactions. These relaxation modes involve chemical and textural equilibria and thus occur at increasingly longer timescales (i. several additional mechanisms of deformation are contributed at distinct timescales of deformation via additional relaxation modes within and between the added Copyright 1995 by the American Geophysical Union. instantaneous recoverable.liquid-like and solid-like behavior . Viscous flow is the delayed non-recoverable component. As a consequence of the multiphase nature of flowing magma the accompanying mechanical models become more complex. any experiment that records strain as a function of time and applied stress can be used to obtain viscosity. is the experimental deformation rate or its inverse. beam bending or fiber elongation).. Stress relaxation involves the recording of stress versus time as . stress relaxation versus steady-state flow). at lower rates of deformation). etc. delayed recoverable and delayed non-recoverable.g.g.g.g. The solid line represents the correlation predicted from the assumption that volume and shear viscosities are equal. 209 210 VISCOSITY AND ANELASTICITY OF MELTS LOG . see Figure 3). G) of a linear viscoelastic melt with a relaxation time r plotted as a function of ex where 61 is the angular frequency of the applied sinusoidal stress. Frequency-dependent or non- . the delayed recoverable strain.e. The characteristic strain rate of the experiment is easily defined in most rheological experiments. forced oscillation techniques in the range of 0.g.gKo. several experimental timescales are compared with structural relaxation times of silicate melts. Each structural or physical component of the system relaxes as a distinct relaxation mode at a distinct timescale of frequency which is a function of pressure and temperature. In contrast nonlinear measurements can deal with the redistribution of phases during macroscopic flow. Implicit in considerations of rheological measurements is the ratio of deformation rate to the relaxation rate of structural components in the material. ultrasonic wave attenuation). Steady-state strain experiments record the equilibrium stress sustained by the liquid due to the constant strain rate being applied to the sample. small in magnitude but up to very high frequencies (from mHz to MHz). The shear relaxation time z = n/G is for the mechanical model of a spring and dash-pot in series (i. and the delayed non-recoverable viscous flow occurring in a linear viscoelastic material upon application of a step function in stress at time..g. Finally.. Ultrasonic measurements are performed on time scales of l-50 ns. K. q. DINGWBLL 211 . The subscripts “0” and “00” indicate zero frequency and infinite frequency values. are applied and the magnitude and phase shift of strain is measured (e. nv. in Figure 4. Such measurements probe the response of the system to stresses without macroscopic rearrangements of the phases. we can distinguish between time domain experiments where a stress is applied and the time variant relaxation of the system to the new equilibrium is measured (e. Calculated frequency dependent behavior of longitudinal.01-150 s and fiber elongation in DELAYED RECOVERABLE STRAIN INSTANTANEOUS ELASTIC STRAIN t=o TIME Figure 2. torsion. creep experiments) and frequency domain experiments where sinusoidal variations of the stress field..Go 0 LOG Wl 3 Figure 3. volume and shear viscosities (rt 1. For example.the stress field decays to zero after the application of a step function of strain. The instantaneous recoverable elastic strain. We can distinguish between experiments performed at low total strains such that the perturbations from equilibrium are small and in the linear regime of stress-strain relations. a Maxwell element).) and moduli (M. t=O. from lo2 to lo6 s. This involves determining the rate at which an 212 VISCOSITY AND ANELASTICITY OF MELTS Figure 4.3 mm and lengths lo-18 mm are commonly used. In a vertically mounted silica glass dilatometer the silica glass holder of the dilatometer supports the beaded glass fiber in a fork. Equation 6 is known as Trouton’s rule. GEOMETRIES The most widely used example of controlled strain rate and measured stress is the rotational (Couette) method (see Figure 5). ?~etcn~. This method has also been used in the investigation of the viscoelastic behavior of silicate melts at/near the glass transition [41]. The strain rate is imposed on an annulus of liquid filling the gap between an inner cylinder (or spindle) and the outer cylinder (or cup) which usually takes the form of a cylindrical crucible. A second silica glass rod holds the lower bead of the fiber in tension.Newtonian effects are seen in frequency domain rheological experiments when the measurement timescale approaches a relaxation mode timescale. Absolute shear viscosities in the range lo9 . Ryan and Blevins [34] provide a description of the physics of Couette viscometry.1-0. 171 Although infinite shear strains are possible in a melt. Shear viscosities in the range 109-1014 Pa s can be ‘determined using fiber elongation techniques (see Figure 5). The relaxation times relating to the various experimental techniques are discussed in Dingwell and Webb (1989). Another form of the Couette viscometer is the cone-and-plate geometry. The cone-and-plate method finds application at lower temperatures and higher viscosities than the concentric cylinder method. The liquid-glass transition as a function of temperature plotted for several silicate melts calculated from Equation 4 together with the timescales on which a range of experimental measurements are performed. A tensile stress (-lo7 Pa) is applied to the melt fiber and the viscosity is determined as the ratio of the applied stress to the observed strain-rate. This avoids the need to pour or melt the silicate material into the cylinder and to immerse the spindle into the liquid at high temperature. 3. is the elongational viscosity and is related to the shear viscosity. 15. The strain rate is delivered to the liquid by rotating either the inner or outer cylinder. . Q. In this geometry the observed vt. The concentric cylinder method is commonly used for viscosity measurements in the range of loo-lo5 Pa s. The shear stress sustained in the liquid is usually recorded as the torque exerted by the liquid on the inner cylinder.IO1 1Pa s can be determined using micropenetration techniques (see Figure 5). The geometry of the cone-and-plate viscometer allows the preparation of starting materials by pre-machining to the final form. by (5) [ 11. therefore.s costt. Glass fibers with a diameter 0. volume strain must be limited in magnitude [25]. 251 for times greater than the relaxation time of the melt. approaches an infinite value with increasing time and Equation 5 becomes [ 11.y . The strain-rate range is machine limited to 10m7.10m4 s. The volume viscosity of a melt. Viscometers based on the cone-and-plate geometry have been used in both steady state (as above) and pulse strain modes. r (m). Maximizing the density contrast reduces errors associated with the estimation of melt density. The falling sphere method may be used for the simultaneous determination of density and viscosity. 361. t (s). Alternatively the falling sphere method may be used with input values of density provided the density contrast between melt and sphere is relativeIy Iarge. the acceleration due to gravity. The counterbalanced sphere and falling sphere viscometers (see Figure 5) are based on Stokes law. 441 for the radius of the sphere. This method extends the lower limit of measurable viscosity using the falling sphere method at high pressure to 10m3 Pa s. High accuracy (+O.lo8 Pa s [12. For a cylindrical specimen of any thickness the shear viscosity can be determined by qs (Pa s> = 2rtmgh5 3V Fh/Gt (27r h3 + V) (8) for the applied mass.l log10 Pa s) is obtained by using a silica glass sample holder and pushrod for temperatures under 1000°C. and time.10” Pa s [2] can be determined. 161 for the case in which the surface area of contact between the melt and the parallel plates remains constant and the cylinder bulges with increasing deformation. Errors in density contrast can be reduced below the uncertainties inherent in the other variables affecting viscosity determination. indenter under a fixed load moves into the melt surface. The shear viscosity of large cylinders of melt or partially molten material can be determined by deforming the cylinder between parallel plates moving perpendicular to their planes. Riebling [30] has described a counterbalanced sphere viscometer which he subsequently used in viscosity determinations in the B203SiO2 [31] and Na20-Al203-Si02 [32] systems. The parallel plate method involves the uniaxial deformation of a cylinder of melt at either constant strain rate [ 181 or constant load [40]. h (m) of the cylinder. cylindrical or spherical in shape [6]. 161 and lo7 . 34. . the applied force. (9) This is the “perfect slip” condition. The indenter may be conical. t (s) [12. Absolute viscosities in the range lo4 . indent distance 1 (m) and time. (t=O and 1 =0 upon application of the force). the height. Very high pressure measurements of viscosity have been made [19] by imaging the falling sphere in real time using a synchrotron radiation source and a MAX 80 superpress. m (kg). For the case in which a spherical indenter is used [8] the absolute shear viscosity is determined from qs (Pa s) = “. g (m2/s).Redrawn from Dingwell ‘and Webb (1989).:zJf. For the case in which the surface area between the cylinder and the plate increases with deformation and the cylinder does not bulge the viscosity is qs (Pa s) = m ’ h2 3V 6h/6t . Specimen deformation rates are measured with a linear voltage displacement transducer.e t (7) [28. This is the “no-slip” condition. Falling sphere viscometry has been employed at 1 atm and at high pressures [13. P (N). . the volume. V (m3) of the material. (4 dependence of the longitudinal viscosity has been observed. x [27]. The real component of the modulus. Methods of determining viscosity: (a) falling been described using a number of different equations. MY. The sphere (b) restrained sphere (c) rotational viscometer (d) simplest form. In studies where the frequency of the applied signal has been CT) I^’ p -1 4$ greater than that of the relaxation frequency of the melt I -.I// Na20-B203-Si02 [23]. frequencyffh\. i. [43]. a(w). basaltic andesite [35].303 $ (14) .. the Arrhenius torsion of a cylinder. Viscosities are calculated for time. and attenuation.The shear and longitudinal viscosities of a melt can be determined from the velocity. Redrawn from Zarzicki (1991). The shear viscosity can be calculated from the velocity and attenuation data in that 17*(o) = M *(O)/iO. often valid for restricted temperature sink point measurement (e) free fiber elongation (f) loaded intervals. and the imaginary component of the modulus. “.l) + iM”(C0) = M”(C0) + iq’(0)4 = q”(O)-0 + iq’(O)-0 (1 1) and the real component of the frequency dependent viscosity is q’(o) = T . or M*(CO) = M’(0.’ Ii shear wave propagation has been observed (BzO. In cases (basalt melts [22]. is a linear dependence of the logarithm of fiber elongation (g) beam bending (h) micropenetration (i) viscosity on reciprocal temperature.oq = logloqo + 2._. equation for time t and distance x [27]. t and distance. c(w). of a shear or longitudinal wave travelling through the melt. (12) lbg. synthetic silicate melts [33]) where the experimental conditions were approaching the relaxation frequency of the melt. .e.t) = A0 expQX expfw(f-x’c (10) DINGWELL 213 gg$fp!i a-. ~. M’(o) = PC*.: ~~A~ the temperature (1000-l 500°C) and frequency (3-22 MHz) conditions required to observe the relaxed (frequencyindependent) longitudinal viscosity of most silicate melts. M “(0) = M’(w)cti~f (where the quality factor Q = M’(o)lM”(o) = 7cflca [27]. Small strains (<10m6) are used and linear stress-strain theory is applicable.T (7-j .. rp i/u Al lb‘ :i 4. . TEMPERATURE DEPENDENCE OF P VISCOSITY (4 m k) (11) 0) The temperature-dependence of silicate liquid viscosity has Figure 5. Na2Si205 [46]). where the amplitude of the wave is A(w. 15 and 0. Quite often the data obtained by a single method of investigation over a restricted temperature or viscosity interval are adequately described by Equation 14. T.303A NT. silicate liquids exhibit non-Ahrrenian viscosity temperature relationships. The degree of “curvature” of the viscosity temperature relationship plotted as log viscosity versus reciprocal absolute temperature varies greatly with chemical composition (see [29] for a summary). Viscosity as a function of pressure for various silicate melts. This consideration is extremely 214 VISCOSITY AND ANELASTICITY OF MELTS IIII K?O M90 5510~ (1300°C) Abyssol Ol~v~ne Tholellle (13OO’C) LIIII 0 10 Prt?ssi?eohboI r 3o ’ Figure 6. CALCULATION SCHEMES A number of empirical calculation schemes for the viscosity of silicate glass melts have been around for several decades [37] but calculation methods for geological melts are a more recent phenomenon. With the possible exception of SiO2 however. 7. Brearley et al. respectively. 6. Redrawn from Scarfe et al. The temperature-dependence of non-Arrhenian data can be reproduced by adding a parameter to Equation 14 to yield The shear viscosity can be calculated from the velocity logI aq =logioqa + 2.where q is the viscosity at temperature. 15. Bottinga and Weill [3] produced a method for the estimation of melt viscosities . (1989). 491. q*l(w) = q*~w> + 4 q*s(o)/3 (13) Angel1 [I] describes the concept of strong and fragile liquids based on the extent of nonArrhenian temperatureMost ultrasonic studies of silicate melts are conducted at dependence of viscosity. [5] also observed a transition from positive to negative pressure dependence of viscosity along the join CaMgSi206-NaAlSi308. sufficient data now exist to demonstrate that. 451. 4( investigated the pressure-dependence of silicate melt viscosities across compositional joins exhibiting both negative and positive pressure dependence of viscosity.To) (15) and attenuation of the shear wave. ‘in general. Kushiro [21] investigated liquids along the SiOz-CaAl204 join observing a linear pressure dependence of viscosity that changed from a negative value at mole fraction CaAl204 = 0. The data from the propagating longitudinal wave results in the determination where To is a constant. 38. Volatile-bearing silicate liquids have also been studied at high pressure [4.2 through pressure invariance at CaAl204 = 0.33 to a positive pressure dependence at CaAl204. This empirical description of the of the longitudinal viscosity from which the volume temperature-dependence of liquid viscosity is called the viscosity can be calculated Fulcher or TVF (Tamann-Vogel-Fulcher) equation [ 14. and 770 and E are termed the frequency or pre-exponential factor and the activation energy. 42. Figure 7 summarizes the effects of Hz0 and F20-1 on the viscosity of NaAISi308 liquid. 0 t -I 12. 3 11. Two studies have 1II Albite-H20-F20-. Additionally the increase of pressure likely leads to more fragile behavior. at 1 atm pressure that was based on the literature data for synthetic melt compositions. In general. All available evidence points to a single relaxation mode being responsible for the onset of non-Newtonian I I I I I I1 12. Figure 6 illustrates the pressure dependence of silicate liquid viscosities to 2 GPa. more fragile.201. ‘z CLA . In contrast the viscosities of some silicate liquids increase with pressure.OH). .0 I ‘. The viscosities of silicate and aluminosilicate melt compositions with relatively low calculated NBO/T (ratio of nonbridging oxygens to tetrahedrally coordinated cations) values decrease with increasing pressure. Shaw [39] included water in his calculation model and with that allowed for the calculation of granitic melt viscosities at low pressures. 7. No intrinsic pressure dependence of viscosity was included. 5. The pressure-dependence of anhydrous silicate liquids has been summarized by Scarfe et al.2 plotted versus reciprocal temperature (X = F.41Si308H20-F20-1 with (X/X+0) = 0. Redrawn from Dingwell (1987). Viscosities of melts in the SySteln &. behavior.important where extrapolations of viscosity to lower temperatures are performed. PRESSURE DEPENDENCE OF VISCOSITY The falling sphere method has been used to study high pressure viscosities of natural and synthetic silicate liquids [ 10. silicate melts are strong liquids in comparison with nonsilicate liquids.5kbar 54r0 $ 3- -II 678 104/T (K) Figure 7.6 . 13. Decreasing SiO2 content generally leads to less Arrhenian. This is the direct consequence of the relaxation mode due to structural relaxation in silicate melts. NON-NEWTONIAN MELT RHEOLOGY The Newtonian viscosity of silicate melts is a low strain rate limiting case. [36]. 7. With increasing strain rate the viscosity of silicate melts eventually becomes strain rate dependent as the inverse of the strain rate approaches the relaxation time of the silicate melt structure. The extent of nonArrhenian temperature dependence varies greatly with composition.1 and 0.d . A. a basalt and a nephelinite) is illustrated in Figure 8. 11. -1.. . The onset of non-Newtonian rheology occurs approximately 3 log10 units of time “above” the relaxation time of each silicate melt approximated from the Maxwell relation. Redrawn from Webb 1 Dingwell (1990b). The onset of non-Newtonian rheology has been extensively investigated [47. Wright. 216 VISCOSITY AND ANELASTICITY OF MELTS 1. NEP -. VA. Arlington. rheology in silicate melts. 481.. . . The onset of non-Newtonian rheology for four geological melts (a rhyolite.L. calculated from the Maxwell relation for each melt.B. STRAIN RATE (s-0 Figure 8. an andesite. C. Redrawn from Webb and Dingwell (199Oa). Shear viscosities of Little Glass Mountain rhyolite (LGM). Crater Lake andesite (CLA).. : L. 345pp. The arrows indicate the calculated rxation strain-rate for these melts.2 I IIIIIII -5 -4 -3 -2 -1 log.and composition-dependenceo f the onset of non-Newtonian viscosity of silicate melts..’ DINGWELL 215 Figure 9. Hawaiian ‘holeiite (HTl3) and nephelinite (NFP) composition melts a function of applied strain-rate. (a) A reduced plot of shear viscosity relative to Newtonian versus strain-rate normalized onto the relaxation strain-rate for Na$Q09 at temperatures from 474 to 506°C. The low-strain-rate limit of Newtonian viscosity is seen below strain rates of 10e4 whereas shear thinning (a decrease in viscosity with increasing shear rate) sets in at higher strain rate. Naval Research Lab. The success of this normalization indicates that the onset of non-Newtonian melt rheology in silicate melts can be easily estimated using values for the Newtonian viscosity and the shear modulus. Strong and fragile liquids. The composition-dependence of the onset of non-Newtonian rheology can be removed in large part through this normalization. With increasing straine the onset of non-Newtonian (strain-rate dependent) lravior is observed. in Relaxations in Complex Sysrems edited by K.t -. These reduced plots based on Equation 4 remove the temperature. Angell. (6) A reduced plot of shear viscosity versus normalized strain-rate for a range of silicate melt compositions. A normalization of the data for several compositions and at several temperatures is illustrated in Figure 9 where the viscosities are normalized to the low-strain-rate limiting value of Newtonian viscosity and the strain rate of the experiment is normalized to the relaxation frequency (the inverse of the relaxation time). Ngai and G. 1984. 3-l I. ... Phys. 307-322. G. 1977. Fontana. 1989.S. Rheological investigation of vesicular rhyolite.S.. Carnegie Inst.E. 12. Sot.B.B. 12. Am. 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A.. 63. 20. 1976. Wash.I.A. 49-88. Anelasticity in the Earth Geodynamics Series. 1867. Spectrum of relaxation times and fluctuation theory: ultrasonic studies on alkaliborosilicate melt. Fujii. 36.. T. Ultrasonic velocity and attenuation in basalt melt. 156-164.S. 22. O’Connell.C. J.S. R. 24 Maxwell.. Herzfeld.. Chem. 507508.. I.. Rough measurement of high viscosities.W. American Geophysical Union. O. Olhoeft.. Volume 4. 1968. H. Hailer. in: High-pressure research in Mineral Physics edited by M.S. 1981. 80. Kushiro. 87. 17. DC. Briickner. 26. 9. Nowick. Brit.. I. On the dynamical theory of gases.B. Akimoto.F. J. 28. 16.. Litovitz.V. Hessenkemper. Lett. . 1978. P. Phys. Absorption and Dispersion of Ultrasonic Waves. Academic Press. Mazurin. 195-200.C. Cambridge Philos. Sol. Washington.H. 21. 5-8. and T. Solid. 105. 563pp.K. 1031-1038. 47. Tamann.F. 38. 33. Riebling.. Non-Newtonian viscous flow in soda-lime-silica glass at forming and annealing temperatures. E. . 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Geochetnicul Society Special Publiccrtion. Phys. J. Geophys. . E. Springer. 1964. Y.O.. Res.Y. Earth Planet.H. 41. . Res. Berlin. Viscosity and configurational entropy of silicate melts. P...S. 159-167. An improved counterbalanced sphere viscometr for use to 175O”C. 40. 42. Structure of sodium aluminosilicate melts containing at least 50 mole% SiO2 at 1500°C..R. unorg. Geochim.. Ochoa and K.M. 39. 35.29. Ultrasonic studies of silicate melts.. Y. J. Sato. Am. 1985.. 95. G.E. Carmichael. 9247-9270. Manghnani. Chetn. Geol. 478-483. Virgo. 313-322. 44.. 32. Ultrasonic measurements of Vp and QP: relaxation spectrum of complex modulus of basalt melt. Am. Viscosities in t B203-Si02 system. 36. J. Richet. and W. Ins. H. Ricbling. Mysen and D. Rivers. Simmons. 1963.. Waseda and E. 37. 1987. 17864. allg. Shaw. Matsubara. 407pp. 33.H.R. 22. Physik Z.163. and R.. The majority of estimates of outer core viscosity is based on whole Earth geodetic and seismological observations.B. T. 645-646. Dingwell.. 1921. Am. S. inferred from the various observational and theoretical methods [24]. Viscoelastic properties of a simple organic glass. 1990. 1. Chern.L. J. and bulk or volume viscosity. The motion associated with eddy viscosity implies the possibility of non-viscous dissipative mechanisms such as ohmic dissipation. 5 1. molecular viscosity (a rheological property of the material) vis-a-vis a modified or eddy viscosity (a property of the motion). In cases where outer core viscosity estimates are based on observations of the attenuation of longitudinal waves. White.. 1968. 451-456. Secco Estimates of outer core viscosity span 14 orders of magnitude. Viscous relaxation and non-Arrhenius behavior in B2O3. Mineral. andesite. 95.B. and D. 125-l 32. 45. q. for damping radial mode oscillation [4]. Glasses and the vitreous state. Montana. is a measure of resistance to isochoric flow in a shear field whereas q” is a measure of resistance to volumetric flow in a 3-dimensional compressional field. . Webb. Phys. Non-Newtonian rheology of igneous melts at high stresses and strain-rates: experimental results for rhyolite. Webb. Geophy. B. and A. Tauke.. and D. 1990a. 47. 1991. both TJ. l990b 49.V.151. J. 1963.S.. Taylor. Litovitz and P.. 15695-15701.5-257. basalt and nephelinite... 46. The onset of non-Newtonian rheology of silicate melts. 156. Res.A.Chem. 76. Am.. Cambridge University Press. Dingwell. 17. 2439-2442. Wehb.. depending on the type of strain involved [ 14. S. Phys.L. Molecular viscosity is separated into nearly equal components of shear viscosity. J. is important for damping whole Earth torsional mode oscillation and 11. Viscosity of the Outer Core R.B. J Geophys. The effect of H20 and CO2 on the viscosity of sanidine liquid at high pressures. 505pp. 67. Zarzicki. This wide range of values may be partially explained by the difference in type of viscosity.B. Chem Mineral. Macedo. Cer. q. A. 1991. Cambridge. and Q play significant roles but only 17. l58. Shear and volume relaxation in Na2Si205. Tobolsky.. 24. 48.L. Rex. 43. 15683-15693... H. 44. 9 5. . Vogel. A. 1926. 50. Das Temperaturabhtingigkcitsgesetz der Viskosit2t von Flussigkciten. Sot. J. J. geometrical spreading. University of Western Ontario.4. 218 SECCO 219 TABLE 1. radial and lateral inhomogeneities will be embodied in derived attenuation values. studies of p-wave attenuation benefit from their short periods (seconds) and all 7 studies cited in Table 2 give upper bound viscosity values within a very confined range of lo*-10’ poises. Other methods of outer core viscosity estimation are from extrapolations launched from experimental data at low (relative to core) pressures and temperatures using various theories of liquid metals and from geomagnetic field observations at Earth’s surface. Tables 1 and 2 are viscosity estimates based on geodetic and seismological studies. It must be noted. 7. that time independent factors that affect seismic wave amplitudes such as scattering.35 . Most of the experimental data on liquid Fe and liquid Fe-N& Fe-S. the density. The data and references are presented in 9 tables. While long period (minutes to years) geodetic phenomena. Both of these suffer from large extrapolations and from the lack of any experimental viscosity data on liquid Fe at pressures of even a few kilobars.In terms of the observation times required by a particular method.7 x 10” “Torsional free oscillations of whole Earth Verhoogen (1974) Yatskiv and Sasao (1975) 2. Dynamic Viscosity Estimates of Outer Core from Geodetic Studies Reference Dynamic Viscosity (Poises) Method”“’ Sato and Espinosa (1967) 0. v. the outer core viscosity estimates inferred from these measurements. respectively.6 x 10-l 5 x 10’ “Chandler wobble . by v = q/p. Table 5 contains experimental shear viscosity data for Copyright 1995 by the American Geophysical Union. however. Confirmation of any observation of inner core oscillation has not yet been made and therefore any so-derived viscosity estimate from geodetic observation or theory must be admitted with caution. length of day R. The data in Tables l-4 are graphically presented in Figure 1. respectively. A. London. Canada N6A 5B7 Mineral Physics and Crystallography A Handbook of Physical Constants AGU Reference Shelf 2 variations. such as the radial and torsional modes of free oscillation. Department of Geophysics. Fe-O and Fe-Si alloys is found in the metallurgical literature and they are all restricted to measurements at a pressure of 1 atm. Secco. reported in some references have been converted to dynamic viscosity. using a value of 10 g/cm’ for p. Tables 3 and 4 are viscosity estimates from geomagnetic and liquid metal theory studies. and polar motion can all be accurately measured. suffer from long observation times which can introduce large uncertainties from additional energy sources and/or sinks affecting the observed phenomenon. ranging from 10-l to 10” poises. Values of kinematic viscosity. A brief description of the method used for each estimate or measurement is also given. Dynamic Viscosity Estimates of Outer Core from Theories of Liquid Metals Reference Dynamic Viscosity (Poises) Method Bullard (1949) Miki (1952) Backus (1968) Clans (1972) Leppaluoto (1972) Bukowinski and Knopoff (1976) .“Chandler wobble Anderson ( 1980) 5 x lo2 “Damping of free oscillation radial modes Molodenskiy (1981) 2 lo7 “Forced nutation of the Earth (value for MCB) Molodenskiy (198 1) I IO” “Tidal variations in the length of day Molodenskiy (198 1) 2 x 1o’O ‘Chandler wobble Gwinn et al (1986) <5. Dynamic Viscosity Estimates of Outer Core From Seismological Studies Reference Dynamic Viscosity (Poises) Method Jeffreys (1959) 5 x lo8 Attenuation of p-waves Sato and Espinosa (1965. 1967) 8.7 x IOX “Damping of inner core translational modes (superconducting gravimeter data) Bondi and Lyttleton (1948) <lo’* ‘Theoretically required for secular deceleration of core by viscous coupling Stewartson and Roberts (1963) <lo’ ‘Theory of rotating fluids Toomre (1966) >6 x 10’ ‘Theoretically required for steady precession by core/mantle viscous coupling Won and Kuo (1973) > 10-l ‘Theoretical evaluation of decay time of inner core oscillation (value for ICB) Toomre (1974) <lo” ‘18.4 x lo4 “Retrograde annual Earth nutation .6 x lo’* Multiply reflected s-waves at mantle/core boundary.4 x IO’ Attenuation of body waves and checked against radial mode Q data TABLE 3.6 year principal core nutation (value for MCB) Aldridge and Lumb (1987) 2.3 x lo5 “Viscous damping only for nearly diurnal free wobble (tidal measurements) Smylie (1992) 7.VLBI measurements (value for MCB) Neuberg et al (1990) <3. Dynamic Viscosity Estimates of Outer Core from Geomagnetism Studies Reference Dynamic Viscosity (Poises) Method Bullard (1949) 1O-2 Magnetic damping of core fluid motions Hide (1971) lo7 Magnetohydrodynamic interactions between fluid motions and bumps on MCB Schloessin and Jacobs (1980) 2x lo5 Decay of free dynamo action during polarity transitions Officer (1986) 2x IOX Value predicts correct order of magnitude of external field and westward drift SECCO 221 TABLE 4.9 x lo7 ‘Decay of inertial waves in outer core ’ theory ” observation 220 VISCOSITY OF THE OUTER CORE TABLE 2. Sacks (1970) lo8 Attenuation of p-waves Suzuki and Sato (1970) 3-7 x 10” Attenuation of s-waves Buchbinder (1971) 2x lo8 Attenuation of p-waves Adams (1972) 4 x lo8 Attenuation of p-waves Qamar and Eisenberg (1974) l-2 x IOR Attenuation of p-waves Zharkhov and Trubitsyn (1978) <<lo’ Attenuation of p-waves Anderson and Hart (1978) 1. 1. The common logarithm of dynamic viscosity (poises) of the outer core plotted as a function of method used for its determination.Schloessin and Jacobs (1980) Anderson (1980) Poirier (1988) Svendsen et al (1989) 2. Fig.lo4 3 x to-* From experimental values for liquid metals at STP Quantum statistical thermodynamics of liquid metals From experimental values of liquid Hg at 10 kb and 400K Andrade formula for melting point viscosity (value for ICB) For a pure Fe outer core. from significant structure theory of liquids (value for MCB) For a pure Fe outer core. Experimental Data of Shear Dynamic Viscosity (centipoises) of Liquid Fe at 1 atm Reference T(“C) 1536 1550 1600 1650 1700 1750 1800 1850 Barfield and Kitchener (1955) Thiele (1958) Hoffman (1962) . as in the reference.5 x lo-* lo-2 lo-*. because of insufficient density data for many of the alloy compositions. 222 VISCOSITY OF THE OUTER CORE TABLE 5.5 x IO-* l-5 x 10-l >lO’ 3. from band structure calculations From experimental values for liquid Fe and Andrade’s pressure effect on viscosity Two structure state theory extrapolated to core pressures Thermodynamic scaling relation between melting temperature and viscosity and diffusivity of metals Liquid state model fitted to high pressure melting data on Fe OUTER CORE VISCOSITY A fA t 4i: f SEISMOLOGY A GEODESY A GEOMAGNETISM THEoRY Method pure liquid Fe and Tables 6-9 contain experimental shear viscosity data for liquid Fe alloys. The viscosities in Tables 6-9 are presented as either dynamic or kinematic viscosities.10-l 5 x lo* 3.4 x lo* lo’. all measured by the oscillating crucible method.7-18. 2 3.62 1545 5.60 5.42 5.93 5.~Arkharov et al (1978) 28.02 1513 5.28 4.48’ 5.43 1652 5.69 1633 5.98 4.9 1516 6.01 5. Experimental Data of Shear Viscosity of Liquid Fe-Ni Alloys at 1 atm Reference Composition Temperature wt% Ni (“(3 Viscosity Dynamic Kinematic (centipoises) (millistokes) Adachi et al (1973) 4.01’ 4.31 5.76 5.Cavalier (1963) Lucas (1964) Vostryakov et al (1964) Nakanishi et al (1967) Kaplun et al (1974) Arkharov et al (1978) Steinberg et al (1981) 7.79’ 4.92 4.96 5.41 5.54 1665 5.30 4.91 1604 5.10 3.44” 5.00 3.81 SECCO 223 TABLE 6 (continued) Reference Composition wt% Ni Temperature CC) --___.11 .7 1502 6.54 4.7 4.15 1519 5.70 5.91 6.54” 5.04 1693 4.9 3.55 3.60” 6.58 4.11 1550 5.6 1471 6.36 9.44’ 5.03 ’ interpolated ’ extrapolated TABLE 6.90 4.72 1596 5.30 4.69’ 4.89’ 5.4 4.22 4.87 5.6 5.95 4.03 4.Viscosity Dynamic Kinematic (centipoises) (millistokes) -.95 1550 5.37 1581 5.7 3. 46 7.45 1700 5.39 TABLE 9.15 1508 7.72 1621 7.41 Vostryakov et al (1964) 0.61 0.70 1605 6.15 1.85 1712 5.83 1707 6. Experimental Data of Shear Viscosity of Liquid Fe-S Alloys at 1 atm Reference Composition Temperature wt% s 3 (“C) Viscosity Dynamic Kinematic (centipoises) (millistokes) Barfield and Kitchener (1955) 1.51 6.02 0.56 3. Experimental Data of Shear Dynamic Viscosity of Liquid Fe-O Alloys at 1 atm Reference Composition Temperature Dynamic Viscosity wt% 0 (“0 (centipoises) Nakanishi et al (1967) 0.91 0.13 2.0 1549 7.69 1758 5. Experimental Data of Shear Viscosity of Liquid Fe-Si Alloys at 1 atm Reference Composition Temperature wt% Si (“C) Viscosity Dynamic Kinematic (centipoises) (millistokes) Romanov and 0.48 1.40 0.16 1529 7.1 1540 9.61 8.0 5.99 8.55 1743 7.1615 4.66 1806 6.00 (+0.012 1600 5.00 4.071 5.90 1592 6.02 wt%C) 1600 6.84 1800 5.43 224 VISCOSITY OF THE OUTER CORE TABLE 8.46 1654 5.39 1600 6.92 1642 6.14 .046 5.36 1756 6.98 TABLE 7.28 1.49 8.62 Kochegarov (1964) 1580 8.04 1789 6.52 1600 8.04 8.70 6.39 1553 6.072 5.41 18.78 1668 7.49 1454 8.6 2.43 0. 2. and Kitchener.41 2. 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J. 829-857.. 476-477. 17. 39. 1970. P. These. The Damping of Core Waves.Ni.Phys. D. J. 1992. 1966.A. 72. Svendsen. 55. 32. 46. YaS. H. Won.lnr. 300-303. and Espinosa. A. Seis.. Sot. and Bass.ActuMetafl. Qamar.. Cameron. Ahrens. 46. 18(3).Geophys. Carnegie Insr.Res.lSi. Thiele. 41. R. 43. The Inner Core Tnnsla-tional Triplet and the Density Near Earth’s Center. 48. Science. Smylie.J. Tyagi. 758-765.Meralloved. 1974.. Romanov. 1678-1682. 414-416. 78.Res. Viscosity Determination in the Earth’s Outer Core from ScS and SKS Phases.P. Union. Chandler Wobble and Viscosity in the Earth’s Core.A. 40. 42.: B. Oscillation of the Earth’s Inner Core and Its Relation to the Generation of Geomagnetic Field. and Kochegarov. Steinberg. New York. V.E.R.T. 1980. 38.. 1761-1767. 44. and Jacobs. A.Earth Planer. 1988. 1958 (cited in Lucas.. Dissipation Factor of the Torsional Mode “T. A. 1964). J. Verhoogen. juillet. Jr. 17(2).G. I..1981. Can. Vatolin. On the Coupling of the Earth’s Core and Mantle during the 26.. M.J. N. and Lord. Sato. 35.1309-1319. 334-335.F. and Espinosa. in: The Earth-Moon System.Astr. A. 45. 37. 1974. B. 38. 158. J.. 1989.J. and Sato.Res. Sacks. 1973. Yatskiv. 33-45. 18. and Yesin. 69.Wash. and Eisenberg. Geophys. A. Toomre.H. R. 1963.. S. 154-186. and Robetts.S. Viscosity of Binary Iron-Silicon Melts in the Low Concentration Range of the Second Component. 1967).. Trans.W. Sato. 905-911. Y. 1964.H. R. Amer.. The Viscosity of Molten Fe. Chandler Wobble and Viscosity in the Earth’s Core. 57. J. A. Nature.A. 92. On the Motion of a Liquid in a Spheroidal Cavity of a Precessing Rigid Body. 1974. Fiz. 1965 (also Bull. J. l-20. O. B. K. Geophys. Toomre. J.F. 1967. 29. Sot. I.G.GeophysJ. A.A. Berlin. Stewartson. Anderson. for a Homogeneous-Mantle Earth with a SoftSolid or a Viscous-Liquid Core. Dissipation in the Earth’s Mantle and Rigidity and Viscosity in the Earth’s Core Determined from Waves Multiply Reflected from the Mantle-Core Boundary. 1964. Plenum Press.Metal.Yrbk. A. 17. Amer. Marsden and A. 72-89.000 Year Precession. On the “Nearly Diurnal Wobble” of the Earth.W. Meralloved. Geophys. Suzuki.Fluid Mech.Earth. Ideal Fe-FeS. J. 255. and Sasao. 335-348. Fiz. Anelasticity of the Outer Core. 249. J. T. 36.E. 31. Vostryakov. 79. 99-105. 33. W. Schloessin. A.A. Dynamics of a Fluid Core with Inward Growing Boundaries. 1970. J. Phys.D. ed. 34..J. and Kuo. Geophys. 47. T. 157-170. . Models of Mantle Viscosity Scott D. 1978. King 1. 45.. 255. 3. such as diffusional flow. the viscosity changes by an order of magnitude at constant stress [c. 24. the stress distribution in subduction zones.f... Department of Earth and Atmospheric Sciences. Plate velocities. The deformation of minerals under mantle conditions generally follows a flow law of the form i = A(f)” P exp(-+) (1) where 6 is the deformation rate. King. Hubbard. grain size and stress [e. in turn. or studying the physical deformation properties of mantle minerals in the laboratory. 651.g. 655. INTRODUCTION The viscosity of the mantle is one of the most important. and estimates of geochemical mixing time scales are all strongly affected by the pattern of convective flow which. 49. cr is the deviatoric stress. T is the temperature in Kelvins.P. R is the gas constant and A is a S. 43. translated and edited by W. Viscosity is defined as therefore. Changes of deviatoric stress by a factor of 2 change the viscosity by an order of magnitude [c. Pachart Pub. and least understood material properties of the Elarth.) For temperature changes of 100 degrees K. p. deformation is directly related to viscosity. Laboratory measurements of deformation indicate that the rheology of upper mantle minerals such as olivine ((Mg.Fe)$iO4) is a strong function of temperature. Both approaches have advantages and drawbacks. D. The question of which mechanism .N. d is the grain size of the rock. 61.Nature.431.. IN 47907-1397 Mineral Physics and Crystallography A Handbook of Physical Constants AGU Reference Shelf 2 constant [c. Other factors. A rheology with a linear stress strain-rate creep mechanism. Purdue University.. 441. 3. 46.B. Q is the activation energy for the deformation mechanism. V. V. Physics of Planetary Interiors. is strongly influenced by the viscosity structure of the mantle. and Trubitsyn.House. 388 pp. Two creep mechanisms are likely to dominate in the mantle. diffusional flow (corresponding to n=l in equation 1) and power-law creep (corresponding to n>l in equation 1). p is the shear modulus. combined with flow models. is referred to as a Newtonian rheology. Tucson. such as partial pressure of oxygen and water may also have important effects.59. There are two approaches to understanding the viscosity structure of the E&h: using observations such as the geoid and post-glacial uplift.. Zharkov.f. deep-earthquake source mechanisms. 1975. (Note the factor of 2 difference in equation (2) compared with the definition used by experimentalists. 441.f. West Lafayette. if the load is then removed. typical mantle strain-rates lie close to the diffusional flow field at this small grain size. 1. the rate of return is also dependent on viscosity. the rate at which the surface deforms will depend on the viscosity of the fluid. spine1 and perovskite have similar normalized flow stresses. constant strain rate contours (given as powers of 10).lo-l4 s. In the upper mantle. power-law creep should dominate at stresses greater than 1 MPa. If a load is placed on the surface of a viscous fluid and allowed to deform the surface to establish hydrostatic equilibrium.Fe)SiO3) and spine1 Copyright 1995 by the American Geophysical Union. Karat0 [21] showed that olivine. .lmm as a function of stress and depth.lo-* s-l) are much larger than those predicted in the lithosphere and mantle (. A deformation map (Figure 1) shows the predicted dominant deformation mechanisms for olivine with grain size O. Karat0 and Li [22] suggest the possibility of a weak zone at the top of the lower mantle (due to the grain size reduction from the spine1 to perovskite phase change). which suggests that. The post-glacial uplift problem. otherwise diffusion creep dominates [46].Fe)2SiO4) can be studied only by analog minerals. Using high temperature creep experiments on a CaTi perovskite analog. respectively [3]. we should apply analog creep measurements to the mantle with great care. While the laboratory measurements are clearly in the power-law creep field. It should be noted that the strain rates achieved in the lab (typically 10m5 . thin lines. Because of the difficulties in interpreting and applying laboratory creep measurements to mantle conditions. Similarly.. 227 228 MODELS OF MANTLE VISCOSITY CATA cl\\\I\!l NH/ 11 z (lOfkml Fig. is a simple illustration.dominates in the mantle depends on the average grain size of the mantle minerals [46]. Thick lines are creep field boundaries. however. the lower mantle should have a higher viscosity than the upper mantle. The deformation of the major high pressure mantle phases perovskite ((Mg.l ). Table 51. C and NH denote Coble and NabarroHerring creep.1 mm. Since creep parameters can differ greatly even for apparently-similar perovskites [44. with grain sizes greater than lmm. ((Mg. models of mantle viscosity based on large-scale geophysical observations continue to be important to geophysics. Viscosity models deduced from these observations are not unique. (o-z)-deformation map for polycrystalline olivine with grain size 0. due to the effect of pressure. as described by Haskell[19]. and require knowledge of models for the surface load (i.e. Cathles [4. McConnell [28] and Cathles [4. supporting the notation of a Newtonian. which are uncertain. overlying an effectively rigid mantle. The correspondence principle asserts that one can construct the Laplace transform of the solution by solving a series of elastic problems over a range of complex frequencies and then inverting to get the time domain response for the viscoelastic problem. modeled as a half space with a uniform viscosity of 1021 Pa s (pascal seconds are the MKS units of dynamic viscosity. a linear rheology (i. while Peltier argues for a uniform viscosity mantle. 1 Pa s = 10 poise).e. The effect of phase changes in the mantle on rebound was considered by O’Connell [34]. O’Connell [33] determined the viscosity of the lower mantle by looking at changes in the ice load and relating them to long wavelength rebound. Peltier [37] solved for the response of a viscoelastic (Maxwell) spherical Earth using the correspondence principle.3 x 1019 Pa s viscosity. Haskell also showed that the viscosity did not change over the interval of time of the analysis. Also. 51 showed the strength of the elastic lithosphere as important only in considering the short wavelength harmonics. 51 presented an alternative viscoelastic formulation which avoids the complexities of the boundary conditions for long time Periods when using the correspondence principle. later adding the effects of varying sea level [42]. with 1. He also used spherical harmonic correlation to look for the rebound signal in the geoid.see 51 proposed that the uplift of central Fennoscandiac ould be attributed to flow in a 100 km thick channel.ice sheet thickness and history). who appealed to the strength of the lithosphere to avoid the formation of a bulge of material squeezed out of the low viscosity channel peripheral to the ice load in his model. 201 proposed that the uplift of Fennoscandia was the result of deep flow. n=l and T constant in equation (1)). the theoretical models are often simplified to keep them tractable. The effects of an elastic lithosphere were first discussed by Daly [7]. O’Connell concluded that the effect of both the olivine-spine1 and the basalt-eclogite phase change on post-glacial are rebound negligible. rather than stress-dependenmt antle. it is difficult to assess whether the differences between Peltier’s and Cathles’ conclusions are due to their methods or ice . while van Bemmelem and Berlage [64 . Cathles argues for an increase in viscosity in the lower mantle. is assumed. Haskell [19. The classic studies of post-glacial rebound illustrate the non-uniqueness of viscosity models derived from observations and flow models. which varies only with depth. commonly. Because no direct comparison of the two methods has been reported. 17. The resulting ODE’s can be solved for response functions (kernels) which de nd only on the viscosity structure. They reason that relative sea level variations far from ice margins are less influenced by poorly-constrained ice models.49. geoid highs should correspond to mass excesses( Figure 2a). was developed by Peltier and Andrews [40]. The difference between Nakada and Lambeck’s models based on relative sea level variations in the Pacific. can then be calculated by convolving the response functions with a distribution of density contrasts as follows where y is the gravitational constant..3) geoid lows are associated with long-wavelength. 16. The equations of motion of an incompressible selfgravitating spherical shell are presented in Richards and Hager [54] and Ricard et al.e. Fennoscandia. using the pattern of density anomalies inferred from seismic tomography [ 11. The geoid (SVp m” . The resulting geoid is a combination of both internal (Figure 2a) and boundary mass anomalies (Figure 2b or 2c) and can be positive or negative. called KING 229 ICE-l. it has been observed that long-wavelength (i. Lambeck and co-workers have used far field absolute sea level changes. 6pim is the density . Because of the limited power in the post-glacial rebound data set.models. From early seismic tomography. a is the radius at the surface. depending on the viscosity structure (compare Figure 2a + 2b versus 2a + 2~). this is opposite of what one predicts. An ice sheet disintegration model. fast (presumably denser) regions in the lower mantle [9]. rebound models are usually reported in very simple parameterizations.51]. c is the radius at the core. a mass anomaly will drive flow that deforms the surface and core mantle boundary (Figure 2b or 2c). and models based on Fennoscandian and Canadian Uplift could be interpreted as reflecting lateral variations in upper mantle viscosity. rather than the rebound histories at sites near formerly-glaciated regions [26. including ice masses of Laurentia. The models still range from the nearlyuniform viscosity (Haskallian) model PT to strongly layered models NL and HRPA (see Table 1). spherical harmonic degree 1 = 2. Table 1 compares a number of recently published viscosity models from post-glacial rebound with geoid and plate velocity studies compiled by Hager [14].50. [50]. 321. Another constraint on mantle viscosity comes from modeling the geoid and dynamic topography of the surface and core mantle boundary. In a static Earth. These equations can be solved by a separation of variables (assuming a radiallystratified viscosity). and Greenland. As shown by Pekris [36] (and others since). A summary of ice sheet models is provided by Peltier [39]. l&23. q(r)) is the geoid response kernel. A simple. In all of the studies discussed. because of the difficulty in defining sources of error may have little 230 MODELS OF MANTLE VISCOSITY TABLE 1. The plate velocity data does not have the depth resolution of the geoid. A Comparison of Recently Published Viscosity Structures Determined by Systematic Forward Modeling (from [14]) Model %m Pa s) 77lm . [12] used observed plate velocities to deduce the radial viscosity structure of the mantle. with an increase in viscosity of a factor of ten at 670 km depth or 1200 km depth. Hager and O’Connell’s model [15] showed that densities from the cooling of ocean plates and subducting slabs alone provide the necessary buoyancy force to drive plates at the observed velocities. it is the seismic velocity models (see equations 3 and 4). 511. but until now no consensus model. the final viscosity model is dependent upon another model. explains the longest wavelength geoid from the inferred densities in the lower mantle [ 11. and Forte et al.. Thus. and Gl(r. the density perturbations in equation 3 can be written as where 6p/6vs is a velocity to density ratio and 6vslm is the seismic velocity perturbation model. The differences between the models from post glacial rebound and the geoid models have led to spirited debates. [50. To transform seismic velocity anomalies into density anomalies. Forte and Peltier [lo]. the geoid does not. Plate velocities constrain the absolute value of the viscosity of the mantle. The velocities of the Earth’s plates are the surface manifestations of convective flow in the mantle. Ricard and Vigny [47]. In post-glacial rebound studies. this is a model of the ice sheet. we assume that changes in seismic velocity can be mapped into changes in temperature and do not represent changes in composition. In the case of the geoid. Seismic velocity variations can be written in terms of elastic moduli for which the limited experimental information places reasonable bounds. because a low viscosity zone can effectively decouple the plates from flow in the deep interior. Most seismic tomographic inversions do not report formal uncertainties (which are difficult to perform and. which is only crudely known. 181. two-layer viscosity model. post-glacial rebound models. This model is different from the two end-member. Ricard et al. The density perturbations (6plm) are determined by seismic velocity perturbation models from seismic tomographic inversions and/or tectonic plate and slab models from boundary layer theory and deep earthquake locations in subduction zones.contrast at a depth r of spherical harmonic degree 1 and order m. based on global sea level variations. based on European sea level variations with emphasis on relative variations in sites away from the ice margins. bMitrovica and Peltier [29] model.6 x 1020 2 x 1021 4. based on sea level variations. fNakada and Lambeck [32] model for Oceanic response.(pa s) PTa MPb LJN2’ LJN3d LNAe NLO’ RVGPg HGPbh HS’ 120 120 100 150 75 Cl%) wm wm 1021 1021 3. with emphasis on near-field sites.5 x 1020 3. ‘Lambeck. based on the assumption that the gravity anomaly over Hudson Bay is totally due to delayed rebound. based on sea level variations with emphasis on relative variations in sites spanning the continental margin.5 x 1021 4 7 x 1021 314 x 1021 7-51%!21 1. eLambeck and Nakada [25] model for Australia. dLambeck.3 x 1022 6 x 1021 6 x 102’ 2 4 15 8 40 100 50 300 30 aPeltier and Tnsbingham [41] model.8 x 1020 2x1020 1020 2. Johnston and Nakada [26] model 2. Johnston and Nakada [26] model 3. an alternative to model 2. . with emphasis on relative variations as a function of island size. the dynamic topography of the surface is reduced and the sum of (a) plus (c) could be positive. The use of different seismic models can produce different viscosity models [23. (c) With an increased viscosity in the lower layer. Lambeck and Boschi [59]. hence negative geoid anomalies. A number of recent papers summarizing these results (and the post glacial uplift. 2. lateral variations in viscosity themselves could also introduce a major source of error in the viscosity models. The sum of (a) and (b) is a negative anomaly in a uniform viscosity medium. hHager and Richards [la] model for relative mantle viscosity from the Geoid.g. only the poloidal part of the plate velocities are driven by viscous flow without lateral variations in viscosity. In theory. meaning). ed. RECENT INVERSION RESULTS Several recent studies form and solve inverse problems rather than repeatedly solving the forward problem. Studies of Earth’s rotation provide constraints on mantle viscosity. Plate velocity models also have associated uncertainties. geoid and plate velocity studies) can be found in Glacial Isostasy.581. from 400 km to 670 km depth has a viscosity of 6 x 1020 Pa s. Because they are ignored in the viscous flow formulations. Polar wander also has recently been demonstrated to provide constraints on mantle viscosity [e. (b) The dynamic flow driven by the mass anomaly causes negative mass anomalies (stripped regions) at the upper and lower boundaries. Sea-Level and Mantle Rheology. There is a surprising convergence of these results and the . the inverse problem provides not only a model. Sabadini and Peltier [57] and Wu and Peltier [67] discuss the changes in Earth’s rotation due to Pleistocene deglaciation.. The resolution and trade-off analyses are not always straight-forward. iA modification of model HRGP that has an asthenospheric viscosity higher by a factor of 10. O’Connell [33] suggests that changing patterns of convection would change the principle moments of inertia of the Earth and that his viscosity model would permit polar wander from convection. suggesting that crude viscosity models may already be pushing the limit of the observations. in addition. 2. Ricard and Sabadini [48] discuss changes in rotation induced by density anomalies in the mantle. as might be expected for Shield regions. KING 231 -v static only dynamic only dynamic only Fig. calibrated for Plate velocities and Advected heat flux [14]. 511.gRicard and Vigny [47] model from the Geoid and Plate velocities. 53. Parentheses on (h) indicate the thickness of the high viscosity lid. An additional layer. (a) The geoid anomaly over a positive mass anomaly (stippled) in a static earth. but also estimates of the resolving power of the data and of the trade-offs between model parameters. Sabadini. so the absolute scale is chosen to be consistent with postglacial rebound and plate velocity studies. Their inversion produced a viscosity model (i. In this paper.e. they parameterized the mantle viscosity in five layers (O-100 km. To convert to absolute viscosities (in Pa s). The plate-like divergence predicted by this model explains 48% of the variance in the observed plate divergence (in the range 1 = l-15). using the lower mantle model of Dziewonski [8] and the upper mantle model of Woodhouse and Dziewonski [66]. 6vslm in equation 4) and Greens functions (kernels) for viscous flow developed in Forte and Peltier [lo]. and angular plate velocities for mantle viscosity. all of the figures will present relative viscosities. invert the topography. 400-670 km. Using a tomographic shear wave model SH425. Using present day plate geometries.2 . one should multiply the horizontal axis scale by 1021 Pa s. rotation poles.1 Plate Velocity Inversion Forte et al. the surface velocity boundary condition is choosen to match the stresses between a no-slip boundary condition at the surface flow driven by the internal density contrasts and 232 MODELS OF MANTLE VISCOSITY 500 . Harmonic coefficients of the observed plate divergence in the degree range 1 = 1-8 were used [lo]..1000 YE 5 1500 8 n 2000 2500 I I l l I!1111 I l l llllll I I I IllILl . Ricard and Wuming [49]. there is a significant trade-off between the top three layers (O-100 km and 400-670 km are correlated and 100-400 km is anti-correlated with the others). However. Geoid models are only sensitive to relative viscosities. [12] used the method of Bayesian inference to invert for the radial viscosity profile which best fit the observed plate velocities. geoid. 100400 km. so a model with a low viscosity in the 100-400 km layer and higher viscosities in the O-100 km layer and 400670 km layers tits the data nearly as well (see also Figure 3). 670-2600 km and 2600 km to the CMB). 2.e. Prior to the inversion.. the variance reduction with an isoviscous mantle was 770%.resulting model differs from the “traditional” models. the best fitting uniform viscosity in each of the five layers) with a low viscosity in the transition zone and high viscosity in the 100400 km layer with a factor of 42 jump at 670 km (see Figure 3).[62] as the driving force (i. the solid line is also an acceptable model. or uplift history. 1-D viscosity models from Forte et al. 421 is more appropriately interpreted as a constraint on the uppermost part of the lower mantle (i. They conclude that the preference of a uniform viscosity in the lower mantle of 1021 Pa s from other studies [e.. models with large increases in viscosity with depth cannot be ruled out by the RSL data as long as the average viscosity in the 670-1800 km depth range is 1021 Pa s. The horizontal extent of the Laurentide ice sheet suggests that this subset of the relative sea level (RSL) data should be sensitive to the viscosity at greater depths than other data subsets [30]. 2. It should be pointed out that Haskell [20] indicated that his result represented the . The viscosities in this are scaled by a characteristic mantle viscosity (q = 1 flow driven by the plates. The resulting viscosity model has a continuous increase in viscosity with depth to the mid-lower mantle.IO-’ IO0 IO’ 102 Relative Viscosity Fig. However. 5. 3. 381. then a decreasein viscosity in the lower one-third of the lower mantle.. An analysis of the relative sea level. Therefore. variance reductions are 44% for geoid. 2. and 19% for poliodal component of the plate velocities.1800 km). 311. this model provides poor fits to the data. The dashed line is the preferred model.e. 0 500 z 1000 25 g 1500 p” 2000 2500 r 670 . with no noticeable discontinuities or low viscosity zones. [12] determined by inverting observed plate velocities for the best fitting 5 layer viscosity model. There is a peak change in viscosity of about two orders of magnitude from the surface to the maximum in the lower mantle.g.2 Post Glacial Uplift Inversions There have been several attempts to form and solve an inverse problem for the viscosity of the mantle using postglacial uplift data [35. 58% for topography. with very weak sensitivity to changes in viscosity of up to an order of magnitude below this depth or in the upper mantle. over Hudson Bay was performed by Mitrovica and Peltier [30. 4. they also solved for the density to velocity ratio @ipIth . The more interesting result is the model that emerged when they considered both geoid and plate velocities in the inversion (Figure 4 . [51] are the only investigators of the recent group to consider chemically stratified mantle models. They performed a Monte Carlo inversion for the viscosity model which best fit both the geoid and plate velocities.56 [8] for the densities in the lower mantle. One of their strongest conclusions is the sensitivity of their modeling to the assumed density model. Using the selfgravitating . the density coefficient for the slab model (&lab). KING 233 km and 670-2900 km regions (Figure 4 .average viscosity of the mantle.C [27].dash dot line).-_---.-m---m I I I111111 IO-2 lo“ loo IO’ Relative Viscosity Fig. [51] from Monte Carlo inversion using geoid and plate velocities. They used L02. Their results suggest that. As they note. giving them six unknowns. I I 22 . In addition. and chose the viscosity value in the O-100 km layer to be 1O22 Pa s.2 [62]. Three representative 1-D viscosity models from Ricard et al. Ricard et al. based on the inversion study. including the plate velocities. However. 4. SH425. and M0DSH. a third model emerged (Figure 4 .heavy dashed line).3 Geoid Inversion Ricard et al. 2. [18] obtained better results with the same formalism using Clayton and Comers’ [6] lower mantle and a boundary layer theory slab upper mantle. [51] considered a three layer mantle. A study by King and Masters [23] considered several published models for S-wave velocity for the densities providing the driving force (6~ in equation 3): MDLSH [63].heavy dashed line). and 670-2900 km layers. and M84C [66] and a slab model for those in the upper mantle. Two classes of models emerged from their study. in addition to the geoid.see equation 4) in the upper and lotier mantle.solid line) and another with the highest viscosity in the transition region and lower viscosity in the upper 100-300 .-me . Hager et al. 300-670. They used the response kernels for Newtonian viscous flow [50]. the data are unable to discriminate between layered or whole mantle models. and viscosities in 100-300. because the geoid is sensitive only to relative viscosity change. The viscosities in this 2P lot are scaled by a characteristic mantle viscosity (rl= 10 Pa s). one with an increasing viscosity with depth (Figure 4 . The largest difference between the viscosity models is a factor of two difference in the viscosity of the 400-670 km layer. The pattern of viscosity with depth for the three models is strikingly similar: a high viscosity from 0 to 400 km depth. This forward model provides good fits to geoid and plate velocities. The model.4 and 5. least-squares scheme with smoothing to inhibit z 1000 x Ii -t i ‘i 1500 ‘I 8i 2000 i. This resembles the two-layer model of Forte and Peltier [ 111. 0 500 2500 : 0 5 10 15 Relative Viscosity Fig. [13] used the recent S-wave model SH8/U4L8 which they describe. The viscosities in this lot are scaled by a characteristic mantle viscosity (11 = 1 B I Pa s). The viscosities in this viscosity (lj = 102 P lot are scaled by a characteristic mantle Pa s). The models are normalized by the viscosity in the 1284 to 1555 region. 5. they inverted for radial viscosity models that best fit the observed 1 = 2-8 geoid (1 = 2-6 for MDLSH) using a nonnegative.. It compares well with Figures 3. 1-D viscosity models from King and Masters [23] determined by inverting the seismically determined density anomalies for the best fitting 11 layer viscosity model using the geoid. and increasing viscosity below 670 km. Forte et al. a low viscosity between 400 and 670 km. Using Frechet kernels [Forte et al. All three of the seismic velocity models predict a low viscosity between 400-670 km depth (Figure 5).Green’s functions for Newtonian viscous flow. following Richards and Hager [54] and Ricard et al. 121. [SO]. they determine the viscosity profile required to fit the geoid. 1-D viscosity model from Forte et al. [13]. wild oscillations. 6. 10-l loo Relative Viscosity Fig. It is interesting to note that the viscosity in the lower mantle increases by a factor of five below 1022 km in addition to an increase at 670 km. which contains a . PP. [12] . as discussed by Panalli [46]. R. A. 156 pp. 288. Anderson. 1978. and R..determined by inversion using the plate velocity data. this could possibly represent a thicker. and the viscosity model from Ricard et al. Theory of the Earth.determined by inversion using the geoid data. British Geographers. Ashby. Lmd. A Geomorphological Study of Postglacial Upliji with Particular Reference to Arctic CaMdo. Inst. Forte et al. less extreme layer. Upon considering both the uncertainty in the internal densities and surface loads and the uncertainties in the viscosity models themselves. Trans. COMPARISON The viscosity model from Forte et al. 59-95. L. However..A. seem compatible with these observations.are remarkably similar. however.T. Furthermore.thin. The viscosity of the . 5. LATERAL VISCOSITY VARIATIONS An area of increasing interest is the role of lateral variations in viscosity and their effect on post-glacial 1.M. Cathles. 3.L. 1989. D.F. Karato’s 1211 results on the strength of garnet are incompatible with this new model.using a Monte Carlo inversion of geoid and plate velocity data . 1970. is quite similar to those determined by King and Masters [23] (Figure 5). in addition to a reasonable fit to the plate velocities with these viscosity and density models. J. Boston. Mantle models with a hard transition zone appear compatible with observations w. [51] . obtain a 65% variance reduction for the observed geoid (1 = 2-8). and their relevance to the rheology of the upper mantle.. Phil. the viscosity models from King and Masters [23] . 57-62. 3. if the transition zone is Ca rich.. because layer thickness and viscosity contrast trade-off directly. Micromechanisms of flow and fracture. it appears that the results from the different observations are compatible. 4. Verrall. the results of the post-glacial uplift inversion by Mitrovica and Peltier [30] and the experimental data. as suggested by some [1]. 4. 2. They also point out that their 234 MODELS OF MANTLE VISCOSITY viscosity model is consistent with recent post-glacial uplift analyses and mineral physics. London. M.. It may be beyond the limit of their data to constrain such a thin layer at the base of the mantle. Sot. low-viscosity zone at the base of the upper mantle and an increase in viscosity in the lower mantle (Figure 6). Andrews. Blackwell Scientific publications. however. A. 7. and W. especially when the radial viscosity is stratified. Geophys..M. 92.M. plate velocity and geoid predictions. 1971.M. Forte. A tomographic analysis of mantle heterogeneities from body wave travel time (abstract). CT. 386 pp. AGU. Forte. AM. B. and A.131-20. Viscous flow models of global geophysical observables 1. and Y. neglecting lateral viscosity variations leads to errors in the magnitude of radial viscosity jumps as much as a factor of two. 89. 82. and R. 9. Zhang and Christensen [68] also find that the effects of lateral viscosity variations are significant. 8. J. and preprints.77691983. R.5929-5952.. Comer. Res. because radial viscosity models underpredict the geoid compared to their lateral viscosity equivalants. L. Geophys. Peltier..R. Richards and Hager [55] suggested this effect would be small for long-wavelength structures in the lower mantle.. 1984. o’Connell. The Viscosity of the Earth’s Mantle. Pcltier. Clayton. A. Geophys.. Geophys.e. forward problems. J.1987. Forte. A.Earth’s mantle. Cathles. and R.. Thanks also to the numerous anonymous reviewers whose comments helped improve this manuscript.M. Special thanks to Kathy Kincade for help in preparing this manuscript... A number of investigations addressing lateral viscosity variations are currently underway. 62. 11. Dziewonski. Princeton. W. Yale University Press.P.. Dziewonski. Daly. R. Acknowledgments. Using perturbation theory on a 2-D Cartesian problem. 96. 271 pp..A.D. AM.W. Ritzler and Jacobi [56]. Res. 10..239-255. reprints. 1975. Large-scale heterogeneities in the lower mantle.159. A.1977. The Changing World of the Ice Age. J. EOS.R. Forte. 12. NJ. and R. REFERENCES University Press. 1934. New Haven. Mapping the lower mantle: determination of lateral heterogeneity in P velocity up to degree and order 6. Trans. Res. Princeton University. Ph.M.. Ricard for providing theses. 6. . The author aeknowkdges support Erom NSF grant EAR-91 17406. Ricard et al.. Peltier. 1991.. 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L&t. Geophys. 55. M. 327-336. and H. Glacial Isostacy. 57. Woodhouse. Res.1989.. and W. Christensen. The creep strength of the Earth’s mantle. Geophys. Geophys..L.. Sot.. 391426.M. and A.553-578. and B. Ashby. Tanimoto.. 65. 100. 1993. Space Phys. M. or yield stress . a sample is put under constant stress (tensile or compressive) and strain is recorded as a function of time. if ts = GEL. des Geomater. Plastic deformation of materials in the Earth. 1992.. P. they cease behaving like elastic solids and become plastic. Plastic deformation is an irreversible. In actuality. the curve E(t) is a creep curve. Plastic Rheology of Crystals J. In many cases. Institut de Physique du Globe de Paris. A perfectly plastic solid undergoes no plastic strain if the applied stress is lower than the elastic limit oEL. isovolume process.. 75252 Paris. the yield stress usually increases with &The constitutive equation can therefore be written cr = f( i . Any increase in applied stress would immediately be relaxed by strain. the plastic strain can take any value. when the yield stress is reached. Geophys. (3= crEL. so that the applied stress cannot be greater than the yield stress. the applied stress necessary for continuing deformation usually increases with strain (hardening ). parallel to the strain axis (Figure la). At high temperatures. The relevant laboratory experiments are then creep tests [45]. France Mineral Physicsa nd Crystallography A Handbook of Physical Constants AGU Reference Shelf 2 machine (usually in tension or compression). Place Jussieu. submitted. Poirier. Time does not explicitly appear in the constitutive equation. J.T). which results in a permanent shear strain after the shear stress that caused it has been removed. rocks and minerals slowly flow under constant stress. Cedex 05. stress remains constant and strain keeps increasing at rate i. Poirier 1. CT=~(E). does not generally occur at constant strain-rate: at high temperatures. in single crystals. however. it depends on the orientation of the stress axis with respect to the crystal lattice. PHENOMENOLOGY OF PLASTIC DEFORMATION When crystals are strained above a certain limit. 4. many crystalline materials exhibit negligible hardening and can reasonably be considered as perfectly plastic solids.effect of lateral viscosity variations on geoid topography and plate motions induced by density anomalies in the mantle. however. Hydrostatic pressure alone does not produce plastic deformation. after a transient stage during which it . at constant strain-rate: deldt = 6 . P. Depart.In creep tests. Standard stress-strain curves for materials <areo btained by straining a sample in a testing J. the stress-sfrain curve. The yield stress usually decreases with increasing grain size and increasing temperature. For perfectly plastic solids. ht. is a straight line. In some cases. and the observed creep-rate is that for which the yield stress is equal to the applied stress. then. where AHo and AV* are the activation enthalpy and volume respectively of the controlling process.decreases. at constant stress. the stress dependence of the activation enthalpy may appear as a spuriously high value of n (n > 5). there is very little hardening. If creep is controlled by only one physical mechanism. but. the creep rate would be continuously decreasing). It can therefore be seen that a solid deforming in steadystate creep under constant stress can be considered as a perfectly plastic solid.e. determined from the slope of the In 6 vs l/T plot. for most materials. Above the elastic limit oEL. However. The creep-rate of polycrystals (and obviously of single crystals) does not generally depend on grain size.a quasi steady-statec an be reached (if not. and Q is the apparent activation energy . the activation energy can be written: Q = AHo + PAV*. if the variable time is introduced. As creep tests are usually performed at temperatures high enough to obtain a measurable creep-rate. more interestingly. In creep tests. where R is the gas constant. stress remains constant. The creep curve is then approximately linear (quasi steady-state creep ) and the corresponding creep-rate depends on the applied stress and on temperature: i =f(o. T is the absolute temperature. The viscosity at constant stress can be defined as: q = 01 i .T). viscosity is independent of CT and it is said to be Newtonian . and. the crystals are free to deform. In many cases. la Stress-strain curve of an elastic-perfectly plastic solid at constant strain rate. if the logarithm of the creep-rate is plotted against the logarithm of the stress to obtain the exponent n of a power law. it can also be considered as a viscousfluid . i. except for very fine-grained polycrystals deforming by diffusion creep . The activation energy increases with hydrostatic pressure P. through an apparent activation volume AV*. the strain-rate becomes approximately constant.: E’ oc exp (-QKI’). 237 238 PLASTIC RHEOLOGY OF CRYSTALS Eat Fig. until eventual failure (Figurelb). the creep-rate depends on stress by a power-law E’ oc on. with II n I 5. creep-rate often increases faster than stress and viscosity decreases with increasing stress (nonNewtonian viscosity ). the activation enthalpy may depend on the applied stress (decreasing as stress increases). If creep-rate depends linearly on stress. Copyright 1995 by the American Geophysical Union. The temperature dependence of the creep-rate usually follows an Arrhenius law . since it flows in shear at constant rate under applied stress. for sequential processes. Several processes. plastic instability occurs. is not the case for ceramics and minerals. The stress sensitivity of strain-rate n (or stress exponent in the creep equation) is an important parameter: if n =1 (Newtonian viscous material). expressed as the ratio H+/Si.1n addition. temperature. metals) is entirely characterized by its dependence on stress.. l/T. lb Constant stress creep curve. for some reason. and strain becomes localized in deformation bands or shear zones. P. and as: 6 = [Xi ~i-l]-l. determined in a range of values of the relevant variable (a.(see next section). fo2. More reliable results are obtained by global inversion of the experimental results. fo2 etc. is usually expressed as: i = i0 fQZm 0” exp (AH@)+PAV* RT ) (1) where so is a constant that often depends on the orientation of the stress axis with respect to the crystal lattice. AV*. it becomes easier to deform an already deformed zone further than to initiate deformation elsewhere. In particular.. pressure and grain-size. deformation is intrinsically stable. for concurrent processes. may act concurrently or sequentially.). with rates E’i. when it is possible. the solids still can be deformed to very G= const. The values of the parameters n. the creep rate of oxides (which constitute most of the minerals relevant to deformation in the Earth) often depends on oxygen fugacity fo2. all the other variables being kept constant... 21. if creep is controlled by only one process. [e. gives only an apparent energy Q. AHg. m. In many cases. however. Strain rate is approximately constant during quasi steadystate . whose thermodynamic state depends on the activity of the components.g. more than one controlling process is active in the experimental range of CTT. If. are usually obtained by fitting a curve to the experimental values of i. 441. The resulting creep-rate can be expressed as: . This situation occurs when strain-softening mechanisms predominate over strain-hardening mechanisms [27. which simultaneously yields best values of all the parameters [51. . This. 481. which does not correspond to any physical process. the creep-rate of silicates is also sensitive to the amount of water present as an impurity.6 = Ci ii .g. The constitutive equation (rheological equation) of pure single crystal oxide minerals. If n = 2. The Arrhenius plot In 6 vs l/T is then usually curved and the fit of a single straight line. The creep rate of pure elements (e. Fig. 3) is due to glide of dislocations on crystallographic slip planes in the direction of their Burgers vector. they also have to overcome localized obstacles. resulting from the motion of defects: point defects. Localized phase transformation under non-hydrostatic stresses may cause shear faulting instabilities [7. as an important transient enhancemenot f the creepr ate during transformation (or as a stress drop in the case of deformation at constant strainrate). in dislocation creep controlled by vacancy diffusion or diffusion creep accommodated by grain-boundary sliding (see [45] for a review).creep. fo2. Deformation at high temperature.g. etc. Deformation at low temperature U/T. and v their velocity. the shear strain rate is given by a transport equation. on the other hand. Theoretical rheological equations such as (1) can be derived from Orowan’s equation by expressing the dislocation density and the dislocation velocity in terms of the relevant physical parameters: T. Non-Newtonian creep. [45]. which may occur infine-grained materials. characteristic of the slip system. in creep experiments. to move along their slip plane dislocations have to go over the potential hills between dense rows of atoms. POWER 239 large strains in a stable manner by the so-called superplastic deformation . plastic deformation occurs when the shear stress resolved on the slip plane in the slip direction is equal to the critical resolved shear stress (CRSS).30]. the shear strain-rate i obeys Orowans equation : where p is the density of mobile dislocations (length of dislocation line per unit volume). Phase transformations strongly interact with plastic deformation. due for instance to the stress field of other dislocations. and is equal to the density of carriers of deformation times the strength of the carriers times their velocity.. the resultant transformation plasticity [45] appears. Orowan’s equation is valid whether shear strain is caused by slip or climb of dislocations. 2. dislocations. 6. In the most frequent case of deformation by motion of dislocations. b is their Burgers vector (strength). P. or grainboundaries. in most cases. Glide of dislocations is driven by the applied shear stress. Applied shear stress provides the driving force for the motion of defects and the rate of motion usually increases with temperature. If the potential hills . c 0. it may also depend on the interaction of several kinds of defects : e. with n 2 3. involves diffusion of point defects (usually vacancies). is potentially unstable and strain-induced structural changes or strain heating may cause shear localization. In general. PHYSICAL MECHANISMS Plastic deformation is the macroscopic result of transport of matter on a microscopic scale. As climb of edge dislocations out of their slip plane is controlled by diffusion of point defects to or from the dislocations. that slip between localized obstacles is easier than overcoming the obstacles. 240 PLASTIC RHEOLOGY OF CRYSTALS Fig.Bo. If one makes the reasonable assumption that. dislocation creep is grain size independent. they have to climb (C) to clear the obstacle and resume gliding (G). Creep is then said to be glidecontrolled. to move by one Burgers vector. If the potential hills are so low. In general.are high (as they are in some minerals. even at high temperature). The difference between the rheological equation for glide-controlled and climbcontrolled creep essentially comes from the physics underlying the expression of the velocity. 2a Glide-controlled creep. Nucleation and migration of the kinks are thermally activated processes. 2b Climb-controlled creep. dislocations tend to remain straight in the deep troughs along the dense rows. also. the dependence of the activation energy on stress can be assumed to be linear: AH (0) = AHo . is the controlling process. the applied stress helps in overcoming the energy barrier and the activation energy decreases by an amount equal to the work done by the stress. Dislocations tend to lie in the potential troughs. in steadystate deformation. the activation energy does not depend on stress. stress-assisted step of passing over the hill between one row of atoms and the next (lattice friction). overcoming of the potential hills is achieved by nucleation and sideways spreading of kink pairs (K). In most cases. Fig. if it is dissociated . the strain is still due to dislocation glide. the dislocation density p is then proportional to cr2. which balances the applied stress 6. and the thermally activated. Edge dislocations emitted by a source (S) glide on their glide plane (G) until they are stopped in front of an obstacle (0). the average distance between dislocations is determined by their long-range stress field. In climb-controlled creep as in glide-controlled creep. climb-controlled creep is rate-limited by thermally activated diffusion and can only occur at high temperatures. dislocations wait in front of the obstacle until they can circumvent it by climbing out of their slip planes and glide until they meet the next obstacle. sideways migration of the kinks then brings the dislocation to the next low-energy trough. only the controlling processes of the strain rate differ. i) In glide-controlled creep (Figure 2a). a dislocation must locally nucleate pairs of kinks over the potential hill. A screw dislocation can in principle glide on all crystallographic planes which contain it. but also causes the creep strain: vacancies travel down the stress-induced chemical potential gradient between crystal faces in tension and in compression..with increasing stress. i. which may be needed to avoid obstacles. and inversely proportional to the cube of the grain size if . but the strain-rate is controlled by the time the dislocations must wait behind the obstacles before circumventing them by climb and gliding further. The creep rate is proportional to the applied stress and to the self-diffusion coefficient. strain results from glide of the dislocations between obstacles. metals) the activation energy for creepi s therefore independenot f stress and equal to the activation energy of self-diffusion [45]. the dislocation must be constricted. ii) In climb-controlled creep (Figure 2b). Climb velocity depends on the diffusive flux of point defects to or from the dislocation. However. Creep-rate increases with decreasing waiting time.it follows that the creep-rate at constant temperature and pressure can be theoreticahy expressed by a power law: E’ oc 03. climb involves multicomponent diffusion and the activation energy for creep is not simply related to the activation energy of diffusion of any one species (see next section and [2. this is by no means always the case.. The diffusive flux of defects responsible for climb is driven by a chemical potential gradient. In the case of crystals of elements (e. the rheological equation of cross-slip controlled creep is basically similar to that of glide-controlled creep. it can usually easily glide in this plane.g. For more complicated minerals.. Although in many instances the stress exponent n of climb-controlled power-law creep is indeed n = 3. it is equal to the coefficient of diffusion of the slower species.e. it is inversely proportional to the square of the grain size if diffusion occurs in the bulk (Herring-Nabarro creep ). diffusion of point defects not only controls the creep rate. Constriction is thermally activated and the activation energy of cross-slip controlled creep decreases . to cross-slip from on plane to another. which is usually assumed to be proportional to the applied shear stress.g. in the case of simple ionic crystals (e. The climb velocity is therefore proportional to the applied stress. Since. usually the anion (oxygen for binary oxides). NaCl).23]). by Orowan’s equation. and for many crystals 3165. thus deforming the crystal in response to the apphed stress.in one plane. the creep rate is proportional to the product of the climb velocity by the dislocation density (proportional to 02). which in turn depends on the diffusion coefficient of the relevant point defects. Although cross-slip helps in overcoming localized obstacles. with increasing climb velocity. and since the activation energy is stress-independent. iii) In diffusion-creep (Figure 2c). It is observed only at low stresses and can probably be considered as climb-controlled creep. The role of pressure is.diffusion occurs along the grain boundaries (Coble creep ). 1982). whenever possible. with a stress-independendti slocationd ensity. Diffusion creep is a mechanism effective only at high temperatures and in polycrystals of small grain sizes. Deformation of the grains of a polycrystal by diffusion creep creates incompatibilities that must be relieved by grain-boundary sliding. A mechanism is dominant over a range in the variables defining the experimental conditions (T. if the corresponding strainrate .221. of course. 5.g. Hydrostatic pressure has little influence on plastic deformation at low temperature during glide-controlled creep. Diffusion creep and grain-boundary sliding are mutually accommodating processes.). Harper-Dorn creep.g. looking for diagnostic features [e. at surfaces normal to the compressive stress. Vacancies (V) diffuse from regions of high equilibrium concentration. by comparing the stress exponent to that of the various models and the activation energy to those for diffusion of different species)... cr. like diffusion creep. It is essential. As the creep rate is linear in stress (Newtonian viscosity). to regions of low equilibrium concentration. P. showing iso-strain rate contours (after Frost and Ashby. at surfaces normal to the extensive stress. but exhibits no grain-size Fig. The determination of the active mechanism of deformation cannot be done entirely on the basis of the experimental rheological equation (e. 2c Diffusion creep. to examine the deformed samples by transmission electron microscopy [40] in order to characterize the dislocations and observe their configurations. 3 Deformation mechanism map for olivine. The parameters of rheological equations such as (1) can be constrained by experiments for various possible deformation mechanisms. etc. Atoms (A) diffuse in the opposite direction. POIRIER 241 TEMPERATURE (“C) 0 02 04 06 08 10 HOMOLOGOUS TEMPERATURE. grain-size. is characterized by a stress exponent n =l. T/l m Fig. important in the creep of materials in the Earth’s mantle and at the pressures of the lower mantle. one must consider a pressure dependence of the activation volume for creep 1461. with grain size 1 mm. diffusion creep can successfully compete with climbcontrolled creep only at low stresses. fo2. dependence. It is only in the case of diffusion-controlled creep (climb-controlled dislocation creep and diffusion creep) that pressure can cause a noticeable decrease in the creep rate through the activation volume for diffusion. under an applied stress of 1GPa [ 111. the stress-strain curves (at constant strain-rate) exhibit a sudden stress drop at the yield stress (yield-point ) followed by a hardening stage. PLASTICITY OF IMPORTANT MINERALS This section deals only with recent investigations on the minerals most widespread in the crust and mantle of the Earth. 3. Deformation-mechanism maps are useful to predict the behavior of a material only in the intervals in which the parameters have been constrained by experiments. whose plastic deformation has been experimentally investigated using single crystals. it has been known that the plastic behavior of quartz is very much dependent on the nature and concentration of water-related defects contained in the crystals.).. thus allowing better understanding of the physical mechanisms. Dislocation glide usually occurs on the basal plane (0001) in the cl 1% direction (a). “dry” quartz (H/106Si c 80) is almost impossible to deform plastically in the laboratory: it is still brittle at 13OO”C. Above the critical temperature. Data on creep of ceramics can be found in [81. quartz crystals.). quartzite.27.1. If all variables defining the experimental conditions. except two. Quartz Since the discovery of water-weakening by Griggs and Blacic [20]. however. or monomineralic rocks (e. diffusion creep. For a review of the plasticity of crustal rocks and minerals. Natural... . Water-related defects might consist of 4 protons (H+) substituted for a Si4+ ion or one OH2 group substituted for an oxygen.g. see [29. which decreases as water content increases. displaying in 2-dimensional space (e. dunite. The plasticity of polycrystalline minerals.. 171.431. will be treated in the “Rock Physics” section. deformation-mechanism maps can be constructed (Figure 3).is greater than those of competing mechanisms. recent electron microscopy work identifies waterrelated defects with high-pressure clusters of molecular water [41]. power-law climbcontrolled creep.. and on the prism planes (lOfi)in the a or c [OOOl] . The boundaries between domains are obtained by equating the rheological equations for the mechanisms dominant in each domain. Below a critical temperature. The creep curves correspondingly exhibit an initial incubation period during which the creep rate increases to decrease later during a hardening stage [ 111. Thus. or c+a. etc. o/p and T/Tm) the domains where various mechanisms are dominant (e.g. Reviews on the influence of water on the plasticity of quartz can be found in [40. wet synthetic quartz is very strong and behaves much as dry natural quartz. 3.g. most experimental work is conducted on “wet” (H+/lO%i > 500). often synthetic. are kept constant. during the incubation period.800 (j3) ” 3.570 (a) 40 . the dislocations are straight and their mobility is low.4 117 I.9 3.directions (the indices of planes and directions are given using Miller-Bravais notation).800 (p) ” 3.200 . 181 support the following mechanisms: i) At low temperatures.0 92 [351 11 1.3 213 ” 11 I. deformation is controlled by lattice friction. At high enough temperatures.162 3. 5.7 33 1. @pm) (“Cl (CFin bars) &J/n-ml) 4300 (2iiO) c 400 .:. W/ml) Fo92 Various F“92 <ill> Fo92 <llO> Foloo uo11 Woo ill11 Fo90 r1011 Fo90 [loll Fo90 UOll Foloo nm Woo w11 . FitzGerald et al.. there may exist a quasi-steady state creep. 370 (2flO) c 400 .I. orientation of the samples with respect to the stress axis (Table 1).570 (a) 80 . 11 570 . High-temperature compression creep of wet single-crystal quartz .0 92 I. 570 . TABLE 2. 370 (1OiO) a 400 . High-temperature compression creep of single-crystal olivines Crystal Orientation of stress axis (pseudo-cubic) Atm. which expand by climb and act as sources. 570 . the elastic strain around the bubbles is relieved by punchedout dislocation loops. [18] also point out the role of microfractures in the nucleation of dislocations.570 (a) 80 . low water fugacity. 9. OH-/Si Slip System T &O n Q Ref. 36.800 (p) ” 10-9. thus increasing the dislocation density. the density of grown-in dislocations is very small. Observations of experimentally deformed crystals using transmission electron microscopy [ll. and high strain rate. ii) At higher temperatures. n Q Ref.200 10-8. following a power law whose parameters depend on the 242 PLASTIC RHEOLOGY OF CRYSTALS TABLE 1. quartz is then very strong. clusters of water molecules precipitate into water bubbles.7 3. plastic yield occurs suddenly with a stress drop (yield point) for an applied stress high enough to make massive multiplication of dislocations possible.7 109 LW 9. 100 30 .1400 1400.6 3.5 3.1600 5 .30 100 100 100 10 .1400 1250 .60 3 .100 20 .7 525 523 523 564 667 536 536 448 460 573 .3 CO2/H2 = 0.1400 1250 .1600 1550 -1650 1500 .1600 1400 .5 2.1680 1250 .7 3.1600 1500 .60 8 .1650 1400 .1 cog2 = 0.40 10 .9 2.1650 1500 .100 co2/H2 = 0.43 cogH2 = 0.43 cog2 = 0.6 2.33 I--WA CO7JH2 = 2.150 10 .Foloo [0111 1430 .25 f”2 = 10e6 Pa H2/cO2 WC02 WC02 f(o) 3. 9Feo.3 x 1o22 3.40 750 . High-temperature creep laws for buffered single-crystal Fog1 olivine Orientation Buffer i0 n m Q i of stress axis (0 inMPa) Wmol) (pseudo-cubic) mw 1.15 290 .2 3.2 330 i2 After [2].33 250 i1 5.2 3.65 3.2 1000 . &I 25 3. 1200°C< T c 1525‘ C .40 700 .5 0.5 El 1.0 x 1o14 3. 0. E2 1. E2 1. e2 0.30 ) .05 300 e2 .0 x 1o22 3.0 370 . E3 mw 1.06 690 .2 x lo5 3.10 1000 .5 0.7Fe0.1 x lo4 3.0 x 1o14 3.3 x 10” 3. [1101 opx 0.23 540 . buffer: opx (Mgo.5 0.5 0.5 0.598 1311 1131 [I31 [I41 WI [321 [321 [321 [101 WI WI POIRIER 243 WI opx 0.5 0.02 3.5 0.16 3. 10-12<f o2 c lo3 atm. .36 230 .5 0. E2 TABLE 3. El 0.5 0.lSi03)o r mw (Mg0.5 0.02 540 El 5. [Olll opx 2.5 0.5 0. mw &l . 2.c =e’oonfo m exp C-Q$T) Flow law: [lo2l l E. the activation energy for creep (of the order of 500 kJ/mol) does not tally with that for diffusion of the slower species: oxygen or silicon (about 335 kJ/mol). rather than by diffusion of the slowest species alone [231. according to the orientation [ 15. and at high temperature (OlO)[lOO] (prism plane of the hcp sublattice in the c direction). with cross-slip on other prism planes such as (001) and (011). and oxygen fugacity. -1I -1 . [llO] mw: d‘ 1 =i 1.1 -1 -1 opx: 1 2 =d.. corresponding to slip on the basal plane of the hcp oxygen sublattice in the a direction. The results (Table 3) show wide variations in activation energy and fo2 dependence according to the experimental conditions: two or three power law equations are needed to describe 244 PLASTIC RHEOLOGY OF CRYSTALS TABLE 4.+[i2‘ 1+ t?. apparently compatible with dislocation creep controlled by climb of edge dislocations. the activity of one component (orthopyroxene or magnesio&istite) must also be specified.1450 Diopside 1000 .1 3.= 6 -1+ d -1 . Examination of deformed samples by transmission electron microscopy suggest that creep can be controlled by climb and/or glide. 211. has an orthorhombic lattice and a slightly distorted hexagonal close-packed oxygen sublattice. High temperature creep of single crystals in various orientations obeys a power-law creep equation with n = 3. +i2 . Fe)zSiO4.$%sion of all the species.1 -1 -1 [oll]mW: E =d.5 (Table 2).. Bai et al [21 performed systematic experiments on olivine buffered against orthopyroxene or magnesiowiistite for various orientations as a function of temperature. [llO]opx: d = i. +d2 . The thermodynamic state of olivine with fixed Fe/Mg ratio is not entirely determined when T.. Olivine Olivine (Mg. One should however note that climb of dislocations should be controlled by multicomponent d. P and fo2 are fixed.The common slip systems are: at low temperature (lOO)[OOl]. [lOl]mw: E.. when climb-control would be expected. 1+i2 . [Oil] opx: 6 = .1 + i. However. the dominant mineral of the upper mantle.1450 Enstatite (En96) 1350 . High-temperature compression creep of single-crystal pyroxenes Crystal T (“c> i0 (cr inMPa) n m Q Ref W/ml) Enstatite (En99) 1350 . stress.1050 . and subsequently deformed in the decoration technique [3] shows that different dislocation same conditions at a constant strain rate of 10m5s1.3 4. with respect .6 x 1011 3.1137 1137 . The stress exponent. suggesting that different mechanisms have to be considered.9 0 4.0 1.8 4. II .5 in all cases (which.5 7.I 11 !I 11 P = 10 kbar r371 [371 Ul [491 [491 [491 r491 [331 phenomenologically the creep behavior over the whole range of experimental conditions. water-related defects increase Examination of deformed samples by the oxidationolivine plasticity .5.5 to 2.1130 1130 .1 x 1015 3.0 x 10-l* 6.1 x 10-23 8. As in the case of quartz.Diopside Slip on (100) 1020 .6 750 880 284 742 85 442 48 526 Buffered by olivine 11 I. For single crystals of olivine treated in a hydrous environment at 1300°C under a hydrostatic pressure of 300 MPa. is a confirmation of its limited usefulness as a criterion for the determination of the physical mechanism of creep). the flow stress is reduced by a factor of 1. in talc Ar 10% HZ-~% H20 1.1 7.2 x lo* 3.1 x 1O-4 6. is equal to 3.1321 Hedenbcrgite 900 . incidentally.9 x lo3 8.1100 4.1321 Slip on (110) 1020 .8 0 2. P = 5-15 kbar. however. 3. which might be confused with clinopyroxenes at low temperatures [33]. Fe)2Si2@ is impossible deform by power-law creep (Table 4). High-temperature creep of (Mg. the glissile dislocations with Burgers vector [OOl] can dissociate on (100) [52]. confirms that several rate-controlling mechanisms may be Samples deformed under wet conditions and examined in transmission electron microscopy exhibited evidence of operating in different experimental conditions. which accounts for the high value of the stress exponent (n = 8). High-temperature compression creep of single-crystal oxides with perovskite structure Crystal Orientation of stress axis . the shear stress can favor the nucleation of very fine lamella of clinoenstatite on (100) planes. The easiest slip system of orthorhombic enstatite as well as of monoclinic diopside is (lOO)[OOl]. enhanced climb of dislocations (dislocation walls.structures parallel the changes in power-law equations and to that of crystals treated in a dry environment [381. the dislocations were pinned by tiny glassy globules (~10 nm). be expected from the extrapolated lower-temperature creep law.3. calcium present as a minor ion in enstatite can diffuse to the clinoenstatite. crystals oriented in such a way that twinning stacking faults. In orthoenstatite. Deformation is therefore probably glide-controlled.). thus forming thin lamella: of Mechanical twinning. and in the direction of the chains. Pyroxenes Although orthopyroxene Mg2Si206 (enstatite) and clinopyroxene MgCaSi& (diopside) are also important minerals of the upper mantle. with no detectable occurrence of climb. In experiments on high-temperature creep of pure diopside. Above the critical temperature. During hightemperature deformation. primarily on the (100) plane in the [OOl] direction. At high temperature. The crystals then becomem uch more creep-resistant han would with increasing iron and aluminum content [37]. Ratteron and Jaoul [49] report a drastic decrease in enstatite obeys a power law (Table 4). their plastic properties have been much less studied than those of olivine. with dislocation glide on the planes of the layers of chains of Si04 tetrahedra. resulting from incipient partial melting well below the currently accepted POWER 245 TABLE 5. etc. it does not seem to activation energy by a factor of almost ten above a critical be sensitive to oxygen fugacity but the creep-rate increases temperature about 200°C below the melting point. Examination of the deformed samples by transmission electron microscopy [ 131 showed that above and below the critical temperature deformation took place primarily by (1 lo] 1/2<1 IO> slip. is the dominant deformation mode for calcic clinopyroxene [26]. on the six{ 110) planes in the cl 10~ directions.0. High-Pressure Mantle Minerals Despite their importance for the rheology of the transition zone and the lower mantle. either on the metastable phases at ambient pressure or in-situ in a diamond-anvil cell. There are however no experiments at very high temperatures in controlled oxygen partial pressure conditions. experiments at about 0. and majorite garnet in the transition zone. with n = 4 and Q = 400 kJ/mol [8].4. (0 in Pa) Wmol) BaTi <l lO> 0. and (Mg. thus causing the observed hardening.0.0. There are good reasons to believe that deformation of magnesiowiistite at lower mantle conditions is not very difficult: crystals formed by decomposition of olivine at high pressure in a diamondanvil cell contain a high density of dislocations [47].67 .6 469 30 [41 KNbO3 <llO> 0. recent high-temperature creep experiments performed at various controlled oxygen fugacities [24] give results (n = 4. there is no information on the plasticity of the high-pressure mantle minerals in the relevant conditions of temperature and pressure.84 .70 . -0.75 .67 .0. there is as yet no high-temperature creep apparatus operating at these pressures. Wiistite Fefwx 0.0. There have been numerous investigations on the plastic properties of the MgO end-member (magnesia or periclase). the only information we have so far on the plastic properties of the silicate high-pressure phases comes from experiments that were performed at room temperature.02 c m c 0.5 274 15 [531 CaTi <loo> 0.11.87 .Fe)Si03 perovskite and (Mg.0.99 Argon -43 3.78 Air -37 3. in air or vacuum are compatible with climb-controlled dislocation creep. The essential high-pressure phases are (Mg.98 Air -92 5.7 415 38 r51 KTa03 <llO> 0. The fluid droplets may effectively act as obstacles to dislocation slip.5Tm. which is easily deformable even at low temperatures. 3.92 Argon -38 3.8.3 444 24 [531 NaNbO3 <lOO> 0.99 Argon -11 1 292 21 [51 CaTi <l lO> 0. All phases other than magnesiowiistite are stable only at high pressures and. There is also qualitative information extracted from the examination of dislocation structures of . Q = 290 kJ/mol) compatible with dislocation creep controlled by the diffusion of oxygen-related point defects whose nature varies with temperature.78 Air -39 2. is always non-stoichiometric and Fedeficient.(pseudo-cubic) Atm In iO n Q g Ref.3 192 14 [531 melting point of diopside. the other end-member. Magnesiowiistite has the NaCl stucture and is stable at ambient pressure.Fe)#iO4 P-phase and y-spinel.Fe)O magnesiowtistite in the lower mantle. stacking faults and dislocations similar to those found in MgA1204 spine1 are observed [39]. However. 1. in their stability field. Bai. in natural y-spine1 (ringwoodite) formed at high temperature in shocked meteorites. from the pressure gradient in the cell. 7. higher than for olivine or enstatite. 48. Karat0 et al. Experimental deformation of diopside and websterite. There is also evidence for the (lll)cllO> slip system as in MgA1204 1121. [251 performed microhardness tests on metastable MgSiO3 perovskite single crystals at room temperature. There is no information on the plasticity or dislocation structures of MgSi03 perovskite at high temperature. it does at least provide reliable qualitative information on the 246 PLASTIC RHEOLOGY OF CRYSTALS dislocation structures. 1978. Although transmission electron microscopy of phases deformed at high temperature. the dependence on temperature of the CRSS may differ considerably for the various slip systems of one mineral (let alone for the slip systems of different minerals). Av6 Lallemant. Thus.G. and dislocations are very straight.J.. 9. experiments on isostructural compounds presumably belonging to isomechanical groups may provide some basis for speculation. it should be emphasized that the yield strength of crystals depends on the critical resolved shear stress (CRSS) of the available slip systems. perovskite and yspinel. 6. They found that at room temperature perovskite was stronger than spine1 or olivine. density. 8. so that the dominant slip system at room temperature may not be the same at high temperature. and the ranking of minerals according to their yield strengths at room temperature cannot be assumed to remain the same at high temperature. prepared in a laser-heated diamond-anvil cell. l27. H. does not provide quantitative information on their strength. Mackwell and D. 4. pointing to glide control of the deformation. and dissociation from which educated guesses on the deformability can be attempted. Kohlstedt..the phases by transmission electron microscopy. 5. they found a high value of the Vickers hardness (Hv= 18 GPa). Q. Tectonophysics. Mechanical results for buffered . 2. 3. it is 1. High-temperature creep of olivine single crystals. S.L. Finally. Meade and Jeanloz [42] estimated the yield strength at room temperature of polycrystalline olivine. 21. reasonable to assume that the slip systems are the same as in other perovskites.P.L. Duclos.. and J. Beauchesne. Mineralogy. 89. Plastic deformation of quartz single crystals. J. Res. and C. High-temperature creep behavior of nearly stoichiometric alumina spinel. I.J. Q. Poirier.B. J. Hightemperature creep of olivine single crystals. 96. 3. Geophys. R. S.C. and D. and L. REFERENCES 10. Kohlstedt. Eur. Therefore. J. Interiors.. 182-198.. probably due to the fact that the distortions and the dislocationc ore structuresa re different: creepp arametersc an be very different even for apparently similar perovskites (Table 5). Bai.. and J. 6219-6234.samples. Green II and D. Langdon. J. 55.M. 11. 1989.19. 1981. Beauchesne.G. Tectonophysics. Plasticity and hydrolytic weakening of quartz single crystals. Bull. Burnley. N.C.R. W. 187-189. 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The role of water in the deformation of olivine single crystals. edited by S. Mackwell. Dislocation nucleation and multiplication in synthetic quartz: relevance to waterweakening. The strength of metal silicates at high pressures and room temperature: implications for the viscosity of the mantle. Hightemperature deformation of diopside single-crystal. 51. 14. 1992. Wright.P. Doukhan and J.5083-0688 Mineral Physics and Crystallography A Handbook of Physical Constants AGU Reference Shelf 2 Copyright 1995 by the American Geophysical Union. Sotin.G. K. D. only representative phase diagrams are shown. Ricoult. 311-317. in Deformation processes in minerals.48. 9-22.C. Meredith. London. 12. Chem.P. Presnall The purpose of this compilation is to present a selected and compact set of phase diagrams for the major Earthforming minerals and to show the present state of knowledge concerning the effect of pressure on the individual mineral stabilities and their high-pressure transformation products.Sotin and S. Transmission electron microscope study of dislocations in orthopyroxene (Mg. 1984. Phase Diagrams of Earth-Forming Minerals Dean C. Res. 39-44. J. Jaoul. POB 830688.. Poirier. C. 49. 96. C. N. Analysis of high-temperature creep experiments by generalized non-linear inversion.. For several of the mineral groups. Richardson.C.27714. Mechanics of Materials. Presnall. 1990. 1985. ceramics and rocks. Kohlstedt. Philos. Van Duysen. Experimental deformation and data processing. University of Texas. 52. Ratteron. and D.Beauchesne. Unwin Hyman. l. and 0.. Price and J. Fe)2Si206.L.286. (2) The presentation of more complex phase diagrams that show mutual stability . Dallas.L. J. The phase diagrams are arranged as follows: Figure Silica 1 Feldspars 2-7 Pyroxenes 8-13 Olivine 14-16 Garnet 17-20 Iron-titanium oxides 21-23 Pargasite 24 Serpentine 25 Phlogopite 25 Iron 26-27 The compilation has been compressed in three ways. Poirier. High-temperature creep of the perovskites CaTi and NaNb03. 3. Phys. Creep of Fe2SiO4 and Co2SiOq single crystals in controlled thermodynamic environment. pp 179-189. C.D. TX 7. edited by D. 53. 1985.P. Doukhan. Geoscience Program. Phys. Interiors. 50. 51. P. Minerals. 74. Poirier. 79-93.. Mug. (1) D. Earth planet.J. G. Barber and P. and J. J. Geophys.Mechanical data.. 1991. [74] for amphiboles. 16. Gilbert et al. Pressure. 1. 70. 31. 62. The high quartz-low quartz curve is from Yoder [172]. 2 . 3 . At about lOOO”C. 331. Qz. Isopleth for the composition. Cor. and from Zhang et al.[4]. The curve of Bohlen and Boettcher would intersect the albite = jadeite + quartz curve at about 1300°C rather than the jadeite + quartz (coesite) = liquid curve. Liq. kyanite. oxides. 1541. and at 35 GPa. Liu [loll synthesized NaAlSigOg in the hollandite structure at . NaAlSigOs [12. Ky. 941. 50. It will be noted that some diagrams are in weight percent and others are in mole percent.[178]. Other useful reviews and compilations of phase diagrams are Lindsley [96] for oxides. quartz. 4 . grossular. The quartz-coesite transition is from Bohlen and Boettcher [24] but note that their curve lies toward the low-pressure side of the range of curves by others [5.63 GPa. Also. The melting curve is from Jackson [77] at pressures below 4 GPa.[168]. Phase relationships for SiO2.1 GPa higher than the curve of Boettcher and Wyllie [22]. from Kanzaki [83] at pressures between 4 and 7 GPa. Gr. which is shown in Figure 1. 23. 3. Tsuchida and Yagi [ 1631 reported a reversible transition between stishovite and the CaC12 structure at 80-100 GPa and T> 1000°C. Liu and Bassett [104] for elements. Reviews of these subsolidus phase relationships and thermodynamic data for calculating the phase diagrams have been presented elsewhere [13. (3) Many subsolidus phase diagrams important to metamorphic petrology and thermobarometry are excluded.?SizOs [67. 600°C for this reaction [81]. [105].latter passes through the “consensus” value of 1.relationships among the various minerals and mineral groups has been minimized. 2. 248 PRESNALL 249 5 10 15 Pressure. Numbers beside curves refer to the following sources: 1 . [178] at pressures above 7 GPa. [60] and Huckenholz et al.[160]. corundum. 122. Fig. the quartz-coesite curve shown by Bell and Roseboom [12] and in this figure is about 0.4 GPa higher at 1300°C than the pressure given by a linear extrapolation of the curve of Bohlen and Boettcher [24]. The . liquid. The albite = jadeite + quartz reaction shown by Bell and Roseboom [12] and in this figure is about 0. and Phase Diagrams for Cerumists [129-1371. CaAI. Locations of dashed lines are inferred. GPa Fig. GPa Fig. Isopleth for the composition.7 GPa to accomodate the data of Jackson [77]. Silica has been synthesized in the FezN structure at 35-40 GPa. However. Boundaries for the tridymite and cristobalite fields are from Tuttle and Bowen [164] except that the cristobalite-high quartz-liquid invariant point has been shifted to 0. they have usually been left as originally published. 89. Minor drafting errors and topological imperfections that were found on a few of the original diagrams have been corrected in the redrafted diagrams shown here. 500-1000°C by Togaya [162]. The temperature of the high quartz-low quartz-coesite invariant point is from Mirwald and Massonne [ 1131. 1131. and silicates at high pressures. T>lOOO”C by Liu et al. In experiments from 8-10 GPa and 700”-lOOO”C. 2 GPa [33. and at 700°C 11 and 11. 63. GPa Fig. SiO2. 1171.1 GPa and temperatures from 800 to 9OO”C. as indicated [49].CaA12Si208 (anorthite) under anhydrous conditions at 1 atm [26. GPO 250 PHASE DIAGRAMS Leucite + Liquid High Sanidine IIOOI IIIIIII_ 0I234 Pressure. Isopleth for the composition.5 GPa [79. 4. 1 GPa.OB Mole percent Or KAISi. 39. 164. anorthite. An CaAlzSizOe Ab NaAISi. 54. [88] synthesized the assemblage K2Si409 (wadeite-type structure) + kyanite (A12Si05) + coesite (SiO2) from the composition KAlSi30s. 121. Temperature-composition sections for the join NaAlSigOs (albite) . Fig. 5. albite. 1751. NaAlSi206. 58. orthoclase. 151-153. ‘“““I’ 1000 I I I . 142. Many others have discussed ternary feldspar geothermometry [lo.pressures from 21 to 24 GPa. 12 GPa. Or. KAlSi30s [93. si o 2 28 Albite Anorthite Fig.Liquid t Corundum _ 7 7001 I I I I I I I I I IO 20 30 40 50 60 70 80 NaAlSi308 Mole Percent 9gaA. 75. Jadeite. PRESNALL 251 Liquid + Corundum 1800 I I 1 I I 1 I I I I 17001600 . I I I 0I234 Pressure. Kinomura et al. At 12 GPa. 900°C Ringwood et al./ . and they synthesized the hollandite structure of KAlSi3Os at 9OO”C. Compositions of coexisting alkali feldspar and plagioclase at 0. and a mixture of NaAlSi04 (CaFezOa-type structure) + stishovite above 24 GPa. Coesite. 80. 6.5 GPa. Ab. 252 PHASE DIAGRAMS 130( 120( Liquid / Leucite t Liquid I lO( Feldspar + Liquid lOO( Feldspar Liquid t Vapor // Orthoclase t Liquid tVapor 70( t Vapor / . 1491.O. 941. An. 139. 156. Note that the phase boundary is essentially isothermal except in the Ab-rich portion of the diagram. [144] synthesized KAlSi3Os in the hollandite structure. and under H20-saturated conditions at 0. 1751. 66. 1651 and ternary feldspar phase relationships [68. Position of dashed curve is inferred. 254 PHASE DIAGRAMS 1601 Pen + Di 3p \ ‘Oen Oen + Di I I I I I I I I’ Mg. diopside. forsterite. liquid. Locations of dashed lines are inferred. albite. and curve 2 is from Boyd and England [33]. Fig. 56. CaMgSi& Curve 1 is from Williams and Kennedy [ 1661 uncorrected for the effect of pressure on thermocouple emf. The join MgzSi206 (enstatite) . 92. GPa Fig. 76.‘CPX .KAlSi308 (orthoclase) under anhydrous conditions at 1 atm [148].2 GPa [29] and 0. see Zerr and Boehler [ 1771. Not shown is a singular point at about 0. Opx. 1751. 65.Orthoclase tVapo 60( 2 Feldspars + Vapor II \ 50( Na*lSi. Di. 91. Isopleth for the composition MgSi03 [7. Liq. a .5 GPa [ 119. For additional data on melting temperatures up to 58 GPa. 20 40 60 80 CaMgSi. For additional data at pressures above 15 GPa. 78. vapor. Oen. 140. PRFBNALL 253 Orthoenstatite Protoenstatite 5 IO 15 20 25 Pressure. 35. 10. See also Yoder [173] for data below 0. Mao et al. and under HZO-saturated conditions at 0. Liq. Many others have also discussed phase relationships on this join [9.O. V. Pig. 7. orthoenstatite. liquid. 1691. Ab. MgzSi04.x + Gt 0 $ 14 -.5 GPa.O. GPa Fig. 106. orthopyroxene.CaMgSi206 (diopside) at 1 atm [43]. 41. 56. 9.7 and 42. protoenstatite. 42. Fo. They interpreted the glass to be a second perovskite phase of CaSi03 composition which inverted to glass on quenching [see also 1021.SI.OB 2o 40 60 80 Mole percent CaMgSi.13 GPa below which enstatite melts incongruently to forsterite + liquid [45]. 127. 36. C. 13001 I I I I I I 2345 Pressure. 9. 57.Si.Or 20 30 40 50 60 70 80 90 Weight percent KAISi. 170.Oe I atm Fig. u Oen + Di \ 8OOV Mg.1 GPa and lOOO”-1200°C. Mole percent 20 ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ II?Gt II + CaSi03Pv -. For CaMgSi206 composition. 1711. 45. 8. pigeonite. 14. [ 1 lo] found a mixture of perovskite (MgSi03) and glass at 21. Melting curve for diopside.O. Temperature-composition sections for the join NaAlSigOg (albite) . Pen. see also Sawamoto [147]. FezSiO4 (fayalite) in equilibrium with Fe at 1 atm [27]. . 2500 1 Anhydrous -L 5 Forsterite I/I Periclase + Liquid ite ie Spine1 1 /I: / / Spine1 \ ] Pressme.5. The thermodynamic models are based on data from other sources [37. Di. 15. . as majorite and high-P clinoenstatite on Figure 7. orthopyroxene. 1501. 5c Di CM _ CaSiL3Pv Di +_ CaSi03 Pv I1 60 Casio I -3 Fig.. See also data of Biggar [ 151 from 1 atm to 0. Phase relationships above 21 GPa are from Ito and Takahashi [76] and those below 21 GPa are from Akaogi et al. Phase relationships for the system Mg2Si04 (forsterite) . Locations of dashed lines are inferred. 123. IO 20 30 40 50 60 70 80 90 Weight percent Fe. perovskite. Lindsley [95] has presented three other similar diagrams at 0. PRESNALL 255 Mole percenl Fig.S. 11. and pigeonite + augite equilibria at 1 atm and 500-1300°C [95]. clinopyroxene. 14. 441. Lindsley and Andersen [97] should be consulted for correction procedures required before plotting pyroxenes on these diagrams for geothermometry. Orthopyroxene + augite. Gt. [3]. Isopleth for the composition Mg2SiOd [48. Fs. Additional studies of the melting relationships are Ohtani and Kumazawa [126] and Kato and Kumazawa [84-861. a high-pressure phase of unknown structure.?. Pressure-composition section for the system MgSiOs-CaSQ at 1650°C [55. 118.. Pv. Thermodynamically modeled subsolidus phase relationships for the system Mg2Si206 (enstatite) CaMgSi206 (diopside) from I. iti E c I400 OLIVINE 1300I200 Mg.5 to 10 GPa [56.. Locations of dashed lines are inferred.SIO. Opx. Di. 1411. diopside (CaMgSi206). ilmenite.. Pressure-composition sections for the join Mg2Si04-Fe2Si04 at various temperatures.5 GPa. Fig. 98. 1. 128. when they are free of Ca on the left-hand margin of this diagram. Garnet and clinopyroxene.O.!?10~ Mole percent Fig. and 1.I. G Pa Fig.. are the same phases. 57. 11. Hd. PvtMw I1 1 /&jL-Pv+Mw+St 25SP Mg. hedenbergite (CaFeSi206). En. 20 40 60 80 Fe. 16.IO -_ Mole percent Casio.. garnet. 12. 571. Cpx. CM. enstatite (MgSi03). diopside.o. Phase relationships to the right of the forbidden zone boundary are metastable relative to augite + olivine + silica. 13.95 GPa. respectively. Fig. ferrosilite (FeSiO3). orthopyroxene + augite + pigeonite. Liu [99] reported that pyrope transforms to perovskite + corundum at about 30 GPa. 01. MgSiO. 20. 341. diopside. Co. 18. and Ca-poor pyroxene (Opx or Cpx) at various pressures and temperatures [69]. 1571 give additional data and discussion of these phase relationships. Ca-rich pyroxene (Cpx). wollastonite. the A1203 content of pyroxene in equilibrium with garnet increases with decreasing pressure to at least 15 mole percent [30. 87. Pv. Ca3A12Si3012. pyrope garnet. [125]. MgSiO. spinel. indicate pressure (GPa) followed by temperature (“C).Other references [51. Fig.Grossular. CaMgSi. Ca-Tschermak’s molecule. PRESNALL 257 A’. +. 3 GPa [30]. Mg3Al$Si3012. perovskite (MgSiOg-FeSiO3 solid solution). and that ilmenite then transforms to perovskite at about 30 GPa.O.O. enstatite. Labels of the type. St. Cagarnet.03 Corundum 1200 OC.O. Wollastonite Diopside Weight percent Enstatite Fig. Grossular. Compositions (unsmoothed) of coexisting garnet (Gt). Pressure-composition section for the join MgSiOjAl203 at 1000 and 1650°C [57.5 GPa. Mg-garnet. ” 30 AI. Mod Sp. 2000. magnesiowiistite (MgO-Fe0 solid solution). 9. 3 GPa CaSiO. corundum. Locations of dashed lines are inferred. Pyrope GPa GPa Diopside Mole % CaSiO. olivine. I- PV Pv + Gt \ P\ \ Gt 1 Al:o. Ca-Gt. 17. The system CaSi03-MgSi03-Al203 at 12OO”C. Di. Isopleth for Mg3A12Si3012. stishovite (SiO2). Phase relationships at pressures less than 5 GPa are from Boyd and England [32]. Gt \ \ \ 101 1 1 1 1 1 1 1 h k 1 ’ ’ I MgSiO. Sp. 821. modified spinel. 5 IO 15 20 25 Mole percent AI. CaAl$i06. see Akaogi and Akimoto [2]. Liu [loo] subsequently revised this result and found that pyrope transforms to the ilmenite structure at about 24-25 GPa. The melting curve at 5 GPa and above is from Ohtani et al. Mw.essure. Wo. 2000 t Llquld Pyrope 1000 I I/ 0 I 2 3 . For additional data along the boundary between the garnet and clinopyroxene + garnet fields at 1 OOO”C. - Fig. 258 PHASE DIAGRAMS L I /I . 5 6 7 8 9 IO GPo Fig. 19. Mg-Gt. En. 200800°C. lOOO”-14OO”C. At 1100 and 1600°C for pressures between 2 and 6. Pyrope. .. 21.- I -. Wiis.. ...1 0.-.-.~ _-_-_-I pL.p?-. Temperature-composition section for the system Fe-O at 1 atm [46. n! )(u 1200 “+ t -‘-‘~ 2 k-/-l.-. ..-..-..-.. ilmenite (FeTiOs). 64..47..-. 1 atm [161].-. .- -.AIR .. Mole percent Hem Fig. Hem.-.-.. -.lDrlhl + \A/iicTlrc 7.I 1 1 -L.3 Fe0 23 24 25 26 27 FesO. Psb..-. Fpb. 22.-ic3L..py(f=JF.__.-..-.-. 29 Fe...- .lC24.-I I I lC20-.-.(/!L.-.__. -. hematite (FezOg). Mt..CY-IRON + WkTlTE .. pseudobrookite (FezTiOs)..@C. Weight % Oxygen Fig. Light dashed lines are oxygen isobars labeled in log oxygen fugacity units (atm).IRON + MAGNETITE -. 1381. wiistite (Fed3 260 PHASE DIAGRAMS o”-1: k -0 -: -2c .-.. Ilm. magnetite (Fe304).- . Light dash-dot lines are oxygen isobars in atm..-. ferropseudobrookite (FeTi205)..cB i’ -.-.--.. - Fe 0.-.p-..O...800.--pJ u I aJ -. ulvospinel (FezTi04).-...-.. \.. The system TiOz-FeO-FqO3 at 13OO”C..o-14-... -. Usp... “J .0-l” .-. -. / y. 120.$!L..-.- .Cl!..IQUID Fe --I”.-.Cj-E.g?-.6’1. PREBNALL 259 Rutile TiOo 1300°c One atm 1*.-.- 600--‘-.. GPa Fig.[103]. Several additional references [61. Small concentrations of other constituents in the vapor are ignored. . Pressure-temperature projection showing the upper temperature stability limits for serpentine. 400 /I 800 1000 Temperature”C 1200 IL IO Fig. 23.[28]. The univariant curves labeled Pa-out (1 . 7 [107].40]. Curves 3 and 4 give the corresponding maximum stability of phlogopite in the presence of forsterite and enstatite.F)2. magnetite. and give the maximum stability of pargasite during melting in the presence of a pure Hz0 or H20-CO2 vapor with Hz0 mole fractions of 1. so that the curve above this pressure is metastable. Holloway [71].hematite (Fe203) solid solution.r i ) Temperature. Preparation of this compilation was supported by Texas Advanced Research Program Grants 009741007 and 009741-066. 108. indicate mole % ulvospinel in the ulvospinel (Fe2Ti04) . and represent more closely the stability of phlogopite in the mantle. and 0. Acknowledgements.[112]. .< .5). Numbers beside curves refer to the following sources: 1 [159].O). Low pressure phase relationships for iron. 3-6 .[115].. Pa-out (0. Curves 36 are not univariant [114].3. Curves 5 and 6 give the maximum stability of phlogopite in the presence (curve 5) and absence (curve 6) of vapor.0. Geosciences Program.[20. Mg$i205(OH)4 (curves I and 2) and phlogopite. 5 . 738. hematite. 2 . . Usp. 6 . The dashed curve labeled OHtnu. and Paout (0. .[109]. stability limits. and Oba [124]. Numbers beside curves refer to the following sources: 1 . / .5) . 211. indicate mole % ilmenite in the ilmenite (FeTiOs) .[90]. 1791 also discuss the WE transition. Ilm. 262 PHASE DIAGRAMS Ethcp) Pressure. and the patterned areas labeled F430H57 and Ftoo are from Holloway and Ford [72] and Foley [52]. 3 . ulvospinel.[6]. 26. I-70. Pressure-temperature projection of pargasite. Hem. (Pa) NaCa2Mg4A13Si6022(OH.5. and by National Science Foundation Grants EAR-8816044 and EAR-9219159. “C Fig. and show the breakdown of pargasite during vapor-absent melting for different proportions of fluorine and hydroxyl in the pargasite.“C 5oc Fig. Temperature-oxygen fugacity (&) grid for coexisting magnetite-ulvospinel solid solution and ilmenite-hematite solid solution pairs [ 1551.[73].[17. 0. 8 . Mt. 24. 9 . Lines with labels of the type. 2 . See Yoder and Kushiro [174] for an earlier study of the stability of phlogopite. 4 . ilmenite. KMg3AISi30to(OH)2 (curves 3-6). Lines with labels of the type. Contribution no. 25.5 GPa on curve 4. 800 900 1000 1100 1200 1300 1400 I Temperature. University of Texas at Dallas. Montana and Brearley [ 1161 speculated that a singular point exists at about 1.magnetite (Fe304) solid solution. PRESNALL 261 Pa-out / ‘Pa-out (0. U-70.3) are from Gilbert [59]. 1977. 7. al-iron. 217-224. .. D.. Akimoto. The quartz . Ito.. 21.[167]. and S. [145] and Anderson [8] have proposed the existence of a new phase.[17-19.[II]. chemical calculation. Akaogi. and A. 36. 94. inner-outer core boundary (329 GPa). For reference to Figure 26 at low pressures. 6.stishovite transformations: New calorimetric measurements and calculation of phase diagrams. Phys. J. M. 4 . Int. Res. Pyroxene-garnet solid-solution 6000 CM IOC II 100 200 300 Pressure. Monatsh. 15. 9. Analysis of shock temperature data for iron. 145157. C. Olivine-modified Fe4Si4012-Fe3A12Si3012 at high spinel-spine1 transitions in the pressures and temperatures. J. High pressure melting curves for iron.. Ahrens. Saxena et al. (Ross et al. 5. REFERENCES equilibria in the systems 3. 5 . Neues Juhrb. Akaogi. physical application. and A. IOC. 10. Navrotsky. 3 . [146] have suggested that al-iron is the liquidus phase down to a pressure of 60-70 GPa. Res. E. and J. Quartz tj coesite transition and the comparative friction measurements in pistoncylinder apparatus using talcalsimagglass (TAG) and NaCl high-pressure cells. core-mantle boundary (136 GPa). center of Earth (364 GPa).coesite . [l l] and Brown and McQueen [38] into agreement. 5.1.[I]. 8. 2. Tan. CM. Earth Planet. The shock data of Yoo et al.. Phys. 1984. Geophys. J. 300 GPa) are at slightly higher temperatures than the data of Brown and McQueen. Numbers beside melting curves and brackets refer to the following sources: 1 . On the basis of molecular dynamics calculations.. Matsui [ 11 l] has also proposed the existence of a new phase at 300 GPa and temperatures above 5000 K. Akella. T. 11.685. Mg4Si4012-Mg3A12Si3012 and Navrotsky. Bundy [40]. 27. 15. 1989. 2. [176] (not plotted but located at 6350 K. M. thermo106. M. 124-134.67115. 381. 1531.. 103. H. 143. the curves of Mirwald and Kennedy [ 1121. Mineral. which brings the data of Bass et al. Gallagher and Ahrens [54] found that earlier shock data from their laboratory [ 1 l] are 1000°K too high. system Mg2SiOq-Fe2SiO4: CaloEarth and Planet. Akaogi. 2 . Bass. Int.. and Boehler [ 171 are used for the a-&-y phase relationships.. 235 GPa and 6720 K. 90.. GPO Fig.[25. High-Press. and geoPRESNALL 263 4.rimetric measurements. that is stable along the liquidus at pressures above about 170 GPa. 151-161. Solid solubility of Al203 in enstatite at high temperatures and l5 kb water pressure. P.. W. Barth. Seifert. Manghnani and Y. Neues Juhrb. Svendsen.. R. 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Holmes.. and J.. J. H. L. H. C. Jr. Yamamoto. 70. 340. B. High-low quartz inversion up to 10. 174. Stormer. D. 206-214. Shock temperatures and melting of iron at Earth core conditions. 35.000 bars. R. Rev.-Y. Akimoto.. 62..polymorph of silica. T. 172. Jeanloz. Geophys. J. C. 1987. Jr. Yoder.. Stewart. AGU. Mem. Williams. R. 1981. Melting of (Mg. For example. and H. 1281. Washington Year Book 80. Glasses. energy. MA 01063 Mineral Physics and Crystallography A Handbook of Physical Constants AGU Reference Shelf 2 Copyright 1995 by the American Geophysical Union. Application of the solid-helium pressure medium in a study of the CI-E Fe transition under hydrostatic pressure.51b efore attempting to use the data presented here. Fei. FORCES AND FLUXES Diffusion is the thermally-activated. 178. and Boehler. 13. Herzberg. p.Li”) to a region (I) of lower chemical potential (pi’) will cause the system Gibbs energy (G) to fall since and using the definition of pi [ 139. the movement of An i moles of chemical component i from a region (II) of high chemical potential (/. and Liquids John B. and Y. the application of the resulting diffusion coefficients to complex geologic problems may not be straightforward. Eos Trans.793. Carnegie Inst. inert conditions to 580 kbar (abstract). relative movement (flux) of atoms or molecules that occurs in response to forces such as gradients in chemical potential or temperature... C. AGU. Zou. Smith College. T. 16. T. K. INTRODUCTION Diffusion is an integral part of many geologic processes and an increasing portion of the geologic literature is devoted to the measurement. 98. to important older literature. 32. A. therefore. Zhang.. 2. Department of Geology. This compilation is intended to be a guide to recent experimentallydetermined diffusion coefficients and. B. M. P. Liebermann. J.. G.177. Gasparik. estimation. J. Diffusion Data for Silicate Minerals. Brady 1.. 147. Geophys. Zerr. Mao.g. C. Res. 168-169. 121. R. 179. . Melting and subsolidus relations of SiO2 at 9-14 GPa. Brady. Bell. 74. and application of diffusion data. To provide a context for the tables. The reader is urged to read one or more diffusion texts [e.Fe)Si03-perovskite under hydrostatic. Although the equa tions for well-constrained experiments are relatively straightforward.78519. a brief summary of the equations required for a phenomenological (macroscopic) description of diffusion follows. Diffusion is spontaneous and. through the papers cited. No. 1993. 99. Northampton.. 272274. 19. 1993. must lead to a net decrease in free J. (3 reducing the number of independent diffusion coefficients to (2n. the matrix of coefficients relating the forces and fluxes is symmetrical L. Second. a chemical potential gradient provides a therm odynamic force for atom movement. The instantaneous. the isothermal. 96. but unfortunately D.s) are “phenomenological diffusion coefficients” [36]. l] have applied these equations successfully in modeling the diffusion evolution of coronas and other textures in some rocks. Most experimentalists achieve this by their experimental . The most obvious simplification of (6) is to limit the number of components to 2 and. components. the number of required diffusion coefficients to 1. and reference frame are properly chosen. 1331 showed that if the forces. they are not generally used to describe diffusion experiments.g.1). Only (n-l) compositions are independent.. Although equations (3)-(5) are theoretically satisfying. 98. isobaric Gibbs-Duhem equation [ 139.451.J. Two impor tant results help limit this complexity. 971. However. the complexity of describing diffusion in multicomponent systems rises 269 270 DIFFUSION DATA rapidly with the number of components.. ncomponent system with respect to reference frame R may be described by (3) where x (m) is distance and the n2 terms L: (moles of i/m. Because each component of the system may move in response to a gradient in the chemical potential of any other component. therefore. = L. Fisher [Sl]. one-dimensional. On a macroscopic scale. Onsager [ 132. p. p. 1341 (4) for the single phase in which the diffusion occurs reduces the number of independent gradients to (n. isothermal diffusive flux JR (moles of i/m2s) of component i in a single-phase. 55. in part because chemical potential gradients are not directly measurable in most cases.1) and the number of diffusion coefficients to (n-1)2. # DF so that (n-1)2 diffusion coefficients Di (m2/s) are needed for (6). First. Joesten 194.: . fluxes. most workers use empirical equations related to (3) that involve measurable compositions Cj (moles of j/m3) [ 1341. 16. linear equations appear to be adequate for relating each diffusive flux to the set of operative forces [137. and others [e.(2) Thus. 99. ) (9) which has many analytical solutions [6. and must be modified if the sample volume does change [lo]. 81. All of the equations (7)-(13) implicitly assume constancy of volume. 321. Chap. notably spherical and cylindrical cases. for which the fixed laboratory reference frame is a mean volume reference frame. More complicated boundary conditions and geometries may require numerical approximation [32. Some commonly used solutions to (5) for planar geometries are given in Table 1 and two of these a~ shown graphically in Figure 1. unless the experiment attains a steady state. However. Additional ways to simplify the treatment of multicomponent systems are addressed in Section 5.design. =Iq$). Commonly-used solutions to equation (9) Boundary Conditions Solution Thin-film Solution Ci + CO for Ix]> 0 as t + 0 c. If Di is not a function of composition (Ci) and. In finite BRADY 271 Table 1. then equation (4) may be simplified to (%). and defines the diffusion coefficient Di (m2/s). Fick’s First Law Ji =-Di relates the instantaneous flux Ji (moles of i/m2s) of component i to the one-dimensional gradient of the concentration of i. 3. time (t) is also a variable and a continuity equation (Fick’s Second Law) (8) must be solved. the distance x that has attained a articular value of Ci after time t is proportional to P Dit .00 for x = 0 as t + 0 } (y)=&exp[&) where cx=lL”(Ci -CO)dx (10) Semi-infinite Pair Solution 1 . not a function of position (x). therefore. 3. dCi/dx (moles of i/m4). Similar analytical solutions exist for related boundary conditions and/or other geometries. In semi-infinite cases such as (10) and (1 I). It is clear from Table 1 and Figure 1 that the parameter fi may be used to characterize the extent of diffusion. FICK’S LAWS Adolf Fick’s [50] empirical equations were used to describe binary diffusion experiments long before the more general equations (3) and (6) were developed. The next two sections present definitions and equations used to describe these binary (Zcomponent) experiments. 17. Approach (a) yields a “tracer diffusion coefficient” for the element that is specific to the bulk composition studied. =Cl for x<O at t=O 1 (E) = ierfc[--&=j (11) Finite Pair Solution Ci =Cl for O<x<h at t=O Ci =CO for h<x<L at t=O (ilC. Experiments in which composition does change significantly are often termed “interdiffusion” or “chemical diffusion” experiments. equations (9)-( 13) may be used with confidence only if Ci does not change appreciably during the experiment. for the same boundary conditions as for equation (1 1). Therefore. Approach (b) yields a “self-diffusion coeffi cient” for the isotopically doped element that is also specific to the bulk chemical composition.Fixed Surface Composition cases such as (12) and (13). 4./~x).CO)/(Cl . was obtained by Matano [122] using the Boltzmann [8] substitution (x=x/& 1 : Equation (14) can be evaluated numerically or graphi tally from a plot of (Ci . or (b) by using diffusional exchange of stable isotopes of the same element that leave the element concentration unchanged. the fractional extent of completion of homogenization by diffusion is proportional to a. If Ci does change significantly in the experiment and Di is a function of Ci. observed compositional profiles might not match the shape of those predicted by (9)-(13). one must assume that Di is a function of Ci. glasses.Ci =CO for x>O at t=O C. DIFFUSION COEFFICIENTS In general. and liquids. In such cases the Di calculated with these equations will be at best a compositional “average” and equation (8) should be considered.CO) versus x. A commonly-used analytical solution to (8). These fi relations provide important tests that experimental data must pass if diffusion is asserted as the rate-controlling process. Both approaches generally ignore the opposite or exchange flux that must occur in dominantly ionic phases such as silicate minerals. where the point x = 0 (the Matano interface) is selected such that . =0 for x=0&L Finite Sheet . This is accomplished either (a) by using a measurement technique (typically involving radioactive tracers) that can detect very small changes in Ci. They also provide simple approximations to the limits of diffusion when applying measured diffusion coefficients to specific problems [ 1471. Graphical solutions to equation (9). (B) The “finite pair” solution of equation (12) is shown for h/L=O.0 0.0 0.4 and various values of Dt/L2 (labels on curves). The initial boundary between the two phases is marked by a dashed vertical line. the Matano interface is the original boundary between the two crystals.6 x 9 3 0. Darken’s analysis showed that in the presence of inert markers the independent fluxes and. Darken [35] and Hartley and Crank [83] showed that for electrically neutral species.-. indicating that more Zn atoms than Cu atoms crossed the boundary.2 -2. Diffusion experiments that follow the Boltzmann-Matano approach have the advantage of determining Di as a function of Ci and the disadvantage of risking the complications of multicomponent diffusion. = (N.8 1.6 0.0 0. Smigelskas and Kirkendall observed that MO wires (inert markers) placed at the boundary between the Cu and brass moved in the direction of the brass during their experiments. the binary (AtiB) interdiffusion coefficients (D.. . cation exchange between ionic crystals.4 -1.4 0. (A) The “thin film” solution of equation (10) is shown with a=1 for various values of fi (labels on lines).8 1.(15) 272 DIFFUSION DATA 0. therefore. ) obtained in a Boltzmann-Matano type experiment and the tracer diffusion coefficients ( Da and D*. 0. For binary.6 0.0 g 0.8 u s u 3 ..5 1.) for the interdiffus ing species are related by D AB-. [32.2 0. X2 x/L Figure 1.0 1.Di + NADIR) where N A is the mole fraction and YA the molar activity coefficient of component A.230-2341. the “tracer” diffusion coefficients of Cu and Zn can be determined in addition to the interdiffusion coefficient DCuZnm.0 (4 s 0.CO) as a function of x2 at any time yields a straight line of slope -l/(4Dit). Plotting ln(Ci . Plotting (Ci -CO)/(Cl CO) as a function of x/L normalizes all cases to a single dimensionless graph.2 0. for which neither (8) nor (14) is correct. Darken developed his analysis in response to the experiments of Smigelskas and Kirkendall [ 1481. who studied the interdiffusion of Cu and Zn between Cu metal and Cu7&&~~ brass. p.4 0. ’ and BZ represents BzbZ. This expression permits interdiffusion coefficients to be calculated from more-easily-measured tracer diffusion coefficients. If a=b.D.“) in appreciably ionic materials such as silicate minerals yields [5. equation (6) or (3) must be used. lo]: I[ 1+ (17) which requires vacancy diffusion if a#b. Multicomponent diffusion presents the possibility that diffusive fluxes of one component may occur in response to factors not included in (7)-( 1 S). In these cases.Z) Ii I+ (18) [ 12 I].A similar analysis for binary cation interdiffusion (AZ w BZ where AZ represents Al”Z.Z + NBZD. 251. 112. are unknown for most materials and most‘workers are forced to assume (at significant peril!) that they are zero. such as gradients in the chemical potentials of other components. For minerals that are not BRADY 213 ideal solutions. Garnet is the one mineral for which offdiagonal diffusivities are available [ 19. Dg or Li. 201 and they were found to be relatively small. The offdiagonal (i#j) diffusion coefficients. coupling of diffusing species. This approach was formalized by Cooper and Varshneya [28. It should be noted in using equations ( I6)-( 19) that the tracer diffusivities themselves may be functions of bulk composition. etc. 201. 113. 19. coefficients Dy to calculate multicomponent interdiffusion coefficient matrices. One approach used by many is to treat diffusion that is one-dimensional in real space as if it were onedimensional in composition space. EXPERIMENTAL DESIGN Rarely is diffusion in geologic materials binary. = (NA. then ( 17) simplifies to D (Daz)( Diz ) AB-. 301 . the “thermodynamic factor” in brackets on the right side of (l6)-( 18) can significantly change the magnitude (and even the sign!) of interdiffusion coefficients from those expected for an idea1 solution [ 12. 5. MULTICOMPONENT DIFFUSION 6. and its inverse offer the most hope for diffusion analysis of multicomponent problems [ 1 15. The full expression is quite long. 95. is to diagonalize the diffusion coefficient matrix for (6) through an eigenvector analysis. even in small quantities [e.g. Diffusion in rocks or other polycrystalline materials may occur rapidly along grain boundaries. a matrix of diffusion coefficients must be determined before the analysis can proceed. or surfaces and will not necessarily record intracrystalline diffusivities. crystal interfaces. but simplifies to (19) if the solid solution is thermodynamically ideal. If water is present. 121.who discuss diffusion in ternary glasses and present criteria to be satisfied to obtain “effective binary diffusion coefficients” from multicomponent diffusion experiments. 49. If the mineral. 46.. and 6il = 0 if i#j. see also 1611 has generalized the relationship (17) to multicomponent minerals. 291. dislocations. Vacancies. 73. 13. 1641. Another approach.. 103. This approach. 102. If polycrystalline materials are used in experiments to measure “intrinsic” or “volume” diffusion coefficients. l l l l . In (19) zi is the charge on cation i. The form of this tensor is constrained by point group symmetry and the tensor can be diagonalized by a proper choice of coordinate system [ 13 I]. 154. diffusion may be a function of crystallographic orientation and the diffusion coefficient becomes a second rank tensor. I 1.g. Experiments involving grain-boundary diffusion [e.Cooper [75.. then an equilibrium oxygen fugacity should be controlled or measured because of its effect on the vacancy concentration. liquid. Therefore. 167. 1581 are beyond the scope of this summary.g. In anisotropic crystals. In general. 150. developed by Cullinan [33] and Gupta and . 411 = 1 if i=j. Lasaga [105. or glass contains a multivalent element like Fe. usmg tracer diffusion A few additional considerations should be mentioned regarding the collection and application of diffusion data. diffusion coefficients obtained with this procedure are functions of both composition and direction in composition space. Although some simplification in data presentation is achieved in this way. it is essential that the mineral being studied is well-characterized. 711. 47. and other crystal defects may have profound effects on diffusion rates [e. Water can have a major effect on diffusion in many geologic materials. then the contributions of “extrinsic” grain-boundary diffusion must be shown to be negligible. Older data may also be found by consulting the compilations of Freer [56. coefficients for diffusion by a single mechanism at different temperatures may be described by an Arrhenius equation D = D. 7. but are not included [see 156. Askill [2]. Almost all of the data listed are for tracer or selfdiffusion. 451 and magnetitetitanomagnetite [65. 41. Chap. 21. Log D. 23. and liquids. Many good. Interdiffusion (chemical diffusion) experiments involving minerals are not numerous and interdiffusion data sets do not lend themselves to compact presentation.” The @t test can be used if data are gathered at the same physical conditions for at least two times. preferably differing by a factor of four or more. Some good data also exist for important non-silicate minerals such as apatite [ 157.” l 274 DIFFUSION DATA which duplicates the sample preparation. . commonly reveals sources of systematic errors. exp (20) and fit by a straight line on a graph of log D (m2/s) as a function of l/T (K-i) [147. heating to the temperature of the experiment. and Harrop [81]. Important tests include the m relations noted in equations (lo)-( 13) and the “zero time experiment. older data have been left out. quenching (after “zero time” at temperature). Diffusion data listed for silicate glasses and liquids have been further restricted to bulk compositions that may be classified as either basalt or rhyolite.water fugacities are an essential part of the experimental data set. but the silicate minerals offered the clearest boundary for this paper. 3. Hofmann [86]. the data included in this compilation have been restricted to comparatively recent experimental measurements of diffusion coefficients for silicate minerals. Because many kinetic experiments cannot be “reversed. DATA TABLE Due to space limitations. and data analysis of the other diffusion experiments. 571.” every effort should be made to demonstrate that diffusion is the rate-controlling process.591. Because diffusion is thermally activated. but can be found by following the trail of references in the recent papers that are included. glasses. The often-overlooked “zero time experiment. These and other important features of diffusion experiments are described in Ryerson [141]. Interdiffusion data for silicate liquids and glasses are more abundant. Neither are non-isothermal (Soret) diffusion data [see 1081. 136. for ease of comparison log D is listed for a uniform temperature of 800°C (1200°C for the glasses and liquids). even though the original data may not warrant such precision. J. B. or Liquid tion Component Range (“C) (MPa) (MPa) (kJ/mole) (m*/s) 8oo”c (“C) m E 4 YW I u Mineral. Chap. Logarithms are listed to 3 decimal places for accurate conversion. (or D) log D ‘IT. cooling rates. S. B. Cherniak. (or D) log D ‘IT. Vondell provided considerable help with the library work. E. Glass.Diffusing Temperature P 02 ma log D. Note that other closure temperatures would be calculated for different crystal sizes. 1061. oxygen fugacity. Mineral. Orienta. Also listed are the conditions of the experiment as appropriate including the temperature range. a sample “closure temperature” (T. The example closure temperatures were included because of the importance of closure temperatures in the application of diffusion data to petrologic [107] and geochronologic [123. m2/s) and form (log D. No attempt was made to reevaluate the data. or the uncertainties given (or omitted) in the original papers. A. 51 problems.l mm and a cooling rate (dT/dt) of 5 K/Ma. Kozak. Ganguly.” D. Watson. pressure range. 82. R. Cooper.” Experiment/Comments Ref. AHl(2. and AH have significance in the atomic theory of diffusion [see 32. 4 log D. Acknowledgments.R) is the slope of the line where R is the gas constant (8. 7 or Liquid tion Component Range (“C) (MPa) (MPa) (kJ/mole) (m2/s) 800°C (“C) [l@l ? 2 . 1211 and may be related for groups of similar materials [162.3143 J/mole. J.303. and an anonymous reviewer. This paper was improved by helpful comments on earlier versions of the manuscript by D. The closure temperature given is a solution of the Dodson [38] equation for a sphere of radius a=O.Diffusing Temperature P 0.) of this compilation. J. Orienta. and their uncertainties. Diffusion data are listed in terms of AH and log D.(m2/s) is the intercept of the line on the log D axis (l/T = 0). and boundary conditions. Use these tabulated log D numbers with caution. the fit.K) and AH (J/mole) is the “activation energy. Extrapolation of the data using (20) to conditions outside of the experimental range is not advisable.) has been calculated for the silicate mineral diffusion data. Freer. Giletti. Glass.” Experiment/Comments Ref. even though this temperature may be outside of the experimental range. N. R. J. However. In many cases data were converted to the units &I. Finally. and sample geometry. 5) -12.6(+10.3 199 Exchange with CO*.20 uB/ 2000 NO “wet” 650-800 100 UB/ “wet” NO 750-900 100 UBo “wet” NO 800 200 uB/ “wet” NO c r I 104.) phlogopite powder (Ann4) (see paper for camp.) ‘80 180 4oAr Sr “wet” NO 650-800 100. bulk analysis. spherical [27] model.) biotite (An& powder (see paper for camp.[loll Mineral.” Experiment/Comments Ref. ion probe too 305 Exchange with 180-enriched [541 . reference) biotite powder chlorite (sheridamte) (see paper) mucovite powder powder muscovite (see powder paper for camp.041 -7. Orienta.854 -16. Glass.229 -17. cylindrical model.0 -16. or Liquid tion Component Range (“C) (MPa) (MPa) (kJ/mole) (m*/s) 800°C (“C) nepheline powder biotite powder (see paper for camp. bulk analysis -9.Diffusing Temperature P O2 4 log Do (or D) log D “T.4 233 Exchange with ‘*O-enriched [541 water.) phlogopite powder (see paper for camp. 6 121. bulk analysis & ion L m F 4 Y4 ii Mineral.506) -18.1 -12. 671 (AV.water.1 w.2 (k7.452) -19. Glass.114 -16.1 (CO)/ co.204) -19. cylindrical model (AV =1.1 163 (f21) -11.523 (f0.4 239 (k8) -7.699(f1.21 -13.4~10-~ m3/mole) Exchange with 41KC1 solu. bulk analysis.1 co2 800-1300 0.F371 t 163 (+21) -8.620 (f0. cylin- I’i 1’2”‘:’ 88 171.6 172 (+25) -1l.9 drical model.: 1100-1300 0. 1 =I@‘4 1000-1300 0.1) -5.9 UB 1180 “wet” 0. u or Liquid tion Component Range (“C) (MPa) (MPa) (kllmole) (m2/s) 800°C (“C) ii Sermanite (syn) lc-axis 1x0 02MgSi207) lkermanite (svn) I c-axis ‘80 (CazMgSizb.1 N2 1100-1300 0.7 -5.2-17.” Experiment/Comments Ref.1 268. cylindrical model.OOO(f1.Diffusing Temperature P O2 4 log Do (or D) log D ‘IT.zO m3/mole) 281 Degassing into water.) 1 Sermanite (syn) ///c-axis / 45Ca UhMgSi207) Sermanite (syn) /c-axis 54Mn 02MgSi207) lkermanite (syn) /c-axis 59Fe 02MgSi207) &ermanite (syn) /c-axis 6oCo GbMgSbO.3 -7.1 N2 .322) -19. Orienta. bulk t621 analysis.) 500-800 0. bulk [771 analysis.98 -13.7 D=lxlO-*’ t t L c t t c on. ion probe too 373 Degassing into water. 1100-1300 0. (AV.194 -20. ion probe profiles wope powder tslSm 1300-1500 3000 UB/ 140 -11.0 57 1 Microprobe profiles.652 -21.1 lo-l3 243 -5.3 . Glass. I I I atmosphere.55) experiments. act + 2.Fas> //c-axis Fe-Mg 1125-1200 0.1 x [Mg/ x10-4) .1 N2 1100-1300 N2 I i robe.301(?0.1..690 -18.49) experiments using model.d. other [1261 liebensbergite (couple) interdiffusion interdiffusion coefficients [128] grossularite C&9 isotropic ‘80 1050 800 UB n.9 725 Exchange with ‘*O-enriched I311 (Al67SP2xAns b2) water.143 + 0.3 78 1 extrapolated to pure Fo forsterite . D also ~1241 divine Fo91Fa9) (couple) interdiffusion tube +9.0)x10-6 m3/mole) almandine isotropic 86Sr 800. or Liquid tion Component Range (“C) (MPa) (MPa) (kJ/mole) (m*/s) 800°C (“C) Mineral.585 -18.7Fa6.740) -22.” Experiment/Comments Ref.8 604 Calculated from interdiffusion WI Spessa4Alm6 (couple) 4300 GrPC (T37.UBI 275.6(f2. sectioning.009 -19. D’s [l-m .3(+3.1 Ah$hPd 850 200 nd. m.1 lo-to.Diffusing Temperature P 02 4 log D. = 5.4 321 Exchange with silicate melt.=5.5) fits of alm-rich composition 9 j! Mineral. UB 208.UB/ 253.8 702 Microprobe profile.292 -19.086 -21.763) -21.UB/ 284.705 [Fe/(Fe+Mg)] olivine //c-axis Ni 1149-1234 evac.9)x10e6 m3/mole) AlmsoPYPzo . fo2 olivine (Fa.d. ion probe profiles almandine isotropic ‘80 8001000 100 UB 301 (+46) . D varies [I41 fayalite powder (couple) interdiffusion w/direction.2 ! 403 Microprobe profile.1x varies with direction and P Wg+Fe)l [Mg/(Mg+Fe)] (AV a= 5. Rutherford backscatter.10. Ion probe. ion probe profiles almandine isotropic 145w 800-1000 100 UB 184 (+29) -12. “sphere” almandine isotropic 167 ET 800.1 air 196 -8. or Liquid g tion Component Range (“C) (MPa) (MPa) (kJ/mole) (m2/s) 800°C (“C) 2 olivine sintered 59Fe 1130 0. microprobe G'61 (Fo93. Orienta.5~10-~~ Exchange with t80-enriched [581 Fe.2 [851 Wd%o-Faloo~ powder 10-12 . ion probe profile Mineral. UB 193 (f10) -8.43 -7.Diffusing Temperature P O2 =a log Do (or D) log D “T.1000 100 UB 205 (+17) -12.4 / 404 Thin Ni film. ).959 -20. ion probe [341 E’m%GrdJrI ) MH profiles AlmsoPYPzo . (AV. D=4.Te.523(*0.d.19) experiments. log D59i+ = -10.n. WI GTPC autoradiography. = 5.6 432 Microprobe profile.5 605 Exchange with 167Er water [311 @l&Pd@Y2) solution.5~10-~m~/mole) olivine(MgzSi04) //c-axis Co-Mg 1150-1300 0. D=2.. Glass.” Experiment/Comments Ref.5(*0.222 (*0.5 ! 562 Exchange with 145Nd water 1311 b%SP2dnd’Y2) solution.602) -22.759 -17.1 air 414 to 444 -1.3) tube profile.8xlO-2’ water. ion probe profiles ww isotropic 25Mg 750-900 200 uB/ 239 (*16) -8. n.isotropic Fe-Mn 1300.(Co2 SiO.000(&0.6 / 588 ! Calculated from interdiffusion VOI Spess94Almg (couple) 4300 GrPC (rt36.602) -21.isotropic Fe 1300-1480 2900.288 -23.3) Microprobe profile.6 526 Calculated from interdiffusion m Spessa4Alm6 (couple) 4300 GrPC (k37. Orientaor .+) (couple) interdiffusion 1300.isotropic Mg 13001480 2900. Rutherford backscatter. anisotropy found olivine (Fo.6 5 14 Thin 25Mg0 film.//c-axis Ni-Mg 1200-1450 0.36) -18. ion probe profiles AlmsoPYPzo . (or D) log D “T.959 (f0.isotropic Mn 1300-1480 2900. (AV.//c-axis Fe-Mg 900-1100 evac.-8. Glass.1000 100 UB 230 (f38) -10.8) Do= 1. Orienta.1400 526 2.5(+18.44 -7. composition.52 -6.6~10-~ m3/mole) AlmzoPYPzo .1480 4000 UBI 224. model [411 Spess94Alm6 (couple) interdiffusion GrPC (k20.0 616 Exchange with %r water [311 b’%SPd% pY2 ) solution. 1 air 288.1 Thin film of 45CaCl.638 (k1. counting surface rhyolite glass and Eu 700-1050 0. (m2/s) 1200°C (“C) T basalt (“alkali”) 1921 Kilauea 1 basalt (“alkali”) 1 melt melt Tenerife basalt (“alkali”) melt Tenerife . aa log Do (or D) log D “Tc” Experiment/Comments Ref.5 Dehydration in air.2 Reduction by graphite. (or D) log D “Tc” Experiment/Comments Ref. B.5) -6. B-track profiles of [891 1921 Kilauea cross-section on film “basalt” (Fe-free) melt 45Ca ilOO-14cKl 0.6 Reduction by graphite.362 (f0. serial sectioning by [116] Tenerife grinding.0) 3.Diffusing Temperature P 0. bulk 1931 New Mexico (fl 1.3 Thin film. (m2/s) 1200°C (“C) Zircon dissolution. OR water GrPC microprobe profiles rhyolite (obsidian) melt 1% LREE 1000-1400 800 UB/ 510.8 . [1381 Lake County. OR water GrPC microprobe profiles rhyolite (obsidian) glass Hz0 400-850 0.3 Reduction by graphite. serial sectioning by [91] (dehydrated) NM melt (f23.770 (k1.272 -10.9 Thin film of Na2 14C03.99) -14.2 (k7. counting surface basalt (tholeiite) melt 45Ca 1260-1440 0. OR 8% water GrPC track profiles of cross section basalt melt 6Li 1300-1400 0. Orientaor Liquid tion Diffusing Temperature P O2 Component Range (“C) (MPa) (MPa) fia (kJ/mole) log D.1 air 490.436) -13.2 Thin film of 6LiC1.081) -11.59) -10.1 air 184.187 -9.8 Thin film.7 Thin film.1 air 46.439 -10. bulk ]401 olivine) BC GrPC Fe0 analysis by titration basalt (alkali melt 0 1350-1450 2000 uB/ 297 (+59) -0.450 (t0.3) -4.11551 Lake County.11 (0. bulk [401 1921 Kilauea GrPC Fe0 analysis by titration basalt (FeTi) melt ‘80 1320-1500 0. serial sectioning by [91] (dehydrated) NM melt etching. bulk ]401 olivine) BC GrPC Fe0 analysis by titration basalt (alkali melt 0 1280-1450 1200 UBI 360(+_25) 1. bulk analysis of sphere “basalt” (Fe-free) melt Ar 1300-1450 looo. (or D) log D “Tc” Experiment/Comments Ref.854 -11.46) -9.9(+59.5 1) -11.4 -3.2 [ Method not described r391’ (synthetic) 3000 basalt (“alkali”) melt 24Na 1300-1400 0.0) -3.2 Dehydration in Nz.59) -18. B-track [152] 1 (synthetic) --I “basalt” (Fe-free) melt 45Ca 1100-1400 2000 UB 208.90 (+0. Monazite dissolution. bulk ]401 olivine) BC GrPC Fe0 analysis by titration basalt (tholeiite) melt 0 1300-1450 1200 uB/ 213 (k17) -3.5 -5.1 Oxidation/reduction of bead. FTIR [1661 Mono Craters profile. Mineral.3 Reduction by graphite.125 -9.211 -10.87) -11.8 Thin film.59 (f1. counting surface rhyolite (obsidian) melt 6% LREE 1000-1400 800 UB/ 251.02 (f0.7 (k5.0 -5. or Liquid tion Component Range (“C) (MPa) (MPa) @J/mole) (m*/s) 1200°C (“C) rhyolite glass and Ce 875-1100 0.56) -12.4 2.8 Exchange with tsO-selected [I51 Galapagos ‘32 02 gas.1 UB 106.1 Co2 251 (+29) -2. low water rhyolite (obsidian) melt with 14CGz 800-1100 1000 UBI 75(?21) -7. [1381 Lake County. [1601 Goose Island co2 (f13.6 Thin film of 45CaCl.1 air 115. B-track t15211 (synthetic) profiles of cross section I Mineral.Liquid tion Diffusing Temperature P O2 Component Range (“C) (MPa) (MPa) =a (kJ/mole) log D.48 -10. B-track [152] ’ (synthetic) profiles of cross section “basalt” (Fe-free) melt 45Ca 1100-1400 1000 UB 141. Glass. ion probe [116] (alkali) profile of cross section basalt melt 0 1160-1360 0.140 (kO.3 Thin film of 45CaCl.068) -10.22) -13.301 -10.284 -10. Glass.9) etching.790 (k2.3 -6.9 -2.4) thermo-gravimetric balance basalt (alkali melt 0 1280-1400 400 UB/ 293(+29) -0. Orienta.629) -14.1 Nz 103@5) -14.1 air 163 (+13) -4.010 (YkO.72 (f0.5(*42.6 Monazite dissolution.1 IW to 215. equilibrium model rhyolite (obsidian) glass H20 510-980 0.40) weight loss.1 -4.113. 1 0.1 0.1 air air air air air air air air air air air ul3/ GrPC CQGM IW h4HN2 NO Pure carbon dioxide atmosphere Graphite-methane buffer Iron-wustite buffer Magnetite-hematite buffer Pure nitrogen atmosphere Nickel-nickel oxide Pure oxygen atmosphere Quartz-fayalite-magnetite buffer UB .1 0.1 0. but fo2 limited by the graphite-bearing piston-cylinder assembly UB/NO Unbuffered. but near nickel-nickel oxide due to the cold seal pressure vessel .1 0.1 0.1 0.1 0.basalt (“alkali”) melt Tenerife basalt (tholeiite) melt 1921 Kilauea basalt (“alkali”) melt Tenerife basalt (tholeiite) melt 46Sc 1300-1400 54Mn sSSr 1300-1400 59Fe 1 1300-1400 1300-1400 6OCo 1260-1440 6OCo 1300-1400 *%r 1260-1440 Tenerife basalt (tholeiite) melt 133& 1260-1440 1921 Kilauea basalt (“alkali”) melt 133& 1300-1400 Tenerife basalt (“alkali”) melt ‘Ts 1300-1400 Tenerife basalt (tholeiite) melt ‘=Eu.1 0. 1320-1440 Key to oxygen fugacity or atmosphere abbreviations in data table 0.Unbuffered oxygen fugacity UBlGrPC Unbuffered.1 0. 5. 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Yurimoto, H., Morioka, M., and Nagasawa, H., Diffusion in single crystals of melilite: I. oxygen, Geochim. Cosmochim. Actu, 53, 2387-2394, 1989. 166. Zhang, Y., Stolper, E. M., and Wasserburg, G. J., Diffusion in rhyolite glasses, Geochim. Cosmochim. Acta, 55, 44 I 456, 199la. 167. Zhang, Y., Stolper, E. M., and Wasserburg, G. J., Diffusion of a multi-species component and its role in oxygen and water transport in silicates, Earth flunet. Sci. Lett., 103, 228240. 199lb. Infrared, Raman and Optical Spectroscopy of Earth Materials Q. Williams 1. INTRODUCTION There are a number of ways in which light interacts with condensed matter. In most cases, these are associated with the electric field of an incident photon interacting with the vibrational or electronic states of materials. The presence and strength of these interactions are principally dependent on bonding properties, the configurations of electronic states, and local symmetry of ions, molecules or crystals. Here, three separate types of light-mediated spectroscopies of interest to geophysics and mineral sciences are examined: 1) infrared spectroscopy; 2) Raman spectroscopy; and 3) optical absorption spectroscopy. Each of these techniques provides complementary information on the vibrational and electronic properties of Earth materials. The bonding properties which produce infrared and Raman-active vibrational bands provide not only a useful fingerprinting technique for determining the presence or abundance of different functional groups, such as hydroxyl or carbonate units, but also (in a bulk sense) fundamentally control a variety of thermochemical properties of materials, including their heat capacity. Moreover, the vibrational spectrum provides basic information on the bond strengths present within a material. Electronic transitions may occur in the infrared, visible or ultraviolet region of the spectrum, and Q. Williams, University of California, Santa Cruz, Institute of Tectonics, Mineral Physics Laboratory, Santa Cruz, CA 95064 Mineral Physics and Crystallography A Handbook of Physical Constants AGU Reference Shelf 2 Copyright 1995 by the American Geophysical Union. commonly produce the colors of many minerals: these are dictated by the local bonding environments and electronic configurations of different elements in crystals or molecules. The role of electronic transitions in controlling the electrical conductivity and in reducing the radiative thermal conductivity of minerals at high temperatures is briefly reviewed, and their relation to spectroscopic observations summarized. Additionally, observations of optical transitions may be used to constrain the energetic effects of different electronic configurations on element partitioning between sites of different symmetries and distortions. 2. VIBRATIONAL SPECTROSCOPY: INFRARED AND RAMAN TECHNIQUES The primary feature of importance in vibrational spectroscopy is the interaction between the electric field associated with a photon and changes induced by vibrational motions in the electronic charge distribution within a material. The most common unit utilized to describe the frequency of these vibrational motions (as well as, in many cases, electronic transitions) is inverse centimeters, or wavenumbers (cm-‘): these may be readily converted to Hertz by multiplying by the speed of light, c (2.998 x lOlo cm/se@, to the wavelength of light (in cm) by taking its inverse, and to energy by multiplying by c and Planck’s constant, h (6.626 x 1O-34 J-W). Here, we focus on infrared and Raman spectroscopic characterization of vibrational states: in this discussion, we explicitly treat only normal Raman scattering and disregard non-vibrational effects such as Raman electronic and magnon scattering and non-linear effects such as the hyper-Raman and resonance Raman effects, none of which have had significant impact to date in the Earth sciences 291 292 INFRARED, RAMAN AND OPTICAL SPECTROSCOPY (see [ 101 for discussion of these effects). In the case of infrared spectroscopy, a photon of energy below -14000 cm-l (and most often below 5000 cm-‘) is either absorbed or reflected from a material through interaction with interatomic vibrations. The primary mcasurcment is thus of the intensity of transmitted or reflected infrared light as a function of frequency. With Raman spectroscopy, a photon of light interacts inelastically with an optic vibrational mode and is either red-shifted towards lower frequency (Stokes lines) or blueshifted to higher frequency (anti-Stokes lines) by an amount corresponding to the energy of the vibrational mode. When such an interaction occurs with an acoustic mode (or sound wave), the effect is called Brillouin spectroscopy (see the section on elastic constants in this volume). Notably, Raman measurements rely on monochromatic light sources (which, since the 1960’s, have almost always been lasers) to provide a discrete frequency from which the offset vibrational modes may be measured. Furthermore, the Raman effect is rather weak: only about 1 in lo5 to lo6 incident photons are Raman scattered, necessitating relatively high powered monochromatic sources, sensitive detection techniques, or both. The vibrational modes measured in infrared and Raman spectroscopy may be described as a function of the force constant of the vibration or deformation and the mass of the participating atoms. For the simplest case of a vibrating diatomic species, this relation may be described using Hooke’s Law, in which where K is the force constant associated with stretching of the diatomic bond, and p is the reduced mass of the vibrating atoms. Clearly, a range of different force constants are required to treat more complex molecules, which have more possible vibrational modes beyond simple stretching motions (see Figure 1): because of the more complex interatomic interactions, different stretching and bending force constantsa re necessitatedA. pproximate equations relating these force constants to the frequencies of vibration for different polyatomic molecules have been reviewed and developed by Herzberg [ 121, while a detailed review of the frequencies of vibrations of different molecules is given by Nakamoto [18]. Figure 1 shows the vibrational modes expected for an isolated silicate tetrahedra, which comprise symmetric and antisymmetric stretching and bending vibrations. That different force constants are required to describe these vibrations is apparent from the atomic displacements illustrated: for example, the symmetric stretch of the tetrahedron depends predominantly on the strength of the Si-0 bond. For comparison, the symmetric bending vibration is controlled principally by the 0-Si-0 angle bending force constant, the magnitude of which is dictated in turn largely by repulsive interactions between the oxygen anions. Considerable insight in distinguishing vibrations such as those shown in Figure 1 from one another has been derived from isotopic substitution experiments, which effectively alter the masses involved in the vibration without significantly affecting the force constants. Within crystalline solids, the number of vibrations potentially accessible through either infrared or Raman spectroscopy in 3n-3, where n is the number of atoms in the unit cell of the material. This simply results from the n atoms in the unit cell having 3 dimensional degrees of freedom during displacements, with three degrees of translational freedom of the entire unit cell being associated with acoustic (Brillouin) vibrations. These 3n-3 vibrations represent the maximum number of observable vibrational modes of a crystal, as some vibrations may be symmetrically equivalent( or energeticallyd egeneratew) ith one another, and others may not be active in either the infrared or Raman spectra. Because the wavelength of even visible light is long relative to the size of crystallographic unit cells, both infrared and Raman spectroscopy primarily sample vibrations which are in-phase between different unit cells (at the center of the Brillouin zone). Characterizing vibrational modes that are out-of-phase to different degrees between neighboring unit cells requires shorter wavelength probes, such as neutron scattering techniques. These shorter wavelength probes are used to characterize the dispersion (or change in energy) of vibrations as the periodicity of vibrations becomes longer than the unit cell length-scale (that is, vibrations occurring away from the center of the Brillouin zone). Such dispersion is characterized by vibrations of adjacent unit cells being out-of-phase with one another [6]. For crystals, a range of bonding interactions (and thus force constants), the crystal symmetry (or atomic locations), and the masses of atoms within the unit cell are generally required to solve for the different vibrational frequencies occurring in the unit cell. Broadly, the calculation of the vibrational frequencies of a lattice entail examining the interchange between the kinetic energies of the atomic displacements and the potential energy induced by the bonding interactions present in the crystal. The primary difficulties with such calculations lie in determining adequate potential interactions, and in the number of different interatomic interactions included in these calculations. Such computations of lattice dynamics WILLIAMS 293 vl -symmetric stretch 800-950 cm-l Raman (often strong) v2-symmetric bend v3-asymmetric stretch vq-asymmetric bend 300-500 cm-l 850-1200 cm-l 400-600 cm-l Present in Raman Infrared (strong), Raman Infrared, Raman Fig. 1. The normal modes of vibration of an SiO4-tetrahedra. Within isolated tetrahedra, all vibrations are Raman-active, while only the v3 and v4 vibrations are active in the infrared. However, environments with non-tetrahedral symmetries frequently produce infrared activity of the VI and v2 vibrations in silicate minerals [modified from [121 and [1811. have contributed major insight into the characterization of different types of vibrational modes in complex crystals: the precise equations and means by which such calculations are carried out have been reviewed elsewhere 13, 91. Whether a given vibrational motion is spectroscopicallya ctive under infrared or Raman excitation is governed by selection rules associated with a given crystal structure. These selection rules are primarily governed by the symmetry of the unit cell, and the differing properties of Raman and infrared activity. Infrared activity is produced when a change in the dipole moment of the unit cell occurs during the vibration. It is this change in the electric field associated with the unit cell which interacts with the electric field of the incident photons. Because of this dependence on vibrational changes in the charge distribution, highly symmetric vibrations are often inactive or weak in infrared spectra: for example, within isolated tetrahedra, both the symmetric stretching and symmetric bending vibrations shown in Figure 1 are infrared-inactive. motion produces a change in the polarizability of a material, then the vibration is Raman active. Notably, while the induced dipole is a vector, the polarizability is a second rank tensor, and it is the symmetric properties of this tensor which allow the prediction of which families of modes will be active when observed along different crystallographic directions. Thus, both Raman and infrared activities are governed by interactions of the electric field of the incoming light with vibrationally produced changes in the charge distribution of the molecule or unit cell. Yet, despite Raman active vibrations depending on changes in the polarizability tensor and infrared active vibrations being generated by changes in the dipole moment, the two sets of vibrations are not always mutually exclusive: for non-centrosymmetric molecules (or unit cells), some vibrations can be both Raman and infrared-active. Finally, the intensities of different vibrations in the two different types of spectroscopy may be related to the magnitude of the changes produced in the dipole moment or polarizability tensor in a given vibration. The physical origin of Raman scattering may be It is the relation of the change in the polarizability viewed from a simple classical perspective in which the tensor and shifts in the dipole moment to the symmetry of electric field associated with the incident light interacts the lattice which enables different vibrations to be with the vibrating crystal. In particular, this interaction associated with different symmetry species, as well as occurs through the polarizability of the material: that is, with possible crystallographic directionality for the its ability to produce an induced dipole in an electric field. infrared and Raman modes. The way in which this It is the oscillations in the polarizability produced by characterization of vibrational mode symmetries is vibrations which cause Raman scattering: if a vibrational conducted is through an application of group theory called 294 INFRARED, RAMAN AND OPTRXL SPECTROSCOPY factor group analysis. This is a means of utilizing the site symmetries of atoms in the primitive unit cell of a crystal (as given, for example, in The International Tables of Xray Crystallography), coupled with character tables of the site symmetry and crystal symmetry group, and correlation tables between different symmetry groups to determine the number, activity, and symmetry of infrared and Raman vibrations of a crystal. Character tables for different symmetries are given in many texts (for example, 5), and correlation tables are given in [73 and [8]: the latter text provides a number of worked examples of factor group analysis applied to minerals and inorganic crystals. Infrared spectra may be presented from two different experimental configurations: absorption (or transmission), or reflection. Sample absorbance is dimensionless, and is defined as A = -log(&), (2) where / is the intensity of light transmitted through the sample, and I, is the intensity of light transmitted through a non-absorbing reference material. Frequently, such data are reported as per cent transmittance, which is simply the ratio I/I0 multiplied by 100 (note that vibrational peaks are negative features in transmittance plots and positive features in absorbance). Because of the intensity of many of the absorptions in rock-forming minerals (greater than -2 p,rn thicknesses in the midinfrared (>-4OO cm-‘) often render samples effectively opaque), such absorbance or transmission data are often generated from suspensions of powdered minerals or glasses within matrices with indices of refraction which approximate those of minerals. Typical examples of such matrices are pressed salts (typically KBr, KI or CsI) and hydrocarbons (for example, Nujol (paraffin oil) or teflon). While relative absorption intensities and locations can often be accurately determined using these techniques (highly polarizable crystals can present difficulties: see pp. 183-188 of [7]), absolute absorption intensity is compromised and orientation information is lost. A second means by which infrared spectra are measured is through measurement of reflection spectra. Reflection spectra of crystals sample two components of each vibrational modes: transverse optic and longitudinal optic modes, while absorption spectroscopy ideally samples only the transverse modes. That there are two types of modes in reflection is because each vibrational motion may be described either with atomic displacements oriented parallel (longitudinal modes) and perpendicular (transverse modes) to the wavevector of the incoming light. Those with their atomic displacements oriented parallel to the wavevector of the incoming light can be subject to an additional electrostatic restoring force produced by the differing displacements of planes of ions relative to one another, an effect not generated by shear. Such transverse and longitudinal modes are thus separated from one another by long-range Coulombic interactions in the crystal [3,6]. In practice, reflection spectra generally have broad flattened peaks, with the lowest frequency onset of high reflectivity of a peak corresponding approximately to the transverseo ptic frequency, while the higher frequencyd rop in reflectivity of a peak is near the frequency of the longitudinal optic vibration. These data are generally inverted for TO and LO frequenciesa nd oscillator strengths (a measure of the intensity of the reflection of the band) using one of two types of analyses: Kramers-Kronig, or an iterative classical dispersion analysis. Such analyses, described in [ 171 and elsewhere, are designed to model the extreme changes in the optical constants (expressed as the frequency dependent and complex index of refraction or dielectric constant) occurring over the frequency range of an optically active vibration. For many minerals, the types of vibrational modes may be divided into two loose categories: internal and lattice modes. Internal modes are vibrations which can be associated with those of a molecular unit, shifted (and possibly split) by interaction with the crystalline environment in which the molecular unit is bonded: the vibrations of the silica tetrahedra shown in Figure 1 are typical examples of the types of motions which give rise to internal modes. Such internal modes are typically associated with the most strongly bonded units in a crystal, and thus with the highest frequency vibrations of a given material. We note also that even the simple picture of molecular vibrations is often complicated by the presence of interacting molecular units within a crystal. For example, it is difficult to associate different bands in feldspars with stretching vibrations of distinct A104 or SiO4 tetrahedra: because of the interlinking tetrahedra, a silica symmetric stretching vibration such as is shown in Figure 1 will involve a stretching motion of the adjoining A104 tetrahedra, and vibrations of these two species must be viewed as coupled within such structures. Lattice modes comprise both a range of (often comparatively low-frequency) vibrations not readily describable in terms of molecular units, and so-called external modes. External modes are those which involve motions of a molecular unit against its surrounding lattice: for example, displacements of the Si04 tetrahedra against their surrounding magnesium polyhedra in forsterite would constitute an external motion of the WILLIAMS 295 tetrahedral unit. Typically, such lattice modes are of critical importance in controlling the heat capacity of minerals at moderate temperatures (of order less than -1000 K). As it is the thermal excitation of vibrational modes which producest he temperatured ependenceo f the lattice heat capacity, considerable effort has been devoted to designing methods to extract thermochemical parameters such as the heat capacity and the Grtlneisen parameter (the ratio of thermal pressure to thermal energy per unit volume) from vibrational spectra at ambient and high pressures [13]. A fundamental limitation on such techniques lies in that infrared and Raman spectra access only vibrations which have the periodicity of the unit cell (that is, effects of dispersion are ignored). Representative Raman spectra of quartz and calcite are shown in Figure 2, along with a powder infrared absorption spectrum of quartz and an unpolarized infrared reflectance spectra of calcite. The factor group analysis of quartz predicts 16 total optically active vibrations, with four being Raman-active (A1 symmetry type), four being infrared-active (A2 symmetry), and eight being both Raman and infrared-active (E symmetry: doubly degenerate). For calcite, such an analysis predicts five Raman active vibrations (lAl, and four doubly degenerate Es symmetry modes) and eight infrared-active vibrations (3Azu and 5 doubly degenerate E,). Two features are immediately apparent from these spectra: first, the differences between the vibrations of the silicate group and those of the carbonate group are immediately apparent: in the infrared, the asymmetric stretching and out-of-plane bending vibrations of the carbonate group are present near 1410 and 870 cm-l, while the strongest high frequency vibrations in quartz lie near 1100 cm-l (the asymmetric stretches of the silica tetrahedra) and 680-820 cm-l (corresponding to Si-0-Si bending vibrations). Moreover, the LO-TO splitting of the asymmetric stretching vibration of the carbonate group is clearly visible in the reflectance spectrum. Within the Raman spectrum, the most intense vibration of calcite is the symmetric stretching vibration of the carbonate group at -1080 cm-l, while that within quartz is predominantly a displacement of the bridging oxygens between tetrahedra at 464 cm-l. At lower frequency (below 400 cm-‘), the spectrum of the carbonate has Raman bands associated with external vibrations of the carbonate group relative to stationary calcium ions. At lower frequencies than are shown in Figure 2 in the infrared spectrum, both lattice-type vibrations of the calcium ions relative to the carbonate groups and displacements of the carbonate groups and the calcium ions both against and parallel to one another OCCIE. Figure 3 shows representative vibrational frequencies of different functional, or molecular-like groupings, in mineral spectra. In the case of many minerals with complex structures, normal modes involving motions of the entire lattice, or coupled vibrations of different functional groups may occur, and these are not included in Figure 3. As expected from Equation 1, there is a general decreasei n frequency with decreasesin bond strength for different isoelectronic and isostructural groupings, such as occurs in the P04-Si04-A104 sequence of tetrahedral anions. While both infrared and Raman spectroscopy represent useful techniques for characterizing bonding environments, vibrational mode frequencies and the molecular species present within minerals, infrared spectroscopy has been d. with units of length2/mole. for some applications a more appropriate measure of the number of species present is not the amplitude of absorption. A)/@. (3) in which c is the weight fraction of a dissolved species. It is the determination of this last parameter on which the quantitative application of Equation 3 depends: typically. SiO2: 465 Quartz Si-0-Si cm-l symmetric stretch Si04-asymmetric stretch Si-0-Si bend 1083 cm-1 807 cm-1 / Raman Lattice modes 207 128 I11 Powder Infrared III1 1300 1200 I100 1000 900 ecu 700 600 . A is the absorbanceo f a diagnosticb and of the dissolveds pecies.groups. Such determinations depend on an application of the Beer-Lambert Law. the amount of dissolved CO2 relative to COs2. d is the path length through the sample. E). M is the molecular weight of the dissolved material. This may be expresseda s c = (M . and the amount of impurities within crystals such as diamond and a range of semiconductors. a non-vibrational means of analysis is used to quantify the amount of dissolved speciesw ithin a sequenceo f samples in order to calibrate the value of E. Specific examples include the determination of the dissolved molecular water and hydroxyl content of glasses and crystals. Second. Several complications exist in the straightforward application of Equation 3: first. in which the amount of absorption is assumed to be proportional to the number of absorbing species present in the sampled region.extensively utilized as a quantitative technique for determining the concentration and speciation of volatile components within samples. but rather the integrated intensity underneath an absorption band (see [21] for a mineralogically-oriented discussion of each of these effects in hydrated species). in that the amount of absorption can depend on the structural environment in which a given species occurs. and E is the molar absorption coefficient of the suspended species. the extinction coefficient can be frequency-dependent.p is the density of the matrix in which the species is suspended. while that of calcite is an unpolarized reflectance spectrum from a single crystal. . WILLIAMS 297 t In-Plane’ Hydroxides O-H Bends O-H Bends SZ. 2.5 nm excitation. Infrared and Raman spectra of SiO2-quartz and CaC03-calcite. Out-oLG!ne Wane Carbonates bends .1) Fig.SiOg-octahedra I Elm’ V & Non-Bridging 0 bends bends . Reflectance Out-of-plane 874 cm-1 In-plane bend / I I I I I I I I I r I1 t 1 I640 1500 I400 1300 1200 II00 IOrn 900 ml 700 600 MO IQI 3w 2m !m Frequency (cm.Frequency (ccl) MO 300 ma IDO CaC03: Calcite 1089 cm-1 CO3-asymmetric stretch 1435 cm-1 Raman :03-symmetric stretch Lattice modes In-plane bend 713 cm-1 284 cm-1 i 155 cm-l LO TO Infrared. Both Raman spectra are from single crystal samples using 514. The infrared spectrum of quartz is an absorption spectrum from powdered material. Asymmetric Stretches Polymerized Silica Networks Inosilicates Orthosilicates Sulfates ketches Bends Bends Stretches Bends/Stretches . Its utility has thus been principally in determining what species are present in a sample.1 1600 1400 1200 1000 800 600 400 200 Frequency (cm-l) Fig. 3. Most of the spectral ranges are derived Tom [3]. The first of these processes involves an ion with a partially filled d.. non-destructive compositional probe of fluid inclusion compositions [e. diffraction of incident infrared light limits the usefulness of infrared techniques.. RAMAN AND OFWCAL SPECTROSCOPY Energy bZ /x AZ AZ ..I. The three processes of primary importance for minerals are: 1) crystal-field absorptions.. Yet..I. the mode designations are identical to those shown in Figure 1.l...I. The application of Raman spectroscopy to quantitative measurement of molecular species is complicated by practical difficulties in determining the absolute Raman scattering cross-section of different species. which have lobes of electron density 298 INFRARED.tIII v3 Vl l---r+ I HH v4 v2 Orthophosphates I v3 I v II. 3. and 3) charge transfer or absorption into the conduction band (4. as opposed to their quantitative abundance. For tetrahedral species. OPTICAL SPECTROSCOPY There are a number of different processes which may generate optical absorption (see [19] for a discussion of different causes of color) in the visible and ultraviolet wavelength range. and Bums in [2]).g. and in maintaining a constant volume of Raman excitation from which scattered light is collected.I..(or in some cases f-) electron shell being incorporated into a crystalline environment whose symmetry produces a difference in energy between the different orbitals. 2) intervalence transitions. for analysis of samples whose sizes are of the order of the wavelength of infrared light (such as some fluid inclusions).... with the motivation of establishing Raman spectroscopy as a quantitative. oxides and other functional groups within minerals.. that for octahedral silicon is from [24]. Considerable effort has thus been devoted to characterizing Raman scattering cross-sections of gas-bearing mixtures. the dx2y2 and dz2 orbitals. 15. Approximate frequency range of common vibrations of silicates. 11ml1. 201. A representative example of this phenomenon is shown in Figure 4: when the five atomic d-orbitals are octahedrally coordinated by anions.. lie at higher energy than the remaining three orbitals because of the larger repulsive interactions between the dx2-y2 and dz2 orbitals and their neighboring anions. The preferential occupation of the lower energy levels produces a net crystal field stabilization energy (CFSE) which contributes to the thermochemical energetics of transition metal-bearing crystals.-0 M oYY --o-M-O. Mn2+. The characteristic magnitude of the CFSE for Fe2+ (d6 configuration) in octahedral coordination in minerals is between about 40 and 60 Id/mole.-> Y . Fe3+. oriented towards the anions. Cg+. Thus. tetrahedrally coordinated cations typically have CFS energies between -30 and -70% that of octahedrally coordinated cations.I X 05 -e3 Q c-v M -o. 4.o r crystal-field split. The re ulsive effect produced by close proximity of the negatively charged oxygen cations to the dx2-v2 and dz f orbitals separates these in energy from the d. Ti3+.Y I dYz 7 d x2 Fig. including forsteritic olivines (peridot: Mg2SiO4 with Fe2+). The surfaces of the d-orbitals represent contours of constant probability that an electron lies within the boundaries. and is associated with both the colors and fluorescent properties of a range of minerals. and dxz orbitals by an amount referred to as the crystal field splitting energy (also as 10 Dq or 4). ruby (Al203 with C2+) and both silicate and aluminate garnets (which may contain a range of transition elements).. For comparison. Characteristic octahedral CFSE values for other transition metal cations with unpaired delectrons generally lie in between these extremes. The effect of octahedral coordination on the different d-orbitals of a transition metal cation (labelled M).O I 0 % BI P0Pa d.. characteristic cohesive energies of divalent . optical absorption may be produced by excitation of electrons into and between these separated. that for octahedral C2+ (d3) is generally between 200 and 275 M/mole. thus producing a net preference of many transition metal ions for octahedral sites. the energetic separation between which is often referred to as 10 Dq or A Such crystal-field effects are observed within c£s containing such transition metal ions as Fe2+. d. energy levels. gems and laser crystals.. Essentially no experimental evidence WILLIAMS 299 exists. 15. Such effects of symmetry are demonstrated by a comparison between octahedral and tetrahedral sites: in tetrahedral sites. as each orbital can contain two electrons of opposite spins. combined with an interpretation of the different crystal field transitions present in this material [4]. The lower than octahedral symmetry of the Ml and M2 sites produces more extensive splitting of the energy levels than occurs in sites of ideal octahedral symmetry. clearly depend on the valence of the cation (as this controls the amount of occupancy in the d-orbitals. 163. but representative values for this quantity are generally greater than 100 Id/mole at ambient pressure. such as distorted octahedra or dodecahedral sites. Estimates of the spin-pairing energy in iron-bearing minerals are poorly constrained. in which the energy required to pair two electrons within an orbital is greater than the crystal field splitting energy. the dx2-y2 and dZ2 orbitals lie at lower energy than the three remaining dorbitals. the high spin to low spin transition of iron in crystalline silicates has been frequently invoked as a possible high pressure phenomena. 161. and electrons enter into the higher energy unoccupied dx2-v2 and dz2 orbitals (eg states) rather than pairing in the lower energy three-fold t2g states. The values of the crystal-field splitting. In more complex environments. a larger number of crystal field bands may be observed because of further splitting of the d-levels. as well as contributing to the amount of cation-anion interaction. For comparison. Historically. a material with distorted octahedral sites. and the type and symmetry of the site in which the ion sits. Furthermore. 15. electrons in low spin configurations fully occupy the t2g states before entering the eg levels. An example of spectra produced by different polarizations of light incident on Fe#i04-fayalite.transition metal ions octahedrally coordinated by oxygen are on the order of 3000-4000 Id/mole [4. discussed in detail elsewhere [4. the anion present (as the charge and radius of the anion will also control the amount of crystal field splitting which takes place). iron essentially always occurs in the high spin configuration in minerals: this is simply a consequenceo f the energy required to pair spins in divalent iron being larger than the crystal field stabilization energy. two possible configurations are possible for octahedrally coordinated cations containing between three and eight d-electrons: high spin configurations. however. Among major transition elements. that indicates that such an electronic transition occurs over the pressure and compositional range of the Earth’s mantle. is shown in Figure 5. through the cation-anion bond strength). . and the solid line parallel to a. Indeed. the dashed line parallel to c. producing both weak spin-forbidden and Laporteforbidden transitions. For example. As the Ml and M2 sites are each distorted from perfect octahedral symmetry. Inter-valence. These selection rules may be relaxed through a range of effects which include orbital interactions. and lack of a centrosymmetric ion site.5 0 Frequency (cm-l) 25. tetrahedrally coordinated cations) generally produce more intense absorptions. The dotted spectrum is taken parallel to the b-axis of this phase.g. charge transfer. vibrational and magnetic perturbations. additional splitting beyond that shown in Figure 4 occurs for the d-orbitals of iron ions within fayalite: this is shown in the insets.000 Octahedral Ml Site M2 Site Splitting Splitting Splitting I I I I I I I I I1 I ! I I 500 1000 1500 Wavelength (nm) Fig. 5. The primary selection rules are related to spin multiplicity (involving conservation of the number of unpaired electrons between the ground and excited state) and to conservation of parity (or.000 cm-’ .The intensities of crystal-field absorption bands can vary over four orders of magnitude: these are governed both by the abundance of the absorbing cation. combined with an interpretation of the observed transitions in terms of the Ml and M2 cation sites of Fe2+ in olivine [from 41. non-centrosymmetric environments (e. and by a combination of the symmetry of the cation environment and quantum mechanical selection rules.0 8 $ e Fz 2 0.000 10. in a manner directly analogous to Equation 3. such crystal field bands are frequently orders of magnitude less intense than the vibrational bandsd iscusseda bove. transitions being only allowed between orbitals which differ in the symmetry of their wavefunction: the Laporte selection rule). Short arrows in insets represent electrons occupying each d-orbital (Fe2+ has six d-electrons). The sharp bands above 20.000 15. Polarized crystal field absorption spectra of Fe2SiO4-fayalite in three different crystallographic orientations. and valence to conduction band transitions are all terms used to describe absorption mechanisms of similar origins: the transfer of electrons between ions in non-metals via an input of energy in the 1. Within many materials.+3) and Ti (+3. k is Boltzmann’s constant (1.. (4) in which d is the electrical conductivity of the material. and relatively short metal-metal distances.g. This edge may be accompanied by discrete bands at slightly lower energy than the edge: such bands are often associated with a binding. and are extremely intense: often three to four orders of magnitude more intense than crystal field transitions. these transitions produce the coloration of many iron and iron/titanium-rich oxides and hydroxides. and are most intense in those minerals which have large quantities of transition metals. 300 INFRARED. Absorptions generated by such cation-anion charge delocalization processes are common in ore minerals such as sulfides and arsenides. This relationship is expressed through Q = 00 exp(-Eg/2kr). RAMAN AND OPTICAL SPECTROSCOPY form of a photon.and moderate-temperature electrical conductivity of insulators and semiconductors: in materials in which the electrical conductivity is not dominated by defect-related processes. these bands occur in the visible region of the spectrum. As such. is generally treated as a constant (although both it and the band gap may be temperature dependent: these dependences are. such oxygen-to-metal charge transfer absorption bands typically occur at high energies in the ultraviolet. These bound electron states are referred to as excitons. The term inter-valence transition is generally used to describe processes associated with the transfer of an electron between transition metal ions. frequently small).are generatedb y spin-forbiddent ransitions. especially those which are able to adopt multiple valence states in minerals. but also occur in excitation of electrons between cations and anions. 00. Furthermore.. such charge transfer bands appear as an absorption edge. rather than a discrete band: this edge is simply generated because all photons with an energy above that of the edge will produce electron delocalization. they also induce effective opacity of most 1.+4). is the energy of the band gap. The pre-exponential factor. 11. E. or photoexcitation of an electron into the conduction band of a material: the separation in energy between the valence and conduction band of materials is commonly referred to as the band gap. There is an intimate association between such processes of electron delocalization and the high. Effectively. such charge transfer between anions and cations is often associated with delocalization of an electron. such as Fe (+2. 221. or attractive force between the photo-excited electron and its ion of origin. Characteristically. and produce the opacity or deep red color in the visible of many such minerals.g. and T is temperature [e.0 . however.381 x 1O-23 J/K). Charge transfer transitions not only occur between transition metal ions. Within oxides. and represents the intercept of a plot of the log of the conductivity and the inverse of temperature. and are discussed in greater detail in solid state physics texts [e. the thermal excitation of electrons into the conduction band represents the primary means by which charge carriers are generated. The role of pressure (in most cases) is to decrease the energy at which such bandgap related absorptions occur (that is. can occur at wavelengths above 4 pm. I(v) = 2mhc2v5(exp[hvlkr] . However. and to lie at a wavelength-independent value between zero and one .1)-l (5) in which the emitted intensity. The dependence of blackbody emission on wavelength at different temperatures. it becomes easier to delocalize electrons as the distance between ions decreases). WILLIAMS 301 silicates in the far ultraviolet. This effect is illustrated in Figure 6. I. the intensity of radiative thermal emission is described by the Planck function. with the wavelength ranges of electronic and vibrational absorptions which inhibit radiative heat transport in mantle minerals illustrated. the effect of a lower energy absorption edge in compressed magnesiowiistite (MgxFel-. It is generally believed that among relevant deep Earth constituents only relatively iron-rich materials (such as FeO) will have absorption edges which decrease to zero energy and metallize over the pressure and temperature interval of the Earth’s mantle.O) may have a significant effect on the electrical conductivity of the deep mantle. such as the M2 site in pyroxenes.010 lo-’ ! Charge-Trmsfer and Band-Gap 1 IO Wavelength ( p m) Fig. Vibrational absorptions (both single vibrational transitions and overtones) absorb strongly at wavelengths longer than about 5 urn. The location of charge-transfer bands is known to be highly sensitive to pressure.z 2 3 5 0.tm. similarly. increasing the efficiency with which they prevent radiative heat transport. with bands in relatively iron-rich phases (such as magnesiowtistite) shifting strongly to longer wavelength with increasing pressure. Such absorptions generate an effective means of impeding radiative conductivity under lower mantle pressure and temperature conditions. 6. e represents the emissivity of the material (assumed to be unity in the case of a blackbody. is a function of frequency (v). if hydroxyl or carbonate units are present.A . iron in the dodecahedral site of garnets can absorb at longer wavelengths than 2 pm (see Bums in [2]). then such vibrational absorptions may extend to 3 pm. Crystal field absorptions of divalent iron in distorted octahedral sites. Among the most intense crystal field absorptions of iron in minerals are those occurring near 1 j. in addition to producing an absolute impediment to radiative thermal conductivity at these depths. Such crystal-field absorption bands tend to broaden markedly at high temperatures. such as are shown in Figure 5. respectively. Chapman and Hall. h. I thank the NSF for support. 1954. given the wavelength ranges over which crystalfield absorptions (which broaden in width at high temperatures)a nd charge-transferb andso ccur in transitionmetal bearing minerals. Cambridge conductivity of mantle materials naturally incorporates both a frequency-dependent absorption coefficient and index of refraction of the material. Huang. no optical absorption data have been reported for silicate perovskite. The Dynamical Theory of Crystal Lattices. Oxford Press. Ashcroft. k and T are the speed of light. 224 pp. Thus. Acknowledgments. 325 pp. and D. radiative conductivity is unlikely to provide a rapid mechanism of heat transport within the deep Earth. R. Figure 6 shows representative values of emitted intensity for a range of temperatures. Mineralogical Applica-tions of Crystal Field Theory.or greybody emission of Equation 5 [23].. Clearly. New York. however... and K. Knittle for helpful comments. T. the absorption of magnesiowiistite at both ambient and high pressures has been wellcharacterized [14]. and an anonymous reviewer. N. along with the wavelength range of different absorption mechanisms occurring in minerals relevant to the Earth’s upper mantle...J. F. Ahrens and E. . along with absorption mechanisms of minerals relevant to the Earth’s upper and lower mantle. as well as the black.. London. Plan&s constant..J. 3. Among lower mantle minerals. the optical properties of mantle minerals play a passive but seminal role in the thermal and tectonic evolution of the planet: were radiative conductivity an efficient means of heat transport through the deep Earth. 1976. Berry.J. 4. Mermin. and D. Burns. This is contribution #207 of the Institute of Tectonics at UCSC. Chemical Bonding and Spectroscopy in Mineral Chemistry. Born. Boltzmann’s constant and temperature. Saunders College Publishing.for a greybody). 420 pp. 826 pp. Figure 6 shows representative values of emitted intensity for a range of temperatures.). Vaughan (eds. 2. Philadelphia. 1985. and c. Solid-State Physics.G.W. M. thermal convection (and its geochemical and geodynamicc onsequencesw) ould not be necessitated. Not shown in Figure 6 are the grain boundary scattering effects which may also act to reduce radiative conductivity over a broad frequency range. The actual radiative thermal 1. B.REFERENCES University Press. 1987. 1972. 234 pp.). An Introduction to Lattice Dynamics. Infrared and Raman Selection Rules for Molecular and Lattice Vibrations: The Correlation Method.T. 13.. Sot. Mineralogical Society..M. N. Hemisphere.S. 18. 1072 pp. 391 pp. 5. New York.).. Harvey.) Reviews in Mineralogy... Infrared and Raman Spectra of Polyatomic Molecules. 1977.. Hcrzberg. F. 12. R. Geophys. Calif... 24. 2nd Ed. 9..A. Res... J. 1992. W. New York. D.. London. 383 pp. 698 PP. McMillan. Washington. Vol. S. 92.C. Cotton. WileyInterscience. Q.. 1974. F. Min. Hawthorne. McDevitt and F. Kothari. and L. (Ed. Fateley. 222 pp. Am. McGraw-Hill. 8. The Infrared Spectra of Minerals. Washington. Molecular Specfra and Molecular Structure: II. San Diego. 8116-8128. Williams. Bentley.C. 1972. New York. Vibrational spectrum of MgSi03 -perovskite: Zero pressure Raman and infrared spectra to 27 GPa.F. 589 pp. Wiley- Interscience. A. New York.. 386 pp. V.R. New York. (Ed. 1981. Molecular Vibrations in Crystals. Ghatak.. 6. 1970. J. New York..G.. Decius. RAMAN AND OPTICAL SPECTROSCOPY mineralogy and geology. Dollish. Chemical Applications of Nonlinear Raman Spectroscopy. Hexter. 1945. Kieffer. Addison Wesley. Farmer. Spectroscopic methods in 302 INFRARED.C. 197 1..C. Chemical Applications of Group Theory. Jeanloz and P.K. Academic Press.. and R. 11..W. A. 632 pp.C. Van Nostrand Reinhold. 10. (Ed. 1988. 3rd Ed. D.. G.. 7. Heat capacity and . F. Mineral. Part II. Solymar. Thermal Radiation Heat Transfer. M.F. New York. New York. Practical aspects of quantitative laser Raman spectroscopy for the study of fluid inclusions.. B.. J.. 20.. edited by R. Siegel. 979-988. Lectures on the Electrical Properties of Materials.65-126. Paterson. 1992. 352 pp. New York. Infrared and Raman Spectra of Inorganic and Coor-dination Compounds. 1072 pp. H. Oxford Univ. Mao. Washington. silicate glasses and similar materials. Wiley. Hofmeister. . Bull. 1983. 105. L... P. New York. 19.S. The determination of hydroxyl by infrared absorption in quartz. 15.J. R. Luminescence and Radiation Centers in Minerals. A..... 4th edition. 16. Pasteris. Nakamoto. Spectroscopy. J. Acta. 1979. Nassau. Charge transfer processes at high pressure. Press. J. 99-159. K. 1992. 1982.entropy: Systematic relations to lattice vibrations. 484 pp. 17.R. 21. Howell. McClure. and A.M. 1976. Solid State Phys. in The Physics and Chemistry of Minerals and Rocks.. 14. WileyInterscience. 20-29.C. New York. and D. pp. McMillan. D. Seitz.K. Strens. Mineral.. 1985.D. 1959. Geochim. 1988. 1986... Rev. 399-525. 5th Ed. K. 482 pp.. Wopenka and J. 9. 454 pp. 52. 1988. Walsh. 22.. 573-581. 23. Electronic spectra of molecules and ions in crystals. Marfunin. Springer-Verlag.S. 18. Spectra of ions in crystals.C. 14. The Physics and Chemistry of Color: The Fifteen Causes of Color. and J. Hemisphere. 3rd Ed....G. 18. Rev. Cosmochim. Infrared and Raman Spectroscopy. Wiley.. D. Mineral. 29.34. Geophys. because they contain no material-specific information on relaxation rates and line widths.33.62. NMR is an element specific spectroscopy. and spectra are primarily sensitive to short-range effects. Potentially interesting nuclides are listed in Tables 1 and 2. but the practicality of the experiment varies tremendously.78. Jeanloz and P. These data serve only for rough comparison. Department of Geology. CA 94305-2 115 Mineral Physics and Crystallography A Handbook of Physical Constants AGU Reference Shelf 2 Copyright 1995 by the American Geophysical Union.88. Stanford. Vibrational spectrum of MgSi03-perovskite: Zero pressure Raman and infrared spectra to 27 GPa.24.. Any nuclide with non-zero nuclear spin thus can. The utility of NMR in understanding the chemistry and physics of materials comes from the small perturbations of nuclear spin energy levels (non-degenerate only in a magnetic field) that are caused by variations in local electron distributions. Stebbins. as well as details of applications [2. McMillan.11. however (especially for solids). in principle.42.56. 92.128. 8116-8128. J.161]. 1411. and to tabulate the most useful data. Q. Stebbins I. Thus. Res. based on resonant frequency. which contain a simple comparison of the relative ease of observation in a liquid sample. although isotopic enrichment can be useful. Nuclear Magnetic Resonance Spectroscopy of Silicates and Oxides in Geochemistry and Geophysics Jonathan F. Stanford University. and abundance. The same can be true for even abundant nuclides of heavy elements. and by the time dependence of these interactions. Williams. 1987. R. F. ties and correspondingly broad NMR spectra.118. which may have extremely wide ranges of frequenJ. be observed by NMR. INTRODUCTION The purpose of this chapter is to very briefly summarize the applications and limitations of NMR spectroscopy in the study of the silicates and oxides that make up the earth’s crust and mantle.61. More extensive reviews have been published recently that give background on the fundamentals. like .. Extensive tabulations of NMR data on silicates have also been published [34.116. spin quantum number. Detection of signals from nuclides with low natural abundance and low resonant frequency is often difficult or impossible. by the distributions of other neighboring spins (electronic or nuclear).43. of course.1 .7 0. at 9.4 16. however.43 89Y 100 19.7 79. visible. NMR parameters for some nuclides of interest in geochemistry: spin l/2 nuclides Isotope Natural NMR frequency abundance%. but these are now well understood in a qualitative sense.2 15.5 171Yb 14. NMR is a good complement to diffraction methods.6 0.5 1 31P 100 161. regardless of the structure.1 1. experiments must be carried out carefully to be accurately quantitative.techniques such as x-ray absorption and Mossbauer spectroscopy.0 126.6 0. Most of the data reported in the tables has been collected by high resolution magic angles spinning (MAS) techniques.1 183~ 14.2 1 25Te 7.4 111.6 0.8 85.6 149. A major drawback of NMR is its low sensitivity when compared to spectroscopies involving higher energy transitions (e.03 195pt 33. Figure 1 suggests. In practice.99 400.4 T.7 3. MHz Receptivity relative to 29Si 1H 99.48 15N 0. Another limitation of NMR is a severe one for the study of natural silicate minerals: paramagnetic ions in abundances greater than a few tenths of one percent can broaden NMR spectra to the point of being impossible to observe or interpret [87].8 0.002 77Se 7.7 0.2 12.6 0.4 40.09 losAg 48.7 l19Sn 8. that some of the orientational information that 303 304 NMR OF SILICATES AND OXIDES TABLE 1.2 6. Interpretations of solid-state NMR spectra still rely primarily on empirical correlations.2 12. and from single crystal and static powder spectra. with important contributions from the new technique of dynamic angle spinning (DAS). with a 1 to 1 correlation between signal intensity and the abundance of a nuclide in a given structural site.6 76.13 1 13Cd 12.3 88.3 1. infrared and Raman).010 19F 100 376.1 100.g.4 l@Trn 100 33.4 2252 29Si 4.1 129Xe 26.6 9.4 2.32 lo3Rh 100 12.0 2700 1% 1.2 18.9 180 57Fe 2. and is particularly useful in amorphous materials and liquids. NMR can be highly quantitative.3 70. Quantitative local structural information on minerals and melts is important to many problems in geochemistry and geophysics. A second nearly unique utiliiy of NMR.6 1lB 312 80. and displacive phase transitions.6 -0. % me2 NMR frequency at 9. NMR parameters for some nuclides of interest in geochemistry: quadrupolar nuclides.9 250 25Mg 512 10.05 18.004 6Li 1 7.3 819 47Ti 512 7.05 35Cl 312 75.15 104. is lost in MAS may prove to be useful in characterizing anisotropic materials. and unfavorabler adioisotopesa re excluded. moment x102*.22 97.08 32.3 43Ca 712 0. Isotope Spin Natural Quadrupolar abundance.4 0.7 5. 1.6 83.7 1.5 -0. See Table 1 for notes.22 24.2 9.1.4 .6 2.01 28.4 -0.R elative receptivity is calculated for low-viscosity liquid samples.9 2.03 23Na 312 100 0.7 27A1 512 100 0. such as diffusion. the fundamental rate may be within this range.1 0.6 0.0 10.2 0.8 71.8 -0.7 *05T1 70. nuclides with large quadrupolar moments (Table 2). that is just beginning to be applied in the geosciences.055 30.04 155.29 22.5 1OB 3 19.5 0.4 T. is in studying dynamics at the time scale of seconds to nanoseconds.10 105. lanthanides.8 39K 312 93.3 0.4 360 14N 1 99. For many geochemically interesting processes.4 Notes for Tables 1 and 2: Data are primarily from tabulation in [49].041 128.7 1.02 4ssc II2 100 -0.0 1.7 7Li 312 92.0028 61. and heavy nuclides with very large chemical shift ranges may be difficult to observe in solids.02 0. Line width and relaxation behavior in solid samples can make this estimates quite misleading.5 0.0 0.2 37.05 56.13 0.58 0.7 I70 512 0.2 27.199Hg 16.085 43.6 37Cl 312 24.0008 59. less favorable isotopes of elementsl isted. MHz Receptivity relative to 29Si 2H 1 0.5 -0.5 230.026 54. Definitions The chemical shift 6 is the perturbation in the resonant (Larmor) frequency v of a nuclide in a particular chemical environment.15 0. caused by screening of the external magnetic field by the surrounding electrons. 6 is genemlly STEBBINS 305 TABLE 2.4 0.3 560 3% 312 0.7 0.6 737 9Be 312 100 0. Noble gasses.04 -0. NMR has proven to be very useful in this area.10 39.5 377 *07Pb 22. In particular. viscous flow. 9 93Nb 912 100 -0.4 99Ru 512 12.7 57.1 -0.21 37.16 25.7 fO.8 18.3 1 108.7 96 67Zn 512 4.08 18.4 1035 53Cr 312 9.6 0.7 69 81Br 312 49.23 55Mn 512 100 0.05 105.9 -0.6 0.3 100 100 11.6 0.1 0.7 l 151n 121Sb 1271 133CS 137Ba 139La 177Hf 181Ta 187Re 912 512 512 712 312 712 712 712 512 95.2 -0.13 131.8 475 59co 712 100 0.4 98.18 14.32 71Ga 312 39.0 0.16 35.12 122.29 68.4 0.2 0.3 99.5 .4 0.3 133 87Sr 912 7.49Ti 712 5. NMR frequency at 9.2 0.1 0.5 0.4 lolRu 512 17.8 -0.11 63cu 312 69.1 174 65cu 312 30.20 113.5 0.30 75As 312 100 0.6 5lV 712 99.2 1.38 94.2 152 73Ge 912 7.0 0.21 106.5 1 91Zr 512 11.03 22.2 1320 95Mo 512 15.8 -0.44 20.24 22.6 0.3 2.1 0.9 18.4 133 87Rb 312 27.9 0.8 0. MHz Receptivity relative to 2gSi I”5Pd 512 22.4 750 61Ni 312 1.7 0.3 17.22 98.4 0.12 26.7 0.7 306 NMR OF SILICATES AND OXIDES TABLE 2 (continued) Isotope Spin Natural abundance.4 T. 2 48. The chemical shift is orientation dependent. whose principle components are usually denoted 611. 163 0. The frequencies of these transitions . is the average of these three components.59 6.1 0./’ tions may be observable.8 16.8 31. For spin l/2 nuelides.99 62.1 96. and is described by the chemical shift anisotropy (CSA) tensor.0 91.2 0.38 64.003 0.Vstandard)/Vstandard.4 1.0 7.44 26. and in solids by rapid sample spinning (MAS NMR) at the “magic” angle 8 with respect to the external field (t3 = r’ . 99 238 1 7 18gOS 312 16. and S33 and which has a unique orientation with respect to the local structure (or with respect to crystallographic axes in a crystalline material).99.07 201Hg 312 13.06 lg7Au 312 100 0.83 -0.8 910 251 257 130 2.9 381 expressed in parts per million relative to a standard.5 52.6 0.28 -0.79 -0.28 0. Siso.9 0.9 0.22 4.7 1.7 56. The isotropic chemical shift.6 0.8 44.0 lg31r 312 62.822.2 80. with 6 = ~06hnple .5 209Bi 912 100 -0.5 3 2. Siso is observed experimentally in liquids where molecular rotation produces rapid isotropic averaging.2 88. 2. often summarized by the nuclear quadrupolar coupling constant QCC=e2qQ/h. For nuclides with spin I > l/2.70.1. Scales in this and other figures are in ppm. The deviation from cylindrical symmetry of this tensor is given by the asymmetry parameter n.’ random powder /$-LAN +qof& spectrum shows three magnetically inequivalent Si sites: bottom spectrum shows spectrum for randomly oriented powder.are controlled by the energy of interactions with the i Ir mykmicc J *. eQ is the nuclear quadrupolar moment. which varies from 0 to 1. If bridging oxygens are considered as those shared with tetrahedral Si or Al (or B or P) neighbors. and non-bridging oxygens to be those shared with larger and/or lower charged M cations. the field gradient and the quadrupolar interaction average to zero and Gire is observed.v \ Fig. In silicates. the largest effect of structure on chemical shift is that of coordination number. center spectrum shows effect of strong preferred i &. 1. The second most important effect is that of the number and identity of first cation neighbors. The full description of the quadrupolar interaction requires the electric field gradient tensor and its orientation relative to the structure. a total of 21 transiorientation in a quartz mylonite [132]. Top . an . Siso is shifted by the isotropic average of the second order quadmpolar interaction.166]. and eq is the principle component of the electric field gradient at the site of interest. APPLICATIONS TO CRYSTALLINE SILICATES AND OXIDES 2. in DAS NMR. Static (non-MAS) 2gSi spectra for quartz. but is not broadened. Signals near to -150 ppm are probably from SiO5 groups [58. 29S i Isotropic chemical shifts for 29Si and CSA data are listed in Tables 3 through 5. l-3cos28 = 0). In liquids with sufficiently rapid isotropic rotation of molecules. Here. Thus. In MAS NMR. STE!BBINS 307 electric field gradient. the central l/2 to -l/2 transition remains shifted and broadenedb y a secondo rder quadrupolar interaction.L ‘2 54. and is in nearly all cases between about -65 and -120 ppm for SiO4 groups. 6 for SiO6 groups is in the range of about -180 to -220 ppm relative to tetramethyl silane (TMS). 117. other tectosilicates [12. 27A 1 NMR studies of 27Al in minerals have been reviewed recently [66]. The greatest efforts have been on synthetic zeolites.1063. Most ./Si disorder has not been detected [63.146]. In geochemistry. and pMg2SiO4. Structures correlations have been used to derive important constraints on Al/Si ordering in a number of minerals.53. In a similar fashion. In MgSiOg ilmenite and perovskite.103. careful combination of NMR spectroscopy with calorimetric observation has provided new insights and details of the energetic control and consequenceso f Si/Al disorder [17. where n designates the number of bridging oxygens (and Q stands for quaternary). 29Si MAS NMR has begun to be applied to high pressure mantle phases that contain SiO6 groups.103. Each Q” species thus has a distinct.146]. such as for sillimanite [59. because of their tremendous technological importance [34.53. but both Mg/Si and WA1 disorder are significant in majorite and majorite-pyrope solid solutions. decreasing n by one tends to increase 6 by about 10 ppm to less negative.20. where it has often provided the key to unraveling quite complex Al/Si ordering patterns. higher frequencies. A number of semi-empiricalc orrelations among number of Al neighbors. For a fixed M cation type. This effect is particularly obvious and well-exploited in tectosilicates.148].52.169].104. Mg. discrepancies in thermodynamic data that had been tentatively ascribed to underestimates of the entropy of disordered synthetic phases have been displaced to other parts of the data base by findings of nearly complete order. bond angles. Increasing the mean Si-O-T angle systematically decreases8 . As a result.102. again best calibrated for tectosilicates. In several cases.74. the substitution of tetrahedral Al for a tetrahedral Si neighbor tends to increase 6 by about 5 ppm.72]. and 6 have been developed that allow rather precise estimates of 6 for tectosilicate structures 1343.Si04 site can be labeled as Q”.95. as shown in Figure 2 [101.2.140] and prehnite [139].120. and data are listed in Tables 6 and 7.60. Similar approaches have been taken for SiO6 groups [47.146]. 29Si MAS NMR spectra of aluminosilicates often have multiple. The bond angle between tetrahedra has a related effect.118].160]. For a few systems. cordierite [107] and sheet silicates [5. Very recently.112. A few correlations have been developed for Si04 groups in general that allow estimation of 6 for most silicate structures [56. the most important examples have been in determining the ordering state in feldspars [64. but somewhat overlapping range of 6. 2. partially overlapping peaks for Si sites with varying numbers m of Al neighbors [Q”(mAl)].127. 29Si NMR data for Q”. 308 NMR OF SILICATES AND OXIDES TABLE 3. Q’. with complete determinations of quadrupolar coupling constants. and electric field gradient tensors.early studies of this nuclide were of single crystals. Single-crystal work on MgAl204 spine1 allowed quantification of octahedrala nd tetrahedralA l site occupanciesa nd ordering state [ 141. 6 values for Al04 groups fall roughly in the range of 50 to 90 ppm relative to aqUeOUS fi@20)(j3+. The quadrupolar parameters have been shown to be roughly correlated with the extent of distortion of the Al site for both octahedral and tetrahedral geometries [43]. and Q2 sites in crystalline silicates. but without precise isotropic chemical shifts. and for Al06 groups in the range of -10 to 15 ppm. As for 29Si isotropic shifts for 27Al in oxides (now determined most commonly by high resolution MAS NMR) are most strongly influenced by coordination number. asymmetry parameters. mineral (s)=synthetic Q” sites: chondrodite forsterite(s) (s) monticellite(s) 6) 6) majorite garnet(s)g 6) 6) afwillite lamite(s) PyropeW Ca-olivine(s) 6) (9 phenacite rutile titanite andalusite kyanite zircon piemontiteg nominal formula 4soa CSAb -611 422 433 ref. MgdSQh(OKF)2 MgzSiO4 Li2SiOq CaMgSiOq NaHgSiO4 . 3 95.4 67.4 72.9 38.6 81.1461 [781 [781 [341 1781 .3 71.3 71.3.83.5 74.2 79.5 69 to 75h j3.5H20 Mg4SiV1Si1V3012e Ba2SiO4 cKa2Si04 Ca3(HSi04)2.8 45 82.6 79.8d 55.159] 64.9 66 44 66.73.MnPeh (Si207)(Si04)OH Ca3A12(SiO& Al$i04(0H.4 [78.Na2H2Si04.3.2 50 81.9 L'81 60 94 W81 b'81 [781 [101.0 73.F)2 6oc [781 61.8 68 to 90f 70.8.2H20 P-Ca2SiOq Mg3A1$G3012e Y-CaTSi Ca3SiOg CaNaHSi04 Be2SiOq ~1% SiO2 in Ti02 CaTiSiOg A12Si05 A12Si05 ZrS i04 ~a2(Al.3 70.2 77. 4 Ligsi207 72.0 CaA1$$07(OH).124] [781 [781 u391 11181 78 116 [78. 6) (s) gehlenite(s) akennanite(s) m&bite(s) hemimorphite 6) lawsonite 6) 6) 6) 83.5.4 Ca2A12Si07 72.0 ZnqSi207(OH)2.7 134 Ca3Si207 74.128] 79 120 [118.6 109 WI r341 74 20 WI 84 1 WI [781 [781 11461 92 28 [I281 r341 [781 109 35 [34.H20 81 123 a-Y2Si207 81.9 p-Mg2SiO4 79.6.461 STEBBINS 309 TABLE 3 (continued) .4 WI 85.83.6 [781 Na6si207 68.5 a-La2Si207 83.2 Ca&O7(OH)6 82.128] [781 11181 grossular topaz Q’ sites..H20 77.76.UOll [781 [78.5 122 Ca2MgSi207 73. piemontiteg (9 6) thortveitite zunyiteg Q2 sites.Al)Si$I& .MnPe)3 (Si207)(Si04)OH In2Si207 p-Y2Si207 SqSi207 A113Si502($OH)14F4Cli LizSiOg Na2S iO3 BaSi03 SrSi0-j MkZSi206 %X&206 CaMgSi206 (Ca.Na)(Mg. (s) w 6) (s) orthoenstatite clincenstatite(s) diopside omphacite spodumene jadeite pyroxene phase(s)g alamosite prehniteg tchermakitic amphibole(s)g triple-chain phase(s)g SC-F pargasite (s) (Q2+Q3) tremoliteg hillebrandite(s) pectolite(s) foshagite(s) xonotlite(s)g walstromite phase wollastonite P-wollastonite(s) Ca2W..mineral (s)=synlhetic nominal formula -&ma CSAb -611 422 433 ref. 97.4 91. 94.3 84.3 [781 91.2 84.6 84.SSiV1g.9 [781 95.4 UW 87.8 92.7 E'81 92.5 76.1.8 80 85 82c 81.5.90.4.4.4 91.6k 83.4 18 29 30 4oi 31 53 59 156 71 140 71 154 73 132 73 148 81 142 c781 .8 85.SSiIV206 Pb12Si12036 Ca2A12Si301o(OH)2 Ca2(Mg4Al)(AlSi70&KW2 N~2W&kQ tdW2 NaCa2MgqScSigA12022F2 Ca2MMWh1)2(OW2 Ca$i03(0H)2 Ca2NaHSi309 CaqWMOW2 Ca6Si6017@Hh CagSi309 Ca3Si309 P-Ca3Si309 86.8.84.96.1.LiAlSi206 NaAlSi206 NaMgg.2.86.87.9 U181 74. 7l 89.6.86.3 86.lOBaCl2 BaTiSis K2SiV1SiIV309 High P phases.3 84.1281 [781 [781 [781 [781 WI 24 85 158 Cl181 1781 TABLE 3 (continued) mineral (s)=synthetic nominal formula CSAb -&ma -611 422 433 ref.91. uncertain structure: .0 87.78.5.8 73.A1)3AlgSi6018@03h@KF)4i Ba7Si702I.4 86. rings: ps-wollastonite(s) 6) tourmaline 6) benitoite wadeite phase(s)g a-CajSi309 W-W4012 Na(Mg.0 50 77 137 [18.128] [1181 ill81 1-W w61 WI u391 [181 85.2 86.Li. 79.3 WI 86m N31 87.[78.8. Q2 sites.128] [118.8.136] W81 W81 L7781 [56. 9 94.2 [781 95.0 W61 75.0.1 U181 92. 7 resolved peaks.3H2. and are of relatively low precision.406 “phase Y” (s)g (CaO)XSiVSi1”04 6) e-Na2Si205 (SF CaSiV1SP05 (SF Na2Siv1Si1”207 (SF [-Na2SiV1Si1”0g (SF Naz(SiV1. (i) Approximate formula. Main peak is at -74. Si-O-B bonds are considered as “bridging”. orientation of tensor with respect to crystallographic axes may not be known.81.“phase E” (s) WmSii. Given typical errors in CSA measurements. and 5: tMost intense peak.3 ppm. respectively. In some cases. (j) CSA data are means for two sites. Giso and CSA data are from different sources and may therefore appear to be slightly discrepant [&so should = (61 I+622+633)/3].781 88.5 0'81 87.4. principle components of CSA tensor are derived from fitting spinning side bands. (b) Unless otherwise noted. (k) Two additional peaks indicate a small amount of Si/Al disorder. second for T2+T3. 108. this is generally not significant. (c) Broad peak (at least 5 ppm width). (m) Broad peak consistent with considerabled isorder. (d) CSA based on single crystal study. (e) Additional data on solid solution series given in reference.14:1 ee ee ee Notes for Tables 3.(n) Ordering schemesc an be complex. (1) First peak is for Tl site.4 97.5 63 63 141 ]71.5 1341 94. (f) Multiple peaks due to partial disorder among octahedral Si and Mg.9 97 .9 1581 11461 . (h) Nine Si sites. (g) Data for another type of Si site listed elsewhere in table or in Table 4 or 5.7m 80 80. (a) Chemical shifts are in ppm relative to tetramethylsilane.6.Si1”)409 83.7.b ut can be characterizedf or tetrahedralS i and Al .8 88.107. placing the Si sites in beryl and datolite in the Q4 and Q3 groups. 29Si NMR data for Q3 and Q4 sites in crystalline silicates. unpublished data. (y) End member: complex series of peaks for intermediate compositions.as (1) disordered. (x) Overlapping peaks due to multiple sites. See Table 3 for notes.4H20 Q-? sites. (s) small peak due to triple-chain site in partially disordered phase. (4) fully ordered or nearly so.OH)2 phlogopite(s)e KMg3AlSi301o(OH)2 palygorskite MgAlSi401o(OH)2~4H20 beidellite Nao. (3) more ordered than required by Alavoidance. Data for end-member compositions only. -72.Mg)2S401o(OH)2. (bb) all=-173. as well as silicates with organic ligands. (ee) Kanzaki. other silicates: sapphirinee datolite sillimanite tremoliteg . (p) CSA components: -43. -107. -161 ppm [128] .3A12(Alo.1 ppm. (5) partially disordered. (w) Approximately 5 peaks resolved for 12 sites. (2) ordered according to Al-avoidance only. (aa) 8 peaks for 8 sites. zeolites. (u) CSA components: -54. ej sites. (q) CSA components: -49. have been excluded for brevity.OH)2 dickite A4Si&o(OHh kaolin& Aldi4Oio(OH)8 endellite A4S4Olo(OHho~8H20 pyrophyllite AWWAotOHh montmorillonite (Al. mineral (s)=synthetic nominal formula -hoa ordering state” ref. Reference contains data on solid solution with pyrope. (t) CSA components: -56.1 [132] . Data for some clay minerals and synthetic silicas.2H20 hectorite (Mg.4HZO sepiolite Mg&j015(OH)2. (z) Approximately 8 peaks for 15 possible sites.7Na0. Stebbins and Xue. -59 ppm [128] . -151 ppm [128] . (dd) Somewhat broadened peak consistent with some Mg/Si disorder. -147 ppm [1281.4 ppm. 622 = 633 = -183.3Si2.3S401otOHh .6.-59. -70. (0) Split peak reported by [4]. (cc) Narrow peak consistent with complete Mg/Si order.Li)2. (v) CSA components from single crystal study: 102. 107. Al-avoidance violated.0. TABLE 4.701o) (OW2 muscovite KAl~SiAl~O~~(OH)~ illitee KA12SiA1301o(OH)$ lepidolite KLi2Al(AlSi301o)(F. -83. layer aluminosilicates: margarite CaA12(A12Si201o)(OH)2 phlogopite KMg3AlSi301o(F. -129 ppm [128] . (r) CSA components: -107. 109. tremolite(s)g tchermakitic amphibole(s)g triple-chain phase(s)g apophyllite serpentine talc xonotlite(s)g 6) 6) 6) 6) 6) 6) tMg3.6)020 73m CaBSi04(0H) 83.5 [941 a-Na2Si205 94.93.5 r341 15.7.2.85?.4Si1.81 91m 89m 90.4s Q@kWdh1)2(OH)2 91.9 1.9.5.4 H81
[email protected]] 1181 [I81 1181 Na2Mg&60idOH)2 87.90.1 5 4 r191 W81 [59.7 84.8.9s Ca2(Mg4Al)(AlSi7022)(OH)2 92.9.6A14.6 1781 Li2Si205 92.4)tA14.1 .7.94 89.5 84 to 87 83.Y 1941 K2Si205 91. 97.94.87.9 91.S r941 BaSi205 93.H20 92.50 93.110 WI a-H2Si205 101.7’ ~azMgdS4011)20-02 91.0 L’81 WsWMOW4 94.2 U181 Ca6tSi6017)(0H)?.4.8 88.5 [941 p-HzSi205 98.96.0t.101.OP A12Si05 86.91. 96.0 U81 WsS401o(OW:! 97. 94.98 95.0 93.126] W61 [118.126] W61 @.northitee @.ow [118.SiO2 coesite SiO2 cristobalite SiO2 tridymite SiO2 107.9 108.95.118] WI WI WI 312 NMR OF SILICATES AND OXIDES TABLE 4 (continued) mineral (s)=syntbetic nominal formula -6isoa ordering state” ref. feldspars: low albitee high albitee microclinee sanidinee anorthitee a.3 4 5 3 C'81 WJW Lm [341 [341 [I 121 Km V81 [341 [781 F’81 [112. silica polymorphs: q. Q4.7 92. feldspathoids: carnegieite(s) scdalite nephelinee .3-l 14.5 109.4” 108.1.113. 6Nao.2H20 87.8 86.6.7.kalsilite(s)e cancrinite scapolitee analcite leucite Q4.102.2y 91.3.8.4AlSi308 CaAl2Si2Og CaAl2Si208 (disordered) 92.6 97.95.96.96.l02.6H20 92.89.2t.9.7t.3 92.104. others: cordierite cordierite petalite NaAlSijOg NaAlSigOg KAlSi-jOg Ko.3HZO 86.6.97. zeolites: thomsonite scolectite natrolite gmelinite chabazite stilbite harmotone heulandite @.7 to 106.84.7.97.3x 82.91.89.5 to 104Sx NaAlSiO4 Na8Al&jO2&12 Na3KAk+i40t& KAlSi04 Na8Al&i6024CO3 Na4Al$i9024ClCa4Al&jO24CO3 NaAlSi206.0 3 78.7 CaAl2Si3010.9 85.72 3 NaCa2AlgSi5020.&0 KAlsi206 82.100.4.8t.6H20 86.106.0.5 .101m 82.88.4 N~Al2Si4012.4.6.88.95.0.6.3 91 to 112X 95.2 84.7 Na2Al2Si3010.4 88.1+. 4?.6H20 95.6.101.108 BaA1&016.1271 WI WOI [1021 D481 [1181 11481 H481 [1181 [1171 r951 1951 [1181 UN U181 VI WI L'21 1721 11181 w71 r1071 [781 STEBBINS 313 TABLE 4 (continued) mineral (s)=synthetic nominal formula -hoa ordering ref.99. 29Si NMR data for SiO6 and SiOs sites in crystalline silicates. known structures: .0 to 108.6 m 128. See Table 3 for notes.98.104.CaAl2Si4012.0.8 CaAl$Gi701g.6 4 D391 102. mineral (s)=synthetic nominal formula -6.5t.6H2O 94. SiO6.127] [1691 [103.108 CaAl2Si7018. Data for end-member compositions only.5 4 U181 TABLE 5.100t Mg2Ak&Olg (disordered) 79 to 1 12aa LiAlSi4010 87c 4 1 [103.6.102.3 u191 100.6H20 95.0aa Mg2&Si5018 (ordered) 79. danburite prehnite belyle Kleddelite zunyite 89 WI 98. a ref.7H20 98. uncertain structure: “phase Y” (Ca0)XSiVSi1V04g 179.6bb [48.5 11461 194. MgSiOg garnet.6 150.l4?1 314 NMR OF SILICATES AND OXIDES Si’” Si”’ I Fig.4 202. TABLE 6. The multiplicity of tetrahedral sites results from partial disorder among six-coordinated Si and Mg neighbors [ 1011.4 208. sheets ilicates.4 199.0 11461 U461 ee ee . 2.a nd phosphatesh aveb eene xcludedf or brevity.7= 11461 197. Black dot marks spinning side band. 27Al NMR data A104 sites in crystalline silicates and oxides. uncertain structure: w CaSivWv05 (SF [-Na2SiV1SiIV0g (SF Na2Siv1SiW207 w Na2(SiV1 SiIv)40g “phaseX ” (s) OQxs~ . Data for a number of clay minerals.1 U461 214.1391 181. synthetic zeolites.7= WI 194.0cc 0461 191.thaumasite ilmenite phase(s) stishovite(s) perovskite phase(s) perovskite phase(s) pyroxene phase(s)g majorite gamet(s)g wadeite phase(s)g 6) 6) SiO6.146] 203. q bayb ppm .6dd [101.3 U461 191.0 IX81 22oc Cl581 193. 29Si MAS spectrum for a high pressure. Mineral (s)=synthetic nominal formula QCC.0. 217.8 200.‘V IQ2 SiOj. 163] 64 [921 66 [921 62 [921 64 1921 70 [921 5.4 0.ref.2H20 I.0 [43.25 81 6.79. 2.Mg)v1204 0) P-A1203 6) ?-A1203 6) “l-A1203 6) X-A1203 6) BaAlV19AlVA11V20t9 Q’ sites: (9 KA102. Al”] neighbors: zunyite Alv1t~A11vSi~020(OH)t4F4Cl garnet phase(s) Gd3A12”tA131V0t2 garnet phase(s) Y~A1~VIA1~lVOt~ spine1(d isordered)(s) (Mg.5 81 WI 5. layer aluminosilicates:d margarite CaAIV1~(AllV~Si~O~o)(OH)~ phlogopitee KMg3AlSi301o(F.qSii.92.1 0.1 SH20 Q2 sites: (9 6) KA102.gS401o(OH):!.3 0. Q” sites.8 80 [921 72 1921 5. others: 6) 6) sillimanite AlV1AlrVSi05 sapphirine (Mg3.Li)3Nao.9 80 [921 [921 STEBBINS 3 15 TABLE 6 (continued) Mineral nominal formula QCC.Allv)~Ot~(OH)~f e-7 sites.6)02o @ sites.129] 72c [86.0 0.6 83 WI 3.OH)2 muscovite KAIV*~SiAIrV~O~~(OH)~ illitee KA12SiA13010(OH)2f hector& (Mg. @ sites.47 0 1431 6..02 0 76. silica analogs: .Mg . 6) BasA1208 Q” sites.6A1”‘4.4)(A1’“4.Al)w(A1. V hsoavb ref.A IV1)~(Si.H20 a-BaA1204.5 0.4H20 penninite (Mg Al”‘)b(Si A11V)40to(OH)8f xanthophyllite Ca2. 5 0.65 6.2 0.1 2.berlinite(s) All’04 tridymite phase(s) APO4 cristobalite phase(s) AlP04 @ sites.21 8.6 0 11 0.75 42.62 3.5 1931 3.601 66C WI 72 [731 76 [731 5.4 0.731 75c [I91 4.2 2.09 0.5 [43. feldspars: albitee microclinee anorthite.22 0.75 0.76 6.37 44.3 0.29 0.2 6.88 5.60.931 0.42 .77 0.8 0.53 77 [921 85 [921 64.5 143.5 0.95 39.8 76 r733 69c [20.8 [54.1111 72 [731 72. OziO ozoo OOiO mOO0 mOi0 mzO0 NaAlSi308 KAlSi30s CaA12Si208 mzi0 @ sites.8 [931 1.8 2.66 7. feldspathoids: sodalitee Na8Al&j024Cl2 nepheline Na3KAk&0t(jf kalsilite(s)e KAlSi04 scapolitee NaqAl3Si9024Cl-CaqA16Si6024C03 analcite NaAlSi&*H20 leucite KAlSi$Qj 4. 66 63.0.169 62.0c 11171 59. Q4 sites.9 [43.63.64.75 4. others: cordiertite. zeolites: thomsonite scolectite natrolite gmelinite chabazite mordenite gismondite & sites.4.7 [531 58. Al( 1) .0 [43.69~ mw 316 NMR OF SILICATES AND OXIDES TABLE 6 (continued) Mineral (s)=synthetic nominal formula QCC.169 60. Tt T5 prehnite 6) 6) 6) 6) (s) 6) Mg2AlqSi501 gnH20 Ca2A1V1A11VSi30to(OH)2 p-LiAlO2 y-LiA102 P-NaA102 KA102 BaAl204 TlA102 Ca-aluminates: 6) 11 6) 11 6) 6) ca3&06.9 P’3961 61.61j.731 61.53 2.4 [731 6 1.94 0.6 0.5 153.90 0.103.73.32 62.4 0. v hsoalb ppm ref.55c [133lw41 0.64.103.73. 0 81.56 3.4 [731 60 83.69 0.4 [731 64.731 59.5.” .50 10.0 69 [431 r431 [139.82 69.2 0..6 0.3 80.7 [731 62. 6) CaA120qh 6) CaA1407.5 78 [911 5.0 1.3 [911 1. Al(l) II II .4 0.4 r731 55.1 76.55 0.5 WI 9.5 W31 9.9 W31 3.5 1.95 80.#179] [92.0 [43.5-4.38 5.2-1.6 0.2 11231 2. Al(l) 11 7 442) Ca4A16013 Ca4A16013~3H20 .34 9.70 80.4 0.66 0.0 4 65 [911 62.88 75.54 78. AV) 6) CaAIV1~AIVAllV~O~~9 Q ” 1.25 WI 9.9 [731 59.4 0.2-86. Al(2) CanAll4033.25 0.32 79.0 81.45 79 [911 2.4 8.0 78.4 0.8 0.9 0.7 0.66.7 2.8 r731 56.3 0.8 0.125] [921 [921 ~921 [921 .7 1.30 0.40 85.2 W31 6.1 0.5 W31 2. (b) Peak positions corrected for second order quadrupolar shift have been included where possible. Where this correction is not made. (e) Approximate formula. SeeT able 6 for notes. (g) Reference includes high T study of phase transition. MAS peak positions and widths will depend somewhat on the magnetic field used. (f) Reference includes data on other solid solution compositions. STEBBINS 317 TABLE 7. (c) MAS peak position. Data for a variety of synthetic zeolites. All A12 A13 . All A12 spine1(o rdered) (disordered) gahnite rutile 6) o-Al*03 BeAl Mg&Q ZnA1204 = 1% Al203 in TiO2 A12Ti05 t=-Yl euchse vesuvianite prehnite spodumene kyanite. T &soa’b ppm ref. A105 sites: 6) Al”2Si207 andalusite. A12 Alv1AlvSi05 augelite Alv1Alv(OH)$04 senegalite A1V1A1V(OH)$‘Oq. and phosphatesh aveb eene xcludedf or brevity. &so at slightly higher frequency.~921 Notes for Tables 6 and 7: a) Relative to A1(H20)63+.H20 6) &Ge207 6) LaAlGe207 vesuvianite Ca19A111Mg2Si18068(0H)~of A106 sites: corundum chrysoberyl. sheets ilicates. 27A1 NMR data for A105 and A106 sites in crystalline silicates and oxides. (d) See [162] for extensive data on clay minerals. Mineral (s)=synthetic nominal formula QCC. (h) Range of data for six sites. 9 VI 36.46 15.27 3.4 7.1 ml 16.38 8.3 2.95 0.0 11e -6.85 -2.76 3.70 <l 2.94 10.17 0.04 0.53 0.8 1.59 9.70 0.8 0.68 0 3.85 0.A14 sillimanite andalusite.37 0.70 5.85 0.5 0.7 8.43.63 0 3.5 .6 5. AIt sapphirine e-net 6) garnet “YAG” (s) grossular almandine wropef Be$412Si@t8 HBeAlSiOs Ca19A111Mg2Si18068(OH)10f Ca2Alv1A11vSi~Oto(OH)2 LiAlsi206 A12Si05 10.94 2.09 0 5.9 0.0 [3.93 0.2 0.39 0 2.0 3.08 <O.l 0 0.7 0.68 0 2.61 0 1.89 6.6 0.731 30.51 0 29 [411 36.0 PI 36 [801 35 [801 41. 129] 143. zoisite. II Sisoayb MHz ppm ref.5 15 5.101] 318 NMR OF SILICATES AND OXIDES TABLE 7 (continued) Mineral (s)=synthetic nominal formula QCC.5 4.79.4c 1431 f431 [1W [66.0 12 gc 0.129] [43.731 123.5 13 4. All.431 u91 [431 [43.6c [43.551 [431 [431 [431 [86.2 Al3 epidote.163] [431 11431 Cl431 2.139] r431 [43.0 7.731 [43.8 2.129] [431 [431 [82.731 r43. Al1 A12 topaz margarite muscovite illitee . A11V)40~o(OH)gf Ca2.67 0.2 [431 4.46 [431 18.8 0.Al)8020(OH)qf AWO3.9 10 11 4c 4c 4c 0.05 0.Mg AlV1)6(Si A11v)40to(OH)4f A4SWioW-h ’ A12%01 o(OW2 (Ca.Mg)4(Si.3 1.44 11.4 2.3 2.6 0.5 1.34 [431 1.16 r431 9.0 1.5 0.2 1. Al(l) 11 t AW 8.7 r731 [731 [54@1 .45 11 5 5.97 4.73 10.38 r431 6.penninite xanthophyllite kaolinite pyrophyllite smectite gibbsite (s) augelite senegalite Ca-aluminates: 6) 6) 6) 6) ethingite(s) 6) A12Si04F2 (A104F2 site) CaAIV12(A11”2Si20~~)(OH)2 KAlV12SiA11V30~~(OH)2 KA12SiA13010(OH)2f (Mg A1V1)&i.0 0.4 0.Na)(A1. r731 [731 WI m KQI W33 W31 4. by fitting of quadrupolar line shapes [34].14. 27Al MAS NMR data have been shown to agree well with site assignments based on stoichiometry [5. Quadrupolar shifts can be as large as 20 or more ppm for data collected at relatively low magnetic fields and/or for sites with large field gradients. by collection of spectra at more than one magnetic field [73. MAS NMR has also been used to estimate the effect of temperature on disorder (Figure 3).1621. In MgAl204 spine1 [45. for example.4 10.71 0.164].1 Tesla) can be very helpful.20.52. .10 WI 1.88].36 0.2 W31 0.36 11231 1.163].g. The new techniques of “dynamic angle spinning” (DAS) and “double rotation” @OR) NMR may prove to be very useful in improving resolution [90.8 10. or even lost entirely because of instrumental dead time.5 =a 9 E911 <l 4-l 16 1911 0.8 r71 [71 2. The distinctions among octahedral and tetrahedral Al have in some cases allowed quantification of disorder and Al site occupancy in silicates and oxides. In a number of sheet silicates. MAS studies at very high magnetic fields (e.103].20 W31 1. but can be almost negligible in many minerals at high magnetic fields.7 11. for sites with relatively large QCC (quadrupolar coupling constant) values. Quadrupolar effects can broaden peaks to the extent of being inadequately narrowed by MAS. The more subtle effects of bond an4 le and second neighbor identity are similar to those for 9Si [2. Determination of Siso from MAS spectra can be done in some cases by detailed analysis of spinning sidebands for the satellite transitions [55.86. and.5 ~3.80 W31 Al05 groups in a few known structures have S values of about 35 to 40 ppm. Many MAS NMR studies of 27A1 of solids have reported only peak positions.19 13.66.09 12.79].60. which are generally shifted to frequencies lower than &so by the second order quadrupolar interaction. allow these sites to be easily distinguished by l1B NMR. applications to silicates have generally been limited by the necessity of working on isotopically enriched samples. The most obvious effect on 170 spectra of silicates with tetrahedral Si is the distinction between bridging and non-bridging oxygens.153. CP MAS NMR has been shown to work well for enhancing signals from oxygens near to protons [ 1571. there are good correlations between increasing cation size and decreased shielding (higher frequencies or larger chemical shifts) [153.154]. The data assembled in Table 8 have been obtained at high magnetic fields by the fitting of MAS.and four-coordinated boron. Indeed. Many applications of this relationship. DAS spectra. but neglect of chemical shift anisotropyc an lead to discrepancies[ 131 1. for example. Isotropic chemical shifts for nonbridging oxygens vary widely (over 1000 ppm) depending on the nature and number of the coordinating cations. The increase in . 27Al MAS spectra for MgAl204 spine1 quenched from the two temperatures shown.152. have been STEBBINS 3 19 L 14oov 250 0 -150 Fig. as well as the effect of coordination number on &so. QCC is well correlated with the electronegativity of the neighbor cations and thus with the covalent character of the M-O bonds [ 115. The large differences between electric field gradients for three. For group II oxides and both bridging and non-bridging oxygens in silicates. 2.154]. Features other than the two labeled peaks are s the intensity of the Al1 B inning side bands.2. 3.The former generally have much larger QCC values.4. l’0 Although 170 can be observeda t natural abundancein liquids and in highly symmetrical sites in crystalline oxides [6]. the latter can be quite informative. or static spectra. Other Nuclides NMR studies of a variety of other nuclei in solid geological materials have provided important structural information [61]. For some materials. DAS and DOR spectra have recentl 7 been shown to be remarkably effective for resolving 1 0 NMR peaks for structurally similar but crystallographically distinct sites in silicates [89].3. In silicates. 47Ti.5. Studies of other nuclides in silicates and oxides are too numerous to mention in detail. rl hsoa’ ref.g. 35Cl. Some data for synthetic zeolites. 19F.1381. Mineral (s)=synthetic nominal formula QCC. 23Na.“ BO” signifies bridging oxygen. As such.peak indicates an increase in disorder with temperature [86]. 19F. The first of these reports extensive work on perovskite-structured oxides.. 27Al. and *07Pb. 25Mg. similar effects on 6iso have been detected for 23Na in silicates [53. ppm miscellaneous oxides. 13C. but have recently included 9Be. and on phase transitions in materials with abundant nuclides of high Larmor frequency (e. dynamical studies have concentrated on the mechanisms and rates of diffusion of both cations (especially 7Li+ and 23Na+) and anions (especially 19F-). 7Li.170]. Dynamics in Crystalline Phases In oxides and silcates. l19Sn. Most of these studies have been done at relatively low magnetic fields and consist primarily of relaxation time measurements.103] as well as aluminofluoride minerals [24]. quantification of results often requires 320 NMR OF SILICATES AND OXIDES TABLE 8. made to borate and borosilicate glasses [ 11. 170 NMR data for crystalline oxides and silicates. 31P. 2. Recently. 6) periclase(s) 6) w 6) rutile(s) anatase(s) 6) baddeleyite (s) 6) 6) 6) 6) 6) zincite(s) 6) 6) 6) litharge(s) .155. 89Y. 51V. as well as oxysalts and oxide superconductorsa re excludedf or brevity.109. 93Nb) [8. 45Sc. 129Xe.136. 93Nb. “NBO” non-bridging oxygen. 39K. 6 . OA4 site 1.2 II .005 COO5 <1. site lf 11 . A4 site 2. site 3 CX-Al2O3O.6 t%Al2O3.5 <l.6 &Al2O3. site 2 11 .Na20 c2.8 ~~-Al203. OA4 site 1.l c2.cuprite( s) 6) 6) (s) aluminum oxides: corundum(s) 6) 6) 6) 6) p-alumina(s) MgO CaO SIO TiO2 Ti02 Ti203 m2 Z102 (tetragonal) 87ZrO2. OA13 site 4.0 11 A1203.17 y-Al2O3.014 <.13MgO (cubic) HfO2 La203 (octahedral site) ” (tetrahedral site) Ce02 v02 ZllO Cd0 HgO(yellow) SnO PbO cu20 &a0 KMnO4 K2WO4. OA4 site 1.02 zo.2 =0.005 <. OA4 site 1. 4 c2.<0.815~ El -18b [6.0.55 75C 73C 73C 72c 72c 0.4 26b 11541 47b [I541 294b [I541 390b [I541 629b [I541 59oc El 558c 161 503c WI 325.4 <1.9 4 4 <0.9 <1.1 ~2.6 79c 76c [13. rl hoa’ ref.335c @I 469c @I 59oc WI 878c [61 ~755. hydronides: .1541 -60 [I541 121e r1541 251c @I 294c El -193 WI -277 El 1197 [I151 437 [I151 429 r1151 422 11151 0.402c WI 383c @I -355d WI 267.9.0 <1.2 4 =0.13 7.1.156] [1561 11561 [I561 [1561 [1561 161 STEBBINS 321 TABLE 8 (continued) Mineral nominal formula QCC.3 co.1. . I.BO Ca3Si309.BO . NBO 11 . 9. NBO . NBO 11 . II II ps-wollastonite 11 11 (s) 19 I. .boehmite(s) . NBO I. 11 I. Al2OH site Mg(W2 Mg2Si04. ..I-0 8. 0 htrnite(s) chain silicates: diopside(s) 9. .* . NBO I. . clinoenstatite(s) I. NBO II . 11 wollastonite(s) 11 11 11 It 0 I. NBO I. NBO . NBO caMgsi206. NBO II . bayerite(s) brucite orthosilicates: forsterite(s) t. AlO( OA4 site 11 A120H site Al(OH). NBO $9 ..BO Mg2si&j.NBO Ca2SiO4. NBO II . NBO 11 .. NBO II . 1 2.1 72i 64i 49i 134i 12gi 122i 122i . NBO 9.15 0.2 4. .39 2.6h 4.0 0.BO 11 .2h 2. .6h 4..lh 5.BO 1.5 4oc 6.13 7o.7h 2.9h 3.0 25g 3.gh 2.83 2.BO a-Casio+.0h 2. NBO I.oh 2.P 2.oc 5.6h 2.8h 3. NBO 11 .9h 2.3h 2. NBO II .3h 2. NBO . .8h 4.1 2.0 0.8 0.8 2.2h 2.11 .74 4. .8h 4. NBO I.9h 2.BO a-SrSiOgj.BO 11 .7h 2.6h 3.3 4oc 6.2h 5. NBO 11 .3 3. 1 94c 0.36 69’ 57i 61i 59’ 62’ 7oi 7oi 115i 114i 107i 97’ 103i 88i 75’ 75i 67’ 0.0.1 91c 0.00 64 0.4 80c [125.1561 U561 WI [I571 if391 WI WY 1891 F391 P391 1891 E391 1891 WI F391 [891 WI WI [891 WI WI if391 P391 E391 [891 WI F391 WI [891 r1531 [I531 r1531 u531 .2 75c 0.13 86i 0.1 105c 0.1 10gc 0. for site 3: 011=561 a22=497. MgOH site framework silicates: cristobalite(s) SiO2 Na-A zeolite(s) (see reference).022=518. Si-O-Al.1 0. for site 2: all=567. v &soa’ ref.13 109.2 31c 4.3 0.a22=530. (e) From MAS. ~iIV-O-SiVI stishovite(s) SiO2 2. corrected using QCC from static spectrum. NBO 11 .45 0.2 0 4og 5. BO high pressure silicates: wadeite phase(s) K2SiV1SiIV309 Si*v-O-Silv 19 11 .2 32= 3.90 0.0 [I651 6.BO 11 . (f) For site 1: 011=564.8 0 5og 1.5 [I651 4.35 62.5 U651 [I531 P531 r1531 r1571 [I571 [I571 u311 U521 U521 11521 Notes for Table 8: a) Relative to H20.1 169c 1.1 0. BO Na-Y zeolite(s) (see reference).2 0.BO Mg$&Olo(OH)2. NBO 11 . .6 0. a33=202 ppm.1 159c 3. (d) Uncorrected for QCC.u531 [I531 322 NMR OF SILICATES AND OXIDES TABLE 8 (continued) Mineral (s)=synthetic nominal formula QCC.2 97. (b) From MAS data.3 0 og 5. Si-O-Al.4 87c 3. MHz ppm BaSiOjj.o-j3=217 ppm. (c) From simulation of MAS data. NBO 11 . Si-O-Al.7 0. BO *a II .1 44c 4.6 0.50 0.13 4ok 3. little or no correction for QCC needed. l l. (g) Based on static spectrum. more direct interpretations. (k) Fit of static spectrum gives CJ~1 =a22=6O. crystalline stoichiometry. as well as extensive discussion of silicate.7 NaAlSi206 92.ts33=208 ppm.62.144]. Other recent reviews do include some tabulations [34]. 29Si NMR data for glasses of simple.These contain information on studies of nuclides not included here.B ecauseo f the wide and continuous ranges of compositions studied. high resolution studies of silicates. for example [57.87<QCC<p~ [891. 29S i The relatively clear relationships between &so and Q species in crystalline silicates has led to a number of attempts to quantify their abundance in glasses.5 CaA12Si208 87. oxide.and chain-silicates [38].1. the direct observation of exchange among multiple sites in a crystal offers the possibility of simpler.29. 19F. In a few recent. CSA not included. and non-oxide glasses [lO.8 NaAlSiO4 86. Separate STEBBINS 323 TABLE 9. 033=-10 ppm. (i) More sites are present than are resolved in MAS spectra. ppm ref.145]. Composition -&so7 mm FWHM. and can have an important influence even in ortho.130.0 KAlSi308 100.9 CaAlZSiOfj 83.61. 3. PQ’ QCCx( l+ IJ2 / 3) li2. and the frequent model-dependent nature of the structural conclusions. borate. Alkali cation dynamics have been studied in a number of framework silicates. especially llB.131]. Si02 NaAlSigOg 98.3 20 . (h) QCC given is actually the “quadrupolar product”. @Derived from DAS data at two magnetic fields. I have tabulated only a few 29Si MAS data on glasses with the stoichiometry of end-member crystalline phases (Table 9).4 Na2Si409 K2Si409 NazSiOg MgSiO3 82. Structural and dynamical changes occurring during displacive phase transitions in silica polymorphs and their aluminum phosphate analogs have been explored in some detail [99. 3. complex models. AMORPHOUS SOLIDS. 23Na 9 and 31P. 0. APPLICATIONS TO GLASSES. AND MELTS Techniques such as NMR become particularly important when the absence of long-range structure limits the information obtainableb y diffraction methods. 5* [44.7.7* 84.1* 14*. It is now clear that speciation is more disordered than required by simple stoichiometry.92.7*.11. but interpretations have converged as data improves [26.5* 11*. Quantitative interpretations have usually depended on assumptions of Gaussian line shape and curve fitting.5 1. peaks for Q species are usually unresolvedi n MAS spectrab ecauseo f greatero verall dis324 NMR OF SILICATES AND OXIDES .CaMgSi206 81.28.77].66X* 12 16 r9a 18 1941 13 [941 15 [94.94.0.5 ppm in peak positions and widths.32. static spectra can permit quantification of Q species in glasses with fewer curve fitting assumptions than for MAS spectra.32.10* 99. and in aluminosilicate glasses.6.77.1 13 [701 105.3*.ll 105.134].8.3 11.3 17 1701 80.5*.7. In a few favorable cases. A number of thermodynamic mixing models for these systems have been based on NMR data [9.12.91. In binary silicate glasses of alkaline earths. but more ordered than predicted by random mixing of bridging and non-bridging oxygens [94.6 14 111.134.79.981 r77. MI [77.0.5 82.7* 12*.166] [771 [771 1771 1771 [701 [701 1701 Notes for Table 9: Uncertainties are generally at least 0.10.135].8* 103.1.90.76.8*.135].2 13.981 15 [94.lO 102. because of the contrasts in chemical shift anisotropy [9.88.3 16 CaS iO3 80.981 10*.81. *Partially resolved shoulder peaks for each Q species are often partially resolved in MAS spectra for alkali silicate glasses (Figure 4).981 11 [94. do indeed become more random with increasing T [9.27]. which is characterized by obvious x-ray diffraction peaks and which therefore contains substantial long-range order.94]. probably because of at least partial “aluminum avoidance” [943. and from different tetrahedral species.1353. One approach to determining the effect of temperature on liquid structure is to quench liquids at varying rates to produce glasses with different “fictive” or glass transition temperatures (Tg). The narrowing of NMR peaks as Al/Si is increased to 1 suggests that some Si-Al ordering occurs. 4. as well as overall disorder in bond angles. This approach has been used to show that Q species distributions.166]. interpretation of NMR spectra of quadrupolar nuclides in glasses is complicated by second-order quadrupolar broadening (possibly leading to signal loss from highly distorted sites).65.98] and Ca. Studieso f alkali silicate glassesq uenchedf rom liquids at pressures to 12 GPa have shown the presence of six coordinated Si (Figure 4). 29Si MAS spectra for Na2Si409 glasses quenched from liquids at 12 GPa and at 1 bar pressures.SP 12 CPa I bar -80 -la. -160 -203 Fig.98]. Black dots mark spinning side bands.166.1%) in glasses formed at 1 bar pressure [137]. Signals from Si with different coordination numbers. can again be useful in determining isotropic chemical shifts [79. Studies have included extensive work on alkali and alkaline earth aluminosilicates [35. although again. which were detectable in most of the samples studied. Mg silicates [70. bond angle distributions have been derived using empirical correlations between 6 and bond angles [44.2. Careful . Six-coordinated Si has also been reported in alkali silicate glasses containing large amounts of P205 [25. order and variety of first neighbor cation arrangements. High coordinate Si has not been observed in NaAlSigOg or SiO2 glasses quenched from liquids at high P [150. It may be impossible to distinguish these effects from those caused by disordered distribution of sites. The latter has now also been detected at low abundance (~0. making quantitative derivation of speciation highly modeldependent. The latter study used the CP MAS technique to study the distribution of silanol groups (Si-OH).167].94. studies at varying magnetic fields can be useful. For pure Si02 glass. 27Al As in crystalline materials.a re labeled[ 166]. is highly disordered with respect to local structure [1.22]. Several NMR studies have suggested that opal-CT. and for the first time demonstrated the existence of five coordinated Si [147.129]. when these are observable. 3. Fitting of spinning side bands. quantification of intensities is essential in determining whether all Al has been detected [651. Static spectra can sometimes be more informative than MAS data. 2H NMR has distinguished among water species in glasses. In hydrous NaAlSigO8 glass. and 29Si NMR have been used in several studies of the interaction of silicate glasses with water at ambient to hydrothermal conditions at a range of pH’s [16.0. High temperature 170 spectra for K2Si409 liquid. 1 943 ‘C ---iAL Fig. “bo” and “nbo” show contributions from bridging and non-bridging oxygens [ 1451. Water in Glass Both static “wideline” and high speed 1H MAS studies have detected and quantified OH. 27A1. and has provided some dynamical inSTEBBINS 325 formation [31]. Very recently.168.169]. Note collapse to single. it has been demonstrated that 170 DAS NMR can accurately quantify bond angles and oxygen site distributions [36]. Systematic compositional effects on the chemical shifts for NBO sites have been noted [61].110. However.113] and in some phosphorus-rich glasses [27] and boroaluminates [ 15.and molecular Hz0 [30.98]. as well.3. Silicate and Aluminate Liquids . llB.971. 170 As in crystals.139.139] and in SiO2 [373.69].SiO2 ternary. whereas in hydrous binary alkali silicate glasses [85. as have pressure effects on 0 site distribution [ 1651. 23Na. The most dramatic findings from 27Al MAS NMR in glasses has been the clear detection of five and six coordinated Al in a variety of compositions. high-coordinate Al has been detected in only slightly peraluminous glasses near to the MgA1204Si02 join [831.4. narrow line caused by exchange of species. it has been shown that high coordinated Al is undetectable and thus comprises less than a few percent of the total Al [65. In carefully quantified studies of glass compositions with M+l20/A1203 or M+*O/A1203 I 1. 3. 3.Al203 . non-tetrahedral Al is abundant only in compositions close to the Si02-A1203 join [ 1141.68]. 23Na 27A1. including those in the Si02-A1203 binary [105. the primary distinction among 0 sites detected by NMR of glasses is that between bridging and non-bridging oxygens (Figure 5). 29Si NMR has clearly shown the presence of SiOH groups.5. In the CaO . 3. and 29Si MAS and CP MAS spectra were interpreted as indicating that OH is bound soley to Na with the possibility of protonated bridging oxygens [67. 170. 5. and 29Si peaks. incomplete exchange and averaging occurs. .149.a nd that of 0 between bridging and non-bridging sites. This approach has shown. A series of relaxation time measurementsh as shown that Si dynamics are greatly affected by the transition from glass to liquid. in situ. high temperature NMR reveals only single 170. silicate species are short lived.81]. Studies have now been made to temperatures greater than 2 100° C.J.142. At lower temperatures. Ahrens.75. B. therefore. including chemical shift anisotropy and quadrupolar couplings. Acknowledgements.1511T. A multi-nuclear high T NMR study of alkali aluminosilicate liquids has detected systematic tempemture effects on averaged chemical shifts that can be interpreted in terms of structural changes [ 1421. are fully averaged [38. with all cations and anions exchanging rapidly among available sites.81.In ionic and partially ionic liquids such as silicates (at least at high silica contents). 326 NMR OF SILICATES AND OXIDES REFERENCES 1. 23Na. Skibsted. 3. that when aluminum oxides. he average peak position can still give structural information however. flow requires the breaking of the strongest bonds in the system (Si-0).121. 2-D exchange NMR spectroscopy just above the glass transition also suggests that exchange among Q species is of key importance in flow even in the very high viscosity range [39]. for which orientational effects that lead to broadening in a solid. 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J.. numerous applications in a wide variety of scientific disciplines have been described. J. 170. 1990. Pressure-induced silicon coordination and tetrahedral structural changes in alkali silicate melts up to 12 GPa: NMR. Xue. Oxygen-17 NMR of quenched high-pressure crystals and glasses. accompanied by reference material on Mossbauer spectroscopy. 1009-1019. Silicon coordination and speciation changes in a silicate liquid at high pressures. and R. High-resolution Si and Al NMR spectroscopic study of Al-Si disordering in annealed albite and oligoclase. Am. as elucidaied by NMR. W. Eos. J. 2. J.. Information from these hyperfine . and B. P. 1991. chemical and magnetic state of the atom. Solids. Kirkpatrick. W. H. Union. F. Mineral. Raman. X. 821. F. J. Poe... and provides a means of studying the local atomic enviroment around the nuclei. 962-964. Xue. J. at least 2OCKclo ntain results of studies on minerals (as estimated from data provided by the MUssbauer Effect Data Center. Stebbins. INTRODUCTION Since the discovery of the Mossbauer effect in 1958. 169. J. 1991. THEORY The Mossbauer effect is the recoilless absorption and emission of y-rays by specific nuclei in a solid [81. Am. This chapter only includes references to transmission studies. 121. D-8580 Bayreuth. 3. while Table 5 lists some common applications of Mtissbauer spectroscopy to mineral studies. Illustration of hyperfine interactions for s7Fe nuclei. EXPERIMENT A transmission Mossbauer spectrometer is very simpIe. The source is moved relative to the absorber. the data should be considered representative Copyright 1995 by tbe American Geophysical Union.4 keV transition in 57Fe and the 23. which can be determined experimentally from the line positions in a Mossbauer spectrum (Figure 1). the absorber (sample) and a detector.g.. The data were chosen from the literature as being typical for each mineral. Formulae relating the Mossbauer line C. and therefore have similar hyperfine properties. Selected references to important experimental considerations are given in Table 4. Postfach 10 12 51. A typical experimental spectrum is illustrated in Figure 2. [105. McCammon. Bayerisches Geoinst. while l19Sn data are listed in Table 11. Germany MineralP hysicsa nd Crystallography A Handbook of Physical Constants AGU Reference Shelf 2 positions and the hyperfine parameters are given in Table 2. 332 McCAMMON 333 Isomesr hift Quadrupoie bare nudeus splitting Magnetic splitting ~~~~ 0 Ah Fig. shifting the energy spectrum due to the Doppler effect. Spectra are commonly plotted as percent transmission versus source velocity (energy).interactions is provided by the hyperfine parameters. 4. particle size. thermal history and degree of crystallinity. 57Fe Mossbauer data of selected minerals are listed in Tables 6 through 10. Suggestedre ferencesf or further information are listed in Table 3. followed by l19Sn. however since hyperfine parameters often depend on chemical composition. 1271). MINERAL DATA Over 100 different Mossbauer transitions have been observed.. Table 1 describes the hyperfine parameters as well as other observables. however the technique can also be performed in a scattering geometry to study surface properties (e. and typically consists of a y-ray source. although unfavourable nuclear properties limit the number of commonly used nuclei. showing the nuclear energy level diagram for .88 keV transition in ii9Sn involve a spin change of 3f2 + l/2. Both the 14. 1. 57Fe is by far the most popular isotope. g. accompanied by the resulting Mossbauer spectrum. one should consult resources such as the Minerals Handbook published by the Mossbauer Effect Data Center (see Table 3).921 . 2.Si03 showing two quadrupole doublets. spin state and coordination of absorber atoms. Each interaction is shown individually. Most spectra were fitted to Lorentzian lineshapes. and the distribution of iron cations between different crystallographic sites may be a function of thermal history.(1) a bare nucleus. the few exceptions are noted in the tables. Chemical compositions are given exactly as reported by the authors (even if the resulting compositions are not electrostatically neutral).96 2 .8Mg0. For more complete information on specific minerals. Mossbauer spectrum of orthopyroxene with composition Fe0.0 Velocity (mm/s) Fig. For example. e. 0. (3) electric quadrupole interaction (quadrupole splitting). j -4.0 0.m I.98 . The relative areas of subspectra can be used as a rough approximation to relative abundance. (2) electric monopole interaction (isomer shift). e. 334 MdSSBAUER SPECTROSCOPY only.94 0.5% ‘E 0. Data for differing compositions are provided for the major mineral groups to illustrate the dependenceo f hyperfine parameterso n composition.0 2. Description of Mossbauer parameters Name Unit Description Isomer shift (8) mm s-l Energy difference between source and absorber nuclei resulting from effects including differences in valence state. [973. TABLE 1. one corresponding to Fe2+ in the Ml site (45% of total area) and one corresponding to Fe2+ in the M2 site (55% of total area).0 -2. a small thermal shift due to atomic vibrations. . Experimentally one observes a single line shifted from a reference zero point by the isomer shift plus the second-order Doppler shift (SOD). Fe3A12Si30i2 is listed under garnet. Minerals are listed by name except when part of a larger structure group.g. not almandine. Centre shift (CS) Quadrupole splitting (mQ) mms -1 The experimental shift of the centroid of a Mossbauer spectrum from a zero . but note that site proportions often vary between different samples of the same mineral. and (4) magnetic dipole interaction (hyperfine magnetic splitting).0 4.0. . the amount of Fe3+ may depend strongly on foa conditions. and dynamic processess uch as relaxation). The separation of peaks 1 and 6 is proportional to the magnitude of the hyperfine magnetic field. = cs + ‘I2 AE. thermal.electric monopole .electric monopole + quadrupole . For an ideal random absorber with no quadrupole interaction the linewidths of the peaks are equal with intensity ratio 3:2:1:1:2:3. Determination of line positions for s7Fe 14. McCAMMON 335 TABLE 2. The quadrupole splitting is given by the energy separation between components. . so for purposes of comparison the isomer shift is often taken to be equal to the centre shift. a quadrupole doublet) whose area is approximatelyr elatedt o the relative abundanceo f that particular site within the absorber. L2=CS-‘/2AE* L.g. mm s-l Splitting of the energy levels caused by interaction between the nuclear quadrupolar moment and an electric field gradient at the nucleus. geometrical.m ) + cs 42AEQ L3=%C(NH ( g3n-&R) ++ ccss --. Line width (0 Relative area (0 mm s-l Full width at half maximum of the peak height.11882 mm s-l T-l h g3n = 0. Each site normally contributes a subspectrum (e.067899 mm s-l T-l .=CS L. the source (self-absorption resulting from decay). and depends on the valence and spin state of the absorber atoms. next-nearestneighboure ffects. . Peaks can be broadened beyond the natural line width by effects due to equipment (vibrational.4 keV transition Hyperfine interactions present Line positions .electric monopole + quadrupole + magnetic dipole (special case of axially symmetric electric field gradient and Ih go HI >> IAEQI) h glR = 0.electric monopole + magnetic dipole (dE. Hyperfine magnetic field 8 Tesla Interaction of the dipole moment of the nucleus and a hyperfine magnetic field causes a splitting of the nuclear energy levels. as well as the coordination and degree of distortion of the crystallographic site. = 0) . The contribution from the SOD is similar in most standard materials.Relative proportion of subspectrum area to the total area. and electronic problems). and the sample (thickness broadening.z+gm) Q &=‘/zhH ( -&2+&n) + cs -‘/==Q .=V~PNH ( 3g3n-an) +cs +‘/2AE* L2= ‘l214vH ( gw.21d1E2p A E &=‘I~PNH ( gw. Experimentally one observes a doublet in s7Fe and l 19Sn spectra with components of equal intensity and linewidth in the ideal random absorber case.electric monopole + quadrupole + magnetic dipole (generacl ase) L.reference point. resulting in six peaks for 57Fe spectra in the simplest case. 1971.g. (continued) Type Reference Journal Analytical Chemistry (American Chemical Society. 5. London. Berlin. U. (eds. CRC Press. Chapman and Hall. Searches of the database are possible. Cambridge. C. Hyperfine Interactions (J. Asheville. pp. 1981. 1986.E. Chapman and Hall.M. Vol. Vol. (ed.E. Data Resource Mossbauer Effect Reference and Data Journal (Mossbauer Effect Data Center. L. Mdssbauer Handbook Series.E.C. Longworth. 1990. pp. and Trautwein. H. J. 336 MijSSBAUER SPECTROSCOPY TABLE 3.J.. Gonser. Databases are set up to run on IBM-compatible microcomputers and can be searched using various options. Miissbauer Spectroscopy. Berlin.. Cambridge University Press. 3. Topics in Applied Physics.Li = ‘12 PN H ( -be + a/z ) +cs +%dEQ Requires calculation of the complete interaction Hamiltonian (e. 1977. 18. Giitlich. B. J. Vol.L. Mitra. F.C. Hawthorne. N. and Gibson. J. Baltzer AG. Asheville.) Spectroscopic Methods in Mineralogy and Geology. Boca Raton.) Handbbok of Spectroscopy. See Chapter on Mossbauer Spectroscopy. T. Stevens. Hawthorne. Springer-Verlag. and Berry. TABLE 3. Pollack.. Link. 1992. G. An Introduction for Inorganic Chemists and Geochemists. London. S. Stevens. NC) contains references and Mossbauer data for nearly all Miissbauer papers published. McGraw Hill. R. T. MSssbauer Spectroscopy and Transition Metal Chemistry. Suggestedre ferencesf or MosSbauesr pectroscopy Type Reference Book Bancroft. T. 62. University of North Carolina. contact the . See Chapter on Mossbauer Spectroscopy. 1973. and the asymmetry parameter of the EFG (?j). Cranshaw. 255340.W. NC) cover many topics including Minerals. Miissbuuer Spectroscopy and its Applications. Mlissbauer Effect Data Center Mtjssbauer Information System (maintained by the MUssbauer Effect Data Center.. [71]).) Mfissbauer Spectroscopy.) Mineral: Data and Mineral: References. (eds. F.) Miissbauer Spectroscopy. (4. and Gibb. 1988. New York.O. R. North Carolina. Applied MBssbauer Spectroscopy. Mdssbauer Effect Data Center.. Cambridge. Rev. 1975. Greenwood. 1978. Zhe. the polar (0) and azimuthal (9) angles relating the direction of H to the electric field gradient (EFG). G. 125R-139R.M. Theory and Practice for Geochemists and Archeologists. White. USA. Mineral. Cambridge University Press.. hyperfine magnetic field (H). A. Robinson. see for example Vol. 403-528.D. Asheville.G.C. 1992. Dickson.). Washington DC) contains biennial reviews (starting in 1966) of Mossbauer spectroscopy. V. NC) contains extensive bibliographic and Mossbauer data entries compiled from the Mossbauer literature. Gibb.P. M&sbauer Spectroscopy. P. Oxford. F. 1983. Principles of Miissbauer Spectroscopy. and Johnson. J. Asheville.G.. There are eight lines involving the following hyperfine parameters: isomer shift (@. Basel) publishes proceedings from various Mossbauer conferences. Stevens (ed. Inc. 68-71. MossbauerM icro Databases( MtissbauerE ffect Data Center. 1986.. Dale. see for example Vol.. USA.N. D.W. (ed.C. Pergamon Press. Mineralogical Society of America. pp. quadrupole Splitting (/\EQ). Springer-Verlag. 221 [13.16(l) 2.99.7Mno.851 [W 1081 L=.201 114.69 vrFe2+ [531 1. 32.93 vrFe2+ 1. H I site Ref mm s-l mm s1 Tesla Nal .o3~0. 1201 Isomer shift reference scales [1161 Goodness of fit criteria 131. s7FeM &ssbauerd ata for selecteds ilicate minerals Absorber T CS(Fe) AEQ H I site Ref mm s-l mm s-l Tesla Amphibole structure W2i.07(l) 1.8c%lxs18022(oH)2 X=Fed”fgo.281 Absorber homogeneity NL501 Preferred orientation of absorber 195.Mossbauer Effect Data Center for details. 58. 1141 u5.sSis&d0Hh RT RT 1. 37.07 MFe2+ uo71 1.991 Geometric effects [16.55(l) 0.3Mno.96Feo.01)2SiO5 Babingtonite Ca2Fel. 97. Methodology References Experimental aspect Reference TABLE 5.31 MFe2+ McCAh4h4ON 337 TABLE 6.81(l) 0.13(l) 1. 15.16(l) 2. 251 TABLE 6.76(l) 0.-rFedi8O&H)2 F%2Mgo. TABLE 4. Applications in mineralogy Application Reference Absorber thickness r74.79( 1) 0.901$ X=WaFe2. including Fe3+/cFe Site coordination Semi-quantitative phase analysis Phase transitions Magnetic structure 110.3Si5014tOH) Chlorite X%&4KW7. including intervalencec harget ransfer Site occupancies. 1031 Conventions for reporting Mossbauer data [117] Oxidation state.l Chloritoid .961 Saturation effects [97. (continued) Absorber T CS(Fe) a.3 Andalusite (Ab. 2A1Si5Ol8 Epidote structure CaaSi3012(OH) X=Alz.20(l) 0.76(l) 1.7All.15(l) 0.67(5) 2.86(l) 1.39(l) 1.zFeo.17(l) 1.23(5) 2.7Mgo.8Feo.9Feo.43BSQ Ilvaite CaFe3Si208(OH)d 77 K RT RT RT RT RT RT RT RT RT RT RT RT RT RT RT RT 1.87(l) 1.1800°C GranoMetite MwJ%.14(3) 1.Fel.16(3) 0.5 Ca3F%Si3012 Ca2.14(l) 2.7 GPa.2 Garnet structure Fe3A12Si3012 Fe2+$e3+2Si3012 quenched from 9.5La0.36(l) 0.44( 1) 0.llOOT WShd%d%% X=All.27(l) 3.1 SiO3 quenched from 18 GPa.12(l) 2.3Si3012 Mgo.7Fel.29(l) .2Si3012tOH) Y=Cal.27(l) 1.86(l) 1.3A~Si2OlotOH)~ Clay minerals c Cordietite A13Mgl.5Cro.44(l) 0.70(3) 1.Peo.34( 1) 1.38(5) 0.2Ce0.40(l) 0.30(l) 2.s YA11.41(l) 2. 33(l) 1.60(l) 1.32(2) 0.51(l) 3.31(l) 0.39(l) 1.36(l) 0.21 .56(l) 0.38 0.3 l(5) 3.48(5) 1.41(l) 0.59 wFe2+ 0.33(l) 0.36(l) 1.60 0.30(2) 1.35(l) 2.54(3) 1.48(2) 2.36(l) 0.03(2) 1.24(l) 3.26(l) 1.73(l) 1.98(l) 1.06(2) 0.21(l) 2.58(l) 3.67(l) 1.70 0.2.39(l) 0.20(l) 1.40 0.1 l(1) 0.10 wFe2+ 0.01(2) 0.94(l) 1.48(2) 0.26(l) 0.29(l) 1.11(l) 0.90(8) 1.28(l) 0.45 MFe” 0.31(l) 1.06(l) 1.60(l) 0.41(l) 1.08(l) 1.20(4) 0.46(l) 0.27 2.19 MFe2+ 0.49(l) 0.55(l) 3.35 1.31 wFe2+ 0.22(l) 1.36 vFe2+ 0. 33 MFes 0.16 0.80 0.17 0.Pe0.92 wFes 0.J~Si3WW2 X=All.58 MFe2+ 0.ozhsios Mica groupb Ko.10 0.0.54 0.98 wFe2+ 0.98FeO.1 .84 0.02 wFe” 0.06 0.83 0.08 wFeG 0.sNao.94 0.46 0.2Mg0.94 0.09 0.09 Fe2+ 0. (continued) Absorber T CS(Fe) AEQ H I site Ref mm s-l mm s1 Tesla Kyanite (~o.06 MFe2+ MFes MFe2+ wFe2+ Fe3+ MFe2+ channel Fe2+ “Fe2+ Fe3+ H131 [401 111 WI [331 1571 r471 1361 [361 [891 r1311 [71 [71 [71 WI uO91 [731 338 MtjSSBAUER SPECTROSCOPY TABLE 6.10 0. 28( 1) 0.3030 X=Ko.SbO.39( 1) 0.~e3+Si04 290 K Orthoclase ~b.21(l) 2.05 0.99(2) 2.38 0.08 1.98(2) 0.20(l) 2.13(l) 2.14(l) 2.62 1..56(l) 0.68(l) 1.3Alo. CaFeSi04 Fe2+o.39(2) 0.+o.36(l) 0.08 1.35(l) 1.4Feo.l Olivine
[email protected](2) 2.66( 1) 0.46(l) 0.63(l) 0.08( 1) 0.o(OH).80( 1) 0.9Nao.48 0.33(2) 0. RT RT RT RT Pyroxene structure FeSi03 RT RT RT RT RT 310K 400K 310 K RT 77 K 77 K RT RT NaFeSi.86(l) . 165OT Pyrophyllite FezMgo.31(l) 0.52 0.91(2) 0.C~A127Sid40@Hh X=Mg2.84(2) 1.75(2) 0.94(2) 1.33 0.41 0.1 Perovskite structure Mgo&eo.23(4) 0.06(l) 2.12(l) 0.osSidh Osumilite XMgl.95FQ.19(4) 1.o.41 0.89(2) 1.30 0.91(2) 0.70 0.02(l) 2.9AL.59 1.19(l) 0.87 1.70 0.99(l) 0.36(2) 0.~SQ quenched from 25 GPa.99(2) 1.70(4) 0.4Sil0.38(2) 0.34(l) 0.1 Ab.08 1.86( 1) 0.51 0.23(4) 0.06(l) 2.52(l) 0.59 0.14(l) 1.12(l) 2. RT 0.30 0. 50 0.50 0.08 IvFeN 1.30( 1) MFes WI WI r411 1391 1761 WI r1111 [I111 r1111 Km 1191 WI WI 1381 WI [381 WI McCAMMON 339 TABLE 6.32 channel Fe2* 1.06( 1) 2.13(l) 2.39( 1) 2.49( 1) 1.50 0.22( 1) 1.42( 1) 0.62(l) 0.13(l) 1.92 XnFe2+ 0.08 Fe3+ 0.54 0.85 wFe3c 0.0.80 0.14(l) 0.22(8) 0.36(l) 0.28(l) 1.30(l) 1.29(l) 1.68 0.50 0.26(2) 1.98(5) 0.46 0.12(l) 1.20 0.18(l) 0.00(l) 3.07(l) 1.59(8) 0.18(l) 1.43(4) 1.14(4) 0.07 vFes 0.19(l) 0.58(l) 0. (continued) Absorber T CS(Fe) me H I site Ref mm s-l mm s-l Teda CaFeAlSi06 RT .16(l) 2.91(l) 3.44(5) 0. &go.5 GPa.2XSi3.99%.ozhsios RT Smectite minerals Cao.riSi04 quenched from 18 GPa.15(2) 1.cFeal)3si4Qo(W2 Titanite CaT&.9Feo.2XSi3.lMgo.16(50) 0.38(2) 0.5Zno.93%.07)3Si20.14(l) 0.lOOO”C I’-Mgo.37(l) 0.3010(OH)2 X=F%&‘k2 RT RT Spine1 struchdre y-Fe2Si04 quenched from 8 GPa.36(4) 0.09(l) 0.05(l) 0.9sFeO.27(5) .35( 1) 1.17OOT Staurolite xA19%%doH)2 X=Fel.37( 1) 1.18(5) 1.16(l) 0. 1 Cao.ssFeo.27(4) 1.04 chfysotile RT RT (M&.35( 1) 0.5Ab.22( 1) 0.36(4) 1.0J3Si2050.l RT RT RT Talc (Mgo.84Feo.401o(OH)2 X=Fel .16)2sio4 quenched from 15.13(l) 1.38(3) 0.6Ab.18CKYC RT 0.13%87)3~i205(oH)4 lizardite RT Sillimanite (~o. antigorite @%0.12(l) 0.Serpentine @&0.37( 1) 0.3Tio.24( 1) 0.l SiO5 RT RT Waakleyite ~-@b0. 06 0.76(l) 2.31 0.09(3) 0.31 1.06 2.ao(l) 1.39 1.98( 1) 0.50(l) 0.70(5) 0.27(5) 1.30(3) 0.83(l) 0.29 0.30 2.52 0.0.09 0.62( 1) 0.78(l) 2.79 0.11 0.70(5) 0.93 0.32 2.79(l) 0.18 1.40 1.58(2) 0.07 0.48( 1) 1*06(l) 1.96(l) 0.81(l) 2.1 l(3) 0.21(l) 0.06 2.14 0.92( 1) O.32 2.65(l) 0.74(2) 0.68 0.25(l) 0.63(l) 1.08(l) 0.55 0.29(3) 0.35(l) 0.70(l) 0.35 0.35( 1) 0.37(5) 0.30 2.99(2) 2.13(l) 0.21 0.65 0.87f 0.96( 1) 0.00(l) VFe3+/vIFe3+ [31 wQ1 [1021 .37(5) 2.17(l) 0.15(l) 0.5( 10) 0.23(l) 0.65( 1) 0.55 1.23 2.81(l) 0.54( 1) 0.21(2) 0.94 0. 4H.&%.15A1204 Fe.O B Goethite a-FeOOHb Haematite CX-FQO~= Ilmenite FeTiOs Lepidochrocite y-FeOOH Magnesiowtistite Mgo.Ti04d Tapiolite FeTa& Wiistite Feo.15F~. see [98] see e..l’%@%103 Pseudobrookite F@TiOS Spine1 structure Fe304 FeCr204 FeA1204 znFe204 WiFe@4 quenched from 1OOO’C Zno.zO Maghemite y-Fe203 Perovskite Cal..Mgo.94 ’ RT RT RT RT . 57Fe Mossbauer data for selected oxide aud hydroxide minerals T CS( Fe) @Q H I site mm s-l mm s-l Tesla Ref Akagadite p-FIZOOH Feroxyhite 6’-FeOOH Ferrihydrite FesHOs . parameter distributions.g. [112] ’ see [59] for a compilation of data f small amount of additional component present 340 MCjSSBAUER SPECTROSCOPY Absorber TABLE 7.WI [1011 m WI r51 WI WI WI PI a see [45] for a detailed discussion of calcic amphibole data b spectra are more realistically described with hyperfine d spectral data were fitted using a relaxation model c site distribution depends strongly on thermal history. 4( 1) -0.62( 1) .55(l) 0.38( 1) 0.55(l) 0.60 0.91(l) 0.RT RT RT RT RT RT RT 310K RT RT RT RT RT RT RT RT 0.3(l) .02(4) 50.8(5) 39.37( 1) 0.37(5) +0.39 0.53( 1) 0.90( 1) 0.22(5) +0.27( 1) 0.61 0.08(5) 50.34(5) 0.38(5) 38.54 0.67 0.21(5) 0.35( 1) 0.0.33 0.33( 1) 0.70( 1) 0.3(5) 0.37( 1) 0.0.52(l) 0.1(l) +1.89(2) 0.1(l) 44.39( 1) 0.95( 1) 0.1(5) 1.2( 1) 0.35( 1) 0.37( 1) 0.4( 1) 0.46 0.4(5) 52.63( 1) 0.48( 1) 0.90(l) 0.29(2) 0.83( 1) .07(l) 0.92(2) 0.35(5) 0.63( 1) 0.40 0.5( 1) 0.30(l) l-06(1) 0. 13 1.81(2) 1.0(2) 52.93( 1) 0.9(l) 0.60(5) 3.6(2) 0.s elenidea nd telluride minerals .46 44.41(l) 51.36 0. 57FeM Ossbauedr ata for selecteds ulphide.7( 1) 0.42( 1) 0.11 0.W) 0.15(5) 0.6(l) 0.78(2) 0.05(10) 0.64 0.15 48.23(2) 0.43 0.57(l) 0.91(8) 0.22( 1) 0.09 m-2 [421 w21 WJI 1351 ml illI WI P91 1561 [931 r931 [781 [911 w31 [771 [1W [791 a spectra data were fitted with a distribution model b see [87] for a discussion of the effect of Al substitution and varying crystal size c see [88] for a discussion of the effect of Al substitution and varymg crystal size d octahedral and tetrahedral sites in FQTi04 have been distinguished using external magnetic fields [ 1231 e there is considerable controversy over fitting models. see [75] for a review McCAMMON 341 TABLE 8.48 0.0.1 l(2) 1.05( 10) 45.39 1.76 0. 89s RT 285 K Sphalerite Zno.d%osS RT Stannite Cu2FeSnS4 Sternbergite 4TezS3 Tetrahed-ite CUs.lNids RT RT RT RT RT RT Pyrite FeS2 Pyrrhotite F%.8 RT RT RT Thiospinel minerals .Fe)AsS Cubanite CuFe& (or-rho) CuFe& (cubic) RT RT RT RT RT RT RT Ldlingite structure FeAs2 FeSbz Marcasite structure FeS2 FeSq FeT% Pentlandite Fe4..Sb4S~2.Fe.2Coo.Absorber T CS(Fe) Me H I site Ref mm s-l mm s-l Tesla Arsenopyrite FeAsS Berthierite FeSb$& Bornite Cu5FeS4 Chalcopyrite CUFeS2 Cobaltite (Co..9Ag. 57( 1) 2.3q 1) 1.69(2) 0.2(5) 0.22( 1) 0.51(l) 0.22( 1) 0.45 23.54 0.54( 1) 0.54 0.5q 1) 0.59 25.39( 1) 0.39( 1) 0.28( 1) 0.7q 1) 0.58( 1) 0.68( 1) .65(l) 0. FeCr2S4 RT RT =3S4 RT 0.26(3) 1.0.1(5) 0.36 0.41 0.45( 1) 1.S.67( 1) .0.90(l) 0.33( 1) 0.46 0.82 0.31(l) 0.37( 1) 0.7(5) 0.83(2) 2.40 0.93 0.20(l) 0.45( 1) 0.61(l) 0.07(2) 27.26(l) 31.58( 1) 0.1(5) 0.60(10) 0.72( 1) 0.32( 1) 0.43( 1) 1.23 0.39(2) 1.59( 1) o.0.36(l) 0.67(3) 0.46 0.8(2) 0.58( 1) 2.FeNi.25(3) 35.67(3) 0.7(5) 0.55( 1) 3 1.48 30.0(5) 0.47( 1) 0.29( 1) 0.26(l) 0.28(2) 0.65( 1) 0.06’ 0.69( 1) .18 0.2 33.15(3) 0.@-w 0.34 “‘Fe3 [@I u71 PI WI WI WI r491 .60 0.1(5) 0.27( 1) 0.66 0. 45 MFes v301 0.lS4 RT 0.Peo.o5S RT 0.88( 1) Co2.69(3) 0.3Mno.p hosphate.O RT RT .95Feo.46 ‘vFe2+ TABLE 9. 57FeM cIssbauedr ata for selectedc arbonate.0.s ulphatea nd tungstate minerals Absorber T CS( Fe) me H I site Ref mm s-* mm s-l Tesla Siderite FeC03 Ankerite CadCO3)2 X=Mm%. (continued) Absorber T CS( Fe) SQ H I site Ref mm s1 mm s-l Tesla FeIn& RT 0.25( 1) 0.~8H.27( 1) “IFe2+ [491 0.0(5) MFe2+ [551 0.69(3) a small amount of additional component present 3.25( 1) 0.88 3 1.l Ferberite FeWOd Jarosite m?3(so4h(“H).55 NFe3’ . Wolfram&e ~e~.54 NFe2+ [431 0.23( 1) Troilite FeS RT 0.WI u 191 r1191 u191 [I191 1691 u191 [701 [431 [491 W91 WI W51 wa ml51 342 MijSSBAUER SPECTROSCOPY TABLE 8.56(10) 0.dWdQ Vivianite WdT’Q).76(4) Wurtzite Zno. 001(2) 33.49(3) O&(5) 1.40( 1) 0.SFeSn$b2S13.15(5) 1.38( 1) 1.1Si3012 YCa2Sn2FqO12 Herzenbergite.02( 1) 33. SnS Incaite. CaSnSiOs Mawsonite. SnO Spine1 structure Co$nO.8A10.08( 1) 0.3 FeNi T CS(Fe) a.98( 1) 1.53(3) 1. Sn2S3 Romarchite. x < 0.21 0. H I site Ref mm s-l mm s-l Tesla 298 K 0.wNm Taenite FetJVi. SnO2 Garnet structure Ca3Fel. .06(l) 0.02( 1) 28.RT RT RT RT 1. Pb3.38 0.21(l) 2.22 0.18(l) 2. C&&2SnS8 Ottemannite.04(3) Fe0 P261 RT 0. 57Fe Mossbauer data for other minerals Absorber Iron a-Fe Kamacite -Feo.48(3) 1.00 +0.45( 1) 0. 11 9SnM cIssbauedr ata for selectedm inerals Absorber T CS(Sn02) A& I site Ref mm s-l mm s-l Berndtite.24(l) 1.9(2) Fe0 141 McCAMMON 343 TABLE 11.25(l) 1.13(2) 1.19 [481 WI 1511 1621 1511 DOI TABLE 10.8(7) Fe0 [301 RT .80(l) 1. SnS2 Cassiterite.11(2) 1.S Malayite.61(l) 0.40(2) Fe0 r41 RT 0.1Sn0.0. 45(5) O-00(5) RT 1.46(5) RT 3.64(2) RT 0.32(4) O.66 mSn4+ 0.2)3Sn2S12 Tin a-Sn /3-Sn RT 1.85(5) 0. Cu2Feo.oo(5) 0.75(8) RT 0.29(5) RT -0.55(l) 0.oo(5) 300K 2.lSnS4 Stannoidite.03(5) RT 0.42(5) 0.71 ?$n4+ %n2+ %n4+ ?jn4+ .30(4) 0.Jno.42(5) 0.25(4) 0.07(2) RT 1.48(5) O.98(5) 1.75(8) RT 0.95(5) 1.02(2) 300K 2.12(4) 1.23(3) RT 1.34 Sn2+ NSn4+ “Sn4+ 0.Mn2Sn04 Zn2Sn04 Mg2SnQ Stannite.07(5) RT 3.00 RT -0.13(4) 3.31(l) %n4+ %n4+ Vn4+ wSn4+ MSn2+ 0.10(5) RT 2.14(5) RT 0.80(8) RT 0.29 Sn2+ 0.48(5) 1.24(4) 0. Cu8(&$n0.40(5) 0.20(8) RT 1. Scripta. 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Fleet.. and cordierite showing intervalence charge transfer. and Bancroft. Accurate site populations from Mossbauer spectroscopy. and Dollase. Rossman. M. and Bums. 1977. The colors of sillimanite. 95.E. Appl. B44. and Ping. D.. E. M. 97. E. 1989. Amer. McDonald. 100. Riedel. Ross II... 893-901. Phys.. 462466.. 1. 98. A.. and Seifert. Solid State Chem. Mineral. G. IV. Meth. R.. D. B. 93-102.. Phys. 96. 1981.. R. 1992.. Mineral. W. 1982. 34-43. 38. Rancourt. D. Res. Mineral. 102. C. M. 1977.. Mineral. D. Phys. 103.. Parkm. Loeffler.. D. M. Instr.. Goldanskii-Karyagin effect versus preferred orientations (texture). Grew.. and Lalonde.Y. Lalonde. G. 77. H. U. L. . Temperature dependent Mg-Fecation distribution in actinolitetremolite. Why MISFIT when you have x2? In Miissbauer Effect Methodology. 1990. 193-203.. Amer. In Absorption Spectroscopy in Mineralogy. Gruverman and C. Eur. G.. 108. D. F. 1985. Iron distribution in orthopyroxene: A comparison of Mdssbauer spectroscopy and x-ray refinement results. A structural investigation of some tin-based coloured ceramic pigments. Skogby. 1992. 109. D. Seifert.. H. J. Shinno. and Smith. 110. 145170. 8. 4.W. Skogby. Hyper. Minerals. J. 547-553. P. P hys.). 196-200. Seidel (eds. Mineral. M.. E. 1977. Minerals. Chem. Abrams. V. Plenum Press. Seifert. Contrib. Annersten. 116. 1977. F. Inter.. pp. 105. Molin. Amsterdam... 107. 263276. Mineral. S.. Sherman. Order-disorder kinetics in orthopyroxenes of ophiolite origin. M... Sot. Chem. 210-214.J. New York.. Skogby. 1983. and Annersten. 1981. Mineral. R. 15. J.. and Tazzoli. Elsevier. Trans. J. 114. Spender. 106.. Domeneghetti. Mijssbauer spectroscopy of grandidierite. Neues Jahr. Schmidbauer. 73. I. Sawicki. Seifert. Compositional dependence of the hyperfine interaction of 57Fe in anthophyllite. Phys. 115.L.. 80. 43-52. and Olesch. Ceram. 112. 91-95. 1988. Petrol. Phys. A Mossbauer study of ferric iron in olivine. 62. R. Coey.Ruby. 1987. M. B.). and Sawicka. Optical (diffuse reflectance) and Mdssbauer spectroscopic study of nontronite and related Fe-bearing smectites.. M. Mineral. 199219.. and Vergo.. Minerals. H. H. N.. J. G. 5. 1981. .Fe)AbBSiO+ Amer.. 1992. pp. H. I. Phase transformation in minerals studied by 57F e Mossbauer spectroscopy. V. 57Fe Mbssbauer study on compositions of the series Fe3+Ta04-Fe2+Ta206. S. Sanghani. D. H.. A. Burragato (eds.. C. D. J.. 441-452.. 113. M. Monatsh. Br. Mineral. and LebkitchnerNeugebauer. A. 111. 109. 1346-1354. McCAMMON 347 Experimental techniques for conversion electron Mossbauer spectroscopy. I. 471-478. Mottana and F. 13. (Mg. F. Vol. 7. Chem. W... A. 1966. Hyper. J. G. Wagner (eds. 17. 70. R. Phys. Stevens. Can.E. 1036-1043. J. G. J. 125-177. A. 3.. D. 465-476. Mineral Chemistry of Metal Sulphides. In Mossbatter Isomer Shifts. 120. CRC Press. and Craig. North-Holland Publ. Anal. 119. Isomer Shift Reference Scales. pp. G. Boca Raton. 417-432... 8.W. Stat. Vol. CRC Press. Solids. In CRC Handbook of Spectroscopy. 1985.K.. 123. and Pipkom. J. 13. Inc. and Lefevre. Violet. J. J. C. 1978. Hyper.). E. Stevens. P. L. D. Van der Woude.. Craig J. Mbssbauer effect in a-Fe20s.. J. 520-522. 1972. R. USA. J. . Determination of the quadrupole splitting distributions of the A. 50. H. Amsterdam. 121. H. and absorption area. 1978.. R. 122. Cambridge. 23. 1981. 125. W. 3. Chem.. 1981. The magnetic properties and Miissbauer spectra of synthetic samples of Fe3S4. 1985. 1966. USA..). Stevens. 2313-2326. 126. 75-87...and B-site ferrous ions in Fe2Ti04. Phys. The Mossbatter effect in marcasite structure iron compounds.. Phys. Ujihira.. intensity.. Chem. J. Analytical applications of conversion electron Mdssbauer spectrometry (CEMS). 27. Vaughan.W.. Inter.. J. Cambridge University Press. A. pp. R. 85-92. In CRC Handbook of Spectroscopy.. Trooster.117. Shenoy and F. Effect of sample thickness on the linewidth. 124. Nomenclature and conventions for reporting Mossbauer spectroscopic data. 1985. A. 221-236. and Gettys. pp.. Temperley. Rev. Amer. The crystal chemistry of ironnickel thiospinels. Vanleerberghe. Boca Raton.. and Morrish. J. Y. Robinson (ed. Mineral. and Viegers. Robinson (ed. M. N. 118. M. and Vandenberghe..). G. Vaughan D. Inc. F. Inter.‘E. Vol. Mijssbauer isomer shift reference scales. 1983. Sol. Co. 901906. 214 alkali feldspar. Debye temperature and thermal pressure. 129.3 14-3 18. in press.. and Cabral.. 132. Annersten. A.. D. Ericsson. Eur. Warenborgh. 1977.u6S4 between 10 K and room temperature. H. phase diagrams. 249-252 viscosity. 0. T. and Kato. 91-98. 127. and Imbert. P. crystals. 322 silicate glasses. J.. 1993. bulk moduli. 61. F.5 Si-29 NMR data. Mineral. 1976. J. A Mbssbauer study of natural gahnite spinels showing strongly temperaturedependent quadrupole splitting distributions. Amer. XI.. Phys. 87.. Chem. G.. A. W. and O’Neill.. Mater. F. Mineral. E.. Chalkogenides of the transition elements. M.. C. Amer. P. 325 See also calcium-aluminates aluminosilicates. 274 activation volume. 1990. Wintenberger. St. shear viscosity.+tFeu.. M.. T. 128. 130. Appl. 260-265. Magn. Mossbatter effect study of 57Fe and l19Sn in stat-mite. an intermediate valency Fe compound. 4339-4342.. stannoidite. Subject Index actinides. Figueiredo. J. Gamin. H. and mawsonite... 238 Al-27 NMR spectra... Synthesis and stability of Fes2+Fe23+Si30t2 (“skiagite”) garnet and phase relations with almandine-“ skiagite” solid solutions. Colloq. J. C. 267-271. O. J. Mljssbauer 57Fe spectrum of the spine1 Co2. Applications of Mbssbauer scattering techniques. 238 activation energy. 131. apparent.. Woodhams. 13 1 activation energy. 2. 324 albite phase diagrams. crystals. Magn. 673-689. 1990. Mineral. 123-129.. J. Woodland. Phys. C.Miissbauer line positions and hyperfine interactions in a iron. Can. 3 1. and Knop. Wagner. 42. . Andre. 37. M. 1971. 307. 221-224 aluminates NMR spectra. layer Al-27 NMR data. 3 11 aluminum oxides dimensionless parameters.. Magnetic structure and Mossbauer data of sternbergite AgFe&. 55. apparent. Yamanaka.. 1976. 250 alloys. diffusion. J. M. Perrin. 274 Arrhenius law. 70 amorphous materials bulk moduli. plasticity. Debye temperature and thermal pressure. 69 mantle mineral data. 335-336 black-body emission. spectra. 337 basalt. NMR spectra. 65 mantle mineral data. bulk moduli. 277 Mossbauer spectra. 73 carbides. 3 Mbssbauer spectra. 160 thermal expansion. shock wave equation of state. NMR spectra. 3-4 shock wave equation of state. shear viscosity. dependence on wavelength at different temperatures. 274. 296 calcium aluminates. 300 bonding properties. NMR spectra. 295 beta-spinel. 238 asymmetry parameter. 117-118 carbonates bulk moduli. 117-l 18 high-temperature electrical conductivity.322-325 amphiboles diffusion. Mossbauer spectra. 271 chemical shift. crystals. 297 chemical diffusion. and velocities. 3 18 calcium oxide dimensionless parameters. 304. specific heat. 152-153 carbon-bearing minerals. 85-86 O-l 7 NMR data. 189 mineral data. specific heat. 303. 337 andesite.282-283 Beer-Lambert law. phase diagrams. and velocities. 105-107 mineral data. diffusion. Al-27 NMR data. 320 thermal expansivity. 249-25 1 Arrhenius equation. Miissbauer spectroscopy. Mossbauer spectra. 342 shock wave equation of state. 134 NMR spectra. phase diagrams.306 chemical shift anisotropy. elastic constants. 321-322 charge transfer band. 32 chain silicates bulk moduli. 307 augite. elastic constants. 245 bibliography. 291 borates mineral data. 255 babingtonite. absorption. 336-337 andalusite. 6 O-17 NMR data.75 elastic moduli. minerals. melts. 209-217 anorthite. 215 anelasticity. diffusion. 83 thermal expansivity. 306 . 160 calcite. 76 elastic moduli. mantle minerals. Harper-Dom creep. 5-6 See also ring silicates 349 350 INDEX Debye temperature. 228 corundum phase diagrams. elastic constants. specific heat. viscosity. 46-48 cyclosilicates bulk moduli. 237 crystals. 240 coesite. 245 cross-slip. 68 mantle mineral data. Herring-Nabarro creep creep mechanism. phase diagrams. 297 crystallographic data. mantle . diffusion. l. dislocations. crystals.256 plastic properties. 218-226 correspondence principle. 229 coordination number. mineral data. crystals. phase diagrams. minerals. 254. 72 Coble creep. NMR spectra. quasi steady-state. crystals. 241 deformation mechanism. 25 1 See also aluminum oxide creep. outer. creep. 239 creep. 337 chloritoid. trigonal crystals crystal structure. 253-254 clinopyroxene phase diagrams. and velocities. glide-controlled. 107-l 10 mineral data. 172 convective flow mantle. crystals. 240 mantle viscosity. dislocation creep.17 crystals plastic rheology. shock waves.chlorite. phase diagrams. plastic deformation. 78 elastic moduli. 240 crystal-field absorptions. climb-controlled. 337 clinoenstatite. 7. mantle viscosity.5-79 deformation-mechanism maps. Mossbauer spectra. 337 clay minerals. elasticity. yield strength. 249 critical resolved shear stress. 85 thermal expansivity. elastic moduli. 237-247 See also cubic crystals. Mossbauer spectra. hexagonal crystals. orthorhombic crystals. 244 closure temperature. 249 compression curves. 227 cristobalite. Mossbauer spectra. 307 core. 239-240 creep. power-law dislocations. 227 mantle viscosity. 1-17 cubic crystals. Debye temperature and thermal pressure. 237 See also diffusion creep. 274 cobalt silicate dimensionless parameters. isotropic. mantle viscosity. Group VII. 23 1 effective binary diffusion coefficients. 174-175 Earth-forming minerals phase diagrams. 57-58 crystals. 185 minerals. 273 dislocations. Group I. bulk moduli. 98-101 high-pressure minerals. multicomponent diffusion. 126 elements. 69-74 elasticity.129 elements. bulk moduli. Group V. 245-246 dielectric permittivity. interdiffusion. P and T derivatives. 46 shock wave equation of state. 64-97 melts. 269-290 See also chemical diffusion diffusional flow. crystals. thermodynamic factor. geological materials. bulk moduli. shock waves. 122-123 elements. 270-273 See also chemical diffusion. minerals. 291 elements. Group II. 253-257 plastic properties. effective binary diffusion coefficients. 273 elastic constants. 123 elements. 239 dislocations. 46-56 mantle minerals at high temperature. crystals. Group IV. 227 diffusion coefficients silicates. 126. 240 olivine. tracer diffusion coefficient diffusion creep crystals. 128 elements. bulk moduli. 129 elastic moduh. phenomenological diffusion coefficients. 45-63 elastic limit. Group VI. mantle minerals. 240 diopside phase diagrams. minerals. bulk moduh. 185 diffusion. mantle viscosity. isotropic. 209 electrical conductivity.128 elements. 239 dislocations. 304 multicomponent.viscosity. 146-152 enstatite . bulk moduli. 187-188 electrical properties. 243-244 diffusion silicates. 229 dynamic yielding. 29 l-302 Earth rotation. 227 diamond-anvil cell equations of state. 237 elastic moduli. 128. 244 dislocation creep. crystals. 185-208 electronic transitions. 29 1 point defects. Group III. 248-268 spectra. 239 dynamic topography. mantle viscosity. self-diffusion coefficient. bulk moduli. 3 15 diffusion. 312 ferropseudobrookite.17 NMR data. 3 15 diffusion. 312 viscosity. 214 feldspathoids Al-27 NMR data. 259 ferrosilite. diffusion. phase diagrams. 256 see also iron silicate Fe-57 line positions for 14. 270-27 1 forsterite heat capacity. 337 equations of state shock waves. partial pressure. 23-27 epidote. phase diagrams. 2 l-23 phase transformations. 257 thermal expansivity. 299 phase diagrams. 254-256 thermoelastic properties. 93-94 garnet. 248-252 Si-29 NMR data. 25 plastic properties. 25 gamma-spinel. 205 phase diagrams. 92-93 See also magnesium silicate framework silicates bulk moduh. 98-142 See also Mie-Gruneisen equation of state fayalite crystal field absorption spectra.4 ke V transition. 19 phase diagrams. grossular dimensionless parameters. 83 phase diagrams. 275-276 log electrical conductivity vs. plasticity. 90 minerals. 65 mantle mineral data. 76 elastic moduh. partial pressure. 322 See also tektosilicates fusion. 90 minerals. 244 enthalpy mantle minerals. enthalpy. Mossbauer spectra. 104-105 0. specific heat. 255 Fick’s laws. 143-174 static compression measurements. 335 Miissbauer spectroscopy. 205 Si-29 NMR data. 73 thermoelastic properties. and velocities. 23-27 entropy mantle minerals.phase diagrams. 245-246 garnet. elastic constants. 254-257 phase relations. 2 l-23 phase transformations. 332-335 feldspars Al-27 NMR data. 279 log electrical conductivity vs. majorite . Debye temperature and thermal pressure. 23 glasses bulk moduli. 166. 120-122 elastic moduli. 258-260 Herring-Nabarro creep. crystals. 245-24. 73 garnet diffusion. minerals. 189-190 log electrical conductivity vs. core viscosity. 134 diffusion. I antle. 220 geophysics. 237 Harper-Dom creep. 8-9 shock wave equation of state. 245 garnet. 173 halides bulk moduli. 204 mineral data. 322-325 phase transitions. positive mass anomaly. 337 Grlineisen ratio. mantle viscosity. phase diagrams.168 INDEX 351 glass transition. 255 Helmholtz free energy. and velocities. phase transitions.phase diagrams. 86-87 hematite. mantle viscosity. elastic moduli. 47-48 Mossbauer spectra. partial pressure. 256-257 thermal expansivity. 8 . 56 heat capacity. 45-63 elastic moduli. 269-290 elasticity. 240 hexagonal crystals. 18-21 hedenbergite. 47 high temperature electrical conductivity. shock wave equation of state. 65 mantle mineral data. 253 plasticity. 20 NMR spectra.256-257 gases. heat capacity. 232-234 geomagnetism studies. 304 germanates. 48 high-pressure minerals. specific heat. pyrope-rich dimensionless parameters. vs. 83 phase diagrams. 153-1. phase diagrams. 227 geoid anomaly. Mossbatter spectra. 231 geoid inversion. 76 elastic moduli. high-pressure silicates mineral data. crystals. 25 Gibbs free energy. 304 geodetic studies. mantle minerals. Debye temperature and thermal pressure. 240-241 heat capacity. 239 grandidierite. elastic constants. 337 phase diagrams. 280 elastic moduli. 2 12 shock wave equation of state. 144-145 geochemistry. temperature. crystals. 20-21 grain-boundary sliding. 219 geoid. core viscosity.55 hardening. 248. crystals. core viscosity. 250 Hugoniot equation of state. 186 interdiffusion. 20 NMR spectroscopy. minerals. bulk moduli. phase diagrams. 249-262 jadeite. liquid. crystals. 13 1 . 221-224 liquid metals theory. 223 iron-titanium oxides. Mossbatter spectra. 271 intervalence transitions.0. bulk moduli. shear viscosity. phase diagrams. 11 l-l 17 mineral data. 321 shock wave equation of state. 269-290 heat capacity. 2 12 . 231-232 iron. liquid.133 iron silicate elastic moduli. 68 mantle mineral data. 222 iron-nickel alloys. 133-134 hydrostatic pressure. shear viscosity. 322 hollandite.258-260 iron bulk moduli. 222-223 iron-oxygen alloys. plastic deformation. 303 phase transitions. 338 lanthanides. phase diagrams. bulk moduli.259-260 ilvaite. elastic constants.252 liquid alloys.17 NMR data. Miissbauer spectra. shear viscosity. 72 isopleths. 224 iron-silicon alloys. phase diagrams. Earth-forming minerals. 340 O-17 NMR data. Lik moduli. 342 phase diagrams. 239 Kroger-Vink notation. 143 hydrides. 250. phase diagrams. 248. 224-225 iron-sulfur alloys. thermal expansion. 337 infrared spectroscopy. phase diagrams. 248.262 iron alloys. 342 kinks. 241 hydrous minerals. 249 kamacite. and velocities. liquid. 221 liquids bulk moduli. shear viscosity. 31-32 hydroxides bulk moduli. 130-131 leucite. 85 thermal expansivity. 3 Miissbauer spectra. 134 diffusion. specific heat. 297 inverse problems. 29 l-302 insulators. 13 1 Mossbauer spectra. 159 ices. point defects. 187-188 kyanite. mantle viscosity. shear viscosity. Miissbauer spectra. 133 ilmenite. liquid. liquid. 253. shear dynamic viscosity. specific heat. 79 elastic mod&. strength. 75 elastic moduli. specific heat. 65 mantle mineral data. 227-236 mantle minerals. elastic constants. 7 1 magnetite. Debye temperature and thermal pressure. 258-260 manganese oxide dimensionless parameters. 23-27 melts elasticity. elastic constants. 256 plasticity. 85 thermal expansivity. 303 magnesiowuestite phase diagrams. 245 magnesium aluminum oxide dimensionless parameters. 168 magic angles spinning. 82-83 thermal expansivity. elastic constants. specific heat. specific heat. and velocities. and velocities. 245-246 viscosity. 72 mantle high-pressure minerals. 45-63 elastic moduli. phase diagrams. 78 elastic moduli. NMR spectra. Debye temperature and thermal pressure. 84-85 thermal expansivity. 77 elastic moduli. frequency. entropy. Debye temperature and thermal pressure. 64-97 MAS. 72 manganese silicate dimensionless parameters.lithosphere. 69 thermoelastic properties. 211 lunar glass. 55-56 electrical properties. elastic constants. 67 mantle mineral data. Debye temperature and thermal pressure. 83-84 thermal expansivity. Debye temperature and thermal pressure. vs. 78 elastic moduli. 68 mantle mineral data. 66 thermal expansivity. See magic angles spinning melting. specific heat. 228 longitudinal viscosity. elastic constants. elastic constants. and velocities. and velocities. 92 magnesium silicate dimensionless parameters. 70 magnesium oxide dimensionless parameters. and velocities. shock wave equation of state. 66 mantle mineral data. 185-208 . 67 high-temperature compression creep. 77 elastic moduli. elastic moduli. silicate glasses. 334 Mossbauer spectroscopy. 85 Mijssbauer spectra. and the different mineral groups Mossbauer parameters. 279-280 dimensionless parameters. glasses. 338 . effect of octahedral coordination on d-orbitals. 202-204 mantle mineral data. 186 metals. 338 Mie-Gruneisen equation of state. elastic moduli. bulk moduli. NMR parameters. 242 high-temperature creep laws. 3 19 O-17 NMR spectra. NMR parameters. 98-142 352 INDEX Mossbauer spectroscopy. 186 Newtonian viscosity. 3 NMR spectroscopy. 298 metallic compounds. 185-208 equations of state.322-325 viscosity and anelasticity. 241 diffusion. 129-130 nuclear magnetic resonance spectroscopy. shear viscosity. crystals. 324-325 olivine crystal-field effects. 124-126 mica. 304 0. quadrupolar. 10 nephelinite. 209-217 See also amorphous materials. 332-347 NMR spectra. 305306 nuclides. 175 minerals crystallographic data.NMR spectra. liquids. transition. silicate melts metal cations. 304 phase diagrams. See nuclear magnetic resonance spectroscopy noble gases. 227-228 deformation mechanism map. 332-347 molar volume. 53-54 native elements.17 MAS NMR spectra. Debye temperature and thermal pressure. 21-23 monoclinic crystals. mineral data. bulk moduli. 304. minerals. minerals. 243 log electrical conductivity vs. 45-63 electrical properties. minerals. 143. 298 deformation mechanism. 248-268 shock wave data.184 thermal expansion. 303-33 1 nuclides. spin l/2. 18-28 See also carbon-bearing minerals. shock waves. Mijssbauer spectra. 240 nitrates. Earth-forming minerals.17 elasticity. 29-44 thermodynamic properties. mineral data. hydrous minerals. 1 . 46 metallic conductors. 2 15 Nemst-Einstein relation. partial pressure. elastic moduli. 254 orthopyroxene Miissbauer spectra. mantle viscosity. 303-33 1 partial molar heat capacities.255-256 phase relations. 338 phase diagrams. 46-47 high temperature electrical conductivity. 4-5 O-17 NMR data. 229 point defects. 4 Mossbauer spectra. crystals.phase diagrams. mantle viscosity. Earth-forming minerals. 248. 239 orthoclase oxide. 155-159 thermal expansion.192 log electrical conductivity vs. 51-52 orthosilicates bulk moduli. 2 1 shock wave equation of state. 320 oxides bulk moduli. 187-188 polar wander. electrical conductivity. phase diagrams. 291-302 Orowan’s equation. partial pressure. crystalline Al-27 NMR data. elastic constants. 11 l-l 17 elastic moduli. 238 plasticity. 248. magnesium aluminum oxide. 340 nuclear magnetic resonance spectroscopy. 269-270 244 phlogopite. 297 See also aluminum oxide. phase diagrams. and velocities. 2-3 Mossbauer spectra. 107-l 10 mineral data. 202 point defects. iron-titanium oxide. 252 orthoenstatite. 333 phase diagrams. Mossbauer spectra. Mossbauer spectra. 342 pigeonite. dislocations. 40 oxides. specific heat. 205 mineral data. 190. 188 thermal expansivity. 3 14-3 18 0.26 1 phosphates mineral data. 7 1 optical absorption spectroscopy. 338 oxide components. minerals. 231 .17 NMR data. transformation. 244 orthorhombic crystals. thermal expansion. 321 osumilite. 30-3 1 vibrations. crystals. magnesium phenomenological diffusion coefficients. 254-255 plagioclase. 254-255 plastic properties. 250-25 1 Planck function. See also superplastic deformation plastic instability. phase diagrams. 239 plate velocities. 301 plastic deformation. phase diagrams. 26 point defect model. 245-246 thermal expansion. Earth-forming minerals. 245 Mossbauer spectra. 23 l-232 Mossbauer spectra. crystal-field effects. 253-254 pseudobrookite. Debye temperature and thermal pressure. minerals. melts. 338 phase diagrams. 23-27 phase transitions. Earth-forming minerals. 255 peridot. 259 pyrophyllite. 301 Raman spectroscopy. 227. 248. 174-175 silicate melts. 209 vs. elastic constants. 294 INDEX 353 relaxation mode. 253. phase diagrams. mantle minerals. 2 12 . mantle viscosity. 304 shock waves. 79 elastic moduli. phase diagrams. 74 power-law creep. 87-89 radiative thermal conductivity. temperature. 296 static NMR spectra.255-256 plasticity. 338-339 phase diagrams. NMR spectra. 306 quasiharmonic approximation. 249 plasticity. shock waves. 2 12 phase velocities. and velocities. 38-39 phase diagrams. 29 l-302 Rankine-Hugoniot equations. 238 plastic properties. mantle viscosity. Mossbauer spectra. 244 pargasite. 244 protoenstatite. minerals. 248-268 phase transformations.261 periclase. 66 mantle mineral data. minerals. 248. 275 phase diagrams. 298 perovskite high-temperature compression creep. manganese oxide oxygen fugacity crystals. 172-174 reflection spectra. phase diagrams. 278-279 high-temperature compression creep. plastic properties. 338 pyroxenes diffusion. 209 relaxation time melts. 307 quartz diffusion.232 potassium chloride dimensionless parameters.post-glacial uplift.253-255 quadrupolar coupling constant. 84 thermal expansivity. 29 1 radiative thermal emission. 24 l-242 spectra. specific heat. entropy. phase diagrams. non-Newtonian. 303-331 phase transitions. 250 sapphirine.261 shear stress. phase diagrams.162 Si-29 NMR data. 248. 3 12 silicate melts high temperature electrical conductivity. 293 vibrations. 6-7 shock waves. crystalline Al-27 NMR data. 248-249 shock wave equation of state. 237-247 rheology. 210 silicates. feldspathoids. ice models. critical resolved. 229 seismic tomography. 4-8 diffusion. crystals. 341-342 self-diffusion coefficient. 16 1. 339 phase diagrams. 215 rheology. clinopyroxene. 256 sealevel variations. Mossbauer spectra. phase diagrams. I86 serpentine Mossbauer spectra. phase diagrams.resonant frequency. crystal-field effects. minerals. feldspars. mantle viscosity. 110-l 11 diffusion. Al-27 NMR data. 269-290 high temperature electrical conductivity. 259 sanidine. 274. 211 sheet silicates bulk moduli. shear viscosity. core viscosity. 303 rheology. 192-200 Miissbauer spectra. See also gamma-spine1 ruby. 307-3 13 silicate glasses. . chain silicates. 227 rhyolite diffusion. 143-l 84 Si-29 NMR spectra. 298 rutile. 201 longitudinal viscosity vs. 2 15 ring silicates bulk moduli. melts. 27 1 semiconductors. 3 15 silica polymorphs diffusion. frequency. 220 selenides. 275 phase diagrams. mantle viscosity. crystals. 33-38 vibration of tetrahedra. cobalt silicate. 322-324 silica analogs.166 thermal expansion. 162. 19-27 shock wave equation of state. 314-318 Si-29 NMR data. 239 shear viscosity. 107-l 10 See also cyclosilicates ringwoodite. 229 seismological studies. vs.28 l-282 shear viscosity. 336-339 nuclear magnetic resonance spectroscopy. 297 See also amphiboles. 308-3 13 silicates crystallographic properties. 277 mineral data. plastic. 339 Sn. Mossbauer spectra. 47 mineral data. phase diagrams. 238 stress creep curve. 303 standard materials. 238 stress exponent climb-controlled creep. 244 sulfates mineral data. manganese silicate. Miissbauer spectra. 339 phase diagrams. 249. 168-171 static compression tests. gamma-spinel. MSssbauer spectra. 107-l 10 mineral data. 79 elastic moduli. 5-6 specific heat. 3 19 elastic moduli. 339 stishovite. 69-74 spine1 Al-27 MAS spectra. silica polymorphs. 74 sorosilicates bulk moduli. Mossbauer spectra. 332-335 sodium chloride dimensionless parameters. mantle minerals. and velocities. 98. Debye temperature and thermal pressure. specific heat. ring silicates. 240 plastic properties. time. 339 phase diagrams. 256 smectite. sheet silicates. olivine.10 Mossbauer spectra. 33 sulfides bulk moduli. Mossbauer spectroscopy. 210 stress-strain curve crystals. elastic constants. 192 mantle mineral data. 66 mantle mineral data. 83 Mossbauer spectra.framework silicates. ulvospinel spin quantum number. 342 talc. 237 plastic solid. See tektosilicates . 253 strain. 253.120 elastic moduli. 47 high temperature electrical conductivity. 239 taenite. 9. shock wave equation of state. pyroxenes. orthopyroxene. 84 thermal expansivity. sorosilicates sillimanite Miissbauer spectra. 4 MSssbauer spectra. 342 shock wave equation of state. magnesium silicate. crystals. equations of state.142 staurolite. 118. 160 thermal expansion. plastic solid. 245 See also beta-spinel. iron silicate. 339 tectosilicates. 33 superplastic deformation. 341-342 thermal expansion. vs.255-256 plasticity. orthosilicates.119. geological materials. 214 temperate dependence. dynamic. crystals. mantle minerals. elastic moduli. phase transitions. minerals. quartz. 241 quartz.174 thermoelastic dimensionless parameters. 27 . mantle minerals. 304 volume viscosity. melts. minerals. 175 tetragonal crystals. Mossbauer spectra. Raman spectroscopy vibrational spectrum. 339 water-weakening. 227-236 mantle models. 28 1 Mossbauer spectra. mantle minerals. non-Newtonian. 29 thermal pressure. vs. 211 wadsleyite. 172. high-temperature. shear viscosity. 291 virtitication. 25 titanite diffusion. 118-120 Miissbauer spectra. 84-94 minerals. crystals. 237 mantle. Miissbauer spectra. 75-82 thermoelastic properties. 29-44 mantle minerals. 69-74 vibrational spectroscopy 354 INDEX minerals. 50 thermal expansion geological materials. 2 13-2 14 See also longitudinal viscosity. 9 1-94 tholeiite. enthalpy. 271 transmission electron microscopy high-pressure minerals. phase diagrams. 69-74 thermal expansivity. elastic moduli. shock waves. 249 trigonal crystals. 75-79 thermobarometry. 273 thermodynamic properties mantle minerals. outer core. 339 tracer diffusion coefficient. 242 tridymite. 341-342 temperature. 230 melts. 237 viscosity. 241 water high pressure electrical conductivity vs. 49 tungstates. Miissbauer spectra. 206 phase relations. 25 viscoelasticity. Newtonian.tektosilicates. 215 tin. mineral data. 218-226 viscosity. 209 viscosity. frequency. 209-217 pressure dependence. mantle minerals. 7-8 tellurides bulk moduli. phase diagrams. 342 ulvospinel. 259-260 velocity. diffusion. 18 thermodynamic factor. 245-246 plastic deformation. 248 thermochemical properties. density. Newtonian viscosity. shear viscosity. volume viscosity viscous flow. 18-28. 343 titanates. 29 1-297 See also infrared spectroscopy. crystals.silicate glasses. 258-260 X-ray diffraction data. phase diagrams. phase diagrams. 28 1 . 3 12 zircon. 237 yoderite. 257 wuestite. 24 1 yield stress. 1-17 yield point. minerals. Mossbauer spectra. 3 16 S-29 NMR data. diffusion. 324-325 wollastonite. quartz. 339 zeolites Al-27 NMR data.