ARTICLE IN PRESSJournal of Physics and Chemistry of Solids 69 (2008) 967–974 www.elsevier.com/locate/jpcs Formability of ABO3 cubic perovskites L.M. Feng, L.Q. Jiang, M. Zhu, H.B. Liu, X. Zhou, C.H. Lià College of Material Science and Engineering, Shanghai University, Shanghai 200072, China Received 29 September 2006; received in revised form 30 October 2007; accepted 3 November 2007 Abstract In this study, 223 binary oxide systems (of which, 34 systems can form cubic perovskites) are collected to explore the regularity of cubic perovskites formability. It is found that the octahedral factor (rB/rO) take the same important role as the tolerance factor (t) to form cubic perovskites in complex oxide system. Regularities governing cubic perovskites formability are obtained by using empirical structure map constructed by these two parameters, on this structure map, sample points representing systems of forming (cubic structure) and non-forming are distributed in distinctively different regions. Prediction criteria for the formability of cubic perovskites are squeezed out, which may be applied to design new substrate or buffer materials with cubic perovskite structure in compound semiconductor epitaxy. r 2007 Elsevier Ltd. All rights reserved. Keywords: A. Oxide; A. Inorganic compounds; D. Crystal structure; D. Phase equilibria; D. Phase transitions 1. Introduction Perovskite is named after a Russian geologist, Count Lev Aleksevich von Perovski [1]. It is one of the most frequently encountered structures in solid-state inorganic compound [2]. Cubic perovskite structure is an ideal perovskite structure, which has ABX3 stoichiometry and cubic crystal structure, as seen in Fig. 1, where, A is a bigger cation (such as Na1+, K1+, Ca2+, Sr2+, Ba2+), B is a smaller cation (such as Ti4+, Nb5+, Mn4+, Zr4+), and X is an anion (such as O2À, F1À, Cl1À) [3–5]. Cubic perovskites are important crystal structure due to their diverse physical/ chemical properties over a wide temperature range. For example, BaCeO3, SrZrO3 have been known as protonic conductor; SrSnO3 and BaSnO3 are sensitive to humidity and oxygen gas, so they can be used as humidity or oxygen sensor. Furthermore, some cubic perovskites exhibit ferromagnetic (such as SrCoO3), ferroelectrics, and dielectric properties [1–4]. Compound semiconductors of III–V group, like GaAs, GaN, and InP, attract increasing attentions because of their high carrier mobility, wide and direct band gap. However, it is still a challenge to fabricate large and high ÃCorresponding author. Tel./fax: +86 21 56332934. E-mail address:
[email protected] (C.H. Li). 0022-3697/$ - see front matter r 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.jpcs.2007.11.007 quality of their heteroepitaxial film, due to lattice mismatch and thermal expansion mismatch between the film and the growth substrate or buffer materials. As one of the most abundant and widely investigated minerals, perovskites compounds are widely studied as the candidate materials of substrate or buffer materials. For example, cubic perovskites has recently gained widespread usage as a substrate or buffer material for the heteroepitaxial growth of high temperature superconductors and other oxide thin films [6]. A perovskite-type crystal (orthorhombic distorted perovskites), NdGaO3, was reported as a succeeded candidate for the GaN substrate [7]; (La,Sr)(Al,Ta)O3 (LSAT) [8] and (RE,Sr)(Al,Ta)O3 (RE, rare earth elements) [9], the mixed perovskite-type crystal, have very good characteristics to be a substrate since it has a fairly small lattice mismatch with GaN. In general, the semiconductor, which has blende structure, can grow on the substrate or buffer layers with cubic structure [10]. The recent success of fabricating large GaAs MESFETs on Si substrates using an SrTiO3 (cubic perovskites) as buffer layer increases the interest of investigating cubic perovskites [11]. Therefore, lots of researchers try to design and synthesize new cubic perovskites used as buffer materials. Obviously, if new cubic perovskites compounds and their lattice constants can be predicted, it is helpful to design new substrate or buffer materials with cubic perovskite ARTICLE IN PRESS 968 L.M. Feng et al. / Journal of Physics and Chemistry of Solids 69 (2008) 967–974 Fig. 1. Ideal perovskite structure illustrated for ABO3. structure. In our previous study [12], a prediction model of lattice constant in cubic perovskites ABX3 was obtained by using two parameters, the sum of ionic radius of B and X atoms and the ‘‘tolerance factor’’ (t ¼ (rA+rX)/ [21/2(rB+rX)]), the lattice constant can be predicted by this model with an average error of 0.63%. So, it is of practical and emergent to find out regularities governing the formation of cubic perovskite-type compounds in order to seek for new buffer materials or substrates for compound semiconductor direct growth. Muller and Roy [2] proposed to plot ‘‘structural map’’, which took the ionic radius of A and B as coordinates to study the distribution of different structures for many ternary structural families. Furthermore, the schematic distribution map of different crystal structure for A1+B5+O3, A2+B4+O3, and A3+B3+O3 systems separately, were given by the same method [2,13]. However, the criterion for cubic perovskites formability was not discussed, possibly due to the lack of accurate data of crystal structure of some ABO3 compounds at that time. In our previous research, we have investigated the regularities governing perovskites formation by using empirical structure map methods and a total 197 binary oxide systems in 2003 [14]. It is found that the octahedral factor (rB/rO) is as important as the tolerance factor (t ¼ (rA+rO)/[21/2(rB+rO)]), with regard to the formability of perovskites. Prediction criterions for the formability of perovskites are obtained by using these two parameters. In this study, the same method will be used to find the regularities governing cubic perovskites formability. 2. tÀrB/rO structural map method In 1926, Goldschmidt had used ‘‘tolerance factor’’ (t ¼ (rA+rO)/[21/2(rB+rO)]) to study the stability of per- ovskites, where rA, rB, and rO are the ionic radii of A, B, and O, respectively. Geometrically, for the ideal perovskites, the ratio of D(A–O) (the bond length of A–O) to pffiffiffi D(B–O) (the bond length of B–O bond) is 2 : 1. Thus, if the bond length is roughly assumed to be the sum of two ionic radius, the t value of a cubic perovskites should be equal to 1.0. Goldschmidt found that, t values of cubic perovskites are in the range of 0.8–0.9. Goldschmidt’s tolerance factor t has been widely accepted as a criterion for the formation of the perovskite structure, many researchers have used it to discuss the cubic perovskites stability, and therefore, it is an important factor for the stability of cubic perovskites, so tolerance factor t constructs one axe of the structure map. However, up to now, it seems that t is not a sufficient condition for the formation of the cubic perovskite structure, for example, in many systems whose t are even with in the range (0.8–0.9), no cubic perovskite structure is stable, such as, LaVO3, DyMnO3, and CaMoO3, as seen in Table 1. So, another important factor governing formability of cubic perovskites should be introduced. As seen in Fig. 1, the cubic perovskite structure is composed of a three-dimensional framework of cornersharing BO6 octahedron. The A-site cation fills the 12 coordinate cavities formed by the BO3 network and is surrounded by 12 equidistant anions. So, the octahedron BO6 is the basic mosaic or unit for cubic perovskites. It is well known that coordination polyhedron has been used to studying the stability of ionic compounds in solid-state inorganic chemistry. In general, if one cation (M) and six anions (X) form an octahedron MX6, the value of the ratio of their ionic radius rM/rX (rM and rX are ionic radius of cation M and anions X, respectively) should be varied with the limited range 0.414–0.732 (we called this factor as the octahedron factors) [4], so the octahedron factor (rB/rO) is as important as the tolerance factor to form cubic perovskites. As mentioned above, in our previous work, the tolerance factor and the octahedron factor are used to span two-dimension structural map to study the formability of perovskites, systems of forming perovskites are successfully distinguished with ones of non-forming perovskites. This success encourages us to use this kind of structural map to investigate the formability of cubic perovskites. 3. Data collection A total of 223 binary oxide systems are collected, as seen in Table 1, of which, 34 systems (denote ‘‘y’’) are found to have cubic perovskite structure, 189 systems (denote ‘‘n’’) cannot form cubic perovskite structure. It is well known, a crystal structure can change with variation of temperature and/or pressure. Compounds with other structure can, therefore, transform into cubic perovskite structure, and vice verse at different temperature and/or pressure. So, the criterion for classifying a forming system is that a compound of cubic perovskites is stabilized at room temperature and one atmosphere pressure. In the 189 ARTICLE IN PRESS L.M. Feng et al. / Journal of Physics and Chemistry of Solids 69 (2008) 967–974 Table 1 Formability, ionic radius, tolerance factor, and octahedral factor of 223 binary oxides systems No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 Systems Cs2O–I2O5 K2O–Ta2O5 BaO–MoO2 BaO–SnO2 CaO–CeO2 BaO–ZrO2 SrO–TiO2 SrO–SnO2 BaO–PbO2 BaO–PuO2 BaO–PrO2 BaO–CeO2 Rb2O–I2O5 K2O–I2O5 SrO–ZrO2 SrO–RuO2 Rb2O–U2O5 K2O–U2O5 Rb2O–Pa2O5 K2O–Pa2O5 BaO–NbO2 BaO–HfO2 SrO–VO2 SrO–NbO2 BaO–TbO2 BaO–AmO2 BaO–NpO2 BaO–PaO2 SrO–MoO2 SrO–CoO2 SrO–FeO2 SrO–HfO2 BaO–ThO2 EuO–TiO2 CaO–VO2 BaO–FeO2 CaO–ZrO2 La2O3–V2O3 Dy2O3–Mn2O3 CaO–ThO2 CdO–ThO2 CdO–CeO2 MgO–CeO2 SrO–ThO2 Ce2O3–Ga2O3 Ce2O3–Fe2O3 Gd2O3–Mn2O3 BaO–UO2 Eu2O3–Cr2O3 La2O3–Rh2O3 La2O3–Ti2O3 Nd2O3–Co2O3 Nd2O3–Mn2O3 Sm2O3–V2O3 PbO–ZrO2 Ce2O3–V2O3 Ce2O3–Cr2O3 Pu2O3–Mn2O3 Pr2O3–Mn2O3 BaO–TiO2 CaO–TiO2 Ce2O3–Al2O3 Eu2O3–Al2O3 Formabilitya y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y n n n n n n n n n n n n n n n n n n n n n n n n n n n n n ˚ rA (A) 1.67 1.38 1.35 1.35 1.00 1.35 1.18 1.18 1.35 1.35 1.35 1.35 1.52 1.38 1.18 1.18 1.52 1.38 1.52 1.38 1.35 1.35 1.18 1.18 1.35 1.35 1.35 1.35 1.18 1.18 1.18 1.18 1.35 1.17 1.00 1.35 1.00 1.03 0.91 1.00 0.74 0.74 0.72 1.18 1.01 1.01 0.94 1.35 0.95 1.03 1.03 0.98 0.98 0.96 1.19 1.01 1.01 1.00 0.99 1.35 1.00 1.01 0.95 ˚ rB (A) 0.95 0.64 0.65 0.69 0.87 0.72 0.61 0.69 0.78 0.86 0.85 0.87 0.95 0.95 0.72 0.62 0.76 0.76 0.78 0.78 0.68 0.71 0.58 0.68 0.76 0.85 0.87 0.9 0.65 0.65 0.59 0.71 0.94 0.61 0.58 0.59 0.72 0.64 0.58 0.94 0.94 0.87 0.87 0.94 0.62 0.55 0.58 0.89 0.62 0.67 0.67 0.55 0.58 0.64 0.72 0.64 0.62 0.58 0.58 0.61 0.61 0.54 0.54 t 0.924 0.964 0.949 0.93 0.748 0.917 0.908 0.873 0.892 0.86 0.864 0.857 0.879 0.836 0.861 0.903 0.956 0.91 0.947 0.902 0.935 0.922 0.921 0.877 0.9 0.864 0.857 0.845 0.89 0.89 0.917 0.865 0.831 0.904 0.857 0.977 0.8 0.842 0.825 0.725 0.647 0.667 0.66 0.78 0.844 0.874 0.836 0.849 0.823 0.83 0.83 0.863 0.85 0.818 0.864 0.835 0.844 0.857 0.854 0.967 0.844 0.878 0.857 rB/rO 0.679 0.457 0.464 0.493 0.621 0.514 0.436 0.493 0.557 0.614 0.607 0.621 0.679 0.679 0.514 0.443 0.543 0.543 0.557 0.557 0.486 0.507 0.414 0.486 0.543 0.607 0.621 0.643 0.464 0.464 0.421 0.507 0.671 0.436 0.414 0.421 0.514 0.457 0.414 0.671 0.671 0.621 0.621 0.671 0.443 0.393 0.414 0.636 0.443 0.479 0.479 0.393 0.414 0.457 0.514 0.457 0.443 0.414 0.414 0.436 0.436 0.386 0.386 Ref. [3,5] [3,5] [3,5] [3,5] [3] [3,5] [3,5] [3,5] [3,5] [3,5] [3,5] [3,5] [5] [5] [5] [5] [5] [5] [5] [5] [5] [5] [5] [5] [5] [5] [5] [5] [5] [5] [5] [5] [5] [5] [15] [16] [17] [18] [19] [3] [3] [3] [3] [3] [3] [3] [3] [3] [3] [3] [3] [3] [3] [3] [3] [3] [3] [2] [2,3] [2,3] [2,3] [2,3] [2,3] 969 ARTICLE IN PRESS 970 Table 1 (continued ) No. 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 Systems Eu2O3–Fe2O3 Gd2O3–Al2O3 Gd2O3–Cr2O3 Gd2O3–Fe2O3 K2O–Nb2O5 La2O3–Al2O3 La2O3–Cr2O3 La2O3–Fe2O3 La2O3–Ga2O3 Na2O–Ta2O5 Nd2O3–Al2O3 Nd2O3–Cr2O3 Nd2O3–Fe2O3 Pr2O3–Al2O3 Pr2O3–Cr2O3 Pr2O3–Fe2O3 Pr2O3–Ga2O3 Pr2O3–V2O3 Sm2O3–Al2O3 Sm2O3–Co2O3 Sm2O3–Fe2O3 Y2O3–Al2O3 Y2O3–Cr2O3 Y2O3–Fe2O3 Na2O–Nb2O5 Na2O–U2O5 Na2O–V2O5 Ag2O–V2O5 Ag2O–Ta2O5 Ag2O–Nb2O5 Ag2O–Sb2O5 Tl2O–I2O5 CaO–MoO2 CaO–RuO2 CaO–SnO2 SrO–CeO2 SrO–PbO2 CaO–UO2 CaO–HfO2 PbO–CeO2 PbO–TiO2 CaO–PbO2 CaO–MnO2 Sm2O3–Cr2O3 Er2O3–Fe2O3 Er2O3–V2O3 Ho2O3–Fe2O3 La2O–Mn2O3 Nd2O3–Ni2O3 Nd2O3–Ti2O3 Nd2O3–V2O3 Pr2O3–Ni2O3 Sm2O3–Ni2O3 Sm2O3–Ti2O3 Tb2O3–Fe2O3 Tb2O3–V2O3 Tm2O3–Fe2O3 Tm2O3–V2O3 Yb2O3–Fe2O3 Yb2O3–V2O3 Lu2O3–Al2O3 Y2O3–Ti2O3 Gd2O3–Ti2O3 Yb2O3–Al2O3 Formabilitya n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n ˚ rA (A) 0.95 0.94 0.94 0.94 1.38 1.03 1.03 1.03 1.03 1.02 0.98 0.98 0.98 0.99 0.99 0.99 0.99 0.99 0.96 0.96 0.96 0.90 0.90 0.90 1.02 1.02 1.02 1.15 1.15 1.15 1.15 1.50 1.00 1.00 1.00 1.18 1.18 1.00 1.00 1.19 1.19 1.00 1.00 0.96 0.89 0.89 0.89 1.03 0.98 0.98 0.98 0.99 0.96 0.96 0.92 0.92 0.88 0.88 0.86 0.86 0.86 0.90 0.94 0.86 ˚ rB (A) 0.55 0.54 0.62 0.55 0.64 0.54 0.62 0.55 0.62 0.64 0.54 0.62 0.55 0.54 0.62 0.55 0.62 0.64 0.54 0.55 0.55 0.54 0.62 0.55 0.64 0.76 0.54 0.54 0.64 0.64 0.6 0.95 0.65 0.62 0.69 0.87 0.78 0.89 0.71 0.87 0.61 0.78 0.53 0.62 0.55 0.64 0.55 0.58 0.56 0.67 0.64 0.56 0.56 0.67 0.55 0.64 0.55 0.64 0.55 0.64 0.54 0.67 0.67 0.54 t 0.852 0.853 0.819 0.849 0.964 0.886 0.851 0.881 0.851 0.839 0.867 0.833 0.863 0.871 0.837 0.867 0.837 0.828 0.86 0.856 0.856 0.838 0.805 0.834 0.839 0.792 0.882 0.929 0.884 0.884 0.902 0.873 0.828 0.84 0.812 0.804 0.837 0.741 0.804 0.807 0.911 0.778 0.879 0.826 0.83 0.794 0.83 0.868 0.859 0.813 0.825 0.862 0.851 0.806 0.841 0.804 0.827 0.79 0.82 0.783 0.824 0.786 0.799 0.824 rB/rO 0.393 0.386 0.443 0.393 0.457 0.386 0.443 0.393 0.443 0.457 0.386 0.443 0.393 0.386 0.443 0.393 0.443 0.457 0.386 0.393 0.393 0.386 0.443 0.393 0.457 0.543 0.386 0.386 0.457 0.457 0.429 0.679 0.464 0.443 0.493 0.621 0.557 0.636 0.507 0.621 0.436 0.557 0.379 0.443 0.393 0.457 0.393 0.414 0.4 0.479 0.457 0.4 0.4 0.479 0.393 0.457 0.393 0.457 0.393 0.457 0.386 0.479 0.479 0.386 Ref. [2,3] [2,3] [2,3] [2,3] [2,3] [2,3] [2,3] [2,3] [2,3] [2,3] [2,3] [2,3] [2,3] [2,3] [2,3] [2,3] [2,3] [2,3] [2,3] [2,3] [2,3] [2,3] [2,3] [2,3] [14] [14] [14] [14] [14] [14] [14] [14] [14] [14] [14] [14] [14] [14] [14] [14] [14] [14] [14] [14] [14] [14] [14] [14] [14] [14] [14] [14] [14] [14] [14] [14] [14] [14] [14] [14] [14] [14] [14] [14] L.M. Feng et al. / Journal of Physics and Chemistry of Solids 69 (2008) 967–974 ARTICLE IN PRESS L.M. Feng et al. / Journal of Physics and Chemistry of Solids 69 (2008) 967–974 Table 1 (continued ) No. 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 Systems Bi2O3–Fe2O3 La2O3–Co2O3 La2O3–Cu2O3 La2O3–Ni2O3 Dy2O3–Fe2O3 Lu2O3–Fe2O3 Bi2O3–Al2O3 Dy2O3–Cr2O3 Er2O3–Cr2O3 Yb2O3–Cr2O3 Ho2O3–Cr2O3 Tm2O3–Al2O3 La2O3–Y2O3 Tm2O3–Cr2O3 Lu2O3–Cr2O3 Er2O3–Al2O3 Dy2O3–Al2O3 Nd2O3–Ga2O3 Gd2O3–Ga2O3 Eu2O3–Ga2O3 Ho2O3–Al2O3 Li2O–Nb2O5 Li2O–Ta2O5 Li2O–V2O5 Rb2O–Nb2O5 Li2O–As2O5 Rb2O–Ta2O5 Cs2O–Nb2O5 K2O–As2O5 K2O–V2O5 Na2O–As2O5 Na2O–P2O5 Cs2O–V2O5 Cu2O–P2O5 K2O–P2O5 Li2O–P2O5 Tl2O–Sb2O5 Na2O–Sb2O3 Li2O–Sb2O5 K2O–Sb2O5 Na2O–Bi2O5 Li2O–Bi2O5 Ag2O–Bi2O5 BaO–GeO2 CaO–SiO2 CoO–TiO2 MgO–GeO2 MgO–TiO2 MnO–TiO2 ZnO–TiO2 FeO–TiO2 NiO–TiO2 FeO–SiO2 ZnO–SiO2 MnO–GeO2 MgO–SnO2 SrO–SiO2 EuO–SiO2 SmO–SiO2 BaO–SiO2 CoO–SiO2 SnO–PbO2 NiO–SiO2 PbO–SiO2 Formabilitya n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n ˚ rA (A) 1.03 1.03 1.03 1.03 0.91 0.86 1.03 0.91 0.89 0.86 0.89 0.88 1.03 0.88 0.86 0.89 0.91 0.98 0.94 0.95 0.89 0.76 0.76 0.76 1.52 0.76 1.52 1.67 1.38 1.38 1.02 1.02 1.67 0.77 1.38 0.76 1.5 1.02 0.76 1.38 1.02 0.76 1.15 1.35 1.00 0.65 0.72 0.72 0.83 0.74 0.61 0.69 0.61 0.74 0.83 0.72 1.18 1.17 1.19 1.35 0.65 0.93 0.69 1.19 ˚ rB (A) 0.55 0.55 0.73 0.56 0.55 0.55 0.54 0.62 0.62 0.62 0.62 0.54 0.9 0.62 0.62 0.54 0.54 0.62 0.62 0.62 0.54 0.64 0.64 0.54 0.64 0.46 0.64 0.64 0.46 0.54 0.46 0.38 0.54 0.38 0.38 0.38 0.6 0.6 0.6 0.6 0.76 0.76 0.76 0.53 0.4 0.61 0.53 0.61 0.61 0.61 0.61 0.61 0.4 0.4 0.53 0.69 0.4 0.4 0.4 0.4 0.4 0.78 0.4 0.4 t 0.881 0.881 0.807 0.877 0.838 0.82 0.886 0.809 0.802 0.791 0.802 0.831 0.747 0.798 0.791 0.835 0.842 0.833 0.819 0.823 0.835 0.749 0.749 0.787 1.012 0.821 1.012 1.064 1.057 1.013 0.92 0.961 1.119 0.862 1.104 0.858 1.025 0.856 0.764 0.983 0.792 0.707 0.835 1.008 0.943 0.721 0.777 0.746 0.785 0.753 0.707 0.735 0.79 0.841 0.817 0.717 1.014 1.01 1.017 1.08 0.805 0.756 0.821 1.017 rB/rO 0.393 0.393 0.521 0.4 0.393 0.393 0.386 0.443 0.443 0.443 0.443 0.386 0.643 0.443 0.443 0.386 0.386 0.443 0.443 0.443 0.386 0.457 0.457 0.386 0.457 0.329 0.457 0.457 0.329 0.386 0.329 0.271 0.386 0.271 0.271 0.271 0.429 0.429 0.429 0.429 0.543 0.543 0.543 0.379 0.286 0.436 0.379 0.436 0.436 0.436 0.436 0.436 0.286 0.286 0.379 0.493 0.286 0.286 0.286 0.286 0.286 0.557 0.286 0.286 Ref. [14] [14] [14] [14] [14] [14] [14] [14] [14] [14] [14] [14] [14] [14] [14] [14] [14] [14] [14] [14] [14] [14] [14] [14] [14] [14] [14] [14] [14] [14] [14] [14] [14] [14] [14] [14] [14] [14] [14] [14] [14] [14] [14] [14] [14] [14] [14] [14] [14] [14] [14] [14] [14] [14] [14] [14] [14] [14] [14] [14] [14] [14] [14] [14] 971 ARTICLE IN PRESS 972 Table 1 (continued ) No. 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 a L.M. Feng et al. / Journal of Physics and Chemistry of Solids 69 (2008) 967–974 Systems MgO–SiO2 SrO–GeO2 PbO–GeO2 CdO–GeO2 CaO–GeO2 BaO–MnO2 CoO–MnO2 NiO–MnO2 La2O3–B2O3 Sc2O3–B2O3 Sm2O3–B2O3 Al2O3–B2O3 Ga2O3–Al2O3 Eu2O3–Ln2O3 Dy2O3–B2O3 Er2O3–B2O3 Eu2O3–B2O3 Gd2O3–B2O3 Ho2O3–B2O3 Y2O3–B2O3 Yb2O3–B2O3 Bi2O3–Sm2O3 V2O3–Cr2O3 V2O3–Al2O3 As2O3–B2O3 Gd2O3–Y2O3 Sm2O3–Y2O3 Tm2O3–B2O3 In2O3–Cr2O3 In2O3–Fe2O3 K2O–Bi2O5 Sc2O3–Al2O3 Formabilitya n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n ˚ rA (A) 0.72 1.18 1.19 1.10 1.00 1.35 0.65 0.69 1.03 0.75 0.96 0.54 0.62 0.95 0.91 0.89 0.95 0.94 0.89 0.90 0.86 1.03 0.64 0.64 0.58 0.94 0.96 0.88 0.80 0.80 1.38 0.75 ˚ rB (A) 0.4 0.53 0.53 0.53 0.53 0.53 0.53 0.53 0.23 0.23 0.23 0.23 0.54 0.8 0.23 0.23 0.23 0.23 0.23 0.23 0.23 0.96 0.62 0.54 0.23 0.9 0.9 0.23 0.62 0.55 0.76 0.54 t 0.833 0.945 0.949 0.916 0.879 1.008 0.751 0.766 1.054 0.933 1.024 0.842 0.736 0.755 1.002 0.993 1.019 1.015 0.993 0.998 0.98 0.728 0.714 0.744 0.859 0.719 0.726 0.989 0.77 0.798 0.91 0.784 rB/rO 0.286 0.379 0.379 0.379 0.379 0.379 0.379 0.379 0.164 0.164 0.164 0.164 0.386 0.571 0.164 0.164 0.164 0.164 0.164 0.164 0.164 0.686 0.443 0.386 0.164 0.643 0.643 0.164 0.443 0.393 0.543 0.386 Ref. [14] [14] [14] [14] [14] [14] [14] [14] [14] [14] [14] [14] [14] [14] [14] [14] [14] [14] [14] [14] [14] [14] [14] [14] [14] [14] [14] [14] [14] [14] [21] [14] ‘‘y’’ represents that binary oxide systems can form cubic perovskite; ‘‘n’’ represents that binary oxide systems cannot form cubic perovskite. systems which cannot form cubic perovskites, 114 systems (from no. 35 to no. 148) have distorted perovskite structure (14 structures resulted by the BO6 octahedron tilting), 75 systems (from no. 149 to no.223) are not perovskite structure and represent at least one of following three condition: (1) there is no new ternary compound; (2) there are new ternary compounds but their is no oxide of the chemical formula ABO3 and (3) there is at least one ABO3 compound but it is not a cubic perovskite structure. Two hundred and twenty-three binary oxides systems with their formability, ionic radius of constituent ions A and B, tolerance factor, the octahedral factor (the ratio of radius of the small cation B over the radii of anion O) and references are listed in Table 1. The ionic radius used here are the values for six coordination number (shannon’s value), which are complemented from Crystal chemistry [5] and Perovskites and high Tc superconductor [3], the ionic ˚ radii of O2À is 1.4 A. 4. Results and discussions A structure map is constructed by the tolerance factor t and the octahedral factor (rB/rO) to study the cubic perovskites formability. As shown in Fig. 2, all cubic perovskites and non-cubic perovskites are located in two different regions, and a clear border between two kinds of compounds is identified. The criterion of cubic perovskites formability is, then, expressed by the following equations: rB ¼ 0:414, (1) rO rA þ rO pffiffiffi ¼ 0:815, 2ðrB þ rO Þ rA þ rO pffiffiffi ¼ 0:964, 2ðrB þ rO Þ rB rA þ rO ¼ À2:0645 pffiffiffi þ 2:29. rO 2ðrB þ rO Þ (2) (3) (4) For all the 34 cubic perovskites compounds, only one compound, CaCeO3, is wrongly discriminated as a ‘‘noncubic perovskites’’. It is not clear why our model does not work for it. The tolerance factor is a widely used parameter in perovskites study, which takes all the ionic radii into ARTICLE IN PRESS L.M. Feng et al. / Journal of Physics and Chemistry of Solids 69 (2008) 967–974 973 0.8 CaCeO3 BaUO3 TlIO3 PbZrO3 KBiO3 PbTiO3 KNbO3 0.7 0.6 Octahedral factor 0.5 0.4 0.3 0.2 0.1 0 0.6 0.7 0.8 0.9 Tolerance factor 1 1.1 1.2 cubic perovskites can not for mcubic perovskites Fig. 2. Classification of cubic perovskite oxides. consideration. It can be defined as rA þ rO t ¼ pffiffiffi . 2ðrB þ rO Þ (5) And it is known that almost all perovskites have a t value ranging from 0.75 to 1.00. According to Goldschmidt’s point, t values of cubic perovskites are in the range of 0.8–0.9. However, t values of 17 cubic perovskites oxides, half of all cubic perovskites, are not in the range of 0.8–0.9, as seen in Table 1. From Fig. 2, it is indicated that t values of cubic perovskites, except CaCeO3, are in the range of 0.815–0.964, which is wider than Goldschmidt’s range. However, t ¼ 0.815–0.964 is a necessary but not a sufficient condition for the formation of the cubic perovskite structure. The 102 systems, the t values of which are in the range (0.815–0.964), cannot form cubic perovskite structure. 82 systems among them have distorted perovskite structure, while 20 systems cannot form perovskites, as seen in Table 1. Octahedral factor (rB/rO) is introduced into prediction of cubic perovskites formation. In our structure map (Fig. 2), the lowest limit of the octahedral factor (rB/rO) for cubic perovskites formation is 0.414, and the highest rB/rO value of cubic perovskites is 0.6785. It is well known that rM/rX value of octahedron MX6 is ranging from 0.414 to 0.732 [4], the values of rB/rO for all 34 cubic perovskites are in this range. However, octahedral factor (rB/rO value is not less 0.414) also is a necessary but not a sufficient condition for the formation of the cubic perovskite structure. The 100 systems in the range (rB/rO is not less 0.414) cannot form cubic perovskite structure, as seen in Table 1, of which, 72 systems have distorted perovskite structure and 28 systems cannot form perovskite structure. The criteria of cubic perovskites formability are shown in Fig. 2 constructed with the tolerance factor t and the octahedral factor (rB/rO). From this figure, it can be seen that only five systems of all 189 ‘‘non-cubic perovskites’’, including BaUO3, TlIO3, KBiO3, PbZrO3, and PbTiO3, are wrongly classified in ‘‘cubic perovskites’’ region by the criterion mentioned above. However, BaUO3, TlIO3, KBiO3, PbZrO3, and PbTiO3 have a structure close to cubic perovskite structure. BaUO3 and PbZrO3 have pseudocubic perovskite structure [3]; TlIO3 has rhombohedral perovskite structure with a ¼ 89.341 (very close to 901) [3]; PbTiO3 has tetragonal perovskite structure at room temperature, a ¼ 3.896, c ¼ 4.136 [3], and a phase transition to cubic perovskite structure can occurs at 590 1C [20]. KBiO3 does not form the perovskite structure but rather forms a cubic structure first ¯ observed in KSbO3 (space group Im3 no. 204) [21]. In Fig. 2, one point, representing KNbO3, just inside the boundary, which has distorted perovskite structure at room temperature, can transfer to cubic perovskite structure at 510 1C [5]. Furthermore, some points near the boundary between ‘‘cubic perovskites’’ and ‘‘non-cubic perovskites’’, as seen in Fig. 2, including CaTiO3, AgNbO3, and AgTaO3, can undergo distorted perovskites to cubic perovskites transformation. AgTaO3, AgNbO3, and CaTiO3 can change into cubic perovskite structure at 530, 610, and 1361 1C, respectively [5,22]. In this research, the cubic structure is not found in A3+B3+O3 perovskites, and there are no A3+B3+O3 compounds in the ‘‘cubic perovskites’’ region, as seen in Fig. 2. According to Galasso’s report [3], DyMnO3 and LaVO3, which belong to A3+B3+O3 perovskites, have cubic perovskite structure previously, however, the later reports indicate that LaVO3 and DyMnO3 have orthorhombic structure at room temperature [18,19]. This is agreement with our result, and may imply other criterion for cubic perovskites formability. Our model gives a simple and effective prediction criterion for cubic perovskites formability. New cubic perovskite structure compounds can be predicted by using this model, and their lattice constant can be predicted by a prediction model of lattice constant in cubic perovskites, which was obtained in our previous study [12]. Using these two models, we can seek for new cubic perovskites which lattice constant is close to compound semiconductor. ARTICLE IN PRESS 974 L.M. Feng et al. / Journal of Physics and Chemistry of Solids 69 (2008) 967–974 [2] O. Muller, R. Roy, The Major Ternary Structural Families, Springer, New York, 1974. [3] F.S. Galasso, Perovskites and High Tc Superconductors, Gordon and Breach, New York, 1990. [4] Z.L. Wang, Z.C. Kang, Functional and Smart Materials: Structural Evolution and Structure Analysis, Plenum Press, New York, 1998. [5] H.C. Chen, Crystal Chemistry, Shandong Education Press, Jinan, 1985 (In Chinese). [6] A. Gupta, B.W. Hussey, T.M. Shaw, Mater. Res. Bull. 31 (1996) 1463–1470. [7] H. Takahashi, J. Ohta, H. Fujioka, M. Oshima, Thin Solid Films 407 (2002) 114–117. [8] K. Shimamura, H. Tabata, H. Takeda, V.V. Kochurikhin, T. Fukuda, J. Cryst. Growth 194 (1998) 209–213. [9] M. Ito, K. Shimamura, D.A. Pawlak, T. Fukuda, J. Cryst. Growth 235 (2002) 277–282. [10] Y.G. Tian, M.S. Cao, C.B. Cao, Introduction of Advanced Materials, Haerbin Institute of Technology Press, Haerbin, 2005 (In Chinese). [11] K. Eisenbeiser, R. Emrickm, R. Droopad, Z. Yu, J. Finder, S. Rockwell, J. Holmes, C. Overgaard, W. Ooms, IEEE Electron Devices Lett. 23 (2002) 300–302. [12] L.Q. Jiang, J.K. Guo, H.B. Liu, M. Zhu, X. Zhou, P. Wu, C.H. Li, J. Phys. Chem. Solids 67 (2006) 1531–1536. [13] A.S. Bhalla, R.Y. Guo, R. Roy, Mater. Res. Innovations 4 (2000) 3–26. [14] C.H. Li, K.C.K. Soh, P. Wu, J. Alloys Compd. 372 (2004) 40–48. [15] H. Falcon, J.A. Alonso, M.T. Casais, M.J. Martinez-Lope, J. Sanchez-Benitez, J. Solid State Chem. 177 (2004) 3099–3104. [16] K. Mori, T. Kamiyama, H. Kobayash, K. Itoh, T. Otomo, S. Ikeda, Physica B 329–333 (2003) 807–808. [17] N.L. Ross, T.D. Chaplin, J. Solid State Chem. 172 (2003) 123–126. [18] R.T.A. Khan, J. Bashir, N. Iqbal, M.N. Khan, Mater. Lett. 58 (2004) 1737–1740. [19] T. Mori, K. Aoki, N. Kamegashira, T. Shishido, T. Fukuda, Mater. Lett. 42 (2000) 387–389. [20] Y. Kuroiwa, S. Aoyagi, A. Sawada, Phys. Rev. Lett. 87 (2001) 217601(1)–217601(4). [21] T.N. Nguyen, D.M. Giaquinta, W.M. Davis, Chem. Mater. 5 (1993) 1273–1276. [22] R. Ali, M. Yashima, J. Solid State Chem. 178 (2005) 2867–2872. This is useful to design new buffer materials or substrates for compound semiconductor direct growth. 5. Conclusions In this research, 223 binary oxide systems are collected, of which, only 34 systems can form cubic perovskites, 114 systems have distorted perovskites, and 75 systems cannot form perovskites. Using these samples, regularities of formability of cubic perovskites are investigated by an empirical two-dimension structural map, which is spanned by octahedral factor (rB/rO) and the tolerance factor. Through this study, the following conclusions are obtained: 1. Octahedral factor (rB/rO) is as important as the tolerance factor (t ¼ (rA+rO)/[21/2(rB+rO)]) for cubic perovskites formability. 2. Both tolerance factor and octahedral factor are a necessary but not sufficient condition for cubic perovskites formability. Using these two factors, the cubic perovskites formability can be reliably predicted. 3. In the structural map that is drawn by the tolerance factor (t ¼ (rA+rO)/[21/2(rB+rO)]) and octahedral factor (rB/rO), the points for cubic perovskites and those for non-cubic perovskites are located in different zones via clear boundary defined by Eqs. (1)–(4). These equations form the criteria for cubic perovskites formability. This simple model may be applied to design new substrate or buffer materials with cubic perovskites structure in compound semiconductor epitaxy. References [1] H. Tanaka, M. Misono, J. Curr. Opin. Solid State Mater. Sci. 5 (2001) 381–387.