Phase Transformation

11/3/2008MSE 280: Introduction to Engineering Materials Phase Transformations Reading: g Callister Ch. 11 • Time and temperature dependence of phase transformations. • Engineering non-equilibrium structures. • Differences in mechanical properties between equilibrium and non non-equilibrium equilibrium structures (steel). • Phase transformations in polymers. 1 © 2007, 2008 Moonsub Shim MSE280 Phase transformation • • • Takes time (transformation rates: kinetics). Involves movement/rearrangement of atoms. Usually involves changes in microstructure. change in number or compositions of phases present (e.g. solidification of pure elemental metals, allotropic transformation, recrystallization, grain growth). 1. “Simple” diffusion-dependent transformation: no 2. Diffusion-dependent transformation: transformation with alteration in phase composition and and, often often, with changes in number of phases present (e.g. eutectoid reaction). 3. Diffusionless transformation: e.g. rapid T quenching to “trap” metastable phases. 2 © 2007, 2008 Moonsub Shim MSE280 1 Nucleation (homogeneous): What hinders nucleation? Surface energy ~ r2 E r (size of nuclei) rc Net energy change = Internal energy ~ r3 © 2007. d (ΔG ) 4 = π ( ΔGv )(3r 2 ) + 4πγ ( 2r ) = 0 dr 3 rc = − 2γ ΔGv rc Sub-in to overall ΔG equation 16πγ 3 ΔG = 3( ΔGv ) 2 * 4 © 2007.11/3/2008 Kinetics of solid state reactions Phase 1 (e. 2008 Moonsub Shim 4 3 πr ΔGv + 4πr 2γ 3 3 MSE280 Kinetics of solid state reactions Critical nucleus size (rc) and the activation energy (ΔG*) Net energy gy = ΔG = 4 3 πr ΔGv + 4πr 2γ 3 surface free energy Volume free energy change Take the derivative and set equal to zero to find max. Need nuclei larger than critical radius before growth occurs! 1. 2008 Moonsub Shim MSE280 2 . liquid) Nucleation of 2nd phase Growth Initially the surface energy dominates but eventually bulk energy takes over.g. e. we then have: rc = − 2γ ΔH f ⎛ Tm ⎞ ⎜ ⎜T −T ⎟ ⎟ ⎝ m ⎠ 2 16πγ 3 ⎛ Tm ⎞ ⎜ ⎟ ΔG = 2 ⎟ 3ΔH f ⎜ ⎝ Tm − T ⎠ * As T decreases both rc and ΔG* become smaller Number of stable nuclei: ⎛ ΔG * ⎞ n* ∝ exp⎜ ⎜ − kT ⎟ ⎟ ⎝ ⎠ 5 LIQUID INSTABILITY at LOWER TEMPERTURES © 2007. 2008 Moonsub Shim MSE280 3 .11/3/2008 Kinetics of solid state reactions In terms of heat of fusion ΔHf (i. • More collisions means higher probability of atoms sticking to each other. the frequency of atoms sticking together is directly related to diffusion: Frequency of attachment: ⎛ Q ⎞ vd ∝ exp⎜ − d ⎟ ⎝ kT ⎠ 6 © 2007. Recall diffusion ⎛ Q ⎞ D = Do exp⎜ − d ⎟ ⎝ kT ⎠ Then. energy release upon solidification): ΔGv = ΔH f (Tm − T ) Tm Tells us how ΔGv changes g with temperature p T1 > T2 With this definition. 2008 Moonsub Shim MSE280 Kinetics of solid state reactions We also need to consider diffusion: • Faster diffusion leads to more collisions between atoms. 11/3/2008 Kinetics of solid state reactions Combining liquid instability and diffusion effects together: R t of Rate f Nucleation N l ti Contribution from liquid instability Nuclea ation rate Contribution from diffusion ⎡ ⎛ ΔG * ⎞ dN ⎛ Q ⎞⎤ = Kn * vd = K ' ⎢exp⎜ − ⎟ exp⎜ − d ⎟⎥ dt ⎝ kT ⎠⎦ ⎣ ⎝ kT ⎠ ⎛ ΔG * ⎞ n* ∝ exp⎜ ⎜ − kT ⎟ ⎟ ⎝ ⎠ ⎛ Q ⎞ vd ∝ exp⎜ − d ⎟ ⎝ kT ⎠ Net rate Liquid instability © 2007. calculate the critical radius and the activation energy. Au is FCC with a = 0. B) Calculate the number of atoms per nucleus of this critical size. 2008 Moonsub Shim Diffusion Tm 7 T MSE280 Example problem: critical radius and activation energy for nucleation A) If pure liquid gold is cooled to 230oC below its melting point. 8 © 2007. 2008 Moonsub Shim MSE280 4 .413nm. 11/3/2008 Kinetics of solid state reactions 2. © 2007. 2008 Moonsub Shim Growth rate 10 T MSE280 5 . Growth: nuclei increase in size All solid All liquid By convention: This process can be described by: rate ≡ 1 t1/ 2 9 y = 1 − exp(−kt n ) Avrami eqn. 2008 Moonsub Shim k and n are time independent constants MSE280 Kinetics of solid state reactions Temperature dependence Arrhenius behavior! ⎛ Q ⎞ rate = A exp⎜ − ⎟ ⎝ RT ⎠ © 2007. 2008 Moonsub Shim MSE280 6 .70wt%C) 70wt%C) Pearlite 12 © 2007.11/3/2008 Kinetics of solid state reactions Combined nucleation and growth rate rate Overall rate of transformation growth nucleation T 11 © 2007. 2008 Moonsub Shim MSE280 Isothermal transformation Initial rapid T change then allow transformation to occur at constant T Eutectoid reaction γ (0.022wt%C) (0 022wt%C) + Fe3C (6 (6.76wt%C) (0 76wt%C) cool heat α (0. t transformation plot (TTT plot) Where does the line shape (e. 50% completion curve) come from? © 2007. 2008 Moonsub Shim time MSE280 7 .11/3/2008 Pearlite T vs. 2008 Moonsub Shim 13 MSE280 TTT plot and relation to rates Recall rates as fxn of T… rat te T overall growth nucleation rate Flip x and y T Plot 1/rate on x-axis T Since rate is defined as: rate ≡ 1 t1/ 2 50% completion curve 14 © 2007.g. 11/3/2008 Pearlite Initial rapid T quench Constant T during transformation Do the microstructures change when we quench to different T? © 2007. 2008 Moonsub Shim 15 MSE280 Pearlite Recall limited diffusion in solids leading to layered structure… Fill in the blank… coarse pearlite structure. 2008 Moonsub Shim 16 MSE280 8 . Initial rapid quench to higher T will lead to ________ Initial rapid quench to lower T will lead to _________ pearlite structure. fine © 2007. 2008 Moonsub Shim 18 MSE280 9 . M t Martensite: it Formed F d when h quenched h d rapid enough to prevent C diffusion. 2008 Moonsub Shim MSE280 Spheroidite Forms when pearlite or bainite structures are heated (below eutectoid T) for an extended period of time.11/3/2008 Bainite & Martensite Coarse pearlite Fine pearlite Bainite Bainite: needles or plates consisting of cementite and ferrite (much finer than fine pearlite). Bainite Martensite Martensite BCT structure of martensite 17 © 2007. Pearlite Partially transformed Heating time Spheroidite Why do spherical shapes dominate at the end? © 2007. Body-centered tetragonal. 4 1 2 3 4 5 Essentially restart transformation process (for the remaining 50%). 2. Rapid cool to 650oC. Quench to RT. 2008 Moonsub Shim MSE280 10 . What happens if the resulting structure is held at t 250oC f for 1d 1day? ? 3. pearlite. 5. 1. What happens if the structure from part 1 is quenched directly to RT? 19 © 2007. 2008 Moonsub Shim MSE280 Example problem Specify final microstructure(s) present and approximate percentage of each for f ll i processing following i condition diti beginning at 760oC. What is the microstructure of steel that has been: (i) instantaneously quenched to 560oC (ii) held for 2s then (iii) Instantaneously quenched to 250oC? 2. Hold for 103s. Rapid cool to 400oC. 4. 2 ~50% transformation to p pearlite. 3.11/3/2008 Example problem 1. Hold 20s. 50% bainite 20 5 Final composition = 50% © 2007. 2008 Moonsub Shim MSE280 11 .13wt%C 22 © 2007.13wt%C γ α α+γ γ + Fe3C α + Fe3C 1.11/3/2008 TTT diagrams at different compositions Eutectoid composition 21 © 2007.g. 1. 2008 Moonsub Shim MSE280 Hypereutectoid composition e. 11/3/2008 Example Starting with austenite having 1.9 % mass fraction coarse pearlite. Nucleation to growth transition is slower since it is not cooled instantaneously initially.13wt%C Fe-C alloy © 2007. what cooling path will produce 6 6.9% mass fraction Bainite? TTT diagram for 1. 46. 2008 Moonsub Shim 24 MSE280 12 .2% 2% mass fraction proeutectoid cementite. What happens when T is varied as transformation occurs? (e. 46.13 wt%C in composition. continuously cool from To to T2 at a constant rate) © 2007. 2008 Moonsub Shim 1.g.13 23 MSE280 Continuous Cooling Transformation Recall % transformed vs. time… Transformation at constant T (T1) Complete transformation occurs faster due lower final T. i ht 675oC (isothermal) Constant cooling rate 25 © 2007. 2008 Moonsub Shim MSE280 CCT diagrams 26 © 2007.11/3/2008 Continuous Cooling Transformation Recall how we arrived at TTT diagram for isothermal cooling… g What happens when T varies during transformation? Looks like the curves are shifted down and t the to th right. 2008 Moonsub Shim MSE280 13 . © 2007.11/3/2008 Microstructures from continuous cooling Note: usually no Bainite is formed in continuous cooling 27 © 2007. 2008 Moonsub Shim 28 MSE280 14 . 2008 Moonsub Shim MSE280 Mechanical behavior of plain carbon steel Fine pearlite Strength increases and ductility decreases with C content. 11/3/2008 How do processing conditions change mechanical properties? coarse pearlite Fine pearlite Bainite Extended heating g Spheroidite Fast quench: higher strength. lower ductility. 29 © 2007. 2008 Moonsub Shim MSE280 15 . 2008 Moonsub Shim MSE280 Austenite ( γ) slow cool (α + Fe 3 C layers + a proeutectoid phase) moderate cool (α + Fe 3 C plates/needles) rapid quench Martensite (BCT phase diffusionless transformation) Pearlite Bainite Martensite T Martensite bainite fine pearlite coarse pearlite spheroidite General Trends reheat Ductil lity Tempered p Martensite Streng gth (α + very fine Fe 3 C particles) 30 © 2007. higher ductility. Slow quench: lower strength. 2008 Moonsub Shim MSE280 16 .11/3/2008 Phase transformation in polymers y • Crystallization. – Crystallization can be induced by strain. – Usually 100% crystallization is not achievable. • Melting. 31 © 2007. 2008 Moonsub Shim MSE280 Crystallization • Many polymer crystallization processes are similar kinetics as discussed earlier in phase transformations (Avrami equation). • Glass transition. P l Polypropylene l Normalized! 32 © 2007. ( q ) • Some differences: – Nucleation and growth • Random entangled chains become ordered and aligned. 11/3/2008 Melting Melting occurs over a range of temperature Melting temperature (Tm) depends on: 1. 5. 2. Degree of branching: more branching leads to lower Tm. 34 © 2007. 2008 Moonsub Shim MSE280 17 . • Polar side groups lead to higher Tm (stronger secondary 33 bonding). Molecular Weight: at relatively low MW. Tm increases with MW. © 2007. Heating rate: faster heating rate leads to higher Tm. how it was crystallized). History of the specimen (e. 3. 2008 Moonsub Shim MSE280 Melting continued… Melting temperature depends on: 4. Chemical composition • Bulky side groups lead to higher Tm (hindered rotation and flexibility).g. 4. Chemical composition • Bulky groups increase Tg. PE (Mn = 107 g/mol) vs. • Polar groups increase Tg. PMMA (n = 5000) 3.11/3/2008 Melting Temperature: example problems For each polymer pair. 3. Polyethylene (n = 5000) vs. Degree of branching: higher density of branching – higher Tg (entangled branches restrict chain motion). • Abrupt changes in: •Stiffness. PE (Mn = 106 g/mol) 35 © 2007.000g/mol) vs. 2. Polystyrene (Mn = 80. Linear polyethylene 2. 2008 Moonsub Shim MSE280 Glass Transition • Transition from rubbery to rigid state. 36 © 2007. Polystyrene (Mn = 800g/mol) 4. determine which will have higher melting temperature. 1. 2008 Moonsub Shim MSE280 18 . Branched polyethylene vs. •Viscosity. Crosslinking increases Tg due to chain motion restriction. Vi it •Coefficient of thermal expansion… Glass transition temperature (Tg) depends on: 1. 2 Molecular weight: higher MW – higher Tg. determine which will have higher glass transition temperature g p . bainite. • CCT diagrams. • TTT plots and relation to reaction rates. • Phase transformation in polymers (consider similarities and differences with metals). • Isothermal transformation. • Microstructures of Fe-C systems at different cooling conditions: – Fine and coarse pearlite. polypropylene b) polystyrene vs. polypropylene 37 © 2007. 38 © 2007. 2008 Moonsub Shim MSE280 19 . – Rates. 2008 Moonsub Shim MSE280 Concepts to remember… • Kinetics of solid state reaction: – nucleation (surface vs volume energies) and growth. H2 H C C Cl H2 H C C CH3 a) poly(vinyl chloride) vs. – Avrami equation. • Processing effects on mechanical properties.11/3/2008 Glass transition: example problems For each polymer pair. spheroidite and martensite.