mse10 - Chapter 10: Phase Transformations ISSUES TO...

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1 Chapter 10 - 1 ISSUES TO ADDRESS. .. • Transforming one phase into another takes time. • How does the rate of transformation depend on time and T ? • How can we slow down the transformation so that we can engineering non-equilibrium structures? • Are the mechanical properties of non-equilibrium structures better? Fe γ (Austenite) Eutectoid transformation C FCC Fe 3 C (cementite) α (ferrite) + (BCC) Chapter 10: Phase Transformations Chapter 10 - 2 Phase Transformations Nucleation – nuclei (seeds) act as template to grow crystals – for nucleus to form rate of addition of atoms to nucleus must be faster than rate of loss – once nucleated, grow until reach equilibrium Driving force to nucleate increases as we increase Δ T – supercooling (eutectic, eutectoid) – superheating (peritectic) Small supercooling Æ few nuclei - large crystals Large supercooling Æ rapid nucleation - many nuclei, small crystals
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2 Chapter 10 - 3 Solidification: Nucleation Processes • Homogeneous nucleation – nuclei form in the bulk of liquid metal – requires supercooling (typically 80-300 ° C max) • Heterogeneous nucleation – much easier since stable “nucleus” is already present • Could be wall of mold or impurities in the liquid phase – allows solidification with only 0.1-10ºC supercooling Chapter 10 - 4 r * = critical nucleus : nuclei < r * shrink; nuclei> r * grow (to reduce energy) Adapted from Fig.10.2(b), Callister 7e. Homogeneous Nucleation & Energy Effects Δ G T = Total Free Energy = Δ G S + Δ G V Surface Free Energy- destabilizes the nuclei (it takes energy to make an interface) γ π = Δ 2 4 r G S γ = surface tension Volume (Bulk) Free Energy stabilizes the nuclei (releases energy) υ Δ π = Δ G r G V 3 3 4 volume unit energy free volume = Δ υ G
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3 Chapter 10 - 5 Solidification T H T r S m Δ Δ γ = 2 * Note: Δ H S = strong function of Δ T γ = weak function of Δ T r * decreases as Δ T increases For typical Δ T r * ca. 100Å Δ H S = latent heat of solidification T m = melting temperature γ = surface free energy Δ T = T m -T = supercooling r* = critical radius Chapter 10 - 6 Rate of Phase Transformations Kinetics - measure approach to equilibrium vs. time • Hold temperature constant & measure conversion vs. time sound waves – one sample electrical conductivity – follow one sample X-ray diffraction – have to do many samples How is conversion measured?
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4 Chapter 10 - 7 Rate of Phase Transformation Avrami rate equation => y = 1- exp (- k t n ) k & n fit for specific sample All out of material - done log t Fraction transformed, y Fixed T fraction transformed time 0.5 By convention r = 1 / t 0.5 Adapted from Fig. 10.10, Callister 7e. maximum rate reached – now amount unconverted decreases so rate slows t 0.5 rate increases as surface area increases & nuclei grow Chapter 10 - 8 Rate of Phase Transformations • In general, rate increases as T r = 1/ t 0.5 = A e - Q / RT R = gas constant T = temperature (K) A = preexponential factor Q
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mse10 - Chapter 10: Phase Transformations ISSUES TO...

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