Chapter 10- Phase Transformations

Chapter 10- Phase Transformations - Chapter 10: Phase...

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Chapter 10: Phase Transformations ISSUES TO ADDRESS. .. • Transforming one phase into another takes time. Fe γ (Austenite) Eutectoid transformation C FCC Fe 3 C (cementite) α (ferrite) + (BCC) Chapter 10 - 1 • How does the rate of transformation depend on time and T ? • How can we control the transformation rate so that we can engineer non-equilibrium structures? • Are the mechanical properties of non-equilibrium structures better?
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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 Growth - nuclei grow in size until reach equilibrium Chapter 10 - 2 Driving force to nucleate increases as we increase 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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Solidification: Nucleation Processes • Homogeneous nucleation – nuclei form in the bulk of liquid metal – requires supercooling (temperature well below the melting point, typically 80-300°C) • Heterogeneous nucleation – much easier since stable “nucleus” is already present • Nuclei form on structural inhomogeneities: impurities in the liquid phase, dislocations, surfaces and interfaces – allows solidification with only 0.1-10ºC supercooling Chapter 10 - 3
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Homogeneous Nucleation & Energy Effects G T = Total Free Energy = G S + G V Surface Free Energy- destabilizes the nuclei (it takes energy to make an interface) γ π = 2 4 r G S γ = surface tension Volume (Bulk) Free Energy stabilizes the nuclei (releases energy) υ π = G r G V 3 3 4 volume unit energy free volume = υ G Chapter 10 - 4 r * = critical nucleus : nuclei < r * shrink; nuclei> r * grow (to reduce energy) Adapted from Fig.10.2(b), Callister 7e.
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Solidification T H T r S m = γ 2 * H S = latent heat of solidification T m = melting temperature γ = surface free energy T = T m -T = supercooling r* = critical radius 2 2 2 3 3 16 * T H T G S m = πγ Note: H S = strong function of T γ = weak function of T r * decreases as T increases For typical T r * ca. 100Å Chapter 10 - 5
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Rate of Phase Transformations Nucleation rate ) exp( ) ) ( exp( * * kT Q kT T G K Kn n d = = ν & Growth rate ) exp( kT Q C g = & Overall transformation rate g n s & & & ~ Chapter 10 - 6
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Nucleation and Growth • Reaction rate is a result of nucleation and growth of nuclei: Chapter 10 - 7 •E xamp le s : Adapted from Fig. 10.10, Callister 7e . Nucleation rate increases with T Growth rate increases with T T just below T E Nucleation rate low Growth rate high γ pearlite colony T moderately below T E γ Nucleation rate med . Growth rate med. Nucleation rate high T way below T E γ Growth rate low IMPORTANT:
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Rate of Phase Transformations Kinetics – time dependence of phase transformation • Hold temperature constant & measure fraction of transformed material 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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This note was uploaded on 04/02/2008 for the course MSE 200 taught by Professor Wholedepartment during the Spring '08 term at N.C. State.

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Chapter 10- Phase Transformations - Chapter 10: Phase...

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