Chapter 11 - Phase transformations

Chapter 11 - Phase transformations - Chapter 11: Phase...

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Chapter 11 - 1 ISSUES TO ADDRESS. .. Transforming one phase into another takes time. How does the rate of transformation depend on time and temperature ? Is it possible to slow down transformations so that non-equilibrium structures are formed? Are the mechanical properties of non-equilibrium structures more desirable than equilibrium ones? Fe γ (Austenite) Eutectoid transformation C FCC Fe 3 C (cementite) α (ferrite) + (BCC) Chapter 11: Phase Transformations
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Chapter 11 - 2 Phase Transformations Nucleation nuclei (seeds) act as templates on which crystals grow for nucleus to form rate of addition of atoms to nucleus must be faster than rate of loss once nucleated, growth proceeds until equilibrium is attained Driving force to nucleate increases as we increase T supercooling (eutectic, eutectoid Small supercooling slow nucleation rate - few nuclei - large crystals Large supercooling rapid nucleation rate - many nuclei - small crystals
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Chapter 11 - 3 Solidification: Nucleation Types Homogeneous nucleation nuclei form in the bulk of liquid metal requires considerable supercooling (typically 80-300°C) Heterogeneous nucleation much easier since stable “nucleating surface” is already present — e.g., mold wall, impurities in liquid phase only very slight supercooling (0.1-10ºC)
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Chapter 11 - 4 r * = critical nucleus : for r < r * nuclei shrink; for r > r * nuclei grow (to reduce energy) Adapted from Fig.11.2(b), Callister & Rethwisch 3e. 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
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Chapter 11 - 5 Solidification T H T r f m γ - = 2 * Note: H and γ are weakly dependent on T r * decreases as T increases For typical T r * ~ 10 nm H = latent heat of solidification T m = melting temperature γ = surface free energy T = T - T = supercooling r* = critical radius
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Chapter 11 - 6 Rate of Phase Transformations Kinetics - study of reaction rates of phase transformations To determine reaction rate – measure degree of transformation as function of time (while holding temp constant) measure propagation of sound waves – on single specimen electrical conductivity measurements – on single specimen X-ray diffraction – many specimens required How is degree of transformation measured?
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Chapter 11 - 7 Rate of Phase Transformation Avrami equation => y = 1- exp (- k t n ) k & n are transformation specific parameters transformation complete log t Fraction transformed, y Fixed T fraction transformed time 0.5 By convention rate = 1 / t 0.5 Adapted from Fig. 11.10, Callister & Rethwisch 3e.
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This note was uploaded on 09/05/2011 for the course EMA 3010 taught by Professor Unknown during the Summer '08 term at University of Florida.

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Chapter 11 - Phase transformations - Chapter 11: Phase...

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