11.Phase%20Transformations - MSE 280: Introduction to...

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1 MSE 280: Introduction to Engineering Materials Reading: Callister Ch. 11 Phase Transformations ISSUES TO ADDRESS. .. Transforming one phase into another takes time. • How does the rate of transformation depend on time and temperature ? Fe γ (Austenite) Eutectoid transformation C FCC Fe 3 C (cementite) α (ferrite) + (BCC) MSE280 © 2007-2009 Moonsub Shim 1 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? • Phase transformations in polymers? 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 Growth: once nucleated, growth proceeds until equilibrium is attained Driving force to nucleate increases as we increase Δ T – supercooling (eutectic, eutectoid) – superheating (peritectic) MSE280 © 2007-2009 Moonsub Shim 2 Small supercooling Æ slow nucleation rate - few nuclei - large crystals Large supercooling Æ rapid nucleation rate - many nuclei - small crystals
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2 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) MSE280 © 2007-2009 Moonsub Shim 3 Kinetics of solid state reactions Phase 1 (e.g. liquid) Nucleation of 2 nd phase Growth 1. Nucleation (homogeneous): What hinders nucleation? E Surface energy ~ r 2 Initially the surface energy dominates but eventually bulk energy takes over. Need nuclei larger than critical radius MSE280 © 2007-2009 Moonsub Shim 4 r (size of nuclei) Internal energy ~ r 3 Net energy change = r c than critical radius before growth occurs! γ π 2 3 4 3 4 r G r v + Δ
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3 Kinetics of solid state reactions Net energy = Δ G = γ π 2 3 4 4 r G r + Δ Critical nucleus size ( r c ) and the activation energy ( G* ) 3 v Volume free energy change surface free energy 0 ) 2 ( 4 ) 3 )( ( 3 4 ) ( 2 = + Δ = Δ r r G dr G d v πγ Take the derivative and set equal to zero to find max. 2 MSE280 © 2007-2009 Moonsub Shim 5 r c v c G r Δ = Sub-in to overall G equation 2 3 * ) ( 3 16 v G G Δ = Δ Kinetics of solid state reactions In terms of heat of fusion H f (i.e. energy release upon solidification): m f T T H G ) ( Δ = Δ Tells us how G v changes with temperature Δ = T T T H r m m f c 2 2 3 m v T With this definition, we then have: T 1 > T 2 MSE280 © 2007-2009 Moonsub Shim 6 2 * 3 16 Δ = Δ T T T H G m m f As T decreases both r c and G* become smaller Number of stable nuclei: Δ kT G n * * exp LIQUID INSTABILITY at LOWER TEMPERTURES
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4 Kinetics of solid state reactions We also need to consider diffusion: • Faster diffusion leads to more collisions between atoms.
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This note was uploaded on 03/15/2010 for the course MSE 280 taught by Professor Johnson during the Fall '08 term at University of Illinois, Urbana Champaign.

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11.Phase%20Transformations - MSE 280: Introduction to...

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