Chapter 10 - Chapter 10 Phase Transformations Kinetics...

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Chapter 10: Phase Transformations - Kinetics ISSUES TO ADDRESS. .. • Transforming one phase into another takes time. Fe γ (Austenite) Eutectoid transformation C FCC Fe 3 C (cementite) α (ferrite) + (BCC) • 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? Chapter 10 - 1 • Are the properties of non-equilibrium structures better?
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Phase Transformations- nucleation & growth 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 T – supercooling (eutectic, eutectoid) – superheating (peritectic) Small supercooling Æ few nuclei - large crystals Large supercooling Æ rapid nucleation - many nuclei, small crystals Chapter 10 - 2
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Solidification: Nucleation Processes • Homogeneous nucleation – nuclei form in the bulk of liquid – 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 - 3
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Homogeneous Nucleation G v (matrix) Chapter 10 - 4 Nuclei G v (nucleus) γ : surface energy (nucleus/matrix) G v = G v (nucleus)- G v (matrix) volume unit energy free volume = υ G
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ANNOUNCEMENTS - 4/12 Reading: Chapter 10 Homework #9 due today Pick up your midterm and graded homework Chapter 10 - 5
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Homogeneous Nucleation & Energy Barrier Chapter 10 - 6 Adapted from Fig.10.2(b), Callister 7e. G T = Change in 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 r * = critical nucleus : nuclei < r * shrink; nuclei > r * grow (to reduce energy) G* is the energy barrier for nucleation
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Solidification: Liquid solid H S = latent heat of solidification T m = melting temperature γ = surface free energy T = T m -T = supercooling r* = critical radius of nucleus T H T r S m γ = 2 * 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 - 7
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Rate of Phase Transformations Kinetics - measure approach to equilibrium vs. time • Hold temperature constant & measure conversion vs. time X-ray diffraction – have to do many samples How is conversion measured? Chapter 10 - 8
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X-Rays to Determine Crystal Structure • Incoming X-rays diffract from crystal planes.
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This note was uploaded on 07/13/2008 for the course MSE 201 taught by Professor Nieh during the Spring '07 term at University of Tennessee.

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Chapter 10 - Chapter 10 Phase Transformations Kinetics...

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