MSE 3300-Lecture Note 16-Chapter 10 Phase Transformations
Transcript of MSE 3300-Lecture Note 16-Chapter 10 Phase Transformations
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MSE 3300 / 5300 UTA Fall 2014 Lecture 16 -
Lecture 16. Phase Transformation
Learning Objectives After this lecture, you should be able to do the following:
1. Understand nucleation and growth processes in phase
transformations
2. Understand the kinetics of phase transformations.
Reading• Chapter 10: Phase Diagrams (10.1–10.4)
Multimedia
• Virtual Materials Science & Engineering (VMSE):
http://www.wiley.com/college/callister/CL_EWSTU01031_S/vmse/
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MSE 3300 / 5300 UTA Fall 2014 Lecture 16 -
Kinetics of Phase Transformation
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MSE 3300 / 5300 UTA Fall 2014 Lecture 16 - 4
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” isalready present — e.g., mold wall, impurities inliquid phase
– only very slight supercooling (0.1-10°
C)
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Driving force for solidification
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At any temperature below Tm there is a driving force for solidification. The liquid solidify at T
< Tm. If energy is removed quickly, the system can be significantly supercooled (or
undercooled).
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Homogeneous Nucleation
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Homogeneous Nucleation
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r * = critical nucleus: for r < r * nuclei shrink; for r > r * nuclei grow (to reduce energy)
Adapted from Fig.10.2(b), Callister & Rethwisch 9e.
Homogeneous Nucleation & Energy Effects
∆GT = Total Free Energy
= ∆GS + ∆GV
Surface Free Energy- destabilizes
the nuclei (it takes energy to make
an interface)
γ = surface tension
Volume (Bulk) Free Energy –
stabilizes the nuclei (releases energy)
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Homogeneous Nucleation
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MSE 3300 / 5300 UTA Fall 2014 Lecture 16 - 10
Solidification
Note: ∆H f and γ are weakly dependent on ∆T
r * decreases as ∆T increases
For typical ∆T r * ~ 10 nm
∆H f = latent heat of solidificationT m = melting temperature
γ = surface free energy
∆T = T m - T = supercooling
r* = critical radius
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Homogeneous Nucleation
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Both r* and G* decrease withincreasing supercooling ( ∆T).
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Rate of Homogeneous Nucleation
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Rate of Homogeneous Nucleation
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Stable particle
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Rate of Homogeneous Nucleation
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Nucleation rate [nuclei per unit volume per second]
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Heterogeneous Nucleation
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Homogeneous Nucleation
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Heterogeneous Nucleation
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Heterogeneous Nucleation
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Heterogeneous Nucleation
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Growth
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Particle growth occurs by long-range atomic diffusion, which involves
several steps—for example, diffusion through the parent phase, across a phase
boundary, and then into the nucleus. The growth rate is determined by the rate
of diffusion, and its temperature dependence is the same as for the diffusioncoefficient (Equation 5.8):
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Transformation Rate
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Kinetics: Rate of Phase
TransformationsKinetics - 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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Temperature Dependence of
Transformation Rate
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• For the recrystallization of Cu, since
rate = 1/t 0.5
rate increases with increasing temperature
• Rate often so slow that attainment of equilibrium
state not possible!
Fig. 10.11, Callister &
Rethwisch 9e.(Reprinted with permission
from Metallurgical
Transactions, Vol. 188, 1950,
a publication of The
Metallurgical Society of AIME,Warrendale, PA. Adapted
from B. F. Decker and D.
Harker, “Recrystallization in
Rolled Copper,” Trans. AIME,
188, 1950, p. 888.)
135C 119C 113C 102C 88C 43C
1 10 102 104
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Summary
1. Phase transformations: nucleation and growth
2. Kinetics of phase transformations
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Homework 8
• 10.2, 10.4, 10.6, 10.11
* Problems from Callister, 9th Edition
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