MSE 3300-Lecture Note 16-Chapter 10 Phase Transformations

8/18/2019 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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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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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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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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Both r* and G* decrease withincreasing supercooling ( ∆T).


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Rate of Homogeneous Nucleation

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Stable particle


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Nucleation rate [nuclei per unit volume per second]


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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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MSE 3300-Lecture Note 16-Chapter 10 Phase Transformations