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Phase Transformations:Kinetics & Development of Microstructure

Stephanie Ann Bermudez, Florencio De los Reyes, Romelyn Jane Obiles

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Materials versatility depends on its range of mechanical

propertieswhich depend on the characteristics of themicrostructures

Development of microstructure involves some type of

transformations

Why study phase transformations?

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Time and temperature dependencies of the phase

transformations are represented on modified phase diagram

Design heat treatment for materials, e.g. alloys to yield thedesirable mechanical properties suited for its application

Most transformations do not occur instantaneously dependence of reaction progress on time (transformation rate)is considered

Why study phase transformations?

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Involve some alteration of the microstructure, important in the

processing of materials

3 Classifications

1. Simple Diffusion-dependent transformations no change in

either the # or composition of the phases presente.g. solidification of pure metal, allotropic transformations,recrystallization and grain growth

Phase transformations: Classifications

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2. Diffusion-dependent transformations some alteration in phase

compositions and the number of phases presente.g. eutectic or eutectoid transformation

3. Diffusionless phase transformations metastable phase isproduced (intermediate phase between initial and equilibrium state)

e.g. martensitic transformation

Phase transformations: Classifications

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With phase transformation, at least one new phase is formed

that has different physical/chemical characteristics and/orstructure than the parent phase

Most transformations do not occur instantaneously: numerous

small particles of the new phase(s), increase in size until it hasreached completion

Phase transformations: Kinetics

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The process of Phase Transformation involves:

1) Nucleation of the new phase(s): formation of small particles,nuclei of the new phase(s). Often formed at grain boundaries andother defects.

2) Growth of the new phase(s) at the expense of the originalphase(s)

Phase transformations: Kinetics

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Phase transformations: Kinetics

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Nucleation: Two types

1) Homogeneous nucleation nuclei of new

phase forms uniformly throughout theparent phase

2) Heterogeneous nucleation nuclei formspreferentially at structuralinhomogeneities

e.g. container surfaces, insolubleimpurities, grain boundaries,dislocations, etc.

Phase transformations: Kinetics

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Using free energy, it will be convenient to study phase

transformations occurring at constant temperature (T) andconstant pressure (P)

G = H TS, H is the enthalpy and S is the entropy

H = U + PV, U is the internal energy and V is the volume

Gibbs Free Energy (G)

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The change in the free energy, G, during phase transformation is

importantUnder constant T and P corresponds to the minimum of G and a

phase transformation occurs spontaneously only when G decreasesin the course of transformation, i.e. G transformation is negative

Depends on the trade off between H and S (e.g. H < 0, S >0

favors transformation)

Gibbs Free Energy (G)

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Consider solidification of a pure material: Is the transition from theundercooled liquid to a solid spherical particle in the liquid aspontaneous one?

Homogeneous Nucleation

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Homogeneous Nucleation

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Homogeneous Nucleation

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As the solid particle begins to form as atoms in the liquid cluster

together, its free energy first increases. As this cluster reaches a size corresponding to the critical radius r*,

growthwill continuewith a decrease in the free energy otherwise;

A cluster of radius less than r* will shrink and redissolve

Embryo: subcritical particle

Nucleus: particle of r > r*

G* is the activation free energy

Homogeneous Nucleation

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Homogeneous Nucleation

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With a lowering of temperature below the equilibrium solidificationtemperature, Tm, nucleation occurs more readily.

Homogeneous Nucleation

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Homogeneous Nucleation

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Homogeneous Nucleation

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Level of supercooling in practical situations often on the order ofonly several degree Celsius

G* is lo

wered

when nuclei form on pre-existing surfaces orinterfaces since the surface free energy, , is reduced.

Easier for nucleation to occur at surfaces and interfaces than anyother sites.

Heterogeneous Nucleation

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Consider an example of heterogeneous nucleation of nucleus ofthe shape of a spherical cap on the wall of a containerwith threesurface energies:

LC = liquid container interface

LS = liquid solid interface

SC = solid container interface

LC = SC + LScos()

cos () = (LC SC)/ LS

Heterogeneous Nucleation

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Heterogeneous Nucleation

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Heterogeneous Nucleation

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Growth step in a phase transformation begins once an embryo hasexceeded the critical size or r > r* and become an stable nucleus

Nucleation

w

ill continue to occur simultaneouslyw

ith

grow

th

of th

enew phase particles until completion

Rough interfaces migrate by continuous growth; atomically flatinterfaces migrate by ledge formation and lateral growth

GROWTH

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The growth rate of a one-component phase and a multi-componentsystems can be described by the Arrhenius equation:

Growth rate = Cexp(-QA/kT) perAtom = Cexp(-Qm/RT) permole

Growth

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Product of Nucleation rateand Growth rate

Hig

h

T

(close toT

m) = low

nucleation and high growthrates = coarse microstructurewith large grains

LowT (strong undercooling) =

high nucleation and lowgrowth rates = finemicrostructurewith smallgrains

Rate of Phase Transformation

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J.F. Shackelford, Introduction to Materials Science For Engineers,5th edition

W.D. CallisterJr., Materials Science and Engineering:AnIntroduction, 7th edition

References