Thermodynamics_of_phase_transformation-lecture_3_handout

8/7/2019 Thermodynamics_of_phase_transformation-lecture_3_handout

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Lecture 3

ENMP211-09A Thermodynamics of Phase Transformation 42 ENMP211-09A Thermodynamics of Phase Transformation 43

Construction of Binary Phase Diagrams Using G-XB curves

Binary phase diagrams can be constructedbased on the G-X B curves of the phasesinvolved.

ENMP211-09A Thermodynamics of Phase Transformation 44

For a simple binary system, we canderive several observations from theG-XB curves for liquid and solid(assuming T m(A)>Tm(B)).

When T=T 1>Tm(A), the shape andthe locations of G-X B curves for theliquid and the solid look like this:

This means that at T 1, only the liquidis the only stable phase across thewhole composition range.

XB


When T=T m(A), the shapeand the locations of G-X Bcurves for the liquid andthe solid look like this:

This means that at T 2, onlyliquid is the only stablephase across the wholecomposition range exceptwhen X B = 0.

When XB

= 0, Both solidand liquid are stable, andthey are in equilibrium.

XB

G


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When T=T 2, and T m(A)>T2>Tm(B), theshape and the locations of G-X B curvesfor the liquid and the solid look like this:

This means that at T 2, solid is the onlystable phase in the composition range of 0=


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Similarly we can construct a simple eutectic phasediagram as shown below:


Note:Phase diagrams follow Gibbs phase rule :P + F = C + 2 (23)

P is the number of phases in equilibriumF is the degree of freedomC is the number of components

When the pressure is kept as a constant, theGibbs phase rule can be modified as:

P + F = C + 1 (24)


The Influence of Surface on Interface on Free Energy

When a phase has a curved surface or interface (withanother phase). The Gibbs free energy of the phase isdifferent from the same phase which does not have acurved surface or interface.

The amount of free energy difference is given by thefollowing equation:

is the surface or interfacial energym is the mass of the phase in molesA is the surface or interfacial area of the phase

G = dAdm (25)


For a spherical particle with a radius, r,

Vm is the molar volume of the phase.

Based on these equations, equation (25) can be changedinto the following equation:

This equation shows that the free energy difference isinversely proportional to the size of the particle.

The free energy difference caused by the surface or interface can change the compositions of the phases inequilibrium in a heterogeneous system.

G =2 V m

r (26)

A = 4 r 2, m =43 r

3/V m


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