PowerPoint 프레젠테이션

재 료 상 변 태

Phase Transformation of Materials

2008.09.16.

박 은 수

서울대학교 재료공학부

Contents for previous class

• Review for last class

• Real solutions

• Ordered phases: SRO & LRO, Superlattice

• Intermediate phase (intermetallic compound)

재 료 설 계

σ/E=

10^-4

10^-3

10^-2

10^-1 σ²/E=C Elastomers Polymers

Foams

wood

Engineering Polymers Engineering

Alloys

Engineering Ceramics

Engineering Composites Porous

Ceramics

Strength σ_y (MPa)

Youngsmodulus, E (GPa)

< Ashby map >

0.1 1 10 100 1000 10000

0.01 0.1

1 10 100 1000

Metallic glasses

재 료 설 계

composite Metals

Polymers

Ceramics

Metallic Glasses

Elastomers

Menu of engineering materials

High GFA

High plasticity

higher strength

lower Young’s modulus high hardness

high corrosion resistance good deformability

Contents for today’s class

• Equilibrium in heterogeneous systems

• Binary phase diagrams

• Gibbs phase rule

Equilibrium in Heterogeneous Systems

We have dealt with the case where the components A and B have the same crystal structure.

What would happen when the components A and B

have a different crystal structure?

→ heterogeneous system

) ln ln

( _{A A B B}

B A

B B A

A

X X

X X

RT X

X

G X G

X G

+ +

Ω +

+

=

Equilibrium in Heterogeneous Systems

α α β β

α β + =

B B

o B

G (X ) and G (X ) are given, would be ( ) X ? If

what G at

Lever rule

Temperature

L

α

R S

C_L C₀ C_α

Chemical Equilibrium (μ, a)

→ multiphase and multicomponent (μ_i^α = μ_i^β= μ_i^γ = …), (a_i^α = a_i^β= a_i^γ = …)

=

α β

A A

μ μ μ

= μ

Equilibrium in Heterogeneous Systems

In X⁰, G₀^β > G₀^α > G₁ α + β 로 분리

두상의 화학 포텐셜 일치

Variation of activity with composition

α β

α β

=

=

A A

B B

a a a a

The most stable state,

with the lowest free energy, is usually defined as the state in which the pure

component has unit activity of A in pure α.

= → 1

= 1

A A

when X a

= → 1

= 1

B B

when X a

α β

when and in equil.

두 성분의 activity 일치

1.5 Binary phase diagrams

1) Simple Phase Diagrams

(4) T₁ > T_m(A) >T₂ > T_m(B) >T₃

가정: (1) completely miscible in solid and liquid.

(2) Both are ideal soln.

(3) T_m(A) > T_m(B)

Draw G

and G

as a function of composition X

at T

, T

(A), T

, T

(B), and T

.

= 0 ΔH_mix^S

= 0 ΔH_mix^L

1) Simple Phase Diagrams

(2) Both are ideal soln.

(3) T_m(A) > T_m(B)

(4) T₁ > T_m(A) >T₂ > T_m(B) >T₃

1.5 Binary phase diagrams

1) Simple Phase Diagrams

2) Systems with miscibility gab

= 0 Δ H

congruent minima 1.5 Binary phase diagrams

> 0 Δ H

How to characterize G^s mathematically

in the region of miscibility gap between e and f?

Regular Solutions

Reference state

Pure metal G_A⁰ =G_B⁰ = 0

) ln

ln

(

B A B

B A

A

G X G X X RT X X X X

X

G = + + Ω + +

G₂ = G₁ + Δ_Gmix

∆_Gmix = ∆_{Hmix - T}∆_Smix

∆_{Hmix -T}∆_Smix

Ideal Solutions

2) Systems with miscibility gab

= 0 Δ H

congruent minima 1.5 Binary phase diagrams

> 0 Δ H

• When A and B atoms dislike each other,

• In this case, the free energy curve at low temperature has a region of negative curvature,

• This results in a ‘miscibility gap’ of α′ and α″ in the phase diagram

• Δ H

>>0 and the miscibility gap extends to the melting temperature. ( when both solids have the same structure.)

4) Simple Eutectic Systems Δ H

= 0

1.5 Binary phase diagrams

>> 0

Δ H

(when each solid has the different crystal structure.)

(4)

(4)