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재 료 상 변 태

Phase Transformation of Materials

2008.09.18.

박 은 수

서울대학교 재료공학부

• Equilibrium in Heterogeneous Systems

• Binary Phase Diagrams

1) Simple Phase Diagrams

2) Systems with Miscibility Gap 3) Simple Eutectic Systems

= 0 ΔH_mix^S

= 0 ΔH_mix^L

= 0

ΔH_mix^L ΔH_mix^S > 0

= 0

ΔH_mix^L ΔH_mix^S >> 0 ) ln

ln

( _{A A B B}

B A B

B A

AG X G X X RT X X X X

X

G = + + Ω + +

Contents for today’s class

• Binary Phase Diagrams

1) Simple Phase Diagrams

2) Systems with Miscibility Gap 3) Simple Eutectic Systems

4) Ordered Alloys

5) Phase dia. containing stable intermediate phases

) ln

ln

( _{A A B B}

B A B

B A

AG X G X X RT X X X X

X

G = + + Ω + +

= 0 ΔH_mix^S

= 0 ΔH_mix^L

= 0

ΔH_mix^L ΔH_mix^S > 0

= 0

ΔH_mix^L ΔH_mix^S >> 0

= 0 ΔH_mix^L

= 0 ΔH_mix^L

< 0 ΔH_mix^S

<< 0 ΔH_mix^S

In X⁰, G₀^β > G₀^α > G₁ α + β 로 분리 두상의 화학 포텐셜 일치

α₁ β₁

α₄ β₄

-RT lna_B^β -RT lna_B^α -RT lna_A^α

-RT lna_A^β

a_A^α=a_A^β a_B^α=a_B^β

G_e

A B A B

High Temp. Low Temp.

L

S S

L

G_A^L

G_A^S G_B^S

G_B^L

G_B^L 변화량 >

G_A^L, G_A^S, G_B^S 변화량 G= H - TS

곡률

>

1) Simple Phase Diagrams

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

(2) Both are ideal soln.

(3) T_m(A) > T_m(B) ΔH_mix^L = 0 ΔH_mix^S = 0

(4) T₁ > T_m(A) >T₂ > T_m(B) >T₃

2/7 5/7

L L+S S

S L

1.5 Binary phase diagrams

1) Simple Phase Diagrams

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

(2) Both are ideal soln.

(3) T_m(A) > T_m(B) ΔH_mix^L = 0 ΔH_mix^S = 0

(4) T₁ > T_m(A) >T₂ > T_m(B) >T₃

2) Systems with miscibility gap _Δ ^L _{= 0}

Hmix ΔH_mix^S > 0

2) Systems with miscibility gap _Δ ^L _{= 0}

Hmix ΔH_mix^S > 0

1.5 Binary phase diagrams

4) Simple Eutectic Systems ^ΔH_mix^{L = 0 ΔH}_mix^{S >> 0}

α L+α L L+β β α

L β

(when each solid has the different crystal structure.)

4) Simple Eutectic Systems ^ΔH_mix^{L = 0 ΔH}_mix^{S >> 0}

β β

3) Ordered Alloys ^ΔHmix^{L = 0}

1.5 Binary phase diagrams

< 0 ΔH_mix^S

ΔH_mix < 0 → A atoms and B atoms like each other.

What would happen when ΔH_mix<< 0?

→ The ordered state can extend to the melting temperature.

How does the phase diagram differ from the previous case?

가.

나.

congruent maxima

Regular Solutions

Reference state

Pure metal G_A⁰ =G_B⁰ = 0

) ln

ln

( _{A A B B}

B A B

B A

AG X G X X RT X X X X

X

G = + + Ω + +

G₂ = G₁ + Δ_Gmix

∆_Gmix = ∆_{Hmix - T}∆_Smix

∆_{Hmix -T}∆_Smix

Intermediate Phase

* Solid solution

Æ random mixing Æ entropy ↑

negative enthalpy ↓

넓은 조성 범위 Î G ↓

* Compound : AB, A₂B…

Æ entropy↓

Æ covalent, ionic contribution.

Æ enthalpy more negative ↓

좁은 조성 범위 Î G ↓

< 0 ΔH_mix^S

<< 0 ΔH_mix^S

5) Phase diagrams containing intermediate phases

5) Phase diagrams containing intermediate phases

1.5 Binary phase diagrams

another solid phase upon cooling

α

The Gibbs Phase Rule

1.5 Binary phase diagrams

In chemistry, Gibbs' phase rule describes the possible number of degrees of freedom (F) in a closed system at equilibrium, in terms of the number of separate phases (P) and the number of chemical components (C) in the system. It was deduced from thermodynamic principles by Josiah Willard Gibbs in the 1870s.

In general, Gibbs' rule then follows, as:

F = C − P + 2 (from T, P).

From Wikipedia, the free encyclopedia

Degree of freedom (number of variables that can be varied independently)

= the number of variables – the number of constraints

2

2 3 2 1

1

1

1 single phase F = C - P + 1

= 2 - 1 + 1

= 2

can vary T and composition independently

2 ^{two phase}

F = C - P + 1

= 2 - 2 + 1

= 1

can vary T or composition

3 eutectic point F = C - P + 1

= 2 - 3 + 1

= 0

can’t vary T or composition For Constant Pressure,

P + F = C + 1

The Gibbs Phase Rule