“Phase Equilibriain Materials” · 2018. 1. 30. · -Binary phase diagrams 1) Simple Phase...
Transcript of “Phase Equilibriain Materials” · 2018. 1. 30. · -Binary phase diagrams 1) Simple Phase...
![Page 1: “Phase Equilibriain Materials” · 2018. 1. 30. · -Binary phase diagrams 1) Simple Phase Diagrams 3) Simple Eutectic Systems G 0 β> G 0 α> G 0 α+β α+ βseparation](https://reader035.fdocument.pub/reader035/viewer/2022062612/6139c0360051793c8c00a87c/html5/thumbnails/1.jpg)
11
Advanced Physical MetallurgyAdvanced Physical Metallurgy
““Phase Phase EquilibriaEquilibria in Materialsin Materials””
EunEun SooSoo ParkPark
Office: 33-316 Telephone: 880-7221Email: [email protected] hours: by an appointment
2009 fall
10. 01. 2009
![Page 2: “Phase Equilibriain Materials” · 2018. 1. 30. · -Binary phase diagrams 1) Simple Phase Diagrams 3) Simple Eutectic Systems G 0 β> G 0 α> G 0 α+β α+ βseparation](https://reader035.fdocument.pub/reader035/viewer/2022062612/6139c0360051793c8c00a87c/html5/thumbnails/2.jpg)
2
Contents for previous class- Equilibrium in Heterogeneous Systems
- Binary phase diagrams1) Simple Phase Diagrams
3) Simple Eutectic Systems
G0β > G0
α > G0α+β α + β separation unified chemical potential
Assume: (1) completely miscible in solid and liquid.(2) Both are ideal soln.
0=Δ SmixH0=Δ L
mixH
2) Variant of the simple phase diagram0>Δ>Δ l
mixmix HH α 0<Δ<Δ lmixmix HH α
miscibility gab Ordered phase
![Page 3: “Phase Equilibriain Materials” · 2018. 1. 30. · -Binary phase diagrams 1) Simple Phase Diagrams 3) Simple Eutectic Systems G 0 β> G 0 α> G 0 α+β α+ βseparation](https://reader035.fdocument.pub/reader035/viewer/2022062612/6139c0360051793c8c00a87c/html5/thumbnails/3.jpg)
3
Contents for today’s class
- Gibbs Phase Rule
- Eutectoid reaction
- Peritectic reaction
Formation of intermediate phases by peritectic reaction
Non-stoichiometeric compounds
- Congruent transformations
![Page 4: “Phase Equilibriain Materials” · 2018. 1. 30. · -Binary phase diagrams 1) Simple Phase Diagrams 3) Simple Eutectic Systems G 0 β> G 0 α> G 0 α+β α+ βseparation](https://reader035.fdocument.pub/reader035/viewer/2022062612/6139c0360051793c8c00a87c/html5/thumbnails/4.jpg)
4
The Gibbs Phase Rule
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 thermodynamicprinciples 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
![Page 5: “Phase Equilibriain Materials” · 2018. 1. 30. · -Binary phase diagrams 1) Simple Phase Diagrams 3) Simple Eutectic Systems G 0 β> G 0 α> G 0 α+β α+ βseparation](https://reader035.fdocument.pub/reader035/viewer/2022062612/6139c0360051793c8c00a87c/html5/thumbnails/5.jpg)
5
For a binary system the equilibria possible are summarised below.
P=cP=c--11P=cP=cP=c+1P=c+1
Invariant reactions which have been observed in binary diagrams are listed below,together with the nomenclature given to such reactions.
![Page 6: “Phase Equilibriain Materials” · 2018. 1. 30. · -Binary phase diagrams 1) Simple Phase Diagrams 3) Simple Eutectic Systems G 0 β> G 0 α> G 0 α+β α+ βseparation](https://reader035.fdocument.pub/reader035/viewer/2022062612/6139c0360051793c8c00a87c/html5/thumbnails/6.jpg)
6
![Page 7: “Phase Equilibriain Materials” · 2018. 1. 30. · -Binary phase diagrams 1) Simple Phase Diagrams 3) Simple Eutectic Systems G 0 β> G 0 α> G 0 α+β α+ βseparation](https://reader035.fdocument.pub/reader035/viewer/2022062612/6139c0360051793c8c00a87c/html5/thumbnails/7.jpg)
7
2
2
231
1
1
1 single phaseF = C - P + 1
= 2 - 1 + 1= 2
can vary T and composition independently
2 two phaseF = C - P + 1
= 2 - 2 + 1= 1
can vary T orcomposition
3 eutectic pointF = C - P + 1
= 2 - 3 + 1= 0
can’t vary T or composition
For Constant Pressure, P + F = C + 1
The Gibbs Phase Rule
![Page 8: “Phase Equilibriain Materials” · 2018. 1. 30. · -Binary phase diagrams 1) Simple Phase Diagrams 3) Simple Eutectic Systems G 0 β> G 0 α> G 0 α+β α+ βseparation](https://reader035.fdocument.pub/reader035/viewer/2022062612/6139c0360051793c8c00a87c/html5/thumbnails/8.jpg)
8
The Gibbs Phase Rule
![Page 9: “Phase Equilibriain Materials” · 2018. 1. 30. · -Binary phase diagrams 1) Simple Phase Diagrams 3) Simple Eutectic Systems G 0 β> G 0 α> G 0 α+β α+ βseparation](https://reader035.fdocument.pub/reader035/viewer/2022062612/6139c0360051793c8c00a87c/html5/thumbnails/9.jpg)
9
Eutectoid reaction
![Page 10: “Phase Equilibriain Materials” · 2018. 1. 30. · -Binary phase diagrams 1) Simple Phase Diagrams 3) Simple Eutectic Systems G 0 β> G 0 α> G 0 α+β α+ βseparation](https://reader035.fdocument.pub/reader035/viewer/2022062612/6139c0360051793c8c00a87c/html5/thumbnails/10.jpg)
10
![Page 11: “Phase Equilibriain Materials” · 2018. 1. 30. · -Binary phase diagrams 1) Simple Phase Diagrams 3) Simple Eutectic Systems G 0 β> G 0 α> G 0 α+β α+ βseparation](https://reader035.fdocument.pub/reader035/viewer/2022062612/6139c0360051793c8c00a87c/html5/thumbnails/11.jpg)
11
Peritectic reaction
![Page 12: “Phase Equilibriain Materials” · 2018. 1. 30. · -Binary phase diagrams 1) Simple Phase Diagrams 3) Simple Eutectic Systems G 0 β> G 0 α> G 0 α+β α+ βseparation](https://reader035.fdocument.pub/reader035/viewer/2022062612/6139c0360051793c8c00a87c/html5/thumbnails/12.jpg)
12
Peritectic reaction0>Δ>Δ l
mixmix HH α
Considerable difference between the melting points
Eutectic reaction
![Page 13: “Phase Equilibriain Materials” · 2018. 1. 30. · -Binary phase diagrams 1) Simple Phase Diagrams 3) Simple Eutectic Systems G 0 β> G 0 α> G 0 α+β α+ βseparation](https://reader035.fdocument.pub/reader035/viewer/2022062612/6139c0360051793c8c00a87c/html5/thumbnails/13.jpg)
13
Eutectic: L→α+β Peritectic: L+α → β
![Page 14: “Phase Equilibriain Materials” · 2018. 1. 30. · -Binary phase diagrams 1) Simple Phase Diagrams 3) Simple Eutectic Systems G 0 β> G 0 α> G 0 α+β α+ βseparation](https://reader035.fdocument.pub/reader035/viewer/2022062612/6139c0360051793c8c00a87c/html5/thumbnails/14.jpg)
14
Peritectic reaction
![Page 15: “Phase Equilibriain Materials” · 2018. 1. 30. · -Binary phase diagrams 1) Simple Phase Diagrams 3) Simple Eutectic Systems G 0 β> G 0 α> G 0 α+β α+ βseparation](https://reader035.fdocument.pub/reader035/viewer/2022062612/6139c0360051793c8c00a87c/html5/thumbnails/15.jpg)
15
Peritectic reaction
![Page 16: “Phase Equilibriain Materials” · 2018. 1. 30. · -Binary phase diagrams 1) Simple Phase Diagrams 3) Simple Eutectic Systems G 0 β> G 0 α> G 0 α+β α+ βseparation](https://reader035.fdocument.pub/reader035/viewer/2022062612/6139c0360051793c8c00a87c/html5/thumbnails/16.jpg)
16
![Page 17: “Phase Equilibriain Materials” · 2018. 1. 30. · -Binary phase diagrams 1) Simple Phase Diagrams 3) Simple Eutectic Systems G 0 β> G 0 α> G 0 α+β α+ βseparation](https://reader035.fdocument.pub/reader035/viewer/2022062612/6139c0360051793c8c00a87c/html5/thumbnails/17.jpg)
17
4.3.4. Formation of intermediate phases by peritectic reaction
![Page 18: “Phase Equilibriain Materials” · 2018. 1. 30. · -Binary phase diagrams 1) Simple Phase Diagrams 3) Simple Eutectic Systems G 0 β> G 0 α> G 0 α+β α+ βseparation](https://reader035.fdocument.pub/reader035/viewer/2022062612/6139c0360051793c8c00a87c/html5/thumbnails/18.jpg)
18
4.3.4. Formation of intermediate phases by peritectic reaction
![Page 19: “Phase Equilibriain Materials” · 2018. 1. 30. · -Binary phase diagrams 1) Simple Phase Diagrams 3) Simple Eutectic Systems G 0 β> G 0 α> G 0 α+β α+ βseparation](https://reader035.fdocument.pub/reader035/viewer/2022062612/6139c0360051793c8c00a87c/html5/thumbnails/19.jpg)
19
4.3.4. Formation of intermediate phases by peritectic reaction
![Page 20: “Phase Equilibriain Materials” · 2018. 1. 30. · -Binary phase diagrams 1) Simple Phase Diagrams 3) Simple Eutectic Systems G 0 β> G 0 α> G 0 α+β α+ βseparation](https://reader035.fdocument.pub/reader035/viewer/2022062612/6139c0360051793c8c00a87c/html5/thumbnails/20.jpg)
20
4.3.4. Formation of intermediate phases by peritectic reaction
(1)
(2)
(3)
(4)
(5)
(1)
(2)
(3)
(4)
(5)
![Page 21: “Phase Equilibriain Materials” · 2018. 1. 30. · -Binary phase diagrams 1) Simple Phase Diagrams 3) Simple Eutectic Systems G 0 β> G 0 α> G 0 α+β α+ βseparation](https://reader035.fdocument.pub/reader035/viewer/2022062612/6139c0360051793c8c00a87c/html5/thumbnails/21.jpg)
21
(2)
Peritectic point virtually coincides with the liquid composition.But, thermodynamically, points P and b is not possible to coincide.
0)( =−A
lS
dXdTSS
))(()(A
lA
A
SA
BAA
lS
dXdX
dXdX
dXdTSS −−=− μμ
lB
SB
lA
SA
ls dGdG μμμμ === ,,At equilibrium,
0/, =≠ AlS dXdTSS
At const P and differentiating with respect toXA
lA
SA XX =
Peritectic point and the liquid composition are so close to each other that the experimental techniquies used were not able to distinguish them.
Temp. maximum or minimum must be present.
![Page 22: “Phase Equilibriain Materials” · 2018. 1. 30. · -Binary phase diagrams 1) Simple Phase Diagrams 3) Simple Eutectic Systems G 0 β> G 0 α> G 0 α+β α+ βseparation](https://reader035.fdocument.pub/reader035/viewer/2022062612/6139c0360051793c8c00a87c/html5/thumbnails/22.jpg)
22
(1)
Decreasing solubility of Zn in Cu with rise in temperaturein contrast to the normal decrease in solubility with fall in temperature
Due to an equilibrium with a disordered intermediate phase(e.g. the β phase above 454 ℃, Fig. 71)
This has been explained as being due to a greater relative movement of the free energy curve of the intermediate phase compared with the αsolid solution with rise in temperature.
![Page 23: “Phase Equilibriain Materials” · 2018. 1. 30. · -Binary phase diagrams 1) Simple Phase Diagrams 3) Simple Eutectic Systems G 0 β> G 0 α> G 0 α+β α+ βseparation](https://reader035.fdocument.pub/reader035/viewer/2022062612/6139c0360051793c8c00a87c/html5/thumbnails/23.jpg)
23
4.3.5. Non-stoichiometeric compounds
![Page 24: “Phase Equilibriain Materials” · 2018. 1. 30. · -Binary phase diagrams 1) Simple Phase Diagrams 3) Simple Eutectic Systems G 0 β> G 0 α> G 0 α+β α+ βseparation](https://reader035.fdocument.pub/reader035/viewer/2022062612/6139c0360051793c8c00a87c/html5/thumbnails/24.jpg)
24
4.3.5. Non-stoichiometeric compounds
![Page 25: “Phase Equilibriain Materials” · 2018. 1. 30. · -Binary phase diagrams 1) Simple Phase Diagrams 3) Simple Eutectic Systems G 0 β> G 0 α> G 0 α+β α+ βseparation](https://reader035.fdocument.pub/reader035/viewer/2022062612/6139c0360051793c8c00a87c/html5/thumbnails/25.jpg)
25
θ phase in the Cu-Al system is usually denoted as CuAl2 although the composition XCu=1/3, XAl=2/3 is not covered by the θ field on the phase diagram.
4.3.5. Non-stoichiometeric compounds
![Page 26: “Phase Equilibriain Materials” · 2018. 1. 30. · -Binary phase diagrams 1) Simple Phase Diagrams 3) Simple Eutectic Systems G 0 β> G 0 α> G 0 α+β α+ βseparation](https://reader035.fdocument.pub/reader035/viewer/2022062612/6139c0360051793c8c00a87c/html5/thumbnails/26.jpg)
26
4.4. Congruent transformations
Congruent transformation:a melting point minimum, a melting point maximum, and a criticaltemperature associated with a order-disorder transformation
![Page 27: “Phase Equilibriain Materials” · 2018. 1. 30. · -Binary phase diagrams 1) Simple Phase Diagrams 3) Simple Eutectic Systems G 0 β> G 0 α> G 0 α+β α+ βseparation](https://reader035.fdocument.pub/reader035/viewer/2022062612/6139c0360051793c8c00a87c/html5/thumbnails/27.jpg)
27
4.4. Congruent transformations
![Page 28: “Phase Equilibriain Materials” · 2018. 1. 30. · -Binary phase diagrams 1) Simple Phase Diagrams 3) Simple Eutectic Systems G 0 β> G 0 α> G 0 α+β α+ βseparation](https://reader035.fdocument.pub/reader035/viewer/2022062612/6139c0360051793c8c00a87c/html5/thumbnails/28.jpg)
28
4.4. Congruent transformations
Relationship between phase diagrams containing congruent and incongruent intermediate phases