Review: Binary Phase Diagrams

1. Review: Binary Phase Diagrams all solutions: when entropy is only configurational: ideal solutions: N0zєXAXB regular solutions: є = AB – ½ (AA + BB) regular, positive enthalpy , є > 0  AB is large  avoid A-B bonds  clustering, unmixing, phase separation

2. Regular solutions, positive enthalpy solid phase is a regular solution, W > 0; liquid phase is a an ideal solution Binary Eutectic Liquid TMA TMA Liquid liquidus liquidus  + L  + L solidus liquidus TMB TMB solidus  + L solidus   ´ ´´ ´+´´ ´ ´´ ´+´´ increasing W

3. Binary Eutectic Phase Diagram For W >> 0, no longer useful to think of A and B as forming a continuous solution T1 XB XB

4. Binary Eutectic Phase Diagram For W >> 0, no longer useful to think of A and B as forming a continuous solution At the eutectic temperature XB XB three phases in equilibrium

5. Regular solutions, negative enthalpy N0zєXAXB regular solutions: є = AB – ½ (AA + BB) regular, negative enthalpy , є < 0  AB is small  favor A-B bonds  ordering, compound formation both terms < 0 and symmetric about XA = 0.5

6. Regular solutions, negative enthalpy solid phase is a regular solution, W < 0; liquid phase is a an ideal solution at high T, TDSmix dominates, at low T, DHmix becomes important DGmix maximize AB bonds ‘AB’ compound a´ a´+ AB AB a´´+ AB a´´ XB

7. Regular solutions, negative enthalpy solid phase is a regular solution, W < 0; liquid phase is a an ideal solution |W| is small so liquid region unaffected a´´ low T a´ a´´+ AB TMA a´+ AB liquid AB L + S(a) DGmix a TMB high T ‘AB’ region narrows at high T XB XB |W|  will impact liquid region

8. Regular solutions, negative enthalpy solid phase is a regular solution, W < 0; liquid phase is a an ideal solution solid with AB (solid) bonds preferred over random liquid TMA T liquid L + S(a) L + S(a´) L + S(a´´) TMA TMB a TMB a also moves up AB a´´ a´ XB XB a´´+ AB a´+ AB increasing |W|

9. Regular solutions, negative enthalpy solid phase W << 0, AB compound forms (g), no longer meaningful treat as a solution; liquid phase is a an ideal solution liquid TMg T TMA L + S(a´) L + S(a´´) TMB TMA TMB a really moves up AB a´´ a´ XB a´´+ AB a´+ AB XB increasing |W|

10. Regular solutions, negative enthalpy solid phase W << 0, AB compound forms (g), no longer meaningful treat as a solution; liquid phase is a an ideal solution consider a, b, g as distinct liquid L TMg TMA G TMB T1 XB XB

11. Shape of G curves wide composition range, anti-site defects narrow composition range, few defects G narrow

12. Now consider non-ideal liquid Wsolid and Wliquid > 0, DHmix > 0  tendency to cluster (unmix) Peritectic XB XB increasing W

13. Now consider non-ideal liquid Wsolid and Wliquid >> 0, A hates B and B hates A,  phase separation even in the liquid Monotectic or XB XB

14. Now consider structure change in solid Eutectoid Liquid = ideal g solid = ideal a/b – not a continuous solution (or W >> 0) L + g T g + b a + g a + b

15. Invariant Reactions