1. 10.5 Liquid and Solid Standard States
Phase Diagram for Transformation between Raoultian Liquid and Solid Solutions
The activities and Choice of Standard States

2. Choice of Standard States
Standard States of GM = 0 is chosen at liquid A and solid B.
Standard States of GM = 0 is chosen at liquid A and liquid B.
Standard States of GM = 0 is chosen at solid A and solid B.

3. Choice of Standard States
solid A and solid B.
liquid A and solid B.
liquid A and liquid B.
The choice of standard states will not alter the positions of the double tangent.

4. The Activities of B with Composition

5. The Activities and Standard States

6. The Activities with Chosen Standard States

7. The Activities of A with Composition

8. The Activity Values with Temperature
( )
If temperature is decreased,

9. The Double Tangents with Temperaturef e f e f e f e f e f e f e f e f e f e f

10. 10.6 Phase Diagrams, Gibbs Free Energy, and Thermodynamic Activity
Phase Diagram for Transformation between Raoultian Liquid Solution and Solid Solution with Miscibility Gap
Phase Diagram for Transformation between Raoultian Liquid Solution and Insoluble Solid Solutions
Dependence of Liquidus Line on Positive Deviation of Liquid Solution from Raoultian behavior

11. Miscibility Gap 1 2 3 4
Two solid solutions (I and II) are competing with one liquid solution.(III)
Two solid solutions (I and II) have different crystal structures.
Two solid solutions (I and II) have the same crystal structure.

12. 10.6 Phase Diagrams, Gibbs Free Energy, and Thermodynamic Activity
Phase Diagram for Transformation between Raoultian Liquid Solution and Solid Solution with Miscibility Gap
Phase Diagram for Transformation between Raoultian Liquid Solution and Insoluble Solid Solutions
Dependence of Liquidus Line on Positive Deviation of Liquid Solution from Raoultian behavior

13. Effect of Temperature on Molar Gibbs Free Energy of Mixing

14. Effect of Temperature on Activities

15. Activities at T1
Activity B for solution III follows the diagonal line, since solution III is ideal liquid solution and liquid B is chosen as standard state.
Activity A for solution III does not follow the diagonal line, not because that solution III is not an ideal solution, but because solid A is chosen as standard state.
Activity B for solution I positively deviates from the diagonal line, because that the solution I is an positively deviated non-ideal solid solution and should positively deviates from the diagonal line, even if solid B in phase I is chosen as standard state. Since liquid B is chosen as standard state, the curve deviates even more positive.
Activity A for solution I positively deviates from the diagonal line, because that the solution I is an positively deviated non-ideal solution and should positively deviates from the diagonal line, as solid A in phase I is chosen as standard state. However, the curve should approach diagonal line as XA approaches 1 to conform to Raoultian behavior of pure element.

16. Activities at T2
Activity B for solution I positively deviates from the diagonal line, because that the solution I is an positively deviated non-ideal solid solution, and should positively deviates from the diagonal line, even if solid B in phase I is chosen as standard state. Since solid B in phase II is chosen as standard state, the curve deviates even more positive.
Activity B for solution III does not follow the diagonal line even though solution III is an ideal liquid solution, since solid B in phase II, and not the liquid B, is chosen as standard state. However, extrapolation of the activity curve passes through the original point A, suggesting the ideal solution.
Activity B for solution II positively deviates from the diagonal line, because that the solution II is an positively deviated non-ideal solid solution and should positively deviates from the diagonal line, as solid B in phase II is chosen as standard state. However, the curve should approach diagonal line as XB approaches 1 to conform to Raoultian behavior of pure element.

17. Activities at TE (Eutectic)
Activity B for solution I positively deviates from the diagonal line, because that the solution I is an positively deviated non-ideal solid solution, and should positively deviates from the diagonal line, even if solid B in phase I is chosen as standard state. Since solid B in phase II is chosen as standard state, the curve deviates even more positive.
Activity B for solution III remains as one single point, with its value equal to that of its conjugate solid solutions of phase I and that of its conjugate solid solutions of phase II.
Activity B for solution III and that of its conjugate solid solutions is slightly higher than activity A for solution III and that of its conjugate solid solutions, as can be deduced from the difference of the intercepts of the triple tangent line to the Gibbs free energy of mixing curves with A and B axes.

18. Activities at T3
Activity B for solution I positively deviates from the diagonal line, because that the solution I is an positively deviated non-ideal solid solution, and should positively deviates from the diagonal line, even if solid B in phase I is chosen as standard state. Since solid B in phase II is chosen as standard state, the curve deviates even more positive.
Activity B for the conjugate solid I and II solutions is slightly higher than activity A for the conjugate solid I and II solutions, as can be deduced from the difference of the intercepts of the double tangent line to the Gibbs free energy of mixing curves with A and B axes.

19. 10.6 Phase Diagrams, Gibbs Free Energy, and Thermodynamic Activity
Phase Diagram for Transformation between Raoultian Liquid Solution and Solid Solution with Miscibility Gap
Phase Diagram for Transformation between Raoultian Liquid Solution and Insoluble Solid Solutions
Dependence of Liquidus Line on Positive Deviation of Liquid Solution from Raoultian behavior

20. Gibbs Free Energy of Mixing Curve for Insoluble Solutions

21. Phase Diagram for Insoluble Solid Solutions
Also note that the equation above can be derived from the equation below with XA(s) = 1.

22. The Calculation of Bi Liquidus Line in Cd-Bi System

23. The Bi Liquidus Line Bi Cd

24. The Calculation of Cd Liquidus Line in Cd-Bi System

25. The Cd Liquidus Line Bi Cd

26. Deviation from Actual Liquidus Lines
ideal
Positive deviation

27. 10.6 Phase Diagrams, Gibbs Free Energy, and Thermodynamic Activity
Phase Diagram for Transformation between Raoultian Liquid Solution and Solid Solution with Miscibility Gap
Phase Diagram for Transformation between Raoultian Liquid Solution and Insoluble Solid Solutions
Dependence of Liquidus Line on Positive Deviation of Liquid Solution from Raoultian behavior

28. Liquidus Lines and 
For  > cr

29. Imminent Immiscibility at Wcr

30. Monotectic Phase Diagram

31. 10.7 The Phase Diagrams of Binary Systems That Exhibit Regular Solution Behavior in The Liquid and Solid States

32. Hypothetical Regular Solution

33. Hypothetical Regular Solution

34. Hypothetical Regular Solution
With increasingly negative values of l and increasingly positive values of s the temperature of the point of contact of the liquidus curve with the solidus curve decreases and the critical temperature in the solid state increases, which eventually produces a eutectic system.

35. Hypothetical Regular Solution

36. Effect of l and s on Phase Diagrams
Assume regular liquid and solid solutions.