1. Lecture 23 Phase Equilibrium  Solid-liquid equilibrium  Gas - liquid/solid equilibrium  Non-ideal systems and phase separation

2. Ideal solutions - solid-liquid In general for a two component system Furthermore, assuming that F ≈ G, molar F is: For ideal solutions

3. Ideal solutions - solid-liquid With X A = 1-X B F as function of composition T > T mA T mB < T < T mA L S XBXB F L S XBXB F

4. Ideal solutions - phase diagram calculations With Where Heat and entropy change of fusion can be taken form experiment or from statistical mechanics formulas

5. Ideal solutions - Phase Diagram L  XBXB T L+ 

6. Non-ideal systems - solid-solid phase separation Two solid phases in equilibrium From Eqs 1 and 2, noticing that there is a symmetry about X = 0.5 and that From the Bragg-Williams approximation (1) (2) XBXB T    + 

7. Non - ideal case: Solid-liquid equilibrium Liquid ideal, solid not From equality of chemical potentials Same for A component Solving for X B of solid and liquid gives the phase diagram

8. Ideal liquid - non-ideal solid phase diagram L  XBXB T L+    +  L+ 