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Unformatted text preview: Exercise - Spinodal phase separation in two dimensions (due 04/09/02)
Use the following free energy model to describe the thermodynamics of a binary solution,
1 α 1 F = ∫ h − c 2 + c 4 + (∇c )2 dV 2 42 V where h and α are positive constants. Please note that c can be positive or negative. It can be related to actual composition, X, through X − [(X a + X β ) 2] c= [(X a − X β ) 2] Therefore, c = -1 and +1 represent the actual equilibrium compositions, Xα and Xβ Exercise (cont.)
1. Show that the spinodal region using the above free energy model is given by − 1 <c< 3 1 3 2. Calculate kc and kmax in terms of h and α for a solid solution with overall composition co. 3. Simulate the spinodal phase separation process using the supplied visual Fortran code for the following four compositions, co = -0.75, -0.35, 0.0, 0.35. Set h =1.0 and α = 1.0. Discuss the results and point out the differences in the simulation results for different compositions. 1 ...
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This note was uploaded on 01/19/2010 for the course MAT SCI 503 taught by Professor Chen during the Spring '02 term at Pennsylvania State University, University Park.
- Spring '02