Phase Separation
To propose a model, an important step is to identify what ingredients should be included in the model so that it has the power to describe the problem. Before presenting our model, let us review some important and commonly met phenomena in materials. One of them is phase separation.
Phase separation can be explained by the curve of Gibbs free energy versus composition. In this case, the Gibbs free energy is the free energy of mixing. For a regular solution of two components A and B. The Gibbs free energy is expressed by
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where gA and gB are the chemical potential of pure component A and B. C is the concentration of B atoms. L is the atom density. k is the Boltzmann constant (1.38´10-23J/K), T is the absolute temperature. The first two terms in the bracket result from the entropy of mixing, and the third term from the energy of mixing. The dimensionless number W measures bond strength. When W = 0, the equation reduces to that of the ideal solution. W also decides the shape of the curve. When W >2, the curve has two minimum points. For an initially uniform phase with concentration Cave, it tends to separate into two phases: a and b. In this way, the system reaches a lower energy. The following picture illustrates a possibility after phase separation: we obtain a discrete a phase embedded in the continuous matrix of b phase. When W <2, the curve is concave up and the system prefers one phase.
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