Kinetics of phase change in a model binary alloy

We discuss the predictions of the phenomenological theory of Metiu, Kitahara, and Ross for the most probable evolution of concentration fluctuations in the Bragg-Williams binary alloy model. The knowledge of the exact (nonlocal) from for the free-energy functional $\mathcal{F}$ permits a precise study of the kinetics of phase change under strongly nonuniform conditions. For every subcritical temperature and concentration in the spinodal region there exists, for both segregating and ordering alloys, an infinite family of periodic stationary states in addition to the usual uniform ones. The stability analysis of these states provides a description of spinodal decomposition in segregating alloys and of the ordering transitions in ordering alloys. The difference in light-scattering properties for the two types of transitions is emphasized. It is also shown that fluctuations separated in space are correlated through the nonlocality of $\mathcal{F}$ and that they cooperate with the nucleation process with an additional term absent in the classical and gradient theories. The solitary wave motion which describes interface motions is obtained from a perturbation on the thermodynamic conditions for phase equilibrium.