Nucleation in disordered systems

A theory of nucleation is proposed for materials with static disorder, such as glasses and doped crystals. Such disorder makes the barriers to nucleation (W) different in different local regions of the system. We develop an optimum fluctuation method, based on the Cahn-Hilliard approach, to find the probability distribution of barriers g(W). The distribution reaches its maximum at W=〈W〉, determined by the average parameters of the system, and decays exponentially for both W<〈W〉 and W>〈W〉. The particular shape of g(W) depends on the relationship between the distance over which the disorder is correlated and the radius of the critical nucleus. In the steady-state regime the nucleation rate is determined by an optimum barrier ${\mathit{W}}_{\mathrm{opt}}$=${\mathit{W}}_{\mathrm{opt}}$(T)<〈W〉 resulting from the competition between the exponential increase in the nucleation rate exp(-W/kT) and the exponential decrease in g(W). Associated with g(W) is also the probability distribution of nucleation rates I=${\mathit{I}}_0$exp(-W/kT). Because of the latter, the nucleus concentration is nonlinear in time and exhibits an S-shaped transient nucleation. © 1996 The American Physical Society.