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 a pproach, to find the probability distribution of barriers g(W). The di stribution reaches its maximum at W=[W], determined by the average par ameters of the system, and decays exponentially for both W<[W] and W>[ W]. The particular shape of g(W) depends on the relationship between t he distance over which the disorder is correlated and the radius of th e critical nucleus. In the steady-state regime the nucleation rate is determined by an optimum barrier W-opt=W-opt(T)<[W] resulting from the competition between the exponential increase in the nucleation rate e xp(-W/kT) and the exponential decrease in g(W). Associated with g(W) i s also the probability distribution of nucleation rates I=I(0)exp(-W/k T). Because of the latter, the nucleus concentration is nonlinear in t ime and exhibits an S-shaped transient nucleation.