Coarsening of multicomponent thin films

The theory for the kinetics of coarsening of multicomponent thin films is studied. The growth and decay rates of surface clusters consisting of more than one chemically distinct species are represented through a formalism based on the theory of real solutions. Explicit expressions are presented for the time evolution of a thin film in terms of the quasichemical rate equation approach that describes the concentrations of clusters of variable size and composition. The continuum limit of the rate equations yields a partial differential equation that applies to the late stage growth. It is found that the traditional Lifshitz-Slezov-Wagner approach, which employs a first-order continuity-type equation, is inadequate to treat the compositional variation of the clusters. Instead, a second-order generalized diffusion equation should be used. A model problem of a binary film, consisting of two types of atoms interacting through nearest-neighbor and next-nearest-neighbor coupling, is studied using a dynamical Monte Carlo method. The cluster size and composition distributions are extracted from the simulations as functions of time. The film kinetics exhibits a crossover behavior between coalescence-diffusion coarsening at short times and Ostwald ripening at long times. Except for very small cluster sizes, the distributions are well represented by a separable two-dimensional scaling-type solution.