Spinodal decomposition of an ABv model alloy: Patterns at unstable surfaces
We develop mean-field kinetic equations for a lattice gas model of a binary alloy with vacancies (ABv model) in which diffusion takes place by a vacancy mechanism. These equations are applied to the study of phase separation of finite portions of an unstable mixture immersed in a stable vapor. Due to a larger mobility of surface atoms, the most unstable modes of spinodal decomposition are localized at the vapor-mixture interface. Simulations show checkerboard-like structures at the surface or surface-directed spinodal waves. We determine the growth rates of bulk and surface modes by a linear stability analysis and deduce the relation between the parameters of the model and the structure and length scale of the surface patterns. The thickness of the surface patterns is related to the concentration fluctuations in the initial state.