Ising Model for Phase Separation in Alloys with Anisotropic Elastic Interaction. I. Theory

We propose a model to study, on an atomistic scale, the eeects of elastic misst strains on the growth and coarsening of domains in phase-separating alloys. The model considered is a two-dimensional square crystal lattice with periodic boundary conditions and with an A or B atom near each site. To model the elastic interaction, nearest and next-nearest neighbors are connected by springs with longitudinal and transverse stiinesses. In addition, there is a chemical interaction between nearest neighbours, favouring like against unlike pairs. A mean eld analysis predicts phase separation into coherent phases, below a temperature which (for a typical set of elastic parameters) increases with the strength of the elastic forces. This critical temperature is less than that for separation into incoherent phases. The analysis also predicts how the anisotropy determines the shapes of domains at early times. A Monte Carlo procedure for implementing Kawasaki dynamics to represent diiusion in this model is described.