Morphological evolution during phase separation and coarsening with strong inhomogeneous elasticity

We studied the morphological evolution during spinodal phase separation and subsequent coarsening in systems with a strong dependence of elastic constants on the composition. An efficient numerical method is developed for solving the two-dimensional inhomogeneous elastic equilibrium equations by using the conjugate gradient method. A simple model binary system with a symmetric miscibility gap is considered. It is shown that the early stages of spinodal phase separation in a solid solution with a 50-50% composition always result in an interconnected morphology, regardless of the degree of elastic inhomogeneity. For systems with strong elastic inhomogeneity, particle splitting and coalescence take place concurrently during coarsening. In the late stages, the morphology has the characteristics that the hard phase forms precipitates surrounded by the soft phase which forms the matrix, similar to that predicted previously by others using first-order approximations. An analysis of the coarsening kinetics shows that although the growth exponent decreases with the increase in the degree of elastic inhomogeneity, there is no freezing of the coarsening kinetics for all the cases that we studied, in contrast to that predicted previously by others. The effect of an externally applied strain on the two-phase morphology in the elastic regime is also discussed.