Morphological evolutionduring phase separation and coarsening with strong inhomogeneouselasticity

Abstract

We studied the morphological evolution during spinodal phaseseparation and subsequent coarsening in systems with a strongdependence of elastic constants on the composition. An efficientnumerical method is developed for solving the two-dimensionalinhomogeneous elastic equilibrium equations by using the conjugategradient method. A simple model binary system with asymmetric miscibility gap is considered. It is shown that theearly stages of spinodal phase separation in a solid solution witha 50-50% composition always result in an interconnectedmorphology, regardless of the degree of elastic inhomogeneity. Forsystems with strong elastic inhomogeneity, particle splitting andcoalescence take place concurrently during coarsening. In the latestages, the morphology has the characteristics that the hard phaseforms precipitates surrounded by the soft phase which formsthe matrix, similar to that predicted previously by others usingfirst-order approximations. An analysis of the coarsening kineticsshows that although the growth exponent decreases with theincrease in the degree of elastic inhomogeneity, there is nofreezing of the coarsening kinetics for all the cases that westudied, in contrast to that predicted previously by others. Theeffect of an externally applied strain on the two-phase morphologyin the elastic regime is also discussed.