Large-scale simulations of Ostwald ripening in elastically stressed solids: I. Development of microstructure

We present the results from large-scale simulations of Ostwald ripening of misfitting second-phase particles in an elastically anisotropic system. We employ the sharp interface description and perform simulations in two dimensions using boundary integral methods combined with state-of-the-art numerical methods such as the fast multipole method. We find that particle shapes are perturbed by elastic interactions at sufficiently large area fractions and particle sizes, and thus the shapes are not given by the equilibrium morphology of an isolated particle. Unlike isolated particles, the morphology transitions from fourfold to twofold shapes are not sharp, but are smeared due to interparticle interactions. However, for a very low area fraction system, the particles remain fourfold symmetric well beyond the bifurcation point, indicating that elastic interactions are essential in inducing a particle shape bifurcation. We find that the evolution of the microstructure is not scale invariant. However, the microstructure is unique, in a statistically averaged sense, for a given ratio of the elastic and interfacial energies.