Two- and three-dimensional equilibrium morphology of a misfitting particle and the Gibbs-Thomson effect

The equilibrium shapes of misfitting precipitates in elastically anisotropic systems are obtained in both two and three dimensions, and the corresponding Gibbs-Thomson equation is derived as a function of the characteristic ratio between elastic and interfacial energies, L′. The effect of elastic inhomogeneity is investigated systematically. For soft or moderately hard particles, the stable equilibrium shape bifurcates from a fourfold symmetric shape to a twofold symmetric one in 2D and from a cubic symmetric shape to a plate-like one in 3D. For a very hard particle, the shape bifurcation is not observed in 2D for the range of L′ investigated, but both plate-like and rod-like shapes are found in 3D. The computed Gibbs-Thomson equation is well approximated by a piecewise linear function of L′. Predictions are made for coarsening of many-particle systems based on an established mean-field theory. The results predict that the elastic stress has no effect on coarsening kinetics where most particles are highly symmetric (fourfold in 2D and cubic in 3D), and the exponent remains 1/3 but the rate constant increases if stress is sufficient to induce symmetry-breaking bifurcation on most particles.