THE EQUILIBRIUM SHAPE OF A MISFITTING PRECIPITATE

We examine the equilibrium morphologies of precipitates with either a tetragonal or purely dilatational misfit in an elastically anisotropic medium with cubic symmetry under conditions of plane strain. We find that particles with a dilatational misfit are nearly spherical at small sizes, take on four-fold symmetric shapes at intermediate sizes and then undergo a supercritical symmetry-breaking bifurcation to two-fold symmetric shapes aligned along the elastically soft directions of the crystal. A tetragonal misfit breaks this four-fold to two-fold supercritical bifurcation when the direction of the tetragonality is coincident with one of the elastically soft directions of the crystal. Such a tetragonal misfit can lead to two-fold equilibrium particle shapes which are local energy minima, or metastable, and in some cases have large negative interfacial curvatures. When the tetragonality is not in an elastically soft direction, the supercritical bifurcation is not broken and the particles can take on unusual diamond-like or S-shaped morphologies.