Effect of elastic stresses on the morphological stability of a solid sphere growing from a supersaturated melt

We examine the effect of the stresses induced by the composition dependence of the lattice parameter on the quasi-stationary growth dynamics of a spherical solid particle in a supersaturated melt. The problem is formulated using the Larché-Cahn thermodynamic formalism. The elastic field generated by the "self-stress" depends on the entire concentration profile in the grown solid. As a result, the "self-stress" induces a "memory" of the interfacial concentration in the solid at a given time on the values of the interfacial concentration at all earlier times. We find that, in the spherical growth regime, this effect modifies the shape of the concentration profile from its stress free profile, but affects only very weakly the growth velocity. We then perform a linear stability analysis and find that elastic effects destabilize the interface via a reduction in the critical radius for shape instability. Moreover, the elasticity induced memory gives rise to a new qualitative effect: l = 1 modes (describing the diffusional migration of the undeformed sphere) are no longer neutral and become weakly unstable.