Morphological instability of a solid sphere of dilute ternary alloy growing by diffusion from its melt

•The shape evolution of a growing ternary alloy in its melt is theoretically studied.•Boundary conditions on the species concentrations or the fluxes have been considered.•The thresholds of the morphological instability have characterized.

The diffusion-limited growth of an initially spherical particle of dilute ternary alloy in contact with its melt has been studied from a theoretical point of view and the effects of interface kinetics and multicomponent diffusion have been characterized on the development of a shape perturbation of the sphere. When both concentrations of the diffusing species are imposed in the far-field, the different radii related to the absolute and relative stability of the particle with respect to the development of spherical harmonics have been determined when a linear kinetics law is considered for the solid/liquid interface. The development of the shape fluctuations of the sphere has been also characterized when the flux of both species are set in the far-field.