Freezing is a liquid-to-solid phase transition. A moving phase boundary releases latent heat; its rate is constrained by heat transport and the Stefan condition. In a solution the liquidus depends on composition, so being below the pure solvent's melting temperature does not imply that the solution must freeze.
A morphological instability amplifies shape perturbations of a solidification interface. Protrusions may receive a larger diffusive supply or encounter larger undercooling, while curvature-induced melting-temperature depression suppresses fine corrugations. Solute rejection can produce constitutional supercooling, destabilizing a planar front and leading to cells or crystal dendrites.
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