Analytical approximations for the evolution of non-equilibrium, stressed planar interfaces

Analytic expressions for the linear and parabolic growth rate constants, and for the time dependence of the interfacial compositions and interfacial velocity associated with the motion of a two-phase planar interface in a multicomponent system are obtained using a linearized gradient approximation for interfaces not in local thermodynamic equilibrium. System geometry is chosen to represent the growth of a plate-like precipitate from supersaturated solution or the growth of a new phase on a thick substrate. The interface is assumed to be coherent, and elastic deformation is allowed in both phases. The analytic expressions are compared to numerical solutions of the complete diffusion equations with a non-equilibrium interface for the binary case and are shown to be in good agreement for ideal solution behavior and moderate supersaturations.