Motion of phase boundary in solid solutions

Motion of a plane phase boundary between two solid solutions was treated theoretically taking into account interphase and diffusional transport of both components. General expressions for different atomic fluxes across the boundary are proposed; the fluxes are assumed to be proportional to the difference between the activity ratios (actual and equilibrium) of a given component on the opposite sides of the phase boundary. For the case of small solute concentrations in each phase, an analytical solution is obtained for the set of equations that describe diffusion of the components in the bulk of the phases and their transport across the phase boundary. Time dependences of the boundary velocity, characteristic linear dimensions of the phases, and the compositions of phases at the boundary were obtained. It is shown that, in the case considered, independent (for each phase) characteristic time and length scales that determine transition from interphase to diffusional regime of the boundary motion can be introduced. It is found that, for a rather wide range of parameters, the direction of phase-boundary motion may change with time. The expressions obtained give a reasonable description of the phase-boundary motion observed in a wide variety of systems.