Growth of a coherent precipitate from a supersaturated solution

A treatment of diffusion limited growth of a coherent spherical precipitate into supersaturated solution is presented. It is found that the growth kinetics are affected by dilatational coherency strains and by compositionally induced strains in the matrix phase. Numerical solutions to the time-dependent problem are obtained and are compared to the quasistationary solution. The parabolic growth coefficient is a function of the transformation strain, partial molar volumes of the components, elastic constants in each phase, interfacial compositions and far-field composition while, in contrast, the growth coefficient in the absence of stress is a function only of the reduced supersaturation. Elastic effects shift the interfacial concentration of the matrix in the direction of the far-field concentration, reducing the effective driving force for growth. At the same time, compositionally induced strains increase the diffusive flux, increasing the growth rate.