Diffusion-Limited Phase Transformations: A Comparison and Critical Evaluation of the Mathematical Approximations

Abstract

Mathematical analyses previously made for diffusion-limited growth and dissolution of spherical and planar precipitates have been reviewed. The analyses include the invariant-field (Laplace), the invariantsize (stationary interface) and the linear-gradient approximations, and where possible, exact solutions of the differential time-dependent diffusion equation and of the independent flux balance. The kinetic parameters are calculated and the different solutions compared. For virtually all cases of practical interest it is shown that the stationary-interface approximation is the best one. By considering a reversed-growth analysis and showing that it is merely an approximation to the dissolution of a spherical precipitate, it is thereby shown that growth and dissolution cannot be generally considered as simply conjugate processes.