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.

Finite element modelling of creep cavity filling by solute diffusion

“…Glicksmann evaluated the movingboundary problem of 3D precipitate growth in relation to the static-boundary case [22], and found that for small supersaturations the difference is negligible. A similar analysis has been done by Aaron and coworkers in the context of diffusional phase transformations [23].…”

Numerical simulation of precipitation in multicomponent Ni-base alloys

“…k Þ with the exact analytical solution of the diffusion problem in a semiinfinite matrix for a binary alloy [8,25]:…”

A model for precipitation kinetics and strengthening in Al–Cu–Mg alloys

“…In the model the growth and coarsening of the existing groups of precipitates during each time step is evaluated by [39,40,41]:…”