Theory of diffusional growth in cellular precipitation

Abstract

A new approach is proposed for the description of cellular precipitation. The crucial difference between the present approach and the previous investigations is that the analysis uses the surface diffusion equation along all three interfaces and matching conditions for the chemical potentials and diffusional fluxes at the triple point. This allows a well-posed problem to be formulated. The solution of this system of local equations gives both the growth velocity and the width of the growing phase as functions of supersaturation and lamellar spacing. It is found that the steady-state growth occurs only if the spacing is above some critical value which depends on the supersaturation. The growth velocity remains finite at this critical spacing. Moreover, the steady-state solutions exist only if some conditions for the material parameters are fulfilled.