Theoretical Considerations on the Diffusion-Controlled Particle Growth in an Isotropic Medium

Abstract

The isotropic diffusion‐controlled growth of spherical precipitates in a binary system is investigated based on the modified diffusion equation of Cahn and approximately taking into consideration the boundary conditions. The most important results obtained are: (1) The growth law of the particle radius R(t) depends remarkably on the course of the concentration profile around the stable nucleus R0 present at t = 0 in the matrix. (2) In certain time intervals the growth law R(t) can be fitted by R ∼ tm, where m decreases with the increase of R0, but increases with the duration of the ageing time t. For t → ∞, m to tends to zero. (3) The case D → 0 (approaching the spinodal curve) is also considered.