Diffusion-Limited Growth of Precipitate Particles

Diffusion-limited precipitation rates are calculated, using theoretical methods derived previously, for systems of precipitate particles which may change shape as they grow. General formulas are presented, including suitable short- and long-time approximations. Explicit growth laws are derived for systems in which particles are disks and rods subjected to various constraints. The growth exponent n in the short-time approximation is found to be 2 for disks of constant thickness. Rods of constant radius that capture atoms only near their ends have n=1. Both disks and rods of constant ratio of their long and short dimensions have n=3/2. These values contrast with growth laws suggested by Wert and Zener for disks and rods, for which they found n=5/2 and 2, respectively. It is shown that growth conditions at the edge of a growing particle are not constant in diffusion-limited circumstances if the entire surface of the particle acts as a sink.