Diffusion-Limited Growth of Precipitate Particles

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Abstract
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.