Multiparticle diffusion analysis

Abstract

The LSW theory for coarsening has a serious drawback: it does not account for diffusional interactions between particles. As a result the coarsening rate of a particle is a function only of the radius of a particle relative to the average particle size. This is not the case in nonzero volume fraction systems, for when a particle of a given size is surrounded by particles larger than itself it must coarsen in a different manner than when this particle is surrounded by particles that are smaller than itself. Diffusional interactions between particles also must lead to a coarsening rate of the system that is a function of the volume fraction. As the volume fraction increases the interparticle separation decreases but the concentration in the matrix at the interfaces of the particles is not a function of the interparticle separation, it set by the Gibbs-Thomson equation. Thus the concentration gradients in the matrix at the interfaces increases with increasing volume fraction and the coarsening rate of the system must therefore increase. Both the physics of local diffusional interactions and the dependence of the coarsening rate on volume fraction are missing from the LSW theory.