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A numerical simulation of the growth and coarsening of completely faceted particles in a two-dimensional closed system is described. The particles grow from a supersaturated solution with driving forces including an anisotropic-Gibbs–Thompson effect. Linear and non-linear growth laws were incorporated. This allows comparison to data obtained from physical experiments of Si 3 N 4  growing from a glass matrix with additions of various rare earths (La, Y, Lu) where particle growth is more or less anisotropic (depending on the particular rare earth dopant). Simulations explore the ranges of kinetic parameters for which particle shapes tend to be dictated by thermodynamic and/or kinetic anisotropy. Comparison to data taken from a series of experiments indicates that La probably has a non-linear growth effect whereas Lu is less so.

A simple model of fully-faceted grain growth and coarsening with non-linear growth laws