Simulations of microstructural evolution: anisotropic growth and coarsening

Two-dimensional calculations of anisotropic growth and coarsening are illustrated. This model is intended to simulate the development of microstructure in materials like silicon nitride. The model is comprised of an ensemble of polygonal particles with anisotropic surface energies and growth mobilities. Particle growth is modeled by linear kinetics with a driving force proportional to a difference between local supersaturation and an equilibrium chemical potential which depends on particle geometry and surface tension. The competition for solute for particle growth is calculated via the diffusion equation, and conservation laws determine the strength of sources (or sinks) in the diffusion equation. Statistics of particles size distributions are obtained and regimes of kinetic behavior are related to transitions from non-equilibrium to near-equilibrium kinetics. Computed microstructures are qualitatively comparable to those observed experimentally.