Application of the Potts Model to Simulation of Ostwald Ripening

Abstract

Many models have been developed to simulate microstructural evolution in recent years. Among these is the Monte Carlo Potts model used to simulate microstructural evolution under a wide range of conditions for a variety of microstructural evolution processes. An advantage of the Potts model is that the thermodynamic and kinetic characteristics are inherent to the technique. In this paper, grain growth by Ostwald ripening will be used as an example to demonstrate how a well‐designed Potts model need not explicitly specify the thermodynamics of the process; rather, it should rely on the statistical‐mechanical nature of the model to simulate the physics of the process. Simulation of Ostwald ripening requires two components forming two‐phase, solid grains in a liquid matrix with solubility of the components forming the solid phase in the liquid phase. Another requirement is Gibbs‐Thomson's behavior for the solid grains where solubility is inversely proportional to size. The incorporation of these characteristics into the Potts model using the statistical‐mechanical nature of the system will be demonstrated in this paper.