Comparison of phase-field and potts models for coarsening processes

We have compared the phase-field model to the Potts model for two coarsening processes, grain growth and Ostwald ripening, both in two-dimensions. The Potts model is a discrete, statistical mechanical numerical simulation technique. In contrast, the phase-field model is a continuum, thermodynamic numerical simulation technique. The similarities and differences in microstructures, kinetics, and grain size distributions obtained for grain growth and Ostwald ripening by the phase-field model and by the Potts model were investigated. Both models gave very similar kinetic, topological and grain size distribution results for grain growth and Ostwald ripening in spite of their different approaches. In this paper, we review each model and its application to coarsening processes, present the results of grain growth and Ostwald ripening and finally, discuss how the physics of grain growth and Ostwald ripening is incorporated into these two different models.