Hybrid Potts-phase field model for coupled microstructural–compositional evolution

In this work, we introduce and demonstrate a hybrid model that combines elements of the Monte Carlo Potts Model with those of the phase field model. This hybrid model is introduced as a method to simulate microstructural evolution processes that are kinetically controlled by long-range diffusion in multi-component systems. The hybrid model uses a digitized microstructure with each site characterized by its microstructural features and its composition. The total free energy of the system is defined by bulk chemical free energy as well as interfacial energy. The coupling between the microstructure and composition is achieved by using the total free energy to drive the evolution in both fields. The kinetics are simulated by a combination of Monte Carlo methods and solution of the Cahn–Hilliard equation. This model is applied to several example problems to demonstrate its capabilities. These are diffusion in single- and two-phase diffusion couples, grain growth in a two-phase system controlled by diffusion and diffusion phase transformation by nucleation and growth of a second phase.