Monte Carlo simulation of microstructure evolution in biphasic systems

Over the past few decades, a variety of models have been proposed in order to investigate the grain growth kinetics and the development of crystallographic textures in polycrystalline materials. In particular, a full understanding of the microstructure evolution is a key issue for ceramic systems, since their mechanical or thermal behaviour is intimately related to their microstructure. Moreover, the development of appropriate simulative tools is crucial to reproduce, control and finally optimize the solid-state sintering process of ceramics. Monte Carlo simulations are particularly attractive because of their ability to reproduce the statistical behaviour of atoms and grain boundaries with time. However, Monte Carlo simulations applied to two-phase materials, such as many ceramic systems, result complex because both grain growth and diffusion processes should be taken into account. Here the Monte Carlo Potts model, which is widely used to investigate the crystallization kinetics for monophasic systems, is modified and extended to biphasic ones. The proposed model maps the microstructure onto a discrete lattice. Each lattice element contains a number representing its phase and its crystallographic orientation. The grain formation and growth are simulated by appropriate switching and reorientation attempts involving the lattice elements. The effect of temperature is also discussed.