Modelling the evolution of phase boundaries in solids at the meso- and nano-scales

Phase boundaries play an important role in setting the properties of multicomponent materials at both the meso- and nano-scales. In this review, we provide an overview of the modelling methods utilized in state-of-the-art research and engineering applications. We review the current physical understanding of how phase boundaries evolve, focusing on multicomponent systems. The recent advances in numerical modelling, fueled by powerful computers, have provided accurate and robust results that allow problems that are beyond the reach of analytic methods to be addressed. While the approaches used in engineering-oriented applications employ simplified microstructures, it is found that such models are quite useful in many problems. The ability to simulate realistic microstructures will further increase the power of materials modelling. We also highlight the differences between the sharp interface and diffuse interface approaches for modelling microstructural evolution. In addition, we identify future research topics in this area.