Simulating Microstructural Evolution using the Phase Field Method

The key to predict material properties is the state of microstructure. Because microstructural evolution is a typical nonlinear, nonlocal, and multiparticle dynamic problem, computer simulations play an ever increasingly important role in predicting key microstructural features and their time evolution during various processes such as phase transformations, domain coarsening, and plastic deformation. A plethora of computational methods and algorithms have been developed in recent years to complement theoretical and experimental studies to explore the high dimensional material- and processing-parameter space, which would not only lower the cost but also increase the efficiency of optimizing existing materials and developing new ones. In this article, a brief account of the basic features of each method, including the conventional front-tracking methods and techniques without front-tracking (such as Continuum/Microscopic/Coarse-Grained Phase Field Method; Mesoscopic/Atomistic Monte Carlo; Cellular Automata; Discrete Lattice Model; Phase Field Crystal Model; Diffusive Molecular Dynamics; Microscopic Master Equations; Inhomogeneous Path Probability Method; and Molecular Dynamics) will be presented first, followed by detailed descriptions of the fundamentals of various phase-field methods at different length scales and their model formulations. The applications of the phase field methods will be demonstrated by examples of coherent precipitation, grain growth, ferroelectric domain structure formation, dislocation core structures, and dislocation-precipitate interactions. Existing challenges and future trends of the phase-field methods are discussed at the end of the article.