Phase-Field Modeling of Grain Growth

Abstract

When a polycrystalline material is held at elevated temperature, the boundaries between individual crystallites, or grains, can migrate, thus permitting some grains to grow at the expense of others. Planar sections taken through such a specimen reveal that the net result of this phenomenon of grain growth is a steady increase in the average grain size and, in many cases, the evolution toward a grain size distribution manifesting a characteristic shape independent of the state prior to annealing. Recognizing the tremendous importance of microstructure to the properties of polycrystalline samples, materials scientists have long struggled to develop a fundamental understanding of the microstructural evolution that occurs during materials processing. In general, this is an extraordinarily difficult task, given the structural variety of the various elements of microstructure, the topological complexities associated with their spatial arrangement and the range of length scales that they span. Even for single-phase samples containing no other defects besides grain boundaries, experimental and theoretical efforts have met with surprisingly limited success, with observations deviating significantly from the predictions of the best analytic models. Consequently, researchers are turning increasingly to computational methods for modeling microstructural evolution. Perhaps the most impressive evidence for the power of the computational approach is found in its application to single-phase grain growth, for which several successful simulation algorithms have been developed, including Monte Carlo Potts and cellular automata models (both discussed elsewhere in this chapter), and phase-field, front-tracking and vertex approaches.