Evaluating microstructural parameters of three-dimensional grains generated by phase-field simulation or other voxel-based techniques

Abstract

The MacPherson–Srolovitz relation expresses the rate of volume change of a grain in a three-dimensional polycrystalline system in terms of microstructural parameters—the mean grain width and the triple line length—as well as isotropic values for the grain boundary mobility and energy. We introduce methods to accurately determine these microstructural measures for grain structures described by a voxel-based microstructure representation, such as those generated by phase-field simulations, Monte Carlo Potts models, or three-dimensional reconstructions of experimentally measured polycrystalline microstructures. We evaluate the mean rate of volume change of grains during a phase-field simulation of grain growth and discuss the results in terms of the MacPherson–Srolovitz relation.