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

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.