Three-dimensional microstructural evolution in ideal grain growth—general statistics

Abstract The idealized grain growth in three dimensions (3D) was studied by the Surface Evolver method that models the process of boundary motion by curvature to minimize the boundary energy. Even starting from arbitrary packing of uniform grains, the boundary network reached steady structure after the incubation and transient period. The parabolic law in grain growth was observed only in a region where the steady structure was maintained. The more general von Neumann–Mullins law on kinetics of grain growth held in both transient period and normal grain growth period. The grain size distribution function and the distribution of the number of faces in steady structure were analyzed in 3D, and compared with the microstructure in cross-section. The perimeter law and Aboav–Weaire law in 3D on topological nature of boundary network structure held not only in the steady structure but also in transient structures.