Three-dimensional grain size distribution: Comparison of an analytical form under a topology-related rate equation with computer simulations and experimental data

Based on a new grain growth rate equation, in which the changing rate of grain size is related to grain size and topological properties, an analytical quasi-stationary grain size distribution was obtained. It is in good agreement with computer simulation results by various methods: Potts model Monte Carlo, Potts model Cellular Automaton, Surface Evolver, vertex and phase-field. It also shows good agreement with the experimental grain size distributions for pure iron and low-carbon steel by serial sectioning, respectively.