Numerical Simulation of Grain Size Distribution in Two-Phase Polycrystalline Materials

Numerical simulations based on the Monte Carlo Potts model are used to study the temporal change of the grain size distribution of two-phase polycrystalline materials, where both phases grow simultaneously. After a sufficiently long time, grain growth in such two-phase systems can be characterized by a self-similar scaled grain size distribution function and an associated growth law. In particular, the grain size distribution is analyzed for a broad range of second phase volume fractions and found to vary with the volume fraction such that the size distribution becomes narrower and higher peaked with decreasing volume fraction of the second phase, where particularly the normal distribution function describes the simulation results very well. On the other hand, for one-phase systems the grain size distribution is in excellent agreement with an analytical grain size distribution function based on a statistical mean-field theory of grain growth that is completely compatible with the principal physical condition of total volume conservation.