3-D phase-field simulation of grain growth: Topological analysis versus mean-field approximations

The characteristics of 3-D grain growth are investigated by a topological analysis of phase-field simulation results compared with theoretical mean-field theories. We found that the size distribution of the grains starting from an arbitrary narrow distribution crosses the self-similar Hillert distribution, and ends in a distribution with relatively longer tails of large grains in which the central peak shifted towards smaller grain size. The distribution of topological classes, as characterized by the number of facets per grain, is found to be time-invariant for the process as a whole. The obtained shape function is in good agreement with the analytical distribution function derived based on the average N-hedron model [Rios PR, Glicksman ME. Act Mater 2008;56:1165]. The volumetric growth rate per topological class also correlates well with the analytical approach obtained by Mullins [Mullins WW. Acta Mater 1956;3:900]. The relationship between grain size and its shape, however, deviates from theoretical predictions.