Topological transformation of grains in three-dimensional normal grain growth

The topological transformation of grains in three-dimensional normal grain growth was analyzed by Brakke's Surface Evolver method that simulated the boundary motion by curvature. The statistics on elemental processes, which change the number of faces f of a grain, were determined from the simulation. The distribution function of the number of faces P( f ) in a steady structure could be predicted from the difference in the current of grains arriving at and leaving from state f. For the disappearance of one grain, face-creation switching occurred 3.7 times and face-elimination switching occurred 13.2 times on the average.