Polyhedral model for self-similar grain growth

The distribution of the number of faces per grain may be extracted routinely from grain simulations and experimental observations of three-dimensional (3-D) reconstructions. However, the only theoretical face number distribution available is the recent reassessment of Hillert’s distribution [Rios PR, Glicksman ME. Acta Mater 2007;55:1565]. The theoretical face distribution derived in that paper, however, provides an inadequate representation of 3-D grain-face data. We derive a new grain-face distribution by using topological relationships based on average N-hedra, and find an improved agreement with simulations based on surface Evolver computations published by Wakai and co-workers. Transformation of the grain-face distribution also provides a satisfactory representation of the grain-size distribution. The present approach, using a polyhedral model for the grain network, adds topological information to the kinetics of grain network evolution, including its influence on metrical parameters such as grain vertex separation.