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. (C) 2007 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.