Regular N-hedra: A topological approach for analyzing three-dimensional textured polycrystals

Polycrystals consist of contiguous irregular polyhedral grains. The irregularity of such polyhedra occurs because their faces are of mixed form, edges are of variable length and vertices are placed non-symmetrically. The geometric variability of the grain shapes makes detailed energetic and kinetic analysis challenging. To circumvent this difficulty a set of regular polyhedra called average N  -hedra (ANHs) were created in an earlier study consisting of NN identical faces that act as topological “proxies” for the corresponding class of irregular network polyhedral cells containing the same number of faces. This paper provides a generalization of ANHs, allowing extension of the original topological analysis to include the description of a small population of grains growing in textured polycrystals. The analysis shows that the mean curvature of “minority” grains depends not only on their size and number of their faces, but also on their boundary energy, providing new insights into the phenomena of recrystallization and grain growth.