Enumeration of Polyhedra for Grain Growth Analysis
The advent of three dimensional data collection, grain reconstruction, and subsequent materials analysis has created opportunities to revisit problems in grain growth and polycrystalline structure. In this paper we review the relevant literature concerning the total number of polyhedral grains of a given number of faces and take the additional first steps at enumerating the topologies of the members within each set. Analysis of the dispersion in topology relative to the idealized N-hedra is presented. The relevance to grain growth simulations and experiments is discussed.
KeywordsPolyhedral graphs Grain growth Monte Carlo methods
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