Complete topology of cells, grains, and bubbles in three-dimensional microstructures

Emanuel A. Lazar, Jeremy K. Mason, Robert D. MacPherson, David J. Srolovitz

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Abstract

We introduce a general, efficient method to completely describe the topology of individual grains, bubbles, and cells in three-dimensional polycrystals, foams, and other multicellular microstructures. This approach is applied to a pair of three-dimensional microstructures that are often regarded as close analogues in the literature: one resulting from normal grain growth (mean curvature flow) and another resulting from a random Poisson-Voronoi tessellation of space. Grain growth strongly favors particular grain topologies, compared with the Poisson-Voronoi model. Moreover, the frequencies of highly symmetric grains are orders of magnitude higher in the grain growth microstructure than they are in the Poisson-Voronoi one. Grain topology statistics provide a strong, robust differentiator of different cellular microstructures and provide hints to the processes that drive different classes of microstructure evolution.

Original languageEnglish
Article number095505
JournalPhysical Review Letters
Volume109
Issue number9
DOIs
StatePublished - 31 Aug 2012
Externally publishedYes

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