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

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 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.