The shape of grains in a polycrystal

Topology and grain size distribution of a two dimensional microstructure produced by a computer tessellation method

“…8. Grain size increased linearly with the number of the sides, which was in accord with other experimental and computer simulation results [6,12,[14][15][16].…”

Post-deposition grain growth in metallic films

“…another useful metric for comparison of experiments and simulations is the average number of neighbors (sides) of the nearest neighbors of each grain, <n NN >, as a function of number of sides, n. For simplicity, <n NN > is termed the average side class of neighbors, and it is used to examine the clustering of grains around grains of a given side class, n. <n NN > was fi rst reported by aboav and Langdon [28] and aboav [29] for two-dimensional sections of three-dimensional grain structures of MgO and was later used by Frost et al [21] for examining simulated two-dimensional grain structures.…”

Three-dimensional virtual grain structure generation with grain size control

“…The topological and morphological characteristics of the Poisson Voronoi tessellation (PVT), where seeds are generated according to a homogeneous Poisson point process, have been intensively studied (Meijering, 1953;Aboav and Langdon, 1969;Hinde and Miles, 1980;Boots and Murdoch, 1983;Weaire et al, 1986;Møller, 1989;Kumar et al, 1994;Oger et al, 1996). The empirical results and rules relating to the mean area and mean perimeter of a 2D PVT, the mean volume and surface area of a 3D PVT, the number of vertices and edges of a typical grain and the length of a typical edge, etc., have been derived.…”