The number of contiguous neighbors of grains in polycrystalline materials

Abstract

The stochastic field approach to grain growth in polycrystalline materials permits to combine the stochastic element of the process with physical mechanisms causing grain growth without violating volume conservation, connectivity, and continuity. However, a stochastic field analysis requires knowledge of the number of nearest neighbors of the grains. Based on the assumption that the number of neighbors is determined by their relative size, the present article derives a linear relationship in two dimensions and a parabolic relationship in three dimensions between the number of contiguous neighbors and the grain radius. The models are found to describe simulated 2D and 3D Voronoi polygons as well as the observed number of neighbors–grain size relationships in polycrystalline aluminum.