Microstructural characteristics of 3-d networks

Abstract

AbstractThe structural characteristics of three-dimensional (3-d) irregular networks, such as random polycrystals, are described using scaling arguments based on the properties of Average N-hedra (ANH’s). ANH’s comprise a special set of highly symmetric polyhedral cells that satisfy topological and geometrical criteria demanded in 3-d space-filling networks. All the geometrical properties of ANH’s may be obtained from exact analytical expressions already derived in [1]. The utility and ease of use of these formulas have been carefully checked against accurate simulations of the excess free energy and evolution kinetics of foams and polycrystals. The vertex-to-vertex distance is chosen in this paper as the consistent gauge to estimate an important microstructure feature set presented here for irregular 3-d networks. In the case of annealed polycrystals this includes the total grain boundary area and its associated stored energy per unit volume, the triple line length per unit volume, and the number density of triple lines and quadra-junctions – all of which may be expressed in terms of the polycrystal's grain number density.