Theory of the arrangement of cells in a network

Lambert, Colin and Weaire, D. L. (1981) Theory of the arrangement of cells in a network. Metallography, 14 (4). pp. 307-318. ISSN 0026-0800

Abstract

A general analysis of the statistics of a random network of threefold vertices is presented. It is demonstrated that Aboav's empirical formula for the number of sides mn on the neighbors of n-sided cells in a polycrystal is consistent with the conjecture that the cells are arranged randomly. Specific models for the development of a random network of cells are investigated and are found to obey relations consistent with Aboav's general formula.