Correlations in topological models of 2D random cellular structures

Abstract

General relations and constraints which must be satisfied by the topological correlations in 2D space-filling random cellular structures are discussed and a topological short-range order coefficient is defined. Topological models of 2D structures are associated with planar tessellations with topologically unstable sites which belong to z)3 polygons. The stable configurations, called states, are obtained by replacing every vertex by z-3 added sides. The topological properties of the latter models are calculated exactly for a distribution of independent and equiprobable states on the various sites and for any value of z. The case of the structures associated with tilings by triangles is thoroughly considered. The calculated correlations are compared with the correlations in alumina cuts and in random Voronoi froths. The variability of the topological properties of 2D random cellular structures is discussed.