Topological models of 2D cellular structure. II. z=5
G. Le Caër · Journal of Physics A Mathematical and General · 1991
For pt.I see ibid., vol.24, p.1307, (1991). Topological models of 2D cellular structures are associated with planar tessellations with topologically unstable sites which belong to z)3 polygons. This degeneracy is removed by replacing every z-vertex by z-3 added sides. A method which uses the diagonal triangulation of the dual tiling is also described. The number of stable configurations, called states, is calculated as a function of z. Topological properties of the associated cellular structures are derived for a distribution of equiprobable and independent states on the various sites and for z ranging from 5 to infinity. The distributions P(n) of the number n of cell sides for the latter distribution of states are typical of the P(n) of planar cuts of polycrystals and differ from the P(n) of soap froths. Deviations from the Aboav-Weaire relation, which describes the correlations between nearest-neighbour cells, occur mainly for n=3 and n)9.