Crystal statistics with long-range forces: II. Asymptotic behaviour of the equivalent neighbour model

Abstract

A theoretical justification is sought for the asymptotic behaviour of the equivalent neighbour model described in the previous paper. An approximation to the lattice constants for this model is suggested in terms of the virial integrals of a hard-sphere gas. For large co-ordination numbers it is found that the dominant terms in series expansion coefficients correspond to simple polygons for which virial integrals can be evaluated exactly to any order. If we take account of these polygonal terms, satisfactory agreement is obtained with the empirical results of the previous paper.