Approximate and exact virial coefficients for hard rectangular parallelepipeds and cubes on a simple cubic lattice

Abstract

The first five virial coefficients for lattice gases of hard rectangular parallelepipeds of ld2 sites (l=2–6, d=2) and of hard cubes of l3 sites (l=2–6) were calculated exactly and in the Percus–Yevick, hypernetted chain, and complete star approximations. The corresponding terms in the direct correlation function for hard cubes were calculated in the Percus–Yevick approximation and it was concluded that simple analytical solutions are improbable for this class of model. The relevance of these results to recent model making for defect complexes in UO2+x was indicated.