A Lattice Model of a Classical Hard Sphere Gas: II

From an examination of the proposed lattice model of a hard sphere gas, several interesting features are observed. It is found that for loose packed lattices it is necessary to consider two regions, one ordered and one disordered, so that the whole pressure-density curve may be described. The disordered region, for these lattices, produces virial coefficients which oscillate in sign every three or four terms, and above a certain density the phase becomes unstable. Treatment of the ordered region is not altogether satisfactory but it appears that the phase disappears below a certain density. Consequently, there is a strong indication that a transition occurs for loose packed lattices, but the nature and position of the transition is still in doubt. For the close packed lattices however, it is found that the gas has virial coefficients which are all positive and so seems to be able to condense into an ordered phase without any transition.