Equations for a Lattice Gas. I. One-Component Systems

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Abstract
An expression is developed for P/kT for a lattice gas with an arbitrary lattice as a power series in the nearest neighbor interaction parameter, λ, with the coefficients functions of the activity, z. This result is applied in some detail to the cubic close packed lattice, for which expressions for the number density, ρ, and the probability of finding a cell adjacent to a filled cell also filled, ρv, are also given. These results are also transformed so as to give P/kT, lnz, and v as power series in λ with the coefficients functions of ρ. A development for P/kT for an arbitrary lattice with different interactions for different distances between lattice sites is also given. The equation permits numerical evaluation without too great difficulty.

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