Occupation Ratio of Large Atoms under Fermi–Dirac Statistics on Integer Lattices

Abstract

When the diameters of atoms being adsorbed and readsorbed randomly on an integer lattice just exceed unity, an adsorbed atom prevents or “blocks” further adsorption on the site of adsorption and on the nearest-neighbor sites, thus influencing the adsorption patterns which may arise. It is shown that the statistical equilibrium which arises under these conditions obeys Fermi–Dirac statistics for which all physically possible patterns are equally probable. The configurational entropy of the gas on the lattice is expressible in the occupation ratio defined as the quotient of the total number of blocked sites and the total number of adsorbed atoms, averaged over all physically possible patterns. A reformulation of this quotient for each pattern as a mean of scores allocated to each adsorbed atom, and the invention of stochastic-pattern-generating processes have made it possible to derive and evaluate the occupation ratio as a function of the adsorption density ρ for various finite and infinite lattices in one and two dimensions.