Miscibility and phase diagram of mixed submonolayers: mean field and hard hexagon approximation

Abstract

The equations which determine the equilibrium between commensurate and incommensurate solid phases of a mixed (Xe-Ar) or (Xe-Kr) submonolayer adsorbed on graphite are written in a mean field theory which takes thermal expansion into account. The mean field potential is given by an integral equation which is solved to first order in temperature. The agreement with experimental data is poor. In the case of Xe-Kr mixtures, when the size difference is small, a phenomenological theory gives good results. At low temperature it is possible to go beyond the mean field approximation and to obtain the qualitative phase diagram. The particular case of a solid of small atoms (Ar) with a weak concentration of big atoms (Kr) can be treated by an approximate version of Baxter's hard hexagon model and the results are promising. An interpolation between mean field and hard hexagons, which the authors call the tough hexagon model, is also introduced.