Renormalization-group treatment of a Potts lattice gas for krypton adsorbed onto graphite

Abstract

Krypton atoms adsorbed in submonolayer quantities onto the basal graphite surface may be represented by a triangular lattice gas with nearest-neighbor exclusion and further-neighbor attraction decreasing with separation. We view this as a three-state Potts model with thermodynamic vacancies which are controlled by a chemical potential. A position-space renormalization-group treatment is performed by adapting Migdal's approximate recursion to the triangular lattice, and results are compared with experimental data. Our temperature versus density phase diagram for krypton submonolayers has an in-registry solid phase separated from a liquid phase by a line of continuous (Potts tricritical) transitions at higher temperatures. At lower temperatures, the solid phase is separated from a gas phase by first-order transitions. The Potts tricritical line meets the coexistence region of the first-order transitions at an isolated fourth-order transition point. This point may be related to the transition of the triplet Ising model, solved exactly by Baxter and Wu. Our "Potts lattice gas" global phase diagram is in a three-parameter space of pair-interaction constants and chemical potential. It contains solid, liquid, and gas phases, variously separated by first-order, Ising critical, three- and four-state Potts, and fourth-order transitions. The Lennard-Jones potential between krypton adatoms determines the planar subspace applicable to krypton submonolayers. Other planes, similarly determined, are applicable to adsorbed nitrogen, methane, and ethane, for which we estimate the temperatures of the fourth-order points. Our treatment also predicts a tricritical end-point topology, instead of the fourth-order point topology, when second-neighbor adatom pair attraction is not much stronger than third- and fourth-neighbor attractions.