Renormalization-group treatment of a Potts lattice gas for krypton adsorbed onto graphite
- 1 May 1978
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review B
- Vol. 17 (9), 3650-3665
- https://doi.org/10.1103/physrevb.17.3650
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.Keywords
This publication has 81 references indexed in Scilit:
- Physical adsorption on patchwise heterogeneous surfaces. 2. Virial coefficient theory analysis of krypton adsorption on graphitized carbon blackThe Journal of Physical Chemistry, 1977
- Ordered Helium Films on Highly Uniform Graphite—Finite-Size Effects, Critical Parameters, and the Three-State Potts ModelPhysical Review Letters, 1977
- Phases of neon monolayers adsorbed on basal plane graphiteJournal of Low Temperature Physics, 1976
- Physical adsorption of patchwise heterogeneous surfaces. I. Heterogeneity, two-dimensional phase transitions, and spreading pressure of the krypton-graphitized carbon black system near 100.deg.KThe Journal of Physical Chemistry, 1975
- Thermodynamic study of themonolayer adsorbed on GrafoilPhysical Review A, 1974
- Triple point of the first monomolecular layer of krypton adsorbed on the cleavage face of graphite. Influence of the structure of this surface on the structure of the first adsorbed layer of rare gasesJournal of the Chemical Society, Faraday Transactions 1: Physical Chemistry in Condensed Phases, 1974
- Phases ofandMonolayer Films Adsorbed on Basal-Plane Oriented GraphitePhysical Review A, 1973
- Ordering Transitions in Helium MonolayersPhysical Review Letters, 1971
- The theory of equilibrium critical phenomenaReports on Progress in Physics, 1967
- Static Phenomena Near Critical Points: Theory and ExperimentReviews of Modern Physics, 1967