Clusters of Lennard-Jones atoms adsorbed on a graphite surface are studied using Monte Carlo simulation. We investigate the stability of registered and nonregistered structures at low temperatures. The model is two dimensional with adatom-adatom interactions specific to krypton, while the amplitude of the hexagonal substrate corrugation potential ${\mathit{V}}_1$ is taken as a variable. In order to allow the density to change continuously, free boundaries have been employed. We locate a thermally induced as well as a field induced phase transition in the plane of temperature and corrugation amplitude. The transition is from a modulated (incommensurate) structure at low corrugation amplitude and low temperature to a registered (commensurate) lattice at stronger corrugation and/or higher temperature. We find that free surfaces enhance the stability of the √3 × √3 R30° structure. Our results support the existence of an incommensurate-commensurate transition driven by thermal expansion as proposed by Gordon and Villain [J. Phys. C 18, 3919 (1985)].

• Received 9 December 1993

DOI:https://doi.org/10.1103/PhysRevE.50.2007