QUASI-HARMONIC THEORY OF 2-DIMENSIONAL CRYSTALS .1. LENNARD-JONES POTENTIALS, QUANTUM CORRECTED CELL THEORY, AND THE QUANTUM-MECHANICAL PRINCIPLE OF CORRESPONDING STATES

The quasiharmonic approximation of lattice dynamics is used to calculate the frequency spectrum, the dynamical contribution to the free energy, and the thermal expansion of a two-dimensional hexagonal lattice. Results for a Lennard-Jones (12, 6) pair potential are presented in a tabular form which enables corresponding-states scalings to be used to form estimates of the thermal expansion for a variety of adsorbed inert gas monolayers. The magnitude of anharmonic corrections to this approximation is tested by comparing the equilibrium lattice constant obtained from quasiharmonic theory with the results of a quantum-corrected cell-model theory. The conclusion is that the quasiharmonic theory may be used to calculate the lattice constant with a precision of 0.01 Å in a proposed analysis of the lateral interactions in an adsorbed xenon monolayer in the temperature range 1 to 50 K. These methods are readily extended to more realistic pair potentials and permit the inclusion of substrate-mediated interactions for physisorbed monolayers. © 1979.