Two-dimensional condensation of atoms adsorbed on a hexagonally packed crystalline surface: CVM theory incorporated with three kinds of sites

This paper presents a cluster variation theory of physical adsorption of atoms on a hexagonally packed crystalline surface. The surface provides three kinds of adsorption sites with different potential energies: two kinds of hollow sites and atop sites. The sites of each kind form a (1 × 1)-1/3 sublattice in the whole triangular lattice. Atoms exclude each other from first nearest neighbor sites because of their large size. The interaction energies between atoms are described by a Lennard-Jones (12, 6) potential. Thermal motion of atoms oscillating around their lattice sites is also incorporated through a cell model. The cluster variation method is applied to hexagon clusters of sites that overlap with each other at rhombus clusters of sites. We calculate the critical temperature of the two-dimensional condensation of Ar as a function of the lattice incompatibility between the substrate and the adsorbate in the range where the substrate lattice is nearly equal to or larger than the adsorbate lattice at zero temperature. Our calculations show quantitatively good agreement with experiment when the Lennard-Jones energy parameter of adsorbed Ar is reduced to 0.6-0.7 times the one of gaseous Ar. The critical temperature shows close parallelism with the apparent interaction energy between atoms at second nearest neighbor sites, which involves the vibrational free energy increment brought about by atoms surrounding at second nearest neighbor sites. The conventional statistical mechanical treatment that makes use only of one sublattice with the deepest potential is found to underestimate both the internal energy and entropy of the adsorbate, in particular at low densities.