Effect of adsorbate-adsorbate interactions on low temperature surface adsorption patterns

Low temperature surface adsorption at thermodynamic equilibrium is studied using a lattice model. So far, we have investigated fee (100) and bee (110) surfaces, with a finite number M of sites in one direction, and an infinite number of sites in the other, and no periodic boundaries. Here, we consider fee (110) surfaces with first- (V), second- (W) and third- (U) neighbor adsorbate-adsorbate interaction energies, considered as arbitrary parameters. Adsorption is assumed to be on-site, or at locations commensurate with the substrate. Thus adsorbates are treated as monomers. A monomer in the gas phase has a chemical potential mu (1) that depends on the gas pressure. With V-0 representing the lattice-adsorbate interaction energy, then mu (1) and V-0 appear as the combination mu= mu (1) + V-0. While keeping the temperature sufficiently few, the gas pressure is gradually increased, accompanied by an increase of mu. The surface begins to fill and phases with increasing coverage are observed until the surface is fully covered. The patterns depend both on the substrate and the adsorbates, and consequently on the interaction energies. A phase is characterized by the coverage theta (0), and the numbers per site, theta, beta and gamma of first- second- and third-neighbor adsorbate-adsorbate, respectively. The occupational characteristics of the phases and most of the transitions between phases are found to fit exact analytic expressions in M, allowing the exact extrapolation to the infinite two-dimensional surface, We have numerically investigated all possible relative values that V, W, and U may have whether attractive or repulsive. A set of phases occurs when V, W, and U are found to satisfy a certain set of inequalities defining an energy region. We have obtained all possible energy regions and the possible phases occurring in every region. Within a given energy region, let {theta (01), theta (1), beta (1), gamma (1)} and {theta (02), theta (2), beta (2), gamma (2)} be two consecutive phases. The value mu (12) of mu at the transition is the one for which the entropy is a local maximum. In all cases, (theta (02) - theta (01)) mu (12) = - V(theta (2) - theta (1)) - W(beta (2) - beta (1)) - U(gamma (2) - gamma (1)). Consider an adsorption system with no surface reconstruction and at thermodynamic equilibrium. Providing first-, second- and third- neighbor interactions are predominant it is sufficient to determine experimentally the patterns and the pressure at the transitions, to obtain a number of linear relations between the various interaction energies. Since there are four interaction energies, V-0, V, W and U, there may be cases where it is possible to determine all of these energies.