Lattice-gas Hamiltonian revisited: O-Pd(100)

Abstract

As an alternative to a cluster expansion (CE) based set of lateral pair-, trio-, quarto interactions between Oxygen adatoms on Pd(100) an analytical longer range elastic substrate mediated interaction with just 3 parameters is proposed to build a lattice-gas Hamiltonian.Both methods rely on the same set of adatom configuration energies of O-Pd(100) derived from first principles. The CE method derives interactions using a set of linear equations. The second method fits the parameters of an elastic interaction model to the configuration energies. The 3 parameters are an isotropic force constant, an anisotropic force constant and the surface Brillouin zone cutoff radius.Assumptions and methods for building a substrate mediated elastic interaction model are detailed. The model is extended to include multisite terms. The elastic interaction is repulsive for the two nearest neighbors, attractive for the 3rd and 4th nearest neighbors and has an oscillating s−3 tail.The results of both methods are compared and the reasons for differences are outlined. A key result of the analytical model is that multisite interactions amongst Oxygen adatoms on Pd(100) are marginal in contrast to the results of the CE method. The focus on pair interactions will allow analytical methods to derive surface order.Assumptions and limitations of both models are discussed and open questions are formulated.