Nonequilibrium percolative c(2×2) ordering: Oxygen on Pd(100)

Abstract

Dissociative adsorption of oxygen on certain (100) metal surfaces has been modeled as random dimer adsorption onto diagonally adjacent empty sites of a square lattice subject to the additional constraint that all six neighboring sites must be empty (the 8-site model). Here we adapt this model to analyze the nonequilibrium c(2×2) ordering recently observed for oxygen on Pd(100) at coverages up to saturation (>1/4 monolayer), under conditions of low temperature and high pressure where effects of diffusive mobility can be ignored. We do, however, propose that adsorption could be followed immediately by short range transient mobility to dissipate excess energy. We first show how exact master equations for this model can be used to obtain analytic expressions for various local quantities of interest: the probability of an empty 8-site configuration (which determines the sticking coefficient), the c(2×2) island edge or domain boundary densities, etc. They also provide a characterization of, e.g., the asymptotic decay of spatial correlations. Near-percolating (percolative) c(2×2) ordering is readily observed in computer simulations of the saturation state. Through a simple extension of the physical model, we provide a framework for analysis of the large scale characteristics of this ordering via correlated polychromatic percolation theory. Corresponding scaling relations and some real space renormalization group analysis are described. Simulation results for average sizes, the effective dimension, and perimeter length to size ratios, of c(2×2) islands, are also presented.