Lattice-Gas Theory of Collective Diffusion in Adsorbed Layers

A general theory for collective diffusion in interacting lattice-gas models is presented. The theory is based on the description of the kinetics in the lattice gas by a master equation. A formal solution of the master equation is obtained using the projection-operator technique, which gives an expression for the relevant correlation functions in terms of continued fractions. In particular, an expression for the collective dynamic structure factor S_c is derived. The collective diffusion coefficient D_c is obtained from S_c by the Kubo hydrodynamic limit. If memory effects are neglected (Darken approximation), it turns out that D_c can be expressed as the ratio of the average jump rate <w> and of the zero-wavevector static structure factor S(0). The latter is directly proportional to the isothermal compressibility of the system, whereas <w> is expressed in terms of the multisite static correlation functions g_n. The theory is applied to two-dimensional lattice systems as models of adsorbates on crystal surfaces. Three examples are considered. First, the case of nearest-neighbour interactions on a square lattice (both repulsive and attractive). Here, the theoretical results for D_c are compared to those of Monte Carlo simulations. Second, a model with repulsive interactions on the triangular lattice. This model is applied to NH₃ adsorbed on Re(0001) and the calculations are compared to experimental data. Third, a model for oxygen on W(110). In this case, the complete dynamic structure factor is calculated and the width of the quasi-elastic peak is studied. In the third example the g_n are calculated by means of the discretized version of a classical equation for the structure of liquids (the Crossover Integral Equation), whereas in the other examples they are computed using the Cluster Variation Method.