LATTICE-GAS THEORY OF COLLECTIVE DIFFUSION IN ADSORBED LAYERS

A general theory for collective diffusion in interacting lattice-gas m odels is presented. The theory is based on the description of the kine tics 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 te rms of continued fractions. In particular, an expression for the colle ctive dynamic structure factor S-c is derived. The collective diffusio n coefficient D-c is obtained from S-c by the Kubo hydrodynamic limit. If memory effects are neglected (Darken approxima tion), it turns out that D-c can be expressed as the ratio of the average jump rate [w] a nd 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 syst ems as models of adsorbates on crystal surfaces. Three examples are co nsidered. First, the case of nearest-neighbour interactions on a squar e lattice (both repulsive and attractive). Here, the theoretical resul ts for D-c are compared to those of Monte Carlo simulations. Second, a model with repulsive interactions on the triangular lattice. This mod el is applied to NH3 adsorbed on Re(0001) and the calculations are com pared to experimental data. Third, a model for oxygen on W(110). In th is case, the complete dynamic structure factor is calculated and the w idth 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 e quation for the structure of liquids (the Crossover Integral Equation) , whereas in the other examples they are computed using the Cluster Va riation Method.