Collective surface diffusion on triangular and square interacting lattice gases

The collective (or chemical) diffusion in interacting repulsive lattice gases is studied both in triangular and square symmetries. The effect of lateral interactions at the saddle point position is taken into account. The collective diffusion coefficient Dc is calculated within the generalized Darken equation (GDE). Under this approximation memory effects are neglected and Dc is expressed as the ratio of the average jump rateand of the zero-wave-vector static structure factor S(0). Both quantities are calculated by the cluster variation method with clusters of seven (in the triangular lattice) and nine (in the square lattice) sites. It is shown that Dc has a very complicated behaviour in the regions of the phase diagrams where ordered phases are formed. This happens at coverages around ?=1/3 and 2/3 in the triangular lattice and around ?=1/2 in the square lattice. The lateral interactions at the saddle point have strong quantitative effects on Dc, but many qualitative features are preserved. In the square lattice case, our results are compared to those of Monte Carlo simulations by Uebing and Gomer, with excellent agreement. This shows that memory effects are not of great importance even at low temperatures.