Collective diffusion in a non-homogeneous interacting lattice gas

Collective diffusion in an interacting adsorbate on a non-homogeneous one-dimensional substrate is investigated within the framework of a variational approximation. The substrate inhomogeneity, appropriate to a periodically stepped adsorbate, is represented by a Schwoebel barrier at the step edge and a modified binding at the step site. An elementary cell of a periodic substrate consists of n identical terrace sites and one step site, i.e. it contains n + 1 sites. The adsorbed particles are allowed to interact with each other, both in equilibrium as well as during the transit of a hopping particle over the potential energy barrier separating the initial and the target adsorption site. The interactions modify the rates of particle jumps between the adsorption sites. Cases n = 1, 3 and 4 are investigated in considerable detail and, where appropriate, a comparison with the available computer simulation results in the literature for an analogous two-dimensional system is made. It is shown that preferential geometrical arrangements at several adsorbate densities (coverages) induced by repulsive intra-adsorbate interactions lead to features on the diffusion coefficient versus the coverage curves which can be consistently interpreted. The origin of these features and their relation to intra-adsorbate correlations are examined and discussed. Where possible, the variational theoretical results are confronted with the results of our own computer simulation studies of diffusion.