Tracer diffusion and correlations in ordered adsorption systems with defect-controlled transport mechanisms

In this study we develop a theory of tracer diffusion in 2D lattice-gas systems with strongly repulsive nearest neighbor interactions. The study is performed for a square lattice in the vicinity of half monolayer coverage. In this case the lattice gas forms a highly-ordered c$(2\times 2)$ phase. The adatom kinetics is reduced to the problem of random walks of long-living structural defects. The correlated motion of tracer-defect pairs is considered. Equations for correlation functions of tracer-vacancy, tracer-excessive adatoms and tracer-dimer pairs are derived and solved in terms of microscopic jump probabilities of defects. The solutions are exact in the case of dominant single defect transport mechanisms. In the case of dimer transport we applied the approximation of short-range correlation length. The values obtained for the correlation factor are in good agreement with the results of computer simulations in the over-stoichiometric range, while for sub-stoichiometric coverages the agreement is not very good