Kinetic lattice-gas model approach to collective diffusion in an ordered adsorbate in two dimensions.

Magdalena A. Zauska-Kotur and Zbigniew W. Gortel

A recently developed approach to microscopic kinetics of an interacting lattice gas is applied to derive an algebraic expression for the coverage dependence of the collective diffusion coefficient in a two-dimensional (2D) adsorbate populating a square lattice of adsorption sites with strong adatom-adatom repulsive nearest-neighbor interactions. Results are valid below the critical temperature for coverages at which the adsorbate is structurally ordered. Interactions between nonactivated particles as well as those between the activated one and its nonactivated neighbors are accounted for. The starting point is Markovian master equations for the kinetics of microscopic states of the system, controlled by jumps of adatoms between adsorption sites. The diffusion coefficient is extracted in the long wavelength and the thermodynamic limits from the diffusive eigenvalue of a microscopic rate matrix associated with the equations. The eigenvalue is evaluated using an Anzatz for the left and the right eigenvectors of the matrix with the adsorbate ordering inscribed into their structure. The results are validated by Monte Carlo simulations of the diffusion process.

Phys. Rev. B 72, 235425 (2005)