Lattice-gas transport at subcritical temperatures

Transport phenomena are considered in a lattice-gas system with attractive nearest neighbor interactions. When the temperature is lowered, the initially uniform adatom distribution is transformed to a mixture of two phases with different densities (first-order phase transition). The diffusion or transport coefficients describing the adatom flows in each phase are very different. We derive analytical expressions for the tracer and the jump diffusion coefficients of the whole system in the low-temperature region, when the concentrations of excessive adatoms in the dilute phase and vacancies in the dense phase can be treated as small parameters. Jump and tracer diffusion coefficients depend exponentially (as e2ϕ) on the interaction parameter ϕ. Our finding is in agreement with results of a Monte Carlo (MC) study. The analytical solutions presented here cover the whole range of adatom concentrations from zero to full monolayer, describing single phases, the two-phase mixture and the phase transition regions in between. The agreement between theoretical results on MC data is good and shows the adequacy of our analytical approach. The theory is generalized to systems with an alternative jump mechanism and to 3D lattices.