Collective surface diffusion near a first-order phase transition

Abstract

For a large class of lattice models, we study the thermodynamic factor, $\ensuremath{\Phi}$, of the collective surface diffusion coefficient near a first-order phase transition between two phases at low temperatures. In a two-phase regime, its dependence on the coverage, $\ensuremath{\theta}$, is $\ensuremath{\Phi}\ensuremath{\approx}\ensuremath{\theta}/[(\ensuremath{\theta}\ensuremath{-}{\ensuremath{\theta}}_{\ensuremath{-}})({\ensuremath{\theta}}_{+}\ensuremath{-}\ensuremath{\theta})N]$, where $N$ is the number of adsorption sites and ${\ensuremath{\theta}}_{\ifmmode\pm\else\textpm\fi{}}$ are the single-phase coverages at the transition. In the crossover between the two-phase and single-phase regimes, $\ensuremath{\Phi}(\ensuremath{\theta})$ is shown to have a more complex behavior. The results are applied to a simple two-dimensional lattice model.