Surface diffusion coefficient near first-order phase transitions at low temperatures
Abstract
We analyze the collective surface diffusion coefficient, Dc, near a first-order phase transition at which two phases coexist and the surface coverage, , drops from one single-phase value, +, to the other one, -. Contrary to other studies, we consider the temperatures that are sufficiently sub-critical. Using the local equilibrium approximation, we obtain, both numerically and analytically, the dependence of Dc on the coverage and system size, N, near such a transition. In the two-phase regime, when ranges between - and +, the diffusion coefficient behaves as a sum of two hyperbolas, Dc ≈ A/N| - -| + B/N| - +|. The steep hyperbolic increase in Dc near rapidly slows down when the system gets from the two-phase regime to either of the single-phase regimes (when gets below - or above +), where it approaches a finite value. The crossover behavior of Dc between the two-phase and single-phase regimes is described by a rather complex formula involving the Lambert function. We consider a lattice-gas model on a triangular lattice to illustrate these general results, applying them to four specific examples of transitions exhibited by the model.