Diffusion of adsorbates on single crystal surfaces of square symmetry: Finite-size scaling and the thermodynamic limit

Abstract

We investigate the influence of different diffusion mechanisms on the finite-size scaling behavior of the tracer surface diffusion coefficient in the close vicinity of a second order phase transition. A given diffusion mechanism emerges from a specific transition algorithm (TA) representing a microscopic model of adatom jumps on the surface. In this work we apply the Monte Carlo method to investigate a lattice gas model of repulsively interacting particles on a square lattice. For all diffusion mechanisms and lattice sizes L studied, the measured tracer surface diffusion coefficient, Dt, is a smooth function of temperature and exhibits an inflexion point at or near the critical temperature. Its derivative, ∂Dt/∂(1/kBT), exhibits cusp-like maxima which are (a) sharply pronounced and (b) converge to Tc(L = ∞) for large lattice sizes. We have analysed the finite-size behavior of Dt and obtained its critical exponent, σt, for each diffusion mechanism considered. The results show that σt is different for the different diffusion mechanism, i.e.σt depends on the choice of the TA.