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, D_t, is a smooth function of temperature and exhibits an inflexion point at or near the critical temperature. Its derivative, ∂D_t/∂(1/k_BT), exhibits cusp-like maxima which are (a) sharply pronounced and (b) converge to T_c(L = ∞) for large lattice sizes. We have analysed the finite-size behavior of D_t and obtained its critical exponent, σ_t, for each diffusion mechanism considered. The results show that σ_t is different for the different diffusion mechanism, i.e.σ_t depends on the choice of the TA.