A comparison of the Kubo-Green and fluctuation methods for the determination of the surface diffusion coefficients of adsorbates was carried out, by means of Monte Carlo simulations, on a square lattice with attractive nearest-neighbor and repulsive next-nearest neighbor interactions. Depending upon the ratio of the later interaction strength to the former strength, the lattice-gas models exhibited first-order or second-order phase transitions at low temperatures. It was found that, in the presence of second-order phase transitions, both methods agreed; even in p(2 x 1) ordered regions of the relevant phase diagram. In the case of systems with first-order phase transitions, there was an appreciable so-called graininess of the lattice gas which remained at temperatures that were well above the critical temperature. This graininess was suggested to represent the early stages of first-order phase transitions between lattice-gas phases of considerably different particle density. It was shown for the first time that such graininess affected determinations of the chemical surface diffusion coefficient. This was because diffusion measurements could depend, to some extent, upon the length scale of the measuring technique.

C.Uebing, R.Gomer: Surface Science, 1995, 331-333, 930-6