Determination of surface diffusion coefficients by Monte Carlo methods: Comparison of fluctuation and Kubo–Green methods

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Abstract
A comparison of the Kubo–Green and fluctuation methods for determining surface diffusion coefficients of adsorbates was carried out by Monte Carlo simulations on a square lattice for various adsorbate–adsorbate nearest-and-next-nearest neighbor interactions. Even in ordered regions of the phase diagrams both methods agree, when the system has been fully equilibrated and nearly so if it has not, provided that the ‘‘local’’ mean square fluctuation is used in the Kubo–Green method for the latter situation. Both the mean square fluctuations and D were found to be extremely sensitive to even small deviations from equilibrium near θ=0.5 below Tc. It was also found that the tracer and jump diffusion coefficients are nearly identical under all conditions. The present work was made possible by the enormous computing power of the Jülich Intel Paragon computer, which allowed both diffusion and equilibration simulations to be carried out simultaneously in the canonical ensemble. Thus the discrepancy between the two methods found at low temperatures in our previous work, where mean square fluctuations were found in the grand canonical ensemble and diffusion in the canonical ensemble, is resolved.

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