Surface diffusivity and the time correlation of concentration fluctuations

Abstract

Time correlation studies of concentration fluctuations have provided most of the recent data on the surface diffusivity of adsorbed gases. We examine the formalism which relates experimentally measured values of the time autocorrelation function, describing the number of particles in a small area element, to the diffusivity. It is shown that an exact expression can be obtained subject to only one important restriction: the decay of concentration fluctuations is characterized by a constant diffusion coefficient. In adsorbed layers, interactions between adatoms are likely to be strong, and the diffusivity is therefore expected to vary with surface coverage. The extent to which the same formalism can be utilized to obtain an effective diffusivity D C for interacting adatoms is examined using Monte Carlo simulations of two-dimensional lattice gases. The validity of the diffusion coefficient D C so derived is tested by comparing it with diffusivities D K obtained from a kinetic model or with values D M derived from a Boltzmann-Matano analysis. For a lattice gas with nearest neighbor interactions amounting to kT ∗, where T ∗ is the temperature of the simulations, agreement between D C and the ordinary diffusivity is good even though the latter varies strongly with concentration. For interactions of longer range, comparisons of D C and D M again reveal good agreement. Only under conditions leading to the formation of a highly ordered superlattice on the surface do we find that the correlation methods fail to yield a diffusivity in agreement with values from the Matano analysis. With this proviso it appears that the present formalism for interpreting autocorrelation studies of diffusion is generally adequate to handle layers of interacting adatoms.