Atomic Displacements in One- and Two-Dimensional Diffusion

Abstract

The statistics of surface diffusion phenomena are developed for the conditions appropriate to measurements in the field-ion microscope. Examined in detail are: (1) The effect of boundaries (lattice steps) on the mean-square displacement in a random walk; (2) the probability density for distances traversed in a two-dimensional walk along nonorthogonal surface channels; (3) the distribution of distances for random walks in which the number of jumps is subject to fluctuation, as it is in real systems. Both reflecting and adsorbing boundaries are found to diminish the mean-square displacement in the same fashion. The effect of nonorthogonality, and even more so of fluctuations, is to enhance the frequency of small displacements when compared with a Rayleigh distribution.