It was recalled that, in recent observations of the Brownian motion of islands of adsorbed atoms and vacancies with a mean radius, R, the cluster diffusion constant, D, had varied as R-1 and R-2, respectively. By means of an analytical continuum description of the step-like boundary of the cluster, a single Langevin equation (rather than 3 special cases) was found for the motion of the cluster boundary. From this were determined the value of D, and the value of the correlation function, G, for fluctuations of the shape around an assumed equilibrium circular shape. For 3 limiting cases, scaling relations were found that were of the form, D  R-. For short elapsed times, it was found that G  t1/(1+), where  was equal to 1, 2, or 3. These values corresponded to the 3 generic surface mass transport mechanisms of straight steps. The results therefore provided a unified treatment of the dynamics of steps and clusters. In order to check how well the continuum results described clusters of that experimental size, Monte Carlo simulations were made of simple lattice gas models. Atomic diffusion parameters were also estimated from available experimental data on the diffusion of large clusters.

S.V.Khare, T.L.Einstein: Physical Review B, 1996, 54[16], 11752