In recent observations of Brownian motion of islands of adsorbed atoms and of vacancies with mean radius R, the cluster diffusion constant varies as R 21 and R 22. From an analytical Langevin description of the cluster's steplike boundary, we find three cases, R 21 , R 22 , and R 23 , corresponding to the three microscopic surface mass-transport mechanisms of straight steps. We thereby provide a unified treatment of the dynamics of steps and of clusters. For corroboration, we perform Monte Carlo simulations of simple lattice gases and derive atomistic diffusion constants.
Classical thermodynamic descriptions of surfaces treat surface orientation as a thermodynamic degree of freedom and thus allow for the possibility of reversible changes in surface morphology as a function of temperature or impurity concentration. The existence of these transitions has been confirmed experimentally. Advances in surface diffraction and imaging techniques now make it possible to characterize such transitions quantitatively in terms of the atomic structure, and particularly in terms of the behavior of steps on surfaces. Statistical mechanical models can be used to analyze the observations to determine the fundamental energetic parameters governing the observed thermodynamic behavior.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.