THEORY OF DIFFUSION IN PERIODIC-SYSTEMS - THE DIFFUSION-COEFFICIENT

The dynamics of classical adatoms at crystal surfaces is studied by th e Fokker-Planck equation (FPE). The interaction with the inhomogeneous substrate is described by periodic adiabatic potential and friction. Employing the matrix continued fraction method the FPE diffusion coeff icient, D, is calculated and compared with the approximate results bas ed on Kramers rate theory and jump theory. Large deviations are found at small potential barriers (high temperature), where the FPE predicts a quasi-free, unactivated regime. At low friction the FPE describes a peculiar multiple-jump diffusion. The effects of the shape of the adi abatic potential and of the position dependence of the friction on D a re important mostly at low and high friction, respectively. On the bas is of FPE theory the phenomenological Arrhenius law is discussed. Natu ral candidates to study the high temperature, unactivated regime are p remelting surfaces and physisorbates.