Activated surface diffusion: Are correlated hops the rule or the exception?

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Abstract
The migration of adsorbed atoms on crystal surfaces is considered. To describe the adatom motion one often uses a generalized Langevin equation (GLE). The time‐dependent friction, which enters the GLE, is caused by the interaction with the crystal excitations. However, the explicit form of the time‐dependent friction is not well known. We show that if the damping is associated with acoustic phonons and the coupling of the adatom with the surface is not too strong, then the friction is Ohmic. An explicit expression for the friction coefficient is given in terms of the basic physical parameters of the crystal and in terms of the activation energy of the adatom on the surface. We find that usually the diffusion occurs in the intermediate damping regime. In this regime nearest neighbor hops are most probable and transition state theory gives an excellent estimate for the rate of escape and for the diffusion coefficient. Using the recently developed turnover theory for surface diffusion [Phys. Rev. E 49, 5098 (1994)] we derive explicit expressions for the evolution of the time‐dependent site distribution and compare it with an experiment where correlated hops have been observed. We conclude that even when the motion is one‐dimensional, correlated hops are to be expected only for sufficiently high temperatures or for physisorbed atoms.