Rate theory for solids. IV. Classical Brownian-motion model

In order to gain insight into classical and quantum-rate theories for solids, a model for interstitial diffusion is presented in which the impurity atom is regarded as a Brownian particle constrained to move in a single direction and subject to a periodic potential. The classical behavior of this model is studied in this paper by the use of computer-simulation techniques; the study of the behavior of this model in the quantum regime is deferred to the following paper. Particular emphasis is placed here on the effect of the magnitude of the Brownian friction coefficient upon the persistence of motion of the impurity atom and how this persistence, in turn, affects the diffusion coefficient.