Random walks and correlation factors in diffusion via the vacancy mechanism in hexagonal-close-packed lattices

Abstract

Abstract Random walks on hexagonal-close-packed lattices are considered. By decreasing the probability of inter-plane jumps relative to that of intra-plane jumps, random-walk properties exhibit features characteristic of a two-dimensional lattice. For a given set of jump probabilities, the number of distinct lattice points visited in an n- step walk S n shows. with increasing n, a transition from an initial two-dimensional-like trend, S n ∼ n/log n, to a three-dimensional trend, S n ∼ n. Correlation factors for self-diffusion via the vacancy mechanism are also calculated exactly for various sets of two-jump frequencies; a previous approximate evaluation by Mullen (1961) is confirmed.