Random walks on diamond and hexagonal close packed lattices

Abstract

Abstract Random walks on the diamond (dia.) and the hexagonal close packed (h.c.p.) lattices are discussed in terms of random walk generating functions for non-Bravais lattices composed of two sublattices. The number of visits to the origin, P(0; 1), for the two lattices is related to that of the face centred cubic (f.c.c.) lattice by P(0; 1) dia. = 4/2P(0; 1) t.c.c. , P(0; 1) h.c.p. = P(0; 1) f.c.c. , The correlation factors for tracer diffusion in the h.c.p. lattice have been calculated rigorously by using the result of random walk calculations, which confirms the values obtained by Compaan and Haven (1958).