Vacancy-assisted diffusion in a crystalline solid could be modelled by means of many particles jumping stochastically to their respective nearest-neighbor lattice sites, with double occupancy forbidden. The diffusion coefficient of a tagged particle, defined in terms of its mean square displacement, depended not only upon the transition rate but also upon the particle concentration. Nakazato and Kitahara (1980) devised a projection operator method to calculate its approximate expression interpolating between the low- and high-concentration limits for a square lattice in any dimension. Their method was applied here to a honeycomb lattice and a diamond lattice, in each of which a set of the nearest-neighbor vectors depended upon a site from which they originated. Compared with simulation results, an explicit expression was found to give a good interpolation for each lattice unless the host particles migrated more slowly than the tagged particle.

Vacancy-Assisted Diffusion in a Honeycomb Lattice and in a Diamond Lattice. Suzuki, Y., Kitahara, K., Fujitani, Y., Kinouchi, S.: Journal of the Physical Society of Japan, 2002, 71[12], 2936-43