Diffusion and correlation effects in nonstoichiometric crystals

The correlated diffusive motion of atoms in the presence of a large concentration of point defects (for example, in nonstoichiometric materials such as some transition metal oxides, fast-ion conductors, and transition metal hydrides) is investigated in terms of the encounter model. Within the framework of this theory the correlation factor f is defined as the ratio of the mean square displacement, 〈R²〉_enc, of a tracer atom in an encounter with a point defect (in units of the nearest-neighbor distance) and the mean number of correlated tracer jumps per encounter, Z_enc. In the limit in which the energy of interaction between different point defects is much smaller than the thermal energy kT, the parameters 〈R²〉_enc and Z_enc (and thus f) are determined as functions of the concentration of point defects by means of a Monte Carlo-type computer simulation technique. Our results for the monovacancy mechanism of self-diffusion in f.c.c., b.c.c., and s.c. crystals are discussed in relationship to the results presented recently by Koiwa, Benoist et al., Sanke et al., DeBruin et al. and Murch et al. The validity of a simple analytical expression for f as a function of the vacancy concentration is investigated.