Electric-field-gradient tensor in cubic crystals with dilute concentration of vacancies: Application to Al

The distribution of electric field gradient (EFG) in Al crystal with dilute concentration of vacancies has been calculated in the approximations of free-electron-screening charge for the valence effect and elastic-continuum model for the size effect. The results, especially the asymmetry parameter, $\eta$, at the nearest-neighbor (1NN) sites and the magnitudes of EFG at the third- (3NN) and fourth- (4NN) neighbor sites, are in very good agreement with those from experiment. The somewhat large value of EFG at 1NN sites is ascribed to the failure of the asymptotic free-electron screening charge distribution around these neighbors. Nonzero values of $\eta$ for the 3NN and 4NN sites are predicted in conformity with symmetry prediction. These are equal to 0.93 and 0.42, respectively, for the 3NN and 4NN sites. The large value of $\eta$ at 3NN sites is mainly due to the greater asymmetry of the EFG from size effect. Unfortunately, experimental values of $\eta$ for the 3NN and 4NN sites are not available to compare with the theoretical prediction.