Electric-field-gradient tensor in nonmagnetic dilute alloys of copper

Calculations are presented for the electric-field gradient $q$, the asymmetry parameter $\eta$, and the direction of the main principal axis of the electric-field-gradient (EFG) tensor, at nearest neighbors (1NN) and second neighbors (2NN) to isolated Zn, Ga, Ge, Ag, Cd, In, Sn, and Sb impurities in copper. A "size effect" contribution, proportional to the local strain about the impurity, is added in tensor fashion to the well-known "valence effect" EFG calculated by Kohn and Vosko and Blandin and Friedel. When the point-charge model is used to evaluate the size-effect EFG tensor, a nonzero asymmetry parameter becomes possible. The calculation also includes an explicit evaluation of the contribution to the EFG of the screening charge which is outside the atomic cell of the host atom being resonated. At the 1NN and 2NN sites the resulting correction to the valence-effect calculation can be as large as 40%; asymptotically, the correction is 17% (assuming $\alpha =23.3\mathrm{}$ for the Kohn-Vosko enhancement factor). When the valence and size effects are combined, good agreement between theory and experiment is obtained. Experimental $q\text{'}\mathrm{s}$ at the 2NN sites in all alloys studied are accounted for by using the parameters $\alpha =18\mathrm{}$, $\lambda =-15\mathrm{}$, where $\alpha$ is the Kohn-Vosko enhancement parameter and $\lambda$ is the EFG-strain coupling constant. These parameters also account well for $q$ and $\eta$ at the 1NN in alloys with the 5th-row impurities Ag, Cd, In, Sn, and Sb, but the optimal fit for the 1NN is with $\alpha =15\mathrm{}$, $\lambda =-18\mathrm{}$. The 1NN data for alloys with the 4th-row impurities Zn, Ga, and Ge can be fit with $\alpha =2\mathrm{}$, $\lambda =87\mathrm{}$, but for no other range of the parameters. The reasons for such different values of $\alpha$ and $\lambda$ are not understood. However, the resulting fir for the 1NN $q$ and $\eta$ is excellent, and the "anomalous" direction of the main principal axis in $\mathrm{Cu}\mathrm{Ge}$ is correctly predicted.