Sign and magnitude of the quadrupole interaction of ${}_{}{}^{111}{}_{}{}^{}\mathrm{Cd}$ in noncubic metals: Universal correlation of ionic and electronic field gradients

The magnitude and sign of the nuclear quadrupole interaction of the 247-keV excited state of ${}_{}{}^{111}{}_{}{}^{}\mathrm{Cd}$ has been measured in a number of noncubic metals by means of the technique of $\beta -\gamma$ time-differential perturbed angular correlations. The state was populated by the unique first-forbidden $\beta$ decay of 7.5-day ${}_{}{}^{111}{}_{}{}^{}\mathrm{Ag}$ which was implanted by an an isotope separator into single crystals of Be, Mg, Ti, Zn, Sn, Re, Hf, and Bi. Well-defined precession patterns indicating unique lattice location of the ${}_{}{}^{111}{}_{}{}^{}\mathrm{Cd}$ impurity have been observed in all these cases except Hf and Bi. The sign and magnitude of the quadrupole coupling constants $e^2\mathrm{qQ}$ have thus been derived. Using lattice-sum calculations for the lattice electric field-gradient (EFG) $e{q}_{\mathrm{latt}}$, $Q=+0.77\mathrm{}$ b for the quadrupole moment of the 247-keV level of ${}_{}{}^{111}{}_{}{}^{}\mathrm{Cd}$ and a Sternheimer antishielding factor ${\gamma }_{\infty }=-29.3\mathrm{}$ for Cd, the EFG presumably due to the conduction electrons $e{q}_{\mathrm{el}}$, has been derived for each of these cases. These results strongly indicate that $e{q}_{\mathrm{el}}$ is linearly related to $e{q}_{\mathrm{latt}}(1-{\gamma }_{\infty })$. In an attempt to examine whether such a simple relation is effective in metallic systems in general, a survey of all $e^2\mathrm{qQ}$ values (with signs) measured in noncubic metals has been made. This survey reveals, for the first time, that in most cases, the values of $e{q}_{\mathrm{el}}$ and $e{q}_{\mathrm{latt}}(1-{\gamma }_{\infty })$ could be connected by a universal correlation according to which $e{q}_{\mathrm{el}}=-Ke{q}_{\mathrm{latt}}(1-{\gamma }_{\infty })$, $\mathrm{}\left|K\right|\mathrm{}\approx 3$ for moderate values of $e{q}_{\mathrm{latt}}(1-{\gamma }_{\infty })$. Based on this universal correlation curve, a number of $e^2\mathrm{qQ}$ values, whose signs are yet undetermined, have been phenomenologically examined and their signs predicted. These general systematics, especially the universality of the correlation of the electronic gradient with the ionic gradient $e{q}_{\mathrm{latt}}(1-{\gamma }_{\infty })$, and its dependence on the ${\gamma }_{\infty }$ of the impurity, is unexpected in the framework of current theoretical models of the EFG in noncubic metals.