Nuclear quadrupole alignment ofLum176andLu177in a lutetium single crystal at low temperatures and systematics of electric field gradients in pure hexagonal transition metals

The quadrupole frequencies for ${}_{}{}^{176}{}_{}{}^{}\mathrm{Lu}_{}^m{}_{}{}^{}$ and ${}_{}{}^{177}{}_{}{}^{}\mathrm{Lu}$ nuclei in a Lu single crystal have been determined by nuclear orientation at temperatures down to 6 mK as -128(16) MHz and +294(37) MHz, respectively. From the observed $\gamma$ anisotropies several $\gamma$-ray multipole mixing ratios could be derived. With the known ground-state quadrupole moment of $Q=3.39\mathrm{}\left(2\right)\mathrm{}$ b for ${}_{}{}^{177}{}_{}{}^{}\mathrm{Lu}$ the electric field gradient of $\mathrm{Lu}\mathrm{Lu}$ is found to be +3.6(5) × ${10}^{17}$ V/${\mathrm{cm}}^2$. This value does not fit into the frame of Raghavan's universal correlation. Taking into account recent data on other systems, a new classification of electric field gradients in hexagonal metals is proposed: The electronic contribution to the total electric field gradient is proportional to the ionic part, the proportionality constant being positive for all group-$\mathrm{III}b$ and -$\mathrm{IV}b$ hexagonal metals and negative for all group-$\mathrm{II}b$, -$\mathrm{VII}b$, and -$\mathrm{VIII}b$ metals.