Temperature Dependence of the Electric Field Gradient at Ytterbium Impurities in Thulium Metal

Time-differential perturbed angular correlations of nuclear $\gamma$ rays from the decay of ${}_{}{}^{172}{}_{}{}^{}\mathrm{Lu}$ to ${}_{}{}^{172}{}_{}{}^{}\mathrm{Yb}$ have been used to measure the temperature dependence of the electric quadrupole hyperfine interaction at dilute ytterbium impurities in polycrystalline thulium metal over the temperature range from 77 to 560 K. The dependence on temperature is found to be relatively weak and almost linear. Based on a value for the quadrupole moment of the 79-keV state obtained from Coulomb-excitation transition probabilities, the electric field gradient (EFG) is (6.15 ± 0.15) × ${10}^{17}$ V/${\mathrm{cm}}^2$ at 77 K, and decreases with increasing temperature by (6.6 ± 0.6) × ${10}^{-4\mathrm{}}$ ${\mathrm{K}}^{-1\mathrm{}}$ of the extrapolated value of $V_{\mathrm{zz}}\left(0\mathrm{} \mathrm{K}\right)=6.33\mathrm{}\times {10}^{17}$ V/${\mathrm{cm}}^2$, with some evidence of leveling off above 500 K. Such a linear temperature dependence is inconsistent with any appreciable contribution to the EFG from an open $4f$ shell, and thus the ionic state of the ytterbium ion is dipositive. The observed EFG is thus due to contributions from the crystal-field and conduction electrons. The temperature variation of the lattice EFG comes mainly from the anisotropy of thermal expansion between the $c$ axis and the basal plane of the thulium lattice. Estimates based on point-charge calculations of the crystal field combined with measured thermal-expansion coefficients yield a magnitude and temperature dependence that are both too small to explain the observed results on this basis. The remaining temperature dependence is ascribed to the effects of local conduction electrons near the Fermi surface.