Mössbauer-Effect Determination of the Crystalline Electric Field Parameters in Thulium Metal

By measuring the temperature dependence of the nuclear quadrupole splitting of the 8.42-keV Mössbauer transition in the paramagnetic state of thulium metal, a determination of the crystalline electric field (CEF) parameters of elemental thulium has been obtained. The nuclear quadrupole interaction was studied within the temperature range 59 to 156°K. It was found that a zero-order calculation was sufficient to fit theory to experiment, and that in particular only $C_2^{}{}_{}{}^0$, ${\rho }_1$ and $\rho _2^{}{}_{}{}^{\prime }$ (where the $\rho$'s account for shielding constants and the temperature-independent contributions to the electric field graident at the nucleus) were needed to fit the theory to the data. The remaining CEF parameters, $C_4^{}{}_{}{}^0$, $C_6^{}{}_{}{}^0$, and $C_6^{}{}_{}{}^6$, were constrained to equal zero in the fitting routine. The over-all splitting of the ${}_{}{}^3{}_{}{}^{}H_6^{}{}_{}{}^{}$ ground multiplet was found to be 76.1 ${\mathrm{cm}}^{-1\mathrm{}}$. This study also includes a determination of electronic shielding factors for thulium. The atomic Sternheimer factor $R_Q$ was found to be 0.16; and the constant ${\sigma }_2$, which represents the shielding of the $4f$ shell from the CEF by the closed outer shells, was found to be 0.34. The latter quantity was obtained under the assumption that screening of the ${\mathrm{Tm}}^{+3\mathrm{}}$ ions by the conduction electrons can be neglected. The direct lattice contribution and the conduction-electron contribution to the net electric field gradient at the Tm nucleus were found to be positive and of the same order of magnitude.