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

Abstract

By measuring the temperature dependence of the nuclear quadrupole splitting of the 8.42-keV M\ossbauer 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\ifmmode^\circ\else\textdegree\fi{}K. It was found that a zero-order calculation was sufficient to fit theory to experiment, and that in particular only $C_{2}^{0}$, ${\ensuremath{\rho}}_{1}$ and $\ensuremath{\rho}_{2}^{\ensuremath{'}}$ (where the $\ensuremath{\rho}$'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 ${\mathrm{cm}}^{\ensuremath{-}1}$. 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 ${\ensuremath{\sigma}}_{2}$, 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 ${\mathrm{Tm}}^{+3}$ 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.