Mössbauer-Effect Determination of Crystalline Electric Field Splittings in Several Intermetallic Compounds of Thulium

By measuring the temperature dependence of the nuclear quadrupole splitting of the ${\mathrm{Tm}}^{169}$ 8.4-keV Mössbauer $\gamma$ transition, a measure of the strength of the crystalline electric field (CEF) in several hexagonal intermetallic compounds of the type $\mathrm{Tm}{X}_2$, where $X$ is another transition element, has been obtained. As in thulium metal, a zero-order model of the CEF incorporating only the ${C_2}^0$ parameter is found sufficient to describe the experimental results. On this basis, the over-all CEF splitting of the ${}_{}{}^3{}_{}{}^{}H_6^{}{}_{}{}^{}$ ground term of the ${\mathrm{Tm}}^{3+}$ ion is found to be 94 ${\mathrm{cm}}^{-1\mathrm{}}$ in Tm${\mathrm{Ru}}_2$, 88 ${\mathrm{cm}}^{-1\mathrm{}}$ in Tm${\mathrm{Re}}_2$, and 42 ${\mathrm{cm}}^{-1\mathrm{}}$ in Tm${\mathrm{Mn}}_2$. The nuclear and ionic shielding parameters $R_Q$ and ${\sigma }_2$ were also determined from the experimental measurements, in reasonable agreement with theoretical expectations. Best agreement between experimental and calculated values of the CEF parameters is obtained when the effective charge on the $X$ ions is taken to be zero. Details of the calculation of the CEF parameter ${C_2}^0$ by the plane-wise summation method for the hexagonal Laves-phase intermetallics are also given.