Soft-Sphere Model for Nuclear Quadrupole Resonance: Rare-Earth Trichlorides under Hydrostatic Pressure

Nuclear quadrupole resonance of ${\mathrm{Cl}}^{35}$ in five hexagonal rare-earth trichlorides under hydro-static pressure up to 5×${10}^3$ kg/${\mathrm{cm}}^2$ showed a decrease in frequency $\nu$ with increase in pressure. The normalized pressure coefficients ${\nu }_0^{-1\mathrm{}} {\left(\frac{\partial \nu }{\partial P}\right)}_T$ varied smoothly between the extremes (-5.586 ± 0.020) × (${10}^{-6\mathrm{}}$ ${\mathrm{cm}}^2$/kg) and (-3.855 ± 0.016) × (${10}^{-6\mathrm{}}$ ${\mathrm{cm}}^2$/kg) for Ce${\mathrm{Cl}}_3$ and Gd${\mathrm{Cl}}_3$, respectively. The negative sign suggested a model with a significant overlap contribution to the electric field gradient and a soft-sphere model was developed in analogy to the Born-Mayer model of inter-ionic repulsive forces. This model proved adequate to explain the systematic variations in ${\nu }_Q$ with compound and was consistent with the pressure dependence of $\nu$. The use of pressure data as a critical test for the model must await reliable compressibility data for the compounds. Pressure data for monoclinic Er${\mathrm{Cl}}_3$ and Yb${\mathrm{Cl}}_3$ are also presented.