Dependence of the Pure Quadrupole Resonance Frequency on Pressure and Temperature

Measurements of the pure quadrupole resonance frequency ($\nu$) of the ${\mathrm{Cu}}^{63}$ nucleus in cuprous oxide, and the ${\mathrm{Cl}}^{35}$ nucleus in potassium chlorate and paradichlorobenzene have been made as a function of pressure in the range 1 to 10 000 kg/${\mathrm{cm}}^2$ for temperatures between -77°C and 100°C. A theory is presented in which the static value of the electric field gradient tensor (${{\phi }_{\mathrm{ij}}}^0$) and the amplitudes ${{\xi }_i}^0$ of the normal modes of the lattice vibrations play a central role. The volume dependence of these quantities can be deduced from $\nu$-versus-volume isotherms which are constructed from the experimental data by using the equation of state. Information on the latter is augmented by theory. It is found that the temperature variation of the resonance frequency at atmospheric pressure can be understood by considering not only the explicit temperature dependence of the vibration amplitudes, but also by including the appreciable effects of the volume expansion on $q_0$ and ${{\xi }_i}^0$. Furthermore, the pressure dependence is found to be explicable in terms of the volume dependence of $q_0$ and ${{\xi }_i}^0$. In ${\mathrm{Cu}}_2$O, it is found that $q_0$ depends on volume roughly as $V^{-1\mathrm{}}$, thereby indicating an ionic character for this crystal. On the other hand, in paradichlorobenzene $q_0\propto V^n$, with $0<n<\mathrm{}0.04\mathrm{}$, thus exhibiting the effect of an increase in the intermolecular hybridization of the C-Cl covalent bond.