Temperature dependence of the nuclear quadrupole resonance frequencies in solids and the external modes approximation for lattice dynamics

Abstract

A discussion is presented on the various terms that may contribute to the temperature dependence of the NQR frequencies in molecular solids. It is shown that the external modes approximation in lattice dynamics is particularly suited to describe these effects in NQR spectroscopy. Two cases may be considered. Case (1): The quadrupole nucleus belongs to a nearly rigid cluster of atoms here called a unit. Case (2): The quadrupole nucleus may be considered as a single atom, not belonging to a complex unit. In this paper only Case (1) will be considered; Case (2) will be discussed elsewhere. It is shown that the separation of variables obtained from the external modes approximation allows a maximum economy of coordinates and conveniently permits a most direct connection with results from microwave experiments. Explicit expressions are obtained for q and η in terms of the librations and internal vibrations of the cluster of atoms that are assumed to surround the quadrupole nucleus. Crossed librational-vibrational averages of type 〈 uxruλv〉 are shown to affect the NQR frequencies in a first approximation, both for η0 ≠ 0 and η0=0. Crossed averages, usually neglected without justification, can be shown to be present whenever the two coordinates involved are modulated at the same frequencies. The translational modes can be shown to produce a first-order Doppler effect which causes no frequency shift, but instead causes a small broadening of the resonance line.