T4Dependence of the Nuclear-Quadrupole Resonance Frequencies in Solids

Nuclear-quadrupole-resonance frequencies are shown to have a $T^4$ dependence which becomes dominant at sufficiently low temperatures; the mechanism is discussed using a diatomic linear-chain model. The uniform-translational character of the acoustic phonons is shown to produce a $T^4$-dependent Doppler shift which is too small to account for the experimental results. The nonuniform $q$-dependent character of the acoustic branch is shown to induce modulations of the librational and vibrational coordinates at the low frequencies of the acoustic phonons. A Debye term is added to the familiar Bayer expression; both terms are shown to be produced by the modulation of the same coordinates, except that they occur at different frequencies.