The temperature-dependence of NQR frequencies

Whatever state they may be in, molecules are in motion and many of their observable properties are averages over this motion. For molecules in the gas-phase there are essentially only two types of motion that need to be considered, vibration and rotation, and the molecules exist in discrete rovibrational states. The values of nuclear quadrupole coupling constants depend slightly on the rovibrational state and this dependence can be analyzed in a straightforward and standard manner [8, 9]. 

When a molecule is incorporated into a crystal lattice, on the one hand additional types of motion, arising from the fact that the molecule may move with respect to its location in the lattice, must be taken into account, while on the other it is no longer possible to assign a motional state to an individual molecule. All the molecules participate in the motions of the lattice, the lattice modes, and the amplitides of these motions are temperature-dependent. The properties of the individual molecules are averages over the ensemble formed by the various lattice modes. 

As is so often the case with phenomena occurring in condensed phases, it is fairly easy to set out the basic theory but extremely difficult to go on from there to quantitative conclusions. If the librational amplitudes about the field-gradient x,y and z axes are 0j, 6y and then it can be shown that the effective quadrupole coupling parameters are given by  

If the complete details of the lattice modes are known, together with the way in which they evolve with temperature, the mean-square amplitudes can be calculated from them, and the temperature-dependence of the NQR frequencies predicted [10, 11], Such a rigorous approach need not be our concern here and it will suffice to note that only oscillations about the axes perpendicular to the field-gradient z-axis have any effect on either the coupling constant or the asymmetry parameter. 

Many of the NQR results that will be discussed have been obtained for whose spin = 3/2, and here the effect of the temperature-dependence of rj on the temperature-dependence of the NQR frequency may be completely neglected. We then have  

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Quite a different situation is experienced in NQR spectroscopy. Dehmelt and Kriiger (1950/1951) 3-6> found that the temperature dependence of NQR frequencies in organic materials is considerable. For instance, the temperature coefficient of i (35Cl) for chlorine bonded to carbon atoms is found to be in the range... 

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