NMR in the quadrupole regime: Polycrystalline spectra

Abstract

NMR in the quadrupole regime for a spin I = 3/2 nucleus involves the transition between the two lowest levels of the nucleus in a strong electric field gradient and an applied magnetic field. The exact theory of the frequency of this transition in the presence of quadrupolar asymmetry and anisotropic chemical shift was presented in earlier papers, in conjunction with experimental results on single crystal samples. This paper studies application of this method to polycrystalline specimens. Perturbation expressions are used to derive the resonant intensity distribution (powder pattern), while histographic techniques are used in the presence of quadrupolar asymmetry (η ≠ 0). The powder pattern is widely distributed over frequency, exhibiting three distinct features (a singularity and two edges), each of which is shown to arise from crystallites whose field gradient tensors have specific orientations with respect to the applied field. Exact theory is easily applied to a study of the field dependence of the transition frequency of each feature. Only two of the aforementioned features were observed in our experiments on powdered paradibromobenzene. The precisely known pure quadrupole transition frequency for this substance was used to increase the precision of the determination of η and of σx and σy, two components of the chemical shift. For practical reasons related to the small magnitude of η in paradibromobenzene, the interpretation of the field dependences of the two observed features could not yield η, σx, and σy independently. The results of this experiment are consistent with earlier work on single crystal specimens, particularly with concurrent work in which η, σx, σy, and σz were independently determined.