The Field Dependence of the Second Order Quadrupolar Interaction in Solids

Most of the NMR active isotopes in the periodic table are quadrupolar, so it is understandable that there is a great deal of interest in obtaining NMR data for quadrupolar nuclei. In the solid state, one typically observes the central transition for spin I = n/2 nuclei. This transition is unaffected by the first order quadrupolar interaction however it is affected by the second order quadrupolar interaction. Magic angle spinning only partially averages the second order quadrupolar interaction and as a result one observes a broadened resonance of the central transition in MAS spectra. In favorable circumstances, the shape of this resonance can be used get information about the quadrupolar coupling and chemical shift tensors. The second order quadrupolar interaction is inversely proportional to the strength of the magnetic field so narrower lines (and therefore higher resolution) are obtained at higher field strengths. This accounts for all of the interest in ultrahigh-field NMR facilities for solids such as the one in Ottawa. The figure below shows the ²⁷Al (I = 5/2) MAS spectrum of kaolinite obtained at three different field strengths, plotted on the same chemical shift scale. In addition to the narrowing of the resonance at higher fields, note that the "center of gravity" of the resonance also shifts with field. The "center of gravity" of the resonance approaches the true chemical shift only in the high field limit and therefore should not be reported in the literature as a "chemical shift".