Dynamic-angle spinning and double rotation of quadrupolar nuclei

Nuclear magnetic resonance (NMR) spectroscopy of quadrupolar nuclei is complicated by the coupling of the electric quadrupole moment of the nucleus to local variations in the electric field. The quadrupolar interaction is a useful source of information about local molecular structure in solids, but it tends to broaden resonance lines causing crowding and overlap in NMR spectra. Magic- angle spinning, which is routinely used to produce high resolution spectra of spin-{1/2} nuclei like carbon-13 and silicon-29, is incapable of fully narrowing resonances from quadrupolar nuclei when anisotropic second-order quadrupolar interactions are present. Two new sample-spinning techniques are introduced here that completely average the second-order quadrupolar coupling. Narrow resonance lines are obtained and individual resonances from distinct nuclear sites are identified. In dynamic-angle spinning (DAS) a rotor containing a powdered sample is reoriented between discrete angles with respect to high magnetic field. Evolution under anisotropic interactions at the different angles cancels, leaving only the isotropic evolution of the spin system. In the second technique, double rotation (DOR), a small rotor spins within a larger rotor so that the sample traces out a complicated trajectory in space. The relative orientation of the rotors and the orientation of the larger rotor within the magnetic field are selected to average both first- and second-order anisotropic broadening. The theory of quadrupolar interactions, coherent averaging theory, and motional narrowing by sample reorientation are reviewed with emphasis on the chemical shift anisotropy and second-order quadrupolar interactions experienced by half-odd integer spin quadrupolar nuclei. The DAS and DOR techniques are introduced and illustrated with application to common quadrupolar systems such as sodium-23 and oxygen-17 nuclei in solids