Magic angle spinning in solid state n.m.r. spectroscopy

Rapid specimen rotation about an axis inclined at the 'magic angle' of 54 degrees 44 $\prime $ to the Zeeman field direction can remove many sources of broadening from the n.m.r. spectrum of a solid and enable finer features to be revealed. In this paper the basic principles of magic angle spinning are given and the effects on the chemical shift interaction, the magnetic dipolar and pseudo-dipolar interactions, both homonuclear and heteronuclear, and the electric quadrupolar interactions are examined. The anisotropic parts of these interactions are removed from the central spectrum and appear as spinning sidebands. The interactions that remain are the isotropic shifts and J couplings as in isotropic fluids. Examples of the effects of magic angle spinning on a variety of interactions are given. When applied to metals the anisotropy of Knight shift is removed, isotropic Knight shifts may be measured with precision, and the Ruderman--Kittel interaction may be determined in the presence of a much larger dipolar interaction. The effects of spinning on homogeneous and inhomogeneous spectra are distinguished. Sources of residual broadening are identified. Magic angle spinning may be used on its own, and may also be successfully combined with multiple-pulse and double resonance n.m.r. methods to obtain high-resolution n.m.r. spectra of powders and polymers.