Pictorial representation of anisotropy and macroscopic reorientations of samples in solid-state NMR: Second-order interactions

The representation of second-order broadening effects in solid-state NMR by general fourth-degree surfaces is presented. Static second-order quadrupol ar and "dipolar-quadrupolar" interactions are treated in a unified way. Mos t experiments involving the fast reorientation of samples such as magic-ang le spinning, variable-angle spinning, dynamic-angle spinning, and double-ro tation and multiple-quantum magic-angle spinning are also illustrated by us ing averaged fourth-degree surfaces. The equations of the surfaces are deri ved analytically and allow the derivation of most results concerning these experiments. This article is an extension of the representation of the firs t-order effects by quadrics to more complex broadening effects. Multidimens ional experiments will also be discussed in this frame. It can be noted tha t this approach is essentially Cartesian. P-2(cos theta) and P-4(cos theta) Legendre polynomials are not explicitly used in this work.