Multiple pulse NMR in rotating solids

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Abstract
An analysis of magic angle sample spinning (MASS) and multiple pulse/MASS NMR experiments is presented. The approach relies on an examination of magnetization vectors of individual crystallites during the experiments, and is similar in spirit to the vector model employed in liquid state spectroscopy. Many features of MASS and multiple pulse/MASS experiments can be understood with this approach. For instance, it is easy to illustrate that vectors from the spin packets refocus once every rotor cycle leading to the formation of rotational echo trains. Furthermore, an examination of the magnetization’s path during a rotor cycle suggests a method to generate spin echoes in a rotating sample which involves two π pulses separated by a rotor period TR. A similar analysis leads to an explanation of the four pulse cycle used to suppress sidebands in MASS spectra (the so-called TOSS experiment) and to multiple π-pulse trains which generate echoes every second through fifth rotor period. In addition, it is shown that the rotor frequency lines which appear in multiple pulse/MASS arise because of errors in the multiple pulse train. Finally, when the cycle time in chemical shift scaling experiments becomes comparable to the rotor period, then distorted powder patterns and sideband patterns with a spacing ‖2νR−νSC‖ are observed, where νR and νSC are the rotation and scaling frequencies, respectively. The origin of these powder and sideband patterns is explained.