Phase cycling in MQMAS sequences for half-integer quadrupole spins

A review in the Progress in Nuclear Magnetic Resonance Spectroscopy journal provides analytical expressions of the first- and second-order quadrupole interactions for a static crystal and for a crystal rotating at variable or magic angle. It provides mathematical notebooks for calculating the analytical expressions of these interactions. These interactions are extensively tested for the case of a solid rotating at the magic angle. The review also focuses on nested phase cycling in MQMAS sequences applied to half-integer quadrupole spins. There are two ways to define the phase cycle for a given coherence transfer pathway that involve finding a solution to the equations, describing the pathway phase of a coherence transfer pathway and using rules developed for nested phase cycling. The review also deals with basic two- and three-pulse MQMAS sequences and determines phase cycles for selecting the desired coherence pathways and reciprocally all coherence transfer pathways selected by a phase cycle.