Magic angle, orientation distribution

The azimuthal mean gives rise to an ambiguous quantity — the magic angle of 54.7°. If the vector orbital is tilted at 54.7°, there will be no variation in / with 0. Conversely, if there is no variation in I with 0, Equation 4.2.1 will reveal that a = 54.7°. An infinite number of orientation distributions can result in an azimuthal mean orientation of 54.7°, but the most important of these is complete disorder. If there is no variation in I with 0, one may speculate but not prove that a sample is disordered. 

If the rate of molecular motion in the sample increases, any of these lineshapes will narrow, but the exact shape will depend on the geometry of motion. If the sample is spun at the magic angle, the resonance collapses to a symmetric peak at ct so. If some preferred orientation is induced in the sample, e.g., by mechanical deformation, the resulting spectrum is a convolution of the original powder pattern with the imposed distribution. CSA spectra of oriented materials have been used to derive order parameters and to propose models for the orientation process [23]. Multiple-pulse experiments are needed to observe the CSA of abundant spins, but not of rare... 

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