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Quadrupolar Powder Pattern

The observed NMR spectrum of a solid powder (no MAS, no molecular motion) is the summed signal from crystallites over all possible orientations relative to the applied field Bo. For a single spin dominated by its quadrupolar interaction (relative to J's, shift anisotropy, dipolar interactions) one would in principle observe a quadrupolar powder pattern as shown below.

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By changing the orientation relative to Bo (set to point along +z) one can visualize how an individual crystallite contributes to the powder pattern. The vertical lines above represent the transitions at a particular orientation. All orientations contribute to the observed powder spectrum. Note what happens at the "magic angle", where q=54.7 when the asymmetry h=0. Also note how rotations about the +z axis affect the spectrum when the asymmetry is zero.

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