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Free induction decay (FID) measured by nuclear magnetic resonance (NMR) in apolycrystalline solid is the isotropic average of the FIDs for individualsingle crystallites. It has been recently proposed theoretically and verifiedexperimentally that the long-time behavior of single-crystal FIDs has theuniversal form of exponentially decaying sinusoidal oscillations.Polycrystalline averaging complicates the situation theoretically, while theavailable experimental evidence is also ambiguous. Exponentially decayingsinusoidal oscillations have been observed for Xe-129 in polycrystalline solidxenon but not for F-19 in the powder of CaF2. In this paper, we present thefirst principles FID calculations for the powders of both CaF2 and solid xenon.In both cases, the asymptotic long-time behavior has the expected form ofexponentially decaying sinusoidal oscillations, which is determined by thesingle crystallite FID with the slowest exponential decay. However, thisbehavior appears only at rather small values of the signal that have not yetbeen measured in experiments. At intermediate times accessible experimentally,a polycrystalline FID depends on the distribution of the exponential decayconstants and oscillation frequencies for single crystallite FIDs. In CaF2,these parameters are relatively broadly distributed, and as a result, thesinusoidal long-time oscillations become somewhat washed out. In contrast, thesingle crystallite parameters are more clustered in solid xenon, and, as aresult, the experimentally observable range is characterized by well-definedoscillation frequency and exponential decay constant even though both of theseparameters do not represent the true long-time behavior. The above differenceof the intermediate FID behavior originates from the difference of the crystalstructures of solid xenon and CaF2.

Asymptotic and intermediate long-time behavior of nuclear free induction decays in polycrystalline solids and powders