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

Abstract

Free induction decay (FID) measured by nuclear magnetic resonance in a polycrystalline solid is the isotropic average of the FIDs for individual single crystallites. It has been recently proposed theoretically and verified experimentally that the long-time behavior of single-crystal FIDs has the universal form of exponentially decaying sinusoidal oscillations. Polycrystalline averaging complicates the situation theoretically, while the available experimental evidence is also ambiguous. Exponentially decaying sinusoidal oscillations have been observed for ${}^{129}$Xe in polycrystalline solid xenon but not for ${}^{19}$F in a powder of CaF${}_{2}$. In this paper, we present first-principles FID calculations for powders of both CaF${}_{2}$ and solid xenon. In both cases, the asymptotic long-time behavior has the expected form of exponentially decaying sinusoidal oscillations, which is determined by the single-crystallite FID with the slowest exponential decay. However, this behavior appears only at rather small values of the signal that have not yet been measured in experiments. At intermediate times accessible experimentally, a polycrystalline FID depends on the distribution of the exponential decay constants and oscillation frequencies for single-crystallite FIDs. In CaF${}_{2}$, these parameters are relatively broadly distributed, and as a result the sinusoidal long-time oscillations become somewhat washed out. In contrast, the single-crystallite parameters are more clustered in solid xenon, and, as a result, the experimentally observable range is characterized by a well-defined oscillation frequency and exponential decay constant, even though neither of these parameters represents the true long-time behavior. The above difference of the intermediate FID behavior originates from the difference of the crystal structures of solid xenon and CaF${}_{2}$.