  Free induction decay (FID) measured by nuclear magnetic resonance (NMR) 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 Xe-129 in polycrystalline solid
xenon but not for F-19 in the powder of CaF2. In this paper, we present the
first principles FID calculations for the powders of both CaF2 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 CaF2,
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 well-defined
oscillation frequency and exponential decay constant even though both of these
parameters do not represent 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 CaF2.
