Transient Nuclear Induction and Double Nuclear Resonance in Solids

Abstract

The behavior of transient nuclear induction signals from solids is described by a stochastic model based on a Markoff process. The model assumes the presence of local dipolar field fluctuations in a crystal due to a set $B$ of coupled nuclei. These fluctuations can destroy or enhance the observed precessional coherence of a different set $A$ of nuclei in the crystal. Coupling among $A$ spins is assumed negligible. The spin echo of $A$ formed at a given time $t$ has an amplitude determined by the magnitude and rate $R$ of field fluctuations. For values of $\mathrm{Rt}$ between zero and the order of unity the echo amplitude decreases, reaches a minimum at $\mathrm{Rt}\ensuremath{\sim}1$, and increases for $\mathrm{Rt}>1$. For $R$ larger than the spin $A$ static line width (when $R=0$) in units of frequency, line narrowing becomes effective, and is reflected in terms of increased lifetime and amplitudes of echo signals. The effect of $B$ spin (${\mathrm{Na}}^{23}$) continuous wave resonance upon the echo relaxation of $A({\mathrm{Cl}}^{35})$ is studied in NaCl${\mathrm{O}}_{3}$, a nuclear quadrupole system. For sufficiently weak cw rf excitation of ${\mathrm{Na}}^{23}$, the behavior of ${\mathrm{Cl}}^{35}$ echoes roughly follows the behavior predicted by the stochastic model for changes in local field fluctuation rate $R$. The effect of coherent oscillations of local fields at larger cw rf excitation is discussed. Zeeman splittings of the ${\mathrm{Na}}^{23}$ quadrupole resonance are studied by the double resonance method. The decay of spin echo signals in liquids, as a result of molecular diffusion, is conveniently described by the stochastic model.