Rotating-Frame Double Resonance and Nuclear Cross Relaxation in LiF

Abstract

This paper resports our study of Hartmann and Hahn's technique of rotating-frame nuclear double resonance (RFDR). We consider the ${\mathrm{Li}}^6$-${\mathrm{Li}}^7$ system in LiF and obtain the cross-relaxation dynamics from the ${\mathrm{Li}}^7$ free-induction-decay data via a general expression which we derive. We find that the presence of ${\mathrm{F}}^{19}$ spins, which constitute a third species interacting strongly with the Li systems in LiF, may easily be taken into account, and that the resulting RFDR behavior does not differ qualitatively from that in a simple two-species system. The cross-relaxation time dependence is well described by an exponential or sum of exponentials for times longer than the order of $T_2$, with nonexponential behavior for shorter times. The cross-relaxation rate $W_{\mathrm{CR}}$ exhibits a Lorentzian dependence on the magnitude of the ${\mathrm{Li}}^6$ rf field, $H_{16}$, for the case where the ${\mathrm{Li}}^7$ system has been adiabatically demagnetized in the rotating frame; these results show that the Gaussian behavior previously assumed is incorrect. For the case where the ${\mathrm{Li}}^7$ rf field is of the order of the local field, $W_{\mathrm{CR}}\left(H_{16}\right)$ is asymmetric about Hahn's double resonance (DR) condition, with the larger $W_{\mathrm{CR}}$ corresponding to $H_{16}$ less than for the DR condition. The cross-relaxation times at the DR condition are on the order of 0.4 msec. We observe no spin-diffusion bottleneck in a sample of LiF with an isotopic abundance of 0.008% ${\mathrm{Li}}^6$. Finally, we draw some general conclusions about the application of RFDR to other problems.