Nuclear Longitudinal Relaxation in Hexagonal Close-PackedH2

Abstract

Measurements of the nuclear-longitudinal relaxation time ${T}_{1}$ in hcp ${\mathrm{H}}_{2}$ are presented. The experiments were performed mainly on solid samples with mole fractions $X$ of molecules with rotational angular momentum $J=1$ equal to or less than $X=0.5$. Pulsed techniques were used at NMR frequencies of 5.5 and 29 MHz. The temperature range was between 0.4 and 13.8 K. The recovery of the NMR signal after saturation was always exponential as a function of time for all samples above $T\ensuremath{\approx}7$ K, and could then be characterized by a single relaxation time ${T}_{1}$. For $Xl0.2$ and $Tl7$ K, the recovery gradually departed from exponential behavior, indicating a more complex relaxation which was studied and discussed in some detail. From the initial slope of the signal recovery at small times, an average value $〈\frac{1}{{T}_{1}}〉$ was obtained that might characterize the relaxation rate of the entire NMR line. At temperatures below the onset of thermally activated diffusion, the relaxation mechanism is believed to be caused by the nuclear-spin flips induced by modulation from the electric quadrupole-quadrupole coupling between $J=1$ molecules, and the results are compared with theories that predict the dependence of ${T}_{1}$ on $X$ in its high-temperature limit. As $X$ decreases, the temperature variation of ${T}_{1}$ between 10 and 4 K becomes surprisingly large and an extrapolation to the limiting high-temperature value ${T}_{1}(\ensuremath{\infty})$, which is of theoretical interest, becomes rather uncertain. Results for ${T}_{1}(\ensuremath{\infty})$ for ${\mathrm{H}}_{2}$ and ${\mathrm{D}}_{2}$ are found to scale in their dependence on the $J=1$ mole fraction down to $X\ensuremath{\approx}0.15$. The departures from scaling below this mole fraction are tentatively attributed to the difficulty in extrapolating the data to ${T}_{1}(\ensuremath{\infty})$. Approximate scaling of ${T}_{1}$ data for ${\mathrm{H}}_{2}$ and ${\mathrm{D}}_{2}$ in their temperature dependence for $X=0.5 \mathrm{and} 0.3$ was demonstrated. In the region above 10 K where diffusion affects ${T}_{1}$, the time $\ensuremath{\tau}={\ensuremath{\tau}}_{0}{e}^{+\frac{E}{{k}_{B}T}}$ between diffusion jumps could be determined from data at 5.5 MHz and compared with that from transverse relaxation measurements (${T}_{2}$) by Hass et al. Excellent agreement is obtained for the activation energy which is found to be $\frac{E}{{k}_{B}}=200\ifmmode\pm\else\textpm\fi{}10$ K in both experiments. This energy and ${\ensuremath{\tau}}_{0}$ from both experiments are discussed in relation to the prediction of Ebner and Sung.