Proton Spin-Lattice Relaxation in Solid and Liquid Hydrogen Deuteride

Abstract

Measurements of the proton spin-lattice relaxation time in solid and liquid HD containing ${\mathrm{H}}_{2}$ (and a smaller amount of ${\mathrm{D}}_{2}$) impurities have been made in the temperature range 1.3-21.9\ifmmode^\circ\else\textdegree\fi{}K. The experiments in the solid were carried out at two radio frequencies, \ensuremath{\sim}10 and \ensuremath{\sim}40 MHz, on samples whose ortho-${\mathrm{H}}_{2}$ concentration had been greatly reduced by ortho-para conversion for several weeks at 4.2\ifmmode^\circ\else\textdegree\fi{}K. Below 8\ifmmode^\circ\else\textdegree\fi{}K, ${T}_{1}$ is strongly temperature-dependent, varying roughly as ${T}^{\ensuremath{-}6.5}$ down to 4\ifmmode^\circ\else\textdegree\fi{}K in the samples with lowest ortho-${\mathrm{H}}_{2}$ concentration. Below 4\ifmmode^\circ\else\textdegree\fi{}K, the temperature dependence decreases to about ${T}^{\ensuremath{-}2}$ at 2\ifmmode^\circ\else\textdegree\fi{}K. The magnetic field dependence of ${T}_{1}$ between 0.5 and 10 kOe, at liquid-helium temperatures, is found to have the approximate form ${T}_{1}\ensuremath{\propto}{H}^{\ensuremath{\alpha}}$, with $\ensuremath{\alpha}$ between $\frac{1}{3}$ and 1. These low-temperature results are interpreted in terms of a fast cross-relaxation process between protons of different species, which gives a relaxation rate $\frac{1}{{T}_{1}}$ proportional to the product of the ortho-${\mathrm{H}}_{2}$ relaxation rate and the ortho-${\mathrm{H}}_{2}$ concentration. Differences between our results and those of Hardy and Gaines are explained by a quenching in our samples of relaxation processes involving mutual interactions of ortho-${\mathrm{H}}_{2}$ molecules, apparently as a result of crystal-field splittings of the rotational levels produced by the appreciable para-${\mathrm{H}}_{2}$ (and perhaps ${\mathrm{D}}_{2}$) impurity concentrations in our samples. We were able to deduce the ortho-${\mathrm{H}}_{2}$ concentrations of our samples (between 7 \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}4}$ and 6 \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}7}$), to determine the intrinsic relaxation time of the ortho-${\mathrm{H}}_{2}$ impurity, which is approximately 16 msec at 4.2\ifmmode^\circ\else\textdegree\fi{}K and 2.5 kOe, and to resolve some of the problems in Hardy and Gaines's interpretation. In the temperature region above \ensuremath{\sim}8\ifmmode^\circ\else\textdegree\fi{}K for the solid substance, self-diffusion-induced relaxation becomes important for our range of sample ortho-${\mathrm{H}}_{2}$ concentrations, and the results are in semiquantitative agreement with the predictions of Bloom's theory. In particular, near the melting point, ${T}_{1}$ is independent of the ortho-${\mathrm{H}}_{2}$ concentration, indicating dominance of an intrinsic HD relaxation mechanism, and ${T}_{1}$ is proportional to ${H}^{2}$. The activation energy for HD molecular self-diffusion was found to be approximately 190\ifmmode^\circ\else\textdegree\fi{}K, which is considerably lower than the value of 302\ifmmode^\circ\else\textdegree\fi{}K previously determined by Bloom. The rate of ortho-para conversion of ${\mathrm{H}}_{2}$ in solid HD was measured to be (0.68\ifmmode\pm\else\textpm\fi{}0.05)%/h, in reasonable agreement with theoretical calculations by Urano and Motizuki. Measurements were also made on the rate of para-ortho relaxation at room temperature in a glass vessel, by monitoring the relaxation time at 4.2\ifmmode^\circ\else\textdegree\fi{}K after various waiting times at room temperature. Proton ${T}_{1}$ measurements in the liquid at 5.9 MHz indicate an increase of ${T}_{1}$ with temperature. From these measurements, the relative relaxation rates due to translational and rotational processes are shown to vary from about 4:1 at the HD boiling point to 50:1 at the melting point, in agreement with Bloom's estimate.