States of Solid Methane as Inferred from Nuclear Magnetic Resonance

As there are different points of view concerning the molecular dynamical states in solid methane, especially concerning the $\ensuremath{\lambda}$-transition at 20.42\ifmmode^\circ\else\textdegree\fi{}K, we have investigated the manner in which the new method of nuclear magnetic resonance throws light on the problem. Both the one-parameter theory and the method of perturbation were applied to the analysis of the proton resonance data given by Thomas, Alpert, and Torrey.The characteristic time ${\ensuremath{\tau}}_{c}$ for molecular reorientation was estimated from the spin-lattice relaxation data, and it was found that above 20\ifmmode^\circ\else\textdegree\fi{}K molecules may be considered to reorient against some fixed hindrances due to neighboring molecules. At about 65\ifmmode^\circ\else\textdegree\fi{}K a marked alteration is present in the dominant mechanism of the above reorientation, which is considered to be either correlated or independent molecular rotation. However, below 20\ifmmode^\circ\else\textdegree\fi{}K most of the molecules seem to be in the ground state of rotational oscillation and occasionally (about ${10}^{7}$ times per second) tunnel or flip to neighboring equivalent orientations. It was proposed that we should discriminate between two pictures of the local magnetic field, possibly in relation to the frequency of resonance. This idea was confirmed by reproducing the line width data.A perturbation calculation, assuming the $F\overline{4}3m$ arrangement of the molecules and taking account of the above situation, gave the entire shape of the absorption line, which was in close agreement with experimental data observed in the lowest temperature range.

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