Lattice dynamics of solid methane

Solid methane seems a comparatively simple example of a molecular crystal. Yet the intemal dynamics of the system are not understood. Specific heat measurements have revealed a phase transformation at 20.4 °K; recently, a second phase change has been found at 8 °K. Both transitions are of the second kind. x-ray investigations have indicated that the first transition does not affect the fcc lattice positions of the carbon atoms. The energy distribution of scattered slow neutrons has been measured for all three phases. Results for the $\alpha$-phase (T >20.4 °K) and the $\beta$-phase (20.4 °K>T >8 °K) were reported at the IAEA Symposium in ChalkRiver. With the present measurements the investigation is extended into the $\gamma$-phase (T < 8°K). As before, the experiments are carried out with the filtered detector technique. Frequency disuibutions, derived from the assembly of experimental results, are compared to theoretical predictions, which are based on a model proposed by James and Keenan for the orientational suucture. The comparison confirms the model for the y-phase. The observed maximum frequency of acoustic vibrations, $f{\omega}_{D}$ = 4 meV, corresponds weil to what one would expect for the assumed octopole-octopole interactions. In addition, two optical bands are observed. The ratio of their mean frequencies is found to be 1.25, which under the assumption of harmonic librations corresponds exactly to the value calculated from the proposed orientational structure. Again for octopoleoctopole interaction the absolute values of these frequencies indicate q = 0.16 e for the effective proton charge. Thermodynamic considerations, applied by James and Keenan to CD$_{4}$, give q=0.13 e. The experimental results contradict, however, the orientational suucture proposed for the $\beta$-phase. For the $\alpha$-phase the theory predicts the absence of long-range orientational order. The neutron investigations show that yet the rotational motions are not entirely unhindered, but a quantitative interpretation of the spectrum observed in this phase has not been attempted