Theory of phase transitions in solid methanes. X. Centering around Phase II in solid CH4

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Abstract
Thermal, spectroscopic, and other properties of methane solids, especially those concerning Phase II of solid CH4 in nuclear spin species equilibration, are theoretically studied from a unified point of view, i.e., the extended James–Keenan model. It assumes a rigid lattice and treats the molecular motions with respect to the rotational degress of freedom in the crystal potential given by Yasuda [Prog. Theor. Phys. 45, 1361 (1971)]. Two adjustable parameters are introduced in order to adapt the assumed crystal potential to the actual situation in the solid state of CH4. Most of the calculations are carried out in the framework of the molecular field method in quantum statistical mechanics. The eight‐sublattice antiferrorotational structure is assigned to Phase II. Thus we have two kinds of site Hamiltonians in this phase, the symmetry groups of which are the direct product groups ?hOh and ?dD2d. Basis functions are doubly symmetry adapted under each of these symmetry groups. Rotational functions are included up to J=8 (sometimes up to J=10). The accuracy of the calculations is tested and the errors in level spacings are estimated at a few percent. The level scheme obtained for Oh‐site features hindered rotations, is independent of temperature, and applies also to all molecules in Phase I. The level scheme of D2d site bears the librational character in its lower energy part and has the lowest levels split through quantum tunneling (the tunneling levels). These level schemes are compared with the results of neutron inelastic scattering experiments and satisfactory agreements are obtained. The two‐term crystalline field employed is justified through comparison with the result of the neutron diffraction experiment on Phase I of CD4. The transition between Phases I and II turns out to be of first order, and the reason for this is given. The nature of the transition is new, being neither the rotational melting proposed by Pauling nor the orientational order–disorder transition by Frenkel. Thermodynamic quantities are worked out, including the free energy, entropy, internal energy, specific heat, and the mean square of the proton spin angular momentum. Anomalous behaviors of the specific heat at low temperatures are studied in detail and compared with observation. The predicted structure of the tunneling levels is again and conclusively confirmed by experiment. The negative thermal expansion observed below about 10 K is nicely reproduced with an additional assumption on the response of the crystal potential upon varying the lattice spacing. The transition between Phases II and III observed at elevated pressure is qualitatively discussed with special reference to the role played by Oh molecules in Phase II, and a quantum nature of the transition below about 10 K is pointed out. The main predictions made in this report are as follows: (1) The tunneling levels have such temperature dependences below about 4 K that their level spacings at 0 K are about 10% larger than those at 4 K. Their effects on the Schottky anomaly in the specific heat and on the nuclear susceptibility at around 1 K are described in detail. (2) Apparently unusual quantum effects are predicted on the transition temperatures between Phases I and II. That of CD4 is the highest and those of CH4 and CT4 appear at about the same temperature. (3) Solid solutions of CH4 and Kr or Xe have double phase transitions in a certain CH4‐rich region, the lowest temperature phase having no orientational order. If the conversion is not allowed, the lower transition does not occur. (4) Solid solutions of CH4 and CD4 have triple transitions in a certain CH4‐rich region, the lowest temperature phase having the same structure as Phase II. (5) The tunneling levels of T species split into two levels, the upper one has the degeneracy six and the lower one the degeneracy three, and the separation is 0.01 K.

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