In order to elucidate the structure of methane solids in phase III, orientational orderings of molecules are studied on the basis of a model potential consisting of a crystalline field (one-body potential), octopole–octopole type, octopole–hexadecapole type, and hexadecapole–hexadecapole type potentials, which are obtained through a multipole expansion of the sum of interatomic Lennard-Jones type potentials. It is assumed that carbon atoms are fixed at sites of a fcc lattice, and that the orientational order has the period not larger than twice the lattice constant of the carbon fcc lattice. In the framework of classical molecular field approximation, we solve consistency equations for molecular fields, and examine stabilities of various solutions which branch off from phase I (disordered phase) or from phase II (partially ordered phase). To this end, Landau’s theorem on the phase transition of second order is extended such that it allows us to determine possible space groups for the lower temperature phase which are related to a given irreducible representation of the space group of the higher temperature phase. Two parameters are introduced to adjust the strengths of the multipolar interactions employed. Solutions with high branching temperatures are studied in detail within a range of parameters which yields the correct structure (Fm3c) for phase II. Referring to the extinction rules found by neutron diffraction experiments on CD4, we conclude that the structure of phase III is described by a solution with the tetragonal space group P42/mbc containing 16 molecules per unit cell (a subgroup of Fm3c). Inclusion of the octopole–hexadecapole type potentials is found to be most essential for stabilizing this structure relative to phase II. Changes in site symmetries at the transition II → III are O→D2, D2d →S4, and Cs. Thus the O-molecules in phase II also become ordered in phase III. However, in comparison with strong molecular fields at S4 and Cs sites, molecules at D2 sites are subjected to a much weaker molecular field. Approximating this multisite structure by a two-site model in tetrahedral fields, we analyze the observed heat capacity anomalies of CH3D and CH2D2 in phase III, and predict their tunneling level structures. Infrared and Raman spectra are also discussed. It is also found that a solution, C2/c containing four molecules per unit cell, becomes most stable at 0 K if the values of the hexadecapolar parameters are reduced and the crystalline field is strengthened.

Maki, K., Kataoka, Y., & Yamamoto, T. (1979). Theory of phase transitions in solid methanes. XII. Orientational order of molecules in phase III. The Journal of Chemical Physics, 70(2), 655–674.