Theory of Phase Transitions in Solid Methanes. III : Mixture of Nuclear Spin Species A and T of CH_4

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Studies of the statistical mechanical properties of the James-Keenan model are extended to mixtures of nuclear spin species A and T with the purpose of elucidating the mechanism of phase transitions in the solid light methane. All the calculations are made on the basis of quantum statistical mechanics in the subspace with J≦4, J being the rotational quantum number. The molecular field approximation is employed. Two types of ordered phases are examined under the assumption of the same symmetry relations and the same sublattice structures as those in the low and high temperature ordered phases of James and Keenan's classical theory. Normal and equilibrium mixtures of nuclear spin species A and T are treated with the further assumption that these nuclear spin species are randomly distributed in the lattice. Various thermodynamical properties including phase diagrams are predicted and compared with experiment. It is found that the nature of the lower transition strongly depends on whether the interspecies conversion is allowed ar not.
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