Theory of Phase Transition in Solid Methanes. VI

Abstract

The James-Keenan model which is extended by inclusion of a crystalline field of octa­ hedral symmetry is studied for the purpose of elucidating the mechanism of phase transitions and the nature of molecular rotation in the solid methane. All the calculations are made in the subspace J<4, J being the rotational quantum number. Four types of solid phase are examined, three of which are assumed to have the same sublattice structures and the same symmetry as in the disordered phase and the low and high temperature ordered phases of James and Keenan's classical theory, and the remainder has a layer structure. First, nuclear spin species A and T are treated separately. Then normal mixture of these nuclear spin species is examined with a further assumption that these nuclear spin species are randomly distributed in the lattice. A simplest possible form of octahedral field is assumed. The strength of the field is taken from the analysis made by Cabana, Savitsky and Hornig of the infrared absorption spectra by methane molecules dispersed in the matrix of Kr and Xe crystals. It is shown that thermodynamic properties of the extended James-Keenan model are similar to those of the original one and normal mixture exhibits the observed double transitions in solid methane when the magnitude of the effective octopole moment is chosen such that the observed upper transition temperature is reproduced. Nuclear spin species A is shown to be more stable than species T, which is in conformity with Wong, Noble, Bloom and Alexander's and Runolfsson, Mango and Borghini's experiments on the mean square value of the proton angular momentum at low temperatures. The effects of variation of. both the magnitude of the effective octopole moment and the strength of the crystalline field are also discussed.