Statistical Theory of Hindered Rotation in Molecular Crystals, II : Quantum Effects

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It is an aim of this paper to explain the quantum effects on the phase transformations due to molecular hinderance in solid hydrogen halides. Although the transition points of these substances are situated in so high temperatures that the behaviour of the system might be regarded as almost classical, there exist the effects of quantum correction, which can be seen in the isotope effects. For the purpose of studying this effects we proceed on the line of the Hartree approximation, where the Hamiltonian contains the kinetic operators in addition to the intermolecular potential ones. The location of the transition point and the jump in the specific heats are obtained, where the nature of phase transformation is of the second kind. In these-obtained expressions the moment of inertia of the molecule is contained. Making use of the transition points of HBr and HI, we expect the transition points of DBr and DI as 91, 8°K and 71, 7°K respectively, in qualitative agreement with the results observed by K. Clusius and G. Wolf: DBr: 93, 5°K, DI: 77, 3°K. And further the transformation heats prove to increase, as the quantum effect decreases, which is in agreement with the observations. The critical value of the ratio of the hindering potential to the moment of inertia, beyond which any ordered state is unable to be realized, is also obtained.
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