Corresponding States in the Frozen Rare Gases

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Abstract
A method is presented for extending the principle of corresponding states to solids at comparatively low temperatures, where quantum effects are appreciable. The method has been applied to solid neon, argon, krypton, and xenon. The principle of corresponding states, as applied to the liquid and vapor states, is used for calculation of the potential energies and interatomic distances of three of the substances in terms of the other. The quantum contribution to the energy is taken into account by assuming the Debye theory for all the solids, and this is related to the potential energy by means of a modified Grüneisen equation. The Debye θ's for three of the solids are determined from that of the other by a dimensional analysis of the mechanical system. Using this information, Cp for neon, argon, and krypton have been calculated from the experimental data for xenon. Agreement of the calculated values with experiment is reasonably good; small deviations may be caused by breakdown of the Debye theory, or may be indications of inexactitude in the law of corresponding states.

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