Theory of the Anomalous Heat Capacity in Solid Hydrogen and Deuterium at Low o-Hydrogen and p-Deuterium Concentration

Abstract

The theory of the anomalous heat capacity for low concentrations of ortho hydrogen in the solid state has been extended by a calculation based on the angular potential energy between adjacent molecules. The effects included were (1) the chemical or valence energy, (2) the electrostatic quadrupole-quadrupole energy, and (3) the inverse sixth-power dispersion energy. The expression used for the first type of interaction was derived theoretically by de Boer, while gas-phase experimental parameters were used to evaluate the second two types of interaction in connection with a theoretical estimate of the anisotropy of polarizability of the hydrogen molecule. It was found that only electrostatic quadrupole-quadrupole interactions had to be considered at one atmosphere, but at higher pressures, the valence forces became important. The case of three ortho hydrogen molecules in a row was also treated in the quadrupole approximation. The heat capacity predicted by this model was somewhat different from that predicted for isolated ortho-ortho pairs. The theory was compared with available one atmosphere data on ortho hydrogen and para deuterium at low concentrations in the solid. The results depend not only on the total ortho concentration but also on the relative concentrations of isolated ortho molecules, isolated pairs of ortho molecules, and more complicated configurations. Nakamura's suggestion (that an additional term in the anomalous heat capacity proportional to the ortho concentration is needed to explain the data) seems to be supported by the analysis, although additional data would be desirable.