Specific Heat Measurements Of Some Solid Gases In A Helium-3 Cryostat

Abstract

The specific heats of solid CO, NO, 0₂, N₂, and some dilute mixtures of 0₂ in CO and N₂ in the temperature range 0.6⁰ to 4⁰K are reported. The measurements were made in a mechanical heat switch calorimeter in a He⁴ cryostat to which had been added a He³ stage. A commercial germanium resistance thermometer was used which was calibrated against the He³ and He⁴ vapor pressure scales. The specific heats of CO and NO were measured in an attempt to settle the question as to the origin of the residual entropy of these two substances. For these cases, there exists a discrepancy between the entropy calculated from spectroscopic data (Sspec) and that calculated from specific heat data (Scal); the difference Spec‐s cal being called the residual entropy. For many years, the usually accepted explanation for the appearance of a positive, finite value of the residual entropy in the cases of CO and NO has been in terms of ‘frozen-in’ non-equilibrium states of the crystal. For these cases, it was assumed that the orientation of the molecules becomes frozen—in at a high temperature because the forces tending to produce orientational order are insufficient to overcome the high potential barriers to molecular rotation in the crystal. In this way, the disorder persists to the absolute zero, resulting in the observed value of the residual entropy. Recently, considerable doubt as to the validity of this kind of argument has been raised, especially because molecular rotation in solid CH₄ has been demonstrated even at 1.8⁰K from a recent spin—lattice relaxation study. In an attempt to find a specific heat anomaly which could remove the residual entropy, this study of CO and NO was undertaken. No anomalous behavior in either case was revealed down to 0.6⁰K. It is pointed out that our present incomplete knowledge of molecular rotation in solids at low temperatures needs to be improved by extensive infrared absorption, spin—lattice relaxation, and other studies in order to be in a better position to understand the origin of the residual entropy in those few simple substances for which such an effect persists. During the course of this work, a sample of CO was found to have been contaminated with CO₂ and air. The specific heat measurements on this sample revealed a rather broad anomaly, not accounted for by the Debye theory. A subsequent experiment in which more oxygen was deliberately added to the sample showed that the anomaly was caused by the oxygen impurity. A further experiment in this series in which oxygen was added to a nitrogen host was performed and the results allowed certain conclusions to be made regarding the origin of the anomaly. The concentrations of oxygen were very low, generally a few tenths percent. The results may be interpreted in terms of a model consistent with the low-lying rotational energy levels of the oxygen molecule. The observed anomaly was in excellent agreement with the Schottky anomaly for a system containing two levels with a degeneracy ratio, upper to lower, of 2:1, and an energy spacing of 5.14⁰.