Specific heats of solid hydrogen, solid deuterium, and solid mixtures of hydrogen and deuterium

Abstract

Measurements have been made in the temperature range 0.5–5 K of the specific heats of pure solid H₂, pure solid D₂, and four solid mixtures of H₂ and D₂ with D₂ fractions between 15 and 95%, all of which systems had low concentrationc of molecules in the rotational stateJ=1. For the H₂,c=0.0023, and for the D₂,c=0.030. It was found that the observed specific heats could be described as the sum of three terms as follows. (1) A lattice specific heat. This was found to follow aT ³ function with θ _D =122 K for solid H₂ and θ_D=113.8 K for solid D₂. For the solid mixtures the lattice specifi heats have in first approximation values given by a weighted mean of the lattice specific heats of the pure components. (2) A Schottky term with a maximum at about 1.3 K for solid H₂ and 1.4 K for solid D₂, which can quantitatively be described in terms of electric quadrupole-quadrupole (EQQ) interactions in nearest-neighbor pairs and triples of molecules in the rotational stateJ=1. This term led to evaluation of г, the EQQ interaction energy, giving г/k=0.9 ± 0.1 K for solid H₂ and 0.93 ± 0.05 K for solid D₂. It was found, moreover, that in solid H₂ there was an appreciable enhancement with time of the number of clusters of molecules in the rotational stateJ=1 at the expense of the number of isolated singles of similar molecules, due to rotation diffusion. On the other hand no rotation diffusion was observed in solid D₂ or in the solid mixtures of H₂ and D₂, except possibly in those mixtures containing 85% H₂. (3) A second anomalous term occurring at temperatures below about 0.8 K and, by extrapolation, having its maximum below 0.5 K (the lowest temperature of our measurements). This anomaly was observed only in those samples containing D₂ and is, as yet, unexplained in detail. A further major conclusion from our results in the temperature range 0.5–5 K is that there was no evidence in the form of a sharp anomalous jump in the specific heat of any of the mixtures which could be interpreted as indicating the occurrence of isotopic phase separation. This absence of phase separation is noted, in spite of the fact that thermodynamically it is energetically favorable in the temperature range of observation.