Measurement of(∂P∂T)Vand Related Properties in Solidified Gases. II. SolidH2

Abstract

We report measurements and their analysis of pressure changes with temperature and ortho-${\mathrm{H}}_{2}$ concentration in solid ${\mathrm{H}}_{2}$ in both the hcp and cubic phases. The temperature range extended from 0.4 to 4.2\ifmmode^\circ\else\textdegree\fi{}K, and the concentration $c$ of ortho-${\mathrm{H}}_{2}$ was between 0.005 and 0.94. The measurements were carried out by means of a sensitive capacitance strain gauge capable of resolving pressure changes of 2\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}5}$ bar. The categories of experiments performed were (1) determination of the pressure $P$ in the hcp phase as a function of ortho concentration at several temperatures; (2) determination of the pressure difference $P (\mathrm{hcp})\ensuremath{-}P (\mathrm{cubic})$ as a function of ortho concentration, and study of the hysteresis in both pressure and temperature of the hcp-to-cubic transition; and (3) measurement of ${(\frac{\ensuremath{\partial}P}{\ensuremath{\partial}T})}_{V}$ at constant ortho concentration in the hcp phase at several different ortho concentrations. The results were analyzed in terms of a lattice contribution and an electric quadrupole-quadrupole (EQQ) interaction, neglecting any effects from other interactions and from crystalline fields. The EQQ interaction parameter determined experimentally was $\ensuremath{\Gamma}=\frac{6{e}^{2}{Q}^{2}}{25{R}^{5}}$, where $\mathrm{eQ}$ is the quadrupole moment of the orthomolecule in the state $J=1$, and $R$ is the nearest-neighbor distance. The theoretical value for a rigid lattice is $\frac{\ensuremath{\Gamma}}{{k}_{B}}=1.00$\ifmmode^\circ\else\textdegree\fi{}K. The results from (1) and (2), extrapolated to pure ortho-${\mathrm{H}}_{2}$, were analyzed using the theory of Miyagi and Nakamura and gave $\frac{\ensuremath{\Gamma}}{{k}_{B}}=0.82\ifmmode\pm\else\textpm\fi{}0.04$\ifmmode^\circ\else\textdegree\fi{}K (value extrapolated to $P=0$). This value was confirmed from the temperature of the maximum of ${(\frac{\ensuremath{\partial}P}{\ensuremath{\partial}T})}_{V}$ at low ortho concentrations. The discrepancy between the experimental and the theoretical values of $\ensuremath{\Gamma}$ is briefly discussed. From ${(\frac{\ensuremath{\partial}P}{\ensuremath{\partial}T})}_{V}$ data with almost pure para-${\mathrm{H}}_{2}$ and from comparison with specific-heat data due to Ahlers, a lattice Gr\"uneisen constant ${\ensuremath{\gamma}}_{L}=2.06\ifmmode\pm\else\textpm\fi{}0.1$ was found. The Gr\"uneisen constant of the EQQ interaction was found to be ${\ensuremath{\gamma}}_{\mathrm{EQQ}}=1.62\ifmmode\pm\else\textpm\fi{}0.1$, in agreement with the theoretically expected value. Evidence was found for redistribution of orthomolecules at low ortho concentration as a function of time. The theoretical expectations for a thermodynamic-equilibrium distribution of molecules in the lattice and that for a random high-temperature distribution are compared with experimental results.