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

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°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×${10}^{-5\mathrm{}}$ 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 $P \left(\mathrm{hcp}\right)-P \left(\mathrm{cubic}\right)$ 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 ${\left(\frac{\partial P}{\partial T}\right)}_V$ 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 $\Gamma =\frac{6e^2{Q}^2}{25R^5}$, where $\mathrm{eQ}$ is the quadrupole moment of the orthomolecule in the state $J=1\mathrm{}$, and $R$ is the nearest-neighbor distance. The theoretical value for a rigid lattice is $\frac{\Gamma }{k_B}=1.00\mathrm{}$°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 $\frac{\Gamma }{k_B}=0.82\mathrm{}\pm 0.04$°K (value extrapolated to $P=0\mathrm{}$). This value was confirmed from the temperature of the maximum of ${\left(\frac{\partial P}{\partial T}\right)}_V$ at low ortho concentrations. The discrepancy between the experimental and the theoretical values of $\Gamma$ is briefly discussed. From ${\left(\frac{\partial P}{\partial T}\right)}_V$ data with almost pure para-${\mathrm{H}}_2$ and from comparison with specific-heat data due to Ahlers, a lattice Grüneisen constant ${\gamma }_L=2.06\mathrm{}\pm 0.1$ was found. The Grüneisen constant of the EQQ interaction was found to be ${\gamma }_{\mathrm{EQQ}}=1.62\mathrm{}\pm 0.1$, 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.