Measurement of(∂P∂T)Vand Related Properties in Solidified Gases. III. SolidD2

Abstract

Measurements in solid ${\mathrm{D}}_{2}$ of pressure changes with temperature and para concentration are reported, and related thermodynamic properties are calculated. The study covers both the hcp and cubic phases in the temperature range $0.4<~T<~4.2$ K and para concentration range $0.02<~c<~0.90$. The measurements were carried out with a capacitance strain gauge capable of resolving pressure changes of 2\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}5}$ bar. Two types of study were made. (a) The pressure changes accompanying the phase transition were determined as a function of $c$, and the hysteresis was studied as a function of the number of cyclings through the transition. (b) The quantity ${(\frac{\ensuremath{\partial}P}{\ensuremath{\partial}T})}_{V}$ was obtained in the cubic and hcp phases as a function of $T$ and $c$. The results were analyzed in terms of separate contributions from the lattice and from the rotation of the paradeuterium molecules ($p$-${\mathrm{D}}_{2}$, lowest rotational level $J=1$). The molecular rotation was assumed to be quenched by the electric quadrupole-quadrupole (EQQ) interaction, and all other effects such as those due to crystal-line field were neglected. The EQQ interaction parameter $\ensuremath{\Gamma}$ was determined experimentally. The results from (a) extend the phase diagram to low para concentrations and show that the transition from the hcp to the cubic phase does not take place below $c=0.55$. The data from thermal cyclings, when analyzed in conjunction with corresponding data from x-ray diffraction, indicate that the changes in pressure (and in other thermodynamic properties) are due mainly to the order-disorder transition of the rotational motions and not to the crystalline phase change per se. The results from (b) give values of $\frac{{\ensuremath{\Gamma}}_{\mathrm{eff}(\mathrm{pair})}}{{k}_{B}}=1.05\ifmmode\pm\else\textpm\fi{}0.07$ K and $\frac{{\ensuremath{\Gamma}}_{\mathrm{eff}(c=1)}}{{k}_{B}}=0.93\ifmmode\pm\else\textpm\fi{}0.05$ K for low and high concentrations of $p$-${\mathrm{D}}_{2}$, respectively. For a rigid lattice, the theoretical value is $\frac{{\ensuremath{\Gamma}}_{0}}{{k}_{B}}=1.20$ K. A comparison is made with values of $\frac{\ensuremath{\Gamma}}{{k}_{B}}$ from a previous determination and with those predicted by the theory of Harris, which takes into account quantum effects in the solid. Anomalies in ${(\frac{\ensuremath{\partial}P}{\ensuremath{\partial}T})}_{V}$ at very low $p$-${\mathrm{D}}_{2}$ concentrations are observed, but are not explained. The entropy of the rotational motion of the $J=1$ state is calculated above 0.4 K and is found to approach $R\mathrm{ln}3$ per mole of $p$-${\mathrm{D}}_{2}$ for $c>~0.6$.