Heat Capacity and Other Properties of Body-Centered CubicHe4

The heat capacity at constant volume, $C_v$, of bcc ${\mathrm{He}}^4$ has been measured for a number of molar volumes covering most of the bcc region of the phase diagram. The results can be represented to within 3% of $C_v$ by a constant Debye $\Theta$ of 16.95°K. Using the discontinuities in the heat capacity at the phase boundaries measured in this and in previous work, the compressibility $\kappa$ is found to be (3.8±0.2)×${10}^{-3\mathrm{}}$ ${\mathrm{atm}}^{-1\mathrm{}}$ and substantially independent of temperature, while values of the expansion coefficient $\alpha$ found by the same method are between 5×${10}^{-3\mathrm{}}$ and 13×${10}^{-3\mathrm{}}$ ${\mathrm{deg}}^{-1\mathrm{}}$. The values of $\alpha$ are consistent with a Gruneisen equation with a Gruneisen constant $\gamma \approx 2.6$, the value found previously for hcp ${\mathrm{He}}^4$. The latent heats at constant volume at the lower and upper triple points $T_1$ and $T_2$ have been measured as a function of volume and give for the maximum entropy change at $T_1$, where (hcp+liq) → (bcc), the value $\frac{\Delta S_1}{R}=(9\mathrm{}\pm 1)\times {10}^{-3\mathrm{}}$. The maximum entropy change at $T_2$, where bcc → (hcp+liq), has the value $\frac{\Delta S_2}{R}=(32\mathrm{}\pm 2)\times {10}^{-3\mathrm{}}$. The triple-point temperatures were found to be $T_1=1.463\mathrm{}\pm 0.002$°K and $T_2=1.7715\mathrm{}\pm 0.001$°K. The intersection of the $\lambda$ line with the bcc phase boundary has been confirmed to be ∼10 mdeg below the upper triple point. The entropy of the bcc phase at the transition line has been computed from the heat-capacity results and the latent-heat measurements, and is found to vary from $\frac{S}{R}=0.037\mathrm{}\pm 0.002$ at $T_1$ to $\frac{S}{R}=0.068\mathrm{}\pm 0.003$ at $T_2$. The relation between $S$ and $C_v$ is the same as for the other low-pressure structures of solid ${\mathrm{He}}^3$ and ${\mathrm{He}}^4$, indicating that the variation of $\Theta$ with $T$ and therefore the lattice spectra are similar. On the supposition that bcc ${\mathrm{He}}^4$ is indeed like the other forms of solid helium, it is estimated that bcc ${\mathrm{He}}^4$ would have a Debye $\Theta$ at 0°K, ${\Theta }_0$, of 21°K for a molar volume of 21 ${\mathrm{cm}}^3$. This value of ${\Theta }_0$, when compared with the measured velocity of sound, indicates that bcc ${\mathrm{He}}^4$ is elastically highly anisotropic, in agreement with the recent theory of Nosanow and Werthamer.