Elastic constants of bccHe4

Longitudinal and transverse sound velocities were measured in single crystals of bcc ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ with known orientation at 21.00 ${\mathrm{cm}}^3$/mole and at 1.612 K. In addition, the temperature dependence of the sound velocities along an isochore and along the melting curve was measured for several samples. No premelting effects were observed. These data were used to determine mode Grüneisen parameters. A least-squares fitting of the data at 1.612 K yielded the reduced adiabatic elastic constants, in units of ${10}^5$ ${\mathrm{m}}^2$/${\sec }^2$, $\frac{C_{11}}{\rho }=1.630\mathrm{}\pm 0.036$, $\frac{C_{12}}{\rho }=1.473\mathrm{}\pm 0.034$, and $\frac{C_{44}}{\rho }=1.137\mathrm{}\pm 0.010$. These moduli imply a compressibility of (3.437 ± 0.072) × ${10}^{-3\mathrm{}}$ ${\mathrm{bar}}^{-1\mathrm{}}$ and a Debye temperature of 19.17 ± 0.05 K. The ratios of the corresponding bcc ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ to ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ elastic moduli at the same molar volume are considerably larger than the classical ratio of unity but in excellent agreement with the quantum-mechanical calculations of Horner. Existing calorimetric data are compared with the present determination of the Debye temperature.