Sound Propagation in X-Ray-Oriented Single Crystals of hcp Helium-4 and bcc Helium-3

Measurements of the longitudinal and transverse sound velocities in x-ray-oriented single crystals of hcp $^{4}\mathrm{He}$ (19.0-20.5 ${\mathrm{cm}}^{3}$/mole) and bcc $^{3}\mathrm{He}$ (21.6 ${\mathrm{cm}}^{3}$/mole) are reported. These data are used to compute the respective second-order adiabatic elastic moduli. The moduli for $^{3}\mathrm{He}$ imply an extremely soft transverse mode in the 101> directions and thus demonstrate that the low-temperature bcc-$^{3}\mathrm{He}$ specific-heat anomaly is due to an anomalous phonon spectrum. The Debye temperatures and volume compressibilities determined by the elastic moduli for both bcc $^{3}\mathrm{He}$ and hcp $^{4}\mathrm{He}$ are in agreement with values determined by other methods.

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