Sound Measurements in Liquid and Solid ${\mathrm{He}}^3$, ${\mathrm{He}}^4$, and ${\mathrm{He}}^3$-${\mathrm{He}}^4$ Mixtures

Using the ultrasonic pulse technique at a carrier frequency of 10 Mc/sec, we have measured the longitudinal velocity of sound in liquid and solid ${\mathrm{He}}^3$, ${\mathrm{He}}^4$, and ${\mathrm{He}}^3$-${\mathrm{He}}^4$ mixtures (0.0, 5.03, 25.0, 74.9, 98.00, 99.84% ${\mathrm{He}}^3$) in the temperature range from 1 to 4.2°K and the pressure range from 1 to 150 atm. An upper limit to the attenuation of sound in the region of the solid investigated is on the order of 0.3 to 0.7 ${\mathrm{cm}}^{-1\mathrm{}}$. Values of the adiabatic compressibility of the liquid along the melting curve of ${\mathrm{He}}^4$ are given. The discontinuity in the propagation velocity at a first-order phase boundary was utilized to locate the solidification curves of these samples and also to investigate the bcc-hcp crystallographic transition in solid samples, including pure ${\mathrm{He}}^4$, similar to that observed in pure ${\mathrm{He}}^3$ by Grilly and Mills. The triple points for this transition in ${\mathrm{He}}^4$ are given by $T_l=1.449\mathrm{}\pm 0.003$°K, $P_l=26.18\mathrm{}\pm 0.05$ atm; $T_u=1.778\mathrm{}\pm 0.003$°K, $P_u=30.28\mathrm{}\pm 0.05$ atm. The upper triple points for the mixtures lie on a straight line connecting ${\mathrm{He}}^3$ and ${\mathrm{He}}^4$ in temperature-pressure space. In addition, by observing the peak in the attenuation of sound, it was possible to measure the $\lambda$ line in ${\mathrm{He}}^4$ and in the 5.0% and 25.0% ${\mathrm{He}}^3$ liquid mixtures. The upper $\lambda$ point for pure ${\mathrm{He}}^4$ is given by $T_s=1.765\mathrm{}\pm 0.003$°K and $P_s=29.90\mathrm{}\pm 0.05$ atm. Comparison is made with existing data wherever possible.