Sound Measurements in Liquid and Solid<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi mathvariant="normal">He</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math>,<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi mathvariant="normal">He</mml:mi></mml:mrow><mml:mrow><mml:mn>4</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math>, and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi mathvariant="normal">He</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math>-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi mathvariant="normal">He</mml:mi></mml:mrow><mml:mrow><mml:mn>4</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math>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\ifmmode^\circ\else\textdegree\fi{}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 ${\mathrm{cm}}^{\ensuremath{-}1}$. 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 ${T}_{l}=1.449\ifmmode\pm\else\textpm\fi{}0.003$\ifmmode^\circ\else\textdegree\fi{}K, ${P}_{l}=26.18\ifmmode\pm\else\textpm\fi{}0.05$ atm; ${T}_{u}=1.778\ifmmode\pm\else\textpm\fi{}0.003$\ifmmode^\circ\else\textdegree\fi{}K, ${P}_{u}=30.28\ifmmode\pm\else\textpm\fi{}0.05$ 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 $\ensuremath{\lambda}$ line in ${\mathrm{He}}^{4}$ and in the 5.0% and 25.0% ${\mathrm{He}}^{3}$ liquid mixtures. The upper $\ensuremath{\lambda}$ point for pure ${\mathrm{He}}^{4}$ is given by ${T}_{s}=1.765\ifmmode\pm\else\textpm\fi{}0.003$\ifmmode^\circ\else\textdegree\fi{}K and ${P}_{s}=29.90\ifmmode\pm\else\textpm\fi{}0.05$ atm. Comparison is made with existing data wherever possible.

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