An experiment on temperature pulse propagation in a bcc crystal of $^{3}\mathrm{He}$ grown at 959 atm shows the existence of second sound in the solid below about 058\ifmmode^\circ\else\textdegree\fi{}K In the temperature range $042\ifmmode^\circ\else\textdegree\fi{}\mathrm{K}lTl058\ifmmode^\circ\else\textdegree\fi{}\mathrm{K}$, reflections of the received pulses were observed In the range $058\ifmmode^\circ\else\textdegree\fi{}\mathrm{K}lTl12\ifmmode^\circ\else\textdegree\fi{}\mathrm{K}$, the temperature pulses were observed to propagate diffusively

Second Sound in Solid Helium

Recent experimental studies of solid helium are reviewed with special attention given to specific heat, isochoric pressure, neutron scattering, sound velocity, and magnetic susceptibility measurements. The relationships among the properties are stressed. Low temperature properties of $^{3}\mathrm{He}$, including exchange, nuclear spin ordering, the melting curve, and Pomeranchuk colling, are discussed. Phase separation in solid $^{3}\mathrm{He}$-$^{4}\mathrm{He}$ mixtures is reviewed.

Thermodynamic, Elastic, and Magnetic Properties of Solid Helium

Inelastic neutron scattering experiments were carried out on large single crystals of the quantum solid bcc $^{4}\mathrm{He}$. The crystals were oriented in the [011] zone and had volumes larger than 5 ${\mathrm{cm}}^{3}$. Both transverse and longitudinal excitations were studied with propagation vectors along the [100], [111], and [011] principal symmetry directions. Dispersion relations along these three symmetry directions are presented and discussed within the context of the results of recent theories for this highly anharmonic solid. The data, which present clear evidence for strong phonon relaxation, are also compared with theoretical linewidth estimates. The elastic constants calculated from these data are $\frac{{c}_{11}}{\ensuremath{\rho}}=1.77\ifmmode\pm\else\textpm\fi{}0.32$, $\frac{{c}_{12}}{\ensuremath{\rho}}=1.58\ifmmode\pm\else\textpm\fi{}0.35$, and $\frac{{c}_{44}}{\ensuremath{\rho}}=1.07\ifmmode\pm\else\textpm\fi{}0.10$ in units of ${10}^{5}$ ${\mathrm{m}}^{2}$/${\mathrm{sec}}^{2}$, in good agreement with the results obtained from ultrasonic and thermodynamic measurements. When the amplitude of the scattering vector $|\stackrel{\ensuremath{\rightarrow}}{\mathrm{Q}}|$ approaches $1.6{a}^{*}=2.44$ ${\mathrm{\AA{}}}^{\ensuremath{-}1}$, where ${a}^{*}$ is the reciprocal-lattice vector of length 1.525 ${\mathrm{\AA{}}}^{\ensuremath{-}1}$, some extra intensity is observed near an energy of 1.4 meV. Evidence that this intensity is indeed real and anomalous, some four times as much as expected from single-phonon scattering, is presented. The physical origin of this extra scattering is not presently known.

Inelastic Neutron Scattering from bcc He 4

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.

Sound Measurements in Liquid and Solid He 3 , He 4 , and He 3 - He 4 Mixtures

In single crystals with the large anisotropy of bcc $^{3}\mathrm{He}$ the wave vector of a sound wave deviates as much as 60\ifmmode^\circ\else\textdegree\fi{} from the direction of energy flow. This effect permits one to find single-crystal elastic constants from previous measurements of the transverse velocity, the Debye temperature and the compressibility: ${c}_{11}=2.35$, ${c}_{12}=1.97$, ${c}_{44}=1.085$ (in ${10}^{8}$ dyn/${\mathrm{cm}}^{2}$) at a molar volume of 24 ${\mathrm{cm}}^{3}$/mole. The constants agree well with measured longitudinal sound velocities and with theoretical constants of Horner, less well with constants obtained from the single-particle theories of Nosanow et al.

Elastic Constants of bcc 3 He from Measurements of Sound Velocity, Debye Temperature, and Compressibility

SHEAR WAVES IN SOLID He$sup 4$

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SHEAR WAVES IN SOLID He$sup 4$