Thermal Conductivity of Hexagonal Close-Packed Solid Helium Four at High Densities

Thermal conductivity measurements between 1.1° K and 7° K have been made on solid helium samples grown under constant pressures from 185 atm to 1050 atm. At high temperatures the phonon mean free path $\overline{l}$ for the highest conductivity samples at six different densities is in good agreement with the expression, $\overline{l}=A\exp \left(\frac{{\theta }_D}{\mathrm{bT}}\right)$, where ${\theta }_D$ is the Debye temperature at $T=0\mathrm{}$° K, $A=2.5\mathrm{}\times {10}^{-8\mathrm{}}$ cm, $b=2.13\mathrm{}$. Several samples grown from gas repurified by an adsorption trap exhibited mean free paths in agreement with this expression over almost four orders of magnitude. Slightly impure samples showed a considerable attenuation in the peak thermal conductivity at pressures above 320 atm. There was some evidence for anisotropy of the thermal conductivity in the umklapp region and for Poiseuille flow in the low-temperature region, but both these effects were considerably smaller than reported by other investigators for specimens grown at lower pressures.