The thermal conductivity of solid ${\mathrm{He}}^4$ and ${\mathrm{He}}^3$ has been measured over the temperature range 0.5 to 2.0°K at a number of molar volumes. In the hcp phase the thermal conductivities of both isotopes show the usual low-temperature maximum. Below the maximum the conductivity is characteristic of boundary scattering with a $T^3$ dependence and a phonon mean free path comparable to the sample diameter. The conductivity above the maximum varies exponentially with $\frac{1}{T}$ over about three orders of magnitude. This is characteristic of umklapp scattering. In the bcc phase of ${\mathrm{He}}^3$ the anomalous behavior found by Walker and Fairbank is confirmed and the extension of the measurements to lower temperature permits observation of more of the anomalous region. The thermal conductivity in the bcc phase of ${\mathrm{He}}^4$ has also been measured.

• Received 14 September 1965

DOI:https://doi.org/10.1103/PhysRev.142.74