Thermal-conductivity measurements in liquidHe4below 0.7 K

High-precision steady-state heat-flow measurements were made in pure liquid ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ under pressures of up to 25 bar. The data cover the temperature range between 0.1 and 0.7 K and were obtained using sample containment tubes which ranged in diameter from 0.14 to 1.4 cm. The data yield information about $\Lambda$, the phonon mean free path for large-angle scattering. At the higher pressures phonon-roton scattering plays a significant role in limiting $\Lambda$. However, at low pressures and temperatures the $\Lambda$ results show evidence that three-phonon processes become dominant. This permits inferences to be made concerning the phonon dispersion relation. In the temperature regime for which $\Lambda$ is comparable with the tube diameter, a phenomenon was observed which is analogous to the Knudsen minimum observed in ordinary-gas flow measurements. These data are compared with the recent calculations of Benin and Maris.