Thermal Conductivity of Oriented Single Crystals of Hexagonal Close-Packed Helium 4

Thermal conductivity measurements have been made on hcp single crystals of helium 4 between 0.36^∘{}K and 1.6^∘{}K. Data on crystals grown at 53.4, 85, and 125.8 atm exhibit a strong orientation dependence in the umklapp region, and Poiseuille flow at temperatures below the thermal conductivity maximum. In the umklapp region, the data are described by two thermal conductivities, K_⊥=A_⊥exp(ΘD2.58T) and K_∥=A_∥exp(ΘD4.62T), the components of the thermal conductivity tensor perpendicular and parallel to the c axis. At 85 atm, A_⊥=1.12×10^-5 W/cm ^∘{} K and A_∥=2.31×10^-4 W/cm ^∘{} K. The umklapp data permit one to determine the orientation of the single crystals. The thermal conductivity in the Poiseuille region is proportional to d²T⁶, where d is the sample diameter. The normal-process relaxation time determined from these data, τN=(2.1±0.4)(ΘDT)³×10^-12 sec, is in good agreement with the results of second-sound experiments.