Measurements of Torsional Oscillations and Thermal Conductivity in Solid 4He

Polycrystalline samples of hcp 4 He of molar volume 19.5 cm 3 with small amount of 3 He impurities were grown in an annular container by the blocked-capillary method. Three concentrations of 3 He, x 3 , were studied: isotopically purified 4 He with the estimated x 3 ≤10 −10 , ‘well-grade’ helium with x 3 ∼3×10 −7 and a specially prepared mixture with x 3 =2.5×10 −6 . The torsional oscillator response and thermal conductivity were investigated before and after annealing. The temperature and width of the torsional anomaly increase with increasing x 3 . Annealing resulted in an increased phonon mean free path but often in little change in the torsional oscillator response. While the magnitude of the torsional anomaly and phonon mean free path can be very different in different samples, no correlation was found between them; this implies that these two properties are controlled by different types of crystal defects. It seems plausible that the mean free path of thermal phonos at ∼200 mK is controlled by vibrating dislocations while the magnitude of the frequency shift of torsional oscillations is governed by static defects such as pinned dislocations and grain boundaries.