Thermal conductivity and torsional oscillations of solid 4He

Brazhnikov, M. Yu.; Zmeev, D. E.; Golov, A. I.

Polycrystalline samples of hcp <^>4He of molar volume Vm = 19,5 cm<^>3 with small amount of <^>3He impurities were grown in an annular container by the blocked-capillary method. Three concentrations of <^>3He, <$E x sub 3>, were studied: isotopically purified <^>4He with the estimated <$E x sub 3~<<~10 sup -10>, commercial "well-grade" helium with <$E x sub 3> ~ <$E 3~cdot~10 sup -7> and a mixture with <$E x sub 3~=~2,5~cdot~10 sup -6>. Torsional oscillations at two frequencies, 132,5 and 853,6 Hz, and thermal conductivity were investigated before and after annealing. The solid helium under investigation was located not only in the annular container but also in the axial fill line inside two torsion rods and dummy bob of the doublefrequency torsional oscillator. The analysis of the frequency shifts upon loading with helium and changing temperatures of different parts of the oscillator suggests that the three techniques probe the properties of solid helium in three different locations: the two different torsion modes respond to the changes of the shear modulus of solid helium in either of the two torsion rods while the thermal conductivity probes the phonon mean free path in solid helium inside the annular container. The temperature and width of the torsional anomaly increase with increasing frequency and <$E x sub 3>. The phonon mean free path increases with increasing <$E times 3>. Annealing typically 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.


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