Thermal conductivity and torsional oscillations of solid ⁴He

Abstract

Polycrystalline samples of hcp ⁴He of molar volume Vm = 19.5 cm³ with small amount of ³He impurities were grown in an annular container by the blocked-capillary method. Three concentrations of ³He, x₃, were studied: isotopically purified ⁴He with the estimated x₃ < 10⁻¹⁰, commercial ‘well-grade’ helium with x₃ ~ 3⋅10⁻⁷ and a mixture with x₃ = 2.5⋅10⁻⁶. 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 x₃. The phonon mean free path increases with increasing x3. 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.