Abstract
The complex shear acoustic impedance of liquid He II has been measured at frequenciesf(=ω/2π) of 20.5, 34.1, and 47.8 MHz from 30 mK to the λ-point Tλ (2.176 K). The impedanceZ was found from the temperature dependence of the quality factor and the resonant frequency of a thickness shear mode quartz crystal resonator immersed in the liquid. The relationship for a hydrodynamic viscous liquidZ(T)=(1−i)(πfηρ n )1/2 was used to measure the temperature dependence of the viscosity η(T) using tabulated values of the normal fluid density ρ n (T). Deviations from hydrodynamic behavior occurred when the viscous penetration depth was less than the superfluid healing length, the phonon mean free path, and the roton mean free path. Near the λ-point,Z(T)/Z(Tλ) was frequency dependent and a value for the superfluid healing lengtha=(0.10±0.01)ε−2/3 nm was found, where ε=(Tλ−T)/Tλ. The effects of van der Waals forces near the crystal surface were also observed and a layer model was used to interpret the measurements. Below 1.8 K only rotons contribute significantly toZ and we determined the roton relaxation time as τ r =8.5×10−14 T −1/3 exp (8.65/T) sec. Below 1.2 K, ωτ r >1 and we investigated the breakdown of hydrodynamics in this region. ForT<0.6 K the resonant frequency of the crystals decreased by Δf/f=2×10−7, but the origin of this effect is not yet known.
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Financial support provided by the SERC, Bedford College, and the Central Research Fund, University of London.
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Lea, M.J., Fozooni, P. & Retz, P.W. The transverse acoustic impedance of He II. J Low Temp Phys 54, 303–331 (1984). https://doi.org/10.1007/BF00683280
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DOI: https://doi.org/10.1007/BF00683280