Measurements of Torsional Oscillations and Thermal Conductivity in Solid 4He

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

doi:10.1007/s10909-012-0665-9

“…We argue that, in our experimental set-up, the TO and thermal conductivity probe solid helium at different locations. The absence of correlations between the TO frequency shifts r f Δ and phonon mean free path , that was reported previously [18,19] (see Fig. 6) might thus not be too surprising.…”

Section: Discussionsupporting

confidence: 66%

“…In this context, the mean free path of thermal phonons becomes the measure of the presence of dislocations as seen by high-frequency (10 9 -10 10 Hz) oscillations of solid helium. Experimental details and some results were published in [18,19].…”

Section: Solid Heliummentioning

confidence: 99%

Thermal conductivity and torsional oscillations of solid 4He

Brazhnikov

¹

,

Zmeev

²

,

Golov

³

2012

Low Temperature Physics

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Polycrystalline samples of hcp 4 He of molar volume V m = 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 , commercial 'well-grade' helium with x 3 ~ 3⋅10 -7 and a mixture with x 3 = 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 x 3 . The phonon mean free path increases with increasing x 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. PACS: 67.80.bd Superfluidity in solid 4 He, supersolid 4 He; 65.40.-b Thermal properties of crystalline solids.

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“…In this version of the paper we report the values of velocity inferred from (13). However, direct optical measurements of the displacement of the oscillator at room temperature suggest that Eq.…”

Section: Amplitude Sweepsmentioning

confidence: 99%

“…This same technique was also used in the detection of an anomalous response in solid helium by E. Kim and M. Chan at Pen State university [10]. Others soon followed with other designs and experiments [11][12][13][14][15][16][17]. Further studies on quantum turbulence and the study of Kelvin wave requires that we lower the frequency region of operation and increase the velocity range of the oscillator.…”

Section: Introductionmentioning

confidence: 99%

A low-frequency, high-amplitude, torsional oscillator for turbulence studies in quantum fluids

Gu'enault¹,

McClintock²,

Poole³

et al. 2022

Preprint

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We describe a new type of torsional oscillator, suitable for studies of quantum fluids at frequencies of ∼ 100 Hz, but capable of reaching high velocities of up to several cm s −1 . This requires the oscillator amplitude to exceed 100 µm, which is much too large for a conventional capacitor-driven device. We describe the new geometry for the oscillator, discuss its design, and report our initial tests of its performance.

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“…The response of hcp 4 He , with various 3 He concentrations, to an AC shear stress has been investigated previously by a range of techniques at different frequencies: shear in a torsional oscillator (TO) (200 Hz-2 kHz) [39], transverse sound (1 Hz-100 kHz) [2,16,[40][41][42][43][44][45][46] and ultrasound [47][48][49][50] , scattering of thermal phonons (8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19)(20)(21)(22)(23)(24) [4,[51][52][53][54][55][56]. Most can be explained in terms of interaction with vibrating dislocations [39,49].…”

Section: Introductionmentioning

confidence: 99%

Characterization of Dislocations in hcp $$^4\hbox {He}$$ by Torsional Oscillator and Thermal Conductivity Measurements

Brazhnikov

¹

,

Mukharsky

²

,

Golov

³

2022

J Low Temp Phys

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We apply two complementary techniques for the characterization of mobile dislocations in samples of hcp $$^4\hbox {He}$$ 4 He with the concentration of $$^3\hbox {He}$$ 3 He $$\sim 3\times 10^{-7}$$ ∼ 3 × 10 - 7 , grown by the blocked capillary method at molar volume 19.5 $$\hbox {cm}^3\,\hbox {mol}^{-1}$$ cm 3 mol - 1 , before and after annealing at temperatures 1.8–2.0 K, and also after work hardening by high-amplitude twisting at 0.03 K and successive recovery at 0.5–1.0 K. The first technique relies on the elastic response of solid helium to oscillatory twisting at frequencies 161 Hz and 931 Hz at temperatures below 1 K, where this response is affected by the presence of mobile dislocations with variable amounts of trapped $$^3\hbox {He}$$ 3 He impurities. Monitoring the non-equilibrium amplitude dependence after moderate forcing allows to compute the length distribution n(L) of mobile dislocations (Iwasa in J Low Temp Phys 171:30, 2013; Fefferman et al. in Phys Rev B 89:014105, 2014). We also test methods of determining n(L) from the equilibrium temperature dependence of either real or imaginary part of the shear modulus at small strain amplitudes, based on the values of the damping force measured by Fefferman et al. [2]. The second technique utilizes measurements of thermal conductivity at temperatures below 0.4 K, i.e., of the dislocation-limited mean free path of thermal transverse phonons (Greenberg and Armstrong in Phys Rev B 20:1049, 1979; Armstrong et al. in Phys Rev B 20:1061, 1979). During a prolonged AC-twisting at a high amplitude of strain exceeding the yield stress, long dislocations disappear being replaced by many short ones which remain mobile. However, upon stopping this twisting, the majority of dislocations become immobilized until the sample is warmed up above 0.5 K to speed-up the recovery of dislocations to their mobile state (Day et al. in Phys Rev B 79:214524, 2009; Beamish and Franck in Phys Rev B 26:6104, 1982). This is different from the immobilization of dislocations by trapped $$^3\hbox {He}$$ 3 He impurities, routinely observed at smaller strain amplitudes, which is characterized by much shorter relaxation times to effectively un-trap $$^3\hbox {He}$$ 3 He atoms and make dislocations mobile again. We investigated the dynamics of the recovery of cold-worked samples, during which short segments quickly disappear, while the longest one appear after longer annealing times; the activation energy was estimated to be 22 K—pointing at the thermal vacancy-assisted process. A complementary characterization by the scattering rate of thermal transverse phonons off crystalline defects rules out non-interacting mobile dislocations as the dominant scatterer. The main conclusion is that while many properties of the sample are consistent with the theory of Granato and Lücke of isolated gliding dislocations (Granato and Lücke in J Appl Phys 27:583, 1956), several observations at low temperatures ($$^3\hbox {He}$$ 3 He -independent immobilization of dislocations after stopping high-amplitude twisting, sporadic avalanche-like relaxation of strain, flat temperature dependence of the phonon scattering rate) point at the presence of interacting dislocations, probably arranged into dislocation walls.

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Measurements of Torsional Oscillations and Thermal Conductivity in Solid 4He

Cited by 3 publications

References 20 publications

Thermal conductivity and torsional oscillations of solid 4He

Thermal conductivity and torsional oscillations of solid 4He

A low-frequency, high-amplitude, torsional oscillator for turbulence studies in quantum fluids

Characterization of Dislocations in hcp $$^4\hbox {He}$$ by Torsional Oscillator and Thermal Conductivity Measurements

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