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

Abstract

AbstractWe 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.