Mechanical behavior of solid helium: Elasticity, plasticity, and defects

Beamish, John; Balibar, S.

doi:10.1103/revmodphys.92.045002

“…The energy of the vortex in a SSP is a periodic function of position and this plays a role similar to the Peierls potential acting on a dislocation in a crystalline solid. Kinks are indeed the low-energy excitations of a dislocation in solid 4 He [51]. The study of the excitations of a vortex in a supersolid is an interesting problem, but it is quite outside the scope of the present paper.…”

Section: Single Vortex In Dipolar Bosonsmentioning

confidence: 90%

Vortex properties in the extended supersolid phase of dipolar Bose-Einstein condensates

Ancilotto

¹

,

Barranco

²

,

Pí

³

et al. 2021

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We study the properties of singly quantized linear vortices in the supersolid phase of a dipolar Bose-Einstein condensate at zero-temperature modeling 164 Dy atoms. The system is extended in the x-y plane and confined by a harmonic trap in the polarization direction z. Our study is based on a generalized Gross-Pitaevskii equation. We characterize the ground state of the system in terms of spatial order and superfluid fraction and compare the properties of a single vortex and of a vortex dipole in the superfluid phase (SFP) and in the supersolid phase (SSP). At variance with a vortex in the SFP, which is free to move in the superfluid, a vortex in the SSP is localized at the interstitial sites and does not move freely. We have computed the energy barrier for motion from an equilibrium site to another. The fact that the vortex is submitted to a periodic potential has a dramatic effect on the dynamics of a vortex dipole made of two counter-rotating parallel vortices; instead of rigidly translating as in the SFP, the vortex and antivortex approach each other by a series of jumps from one site to another until they annihilate in a very short time and their energy is transferred to bulk excitations.

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“…Solid helium provides a special opportunity to gain further insight into the structure and dynamics of dislocation networks [10,11]. On the one hand, it is just another solid that can be made extremely perfect and pure because only isotopic impurities remain dissolved below its solidification temperature of order 2 K, and their concentration can be controlled in a wide range.…”

Section: Introductionmentioning

confidence: 99%

“…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

2

0

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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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“…Such a network would be unstable due to the superclimb effect, but other (non-superfluid) dislocations provide a stabilizing framework 20 -due to the binding between the superfluid and non-superfluid edge dislocations 21 . At this point it is important to emphasize that the hcp solid 4 He displays also an unusual mechanical response characterized by so called giant plasticity 22 as well as strongly non-linear behavior 23,24 of basal dislocations.…”

Section: Introductionmentioning

confidence: 99%

Thermal and structural properties of topological defects in solid Helium-4: Strain induced martensitic transformation from hcp to fc orthorhombic lattice

Kuklov¹,

Polturak²,

Prokof’ev³

et al. 2021

Preprint

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Several experimental studies have reported thermally activated behavior of the mechanical response of solid 4 He which does not fit into the model of thermally activated Frenkel pairs in an ideal crystal. The purpose of the present work is to investigate how structural topological defects modify the response. Using quantum Monte Carlo Worm Algorithm, we study temperature dependence of fluctuations of the total number of particles in samples of hcp solid 4 He containing several types of dislocations. Such fluctuations can be described by the thermal activation law with the activation energy dependent strongly on the type of the dislocation and the crystal density. The extracted values cover a range from about 1K to 20K. It is also found that annihilation of a jog-antijog pair can produce a local region of the solid characterized by the orthorhombic symmetry. This serendipitous observation suggests that hcp solid 4 He can undergo a displacive phase transition into the orthorhombic crystal under uniaxial stress of about 10-15%.

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Mechanical behavior of solid helium: Elasticity, plasticity, and defects

Cited by 26 publications

References 237 publications

Vortex properties in the extended supersolid phase of dipolar Bose-Einstein condensates

Vortex properties in the extended supersolid phase of dipolar Bose-Einstein condensates

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

Thermal and structural properties of topological defects in solid Helium-4: Strain induced martensitic transformation from hcp to fc orthorhombic lattice

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