Simultaneous investigation of shear modulus and torsional resonance of solidHe4

Abstract

We investigate the origin of a resonant period drop of a torsional oscillator (TO) containing solid 4 He by inspecting its relation to a change in elastic modulus. To understand this relationship directly, we measure both phenomena simultaneously using a TO with a pair of concentric piezoelectric transducers inserted in its annulus. Although the temperature, 3 He concentration, and frequency dependence are essentially the same, a marked discrepancy in the drive amplitude dependence is observed. We find that this discrepancy originates from the anisotropic response of polycrystalline solid 4 He connected with low-angle grain boundaries by studying the shear modulus parallel to and perpendicular to the driving direction.The change in the shear modulus µ and the dissipation Q −1 of solid 4 He at low temperature [1-9] have been understood thoroughly by the Granato-Lucke (GL) model [10][11][12]. According to this model, in a dislocation network, dislocations glides under applied stress, which leads to an additional strain field. This strain decreases the µ of a solid from its intrinsic value. However, the slip motion can be effectively damped by binding of dislocation segments with impurities at low temperatures. The pinning of dislocations is regulated by the finite binding energy, E b , between dislocations and impurities in a solid, such that the pinning can be promoted only at sufficiently low temperatures. These weakly bound impurities on the dislocations are detached as a result of increasing temperature and/or external stress, which can be described by the Debye relaxation process and characterized by a relaxation time τ and an activation energy E b [4,8,9]. Solid 4 He is a golden testbed for the GL model because the only impurities in solid 4 He are an extremely low concentration of 3 He atoms. The properties of dislocation in solid 4 He, such as the average network length, dislocation density, and length distribution have been extensively studied by .Another interesting observation of solid 4 He is that the resonant period of a torsional oscillator (TO) containing solid 4 He decreases below 0.2 K [13][14][15][16][17][18][19][20][21][22][23][24][25]. This was initially interpreted as a result of the reduction of the rotational inertia of solid 4 He, and considered as the appearance of a putative supersolid phase. Nevertheless, both the µ and TO response exhibited fundamentally identical dependences on the temperature, driving amplitude, frequency, and amount of 3 He impurities [1,25,26]. To investigate the underlying relationships between them, Kim et al.[25] measured the shear modulus change (∆µ) and the resonant period drop (∆prd) simultaneously by inserting a pair of flat piezoelectric transducers (PZT) into the center of a TO. Even though a similar temperature dependence was observed, the drive amplitude responses were different. When a large AC voltage was applied to a driving transducer, the ∆µ of solid 4 He at the center channel was fully suppressed, but the shift in the resonance period of the TO was ...

Simulation and understanding of atomic and molecular quantum crystals

“…Meanwhile, few years later Day and Beamish (2007) measured the shear modulus in solid helium and found a striking resemblance with the temperature dependence of the oscillation period reported by Kim and Chan: the shear modulus increased as the temperature was lowered below ∼ 0.1 K. Day and Beamish attributed that increase in stiffness to the temperature dependence of the mobility of dislocations in the solid, which could be pinned by static 3 He impurities. Day and Beamish's findings motivated a series of subsequent theoretical and experimental studies which have demonstrated that a change in the moment of inertia of the experimental torsional cell can be correlated to a change in the structure of the solid inside of it (Reppy, 2010;Maris, 2012;Shin et al, 2016). In 2012, Kim and Chan completely redesigned their torsional oscillator setup making it stiffer, and the original mass-decoupling signal disappeared to within the experimental errors (see also, Kim and Chan, 2014).…”