Defects and Glassy Dynamics in Solid 4He: Perspectives and Current Status

We review the anomalous behavior of solid ⁴He at low temperatures with particular attention to the role of structural defects present in solid. The discussion centers around the possible role of two level systems and structural glassy components for inducing the observed anomalies. We propose that the origin of glassy behavior is due to the dynamics of defects like dislocations formed in ⁴He. Within the developed framework of glassy components in a solid, we give a summary of the results and predictions for the effects that cover the mechanical, thermodynamic, viscoelastic, and electro-elastic contributions of the glassy response of solid ⁴He. Our proposed glass model for solid ⁴He has several implications: (1) The anomalous properties of ⁴He can be accounted for by allowing defects to freeze out at lowest temperatures. The dynamics of solid ⁴He is governed by glasslike (glassy) relaxation processes and the distribution of relaxation times varies significantly between different torsional oscillator, shear modulus, and dielectric function experiments. (2) Any defect freeze-out will be accompanied by thermodynamic signatures consistent with entropy contributions from defects. It follows that such entropy contribution is much smaller than the required superfluid fraction, yet it is sufficient to account for excess entropy at lowest temperatures. (3) We predict a Cole-Cole type relation between the real and imaginary part of the response functions for rotational and planar shear that is occurring due to the dynamics of defects. Similar results apply for other response functions. (4) Using the framework of glassy dynamics, we predict low-frequency yet to be measured electro-elastic features in defect rich ⁴He crystals. These predictions allow one to directly test the ideas and very presence of glassy contributions in ⁴He.     

The Glassy Response of Solid 4He to Torsional Oscillations

We calculated the glassy response of solid ⁴He to torsional oscillations assuming a phenomenological glass model. Making only a few assumptions about the distribution of glassy relaxation times in a small subsystem of otherwise rigid solid ⁴He, we can account for the magnitude of the observed period shift and concomitant dissipation peak in several torsion oscillator experiments. The implications of the glass model for solid ⁴He are threefold: (1) The dynamics of solid ⁴He is governed by glassy relaxation processes. (2) The distribution of relaxation times varies significantly between different torsion oscillator experiments. (3) The mechanical response of a torsion oscillator does not require a supersolid component to account for the observed anomaly at low temperatures, though we cannot rule out its existence.     

Elastic Properties of Solid 4He

The shear modulus of solid ⁴He increases below 200 mK, with the same dependence on temperature, amplitude and ³He concentration as the frequency changes recently seen in torsional oscillator (TO) experiments. These have been interpreted as mass decoupling in a supersolid but the shear modulus behavior has a natural explanation in terms of dislocations. This paper summarizes early ultrasonic and elastic experiments which established the basic properties of dislocations in solid helium. It then describes the results of our experiments on the low temperature shear modulus of solid helium. The modulus changes can be explained in terms of dislocations which are mobile above 200 mK but are pinned by ³He impurities at low temperature. The changes we observe when we anneal or stress our crystals confirm that defects are involved. They also make it clear that the shear modulus measured at the lowest temperatures is the intrinsic value—it is the high temperature modulus which is reduced by defects. By measuring the shear modulus at different frequencies, we show that the amplitude dependence depends on stress in the crystal, rather than reflecting a superfluid-like critical velocity. The shear modulus changes shift to lower temperatures as the frequency decreases, showing that they arise from a crossover in a thermally activated relaxation process rather than from a true phase transition. The activation energy for this process is about 0.7 K but a wide distribution of energies is needed to fit the broad crossover. Although the shear modulus behavior can be explained in terms of dislocations, it is clearly related to the TO behavior. However, we made measurements on hcp ³He which show essentially the same modulus stiffening but there is no corresponding TO anomaly. This implies that the TO frequency changes are not simply due to mechanical stiffening of the oscillator—they only occur in the Bose solid. We conclude by pointing out some of the open questions involving the elastic and TO behavior of solid helium.     

Generalized Rotational Susceptibility Studies of Solid 4He

Using a novel SQUID-based torsional oscillator (TO) technique to achieve increased sensitivity and dynamic range, we studied TO’s containing solid ⁴He. Below ～250?mK, the TO resonance frequency f increases and its dissipation D passes through a maximum as first reported by Kim and Chan. To achieve unbiased analysis of such ⁴He rotational dynamics, we implemented a new approach based upon the generalized rotational susceptibility $\chi_{{}^{4}\mathrm{He}}^{ - 1}(\omega,T)$ . Upon cooling, we found that equilibration times within f(T) and D(T) exhibit a complex synchronized ultraslow evolution toward equilibrium indicative of glassy freezing of crystal disorder conformations which strongly influence the rotational dynamics. We explored a more specific $\chi_{{}^{4}\mathrm{He}}^{ -1}(\omega,\tau(T))$ with τ(T) representing a relaxation rate for inertially active microscopic excitations. In such models, the characteristic temperature T ^? at which df/dT and D pass simultaneously through a maximum occurs when the TO angular frequency ω and the relaxation rate are matched: ωτ(T ^?)=1. Then, by introducing the free inertial decay (FID) technique to solid ⁴He TO studies, we carried out a comprehensive map of f(T,V) and D(T,V) where V is the maximum TO rim velocity. These data indicated that the same microscopic excitations controlling the TO motions are generated independently by thermal and mechanical stimulation of the crystal. Moreover, a measure for their relaxation times τ(T,V) diverges smoothly everywhere without exhibiting a critical temperature or velocity, as expected in ωτ=1?models. Finally, following the observations of Day and Beamish, we showed that the combined temperature-velocity dependence of the TO response is indistinguishable from the combined temperature-strain dependence of the ⁴He shear modulus. Together, these observations imply that ultra-slow equilibration of crystal disorder conformations controls the rotational dynamics and, for any given disorder conformation, the anomalous rotational responses of solid ⁴He are associated with generation of the same microscopic excitations as those produced by direct shear strain.     

Pinning Mechanism of the Dislocation Lines in bcc Solid 3He

The strain amplitude dependence of the energy dissipation and the shear modulus at several temperatures are measured in bcc solid ³ He and the results are compared with the model of a pinned dislocation loop of Granato and Lücke. In spite of the pure solid, the strong amplitude dependence of the dissipation is found in bcc solid ³ He by the high-Q torsional oscillator measurements, in contrast with the result of the ultrasonic and the torsional-oscillator measurements in hcp solid ⁴ He. In pure solids, the loop length of the dislocations cannot be limited by impurities. In order to clarify a pinning mechanism, the loop length and the network length are obtained from the experimental result by using the model of Granato and Lücke. Where, the loop length is determined by the pinning centers, and the network length is limited by the dislocation network nodes. It is found that the temperature dependence of the loop length is the same as that of the network length. This result shows that the pinning centers are the network nodes of the dislocation lines in ultra pure bcc solid ³ He.     

Dislocation Mobility and Anomalous Shear Modulus Effect in $$^$$He Crystals

We calculate the dislocation glide mobility in solid \(^4\)He within a model that assumes the existence of a superfluid field associated with dislocation lines. Prompted by the results of this mobility calculation, we study within this model the role that such a superfluid field may play in the motion of the dislocation line when a stress is applied to the crystal. To do this, we relate the damping of dislocation motion, calculated in the presence of the assumed superfluid field, to the shear modulus of the crystal. As the temperature increases, we find that a sharp drop in the shear modulus will occur at the temperature where the superfluid field disappears. We compare the drop in shear modulus of the crystal arising from the temperature dependence of the damping contribution due to the superfluid field, to the experimental observation of the same phenomena in solid \(^4\)He and find quantitative agreement. Our results indicate that such a superfluid field plays an important role in dislocation pinning in a clean solid \(^4\)He at low temperatures and in this regime may provide an alternative source for the unusual elastic phenomena observed in solid \(^4\)He.     

Experimental Study of Classical and Quantum Internal Friction in Solid 4He

We measured the dissipation resulting from internal friction in hcp solid ⁴He at temperatures between 0.8 K and 2.5 K. Solid ⁴He is contained inside an annular metal cell forming a part of a torsional oscillator. An oscillatory motion of the cell walls applies shear stress on the solid ⁴He. The resulting shear strain within the solid ⁴He generates dissipation because of the internal friction. The experimental sensitivity was high enough to detect dissipation caused by internal friction associated with elementary excitations of the solid. At temperatures below 1.6 K, internal friction is associated with diffusion of single point defects responsible for the climb of dislocations. At higher temperatures, the main mechanism of internal friction appears to be associated with phonon exchange between parts of the solid moving relative to each other under the applied shear stress. This particular dissipative mechanism was called “quantum phonon friction” [Popov in Phys. Rev. Lett. 83:1632–1635, 1999]. The physical mechanism associated with this type of friction involves an irreversible transfer of momentum from the phonons to the lattice via an Umklapp process. Our data are in a very good agreement with this model.

     

Tunneling Defect Nanoclusters in hcp 4He Crystals: Alternative to Supersolidity

A?simple model based on the concept of resonant tunneling clusters of lattice defects is used to explain the low temperature anomalies of hcp ⁴He crystals (mass decoupling from a torsional oscillator, shear modulus anomaly, dissipation peaks, heat capacity peak). Mass decoupling is a result of an internal Josephson effect: mass supercurrent inside phase coherent tunneling clusters. Quantitative results are in reasonable agreement with experiments.     

Relaxation modulus—complex modulus interconversion for linear viscoelastic materials

This paper is aimed at exploring the interconversion path between the relaxation modulus E(t) and the corresponding complex modulus E ^?(ω) for linear viscoelastic solid materials. In contrast to other approximate methods, the fast Fourier transform (FFT) algorithm is directly applied on the time-dependent part of the viscoelastic response R(t). Firstly, the method foundations are presented. Then, a theoretical example is performed by means of a generalized Maxwell model, where the influence of sampling conditions and eventual experimental error and data dispersion is analyzed. Finally, an application example using experimental data is carried out to assess the method. As a result, the proposed procedure allows obtaining the complex modulus by means of relaxation tests, and vice versa.     

Interplay of Non-linear Elasticity and Dislocation-Induced Superfluidity in Solid 4He

The mechanism of the roughening induced partial depinning of gliding dislocations from ³He impurities is proposed as an alternative to the standard “boiling off”. We give a strong argument that ³He remains bound to dislocations even at large temperatures due to very long equilibration times. A scenario leading to the similarity between elastic and superfluid responses of solid ⁴He is also discussed. Its main ingredient is a strong suppression of the superfluidity along dislocation cores by dislocation kinks (D. Aleinikava, et. al., arXiv:0812.0983, 2008). These kinks, on one hand, determine the temperature and ³He dependencies of the generalized shear modulus and, on the other, control the superfluid response. Several proposals for theoretical and experimental studies of solid ⁴He are suggested.     

Measurements of the Dielectric Constant of Solid Helium at Low Temperatures

A careful measurement of the dielectric constant of solid ⁴He was made to search for signatures associated with the reported onset of nonclassical rotational inertia and shear modulus stiffening. The samples studied include zero-pressure liquid, solid-liquid mixtures on the melting-curve and solid helium. It was found that the dielectric constant of solid ⁴He decreases smoothly with temperature below 300?mK, showing no measurable anomalies down to 50?mK. The new measurements do not show the anomalous upturn effect that was reported in our previous measurements.     

A Novel Design of a Low Temperature Preamplifier for Pulsed NMR Experiments of Dilute 3He in Solid 4He

Recent experimental studies of solid ⁴He indicate a strong correlation between the crystal defects and the onset of a possible supersolid state. We use pulsed NMR techniques to explore the quantum dynamics of the ³He impurities in the solid ⁴He in order to examine certain theoretical models that describe how the disordered states are related to supersolidity. Because of the very small signal-to-noise ratio at low ³He concentration and the long spin-lattice relaxation time (T ₁), it is essential to significantly enhance the NMR sensitivity to be able to carry out the experiments. Here we present the design of a novel low temperature preamplifier which is built with a low noise pseudomorphic HEMT transistor that is embedded into a cross-coil NMR probe. With a low power dissipation of about 0.7 mW, the preamplifier is capable of providing a power gain of 30 dB. By deploying the preamplifier near the NMR coil below 4 K, the noise temperature of the receiver is reduced to approximately 1 K. This preamplifier design also has the potential to be adapted into a low temperature amplifier with both input and output impedance at 50 Ω or a low temperature oscillator.     

Simultaneous Measurement of Torsional Oscillator and?NMR in Solid 4He with 10?ppm of 3He

We have performed the simultaneous measurement of torsional oscillator and NMR in solid ⁴He with 10 ppm of ³He at 3.6 MPa. In this solid, NCRI response appears below about 400 mK. NMR measurement shows that there is the same kind of phase-separated ³He cluster which is found in our previous measurement in solid ⁴He with over a hundred ppm of ³He. When we warm the solid above the phase separation temperature, the cluster disappears gradually. Below and above the phase separation temperature, the distribution of ³He atoms changes significantly with long time constant, which is as long as a day. However, even in such a long time span, we do not observe any systematic changes in the torsional oscillator response. This result suggests that the phase separation and related changes of the distribution of ³He is not directly related to the impurity effect of the NCRI response.     

Low Frequency Elastic Measurements on Solid ^{4}He in Vycor Using a Torsional Oscillator

Torsional oscillator (TO) experiments involving solid \(^{4}\) He confined in the nanoscale pores of Vycor glass showed anomalous frequency changes at temperatures below 200 mK. These were initially attributed to decoupling of some of the helium’s mass from the oscillator, the expected signature of a supersolid. However, these and similar anomalous effects seen with bulk \(^{4}\) He now appear to be artifacts arising from large shear modulus changes when mobile dislocations are pinned by \(^{3}\) He impurities. We have used a TO technique to directly measure the shear modulus of the solid \(^{4}\) He/Vycor system at a frequency (1.2 kHz) comparable to that used in previous TO experiments. The shear modulus increases gradually as the TO is cooled from 1 K to 20 mK. We attribute the gradual modulus change to the freezing out of thermally activated relaxation processes in the solid helium. The absence of rapid changes below 200 mK is expected since mobile dislocations could not exist in pores as small as those of Vycor. Our results support the interpretation of a recent TO experiment that showed no anomaly when elastic effects in bulk helium were eliminated by ensuring that there were no gaps around the Vycor sample.     

Plastic Properties of Solid 4He Probed by a Moving Wire: Viscoelastic and Stochastic Behavior Under High Stress

We present measurements of a thin wire moving through solid ⁴He. Measurements were made over a wide temperature range at pressures close to the melting curve. We describe the new experimental technique and present preliminary measurements at relatively high driving forces (stresses) and velocities (strain rates). The wire moves by plastic deformation of the surrounding solid facilitated by quantum tunneling of vacancies and the motion of defects. In the bcc phase we observe very pronounced viscoelastic effects with relaxation times spanning several orders of magnitude. In the hcp phase we observe stochastic step-like motion of the wire. During the step, the wire can move at extremely high velocities. On cooling, the wire ceases to move at a temperature of around 1 K. We are unable to detect any motion at lower temperatures, down to below 10 mK.     

Glass strengthening by polymeric coatings: combined effect of mechanical properties and confinement

We consider the impact of the mechanical behaviour of polymeric coatings on glass strengthening. We have performed rupture stress measurements and compared the strengthening measured in the rubbery state and the glassy state. We evidence a moderate decrease of the strengthening when the temperature exceeds the glass transition temperature of the coating. Based on the predictions of crack bridging models, we show that the limited difference of strengthening between glassy and rubbery states can be understood if confinement of the polymer inside the crack is taken into account. Similarly, our results suggest that confinement severely limits the shear deformation of polymeric coatings and suppresses viscoelastic dissipation.