Elastic Properties of Solid 4He

Abstract

The shear modulus of solid 4 He increases below 200 mK, with the same dependence on temperature, amplitude and 3 He 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 3 He 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 3 He 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.

The Plastic Flow of Solid 4He Through a Porous Membrane

“…The anomalous behavior of solid 4 He in the temperature region below ~300 mK is still open to arguments and therefore attracts huge interest of both experimenters and theorists (e.g., see surveys [1,2]). One of the possible scenarios considers a change in the plasticity of solid helium.…”

Elastic constants of incommensurate solid4He from diffusion Monte Carlo simulations

“…Concerning possible temperature effects, it is well known that the contribution of phonon excitations to the thermal energy of solids reduces the speeds of sound by an amount that is proportional to T 4 , thus implying a ∝T 8 dependence in the elastic constants. 33 Our zero-temperature conclusions on C 44 , therefore, can be fairly generalized to the regime of ultralow temperatures (that is, few mK). In fact, the ground-state results reported in this study are in very good agreement with those obtained by Ardila et al for hcp 4 He at T = 1 K using the path-integral Monte Carlo method, 34 and by Pessoa et al at zero temperature using the variational Monte Carlo approach.…”

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

“…Equation (9) implies that the period shift exceeding 5 nsec observed during freezing and melting of the helium in the Vycor in [11] corresponds to an apparent shear modulus change of 770 MPa. The contribution of the helium to the shear modulus of the Vycor+helium system should be of order the stiffness of the helium [1], but 770 MPa is almost ten times greater than c 33 , the largest component of helium's stiffness tensor [27], at the 65 bar maximum pressure of the measurement in [11]. It is more likely that the period increases in [11] mainly result from bulging of the Vycor portion of the TO and consequent increases in the moment of inertia due to increases in helium pressure.…”