John Beamish

Low-temperature shear modulus changes in solid 4He and connection to supersolidity

Superfluidity—liquid flow without friction—is familiar in helium. The first evidence for ‘supersolidity’, its analogue in quantum solids, came from torsional oscillator measurements involving 4He. At temperatures below 200 mK, the torsional oscillator frequencies increased, suggesting that some of the solid decoupled from the oscillator. This behaviour has been replicated by several groups, but solid 4He does not respond to pressure differences, and persistent currents and other signatures of superflow have not been seen. Both experiments and theory indicate that defects are involved; these should also affect the solid’s mechanical behaviour. Here we report a measurement of the shear modulus of solid 4He at low frequencies and strains. We observe large increases below 200 mK, with the same dependence on measurement amplitude, 3He impurity concentration and annealing as the decoupling seen in the torsional oscillator experiments. We explain this unusual elastic behaviour in terms of a dislocation network that is pinned by 3He at the lowest temperatures but becomes mobile above 100 mK. The frequency changes in the torsional oscillator experiments appear to be related to the motion of these dislocations, perhaps by disrupting a possible supersolid state.

Pressure-driven flow of solid helium.

The recent torsional oscillator results of Kim and Chan show an anomalous mass decoupling, interpreted by the authors as a supersolid phase transition, in solid (4)He. We have used a piezoelectrically driven diaphragm to study the flow of solid helium through an array of capillaries. Our measurements showed no indication of low temperature flow, placing stringent restrictions on supersolid flow in response to a pressure difference. The average flow speed at low temperatures was less than 1.2 x 10(-14) m/s, corresponding to a supersolid velocity at least 7 orders of magnitude smaller than the critical velocities inferred from the torsional oscillator measurements.

Deformation of Silica Aerogel During Fluid Adsorption

Aerogels are very compliant materials\char22{}even small stresses can lead to large deformations. In this paper we present measurements of the linear deformation of high porosity aerogels during adsorption of low surface tension fluids, performed using a linear variable differential transformer. We show that significant deformation can occur under conditions common in studies of helium in aerogel, and that the degree of deformation of the aerogel during capillary condensation scales with the surface tension. This scaling may then be used to suggest limits on safe temperatures for filling and emptying low density aerogels with helium.

Freezing and Pressure-Driven Flow of Solid Helium in Vycor

The recent torsional oscillator results of Kim and Chan suggest a supersolid phase transition in solid 4He confined in Vycor. We have used a capacitive technique to directly monitor density changes for helium confined in Vycor at low temperature and have used a piezoelectrically driven diaphragm to study the pressure-induced flow of solid helium into the Vycor pores. Our measurements showed no indication of a mass redistribution in the Vycor that could mimic supersolid decoupling and put an upper limit of about 0.003 microm/s on any pressure-induced supersolid flow in the pores of Vycor.

Intrinsic and dislocation-induced elastic behavior of solid helium

Recent experiments showed that the shear modulus of solid 4He stiffens in the same temperature range (below 200 mK) where mass decoupling and supersolidity have been inferred from torsional oscillator measurements. The two phenomena are clearly related and crystal defects, particularly dislocations, appear to be involved in both. We have studied the effects of annealing and the effects of applying large stresses on the elastic properties of solid 4He, using both acoustic resonances and direct low-frequency and low-amplitude measurements of the shear modulus. Both annealing and stressing affect the shear modulus, as expected if dislocations are responsible. However, it is the high temperature modulus which is affected; the low temperature behavior is unchanged and appears to reflect the intrinsic modulus of solid helium. We interpret this behavior in terms of dislocations which are pinned by isotopic 3He impurities at low temperatures and so have no effect on the shear modulus. At higher temperatures they become mobile and weaken the solid. Stressing the crystal at low temperatures appears to introduce new defects or additional pinning sites for the dislocation network but these effects can be reversed by heating the crystal above 500 mK. This is in contrast to dislocations produced during crystal growth, which are only annealed at temperatures close to melting.

Critical dislocation speed in helium-4 crystals

Our experiments show that in 4He crystals, the binding of 3He impurities to dislocations does not necessarily imply their pinning. Indeed, in these crystals, there are two different regimes of the motion of dislocations when impurities bind to them. At lowdriving strain ? and frequency ω,where the dislocation speed is less than a critical value (45 µm/s), dislocations and impurities apparently move together. Impurities really pin the dislocations only at higher values of ?ω. The critical speed separating the two regimes is two orders of magnitude smaller than the average speed of free 3He impurities in the bulk crystal lattice.We obtained this result by studying the dissipation of dislocation motion as a function of the frequency and amplitude of a driving strain applied to a crystal at lowtemperature.Our results solve an apparent contradiction between some experiments, which showed a frequency-dependent transition temperature from a soft to a stiff state, and other experiments or models where this temperature was assumed to be independent of frequency. The impurity pinning mechanism for dislocations appears to be more complicated than previously assumed.

Nonlinear elastic response in solid helium: critical velocity or strain?

Torsional oscillator experiments show evidence of mass decoupling in solid 4He. This decoupling is amplitude dependent, suggesting a critical velocity for supersolidity. We observe similar behavior in the elastic shear modulus. By measuring the shear modulus over a wide frequency range, we can distinguish between an amplitude dependence which depends on velocity and one which depends on some other parameter such as displacement. In contrast with the torsional oscillator behavior, the modulus depends on the magnitude of stress, not velocity. We interpret our results in terms of the motion of dislocations which are weakly pinned by 3He impurities but which break away when large stresses are applied.

Helium adsorption in silica aerogel near the liquid-vapor critical point

We have investigated the adsorption and desorption of helium near its liquid-vapor critical point in silica aerogels with porosities between 95% and 98%. We used a capacitive measurement technique which allowed us to probe the helium density inside the aerogel directly, even though the samples were surrounded by bulk helium. The aerogels very low thermal conductivity resulted in long equilibration times so we monitored the pressure and the helium density, both inside the aerogel and in the surrounding bulk, and waited at each point until all had stabilized. Our measurements were made at temperatures far from the critical point, where a well-defined liquid-vapor interface exists, and at temperatures up to the bulk critical point. Hysteresis between adsorption and desorption isotherms persisted to temperatures close to the liquid-vapor critical point and there was no sign of an equilibrium liquid-vapor transition once the hysteresis disappeared. Many features of our isotherms can be described in terms of capillary condensation, although this picture becomes less applicable as the liquid-vapor critical point is approached and it is unclear how it can be applied to aerogels, whose tenuous structure includes a wide range of length scales.

Doping dependence of the critical field Hc2 and the transition temperature in Zn doped YBa2(Cu1−xZnx)3O7−δ

We present data on the doping dependence of Tc in Zn doped YBa2(Cu1−xZnx)3O6.94, for x up to 10.6%. We find re-entrant behaviour in the range between 9.0 and 10.6% Zn. Data on the magneto-resistance of a sample with extremely low Tc (9% Zn, zero field resistive onset near 3.5 K) show linear normal resistance in all fields down to 1.8 K in 17.5 T. A resistively defined critical field H*, related to Hc2, shows divergent behaviour. The temperature dependence of H* is well represented by expressions derived for the Bose condensation of pre-formed pairs.

Freezing and melting of helium in different porous media

We have studied the freezing and melting of4He confined in several porous media with very different structures. These include Vycor glass, which has very small pores with a rather narrow size distribution, a silica aerogel with a much more open geometry and a wider range of pore sizes, and an alumina membrane with larger but non-intersecting pores. We measured the velocity and attenuation of ultrasonic waves, which allowed us to detect the decoupling of any superfluid in the pores as well as the modulus changes associated with freezing and melting. We find that the shift of the melting curve due to confinement is smaller in the aerogel than in Vycor, but the hysteresis between freezing and melting is similar. The effects of confinement are very small for the alumina membrane and hysteresis is only observed at the lowest pressures.