When submitted to large stresses at high temperature, usual crystals may irreversibly deform. This phenomenon is known as plasticity and it is due to the motion of crystal defects such as dislocations. We have discovered that, in the absence of impurities and in the zero temperature limit, helium 4 crystals present a giant plasticity that is anisotropic and reversible. Direct measurements on oriented single crystals show that their resistance to shear nearly vanishes in one particular direction because dislocations glide freely parallel to the basal planes of the hexagonal structure. This plasticity disappears as soon as traces of helium 3 impurities bind to the dislocations or if their motion is damped by collisions with thermal phonons.

We have measured the elasticity of high quality ultrapure ⁴He single crystals in the low temperature region where supersolidity is supposed to occur. At 20 mK, our results are consistent with elastic coefficients previously measured at 1.2 K. As the temperature increases from 20 to 100 mK, a large softening occurs because dislocations unpin from ³He impurities. In the absence of ³He impurities, dislocations are free to move down to 20 mK; the crystals are soft. The large magnitude of this anomalous softening shows that dislocations form a mobile mosaic structure. It illustrates the remarkable quantum plasticity of ⁴He crystals.

The mechanical behavior of crystals is dominated by dislocation networks, their structure and their interactions with impurities or thermal phonons. However, in classical crystals, networks are usually random with impurities often forming non-equilibrium clusters when their motion freezes at low temperature. Helium provides unique advantages for the study of dislocations: crystals are free of all but isotopic impurities, the concentration of these can be reduced to the ppb level, and the impurities are mobile at all temperatures and therefore remain in equilibrium with the dislocations. We have achieved a comprehensive study of the mechanical response of 4 He crystals to a driving strain as a function of temperature, frequency and strain amplitude. The quality of our fits to the complete set of data strongly supports our assumption of string-like vibrating dislocations. It leads to a precise determination of the distribution of dislocation network lengths and to detailed information about the interaction between dislocations and both thermal phonons and 3 He impurities. The width of the dissipation peak associated with impurity binding is larger than predicted by a simple Debye model, and much of this broadening is due to the distribution of network lengths.

A number of recent experiments have used torsional oscillators to study the behavior of solid helium. The oscillator frequencies increased at temperatures below 200 mK, an effect attributed to decoupling of a fraction of the helium mass-the signature of a "supersolid" phase. However, helium's shear modulus also increases below 200 mK and the frequency of a torsional oscillator depends on its elastic properties, as well as on its inertia. In many experiments helium is introduced via a hole in the torsion rod, where its shear modulus contributes to the stiffness of the rod. In oscillators with relatively large torsion rod holes, changes in the helium's shear modulus could produce the entire low temperature frequency shifts that have been interpreted as mass decoupling. For these oscillators we also find that the known elastic properties of helium in the torsion rod can explain the observed TO amplitude dependence (which has been interpreted as a critical velocity) and the TO dissipation peak. However, in other oscillators these elastic effects are small and the observed frequency changes must have a different origin.In its simplest form, a torsional oscillator (TO) consists of a rigid "head" (with moment of inertia I ) attached to a stationary base by a torsion rod (with torsional stiffness K). Its resonant frequency is given by f = (1/2π ) √ K/I and can be measured very precisely for a high Q oscillator. If the torsion rod's stiffness is constant, this provides a direct and sensitive technique to measure the moment of inertia. Such oscillators have been widely used to study superfluidity in liquid 4 He and 3 He, by confining the helium in narrow channels or small pores in the TO head. 1-3 In appropriate geometries, the zero viscosity superfluid fraction decouples from the walls of the cavity, reducing the effective moment of inertia. The increase in the TO frequency is then a direct measurement of the superfluid density ρ s .The TO technique has recently been used to study the behavior of solid 4 He. [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18] At temperatures below 200 mK, the TO frequency increases and, in analogy to measurements with liquid helium, this has usually been interpreted in terms of mass decoupling-the "nonclassical rotational inertia" (NCRI) which would characterize a supersolid. However, the behavior of a torsional oscillator can be sensitive to a number of effects in addition to the solid helium's inertia, for example, the pressure dependence of the TO background, possible slip at the walls, dissipation in the helium and, most importantly, the solid helium's shear rigidity. [19][20][21] Any increase in the shear modulus of the helium will stiffen the oscillator and raise its frequency, an effect which could be misinterpreted as mass decoupling. Recent low frequency measurements showed that the shear modulus of solid 4 He, μ He , increases significantly below 200 mK, with the same dependence on temperature, 3 He concentration, and frequency as the TO anomaly. [22][23][24][25] This behavio...