Giant Plasticity of a Quantum Crystal

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.

Figure 1

The shear modulus of crystal X15a as a function of temperature. Around 0.2 K, the shear modulus is reduced to 72 bar, much less than the normal value (127 bar).

Figure 2

Comparison of two “type 2” crystals: X15c and X21 grown, respectively, from ultrapure and from natural ${}^4\mathrm{He}$. The $T$ domain of the giant plasticity depends on both purity and strain amplitude. On graph (a), two ticks on the vertical axis indicate the predicted value of the shear modulus for immobile dislocations. The lower graph (b) shows that the dissipation is negligible in the high plasticity region of X15, as for immobile dislocations in the zero temperature limit of X21.

Figure 3

Measurements (a) for different crystal orientations (b) show that the plasticity is highly anisotropic. Ticks on the vertical axis show the predicted shear modulus with immobile dislocations, in excellent agreement with measurements in the low temperature limit where dislocations are pinned by ${}^3\mathrm{He}$.

Figure 4

Assuming that dislocations glide in the basal plane, one finds the same variation of $c_{44}$ by $62\pm 8\%$ for X2, X5, X6, and X21, which are crystals with different orientations grown in the same conditions. Assuming that they glide in the prismatic planes leads to absurd results (see text).

Figure 5

The relative amplitude of $c_{44}$ for 4 different crystals at 20 mK as a function of the stress projected on the basal plane (“resolved”). At a threshold stress around 1 $\mu \mathrm{bar}$, dislocations break away from ${}^3\mathrm{He}$ impurities [6, 14]. This threshold is larger when increasing the stress than when decreasing it. Being free of impurities, X4 shows a reduction of $c_{44}$ by 80%, independent of stress.