This review addresses experiments on elasticity, plasticity, and flow of solid ${}^4\mathrm{He}$ and ${}^3\mathrm{He}$, focusing on dislocations and other defects that are responsible for the unusual mechanical behavior of such quantum crystals. Helium’s zero point motion prevents it from freezing unless pressure is applied and makes the solid extremely compressible, with elastic constants orders of magnitude smaller than those of conventional solids. Tunneling allows defects to remain mobile at low temperatures, so dislocations have much larger effects on mechanical properties than in conventional solids. At temperatures below 400 mK, dislocations in hexagonal-close-packed (hcp) ${}^4\mathrm{He}$ are essentially undamped and, in the absence of pinning by ${}^3\mathrm{He}$ impurities, glide freely in the basal plane. In this regime, dislocation motion reduces the shear modulus by as much as 90%, an effect that has been referred to as “giant plasticity” although it is reversible and so might be better described as “softening.” In this low temperature regime, macroscopic plastic deformation occurs via sudden dislocation avalanches with a wide range of time and length scales. At higher temperatures, dislocation motion is damped, introducing dissipation in elastic measurements, and thermally activated defect motion makes helium crystals extremely ductile, flowing under millibar stresses near melting. During the last decade, most of the properties of the dislocations that are responsible for the elastic effects described in this review have been accurately measured: their orientation, density, and length distributions, the nature of their networks, and their binding to isotopic impurities. Despite this detailed understanding of mobile dislocations, there remain open questions. Much less is known about defects’ roles in the elastic and plastic behavior of hcp and bcc ${}^3\mathrm{He}$ crystals and even in hcp ${}^4\mathrm{He}$, and almost nothing is known about other types of dislocations that are immobile and thus do not affect elastic properties. These might be responsible for recently observed superfluidlike mass flow in ${}^4\mathrm{He}$ at low temperatures, although it is now clear that the apparent mass decoupling seen in torsional oscillator experiments with solid ${}^4\mathrm{He}$ was due to the elastic effects described in this review, not to supersolidity.

• Received 3 January 2020

DOI:https://doi.org/10.1103/RevModPhys.92.045002