Elastic properties of solid helium

Following recent torsional oscillator measurements which appear to show the 'non-classical rotational inertia' which characterizes a supersolid, a number of experiments have searched for evidence of unusual behavior in other properties. We have developed a new technique for measuring the shear modulus of solid helium at low frequencies and small strains. In hexagonal close packed He-4, the shear modulus increases dramatically below 200 mK, the temperature range where decoupling is seen in torsional oscillators. The modulus anomaly is frequency independent, depends strongly on strain amplitude, and is very sensitive to He-3 impurities. In these and other ways, the shear modulus closely mirrors the torsional oscillator behavior and it is clear that the two phenomena are closely related. We attribute the shear modulus effects to the elastic response of mobile dislocations and their pinning by He-3 impurities at low temperatures. A question then arises: are the modulus increases responsible for the frequency changes seen in torsional oscillator experiments? The expected frequency shifts appear to be much too small to explain the apparent decoupling, nor can elastic effects explain the 'blocked annulus' results or the behavior in small pores. In order to clarify the relationship between the shear modulus and torsional oscillator behaviors, we have recently made modulus measurements on He-3, where no supersolid response is expected. Since dislocation motion depends on crystal structure it was important that these measurements be extended to the hexagonal close packed phase of He-3, not just the body centered cubic phase.