Elastic properties of solid helium

Abstract

Following recent torsional oscillator measurements which appear to show the‘non-classical rotational inertia’ which characterizes a supersolid, a number ofexperiments have searched for evidence of unusual behavior in other properties.We have developed a new technique for measuring the shear modulus ofsolid helium at low frequencies and small strains. In hexagonal close packed4He, the shear modulus increases dramatically below 200 mK, the temperature range wheredecoupling is seen in torsional oscillators. The modulus anomaly is frequencyindependent, depends strongly on strain amplitude, and is very sensitive to3He impurities. In these and other ways, the shear modulus closely mirrors the torsionaloscillator behavior and it is clear that the two phenomena are closely related. We attributethe shear modulus effects to the elastic response of mobile dislocations and their pinning by3He impurities at low temperatures. A question then arises: are the modulus increasesresponsible for the frequency changes seen in torsional oscillator experiments? Theexpected 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 insmall pores. In order to clarify the relationship between the shear modulus andtorsional oscillator behaviors, we have recently made modulus measurements on3He, where no supersolid response is expected. Since dislocation motion depends on crystal structureit was important that these measurements be extended to the hexagonal close packed phase of3He, not just the body centered cubic phase.