Dependence of dislocation damping on helium-3 concentration in helium-4 crystals

Abstract

Abstract. The mechanical properties of crystals are strongly affected by dislocation mobility. Impurities can bind to dislocations and interfere with their motion, causing changes in the crystal's shear modulus and mechanical dissipation. In 4 He crystals, the only impurities are 3 He atoms, and they can move through the crystal at arbitrarily low temperatures by quantum tunneling. When dislocations in 4 He vibrate at speeds v < 45 µm/sec, bound 3 He impurities move with the dislocations and exert a damping force B3v on them. In order to characterize 4 He dislocation networks and determine the 3 He binding energy, it is usually assumed that B3 is proportional to the concentration of 3 He bound to the dislocations. In this preliminary report, we determine B3 in a crystal with 2.32 ppm 3 He and compare with our previous measurements of B3 in natural purity 4 He crystals to verify the assumption of proportionality. IntroductionRecent work [1,2,3,4,5] has demonstrated that the mechanical properties of hcp 4 He crystals can be understood in great detail by modeling their dislocations as elastic strings that vibrate between pinning points [6]. At low dislocation speeds and low temperatures, 3 He impurities bind to the dislocations and move with them, damping their vibrations [3]. The binding energy E B was determined from the frequency dependence of the peak dissipation temperature under the assumption that the damping due to 3 He is proportional to the concentration of 3 He atoms bound to the dislocations [3,5,7]. In order to test this assumption, we are measuring the 3 He damping coefficient as a function of the 3 He concentration in the helium gas that we use to grow our crystals. In this preliminary paper, we report the 3 He damping coefficient for a crystal with a 2.32 ppm bulk 3 He concentration and compare with that of crystals made of natural purity helium. We find a linear dependence on 3 He concentration. Dislocations in 4 He crystals are strongly pinned where they intersect, forming a network characterized by an average length L N between network nodes and a density Λ that is given by the total dislocation length per unit volume of the crystal. In the absence of damping, the dislocations vibrate elastically between pinning points in response to an oscillating stress. (No effect of the lattice potential on dislocation vibrations has been detected in hcp 4 He [1].) This