Dislocation networks in4He crystals

Abstract

The mechanical behavior of crystals is dominated by dislocation networks, their structure and their interactions with impurities or thermal phonons. However, in classical crystals, networks are usually random with impurities often forming non-equilibrium clusters when their motion freezes at low temperature. Helium provides unique advantages for the study of dislocations: crystals are free of all but isotopic impurities, the concentration of these can be reduced to the ppb level, and the impurities are mobile at all temperatures and therefore remain in equilibrium with the dislocations. We have achieved a comprehensive study of the mechanical response of 4 He crystals to a driving strain as a function of temperature, frequency and strain amplitude. The quality of our fits to the complete set of data strongly supports our assumption of string-like vibrating dislocations. It leads to a precise determination of the distribution of dislocation network lengths and to detailed information about the interaction between dislocations and both thermal phonons and 3 He impurities. The width of the dissipation peak associated with impurity binding is larger than predicted by a simple Debye model, and much of this broadening is due to the distribution of network lengths.

Simulation and understanding of atomic and molecular quantum crystals

“…If in the case of point defects it can be said that theory has led the way to their (partial) understanding, in the case of dislocations is the other way around. At present, most of what we know about dislocations in quantum solids comes from recent experiments performed by the groups of Beamish, in the University of Alberta, and Balibar, in the Ecole Normale Supérieure de Paris (see, for instance, Haziot et al, 2013a;Haziot et al, 2013b;Fefferman et al, 2014;Souris et al, 2014a). Such a gap between theory and experiments is due to several reasons.…”

“…They found that µ increased with decreasing T below a certain temperature of 0.15 K. The observed increase in stiffness was rationalised in terms of line defects mobility: below a particular temperature threshold the dislocations present in the crystal could be pinned by 3 He impurities, in spite of the incredibly small concentration of the latter (i. e., just 200 parts per billion of 4 He atoms). This argument has been subsequently ratified by a number of compelling experimental works carried out by the groups of Beamish, in the University of Alberta, and Balibar, in the Ecole Normale Supérieure de Paris (see, for instance, Haziot et al, 2013a;Haziot et al, 2013b;Fefferman et al, 2014;Souris et al, 2014a). Remarkably, Haziot et al (2013c) have recently shown that in ultra-pure single crystals of 4 He the resistance to shear along one particular direction nearly vanishes at around T = 0.1 K, whereas normal elastic behavior is observed in the others.…”

“…Consider the classical elastic contribution to the formation energy per unit length of an edge dislocation (Cotterill and Doyama, FIG. 14: (Color online) The measured distribution, N (L N ), of lengths, L N , between dislocation network nodes in a 4 He crystal at T = 27 mK; the contribution to the shear modulus from each dislocation length is also indicated. From Fefferman et al, 2014Fefferman et al, . 1966):…”

Low Frequency Elastic Measurements on Solid $$^{4}$$ 4 He in Vycor Using a Torsional Oscillator

“…A comparable change for helium in Vycor would change the system's transverse sound speed by about 0.2 %. However, the shear modulus changes in bulk 4 He are due to the motion of dislocations which can glide very easily in the basal plane of hcp 4 He [14][15][16][17]. At high frequencies these dislocations are strongly damped by thermal phonons, which greatly reduces their effects on elastic constants.…”

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

“…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.…”