Dislocation networks in 4He crystals

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 nonequilibrium 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 parts per 10(9) (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 He-4 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 stringlike 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 He-3 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.