Nonlinear Ultrasound Propagation in Solid $^4\hbox {He}$ Compared with Shear Modulus Experiments

Abstract

Ultrasound attenuation ($\alpha$) and velocity (V) at 9.6 MHz are measured in polycrystalline hcp $^4\hbox {He}$. The ultrasound signal above 200 mK is linear and understood in terms of resonant vibration of dislocation segments pinned between network nodes with an average pinning length of 3.7 $\mu \hbox {m}$, much shorter than 59 $\mu \hbox {m}$ estimated from a shear modulus measurement. Dramatic changes in $\alpha$ and V are observed below 200 mK. The changes are strongly dependent on temperature and are nonlinear and hysteretic. These effects result from pinning of dislocations by $^3\hbox {He}$ impurities (nominal concentration of 0.3 ppm). The dislocation damping constant due to thermal phonons, the binding energy between dislocation and $^3\hbox {He}$, and the average network pinning length obtained from the ultrasound data are compared with those from the shear modulus experiments.