Temperature and Frequency Dependence of The Sound Velocity in hcp4He Crystals

The longitudinal sound velocity in hcp 4 He single crystals grown at 35.5 atm has been measured between 0.25 and 1.7 K at 10, 30, and 50 MHz. Above about 1 K, the change in the velocity is proportional to T 4 and independent of the frequency. Below 1 K the velocity change varies from crystal to crystal, depends on the frequency, and shows an annealing effect. These anomalous behaviors are caused by the interaction between the sound and the vibration of dislocations. The dislocation density \(\), the average pinning length L , and the damping constant B are obtained using the Granato-Lücke theory. Typical values are \({=}10⁶\) cm -2 , L =5·10 -4 cm, and B =3·10 -7 · T 3 cgs when an exponential distribution for the pinning lengths is assumed. The choice of other distributions is discussed as well. Also discussed is the sound attenuation due to the dislocation vibration.