Orientation Dependence of Ultrasonic Attenuation in Copper

The ultrasonic attenuation of longitudinal phonons in copper single crystals has been measured in a temperature range from 2 to 80°K, and in a frequency range from 8 to 72 Mc/sec; these measurements cover a range in $\mathrm{ql}$ from 0.07 to 4.0. Analysis of these results shows that for values of $\mathrm{ql}\gg 1$, the attenuation associated with the electron-phonon interaction is a function of crystalline orientation. For values of $\mathrm{ql}\ll 1$, the attenuation is found to be independent of crystalline orientation, and in good agreement with a free-electron model. The attenuation associated with the dislocation-phonon interaction is also found to be orientation-dependent. Calculations in which the deviations of the real Fermi surface from a free-electron sphere are considered do not account fully for the anisotropic behavior of the attenuation; hence one concludes that the deformation of the Fermi surface as a function of the direction and polarization of the imposed phonons must be the significant quantity.