Ultrasonic Attenuation in Aluminum

Abstract

The normal-state ultrasonic attenuation of longitudinal waves propagating along the principal symmetry directions in aluminum has been measured over a wide range of $\mathrm{ql}$, where $q$ is the phonon wave number and $l$ is the electron mean free path. The usual quadratic frequency behavior at low $\mathrm{ql}$ and linear frequency behavior at high $\mathrm{ql}$ is observed for the electronic attenuation. At high $\mathrm{ql}$ the limiting values of attenuation divided by frequency are found to be strongly anisotropic and not in agreement with the free-electron prediction. Calculations assuming an isotropic deformation parameter with a pseudopotential representation of the Fermi surface show strong anisotropy, but the agreement with experiment is not good. From the pseudopotential Fermi surface generalized to include the effects of static strain, the anisotropy of the deformation tensor has been calculated. Using this model of the deformation, good agreement is achieved not only with the ultrasonic data but also with area changes observed from de Haas-van Alphen measurements under hydrostatic pressure.