Ultrasonic Absorption by Superconducting Nb-Zr Alloys

Ultrasonic attenuation studies in dilute superconducting Nb-Zr alloys have revealed strongly temperature-dependent absorption peaks which cannot be explained in terms of single electron-phonon scattering processes. The set of temperatures at which these peaks occur is dependent on the frequency of the sound wave and the strain content of the sample. A phenomenological model is proposed which interprets the absorption peaks as being due to an exchange of energy which occurs when the sound frequency is equal to one of a set of collective excitation modes of the electron gas. The assumptions on which the model is based are the same as those which yield collective excitations within the energy gap in more fundamental descriptions of the superconducting state. The phenomenological treatment involves a hydrodynamic approach in a finite superconducting phase, based on volume derivatives of the electronic free energy under conditions of charge neutrality. The interaction constant for the collective excitations is empirically assumed to be decreased by the factor, $\chi \left(r_0\right)\equiv {\xi }^{-1\mathrm{}}{r}_0\exp (\alpha -\xi {r_0}^{-1\mathrm{}})$, when the extent of the superconducting phase $r_0$ is less than the coherence distance $\xi$. Good agreement between the experimental data and the results of the proposed model is obtained.