Ultrasonic Attenuation in Metals in the Fluid-Dynamic Approximation

Ultrasonic attenuation in metals has been discussed from diverse points of view, and for the most part the derived attenuation formulas reduce in the first-order low-frequency limit to the viscous dissipative expression originally proposed by Mason. We undertake here a treatment for the low-frequency range which makes immediate contact with the transport-theory formalism of classical gases. "Fluid"-dynamic equations for the metal are formulated. For the electron-gas component a complete set of transport coefficients, including the several diffusion coefficients, is derived in a unified way on the simplifying assumption of a constant relaxation time. The acoustic attenuation coefficient for a longitudinal wave is deduced; the dominant term is of course the shear viscous one, but thermal and diffusion effects are also explicit.