Ultrasonic Attenuation at Low Temperatures for Metals in the Normal and Superconducting States

Abstract

At very low temperatures the mean free paths of electrons in metals become so large with respect to their values at room temperature that they can acquire momentum from collisions with lattice vibrations which result in ultrasonic attenuation when the electrons are in the normal state. This attenuation drops to zero in the superconducting state. Original measurements in impure lead, tin, and copper showed an attenuation proportional to the square of the frequency which could be directly related to the electron viscosity calculated from the number N, the mass m, the mean free path l and the mean velocity 0 of the electrons. Recently some very pure tin samples have been obtained and much larger effects have been measured due to the increased conductivity at low temperatures. Six oriented samples have been measured and from the measurements the six elastic constants and six viscosity coefficients have been obtained. These correspond to those for a tetragonal crystal. As the mean free path becomes longer than the acoustic wavelength, the loss is determined by a scattering process and the loss for a given frequency approaches a limiting value in agreement with a theoretical prediction of Pippard. The loss for longitudinal waves is from 2.5 to 7.5 times the predicted value while that for shear waves is about 1.5 times the theoretical value of Pippard's. Measurements of the elastic constants have been made through the super conducting range and the only discontinuity that occurs is that due to the thermodynamically predicted value. The change for a longitudinal wave is less than that predicted for a volume change in agreement with a theoretical derivation. No relaxation effect occurs for the measured velocity even for very pure tin.