Measurements were made of the ultrasonic shear wave attenuation in superconducting aluminum, using 99.999% pure single crystals with parallel faces in the [100], the [110], and the [111] directions. It was found that the temperature dependence of the attenuation could be separated into two parts: a sharp decrease in attenuation very close to the transition temperature and a residual attenuation having a temperature dependence similar to that for the longitudinal waves. The method of adiabatic demagnetization was used to lower the temperature to 0.3°K, and an extrapolated plot of the residual attenuation in this range could be used to determine an effective BCS energy gap. The fraction of the total attenuation represented by the residual attenuation was found to be strongly temperature-dependent. Application of a magnetic field was found to lower the transition temperature as would be expected. In fact, it was found that the method of ultrasonic attenuation could be used to determine the critical fields accurately near the zero-field value, where permeability measurements are difficult. A theory was developed to explain the behavior of the shear-wave attenuation as a function of temperature. The formulation began with approximations which should be valid in the London region and employed a self-consistent method for determining the dissipative forces on the lattice. Suitable modification extended the theory to cover the entire superconducting temperature range. Using the theoretical results, it is possible to determine the parameters $\tau$ and $l$, the electron relaxation time and mean free path, for one orientation and frequency and then predict the correct results for other frequencies at the same orientation. One thus obtains the correct frequency dependence for the total electronic attenuation. Some correlation was made between results for different orientations.

• Received 18 February 1964

DOI:https://doi.org/10.1103/PhysRev.136.A893