Attenuation of Longitudinal Ultrasound in Superconducting Lead

Abstract

The ultrasonic pulse-echo technique was used to measure the absorption of ultrasound in superconducting and normal single-crystal lead. Longitudinal sound waves were propagated in the [100], [110], and [111] crystallographic directions at frequencies between 10 and 70 Mc/sec. The purpose of this investigation was to measure the temperature dependence of the superconducting energy gap as well as to attempt to observe its anisotropy. Sufficiently reliable data at low temperatures to do the latter could not be obtained with the present apparatus. The temperature dependence could be reliably measured above a reduced temperature ($t=\frac{T}{{T}_{c}}$) of 0.5, and an average zero-temperature energy gap of $2\ensuremath{\Delta}(0)=(4.1\ifmmode\pm\else\textpm\fi{}0.2)k{T}_{c}$ was obtained using the BCS temperature dependence for extrapolation. In the course of this investigation, we found the attenuation to be amplitude-dependent in the superconducting state, while at the same temperature in the normal state it was amplitude-independent. The energy gap quoted above was measured at the smallest possible amplitudes. The empirical nature of the amplitude effect and its consequences in the determination of the energy gap in lead are discussed. The possibility is pointed out that disagreements between energy-gap temperature dependences predicted by BCS theory and those derived from ultrasonic measurements in elements other than lead may be due to this effect.