Ultrasonic Determination of the Superconducting Energy Gap in Tantalum

Ultrasonic measurements have been performed on two single crystals of tantalum axially oriented on $〈110〉$. The temperature dependence of the attenuation coefficient of longitudinal waves propagating in this direction was used to compute the temperature dependence of the superconducting energy gap of tantalum. It was found to be closely predicted by the Bardeen-Cooper-Schrieffer theory. The zero-temperature energy gaps of the two were $(3.4\mathrm{}\pm 0.2)k{T}_c$ and $\mathrm{}(3.5+0.2)k{T}_c$, respectively, which are compatible with BCS result, $2{\epsilon }_0\mathrm{}\left(0\right)=3.5\mathrm{}k{T}_c$. In the frequency range of these experiments, 45 to 340 Mc/sec $\mathrm{ql}$ was smaller than one.