Ultrasonic Measurements in Normal and Superconducting Niobium

Phonon attenuation versus temperature measurements have been made on single-crystal niobium from 1.3 to 10°K for longitudinal phonon frequencies of 30 and 220 Mc/sec using the echo technique. In addition, the frequency dependence of the normal attenuation at 1.42°K has been determined from 30 Mc/sec to approximately 450 Mc/sec. Finally, time-of-flight shear and longitudinal measurements have been made at 4.2°K and 30 Mc/sec. By averaging numerous experimental points it has been calculated that the superconducting energy gap is $(3.63\mathrm{}\pm 0.06)k{T}_c$ for sound propagation along the [100], [110], and [111] crystallographic axes; that the normalized gap varies more strongly with the reduced temperature near $T_c$ than is predicted by the BCS theory; that the Debye temperature at 4.2°K is (271±5)°K, as calculated from the computed elastic constants; and that the ratio of superconducting-to-normal attenuation falls below the value predicted by BCS as the temperature is increased towards $T_c$ for the 30-Mc/sec phonons. The attenuation varied as the square of the frequency below 110 Mc/sec, while for the higher frequencies the dependence on frequency decreased. Thus, at 220 Mc/sec, $\mathrm{ql}\sim 1$. The samples were grown by an electron beam zone refining technique; and from well-oriented samples, experimental crystals were selected on the basis of mass spectrographic analyses and by measurements of $T_c$ by the ultrasonic method. A typical acceptable sample was at least 99.8% pure and had $T_c=(9.15\mathrm{}\pm 0.02)$°K. Other typical values were a resistivity ratio of 520±50 and upper critical magnetic fields of 1710±20 Oe and 2020±20 Oe at 4.2 and 1.4°K, respectively. The results are briefly discussed in terms of several models and calculations which have been reported in the literature.