Specific-Heat and Magnetic Measurements in Superconducting Ta-Nb Alloys

The specific heats of Ta and the Ta-Nb alloys ${\mathrm{Ta}}_{0.963}$ ${\mathrm{Nb}}_{0.037}$, ${\mathrm{Ta}}_{0.86}$ ${\mathrm{Nb}}_{0.14}$, ${\mathrm{Ta}}_{0.595}$ ${\mathrm{Nb}}_{0.405}$, and ${\mathrm{Ta}}_{0.42}$ ${\mathrm{Nb}}_{0.58}$ were measured from 1.5 to 7 K in both normal and superconducting states. The electronic specific-heat coefficient $\gamma$ and the Debye temperature ${\Theta }_D$ were obtained from normal-state measurements below 4.2 K. The electron-phonon coupling factor $\lambda$ and the bare-band-structure density of states at the Fermi surface $N_{\mathrm{bs}}\mathrm{}\left(0\right)\mathrm{}$, calculated from these results using McMillan's theory, show a smooth increase with increasing Nb concentration. The values of $\lambda$ are also compared with the predictions of Hopfield's theory. The thermodynamic critical field $H_c\mathrm{}\left(T\right)\mathrm{}$ for these intermediate coupling alloys was determined by integrating the difference between the normal and superconducting specific heat $\Delta C\left(T\right)\mathrm{}$. A comparison with independent values of $H_c\mathrm{}\left(T\right)\mathrm{}$ obtained from magnetization measurements carried out on the same samples shows agreement at low temperatures and suggests the magnetic measurements tend to emphasize sample inhomogeneities particularly near $T_c$. Finally, $\lambda$ is compared with other indicators of strong coupling in superconductors such as the deviation of $H_c\mathrm{}\left(T\right)\mathrm{}$ from $T^2$ behavior, $\frac{\Delta C}{\gamma T_c}$, $\frac{2\Delta \mathrm{}\left(0\right)\mathrm{}}{k_B{T}_c}$, and $\frac{H_c^2\mathrm{}\left(0\right)\mathrm{}}{\gamma T_c^2}$ determined for these alloys from the specific-heat measurements.