Lead-alloying effects on the superconducting critical field curve of indium

The effects of lead alloying on several features of the superconducting critical-field curve of indium have been studied. Both the anisotropy and linear effects were observed in T_c for the 0–4 at.% lead alloys. The coefficient of the linear effect K^Pb was measured directly and found to be 0.144 °K/μΩ cm. Using the theory of Markowitz and Kadanoff, the value of the mean-squared anisotropy ⟨a²⟩ of the superconducting energy gap in indium is found to be 0.0072 ± 0.0007, and in indium doped with lead the mean collision time for transport is found to be at least three times larger than that for the smoothing out of the gap anisotropy. The superconducting transition temperature T_c is found to increase linearly with doping in the 3–4 at.% lead concentration range. This confirms earlier work and raises a question as to why there is no unusual behavior in T_c near 3.5 at.% lead, since several other properties of the system including residual resistivity, thermoelectric power, lattice spacings, and electronic specific heat all exhibit anomalous behavior near both 3.5 and 7.0 at.% lead, whereas T_c only exhibits unusual behavior near 7.0 at.% lead. Critical-field-curve measurements in 0–0.8 at.% lead samples are found to qualitatively confirm the predictions of Clem for effects of alloying on the critical-field curve of an anisotropic superconductor. Using the analysis of Clem, ⟨a²⟩ = 0.007 is found from data on $\frac{d{H}_c}{dT|T_c}$. The similarity conditions on $\frac{H_0\left(x\right)}{T_c\left(x\right)}$ and h(x,t), where x is impurity content, are found to be violated for indium doped with lead. A linear effect in H_0(x) which is stronger than the linear effect in T_c(x) is also observed.