Superconductive Supercooling and Superheating of Small Cadmium Spheres: Size Effects

Supercooling and superheating have been observed for samples composed of small cadmium spheres of uniform well-defined sizes. The data obtained for large sphere diameters are independent of size and represent, by all indications, ideal bulk properties. The supercooling data for such spheres have been used to obtain the Ginsburg-Landau parameter $\kappa$ and, in conjunction with BCS expressions, the penetration depth $\lambda$ and the coherence length ${\xi }_0$. The temperature dependence of the supercooling field $H_{\mathrm{sc}}$ shows an anomaly for $t\sim 0.8$, very similar to that previously reported for Al and Zn. The superheating field of these "bulk" spheres shows strong effects of the nonlocal electrodynamics below $T_c$. Spheres of diamters equal to or smaller than 10 μ show strong size effects in the supercooling and superheating fields, especially near $T_c$. The results are examined in the light of existing theories of critical fields for small spheres. A systematic decrease of the critical temperature with sphere size has also been observed. It seems related to a decrease in the gap anisotropy, produced by boundary scattering. These results are analyzed in terms of the theory of Markowitz and Kadanoff.