BCS and polycrystalline high-Tc materials

We examine the behavior of a small superconducting grains using a BCS-like theory, in which the effects of the small size of the system are taken into account. Such effects are expected to be important in the analysis of polycrystalline high-Tc materials, where the individual grains are weakly coupled. Both the shift in Tc and the sharpening of the peak in the specific heat observed during the sintering process of high-Tc materials can be qualitatively understood by taking into account finite size effects. Furthermore, it is shown that the average of the gap parameter remains finite above the critical temperature resulting in a tail in the upper bound for the critical current. This is in qualitative agreement with experiment, where a tail in the critical current and a smeared-out transition have been observed in polycrystalline Y1.2Ba0.8Cu2Ox bulk samples and in sputtered Bi-Sr-Ca-Cu-O films. (orig.)