Thermal properties of small Pb spheres at low temperatures

The specific heat and thermal conductivity of 0.10-mm- and 0.34-mmdiameter spheres of Pb are reported (2–30 K). The former spheres are 99.99% Pb, the latter spheres are Pb + 5% Sb. Both types of spheres undergo a superconducting transition at 7 K, and the changes in the specific heats at the transition correlate well with the electronic coefficient determined for bulk Pb. The 5% Sb addition increases the specific heat by as much as 30%, due to an enhancement of the localized, non-Debye excitations present in pure Pb. The Debye temperatures of the spheres are 102–103 K. The thermal conductivities of packed columns of the spheres are due to lattice rather than electron transport and are about 10³ times smaller than the thermal conductivity of bulk superconducting Pb. The 0.34-mm-diameter spheres have double the thermal conductivity of the 0.10-mm-diameter spheres, in contrast to the predictions of the elastic theory of Chan and Tien. An oxide layer may be the cause of the additional thermal resistance of the smaller spheres. T ³ boundary scattering occurs below 3 K for both sphere sizes and is consistent with specific heat and elastic-constant data for bulk Pb.