Heat pulse study of superconducting lead/indium alloys

Heat pulses have been used to investigate the thermal transport properties of dilute solutions of indium in lead from 1.4 K to 4.2 K. The measured temperature profiles resulting from the arrival of a heat pulse at a sensitive bolometer were fit to the solution of the standard diffusion equation to determine the thermal diffusivity. The data were combined with specific heat data measured elsewhere to calculate the thermal conductivity of the alloys in their superconducting state. This data was further reduced to yield the lattice thermal conductivity. Analysis was performed on this data to determine the relative strengths of four phonon scattering mechanisms, dislocations, boundaries, point defects and electrons. In no case was a transition from diffusive flow to ballistic flow observed, including a sample of pure lead that was measured for comparison with other results. While the thermal conductivity is in good agreement to previous studies, the maximum mean free path over the temperature range studied is an order of magnitude smaller than the thickness of the sample. The fit to the lattice thermal conductivity data was performed in two ways. First by holding the boundary term constant at the smallest dimension of the sample and second by disregarding the dislocation term. In the former case, a dislocation density, much larger than expected from the quality of the crystals, was required for the fit. In the latter case the boundary term was on the order of 10 to 100 microns. No attempt was made to produce a null field at the position of the sample and the resulting inclusions of normal state material within the sample might reduce the boundary term to this size. However, since the two scattering mechansisms differ by only one power in their frequency dependence, with the present experimental data they cannot be resolved. A study of the material in zero magnetic field might resolve this question