An experimental study has been made of some aspects of the thermal conductivity of superconducting tin and indium below 1°K. Experiments at the lowest temperatures, where the thermal conductivity of the lattice is dominant, and for tin varies as
T
3
, have been mainly directed towards studying the size effect in the conductivity due to the scattering of phonons at the specimen surface. Electropolishing tin has been found to increase the thermal conductivity considerably; a simple analysis of the results shows that almost complete specular reflexion of phonons is attainable. The analysis confirms the existence of an internal scattering of phonons, describable at the lowest temperatures by a temperature-independent mean free path which does not vary when the diameter of the specimen is reduced, but is very sensitive to any damage suffered by the crystal. The lattice conductivity of indium, which is anomalous in having a
T
4
rather than a
T
3
variation, appears to be limited mainly by internal scattering and it is tentatively suggested that the internal scattering is mainly due to the reradiation from dislocations oscillating in the phonon field. At somewhat higher temperatures (above about 0.7 but below 1°K) the thermal conductivity is predominantly electronic and the results indicate that here too the ‘effective’ electronic mean free path is size-dependent due to boundary scattering. From an analysis of this size-dependence in tin, the ‘intrinsic’ electronic mean free path in the superconducting state is deduced and found to be between ten and thirty times as long as in the normal state. The results suggest also that the electronic velocity in the superconducting state is something like one-third of the Fermi velocity.
