The thermal resistance at boundaries between indium and single crystal sapphire has been measured with the indium superconducting and normal. The effective temperature at the sapphire side of a boundary was determined from the condition of radiative equilibrium at the surfaces of the crystal. It was found that the thermal conductance of indium-sapphire boundaries can be represented by the sum of a $T^2$ term and a $T^3$ term. For two samples, the $T^3$ terms are, respectively, ${0.0295\mathrm{T}}^3$ and $0.0281T^3\pm 0.0016T^3$ W/(${\mathrm{cm}}^2$—deg). These numbers are within the range of possible values expected on the basis of the acoustic mismatch theory of Little. For the two samples the $T^2$ terms are ${0.0059\mathrm{T}}^2$ and $0.0098{\mathrm{T}}^2\pm 0.001{\mathrm{T}}^{2}W$ (${\mathrm{cm}}^2$—deg) with the indium superconducting, and are increased by $(1\mathrm{}\pm 0.4)\times {10}^{-3\mathrm{}}{T}^2$ when the indium is normal. The values obtained as a matter of course for the thermal conductivity of sapphire are in agreement with the Casimir theory as modified to include the effects of finite crystal length and specular reflection of phonons at the crystal surfaces.

• Received 5 March 1964

DOI:https://doi.org/10.1103/PhysRev.135.A1028