Thermal Conductivity of Indium-Thallium Alloys at Low Temperatures

Abstract

The thermal conductivity of a series of homogeneous, solid solution indium-thallium alloys containing up to 50 atomic percent of thallium has been measured as a function of temperature at liquid helium temperatures and as a function of both longitudinal and transverse magnetic fields below ${T}_{c}$, the superconducting transition temperature in zero field. The normal-state results agree quite well with the quasi-free electron theory of metals. The superconducting-state results agree with the hypotheses that electrons in the "superconducting phase" neither transport heat nor scatter phonons.For pure indium, it was found that $\frac{{K}_{\mathrm{es}}}{{K}_{\mathrm{en}}}=\frac{2{t}^{2}}{(3+{t}^{4})}$, where ${K}_{\mathrm{es}}$ and ${K}_{\mathrm{en}}$ are the electronic thermal conductivities at a given temperature when the specimen is superconducting and when it is nonsuperconducting, respectively, and $t=\frac{T}{{T}_{c}}$.For all the alloy specimens the ratio of the lattice thermal conductivities comprised a family of curves such that ${t}^{\ensuremath{-}3}<\frac{{K}_{\mathrm{gs}}}{{K}_{\mathrm{gn}}}<{t}^{\ensuremath{-}6}$.A thermal resistivity maximum was found to accompany the isothermal destruction of superconductivity by either a longitudinal or a transverse magnetic field in specimens containing 15 percent Tl or more. When the applied field was reduced to zero, the final thermal resistivity of most of these specimens was greater than would be expected for a simple mixture of superconducting and "frozen-in" normal regions, the concentration of the latter being estimated from magnetic induction measurements. Both this effect and the maxima themselves are thought to be manifestations of an increased lattice thermal resistivity due to alteration of the mean free path of phonons when they approach the boundary between a superconducting and a normal region.