Lattice Thermal Conductivity of Superconducting Niobium Carbide

The unusually low lattice thermal conductivity of the transition-metal carbides at low temperatures has been attributed to the scattering of phonons by conduction electrons. An experiment which confirms this interpretation is reported. Thermal conductivity measurements on single-crystal Nb${\mathrm{C}}_{0.96}$ through its superconducting critical temperature (9.8°K) show that the lattice component of the thermal conductivity, $K_{l3\mathrm{}}$, increases greatly below $T_c$ because of decreased phonon-electron scattering. The maximum increase in lattice thermal conductivity from this effect occurs at 3°K with $\frac{K_{\mathrm{ls}}}{K_{\ln }}$ equal to 160. The theories of Bardeen, Rickayzen, and Tewordt and of Klemens and Tewordt for the influence of electrons and point defects on lattice conductivity provide a quantitative interpretation of the effect. The best fit to the Nb${\mathrm{C}}_{0.96}$ data is for $\frac{2\epsilon \mathrm{}\left(o\right)\mathrm{}}{k{T}_c}=4.0\mathrm{}$. The behavior of Nb${\mathrm{C}}_{0.96}$ is in contrast to that of Nb${\mathrm{C}}_{0.76}$, which remains in the normal state throughout the temperature interval studied and shows no increase in thermal conductivity.