Low-Temperature Electrical and Thermal Resistivities of Tungsten

Measurements of $\rho$ and $\mathrm{WT}$ ($\rho$ is the electrical resistivity and $W$ is the thermal resistivity) of high-purity single-crystal specimens of tungsten have been performed in the temperature range 1.5-6.0 K. The temperature dependence of $\rho$ and $\mathrm{WT}$ was found to be predominantly quadratic, in agreement with observations in other transition metals. We attribute this behavior to electron-electron scattering between different branches of the Fermi surface. The validity of Matthiessen's rule for impurity and boundary scattering was investigated to determine whether the contributions of electron-electron scattering ${\rho }_e$ and $W_{e}T$ could be meaningfully separated from the total resistivities $\rho$ and $\mathrm{WT}$. In those samples in which boundary scattering contributed least to the total resistivities, Matthiessen's rule was found to be reasonably well obeyed for the electrical resistivity, while deviations were observed for the thermal resistivity. The Lorenz number for electron-electron scattering, $L_e=\frac{{\rho }_e}{W_{e}T}$, for these samples was found to range from 0.2×${10}^{-8\mathrm{}}$ to 0.4×${10}^{-8\mathrm{}}$ WΩ/${\mathrm{K}}^2$.