Understanding the thermal conductivity and Lorenz number in tungsten from first principles

Abstract

Listen

Translate article

Tungsten is known to have a Lorenz number $L$ larger than the Sommerfeld value (${L}_{0}={\ensuremath{\pi}}^{2}{k}_{B}^{2}/3{e}^{2}=2.445\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}8}\phantom{\rule{0.16em}{0ex}}{\mathtt{V}}^{2}/{\mathtt{deg}}^{2}$) by 30%. By performing fully first-principles calculations, we are able to calculate the electrical conductivity ($\ensuremath{\sigma}$) and quantify the electronic (${\ensuremath{\kappa}}_{e}$) and the lattice (${\ensuremath{\kappa}}_{\mathtt{ph}}$) contributions to the thermal conductivity with a high accuracy. We show that the deviation of $L$ is entirely due to ${\ensuremath{\kappa}}_{\mathtt{ph}}$, and ${\ensuremath{\kappa}}_{e}/\ensuremath{\sigma}T$ agrees with ${L}_{0}$ within 5%. At room temperature, ${\ensuremath{\kappa}}_{\mathtt{ph}}$ is 46 W/m-K, one order of magnitude larger than that in other metals even with smaller atomic mass and higher Debye temperature, and likely the largest of all metals. The large ${\ensuremath{\kappa}}_{\mathtt{ph}}$ is ascribed to the surprisingly weak anharmonic phonon scattering. Apart from the not-strong anharmonic interatomic interaction, the weak anharmonic phonon scattering is also facilitated with the large atomic mass, leading to small thermal displacement. The interplay between the phonon-phonon and electron-phonon scatterings leads to weak temperature dependence of ${\ensuremath{\kappa}}_{\mathtt{ph}}$, and signifies the importance of an accurate solution to the Boltzmann transport equation beyond the conventional relaxation time approximation. Our findings give insights into the phonon transport in metals.