Large lattice thermal conductivity, interplay between phonon-phonon, phonon-electron, and phonon-isotope scatterings, and electrical transport in molybdenum from first principles

We describe an ab initio phonon Boltzmann transport equation (BTE) approach accounting for phonon-electron scattering in addition to the well-established phonon-phonon and isotope scatterings. The phonon BTE is linearized and can be exactly solved beyond the relaxation time approximation (RTA). We use this approach to study the lattice thermal conductivity (kappa(ph)) of molybdenum (Mo). kappa(ph) of Mo is found to possess several anomalous features: (1) like in another group VI element tungsten (W), kappa(ph), with a large value of 37 W m(-1) K-1 at room temperature, follows weak temperature dependence due to interplay between phonon-phonon (ph-ph), phonon-electron (ph-el), and phonon-isotope (isotope) scatterings; and (2) compared with W, though Mo is much lighter in mass, Mo has a smaller kappa(ph). This is attributed to weaker interatomic bonding, larger isotope mixture, and larger density of states at Fermi level in Mo. In isotopically pure samples, kappa(ph) increases from 37 to 48 W m(-1) K-1 at room temperature. Considering the similarity of the phonon dispersion, our work suggests that chromium should also have a large kappa(ph), which, rather than the complexity of the electronic band structure argued in the literature, accounts for the significant deviation of measured Lorenz number L from the expected Sommerfeld value. The electrical conductivity (sigma) and electronic thermal conductivity (kappa(e)) of Mo are also calculated by using an ab initio electron BTE approach. sigma and the total thermal conductivity (kappa) agree with the experimental data reasonably. These results demonstrate that the ab initio calculations can quantify the lattice and electronic contributions to kappa. We also look into the cumulative sigma and kappa(ph) with respect to electron and phonon mean free paths (MFPs), respectively, in order to reveal the size effect in Mo. The MFPs of electrons contributing to conductivity range from 5 to 22 nm, whereas the MFPs of phonons primarily distribute between 5 and 73 nm with more than 80% contribution to kappa(ph). This suggests that a reduced Lorenz number can be observed in Mo nanostructures when the relevant size goes below similar to 70 nm.