Ab initio variational approach for evaluating lattice thermal conductivity

Abstract

We present a first-principles theoretical approach for evaluating the lattice thermal conductivity based on the exact solution of the Boltzmann transport equation. We use the variational principle and the conjugate gradient scheme, which provide us with an algorithm faster than the one previously used in literature and able to always converge to the exact solution [Omini and Sparavigna, Physica B: Condens. Matter 212, 101 (1995)]. Three-phonon normal and umklapp collisions, isotope scattering, and border effects are rigorously treated in the calculation. Good agreement with experimental data for diamond is found. Moreover we show that by growing more enriched diamond samples it is possible to achieve values of thermal conductivity up to three times larger than those commonly observed in isotopically enriched diamond samples with $99.93%$ C${}^{12}$ and $0.07$ C${}^{13}$.