Intrinsic thermal conductivity of ZrC from low to ultrahigh temperatures: A critical revisit

Abstract

Current phonon transport theory based on ground-state calculations has been successful in predicting thermal conductivity at room and medium temperatures but may misrepresent behavior at high temperatures. In this work, we predict the thermal conductivity ($\ensuremath{\kappa}$) of ZrC including electronic and phonon contributions from 300 to 3500 K, by including high-order phonon scattering; lattice expansion; temperature-dependent (TD) second-, third-, and fourth-order force constants (2FC, 3FC, and 4FC); and interband phonon conduction by using first principles. For the phonon transport, we find that four-phonon scattering (4ph) significantly reduces the phonon thermal conductivity (${\ensuremath{\kappa}}_{\mathrm{ph}}$), by as much as $\ensuremath{\sim}75%$ at 3500 K. After including 4ph scattering and all other factors, ${\ensuremath{\kappa}}_{\mathrm{ph}}$ shows a $\ensuremath{\sim}{T}^{\ensuremath{-}1.5}$ rather than $\ensuremath{\sim}{T}^{\ensuremath{-}1}$ dependence. TD 2FC decreases three-phonon scattering rates but increases 4ph rates by decreasing and increasing the scattering phase spaces, respectively. For 4ph phase space, the TD 2FC flattens phonon bands, and allows more redistribution-4ph processes $(1+2\ensuremath{\rightarrow}3+4)$ to happen. The combination effect of TD 2FC and TD 4FC reduces 4ph rates of acoustic modes but increases those of optical modes. The TD 3FC and 4FC decrease the phonon scattering cross section and increase the ${\ensuremath{\kappa}}_{\mathrm{ph}}$ significantly (by 52% at 3500 K). The contribution from interband (Wigner) phonon conduction is small, even at ultrahigh temperatures. For electronic thermal transport, we find that it is sensitive to and can be changed by 20% by the TD lattice constants. The Lorenz number varies from 1.6 to $3.3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}8}\phantom{\rule{0.16em}{0ex}}\mathrm{W}\phantom{\rule{0.16em}{0ex}}\mathrm{\ensuremath{\Omega}}\phantom{\rule{0.16em}{0ex}}{\mathrm{K}}^{\ensuremath{-}2}$ at different temperatures. The theoretical prediction in the literature overpredicts ${\ensuremath{\kappa}}_{\mathrm{ph}}$ (e.g., $\ensuremath{\sim}28%$) and underpredicts the ${\ensuremath{\kappa}}_{\mathrm{el}}$ (e.g., $\ensuremath{\sim}38%$), resulting in an overall underprediction of $\ensuremath{\kappa}$ ($\ensuremath{\sim}26%$ at 1500 K). The impacts of grain size and defects are found to be strong, leading to the lower observed thermal conductivity in experiments.