MAX phase $\mathrm{T}{\mathrm{i}}_2\mathrm{SC}$ comes under the category of hexagonal ternary carbides whose room-temperature (RT) total thermal conductivity $\left({\kappa }_{\mathrm{T}}={\kappa }_{\mathrm{e}}+{\kappa }_{\mathrm{ph}}\right)$ is experimentally reported to be the highest amongst all in the 211 category and one of the highest values across the broader MAX-phase family. It shows anomalous temperature $\left(\mathrm{T}\right)$ dependence of ${\kappa }_{\mathrm{T}}$ at high $T$ over a broad range of temperatures. In this study, employing first-principles-based phonon-electron calculations, we quantify the contributions of both electron (${\kappa }_{\mathrm{e}}$) and phonon (${\kappa }_{\mathrm{ph}})$ separately to its thermal conductivity without considering the Sommerfeld value as the decoupling factor. We demonstrate that the weak temperature dependence of ${\kappa }_{\mathrm{T}}$ above RT arises from the comparable phonon-electron interaction relative to the phonon-phonon interaction, and the room-temperature contribution of ${\kappa }_{\mathrm{ph}}$ is 50% of the total thermal conductivity. The phonon-electron interaction is found to be higher throughout the whole frequency range compared to the anharmonic phonon-phonon interaction because of the large density of states around the Fermi energy, hence high metallicity, arising from two opposing types of interactions, antibonding $\mathrm{Ti}d\text{−}\mathrm{S}p$ and bonding $\mathrm{Ti}d\text{−}\mathrm{Ti}d$. The anharmonic phonon-phonon scattering rate is also noted to be higher in $\mathrm{T}{\mathrm{i}}_2\mathrm{SC}$ than in other group-d carbides due to significant cross-plane phonon-phonon coupling and an asymmetric bonding environment. At temperatures below 400 K, the electronic Lorenz number significantly deviates from its conventional Sommerfeld value. Despite the strong structural anisotropy in $\mathrm{T}{\mathrm{i}}_2\mathrm{SC}$, its electrical transport is isotropic, while thermal transport shows only weak anisotropy. This behavior originates from the compensation between group velocities and scattering rates either across different electronic bands and phonon modes, or between their energy-dependent directional averages.

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• Electrical conductivity
• Thermal conductivity
• MAX phase compounds
• Density functional calculations