Anomalous strain-dependent thermoelectric properties of cubic stuffed-diamond Li Cu 3 Ti Q 4 ( Q  =  S , Se )

Developing high-performance thermoelectric (TE) materials composed of low-toxic elements alternative to $\mathrm{Pb}$-based compounds is essential for the widespread application of TE technology. Recently, a new stuffed-diamond structure ${\mathrm{Li}\mathrm{Cu}}_{3}{\mathrm{Ti}\mathrm{Q}}_{4}$ ($\mathrm{Q}$ = $\mathrm{S},\phantom{\rule{0.2em}{0ex}}\mathrm{Se}$) with moderate band gap and low hole carrier effective masses has been synthesized [J. Am. Chem. Soc. 144, 12789 (2022)], which could be a promising candidate for TE applications. Here, based on first-principle calculations combined with Boltzmann transport theory, we systematically study the electronic and thermal transport properties of ${\mathrm{Li}\mathrm{Cu}}_{3}{\mathrm{Ti}\mathrm{Q}}_{4}$ to elucidate the thermoelectric performance. The results show that the lattice thermal conductivities of ${\mathrm{Li}\mathrm{Cu}}_{3}{\mathrm{Ti}\mathrm{S}}_{4}$ and ${\mathrm{Li}\mathrm{Cu}}_{3}{\mathrm{Ti}\mathrm{Se}}_{4}$ are 2.4 and 2.1 W/mK at 300 K within the framework of the four-phonon scattering, respectively, which is comparable to various typical TE materials such as $\mathrm{Pb}\mathrm{Te}$ and ${\mathrm{Sb}}_{2}{\mathrm{Te}}_{3}$. In addition, ${\mathrm{Li}\mathrm{Cu}}_{3}{\mathrm{Ti}\mathrm{Q}}_{4}$ behaves as a degenerate semiconductor and possesses a large power factor [0.6--1.5 mW/(cm ${\mathrm{K}}^{2}$)] in the temperature range of 300--700 K. Consequently, the calculated figure of merit (ZT) value of p-type ${\mathrm{Li}\mathrm{Cu}}_{3}{\mathrm{Ti}\mathrm{Q}}_{4}$ can reach 0.8 at 700 K, and the ZT value could be further improved to \ensuremath{\sim}1.6 under a small strain of 3%, mostly owing to the strain-induced thermal conductivity reduction. It is also found that the lattice thermal conductivity of ${\mathrm{Li}\mathrm{Cu}}_{3}{\mathrm{Ti}\mathrm{S}}_{4}$ is abnormally lower than that of ${\mathrm{Li}\mathrm{Cu}}_{3}{\mathrm{Ti}\mathrm{Se}}_{4}$ under strain conditions, in contradiction with the conventional Keyes theory in which heavier compounds tend to have lower thermal conductivity. A comparative analysis of phonon anharmonicity of ${\mathrm{Li}\mathrm{Cu}}_{3}{\mathrm{Ti}\mathrm{S}}_{4}$ and ${\mathrm{Li}\mathrm{Cu}}_{3}{\mathrm{Ti}\mathrm{Se}}_{4}$ reveals that weakening bond stiffness, high charge transfer between the $\mathrm{Cu}$ and $\mathrm{Q}$ atoms, and a narrowing of the phonon gap lead to strong acoustic phonon scattering rates, which arises from the unique metavalent bonding in ${\mathrm{Li}\mathrm{Cu}}_{3}{\mathrm{Ti}\mathrm{S}}_{4}$. Our findings provide valuable insights into the strain-modulated anharmonic phonon dynamics and suggest promise for ${\mathrm{Li}\mathrm{Cu}}_{3}{\mathrm{Ti}\mathrm{Q}}_{4}$ as an intermediate-temperature thermoelectricity.