Interaction of acoustic and optical phonons in a soft-bonded Cu-Se framework of large unit cell minerals with anionic disorders

Abstract

In general, optical and acoustic phonons have different energy scaling and are separated by an energy gap. However, the two phonon branches can also interact and provide an inherently poor thermal conductivity in complex minerals with a large number of atoms per unit cell. For instance, the copper-chalcogenide based minerals with high crystalline anharmonicity are inherently poor thermal conductors. We have studied large unit cell ${\mathrm{Cu}}_{26}{\mathrm{Nb}}_{2}{\mathrm{Sn}}_{6}{\mathrm{Se}}_{32}, {\mathrm{Cu}}_{26}{\mathrm{Nb}}_{2}{\mathrm{Sn}}_{6}{\mathrm{Se}}_{31.5}$, and ${\mathrm{Cu}}_{26}{\mathrm{Nb}}_{2}{\mathrm{Sn}}_{6}{\mathrm{Se}}_{30}{\mathrm{Te}}_{2}$ synthetic minerals with a strategically tailored anionic disorder. These compounds have a $p$-type degenerate behavior with carrier concentration $(\ensuremath{\sim}2.7--\ensuremath{\sim}15.3)\ifmmode\times\else\texttimes\fi{}{10}^{20}\phantom{\rule{0.16em}{0ex}}\mathrm{c}{\mathrm{m}}^{\ensuremath{-}3}$, at 300 K and a very low lattice thermal conductivity, $(\ensuremath{\sim}0.76--\ensuremath{\sim}1.49)\phantom{\rule{0.16em}{0ex}}\mathrm{W}\phantom{\rule{0.16em}{0ex}}{\mathrm{m}}^{\ensuremath{-}1}\phantom{\rule{0.16em}{0ex}}{\mathrm{K}}^{\ensuremath{-}1}$ at $\ensuremath{\sim}625\phantom{\rule{0.16em}{0ex}}\mathrm{K}$. Here, the softening of Cu-Se bonds and hence the crystal framework play an important role for very poor thermal conductivity. The existence of two low frequency Raman active optical modes (at $\ensuremath{\sim}55$ and $72\phantom{\rule{0.16em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$) associated with soft Cu and Se atoms, three localized Einstein modes in specific heat, suggest a high scattering of acoustic and optical branches with very short phonon lifetime $(\ensuremath{\sim}0.3--0.6\phantom{\rule{0.16em}{0ex}}\mathrm{ps})$. The excess vibrational density of states at low energies with compressed and flat optical branches strongly hinders the heat transport. The involvement of the Te atom at Se sites results in a lowering of the acoustic phonon cutoff frequency and the softening of optical phonons, significantly. Overall, ${\mathrm{Cu}}_{26}{\mathrm{Nb}}_{2}{\mathrm{Sn}}_{6}{\mathrm{Se}}_{30}{\mathrm{Te}}_{2}$ has the lowest thermal conductivity at $\ensuremath{\sim}625\phantom{\rule{0.16em}{0ex}}\mathrm{K}$ and is a promising thermoelectric material because of robust acoustic-optical phonon scattering, very low sound velocity, and high crystalline anharmonicity.

Topics & Concepts