Mechanism for anisotropic diffusion of liquid-like Cu atoms in hexagonal β−Cu2S

Abstract

${\mathrm{Cu}}_{2}\mathrm{S}$ in its high-temperature phases is a promising candidate for thermoelectric materials with the combination of a solid S lattice and liquidlike Cu atoms in the context of the so-called phonon-liquid electron-crystal (PLEC) mechanism. The atomic dynamics associated with the high Cu mobility is a critical component in our understanding of the low thermal conductivity in these materials. Among various possible PLEC compounds that have been studied experimentally, hexagonal $\ensuremath{\beta}\ensuremath{-}{\mathrm{Cu}}_{2}\mathrm{S}$ is a unique case that exhibits anisotropic diffusion channels for Cu atoms in the presence of crystalline S layers. To unveil the diffusion mechanism for such liquidlike Cu atoms, we present first-principles molecular dynamics simulations over 50 ps for hexagonal ${\mathrm{Cu}}_{2}\mathrm{S}$ at 450 K. Quantitative analysis of the atomic radial distributions, mean-square displacements, velocity autocorrelations, and atomic trajectories is reported and confirms the liquid-solid hybrid features. Our simulations reveal the preference of threefold triangular sites by Cu atoms in the S lattice. The triangular sites in the interlayer region do not bind Cu atoms strongly, allowing them to diffuse in the horizontal direction between S layers like a mobile liquid with a calculated diffusion coefficient $\ensuremath{\sim}5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}\phantom{\rule{4pt}{0ex}}{\mathrm{cm}}^{2}$/s. The corresponding atomic trajectories have a wide spread and cannot be described by the Chudley-Elliott jump diffusion model. In contrast, Cu atoms are more strongly confined at the triangular sites within the S planes, and Cu diffusion takes place only when the atom hops out of the S layer and enters the interlayer region. This yields a 50% smaller diffusion coefficient in the vertical direction. The anisotropic diffusion channels for liquidlike Cu atoms in hexagonal $\ensuremath{\beta}\ensuremath{-}{\mathrm{Cu}}_{2}\mathrm{S}$ may provide an additional degree of freedom in designing promising systems for future energy applications.