An ultralow lattice thermal conductivity of 0.14 W$cdot$ m$^{-1} cdot$ K$^{-1}$ along the $vec b$ axis of As$_2$Se$_3$ single crystals was obtained at 300 K by first-principles calculations involving the density functional theory and the resolution of the Boltzmann transport equation. This ultralow lattice thermal conductivity arises from the combination of two mechanisms: 1) a cascade-like fall of the low-lying optical modes, which results in avoided crossings of these with the acoustic modes, low sound velocities and increased scattering rates of the acoustic phonons; and 2) the repulsion between the lone-pair electrons of the As cations and the valence $p$ orbitals of the Se anions, which leads to an increase in the anharmonicity of the bonds. The physical origins of these mechanisms lie on the nature of the chemical bonding in the material and its strong anisotropy. These results, whose validity has been addressed by comparison with SnSe, for which excellent agreement between the theoretical predictions and the experiments is achieved, point out that As$_2$Se$_3$ could exhibit improved thermoelectric properties.
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