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Electron and phonon transport in shandite-structured Ni$_3$Sn$_2$S$_2$

The shandite family of solids, with hexagonal structure and composition A3M2X2 (A = Ni,Co,Rh,Pd; M = Pb,In,Sn,Tl; X = S,Se), has attracted recent research attention due to promising applications as thermoelectric materials. Herein we discuss the electron and phonon transport properties of shandite-structured Ni3Sn2S2, based on a combination of density functional theory (DFT), Boltzmann transport theory, and experimental measurements. Ni3Sn2S2 exhibits a metallic and non-magnetic groundstate with Ni$^0$ oxidation state and very low charge on Sn and S atoms. Seebeck coefficients obtained from theoretical calculations are in excellent agreement with those measured experimentally between 100 and 600 K. From the calculation of the ratio $σ$/$τ$ between the electronic conductivity and relaxation time, and the experimental determination of electron conductivity, we extract the variation of the scattering rate (1/$τ$) with temperature between 300 and 600 K, which turns out to be almost linear, thus implying that the dominant electron scattering mechanism in this temperature range is via phonons. The electronic thermal conductivity, which deviates only slightly from the Wiedemann-Franz law, provides the main contribution to thermal transport. The small lattice contribution to the thermal conductivity is calculated from the phonon structure and third-order force constants, and is only ~2 Wm$^{-1}$K$^{-1}$ at 300 K (less than 10% of the total thermal conductivity), which is confirmed by experimental measurements. Overall, Ni$_3$Sn$_2$S$_2$ is a poor thermoelectric material (ZT~0.01 at 300 K), principally due to the low absolute value of the Seebeck coefficient. However, the understanding of its transport properties will be useful for the rationalization of the thermoelectric behavior of other, more promising members of the shandite family.