Enhanced thermoelectric performance of Mg2Si1−xSnx codoped with Bi and Cr

Abstract

Magnesium silicides are favorable thermoelectric materials considering resource abundance and cost. Chromium (Cr) doping in magnesium silicides has not yet been explored. Using first-principles calculations, we have studied the stability of ${\mathrm{Mg}}_{2}\mathrm{Si}$ with chromium (1.85, 3.7, 5.55, and 6.25% Cr) and tin (12.5 and 50% Sn). Three ${\mathrm{Mg}}_{2}\mathrm{Si}$ compounds doped with Sn, (Sn + Bi), and (Sn + Bi + Cr) are used to explain doping effects on thermoelectric performance. Notably, Cr behaves nonmagnetically for $\ensuremath{\le}2%\phantom{\rule{0.28em}{0ex}}\mathrm{Cr}$, after which ferromagnetic ordering is favored ($\ensuremath{\le}12.96%$ Cr), despite its elemental antiferromagnetic state. With alloying of Sn (70.4%), ${\mathrm{Mg}}_{2}\mathrm{Si}$ remains an indirect-band-gap semiconductor, but adding small amounts of Bi (3.7%) increases the carrier concentration such that electrons occupy conduction bands, making it a degenerate semiconductor. ${\mathrm{Mg}}_{2}{\mathrm{Si}}_{0.296}{\mathrm{Sn}}_{0.666}{\mathrm{Bi}}_{0.037}$ is found to give the highest thermoelectric figure of merit (ZT) and power factor (PF) at 700 K, i.e., 1.75 and 7.04 $\text{mW}\phantom{\rule{4.pt}{0ex}}{\text{m}}^{\ensuremath{-}1}\phantom{\rule{0.16em}{0ex}}{\text{K}}^{\ensuremath{-}2}$, respectively. Adding small %Cr decreases ZT and PF to 0.78 and 4.33 $\text{mW}\phantom{\rule{4.pt}{0ex}}{\text{m}}^{\ensuremath{-}1}\phantom{\rule{0.16em}{0ex}}{\text{K}}^{\ensuremath{-}2}$, respectively. Such a degradation in thermoelectric (TE) performance is attributed to two factors: (i) uniform doping acting as an electron acceptor, decreasing conduction, and (ii) the loss of low-lying conduction band degeneracy with doping, decreasing the Seebeck coefficients. A study of configurations of Cr doping suggests that Cr has a tendency to form clusters inside the lattice, which play a crucial role in tuning the magnetic and TE performance of doped ${\mathrm{Mg}}_{2}\mathrm{Si}$ compounds.