Thermoelectric properties of $n$-Mg$_{2}$(SiGe)$_{0.8}$Sn$_{0.2}$ solid solution

High values of the thermoelectric figure of merit ($ZT$ = 1.5) in Mg$_{2}$Si–Mg$_{2}$Sn solid solutions are caused by a low thermal conductivity and a complex band structure, which is optimal at the ratio of solid-solution components of 40% Mg$_2$Si and 60% Mg$_2$Sn. However, the presence of magnesium stannide in a high concentration impairs the mechanical properties and chemical stability of the material limiting its application at high temperatures. Magnesium silicide has a higher stability but a lower figure of merit. The figure of merit is much lower in Mg$_2$Si-rich solid solutions and amounts to $ZT$ $\sim$ 1. The possibility of increasing $ZT$ in the Mg$_{2}$(SiGe)$_{0.8}$Sn$_{0.2}$ solid solution with the additional inclusion of Mg$_2$Ge in small quantities is investigated here. Samples of Mg$_{2}$(SiGe)$_{0.8}$Sn$_{0.2}$ ($x<$ 0.03) solid solution are prepared by hot pressing. The temperature dependences of the coefficients of the thermoelectric power, electrical conductivity, and thermal conductivity are measured in the range of 300–800 K. An increase in the thermoelectric figure of merit to $ZT$ = 1.1 is shown at $T$ = 800 K in the Mg$_{2}$(SiGe)$_{0.8}$Sn$_{0.2}\langle\mathrm{Sb}\rangle$ solid solution.