The band structure of Mg${}_2$Si${}_{1-x}$Sn${}_x$ solid solutions with 0.250 ⩽ $x$ ⩽ 0.875 is calculated using the first-principles pseudopotential method. It is found that the low-lying light and heavy conduction bands converge and the effective mass reaches a maximum value near $x$ $=$ 0.625. Using the semiclassical Boltzmann transport theory and relaxation-time approximation, we find that the system with $x$ $=$ 0.625 exhibits both higher Seebeck coefficient and higher electrical conductivity than other solid solutions at intermediate temperatures. By fitting first-principles total energy calculations, a modified Morse potential is constructed, which is used to predicate the lattice thermal conductivity via equilibrium molecular dynamics simulations. Due to relatively higher power factor and lower thermal conductivity, the Mg${}_2$Si${}_{0.375}$Sn${}_{0.625}$ is found to exhibit enhanced thermoelectric performance at 800 K, and additional Sb doping is considered in order to make a better comparison with experiment results.

• Received 13 April 2012

DOI:https://doi.org/10.1103/PhysRevB.85.205212