Lattice strain and band overlap of the thermoelectric composite Mg2Si1−xSnx

${\mathrm{Mg}}_{2}{\mathrm{Si}}_{1\text{\ensuremath{-}}x}{\mathrm{Sn}}_{x}$ solid solutions show enhanced thermoelectric performance when the Sn mole fraction $x$ is approximately $x=0.7$. This has been discussed in terms of complexity of the electronic structure arising from the crossover of two bottom conduction bands, but direct detailed understanding of the origins and the precise nature of this band convergence is limited. Here, we report first-principles calculations of the band edge changes analyzed by band unfolding and crystal orbital Hamilton population techniques. We find that strain is particularly important at this crossing. ${\mathrm{Mg}}_{2}\mathrm{Si}$ and ${\mathrm{Mg}}_{2}\mathrm{Sn}$ show opposite trends in the conduction band edge shifts leading to a band crossover at $x\ensuremath{\sim}0.625$. However, there are also important effects due to disorder. Transport calculations show that enhancement of the figure of merit $ZT$ value owes to the combined effects of lattice strain, band edge overlap, composition change, and disorder.