The crystal structure of a polycrystalline sample of higher manganese silicide (HMS) has been determined by means of the $\left(3+1\right)$-dimensional superspace group approach. The structural parameters were refined with a superspace group of $I{4}_1/amd\left(00\gamma \right)00ss$ using powder neutron-diffraction data collected at 295 K. The compound belongs to a composite crystal family consisting of [Mn] and [Si] subsystems, with an irrational $c$-axis ratio (misfit parameter) of $\gamma =c_{\text{Mn}}/c_{\text{Si}}\sim 1.74$. Significant in-plane rotational modulation was revealed in the “chimney”-[Si] subsystem, while positional modulation in the “ladder”-[Mn] subsystem was only realized along $c_{\text{Mn}}$. The electronic structure of the sample was calculated on the basis of a commensurate approximation of the modulated structure using the full potential linearized augmented plane-wave method. The obtained band gap of $E_g\sim 0.6\text{eV}$ agreed well with the experimentally observed one. It appears that the band gap and density of states of the HMS samples depend on the positional modulation of the Si atoms. The various controversial formulas (for example, ${\text{Mn}}_4{\text{Si}}_7$, ${\text{Mn}}_{11}{\text{Si}}_{19}$, and so on) of the HMS phases reported thus far can be regarded as commensurate cases of a series of incommensurate ${\text{MnSi}}_{\gamma }$ phases in which the $\gamma$ value ranges from $\sim 1.70$ to 1.75.

Mg₂Sn is a potential thermoelectric (TE) material that can directly convert waste heat into electricity. In this study, Mg₂Sn single-crystal ingots are prepared by melting under an Ar atmosphere. The prepared ingots contain Mg vacancies (V_Mg) as point defects, which results in the formation of two regions: an Mg₂Sn single-crystal region without V_Mg (denoted as the single-crystal region) and a region containing V_Mg (denoted as the V_Mg region). The V_Mg region is embedded in the matrix of the single-crystal region. The interface between the V_Mg region and the single-crystal region is semi-coherent, which does not prevent electron carrier conduction but does increase phonon scattering. Furthermore, electron carrier concentration depends on the fraction of V_Mg, reflecting the acceptor characteristics of V_Mg. The maximum figure of merit zT_max of 1.4(1) × 10⁻² is realised for the Mg₂Sn single-crystal ingot by introducing V_Mg. These results demonstrate that the TE properties of Mg₂Sn can be optimised via point-defect engineering.