Supplementary material

Fig. S1. XRD patterns for undoped, Sb-doped (2%) and Bi-doped (2%) Mg2Si, showing the full range of diffraction peaks. Fig.S2. Definition of parameters in the supercell of Mg2Si. "a" denotes the overall lattice length, "d" denotes the bond length between neighbors, and "𝑑𝑖𝑚𝑝" denotes the bond length between the impurity and its nearest neighbors. Red spheres represent Si atoms, gray spheres represent Mg atoms, and blue spheres represent impurity atoms. The crystal structure visualization was generated using VESTA. Fig. S3. Histogram of bond lengths "d." Black represents undoped, blue represents Sb- doped, and green represents Bi-doped. (a)-(c) 2×2×2 supercell, (d)-(f) 3×3×3 supercell.