Density functional theory (DFT) calculations within the local density approximation (LDA) method were employed to investigate the electronic structure and tuning mechanisms of framework‐substituted Type‐I tin–based clathrates. The calculation reveals that Ga (or Al) preferentially occupies Wyckoff 6 c crystallographic sites, whereas the remaining framework‐substituted atoms reside at 16 i sites, significantly enhancing the material stability. For K 8 Ga 8 Sn 38 , we investigated two configurations involving a Ga–Ga‐bond‐free structure (i) and a Ga–Ga‐bond‐maximized variant (ii). Configuration (ii) is energetically disfavored because of the asymmetric bond strength distribution within the Ga‐centered tetrahedral sp 3 network. The structural effects of guest and framework substitution in the Rb 8 Al 8 Sn 38 clathrate were studied. K 2 Rb 6 Al 8 Sn 38 , formed by substituting K for Rb in dodecahedra, increased the bulk modulus B 0 to 46.092 GPa versus 43.369 GPa for Rb 8 Al 8 Sn 38 , indicating enhanced cage‐guest size matching and rigidity. Concurrent Al‒Sn bond strength recovery offset volume expansion. Conversely, Ga substitution yielding Rb 8 Ga 8 Sn 38 decreased B 0 to 40.955 GPa, revealing poorer size matching and increased strain at larger volumes. The nonmonotonic B 0 vs. volume behavior stems from dual effects, including framework bond strength and guest‐cage size matching. All the compounds are semiconductors, with intrinsic bandgaps decreasing as follows: 0.6247 eV (Rb 8 Ga 8 Sn 38 ) > 0.6019 eV (Rb 8 Al 8 Sn 38 ) > 0.5932 eV (K 2 Rb 6 Al 8 Sn 38 ). This reduction is attributed to Al‐ p orbital contributions lowering the conduction band minimum (CBM) and a sharp decrease in the K‐atom density of states (DOS) near the conduction band edge.
Xue et al. (Thu,) studied this question.