Filling Fraction Limit for Intrinsic Voids in Crystals: Doping in Skutterudites

The doping limit or the filling fraction limit (FFL) of various impurities for the intrinsic voids in the lattice of ${\mathrm{CoSb}}_3$ is studied by the density functional method. The FFL is shown to be determined not only by the interaction between the impurity and host atoms but also by the formation of secondary phases between the impurity atoms and one of the host atoms. The predicted FFLs for Ca, Sr, Ba, La, Ce, and Yb in ${\mathrm{CoSb}}_3$ are in excellent agreement with reported experimental data. A correlation between the FFL of an impurity atom and its valence state and electronegativity is discovered.