Abstract
The filling fraction limits (FFLs) of various impurities for the intrinsic voids in the lattice of $\mathrm{Co}{\mathrm{Sb}}_{3}$ are studied by combining the density functional method and thermodynamic analysis. The FFL for the voids is shown to be determined by both the interaction between the impurity and the host atoms and the secondary phase formation ability of the impurity atoms with one of the host atoms. The FFLs predicted for impurities Ca, Sr, Ba, La, Ce, and Yb in skutterudite $\mathrm{Co}{\mathrm{Sb}}_{3}$ agree very well with the experimental values. Several models are proposed to explain the various formation energies quantitatively, which unveil the physics behind the FFLs. The correlation between various energies and chemical bonding, lattice strain, and the effective charge state of impurities is investigated systematically. A simple selection rule for forming stable filled skutterudites is discovered, and it agrees with the experimental observations.
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