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Vibrational and structural properties of the $R$Fe$_{4}$Sb$_{12}$ ($R=$Na, K, Ca, Sr, Ba) filled skutterudites

Vibrational and elastic properties of the $R$Fe$_{4}$Sb$_{12}$ skutterudites are investigated by, respectively, temperature $(T)$ dependent extended X-ray absorption fine structure (EXAFS) and pressure $(P)$ dependent x-ray diffraction (XRD) experiments. The Fe $K$-edge EXAFS experiments of the $R=$ K, Ca and Ba materials were performed in the $T$-interval $6<T<300$ K and XRD experiments of the $R=$ Na, K, Ca, Sr and Ba materials were performed in the $P$-interval $1\text{ atm }<P<16$ GPa. From EXAFS, we obtained the correlated Debye-Waller parameters that were thus analyzed to extract effective spring constants connected with the Fe-$Y$ (where $Y=$ either $R$, Fe or Sb) scattering paths. Our findings suggest that in the case of the light cations, $R=$ K or Ca, the $R$ atoms are relatively weakly coupled to the cage, in a scenario reminiscent to the Einstein oscillators. From the XRD experiments, we obtained the bulk modulus $B_{0}$ for all $R=$Na, K, Ca, Sr and Ba materials, with values ranging from $77$ GPa ($R=$ K) to $R=99$ GPa ($R=$ Ba) as well as the compressibility $β$ as a function of $P$. The trend in $β$ as a function of the $R$ filler is discussed and it is shown that it does not correlate with simple geometrical considerations but rather with the filler-cage bonding properties.