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