Antimony vibrations in skutterudites probed by ${}^{121}\mathrm{Sb}$ nuclear inelastic scattering

The specific lattice dynamic properties of antimony in the unfilled $\mathrm{Co}{\mathrm{Sb}}_3$ and filled $\mathrm{Eu}{\mathrm{Fe}}_4{\mathrm{Sb}}_{12}$ skutterudites have been determined by nuclear inelastic scattering at the ${}^{121}\mathrm{Sb}$ nuclear resonance energy of $37.1298\left(2\right)\mathrm{keV}$ with a $4.5\mathrm{meV}$ high-resolution backscattering sapphire monochromator. The Sb partial vibrational density of states (DOS) shows a maximum centered at 17 and $16\mathrm{meV}$ in $\mathrm{Co}{\mathrm{Sb}}_3$ and $\mathrm{Eu}{\mathrm{Fe}}_4{\mathrm{Sb}}_{12}$, respectively. The difference between the Sb DOSs of $\mathrm{Co}{\mathrm{Sb}}_3$ and $\mathrm{Eu}{\mathrm{Fe}}_4{\mathrm{Sb}}_{12}$ reveals that upon filling there is a transfer of 10% of the vibrational states toward lower energy. Further, a likely indication of the coupling between the guest and the host lattice in rattler systems is observed, a coupling that is required to reduce the lattice thermal conductivity.

Figure 1

Schematic view of the experiment, showing the location of the double-crystal Si(111) high-heat-load monochromator (HHLM), the high-resolution monochromator (HRM), which consists of a cooled, temperature-controlled, sapphire single crystal, the ${}^{121}\mathrm{Sb}$-containing sample S, and the Si avalanche photodiode x-ray detectors ${\mathrm{D}}_{\mathrm{NIS}}$ and ${\mathrm{D}}_{\mathrm{NFS}}$, used to collect the nuclear inelastic and forward scattering by the sample, respectively.

Figure 2

Temperature-energy dependence of the nuclear forward, open symbols, and nuclear inelastic, closed symbols, scattered intensity from $\mathrm{Co}{\mathrm{Sb}}_3$ (a) and $\mathrm{Eu}{\mathrm{Fe}}_4{\mathrm{Sb}}_{12}$ (b), with both samples at $25\mathrm{K}$. The lines are a guide for the eye. The dashed line in (b) is the calculated nuclear inelastic scattering spectrum with the Sb DOS in $\mathrm{La}{\mathrm{Fe}}_4{\mathrm{Sb}}_{12}$ (Ref. 7). The temperature $T_0=146.54\mathrm{K}$ of the sapphire crystal (see upper scale) corresponds to $E_0=37.1298\left(2\right)\mathrm{keV}$. The dashed arrows indicate the different shape at $\sim 7\mathrm{meV}$ (see text).

Figure 3

(a) Sb DOSs in $\mathrm{Co}{\mathrm{Sb}}_3$ and $\mathrm{Eu}{\mathrm{Fe}}_4{\mathrm{Sb}}_{12}$, and the calculated Sb DOS in $\mathrm{La}{\mathrm{Fe}}_4{\mathrm{Sb}}_{12}$ (Ref. 7), filled curve; (b) the DOS difference of $\mathrm{Eu}{\mathrm{Fe}}_4{\mathrm{Sb}}_{12}$ minus $\mathrm{Co}{\mathrm{Sb}}_3$; (c) the Eu DOS in $\mathrm{Eu}{\mathrm{Fe}}_4{\mathrm{Sb}}_{12}$ (Ref. 10) and the calculated La DOS in $\mathrm{La}{\mathrm{Fe}}_4{\mathrm{Sb}}_{12}$ (Ref. 7); calculations for $\mathrm{Eu}{\mathrm{Fe}}_4{\mathrm{Sb}}_{12}$ are not yet available. The calculated DOSs have been scaled to improve visibility. The arrows emphasize the Eu rattler peak and indicate the likely coupling contribution in the Sb DOS.

Figure 4

(a) Dispersion relation in reciprocal lattice units; (b) calculated element-specific DOSs, with a $0.5\mathrm{meV}$ resolution.