Intrinsic ultralow lattice thermal conductivity of the unfilled skutterudite ${\mathrm{FeSb}}_3$

It is generally accepted that unfilled skutterudites process high lattice thermal conductivity ${\kappa }_l$ that can be efficiently reduced upon filling. Here by using first-principles Boltzmann-Peierls transport calculations, we find pure skutterudite of ${\mathrm{FeSb}}_3$ with no filler in fact has an intrinsic ultralow ${\kappa }_l$ smaller than that of ${\mathrm{CoSb}}_3$ by one order of magnitude. The value is even smaller than those of most of the fully filled skutterudites. This finding means that with ${\mathrm{FeSb}}_3$ as a reference, filling does not necessarily lower ${\kappa }_l$. The ultralow ${\kappa }_l$ of ${\mathrm{FeSb}}_3$ is a consequence of the overall softening of phonon spectrum, especially the lowering in frequency of optical phonon branches associated with the weakly bonded ${\mathrm{Sb}}_4$ rings. They overlap more with heat-carrying acoustic phonons and significantly increase the phase space for three-phonon anharmonic scattering processes. This provides an alternative non-filling-related mechanism for lowering the ${\kappa }_l$ of skutterudites.

Figure 1

Calculated temperature dependence of ${\kappa }_l$ (in W/mK) of unfilled skutterudites (${\mathrm{FeSb}}_3, {\mathrm{CoSb}}_3$ [50]) and several fully filled skutterudites (${\mathrm{LaFe}}_4{\mathrm{Sb}}_{12}, {\mathrm{CeFe}}_4{\mathrm{Sb}}_{12}, {\mathrm{YbFe}}_4{\mathrm{Sb}}_{12}$ [34], ${\mathrm{BaFe}}_4{\mathrm{Sb}}_{12}$ [34], and ${\mathrm{BaCo}}_4{\mathrm{Sb}}_{12}$ [33]). The experimental ${\kappa }_l$ for ${\mathrm{CoSb}}_3$ (open symbols) are taken from Morelli et al. [51] (stars) and Caillat et al. [12] (squares). The inset shows crystal structures of unfilled and fully filled skutterudites.

Figure 2

Analysis of key factors that may affect ${\kappa }_l$ for ${\mathrm{FeSb}}_3, {\mathrm{CoSb}}_3$, and the filled skutterudites of $\mathrm{La}/{\mathrm{YbFe}}_4{\mathrm{Sb}}_{12}$: (a) heat capacity, (b) phonon velocity, (c) interatomic force constant, and (d) scattering phase space. In (b) the phonon velocity is calculated by averaging the group velocities of the long-wavelength (both transverse and longitudinal) acoustic phonons along different phonon momentum directions. In (c) the notation of $M^{n\text{th}}$ represents that the $n\mathrm{th}-\mathrm{order}$ IFCs of the compound $M$ is used to replace the original IFCs when calculating the room-temperature ${\kappa }_l$.

Figure 3

Calculated heat capacity as a function of temperature for ${\mathrm{FeSb}}_3, {\mathrm{CoSb}}_3, {\mathrm{LaFe}}_4{\mathrm{Sb}}_{12}$, and ${\mathrm{CeFe}}_4{\mathrm{Sb}}_{12}$. The available experimental data for ${\mathrm{CoSb}}_3$ [40] and ${\mathrm{LaFe}}_4{\mathrm{Sb}}_{12}$ [9] are shown for comparison. The agreement between our calculation and the experiments is good.

Figure 4

Calculated anharmonic scattering rates of ${\mathrm{FeSb}}_3$ (red circles), ${\mathrm{CoSb}}_3$ (green squares), ${\mathrm{LaFe}}_4{\mathrm{Sb}}_{12}$ (blue triangles), and ${\mathrm{YbFe}}_4{\mathrm{Sb}}_{12}$ (cyan diamonds) at 300 K. The normalized cumulative ${\kappa }_l$ as a function of $\omega$ is shown in the inset.

Figure 5

(a)–(c) Calculated phonon dispersion curves of ${\mathrm{FeSb}}_3, {\mathrm{CoSb}}_3$ and ${\mathrm{LaFe}}_4{\mathrm{Sb}}_{12}$. The size of circle represents the magnitude of Grüneisen parameter $\gamma$ for each mode; positive $\gamma$ is shown in blue, negative is in red. In (b) and (c) some phonon branches taken from ${\mathrm{FeSb}}_3$ (in orange) and ${\mathrm{YbFe}}_4{\mathrm{Sb}}_{12}$ (in cyan) are shown for comparison. For ${\mathrm{LaFe}}_4{\mathrm{Sb}}_{12}$ in (c), the available experimental data from inelastic neutral scattering measurements [52] are shown (with magenta circles) for comparison. (d) Eigenvector of the lowest optical mode at the $\mathrm{\Gamma }$ point for ${\mathrm{FeSb}}_3$. The ${\mathrm{Sb}}_4$ ring is indicated with red dashed lines. (e) The (projected) phonon density of states (PHDOS).

Figure 6

Contour plot in the (100) plane of charge density on the ${\mathrm{Sb}}_4$ ring [see Fig. 5] in (a) ${\mathrm{FeSb}}_3$, (b) ${\mathrm{CoSb}}_3$, and (c) ${\mathrm{LaFe}}_4{\mathrm{Sb}}_{12}$. The contour range is from 0 (blue) to 0.05 (red) $\mathrm{electron}/{\AA }^3$.

Figure 7

The normalized cumulative ${\kappa }_l$ of ${\mathrm{FeSb}}_3$ as a function of the phonon mean free path $l_{\mathrm{ph}}$ at 300 K. The maximum phonon $l_{\mathrm{ph}}$ among all the modes that conduct heat efficiently, which corresponds to the onset point of the cumulative ${\kappa }_l$ approaching 1.0, is indicated.