A novel crystallographic location of rattling atoms in filled Eu _x Co₄Sb₁₂ skutterudites prepared under high-pressure conditions

3.1 Structural characterization

Preliminary characterization of Eu _x Co₄Sb₁₂ was performed by laboratory XRD for some pellets ground into powder; a typical XRD pattern is shown in Figure 1a. The pattern corresponds to the skutterudite structure, defined in the space group I m 3 ‾ (No. 204). No impurities, such as Sb, were observed in the pattern.

Figure 1:

Rietveld plots from X-ray diffraction data: (a) Laboratory XRD pattern with Cu Kα radiation and (b) SXRD pattern for Eu _x Co₄Sb₁₂ at room temperature (x = 0.02(1)). The inset shows the quality of the fit in the high-angle region. Experimental points (red crosses), calculated profile (black line), difference (blue line), and Bragg reflections (green symbols).

The high angular resolution of SXRD data was essential to thoroughly investigate the structural features of Eu_0.5Co₄Sb₁₂ nominal composition. The crystal structure was refined in the skutterudite I m 3 ‾ model, where Sb atoms are located at 24g (0, y, z), Co at 8c (¼, ¼, ¼) and Eu was preliminary set at 2a (0, 0, 0) Wyckoff positions. An excellent fit to the 295 K pattern was reached, as illustrated in Figure 1b, with unit cell parameter a = 9.03648(2) Å. However, the refinement of the Eu occupancy factor at 2a sites invariably converged to a slightly negative value (f _occ = −0.017), indicating that the rattling atom was not located at this position. Difference Fourier maps from the unfilled skutterudite framework CoSb₃ and the experimental SXRD data, showed conspicuous peaks of positive density at 12d (x, 0, 0) sites, with x ∼ 0.25, as illustrated in Figure 2a. Two additional 2D Fourier difference plots are included at the Supplementary Information (SI) as Figure S1. A full refinement of the crystal structure including Eu at 12d yielded positive occupancy and displacement factors. The refined Eu content is much lower than the nominal stoichiometry, with total x = 0.02(1) for nominal x = 0.5. Similar average filling levels have been described elsewhere for La-filled skutterudites [7] or Y-filled specimens [16]. Also, a slight Sb deficiency is observed after the final run; the refined stoichiometry is Eu_0.02(1)Co₄Sb_11.95(1). Indeed, an even more defective Sb sublattice has been frequently observed in skutterudites prepared under high-pressure conditions [12], [13], [14]; e.g. for the unfilled specimen, a refined stoichiometry Co₄Sb_11.60(1) was determined [12]. The final structural parameters, including anisotropic displacement parameters for Co and Sb, and agreement factors for the final refinement, are included in Table 1. The difference with the nominal Eu content can be accounted for by the presence of tiny amounts of Eu₃Sb₂, EuO and other unidentified minor impurities in the SXRD pattern (unobservable in the laboratory XRD pattern, Figure 1a). We can speculate that there is a thermodynamic equilibrium that requires an excess of filler to achieve a certain filling fraction.

Figure 2:

Views of the skutterudite unit cell: (a) Difference Fourier map showing yellow regions with positive scattering density at 12d sites. (b) View of the skutterudite crystal structure, consisting of a framework of [CoSb₆] octahedra sharing vertices, with Eu atoms located in the large cages left in between. Eu are found to be statistically occupying 12d sites, conforming regular octahedra centered at 2a (0, 0, 0) positions.

Figure 2b displays a view of the Eu _x Co₄Sb₁₂ crystal structure, highlighting the framework of corner-sharing, heavily tilted [CoSb₆] octahedra. The Eu atoms were found statistically distributed at high multiplicity 12d sites, with a weak occupancy. This contrasts with the usually described filling of the 2a cages in skutterudites, in oversized cages where the filler elements are described to rattle, thus acting as a sink for phonons and, therefore, drastically reducing the lattice component of the thermal conductivity. In the present case, the Eu filler is also in this cage but it is found to be out of center, delocalized in an octahedral configuration within the cavity left in between each 8 [CoSb₆] octahedra. This configuration determines two types of Eu–Sb distances, at 1.71(1) and 3.10(1) Å. It is evident that the first distance is unrealistic, but considering the weak Eu occupancy and the Sb vacancies in the structure, we can accept that the Eu presence in a certain position is coupled to a Sb vacancy, and thus, supporting this arrangement.

3.2 Thermal evolution

The thermal evolution of the crystal structure was determined from temperature-dependent SXRD patterns collected at 473, 673, 873 and 1023 K. The skutterudite framework is preserved up to 873 K, exhibiting the expected thermal expansion. Eu is located at 12d sites at 473 and 673 K, but at 873 K the Eu occupancy fades down. This reduced filling fraction reveals a segregation of the rare-earth element from the skutterudite framework, and it indicates a thermally activated reorganization of the atomic structure at high temperature, revealing the metastable nature of this compound prepared under high-pressure. Table S1 at the Supplementary Information includes the main structural parameters above RT, and Figure S2 illustrates the quality of the fits to the SXRD patterns at these temperatures. Finally, at 1023 K, a total decomposition of the skutterudite structure is observed, to give a mixture of Sb and CoSb₂.

3.3 Debye model

Although the mean-square displacements (MSDs) of the Eu atoms were not properly derived from the Rietveld refinement, we have evaluated the lattice dynamics of Eu_0.02(1)Co₄Sb₁₂ by following the thermal dependence of the anisotropic displacement parameters u i j (in units of Ų) of Co and Sb atoms. The dynamic contribution to the MSDs can be described using the Debye model [24], as expressed below:

such that, θ D represents the Debye temperature, m is the atomic mass, d s 2 denotes the static disorder, T is the absolute temperature, and ( ℏ , k B ) maintain their usual meaning in physics. Besides, the components u i j were diagonalized to provide information on the displacements along the principal axes. The Co atoms are at 8c sites, which are more symmetric than sites 24g of Sb atoms. For such a reason, the tensor u i j of Co has two independent components u x and u y = u z , while for Sb the tensor u i j presents three independent components, namely u x , u y , and u z . From these values, the isotropic displacement parameters u i s o C o = ( u x + 2 u y ) / 3 and u i s o S b = ( u x + u y + u z ) / 3 were used to estimate the Debye temperature ( θ D ) of the Eu _x Co₄Sb₁₂ by averaging the isotropic displacements by the atomic masses of Co and Sb atoms. Then, the estimated value of θ D was 273(2) K, which is in good agreement with the previously reported values in literature for CoSb₃ [12].

The evaluation of the Debye temperature along diagonal elements of u i j can provide information on the vibrational properties and lattice dynamics more precisely than a simple estimation using the isotropic displacement parameters. Figure 3 displays the thermal evolution of the anisotropic displacements factors for Co and Sb atoms. For Co atoms, the Debye temperature from u x was θ D  = 359(2) K, while that value from u y = u z was θ D  = 402(2) K. It means that u x is a parallel vibration along the bond Co–Sb because this value agrees with the Einstein temperature estimated from EXAFS analyses ( θ E  = 345 K) [25]. For Sb atoms, the Debye temperatures from u x , u y , and u z were 208, 244, and 264 K, respectively. It denotes that u x and u y represent displacements along the bonds d 1 (short Sb–Sb bond) and d 2 (long Sb–Sb bond) of the [Sb₄] rings, since their Debye temperatures are in good agreement with the values also extracted from EXAFS data [25]. The lattice properties coming from the framework of corner-sharing [CoSb₆] octahedra seem not to be dramatically affected by the presence of Eu atoms at interstitial sites, maintaining their Debye energies almost unchanged as compared to the pristine CoSb₃.

3.4 Oftedal plots

As mentioned, the CoSb₃ skutterudite structure (Figure 2b) mainly consists of a framework of corner-sharing [CoSb₆] octahedra, so severely tilted that Sb atoms are at bonding distances in rectangular [Sb₄] rings (Figure 4a). Therefore, there are two main covalent interactions: one between Co and Sb atoms, in [CoSb₆] units, and the second one between every four Sb atoms, in the mentioned rings. These rings are characteristic of this type of structure [26], and the size and degree of distortion from the perfect square shape are determined by the y and z Sb positional parameters. The covalent interactions among pnictogen atoms have been analyzed in several works in terms of the electronic properties of the material, and this interaction is closely related to the band gap and valence band representation [19, 26].

Figure 3:

Temperature dependence of the diagonal elements of the anisotropic displacements u i j for (a) Co and (b) Sb atoms. The dotted lines are the best fits to the experimental data using the Debye model. The standard deviations are much smaller than the size of the symbols. Abbreviations: ε D = k B θ D is the Debye energy.

As a consequence of the framework symmetry, there are only three main parameters to specify the structure: the lattice parameter a , and y and z atomic positions of Sb, besides the filling fraction (FF) or occupancy of the filler M atom (x). Figure 4b displays the evolution of the lattice parameters depending on the filling fraction of the 2a positions. This plot includes precedent materials prepared under the same high-pressure conditions, containing La, Ce, Sr, K, and Yb as filler elements [12], [13], [14], [15], [16]. All of them have been investigated by SXRD. The labels indicate the refined occupation of the filler. The main trend is a linear behavior with the filling fraction. The present Eu_0.02(1)Co₄Sb₁₂ sample falls within this trend, slightly smaller in unit-cell parameter than Y_0.02Co₄Sb₁₂, with the same occupancy, perhaps due to the different position exhibited by the rattling element: 12d for Eu and 2a for Y [16].

Figure 4:

Features of the Eu _x Co₄Sb₁₂ structure: (a) [Sb₄] rings in the skutterudite structure, occurring because of the strong tilting of [CoSb₆] octahedra. (b) Evolution of the unit-cell parameter of the skutterudite against the filling fraction, for specimens previously synthesized under high-pressure conditions (taken from Ref. [16]), where the Eu sample falls among the slightly filled materials.

Figure 5a shows the Oftedal plot with different skutterudite compositions, prepared under high-pressure conditions. The Oftedal plot consists of a representation of the z versus y fractional positions of Sb within the crystal structure. The so-called Oftedal line with (y + z) = 0.5 corresponds to a perfectly square [Sb₄] ring. We observed that the y and z parameters, determined from SXRD data, increase with the filling fraction, as it has been also described for other skutterudite compounds [27]. Our Eu specimen roughly falls within the observed trend regarding y and z values. Figure 5b represents the experimental (y + z) parameters with respect to the filling fraction. At first glance, the (y + z) magnitude behaves as the lattice parameter; however, there are important deviations. There is a pronounced effectiveness in reducing the rectangular distortion of the [Sb₄] rings as the filling fraction increases. Previous studies on the contribution of an additional electronic band to carrier transport have shown an increasing valley degeneracy and improvements in the ratio of electrical conductivity and Seebeck coefficient [28]. These indicate a direct relation of the [Sb₄] ring structural parameters with the energy difference of conduction bands. Particularly, a high band degeneracy is predicted for Sr-filled CoSb₃ [29], exhibiting particularly good thermoelectric properties [16, 29]. Regarding Eu, its poor filling implies substantially distorted [Sb₄] rings, and poor thermoelectric behavior, as described below.

Figure 5:

Oftedal analysis, including other skutterudites: (a) Oftedal plot, including the Oftedal line (red line) for (y + z) = 0.5 and (b) (y + z) parameter against filling fraction (x or FF) for the differently filled skutterudites phases prepared under high-pressure. Single-filled skutterudite structural parameters of M _x Co₄Sb₁₂ (M = La, Ce, K, Sr, Yb) correspond to high-pressure samples studied from SXRD data [13, 14, 16]. Eu_0.02(1)Co₄Sb₁₂ roughly follows the observed trend.

3.5 Scanning electron microscopy (FE-SEM)

Grain boundary and morphology have been examined by FE-SEM to assess the compactness and homogeneity of the samples. Figure 6 illustrates two SEM images of Eu_0.02(1)Co₄Sb₁₂ sample, showing large grains above 5 μm in size, and a highly compact microstructure, as well-sintered pellets resulting from the high-pressure synthesis. Figure S3 illustrates more views of the microstructure of this sample and Figure S4 contains the results of an EDX study, yielding Eu:Co:Sb ratios similar to those expected.

Figure 6:

SEM micrographs of the as-grown pellets of Eu_0.02(1)Co₄Sb₁₂. (a) ×10,000 and (b) ×16,000 magnification.

3.6 Thermoelectric properties

The electrical transport properties of the Eu_0.02(1)Co₄Sb₁₂ are displayed in Figure 7a. The data of unfilled CoSb_3−δ , Ce_0.5- and La_0.5- filled skutterudites prepared under the same high-pressure conditions [12], [13], [14] are shown for the sake of comparison. We can notice that, surprisingly, the resistivity of Eu_0.02(1)Co₄Sb₁₂ at room temperature, ∼3 × 10⁻⁴ Ω m, is slightly higher than that of CoSb₃. However, the resistivity of the Eu-doped filled compound is closer to that of Ce_0.5Co₄Sb₁₂ as temperature increases, reaching a minimum of 5.2 × 10⁻⁵ Ω m at 750 K.

Figure 7:

Temperature dependence of (a) resistivity and (b) Seebeck coefficient of Eu_0.02(1)Co₄Sb₁₂. The additional compositions, in their nominal chemical formula, have been added for the sake of comparison, namely CoSb₃ and M_0.5Co₄Sb₁₂ (M = La, Ce).

The Seebeck coefficient is plotted in Figure 7b. Such a parameter always lies between 70 and 120 μV/K throughout the entire measured temperature range, similar to other filled skutterudites [14, 30–32]. The Seebeck coefficient for Eu_0.02(1)Co₄Sb₁₂ is always higher than that measured for the La-filled compound, but it is also remarkably lower than that value for the nominal composition Ce_0.5Co₄Sb₁₂.

The thermal conductivity of Eu_0.02(1)Co₄Sb₁₂ is shown in Figure 8a, together with data, for the sake of comparison, of similar skutterudites also synthesized under high-pressure [12], [13], [14]. The thermal conductivity of Eu-filled compound is lower at all temperatures than that of the unfilled skutterudite. It is worth noting that, at room temperature, its thermal conductivity is higher than that shown by the Ce- and La- filled skutterudites, which is probably due to the lower filling fraction reached by Eu in the CoSb₃ structure (∼0.02(1)). However, as temperature increases, the Eu_0.02(1)Co₄Sb₁₂ compound reaches the lowest thermal conductivity compared to the other compositions prepared by high-pressure synthesis, with a minimum value of 0.82 W m⁻¹ K⁻¹ from 723 up to 773 K. Moreover, these are extremely low compared to other single-filled CoSb₃ derivatives [14, 30, 31], and thus, suggests a stark phonon scattering enhancement due to the distinctive crystallographic position of Eu atoms at 12d sites coupled with Sb vacancies. In fact, Eu-filled CoSb₃ prepared by conventional methods still show lower lattice thermal conductivity at high temperature than other filled CoSb₃, slightly above that reported here [33].

Figure 8:

Temperature dependence of (a) total thermal conductivity and (b) its lattice and electronic contributions for Eu_0.02(1)Co₄Sb₁₂. Additional compositions, in their nominal chemical formulae, have been added for the sake of comparison, namely CoSb₃ and M_0.5Co₄Sb₁₂ (M = La, Ce).

The two different contributions to the thermal conductivity, the lattice and the electronic parts, are displayed in Figure 8b. We can see that they follow the same trend than the total thermal conductivity, reaching a minimum value at 773 K. It can also be noticed that, for the case of Eu_0.02(1)Co₄Sb₁₂, the electronic contribution is only relevant beyond 600 K, when the electrical resistivity of the compound is lower enough. Moreover, beyond this temperature it is when the Eu-filled skutterudite shows its highest thermoelectric figure of merit, ZT, reaching a value of ∼0.12 at 723 K (see Figure S5). This maximum is superior than that observed in the La_0.5Co₄Sb₁₂ nominal composition prepared under high pressure, owing to its lower resistivity with respect to that of the La-filled compound beyond 550 K.