Ce Filling Limit and Its Influence on Thermoelectric Performance of Fe₃CoSb₁₂-Based Skutterudite Grown by a Temperature Gradient Zone Melting Method

Abstract

CoSb₃-based skutterudite is a promising mid-temperature thermoelectric material. However, the high lattice thermal conductivity limits its further application. Filling is one of the most effective methods to reduce the lattice thermal conductivity. In this study, we investigate the Ce filling limit and its influence on thermoelectric properties of p-type Fe₃CoSb₁₂-based skutterudites grown by a temperature gradient zone melting (TGZM) method. Crystal structure and composition characterization suggests that a maximum filling fraction of Ce reaches 0.73 in a composition of Ce_0.73Fe_2.73Co_1.18Sb₁₂ prepared by the TGZM method. The Ce filling reduces the carrier concentration to 1.03 × 10²⁰ cm⁻³ in the Ce_1.25Fe₃CoSb₁₂, leading to an increased Seebeck coefficient. Density functional theory (DFT) calculation indicates that the Ce-filling introduces an impurity level near the Fermi level. Moreover, the rattling effect of the Ce fillers strengthens the short-wavelength phonon scattering and reduces the lattice thermal conductivity to 0.91 W m⁻¹ K⁻¹. These effects induce a maximum Seebeck coefficient of 168 μV K⁻¹ and a lowest κ of 1.52 W m⁻¹ K⁻¹ at 693 K in the Ce_1.25Fe₃CoSb₁₂, leading to a peak zT value of 0.65, which is 9 times higher than that of the unfilled Fe₃CoSb₁₂.

1. Introduction

With the consumption of traditional fossil fuels and the aggravation of environment pollution, exploring new and effective energy utilization techniques has experienced increasing significance [1,2,3]. Thermoelectric technology, enabling the direct energy conversion between heat and electricity, has provided a promising and eco-friendly energy solution [4,5,6]. The thermoelectric performance is fundamentally characterized by the material dimensionless figure-of-merit (zT), defined as zT = S²σT/κ, where S, σ, κ and T are the Seebeck coefficient, electrical conductivity, thermal conductivity (comprised of electronic contribution κ_e and lattice contribution κ_l) and temperature in Kelvin, respectively [7,8,9]. High power factor (S²σ) and low κ are necessary for high zT [8,9]. S, σ, and κ_e are related to each other as a function of other fundamental parameters, such as carrier concentration (n) [10,11,12]. These fundamental parameters need to be optimized. Typically, the n of thermoelectric materials can be optimized by valence electron counts engineering [13,14], modulation doping [15], and band gap engineering [16]. Other than the interrelated parameters, reducing κ_l can achieve a low κ and high zT [17]. The reduced κ_l can be achieved by introducing additional structure defects, such as point defects [18], dense grain boundaries [19], and nanoprecipitates [20,21] for strengthening phonon scattering.

Among thermoelectric materials, skutterudites, especially CoSb₃-based skutterudites, are promising application prospect in the field of mid-temperature power generation [22,23,24]. Binary CoSb₃ is an intermetallic compound formed by a peritectic reaction [25]. CoSb₃ is a body-centered cubic cage-like crystal structure (Im-3 space group) with two void positions at the 2a sites (0, 0, 0) and (1/2, 1/2, 1/2) in the unit cell [26,27]. Intrinsic CoSb₃ is a p-type semiconductor with high S and high carrier mobility (µ) [28]. However, the strong Co-Sb covalent bonding induces high κ_l (~7.5 W m⁻¹ K⁻¹ at room temperature) of intrinsic CoSb₃, limiting its thermoelectric performance [29,30].

To reduce the κ_l of intrinsic CoSb₃, filling the void position at the 2a site with small atom can tune CoSb₃ into filled-CoSb₃ (R_xCo₄Sb₁₂, R is the filling elements and x is the filling fraction), which possesses a feature of phonon glass and electron crystal (PGEC) [31]. The fillers are loosely bounded and rattle near the equilibrium positions and significantly scatter the low-frequency phonons, leading to decreased κ_l and improved zT [32,33]. The fillers can be rare-earth atoms [18,34], alkaline-earth atoms [35], alkaline metals atoms [36]. Pei et al. [36] found that n-type Na_0.48Co₄Sb₁₂ had a reduced room-temperature κ_l of 3.5 W m⁻¹ K⁻¹ in accordance with a peak zT of 1.25. Alkaline-earth Ba can be filled into the void position at the 2a site of CoSb₃ to form n-type filled-CoSb₃ and approach a decreased κ_l of 0.73 W m⁻¹ K⁻¹ and a peak zT of ~1.0 in Ba_0.51CO₄Sb₁₂ [35]. Yb is another utilized rare-earth filler since the relatively high atomic mass and small ionic radius [18,37], which can lead to a low κ_l of 0.62 W m⁻¹ K⁻¹ in n-type Yb_0.47Co₄Sb₁₂ [38]. However, rare-earth Ce has a low filling fraction in CoSb₃ comparing with Yb. Morelli et al. [39] prepared n-type Ce-filled CoSb₃ by arc melting and found a low filling fraction of ~0.1. Even though with a low Ce filling fraction, the κ_l was strongly depressed and a low κ_l of ~4 W m⁻¹ K⁻¹ was obtained, which is only half of the unfilled CoSb₃. To improve the Ce filling fraction in undoped CoSb₃, Tang et al. [40] used phase diagram method to increase this value up to 0.2. Due to the increased filling fraction, a further reduced κ_l of ~2 W m⁻¹ K⁻¹ and a zT value of 1.3 at 850 K were obtained in n-type Ce_0.14Co₄Sb₁₂ prepared by melting-quenching-annealed-sintering. Besides, the thin film CoSb₃ sample prepared by deposition experienced increased Ce-filling fraction. Smalley et al. [41] reported a high Ce-filling fraction of ~0.55 in deposited CoSb₃ film.

Although heavy filling in the void position remarkably reduces the κ_l of CoSb₃-based thermoelectric materials, heavily filled CoSb₃-based materials are generally n-type semiconductors because the fillers function as electron donors [20,34,41]. In term of the assembly of thermoelectric devices, both p-type and n-type materials are required. Hence, p-type CoSb₃-based thermoelectric materials are necessary. To achieve low κ_l of p-type CoSb₃-based thermoelectric materials, Fe has been partially used to substitute Co [6,18,40], behaving as the electron acceptor to tune into p-type. Particularly, after Fe substitution at the Co site, CaFe_3.5Co_0.5Sb₁₂ has a high S²σ of 33 μW cm⁻¹ K⁻² with a positive S of 170 μV K⁻¹ and a low κ_l of ~0.9 W m⁻¹ K⁻¹ at 773 K [42]. Furthermore, charge-compensational doping by the substitution at Co or Sb sites has been widely applied to increase the filling faction of Ce in bulk CoSb₃-based skutterudites, which can simultaneously tune n-type CoSb₃ skutterudites into p-type ones [43,44]. Tanahashi et al. [45] found a Ce filling fraction of ~0.9 in p-type CoSb₃-based skutterudites with the nominal composition of CeFe₃CoSb₁₂, which is prepared by gas-phase atomization and sintering and approached a zT of 0.63 at 700 K. Chen et al. [46] reported a p-type Ce_0.95Fe₃CoSb_12.1 grown by scanning laser melting method combined with spark plasma sintering and achieved the Ce filling fraction of 0.85 and the zT of ~0.79 at 750 K.

As suggested in Figure 1a–f, crystal structures of the unfilled and Ce-filled Fe₃CoSb₁₂ and corresponding density functional theory (DFT)-calculated band structures and density of states (DOS) were firstly investigated. As can be seen, Ce-filling introduces an impurity level near the Fermi energy (E_F), which is mainly contributed by the f orbital of Ce atom. Besides, Ce-filling also increases the slope of DOS near E_F and correspondingly contributes to increased S [47,48]. Additionally, filled CoSb₃-based thermoelectric materials can be fabricated by various methods, such as traditional melting-quenching-annealing-sintering [49], melt-spinning combined with spark plasma sintering technique (MS-SPS) [50], high-energy ball-milling combined with hot pressing (BM-HP) technique [51], and temperature gradient zone melting (TGZM) method [52,53]. Among them, TGZM is a novel material preparation method, which can synthesize CoSb₃-based skutterudites with faster speed and higher purity by avoiding the complex peritectic solidification process. Effects of Ce fillers and its filling fraction in TGZM-prepared Fe₃CoSb₁₂ might be different from that prepared by other methods. In this study, we employed the novel TGZM method to investigate the influence and filling fraction of Ce in Fe₃CoSb₁₂. A series of Ce-filled p-type Ce_xFe₃CoSb₁₂ (x = 0 to 1.5) samples were prepared. We found that the maximum filling level of Ce is 0.73 in the TGZM-prepared Ce_1.25Fe₃CoSb₁₂ with a measured composition of Ce_0.73Fe_2.73Co_1.18Sb₁₂. The synergistic effect on Fe substitution at the Co and Ce-filling result in reduced n_H to 1.03 × 10²⁰ cm⁻³ in Ce_1.25Fe₃CoSb₁₂. A low κ_l of 0.91 W m⁻¹ K⁻¹ at 693 K can be obtained in the Ce_1.25Fe₃CoSb₁₂, significantly contributing to an increased zT of 0.65 at 693 K.

2. Materials and Methods

2.1. Samples Preparation

Initial ingots of (Fe₃Co)-95 at. % Sb filled with x at. % Ce (x = 0, 0.25, 0.5, 0.75, 1, 1.25, 1.5) were prepared by induction melting at 1473 K for 30 min in a vacuum induction furnace (Xi’an, China) (~10⁻³Pa) followed by a furnace cooling. Elements Fe (99.95 at. %), Co (99.95 at. %), Sb (99.995 at. %), and Ce (99.9%), purchased from CNBM (Chengdu, China) Optoelectronic Materials Com., Ltd., were properly weighed as raw materials according to the nominal compositions. Extra Sb was added to obtain the samples of nominal composition Ce_xFe₃CoSb₁₂ after the TGZM process. Besides, extra Ce was introduced to compensate the Ce loss during TGZM process. The as-cast ingots were cut into cylinder samples with a diameter of 12.8 mm, and the oxide layer on the surface was cleaned before being put into a high-purity alumina tube with an inner diameter of 13 mm to execute the TGZM process, which was described in detail in previous reports [54,55]. The TGZM process was then conducted in a homemade directional solidification furnace of a thermal stabilization time of 48 h with an estimated temperature gradient of 40 K/mm. The TGZM-grown samples were obtained from the mushy zone formed during the TGZM process. The obtained samples were cleaned, polished, and carried out microstructure characterization and performance tests. Samples throughout the manuscript are described as their nominal compositions after the TGZM process.

2.2. Microstructure Characterization

The crystal structures of as-fabricated samples were determined by powder X-ray diffraction (XRD-7000, Shimadzu, Japan) with Cu-K_α radiation. The lattice parameters were obtained by Rietveld analysis. Scanning electron microscopy (SEM, Verios G4, FEI, equipped with EDS, Hillsboro, OR, USA) was used to acquire the morphologies of the sample’s surface and a Double Cs Corrector Transmission Electron Microscope (Cs-TEM, Themis Z, FEI, Hillsboro, OR, USA) was used to characterize their microstructure and chemical features. The actual chemical content was obtained by taking the average of fifteen different positions of each sample. Electron backscattered diffraction (EBSD, Thermo QuasOr type, Waltham, MA, USA) attached to FEI Helios G4 CX type SEM (Hillsboro, OR, USA)was used to determine the crystal orientation relationship.

2.3. Properties Measurements

The samples with 12.7 mm in diameter and 1.5 mm in thickness were used to measure their thermoelectric properties from 303 K to 813 K. In our measurements, σ and S were measured simultaneously using the LSR-3 system (Linseis, Zelb, Bavaria, Germany) under the helium atmosphere. κ was calculated by κ = D·C_P·ρ, where D is the thermal diffusivity measured by LFA-1000 (Linseis, Zelb, Bavaria, Germany), C_P the specific heat obtained by DSC (STA-449C, Netzsch, Germany), and ρ the density obtained by the Archimedes method. The Hall coefficient (R_H), measured on the PPMS system (CFMS-14T, London, UK) with a magnetic field of ±2T, was used to calculate the room-temperature Hall carrier concentration (n_H), determined by the formula [18]: n_H = 1/eR_H, where e represents the electron charge.

2.4. Density Functional Theory (DFT) Calculations

The physical properties of Fe₃CoSb₁₂, CeFe₃CoSb₁₂ were calculated using the Cambridge Serial Total Energy Package (CASTEP) [56]. The exchange-correlation interactions were described using the generalized gradient approximation (GGA) with the Perdew-Burke-Ernzerhof (PBE) type [57]. The plane wave cutoff energy was 450 eV for geometry optimization, band structures, and density of states calculations. The Monkhorst-Pack grid parameters were set to 8 × 8 × 8 (34 Irreducible k-points) for calculations. The Convergence tolerances were set to 1.0 × 10⁻⁵ eV/atom, 0.03 eV/Å, 0.05 GPa and 0.001 Å for energy, maximum force, maximum stress and maximum displacement, respectively.

3. Results and Discussion

3.1. Microstructure and Phase Composition

To understand crystal structures of the as-prepared Ce_xFe₃CoSb₁₂ (x = 0 to 1.5), we firstly investigated powder X-ray diffraction (XRD) patterns and the results are shown in Figure 2a. Main diffraction peaks of samples can be identified as the body-centered cubic CoSb₃ with a lattice parameter a of 9.034 Å and a space group of Im-3 (JCPDS 19-0336). Due to the characteristic of eutectic reaction, a small number of Sb impurities are observed. Figure 2b plots the corresponding a of the as-prepared Ce_xFe₃CoSb₁₂ (x = 0 to 1.5). The calculated a increases with increasing the Ce-filling content and stabilizes at the x of 1.25. The increased a should be attributed to Ce-filling induced lattice expansion. TEM investigations were carried out to further understand the crystal structure of the as-fabricated Ce_xFe₃CoSb₁₂. Figure 2c is an atomic-resolution TEM high-angle annular dark-field (HAADF) image of CeFe₃CoSb₁₂. The inset of Figure 2c is superimposed a 2 × 2 × 2 supper cell model for the CeFe₃CoSb₁₂ along the [100] direction, well-matched with the observed lattice. Figure 2d is a selected area electron diffraction (SAED) pattern and can be indexed along the [100] zone-axis. Figure 2e presents the corresponding inverse Fast Fourier transform (IFFT) image along with the (011) planes. The observed d spacing between (011) planes is ~6.64 Å, which is larger than that of CoSb₃ (~6.39 Å). Besides, no obvious lattice distortion can be observed from Figure 2e, indicating that the as-fabricated samples have a high crystallinity. Figure 2f–h show the EBSD inverse pole figure (IPF) maps of the Ce_1.25Fe₃CoSb₁₂. As can be seen, no obvious texture information can be observed, indicating the isotropic thermoelectric performance of the as-fabricated Ce_xFe₃CoSb₁₂.

To understand the composition of the as-fabricated Ce_xFe₃CoSb₁₂, we conducted SEM image and the corresponding EDS maps of the Ce_1.25Fe₃CoSb₁₂ and the results are shown in Figure 3a–e. As can be seen, Fe, Co, Sb, and Ce are evenly distributed in the as-fabricated Ce_1.25Fe₃CoSb₁₂. A typical high-resolution TEM (HRTEM) HAADF image of the CeFe₃CoSb₁₂ is shown in Figure 3f. Figure 3g–i are the corresponding elemental maps in atomic scale. Figure 3j is a magnified overlap of elemental maps where the dark green balls represent Ce fillers. As can be seen, Ce filler sits at the 2a sites in the cage among the Sb-icosahedron (pink ball).

Figure 4a shows typical EDS spectra of the Ce_xFe₃CoSb₁₂. All samples are composed of Ce, Fe, Co, and Sb without other impurity elements. Figure 4b shows the average atomic ratios of Fe, Co, Sb, and Ce elements in each sample based on the statistic EDS results. As can be seen, the Ce-filling level in the samples increases at first and then tends to be stabilized at the x of 1.25, which is consistent with the peak shift from XRD. Figure 4c compares the Ce-filling fraction of Fe-doped CoSb₃ prepared by different methods. The Ce filling fraction varies with the preparation method and Fe/Co ratio. The Fe/Co ratio in the actual composition of the samples shown in the red dotted box in Figure 4c is close to ~2.5. Under the similar Fe/Co ratio, a relative high filling fraction of 0.73 is achieved in a composition of Ce_0.73Fe_2.73Co_1.18Sb₁₂ prepared by the TGZM method in this study. Figure 4d shows the TEM-EDS spectrum and maps of the CeFe₃CoSb₁₂. As can be seen, Fe, Co, Sb, and Ce elements are homogeneously distributed on a micro-scale, indicating successful Fe substitution at the Co site and Ce-filling.

3.2. Thermoelectric Transport Properties

To understand the thermoelectric properties of the as-fabricated Ce_xFe₃CoSb₁₂ (x = 0 to 1.5), σ, S, S²σ, and κ were measured at the temperature range between 303 and 813 K. Figure 5a depicts temperature-dependent σ of the Ce_xFe₃CoSb₁₂. The Fe₃CoSb₁₂ has a higher σ (1302 S cm⁻¹) comparing with the Ce-filled samples in the entire measured temperature. With increasing the Ce-filling level, the σ of the Ce_xFe₃CoSb₁₂ decreases from 1302 S cm⁻¹ of the Fe₃CoSb₁₂ to 638 S cm⁻¹ of the Ce_1.25Fe₃CoSb₁₂ at 303 K. The slight increase of σ from x = 1.25 to 1.5 might be attributed to the slightly increased Sb content (as evidenced by the XRD peak intensity in Figure 2a). Besides, the nearly linear decrease of σ with increasing the temperature indicates that the as-fabricated Ce_xFe₃CoSb₁₂ is a degenerated semiconductor. With increasing the Ce content, S increases from 62 μV K⁻¹ of the Fe₃CoSb₁₂ to 117 μV K⁻¹ of the Ce_1.25Fe₃CoSb₁₂ at 303 K (Figure 5b). The maximum S value of 168 μV K⁻¹ at 693 K can be obtained in the Ce_1.25Fe₃CoSb₁₂. The positive S indicates that the Ce_xFe₃CoSb₁₂ is p-type, which is consistent with the calculation of the band structures. A classic single parabolic band (SPB) model was used to evaluate the effective mass m* as described by Equations (1)–(4) [18,60]:

$$S=\pm \frac{k_B}{e}\left(\frac{2F_1\left(\eta \right)}{F_0\left(\eta \right)}-\eta \right)$$

(1)

$$m^{*}=\frac{h^2}{2k_{B}T}\left[\frac{n{r}_H}{4\pi F_{1/2}\left(\eta \right)}\right]$$

(2)

$$r_H=\frac{3}{2}\frac{F_{1/2}\left(\eta \right)F_{-1/2}\left(\eta \right)}{2F_0^2\left(\eta \right)}$$

(3)

$$F_n\left(\eta \right)={\displaystyle {\int }_0^{\infty }\frac{x^n}{1+e^{x-\eta }}}\mathrm{d}x$$

(4)

where e is the electron charge, η the reduced Fermi energy, η = E_F/k_BT, F_n(η) the Fermi integral and r_H the Hall factor. Figure 5c shows the Pisarenko plot of Fe₃CoSb₁₂ with the measured room-temperature n_H and corresponding S of Ce-filled Fe₃CoSb₁₂ samples. With increasing Ce-filling level, the experimental S values corresponding to the n_H deviates from the Pisarenko plot to a higher level, indicating that Ce-filling led to an increase of the m*. This should be attributed to the increased DOS near the edge of the band structure (Figure 1e,f) induced by Ce-filling. The maximum S²σ (Figure 5d) significantly increases from 6.7 μW cm⁻¹ K⁻² of the Fe₃CoSb₁₂ to 14.4 μW cm⁻¹ K⁻² of the Ce_1.25Fe₃CoSb₁₂ at 693 K.

Figure 5e plots temperature-dependent κ of the as-fabricated Ce_xFe₃CoSb₁₂ (x = 0 to 1.5). With increasing the Ce-filling level, the κ gradually decreases and approaches 1.52 W m⁻¹ K⁻¹ of Ce_1.25Fe₃CoSb₁₂ at 693 K. The κ_e can be calculated as κ_e = LσT (Figure 5f), where L is the Lorenz number calculated based on SPB model. With increasing the Ce-filling level, the κ_e significantly reduces due to reduced σ. Figure 5g presents temperature-dependent κ_l, calculated by κ-κ_e. The κ_l of the Ce-filled Fe₃CoSb₁₂ is much lower than that of the unfilled Fe₃CoSb₁₂. The k_l reduces with increasing the Ce-filling level and approaches a lowest κ_l of 0.91 W m⁻¹ K⁻¹ at 693 K in the Ce_1.25Fe₃CoSb₁₂. This should be primarily attributed to the rattling effect for strengthening short-wavelength phonon scattering, induced by Ce-filling [64]. Figure 5h displays temperature-dependent zT of the as-fabricated Ce_xFe₃CoSb₁₂ (x = 0 to 1.5). Benefitting from the enhanced S²σ and significantly reduced k, a peak zT value of 0.65 can be achieved in the Ce_1.25Fe₃CoSb₁₂ at 693 K, which is 9 times higher than that of the unfilled Fe₃CoSb₁₂. Figure 5i compares the room-temperature κ of nominal Ce_1.25Fe₃CoSb₁₂ in this study prepared by TGZM with the reported κ of p-type Ce-filled and Fe-doped CoSb₃ prepared by other methods. As can be seen, a relatively lower κ is obtained in TGZM prepared Ce_1.25Fe₃CoSb₁₂, which is due to the higher Ce filling fraction with an optimized Fe/Co ratio. Besides, the maximum zT values of different Ce-filled and Fe-doped CoSb₃ prepared by various methods are compared and shown in Figure S1 of the Supplementary Material, indicating a higher zT value can be obtained by optimizing Ce-filling fraction and Fe/Co ratio.

4. Conclusions

In this study, under the guidance of the DFT calculation, where Ce-filling can introduce an impurity level near the E_F and increase the thermoelectric performance of the Fe₃CoSb₁₂, we have designed and prepared the p-type Ce_xFe₃CoSb₁₂ (x = 0 to 1.5) by a facile TGZM method. The Ce-filling limit in TGZM-prepared Fe₃CoSb₁₂ was found to be 0.73 with a measured composition of Ce_0.73Fe_2.73Co_1.18Sb₁₂. The filling limit is approached at the nominal composition of Ce_1.25Fe₃CoSb₁₂. Under the synergistic effect, Fe substitution at the Co site and Ce-filling, an optimal n_H of 1.03 × 10²⁰ cm⁻³ is approached. The high S of 168 μV K⁻¹ at 693 K due to the increase of the Ce filling level induces a high S²σ of 14.4 μW cm⁻¹ K⁻² at 693 K in the Ce_1.25Fe₃CoSb₁₂, which is increased by 100% comparing with that of the Fe₃CoSb₁₂. The rattling effect of Ce fillers strongly strengthens phonon scattering, leading to reduced κ_l as low as 0.91 W m⁻¹ K⁻¹ at 693 K in the Ce_1.25Fe₃CoSb₁₂. Benefiting from the low κ of 1.52 W m⁻¹ K⁻¹ induced by both optimized n_H and reduced κ_l, a peak zT value of 0.65 at 693 K can be achieved in the Ce_1.25Fe₃CoSb₁₂, which is 9 times higher than the Fe₃CoSb₁₂.