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

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 Ce0.73Fe2.73Co1.18Sb12 prepared by the TGZM method. The Ce filling reduces the carrier concentration to 1.03 × 1020 cm−3 in the Ce1.25Fe3CoSb12, 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 Ce1.25Fe3CoSb12, leading to a peak zT value of 0.65, which is 9 times higher than that of the unfilled Fe3CoSb12.


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 = S 2 σT/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 (S 2 σ) 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.
To reduce the κ l of intrinsic CoSb 3 , filling the void position at the 2a site with small atom can tune CoSb 3 into filled-CoSb 3 (R x Co 4 Sb 12 , 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 0.48 Co 4 Sb 12 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 CoSb 3 to form n-type filled-CoSb 3 and approach a decreased κ l of 0.73 W m −1 K −1 and a peak zT of~1.0 in Ba 0.51 CO 4 Sb 12 [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 0.47 Co 4 Sb 12 [38]. However, rareearth Ce has a low filling fraction in CoSb 3 comparing with Yb. Morelli et al. [39] prepared n-type Ce-filled CoSb 3 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 CoSb 3 . To improve the Ce filling fraction in undoped CoSb 3 , 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 0.14 Co 4 Sb 12 prepared by meltingquenching-annealed-sintering. Besides, the thin film CoSb 3 sample prepared by deposition experienced increased Ce-filling fraction. Smalley et al. [41] reported a high Ce-filling fraction of~0.55 in deposited CoSb 3 film.
Although heavy filling in the void position remarkably reduces the κ l of CoSb 3 -based thermoelectric materials, heavily filled CoSb 3 -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 CoSb 3based thermoelectric materials are necessary. To achieve low κ l of p-type CoSb 3 -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 3.5 Co 0.5 Sb 12 has a high S 2 σ 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 CoSb 3 -based skutterudites, which can simultaneously tune n-type CoSb 3 skutterudites into p-type ones [43,44]. Tanahashi et al. [45] found a Ce filling fraction of 0.9 in p-type CoSb 3 -based skutterudites with the nominal composition of CeFe 3 CoSb 12 , 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 0.95 Fe 3 CoSb 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 Fe 3 CoSb 12 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 CoSb 3 -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 CoSb 3 -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 Fe 3 CoSb 12 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 Fe 3 CoSb 12 . A series of Ce-filled p-type Ce x Fe 3 CoSb 12 (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 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 (EF), which is mainly contributed by the f orbital of Ce atom. Besides, Ce-filling also increases the slope of DOS near EF 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-annealingsintering [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 Cefilled p-type CexFe3CoSb12 (x = 0 to 1.5) samples were prepared. We found that the maximum filling level of Ce is 0.73 in the TGZM-prepared Ce1.25Fe3CoSb12 with a measured composition of Ce0.73Fe2.73Co1.18Sb12. The synergistic effect on Fe substitution at the Co and Ce-filling result in reduced nH to 1.03 × 10 20 cm −3 in Ce1.25Fe3CoSb12. A low κl of 0.91 W m −1 K −1 at 693 K can be obtained in the Ce1.25Fe3CoSb12, significantly contributing to an increased zT of 0.65 at 693 K.

Samples Preparation
Initial ingots of (Fe 3 Co)-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 −3 Pa) 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 x Fe 3 CoSb 12 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.

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.

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.

Density Functional Theory (DFT) Calculations
The physical properties of Fe 3 CoSb 12 , CeFe 3 CoSb 12 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.

Microstructure and Phase Composition
To understand crystal structures of the as-prepared Ce x Fe 3 CoSb 12 (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 CoSb 3 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 x Fe 3 CoSb 12 (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 x Fe 3 CoSb 12 . Figure 2c is an atomic-resolution TEM high-angle annular dark-field (HAADF) image of CeFe 3 CoSb 12 . The inset of Figure 2c is superimposed a 2 × 2 × 2 supper cell model for the CeFe 3 CoSb 12 along the [100] direction, well-matched with the observed lattice. Figure 2d Figure 4a shows typical EDS spectra of the CexFe3CoSb12. 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  Figure 4a shows typical EDS spectra of the Ce x Fe 3 CoSb 12 . 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 CoSb 3 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 0.73 Fe 2.73 Co 1.18 Sb 12 prepared by the TGZM method in this study. Figure 4d shows the TEM-EDS spectrum and maps of the CeFe 3 CoSb 12 . 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.   [58] arc melting (AM) for CeFe2Co2Sb12 [59] and CeFe0.75Co3.25Sb12 [39], gas-atomized powder sintering (GS) for CeFe3CoSb12, [45] scanning laser melting and spark plasma sintering (SS) for Ce0.95Fe3CoSb12.1 [46] and temperature gradient zone melting (TGZM) for this study.
(d) Typical TEM-EDS spectrum of the CeFe3CoSb12. The insert of (d) is the HAADF image, corresponding elemental maps and component analysis.

Thermoelectric Transport Properties
To understand the thermoelectric properties of the as-fabricated CexFe3CoSb12 (x = 0 to 1.5), σ, S, S 2 σ, and κ were measured at the temperature range between 303 and 813 K. Figure 5a depicts temperature-dependent σ of the CexFe3CoSb12. 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 CexFe3CoSb12 decreases from 1302 S cm −1 of the Fe3CoSb12 to 638 S cm −1 of the Ce1.25Fe3CoSb12 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 evi-  [59] and CeFe 0.75 Co 3.25 Sb 12 [39], gas-atomized powder sintering (GS) for CeFe 3 CoSb 12 , [45] scanning laser melting and spark plasma sintering (SS) for Ce 0.95 Fe 3 CoSb 12.1 [46] and temperature gradient zone melting (TGZM) for this study. (d) Typical TEM-EDS spectrum of the CeFe 3 CoSb 12 . The insert of (d) is the HAADF image, corresponding elemental maps and component analysis.

Thermoelectric Transport Properties
To understand the thermoelectric properties of the as-fabricated Ce x Fe 3 CoSb 12 (x = 0 to 1.5), σ, S, S 2 σ, and κ were measured at the temperature range between 303 and 813 K. Figure 5a depicts temperature-dependent σ of the Ce x Fe 3 CoSb 12 . The Fe 3 CoSb 12 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 x Fe 3 CoSb 12 decreases from 1302 S cm −1 of the Fe 3 CoSb 12 to 638 S cm −1 of the Ce 1.25 Fe 3 CoSb 12 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 x Fe 3 CoSb 12 is a degenerated semiconductor. With increasing the Ce content, S increases from 62 µV K −1 of the Fe 3 CoSb 12 to 117 µV K −1 of the Ce 1.25 Fe 3 CoSb 12 at 303 K (Figure 5b). The maximum S value of 168 µV K −1 at 693 K can be obtained in the Ce 1.25 Fe 3 CoSb 12 . The positive S indicates that the Ce x Fe 3 CoSb 12 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]: where e is the electron charge, η the reduced Fermi energy, η = E F /k B T, F n (η) the Fermi integral and r H the Hall factor. Figure 5c shows   [59] CeFe4Sb12 [61] and Ce0.6Fe3CoSb12 [62] prepared by TM, CeFe3CoSb12 prepared by GS, [45] Ce0.95Fe3CoSb12.1 prepared by SS, [46] and Ce0.86Fe3CoSb12.09 prepared by melt spinning and spark plasma sintering (MS) [63].
Figure 5e plots temperature-dependent κ of the as-fabricated CexFe3CoSb12 (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 Ce1.25Fe3CoSb12 at 693 K. The κe can be calculated as κe = LσT (Figure 5f), where L is the Lorenz number calculated based on SPB model. With increasing the Ce-filling level, the κe significantly reduces due to reduced σ. Figure 5g presents temperature-dependent κl, calculated by κ-κe. The κl of the Ce-filled Fe3CoSb12 is much lower than that of the unfilled Fe3CoSb12. The kl reduces with increasing the Ce-filling level and approaches a lowest κl of 0.91 W m −1 K −1 at 693 K in the Ce1.25Fe3CoSb12. This should be primarily at-  [61] and Ce 0.6 Fe 3 CoSb 12 [62] prepared by TM, CeFe 3 CoSb 12 prepared by GS, [45] Ce 0.95 Fe 3 CoSb 12.1 prepared by SS, [46] and Ce 0.86 Fe 3 CoSb 12.09 prepared by melt spinning and spark plasma sintering (MS) [63]. Figure 5e plots temperature-dependent κ of the as-fabricated Ce x Fe 3 CoSb 12 (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 1.25 Fe 3 CoSb 12 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 Cefilling level, the κ e significantly reduces due to reduced σ. Figure 5g presents temperaturedependent κ l , calculated by κ-κ e . The κ l of the Ce-filled Fe 3 CoSb 12 is much lower than that of the unfilled Fe 3 CoSb 12 . 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 1.25 Fe 3 CoSb 12 . 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 x Fe 3 CoSb 12 (x = 0 to 1.5). Benefitting from the enhanced S 2 σ and significantly reduced k, a peak zT value of 0.65 can be achieved in the Ce 1.25 Fe 3 CoSb 12 at 693 K, which is 9 times higher than that of the unfilled Fe 3 CoSb 12 . Figure 5i compares the room-temperature κ of nominal Ce 1.25 Fe 3 CoSb 12 in this study prepared by TGZM with the reported κ of p-type Ce-filled and Fe-doped CoSb 3 prepared by other methods. As can be seen, a relatively lower κ is obtained in TGZM prepared Ce 1.25 Fe 3 CoSb 12 , 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 CoSb 3 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.

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 Fe 3 CoSb 12 , we have designed and prepared the p-type Ce x Fe 3 CoSb 12 (x = 0 to 1.5) by a facile TGZM method. The Ce-filling limit in TGZM-prepared Fe 3 CoSb 12 was found to be 0.73 with a measured composition of Ce 0.73 Fe 2.73 Co 1.18 Sb 12 . The filling limit is approached at the nominal composition of Ce 1.25 Fe 3 CoSb 12 . Under the synergistic effect, Fe substitution at the Co site and Ce-filling, an optimal n H of 1.03 × 10 20 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 S 2 σ of 14.4 µW cm −1 K −2 at 693 K in the Ce 1.25 Fe 3 CoSb 12 , which is increased by 100% comparing with that of the Fe 3 CoSb 12 . 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 1.25 Fe 3 CoSb 12 . 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 1.25 Fe 3 CoSb 12 , which is 9 times higher than the Fe 3 CoSb 12 .

Data Availability Statement:
The data presented in this study are available upon request from the corresponding author.