Thermoelectric transport properties of BaFe₂Fe₁₆O₂₇ hexaferrites

INTRODUCTION

Over the past decades, developing thermoelectric technology to directly convert energy between heat and electricity has drawn significant attention^[1,2]. The dimensionless figure of merit (zT) of thermoelectric material is a vital parameter to determine the maximum conversion efficiency, which is defined as zT = S²σT/κ, where S, σ, T, and κ are the Seebeck coefficient, electrical conductivity, absolute temperature, and thermal conductivity, respectively^[3]. A high zT value usually achieves high conversion efficiency, so decoupling the interrelation between the electrical transport parameters S, σ and thermal transport parameter κ has been the key task for thermoelectric research^[4-7]. Moreover, exploring new thermoelectric materials with eco-friendly and earth-abundant elements is economically and sustainably essential to large-scale production and commercial applications^[8-10].

Oxide ceramics have been widely studied as promising thermoelectric materials by virtue of low cost, low toxicity, good stability, and simple preparation methods^[11,12]. Starting from the single-crystalline Na_xCoO_2-δin 2001^[13], several promising thermoelectric oxides, such as Ca₃Co₄O₉^[14], In₂O₃^[15], and SrTiO₃^[16]_, have been discovered or developed. Particularly, in the early 2010s, the layered compound BiCuSeO with an inherent “phonon glass, electron crystal” has been found to show exceptional thermoelectric performance, reaching a maximum zT of around 1.4^[17,18]. Therefore, complex-structured materials are considered potential thermoelectric candidates. However, considering the vast number of oxide materials, the transport properties and thermoelectric performance are still to be studied for a variety of materials.

Hexaferrites, a large family of multinary iron oxides, have attracted great attention for various applications such as magnetic recording, electromagnetic wave control, and communication equipment manufacture^[19-22]. They exhibit superior magneto-crystalline anisotropy, good chemical stability and low cost^[23-25]. In recent years, hexaferrites have also been found to possess new properties such as multiferroicity and low-field magnetoelectric effects at room temperature, making them a popular material system in condensed matter physics^[26,27]. According to their building blocks and the stacking order, there are six types of hexaferrites including W-type, M-type, X-type, Y-type, Z-type, and U-type ferrites^[25]. As to the electrical and thermal transport properties, all types of hexaferrites adopt a large and complex unit cell, which is likely to give rise to abundant optical phonons damping heat transport^[28]. Among them, W-type hexaferrites BaMe₂Fe₁₆O₂₇ (abbreviated as Me₂W, where Me denotes a divalent metal) are particularly interesting for thermoelectrics since they exhibit relatively high and tuneable electrical conductivity by virtue of the coexistence of Me²⁺ and Fe^3+[29-31]. However, little knowledge is available regarding the thermal transport properties, which are important not only to thermoelectrics but also to thermal management in electromagnetic applications.

The synthesis, transport properties, and thermoelectric performance of a series of W-type hexaferrites BaFe_2-xCo_xFe₁₆O₂₇ (abbreviated as Fe_2-xCo_xW) are reported in this study. Polycrystalline materials with high phase purity and crystallinity are successfully synthesized via a solid-state reaction in a nitrogen atmosphere. Electrical and thermal transport properties are comprehensively studied combining both experiments and modeling. Low κ values are achieved by Co substitution and the thermal transport properties are well modeled. This work largely enriches the knowledge on the thermoelectric transport physics and mechanisms of hexaferrites.

MATERIALS AND METHOD

A solid-state reaction method was used to synthesize pristine and cobalt-substituted W-type hexaferrites with nominal compositions of BaFe_2-xCo_xFe₁₆O₂₇ (x = 0, 0.2, 0.4, 1). BaCO₃, Fe₂O₃ and Co₃O₄ powders of analytical purity were used as the raw materials and mixed well after being weighted according to formula. Then, the mixture was first subjected to high-temperature calcination of 1,200 °C for 20 h in a tube furnace in a flowing nitrogen atmosphere. The resulting materials were ground into fine powders by using a mortar and pestle after calcination, followed by adding a self-prepared 5 wt% polyvinyl alcohol (PVA) solution as an adhesive for the granulation process. Finally, the granulated powder was compacted into disk-shaped pellets and preheated at 600 °C for 1.5 h in the air to expel the PVA, followed by another sintering process in nitrogen at 1,240 °C for 4 h to obtain the BaFe_2-xCo_xFe₁₆O₂₇ (x = 0, 0.2, 0.4, 1.0) ceramics.

Powder X-ray diffraction (XRD, Bruker D8 Advance) was employed to determine the phases of all materials. A scanning electron microscope (SEM, ZEISS Sigma300) was used to examine surface microstructures. The σ and S were measured ranging from 300 to 1,000 K under a helium atmosphere by ZEM-3 (ULVAC-RIKO) apparatus. The κ was calculated according to κ = dλC_p. Here, the density d and the thermal diffusivity λ were measured by the Archimedes method and laser flash method (LFA-457, Netzsch), respectively. Additionally, Dulong-Petit law was used to estimate the specific heat capacity C_p. Physical Property Measurement System (PPMS, Quantum Design) was employed to measure the low-temperature heat capacity. Raman measurements were conducted by a Raman spectrometer using a 633 nm laser (HORIBA Scientific). Measurement uncertainties for S, σ, and κ are around 5%, 5% and 7%, respectively^[5].

Vienna Ab initio Simulation Package (VASP) was used to perform the density functional theory (DFT) calculations^[32]. The generalized gradient approximation (GGA) parameterized by Perdew, Burke and Ernzerhof (PBE) was used for the exchange-correlation terms^[33]. The 5s²5p⁶6s², 3d⁷4s¹, and 2s²2p⁴ electrons were treated as valence electrons in the projector-augmented wave (PAW) potentials for Ba, Fe and O, respectively^[34]. All GGA + U calculations used Dudarev’s approximation with U equivalent to the U_eff parameter (U_eff = U - J, where U and J represent Hubbard on-site Coulomb energy and the exchange parameter, respectively)^[35]. An energy cutoff of 600 eV for the plane waves was adopted and reciprocal space was sampled on G-centered k-point grids with a resolution of 0.03 π/Å, with convergence thresholds of 1 × 10^-6 eV for electronic energy and 1 × 10^-2 eV/Å for force. U = 4 eV was used for Fe 3d orbital in all GGA + U calculations. All calculations were spin-polarized with atomic spin configurations initialized according to the Gorter scheme. Elastic constants were determined according to the energy-strain method and the elastic tensor was processed using the Voigt-Reuss-Hill approximation^[36]. Visualization for Electronic and Structural Analysis (VESTA) software was used to model the structures of the material^[37] and visualize the charge densities and the electron localized function (ELF).

RESULTS AND DISCUSSION

XRD and microstructure analysis

Figure 1A shows the hexagonal crystal structure of BaFe₂Fe₁₆O₂₇ material (space group P6₃/mmc). Blocks of R (BaFe₆O₁₁)^2- and S (Fe₆O₈)²⁺ are usually used to describe the crystal structure of the W-type hexaferrite BaFe₂Fe₁₆O₂₇, and the stacking arrangement of the material is RSSR*S*S*, where the asterisk indicates a specific block rotated 180° around the c axis^[38-40]. As presented in Figure 1A and Supplementary Figure 1, the calculated Bader charge of Fe ions in BaFe₂Fe₁₆O₂₇ ranges between +1.44 and +1.76. This is slightly lower than the values in literature reported before^[41]. The Bader charge for Ba is +1.58, while the value for O is in a range of (-1.0~-1.21), similar to the reported charge value of -1.16 for O atomic calculated in water molecular^[42]. Supplementary Figure 1A presents the calculated electron localization function (ELF) and charge density of BaFe₂Fe₁₆O₂₇. It is clearly seen that electrons from the Ba and Fe are transferred to the nearby oxygen, a typical characteristic of the ionic material.

Figure 1. (A) Crystal structure of BaFe₂Fe₁₆O₂₇. The local bonding of Ba and Fe (at 6g and 4e sites) ions are highlighted. (B) Powder XRD patterns of BaFe_2-xCo_xFe₁₆O₂₇ (x = 0, 0.2, 0.4, 1.0) hexaferrites. (C) Raman spectra and (D-G) SEM surface images of BaFe_2-xCo_xFe₁₆O₂₇.

Room-temperature XRD patterns of all BaFe_2-xCo_xFe₁₆O₂₇ (x = 0, 0.2, 0.4, 1.0) hexaferrites are presented in Figure 1B. All the diffraction peaks can be indexed to the standard BaFe₁₈O₂₇ compound, and no secondary phases are observed. The Co substitution does not cause an obvious shift in the XRD peak positions, likely due to the similar ionic radii between Co²⁺ (~0.82 Å) and Fe²⁺ (~0.83 Å). As displayed in Figure 1C, the dominant Raman peaks of all BaFe_2-xCo_xFe₁₆O₂₇ (x = 0, 0.2, 0.4, 1.0) hexaferrites are located at 124, 174, 213, 276, 321, 463, 514 and 670 cm^-1, relating to the intrinsic vibrations of hexagonal hexaferrite crystal^[43]. Lamellar grains are observed by SEM [Figure 1D-G], consistent with the hexagonal layered structure. Noticeably, micro-sized pores are found, resulting in a low relative density of 64.7%~73.2%.

Electrical transport properties

Considering the cases of both spin up and spin down for Fe ions, we calculated the electronic band structures of BaFe₂Fe₁₆O₂₇. As displayed in Figure 2A and B, the conduction-band minimum and valence-band maximum are located on the Γ and H points, respectively. Along the direction parallel to the c-axis, eigenenergy dispersion curves change slowly, while curves perpendicular to the c-axis are steep, indicating a larger effective mass of carriers along the c-axis, which aligns well with expectations for layered materials. The computed total density of state (TDOS) presented in Figure 2C for BaFe₂Fe₁₆O₂₇ shows a small band gap of ~ 0.17 eV. Besides, the calculated high symmetry points of BaFe₂Fe₁₆O₂₇ are presented in Figure 2D.

Figure 2. (A) Spin up and (B) Spin down energy band structures along the high symmetry directions. (C) Total density of states of BaFe₂Fe₁₆O₂₇. (D) Calculated high symmetry points of BaFe₂Fe₁₆O₂₇.

Figure 3A and B presents the temperature-dependent σ and S for all BaFe_2-xCo_xFe₁₆O₂₇ (x = 0, 0.2, 0.4, 1.0) hexaferrites from 300 to 1,000 K. For all the samples, the σ values are around 10¹-10² S m^-1 at 300 K and increase with temperature, exhibiting a non-degenerate semiconductor behavior. Below ~900 K, Co-doped samples show relatively lower σ values compared with the pristine ones. In the whole temperature range, all S values are negative, indicating an n-type conduction behavior. In line with the composition-dependence of electrical conductivity, the alloyed samples exhibit higher S values than the undoped ones. This suggests that Co substitution probably decreases the carrier concentration. Moreover, according to a previous study^[41], valence states of 6g sites can be changed from mixed valence state to 3+ by Co doping. Therefore, the energy of Fe will increase and enter into the conduction band, leading to the disappearance of ‘‘heavily doping states’’ and thus the decrease of the carrier concentration and electrical conductivity. For BaFe₁Co₁Fe₁₆O₂₇, the sudden decrease of S with T around 800 K suggests a phase transition. This phase transition may be a magnetic phase transition caused by magnetic moment arrangement changes originating from the change of lattice parameters at high temperatures^[25,44]. Maximum power factors (PFs) reach 0.26 μW cm^-1 K^-2 for Fe₁Co₁W at 1,000 K [Figure 3C]. As shown in Figure 3D, the S and σ roughly follow the single parabolic band (SPB) model^[45].

Figure 3. Temperature-dependent (A) σ, (B) S, and (C) PF between 300 and 1,000 K for BaFe_2-xCo_xFe₁₆O₂₇. (D) Room-temperature Svs. σ plot. The dashed line is fitted based on SPB model using a fixed weighted mobility.

ELASTIC AND THERMAL PROPERTIES

We carried out the DFT calculation to obtain the elastic parameters of pristine BaFe₂Fe₁₆O₂₇. As shown in Table 1, the average sound speed and the Debye temperature θ_D calculated are 3,667 m/s and 517 K, respectively. The values are higher than common thermoelectric materials, reflecting the stiffer bonding of BaFe₂Fe₁₆O₂₇^[46,47]. The low-temperature heat capacity was measured and modeled for further understanding of the lattice dynamics. One Debye mode and two Einstein modes are needed to accurately describe the data, as presented in Figure 4^[48,49]. The fitted Debye temperature is 516 K [Supplementary Table 1], which is in excellent consistency with the DFT calculation above (517 K). The Einstein temperatures are fitted to be 47.7 and 127 K, corresponding to the phonon energies of 4.1 and 11 meV, respectively. The low-energy optical phonons are also consistent with the Raman measurement mentioned above (peak around 124 cm^-1, aka 15.4 meV), which should damp part of the heat transport.

Figure 4. C_p/T as a function of T² for BaFe₂Fe₁₆O₂₇ at low temperature. Black squares represent the experimental data. The red solid line represents the fitted curve by using one Debye mode and two Einstein modes. The other dashed lines represent the electronic term φ, Debye term β, and two Einstein terms, Θ_E1 and Θ_E2, respectively. The adjusted R² value for the fitted curve is 0.99959 and the Chi-squared value is 6.058 × 10^-3.

Figure 5A shows the temperature-dependent κ for all BaFe_2-xCo_xFe₁₆O₂₇ samples. Considering the low σ, the electronic portion of κ contributes as low as 1%-3% at 300 K, so the lattice thermal conductivity (κ_L) can be treated numerically equal to the total one. Low κ values of 1.27 W m^-1 K^-1 at 300 K and 0.69 W m^-1 K^-1 at 750 K are obtained in the Fe_1.8Co_0.2W sample. The room-temperature κ values are pretty low among oxides compared to other counterparts such as In_1.99Ge_0.01O₃ (11.5 W m^-1 K^-1)^[15], SrTiO₃ (8.1 W m^-1 K^-1)^[50] and Ca₃Co₄O₉ ceramic (2.3 W m^-1 K^-1)^[51]. Nonetheless, the values may not reflect the intrinsic properties of the samples since there exists an appreciable number of pores. Therefore, for further analysis, we correct the thermal conductivity values by the porosity via^[52]

Figure 5. (A) Thermal conductivity (κ) varying with temperature for BaFe_2-xCo_xFe₁₆O₂₇ hexaferrites. (B) Porosity-corrected thermal conductivities as functions of content of Co for BaFe_2-xCo_xFe₁₆O₂₇ at 300 K. (C) Point-defect scattering parameter Γ, Γ_mass and Γ_strain as a function of Co content. (D) zT varying with temperature.

where κ_real is the measured thermal conductivity, κ_dense corresponds to that of fully dense samples, and Φ is the porosity. The corrected thermal conductivities as a function of Co content at room temperature are shown in Figure 5B. Apparently, the existing pores can lead to the decrease of the thermal conductivity but their influence on the thermoelectric performance can be complicated as they will also lower the carrier mobility, thus reducing electrical conductivity. There is a ~20% reduction of κ when x increases from 0 to 0.4. This reduction is mainly attributed to the point defect scattering induced by Co substitution for Fe. Based on the fitted results within the Debye-Callaway framework, we derive the point-defect scattering parameter Γ, which includes mass fluctuation (Γ_mass) and strain field fluctuation (Γ_strain)^[53]. The fitted results of temperature-dependent thermal conductivity are presented in Supplementary Figure 2. As plotted in Figure 5C, Γ_strain dominates the point-defect scattering. This is reasonable since the mass difference between Co and Fe is less than 6%, so the contributions of Γ_mass should be small.

Figure 5D presents the zT for all BaFe_2-xCo_xFe₁₆O₂₇ (x = 0, 0.2, 0.4, 1.0) samples calculated based on the measured transport properties. The reduced thermal conductivity compensates for the deterioration in electrical properties, resulting in a similar calculated zT in all BaFe_2-xCo_xFe₁₆O₂₇ samples. Maximum zT around 0.03 at 1,000 K is achieved for all BaFe_2-xCo_xFe₁₆O₂₇ samples. Further optimizing the electrical transport properties may push zT to higher values.

CONCLUSIONS

In summary, thermoelectric transport properties of polycrystalline BaFe_2-xCo_xFe₁₆O₂₇ (x = 0, 0.2, 0.4, 1.0) hexaferrites have been systematically investigated. The DFT calculations indicate a band gap of around 0.17 eV and a strong anisotropy in band structure. The materials exhibit an n-type conduction behavior and Co substitution can tune the electrical transport properties effectively. Low κ values of 1.27 W m^-1 K^-1 at 300 K and 0.69 Wm^-1K^-1 at 750 K have been achieved in the Fe_1.8Co_0.2W sample. The low thermal conductivity can be ascribed to point-defect scattering, the low-energy optical phonons, and the pores formed during synthesis. This work enriches the knowledge on the thermoelectric properties of hexaferrites.