∼100% enhancement of cryogenic thermoelectric performance of Bi₈₀Sb₂₀ alloys by incorporation of Fe₃O₄ nanoparticles

Abstract

Bi₈₀Sb₂₀-based alloys are promising candidates for thermoelectric applications below room temperature. However, their inherently low thermoelectric performance, characterized by a limited power factor and high lattice thermal conductivity, severely hinders practical utilization. To address this challenge, we introduce Fe₃O₄ nanoparticles as a second phase to construct Bi₈₀Sb₂₀/Fe₃O₄ nanocomposites via a high-efficiency mechanical alloying process, assisted by stearic acid dispersion, followed by spark plasma sintering. The incorporation of nano-Fe₃O₄ leads to enhanced carrier mobility and intensified phonon scattering at nanoparticle interfaces, resulting in a remarkable threefold increase in the power factor and a 20–40% reduction in lattice thermal conductivity. As a result, the optimized composite with 0.4 vol% Fe₃O₄ achieves a peak zT of 0.31 at 242 K – representing nearly a 100% improvement over the pristine matrix – and an average zT of 0.29 in the range of 150–300 K. In addition to the thermoelectric enhancements, the Vickers hardness of the composites is also significantly improved. These findings demonstrate the potential of superparamagnetic Fe₃O₄ nanoparticle incorporation as an effective strategy for the simultaneous enhancement of both thermoelectric and mechanical properties in Bi₈₀Sb₂₀-based alloys, offering a viable pathway for low-temperature power generation and refrigeration applications.

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Heng Liu

Dr Heng Liu is currently a specially appointed assistant professor at the Advanced Institute for Materials Research (WPIAIMR), Tohoku University, Japan. He earned his PhD degree from the Department of Chemical Engineering, University of Manchester, UK in 2024, and his MS degree in material engineering from Central South University, China, in 2020. His primary research interests focus on first-principles calculations and new computational methodology development for understanding modern energy and environmental technologies.

Introduction

Thermoelectric (TE) refrigeration devices stand out as environmentally friendly solid refrigeration options, eliminating the need for refrigerants or emissions. They offer significant benefits such as compact size, high reliability, and silence, making them highly suitable for cooling precision devices like charge-coupled device cameras, laser diodes, infrared detectors, and blood analyzers, among others.^1,2 Besides cooling, TE systems can convert thermal gradients into electricity, enabling self-powered operation for vapor-driven energy harvesting, 3D-printed flexible electronics, and stimuli-responsive sensing, among others. This dual functionality, simultaneous energy conversion and temperature/stress detection, eliminates external power requirements while demonstrating transformative potential for multifunctional integrated devices.^3–5 The TE performance of materials is measured by the dimensionless figure of merit (zT), defined as zT = S²σT/κ, where S represents the Seebeck coefficient, σ the electrical conductivity, κ the thermal conductivity, and T the temperature. S²σ is termed the power factor (PF), reflecting the comprehensive electrical performance, while κ comprises both electronic thermal conductivity (κ_e) and lattice thermal conductivity (κ_L).^6–8 Because these parameters are interdependent, to achieve a high zT value, it is crucial to develop strategies that can decouple these parameters, to simultaneously enhance electronic transport and depress phonon transport.⁹

Over the past two decades, the TE performance of a wide range of materials, including Bi₂Te₃,^10,11 CoSb₃,^12,13 PbSe,¹⁴ PbTe,^15,16 half-Heusler compounds,^17,18 Cu₂Se,^19,20 SiGe²¹ and others, has been significantly improved via various strategies, such as phonon-glass-electron-crystal and phonon-liquid-electron-crystal concepts, band structure engineering, nanocomposite approaches, etc. These efforts have led to a peak zT exceeding 2.0. However, most of these materials operate effectively only above room temperature (T > 300 K), while the development of low-temperature TE materials (T < 300 K) remains relatively limited. In addition to emerging materials such as YbAl₃,²² CeRhSn²³ and CsBi₄Te₆,²⁴ Bi–Sb alloys are among the most promising candidates for cryogenic TE applications.²⁵ Single crystal Bi–Sb alloys have demonstrated a maximum zT of ∼0.6 at 300 K,²⁶ while showing inherent brittleness and cleavage failure. High-energy ball milling^27,28 and wet chemical reaction^29,30 techniques have been employed to fabricate nanostructured Bi–Sb alloys with improved mechanical integrity. Nonetheless, polycrystalline Bi–Sb alloys typically suffer from reduced electrical transport properties due to random grain orientation compared to their single-crystal counterparts.³¹ Therefore, achieving fine-grained microstructures that not only suppress cleavage failure but also leverage high-density grain boundaries for effective phonon scattering without significantly degrading carrier transport is critical for advancing cryogenic TE materials.

Besides moderate doping,^32,33 the inclusion of second-phase nanoparticles, nanowires, or nanotubes into a crystalline matrix also represents a prominent strategy to improve the TE properties of bulk materials.³⁴ The incorporation of nanoscale second phases inevitably introduces a variety of structural imperfections such as grain boundaries, dislocations, nanopores, and phase interfaces. These defects serve as effective phonon scattering centers, thus reducing lattice thermal conductivity.³⁵ Meanwhile, interfacial band bending and associated energy filtering effects can also enhance the Seebeck coefficient,³⁶ offering a pathway to improve the overall zT value. Recent studies have demonstrated that magnetic nano-inclusions are effective in enhancing the TE performance of TE composites. For example, the incorporation of superparamagnetic Co nanoinclusions into a filled CoSb₃ matrix has been shown to improve TE properties by decoupling phonon and electron transport.³⁷ Poudeu et al.³⁸ reported that magnetic interaction between Ti(Ni, Fe)Sn nanoinclusions and the spin of itinerant carriers could significantly enhance the electrical properties while simultaneously suppressing the thermal conductivity of the (Ti, Zr, Hf)Ni(Sn, Sb) alloy. Superparamagnetic Fe₃O₄ nanoparticles, known for their mixed-valence character, can reduce thermal conductivity through phonon-magnetic moment interactions.³⁹ It has been reported that introduction of Fe₃O₄ nanoinclusions into BiSbTe and YbAl₃ matrices can effectively suppress κ_L, thereby significantly improving zT.^40,41

Based on the above, the application of Fe₃O₄ magnetic nanoinclusions to enhance the TE properties of n-type Bi–Sb-based alloys below 300 K presents a promising strategy for the commercial development of cryogenic TE materials. To achieve efficient dispersion of Fe₃O₄ nanoparticles and reduce processing costs, Bi₈₀Sb₂₀/Fe₃O₄ composites were synthesized via direct ball milling of elemental powders with nano-sized Fe₃O₄, followed by spark plasma sintering. This ball milling approach offers a higher dispersion efficiency and lower cost compared to the conventional melt-then-mill route, making it more suitable for scalable fabrication. This study presents a detailed analysis of the synthesis procedure, the electrical and thermal transport properties, and the mechanisms responsible for the observed thermoelectric performance.

Experimental section

Synthesis

Bi₈₀Sb₂₀/x vol% Fe₃O₄ composites were synthesized via dry ball-milling of elemental powders: bismuth (99.9% Sinopharm), antimony (99.99% Alfa Aesar), and nano-sized Fe₃O₄ powders (Aladdin, 99%) at varying volume fractions (0, 0.2, 0.4, 0.5, and 0.8 vol%). Stearic acid (99.9% Alfa Aesar) was added as a process control agent to prevent powder adhesion to the milling container walls. For this purpose, the weighed powders were transferred into a stainless steel milling container and sealed under an argon atmosphere in a glovebox. Using a ball-to-powder ratio of 6 : 1 and 1200 rpm, the powders were ball milled for 8 hours. The stearic acid in the Bi–Sb powders was cleaned with acetone before SPS sintering. Specifically, the Bi₈₀Sb₂₀/x vol% Fe₃O₄ milled alloyed powders were loaded into the graphite SPS die in the glovebox. Then, they were sintered at 513 K through the spark plasma sintering (Sojitz, SPS-725) technique for 10 min with a uniaxial pressure of 65 MPa under vacuum to form a pellet with dimensions of 10 mm diameter and 4 mm thickness, as shown in Fig. 1. For performance comparison, an alternative dispersion approach was investigated. A Bi₈₀Sb₂₀/0.2 vol% Fe₃O₄ composite was prepared using wet ball milling (in ethanol solvent with 1-hour ultrasonic pre-dispersion), followed by the standard SPS process described above.

Fig. 1 Schematic diagram of the preparation process of Bi₈₀Sb₂₀/x vol% Fe₃O₄ (x = 0, 0.2, 0.4, 0.5, 0.8) composites.

Calculations

Spin-polarized density functional theory computations were conducted via the Vienna ab initio Simulation Package (VASP) code.⁴² The calculations employed a plane-wave basis set in conjunction with the projector augmented-wave (PAW) method.⁴³ The generalized gradient approximation (GGA),⁴⁴ incorporating spin–orbit coupling (SOC) effects,⁴⁵ as parameterized by the Perdew–Burke–Ernzerhof (PBE) functional,⁴⁶ was employed to describe the electron exchange–correlation interactions. All structural models were constructed using the Atomic Simulation Environment (ASE) Python library.⁴⁷ The convergence criterion for structural relaxation was set such that the residual force on each atom was less than 0.03 eV Å⁻¹. To account for the strong on-site Coulomb interactions of the localized d electrons in Fe, a Hubbard U correction (DFT + U) was applied.⁴⁸ The specific U and J values for Fe were 5.3 eV and 0 eV, respectively, based on the recommendations of the Materials Project database.⁴⁹

Characterization

The phase compositions were analyzed using an X-ray diffractometer with Cu Ka sources (XRD, D8 Advance, Bruker), field emission electron microscopy (FESEM, ZEISS, Supra55) coupled with Energy Dispersive X-ray Spectroscopy (EDS, Oxford, UK) and Field Emission Transmission Electron Microscopy (FETEM, JOEL 2100F) coupled with Energy Dispersive X-ray Spectroscopy (EDS, Oxford, UK). Synchrotron powder diffraction XRD and GIWAXS were performed using a Shanghai Light Source BL17B line station. The Vicker Hardness was measured by using a microhardness tester (HV-1000Z) with a load of 0.2 N and a loading time of 10 s. The electrical conductivity, Seebeck coefficient and thermal conductivity tests were conducted using a comprehensive physical property testing system (PPMS-9, Quantum Design). Specimen preparation followed these protocols: diamond wire cutting of sintered pellets into 5.0 × 2.0 × 1.5 mm³ strips; sequential polishing with abrasive paper; application of colloidal graphite electrodes on terminal faces; vacuum annealing at 110 °C for 15 min. Hall measurements are performed using the five-wire method, with multi-point voltage–current combinations under an externally applied vertical magnetic field. The measurement uncertainties are quantified as follows: electrical conductivity ± 5%, Seebeck coefficient ± 7%, thermal conductivity ± 7%, and Hall coefficient ± 5%.

Results and discussion

Phases and microstructures

During the ball milling process, Bi–Sb powders tended to adhere to the walls of the milling container, which not only reduced the material yield but also increased preparation cost. To mitigate this issue, stearic acid was added in varying concentrations (0.5 wt%, 1 wt%, and 3 wt%) as a processing aid to enhance the powder dispersibility and reduce wall adhesion (Fig. 1). When the stearic acid content was 0.5 wt%, wall sticking was still observed during ball milling. In contrast, no adhesion was observed at concentrations of 1 wt% and 3 wt%. The improvement in powder dispersibility and reduction in wall adhesion could be attributed to the surface-active properties of stearic acid. The stearic acid is a long-chain saturated fatty acid (CH₃(CH₂)₁₆COOH) containing a polar carboxyl (–COOH) group at one end and a nonpolar hydrocarbon tail. During the ball milling process, the carboxyl group can adsorb onto the surface of metal particles through weak chemical interactions or hydrogen bonding, while the hydrophobic alkyl chain extends outward, forming a steric barrier. This molecular arrangement reduces interparticle cohesion and prevents cold welding between particles, thus enhancing flowability and minimizing their tendency to adhere to the milling vessel walls. However, since stearic acid constitutes an impurity phase, its content should be minimized. Therefore, a stearic acid concentration of 1 wt% was ultimately selected for the synthesis of Bi₈₀Sb₂₀/x vol% Fe₃O₄ composites. First, due to the principle of “like dissolves like”, the stearic acid was initially removed using acetone, followed by drying and subsequent sintering. In addition, considering that the volatilization temperature of the stearic acid is approximately 423 K,⁵⁰ any residual stearic acid that may remain after cleaning can still be effectively eliminated during the SPS process at 513 K. Specifically, as shown in Fig. S1, the C=O stretching vibration peak at approximately 1700 cm⁻¹ is widely recognized as a key characteristic signal for determining the presence of stearic acid, while the –(CH₂)_n– peak at 720 cm⁻¹ is a critical identifying peak for long-chain fatty acid compounds. However, comparative spectral analysis revealed that neither of these characteristic peaks was observed in the composite material, indicating that stearic acid had been effectively removed.

The crystalline phases of Bi₈₀Sb₂₀/x vol% Fe₃O₄ composites were analyzed by XRD. As shown in Fig. 2a, the characteristic diffraction peaks of all the nanocomposites can be well indexed to the rhombohedral phase of Bi (PDF#44-1246). Bi and Sb form a complete solid solution in the rhombohedral A7 crystal structure, owing to their identical and similar lattice parameters (Bi: a = 4.5 Å and c = 11.8 Å; Sb: a = 4.34 Å and c = 11.3 Å).⁵¹ No diffraction peaks corresponding to Sb or other impurities are observed in the Bi₈₀Sb₂₀ sample, further confirming the formation of a homogeneous Bi–Sb alloy via a solid solution mechanism. The lattice parameters a and c (Fig. 2b) remained nearly unchanged with varying Fe₃O₄ content, suggesting that the dispersion of Fe₃O₄ does not alter the crystal structure of the Bi₈₀Sb₂₀ matrix. Moreover, no characteristic diffraction peaks of Fe₃O₄ are observed in any of the nanocomposites, which can be attributed to its low volume content, only up to 0.8%, well below the typical XRD detection limit. However, high-sensitivity synchrotron powder XRD enables more refined structural characterization of the composites. As shown in Fig. 2c, synchrotron XRD measurements were conducted on the Bi₈₀Sb₂₀/0.4 vol% Fe₃O₄ and Bi₈₀Sb₂₀ samples. The results confirm that the diffraction peaks corresponding to the rhombohedral lattice of Bi are consistent with those obtained from the conventional XRD analysis. In addition, weak but distinct peaks attributable to Fe₃O₄ are observed and match well with the reference data from the standard PDF card (#26-1136).

Fig. 2 (a) XRD patterns of the Bi₈₀Sb₂₀/x vol% Fe₃O₄ (x = 0, 0.2, 0.4, 0.5, 0.8) nanocomposites. (b) Lattice parameters of the composites with different Fe₃O₄ contents. (c) Synchrotron radiation powder X-ray diffraction (PXRD) of Bi₈₀Sb₂₀ and Bi₈₀Sb₂₀/0.4 vol% Fe₃O₄ bulks. Grazing Incidence Wide Angle X-ray Scattering (GIWAXS) of Bi₈₀Sb₂₀ (d) and (e) Bi₈₀Sb₂₀/Fe₃O₄. (f) Surface backscattered electron (BSE) images and energy dispersive X-ray spectroscopy (EDS) elemental mapping for Bi₈₀Sb₂₀/0.4 vol% Fe₃O₄ bulk. Cross-sectional SEM images of the Bi₈₀Sb₂₀ (g) and (h) Bi₈₀Sb₂₀/0.4 vol% Fe₃O₄ bulk.

In the GIWAXS 2D scattering patterns shown in Fig. 2d and e, the scattering vector q_xy corresponds to specific Bi crystal facets: q_xy = 2.76 Å⁻¹ for the (110) plane, 2.65 Å⁻¹ for (104), 1.915 Å⁻¹ for (012), and q_xy = 1.58 Å⁻¹ for (003). After the incorporation of 0.4 vol% Fe₃O₄, the overall diffraction pattern of the Bi₈₀Sb₂₀/Fe₃O₄ composite remains largely unchanged compared to the pristine Bi₈₀Sb₂₀ sample, suggesting that the small amount of Fe₃O₄ has minimal impact on the crystal orientation or structural ordering of the matrix. Notably, weak diffraction peaks corresponding to Fe₃O₄ are observed in the PXRD patterns of the samples, owing to the high sensitivity of this technique. In contrast, no corresponding signals of Fe₃O₄ are shown in the GIWAXS patterns, likely because it probes only the near-surface region where the Fe₃O₄ content may be insufficient for detection.

The elemental distribution in Bi₈₀Sb₂₀/x vol% Fe₃O₄ (x = 0.2, 0.4, 0.5, 0.8) bulk samples was further characterized using backscattered electron (BSE) imaging combined with energy-dispersive X-ray spectroscopy (EDS) elemental mapping. As shown in Fig. 2f and S2, the BSE images show that the Fe₃O₄ particles are uniformly distributed within the Bi₈₀Sb₂₀ matrix, with no evidence of extraneous impurity elements, confirming the successful formation of the Fe₃O₄/Bi₈₀Sb₂₀ composite. However, slight inhomogeneities in the Fe distribution are observed in the samples with x = 0.5 and 0.8, likely due to localized agglomeration of the Fe₃O₄ phase. Even though ball-milling mechanical alloying is a useful and scalable synthesis method, complete homogeneity of a second-phase additive (especially at low content) is hard to guarantee. Some agglomeration is almost unavoidable during the ball milling process unless highly optimized conditions are used. Fig. 2g, h and S3 present scanning electron microscopy (SEM) images of the fractured cross sections of the Bi₈₀Sb₂₀/x vol% Fe₃O₄ composites. Compared to pristine Bi₈₀Sb₂₀, the composite samples display a mixed microstructure comprising both large, smooth grains and smaller flake-like grains on the order of several hundred nanometers. This multiscale grain structure is beneficial for phonon scattering across a wide range of wavelengths, thereby effectively reducing the lattice thermal conductivity.

The microstructural features of Bi₈₀Sb₂₀/x vol% Fe₃O₄ composites were further characterized by field emission transmission electron microscopy (FE-TEM) (Fig. 3a). Fast Fourier transform (FFT) analysis of the interface region (Fig. 3b) distinctly delineated the lattice periodicity of the constituent phases: Fe₃O₄ exhibited an interplanar spacing of 0.244 nm, corresponding to the (311) plane, while Bi₈₀Sb₂₀ displayed an interplanar spacing of 0.324 nm, corresponding to the (012) plane. The findings indicate that the two phases retain their crystal structures despite being tightly bound at the interface. EDS analysis further confirms that Fe₃O₄ is encapsulated within the Bi₈₀Sb₂₀ main phases (Fig. 3c–f). This interfacial structure could possibly facilitate charge transfer and enhance the electrical properties of the composites.⁵² In localized TEM-EDS analysis, oxygen signals often appear delocalized due to the high mobility and broad spatial response of light elements. As such, the presence of O outside Fe₃O₄ particles should be interpreted cautiously, as it does not necessarily indicate incorporation into the Bi₈₀Sb₂₀ matrix.

Fig. 3 (a) Field emission transmission electron microscopy (FE-TEM) image of the Bi₈₀Sb₂₀/Fe₃O₄ sample and (b) magnified view of the local interface. The inset displays the Fast Fourier Transform (FFT) patterns of the two phases and EDS mapping of (c) Fe, (d) O, (e) Bi and (f) Sb within the Bi₈₀Sb₂₀/Fe₃O₄ in (a).

TE properties of Bi₈₀Sb₂₀/x vol% Fe₃O₄ nanocomposites

The temperature dependence of the electrical conductivity, σ, of the Bi₈₀Sb₂₀/x vol% Fe₃O₄ composites in the range of 150–300 K is shown in Fig. 4a. The electrical conductivity, σ, increases with temperature, indicating typical semiconducting behavior. This is because the rise in temperature brings about more excited electrons into the conduction band, which leads to an increase in carrier concentration, n (Fig. 4b). Notably, the σ of the x = 0.4 sample shows a pronounced enhancement, reaching 4.2 × 10⁵ S m⁻¹ at room temperature, almost three times higher than that of pristine Bi₈₀Sb₂₀. This improvement is primarily due to a sharp increase in carrier mobility, μ (Fig. 4c). The observed sharp increase in carrier mobility upon the incorporation of trace amounts of Fe₃O₄ nanoparticles can be attributed to the dynamic interactions between their superparamagnetic nature and electron transport. Specifically, Fe₃O₄ nanoparticles exhibit thermally fluctuating magnetic moments, which give rise to localized, time-varying magnetic fields within the Bi₈₀Sb₂₀ matrix. These localized magnetic fields interact with the charge carriers in two key ways. First, they modulate the scattering environment by disrupting conventional scattering mechanisms such as phonon scattering, point defect scattering, and grain boundary scattering. This dynamic magnetic environment effectively perturbs the trajectories of electrons in a manner that reduces their momentum relaxation rate, thereby enhancing mobility. Second, the fluctuating magnetic fields can induce a weak Lorentz-like force on the carriers, subtly redirecting their paths toward lower-scattering channels. This promotes more coherent carrier motion by enabling electrons to bypass energetically unfavorable regions or local scattering centers. Collectively, these effects—scattering suppression and path redirection—synergistically contribute to a significant enhancement in μ (Fig. 4d). This mechanism is supported by prior theoretical and experimental reports on magnetic-field-assisted transport in nanocomposites, particularly those incorporating superparamagnetic inclusions.^48–54

Fig. 4 Temperature dependence of (a) electrical conductivity, σ; (b) carrier concentration, n; (c) mobility μ for Bi₈₀Sb₂₀/x vol% Fe₃O₄ (x = 0.2, 0.4, 0.5, 0.8). (d) Mechanisms for enhancement of mobility after the addition of Fe₃O₄ into Bi₈₀Sb₂₀. (e) Electronic band diagram near the interface of Fe₃O₄ and Bi₈₀Sb₂₀. (f) Temperature dependence of the Seebeck coefficient, S, for Bi₈₀Sb₂₀/x vol% Fe₃O₄ (x = 0.2, 0.4, 0.5, 0.8) samples. (g) Room-temperature S as a function of n for all Bi₈₀Sb₂₀/x vol% Fe₃O₄ samples. The blue solid line represents calculations from the parabolic band model with the effect mass m* = 0.22 m_e. (h) Temperature-dependence of the power factor, PF, for all Bi₈₀Sb₂₀/x vol% Fe₃O₄ samples.

As shown in Fig. 4e, when Bi₈₀Sb₂₀ comes into contact with Fe₃O₄, a Schottky barrier forms at the interface due to the work function difference (ΔΦ ≈ 0.81 eV) between the n-type semiconductor Bi₈₀Sb₂₀ (Φ = 4.98 eV) and the metallic Fe₃O₄ (Φ = 5.79 eV) and Fig. S4 provides the electronic energy band arrangements of Fe₃O₄ and Bi₈₀Sb₂₀, which are calculated based on the DFT method. This leads to upward band bending on the Bi₈₀Sb₂₀ side. This creates an energy barrier that carriers must overcome to enter the Fe₃O₄ phase or traverse the interface. For low-energy electrons, this barrier can act as an obstacle, causing partial carrier reflection or scattering at the interface, thereby reducing the effective carrier mobility. At higher Fe₃O₄ content over 0.4 vol%, this effect with accumulation would decrease μ. As the temperature increases, the amplitude and frequency of phonons rise, significantly enhancing the probability of carrier-phonon collisions, which leads to a decrease in carrier mobility. Since phonon scattering remains the dominant mechanism in the 150–300 K range, the overall μ continues to decrease, even in the presence of thermionic emission effects across Schottky barriers.

The S of all samples is negative across the measured temperature range, confirming that electrons are the dominant charge carriers (Fig. 4f). Overall, the absolute values of S decrease with increasing temperature, which is inversely related to the trend of n. Notably, Fe₃O₄ incorporation enhances the S of the composites below 220 K. Above 220 K, the observed reduction in S with temperature for the composites is attributed to the increase of n, as confirmed in Fig. 4b. For the Bi₈₀Sb₂₀ matrix, at lower temperatures (below 180 K), the n increases with temperature (Fig. 4b) as more carriers are thermally excited from impurity states. The S increases concurrently (Fig. 4f) due to the energy-dependent scattering of these activated carriers and the upward shift of the Fermi level towards the conduction band edge. Then, an intermediate plateau occurs until 260 K, indicating the exhaustion of extrinsic carriers before significant intrinsic excitation occurs. The S coefficient reaches its peak value during this regime. Above 260 K, the n rises sharply again (Fig. 4b) due to intrinsic thermal excitation across the narrow band gap. The S subsequently decreases (Fig. 4f) as the detrimental contribution from minority carriers (bipolar diffusion) becomes significant, opposing the thermoelectric voltage generated by majority carriers.

Fig. 4g shows the fitted Pisarenko plot at 300 K on the basis of the single parabolic band (SPB) model under the assumption of acoustic phonon scattering.^55,56 The experimental data for all Bi₈₀Sb₂₀/x vol% Fe₃O₄ samples align well with the fitted curve, indicating that the effective mass, m*, remains nearly unchanged (∼0.22 m_e) upon Fe₃O₄ addition. This suggests that the m* of the Bi₈₀Sb₂₀ matrix is largely preserved and that Fe₃O₄ nanoparticles influence TE performance primarily by tuning the carrier concentration rather than altering the band structure. Finally, based on the measured σ and S values, the PF values were calculated for all samples. Due to the higher σ and S, the x = 0.4 sample shows the highest PF of 34.4 μW cm⁻¹ K⁻² at 194 K—nearly three times higher than that of the matrix (Fig. 4h).

The total thermal conductivity, κ, of a material consists of lattice thermal conductivity, κ_L, electronic thermal conductivity, κ_e, and bipolar thermal conductivity, κ_b. κ_L arises predominantly from phonon transport, whereas κ_e results from heat transport by carrier transport. The narrow band gaps of Bi–Sb alloys facilitate intrinsic excitations, leading to substantial electron–hole pair diffusion and additional κ_b.^57,58 The temperature dependence of κ for all samples is presented in Fig. 5a. For all the composite samples, κ increases with temperature. However, as the Fe₃O₄ content increases, the overall thermal conductivity initially increases and then decreases. The κ_e was calculated (Fig. 5b) according to the Wiedemann–Franz Law:

κ_e = LσT (1)

where L was estimated (Fig. S5) based on the single parabolic band (SPB) model with acoustic phonon scattering. The equations used in the SPB model are shown as follows:where κ_B, e, λ, η, F, ξ and j are the Boltzmann constant, elementary charge, scattering factor, reduced chemical potential, Fermi integral function, reduced carrier energy and power of integral variable.

Fig. 5 Temperature dependence of (a) thermal conductivity κ; (b) electronic thermal conductivity, κ_e; (c) lattice thermal conductivity, κ_L for Bi₈₀Sb₂₀/x vol% Fe₃O₄ (x = 0.2, 0.4, 0.5, 0.8). (d) Lattice thermal conductivity, κ_L, as a function of the filling fraction (x) for Bi₈₀Sb₂₀/x vol% Fe₃O₄ at 300 K (x = 0.2, 0.4). (e) Contribution from various phonon scattering mechanisms to κ_L in Bi₈₀Sb₂₀, Bi₈₀Sb₂₀/0.4 vol% Fe₃O₄. U, GB and PD denote the Umklapp phonon–phonon process, grain boundary scattering and point defect scattering, respectively. (f) Schematic representation of different scattering mechanisms within Bi₈₀Sb₂₀/Fe₃O₄ materials.

By deducting the κ_e from the total thermal conductivity, the sum of κ_b and κ_L is shown in Fig. S6a. By further deducting the estimated κ_b (Fig. S6b), the κ_L is obtained (Fig. 5c). It shows that the κ_L of the Bi₈₀Sb₂₀/Fe₃O₄ composites at 300 K decreases with increasing Fe₃O₄ content, reaching a minimum at x = 0.4. Fig. 5d plots room-temperature κ_L as a function of the Fe₃O₄ volume fraction. The κ_L of Bi₈₀Sb₂₀/Fe₃O₄ composites exhibits a non-monotonic variation with increasing Fe₃O₄ content. As the Fe₃O₄ content increases to x = 0.4, κ_L decreases from ∼0.88 W m⁻¹ K⁻¹ to ∼0.54 W m⁻¹ K⁻¹, representing a ∼39% reduction compared to the matrix. However, it subsequently increases to approximately 1.2 W m⁻¹ K⁻¹ at x = 0.5 vol%, before decreasing again to ∼1.0 W m⁻¹ K⁻¹ at x = 0.8 vol%. At very low loading (x = 0.2 vol%), Fe₃O₄ nanoparticles primarily act as isolated phonon scattering centers, introducing mass and strain field fluctuations at the interfaces, but their overall density remains limited. The sharp decrease in κ_L up to x = 0.4 vol% may be attributed to the optimal dispersion of Fe₃O₄ (Fig. 5c), which maximizes phonon scattering at grain boundaries and heterointerfaces. However, beyond this threshold, particle agglomeration during consolidation likely reduces the effective interfacial area, diminishing phonon scattering efficiency. Simultaneously, the relatively high intrinsic thermal conductivity of Fe₃O₄ (5.9 ± 0.6 W m⁻¹ K⁻¹)⁵⁹ contributes to an increased volumetric heat transport, resulting in the observed rise in κ_L at x = 0.5 vol%. At even higher loading (x = 0.8 vol%), a minor suppression of κ_L could be due to the increased density of heterointerfaces, which enhances phonon scattering—especially for mid- to long-wavelength phonons. Additionally, localized strain and lattice mismatch at these interfaces may intensify at higher filler content, further impeding phonon transport. Overall, the non-monotonic evolution of κ_L arises from the competing effects of interface scattering, filler aggregation, and the intrinsic transport characteristics of the Fe₃O₄ phase.

To further analyze the contributions of different phonon scattering mechanisms to κ_L, the Callaway model was employed to fit the low-temperature lattice thermal conductivity of both Bi₈₀Sb₂₀ and Bi₈₀Sb₂₀/0.4 vol% Fe₃O₄. The Callaway model is expressed as

where x = ħω/k_BT, k_B is Boltzmann's constant, ħ is the reduced Planck's constant, v is the average sound velocity, θ_D is the Debye temperature, ω is the phonon frequency, and τ(x) is the total phonon scattering relaxation time. In this study, three primary phonon scattering mechanisms are considered: Umklapp process (U), grain boundary (GB) and point defect (PD). Thus, τ(x) can be expressed aswith the corresponding terms given by grain boundary scattering, v/G, where G is the average grain size; point defect scattering, Aω⁴; Umklapp scattering, Bω²Te^−θ_D/3T. Here, A and B are the fitting parameters for point defect scattering and Umklapp scattering, respectively. The fitting coefficient parameter values are listed in Table S1. Based on these parameters, the relative contributions of different phonon scattering mechanisms to κ_L are extracted, as shown in Fig. 5e. It is evident that in the low temperature region (T < 50 K), Umklapp and grain boundary scattering are dominant. The Callaway model analysis indicates that point defect scattering becomes the dominant mechanism reducing κ_L above 50 K, significantly surpassing the contribution from grain boundary scattering. This conclusion is quantitatively supported by the scattering contributions (Table S2) derived from the model fitting. Δκ_B represents reduction of κ_L attributed to grain boundary scattering, while Δκ_PD denotes additional reduction attributed to point defect scattering. As shown in Fig. S7, the ratio of Δκ_PD/Δκ_B increases markedly from 3.2 at 50 K to 5.8 at 300 K. This demonstrates that point defect scattering contributes significantly more than grain boundary scattering across this temperature range and its relative dominance increases with rising temperature.

As shown in Fig. 5f, the dominant sources of the scattering captured by the large Δκ_PD value in the Callaway model fitting are: (1) intrinsic point defects: the substitutional disorder of Sb atoms on Bi sites) in the Bi₈₀Sb₂₀ solid solution matrix; (2) nano-Fe₃O₄-induced localized scattering: the atomic-scale disorder and, critically, the strong localized strain fields generated by the embedded nano-Fe₃O₄ particles. While the interfaces are extended defects, their phonon scattering effect at medium-to-high frequencies (T > 50 K) is effectively modeled within the point defect scattering framework due to its localized, short-wavelength nature. The synergistic combination of these two sources—especially the significant amplification provided by the nanocomposite-induced strain fields—leads to the exceptionally strong suppression of κ_L observed at higher temperatures. Isolating the exact quantitative contribution solely from the strict point defects versus the interface/strain effects within the aggregate Δκ_PD would require sophisticated multiscale modeling beyond standard Callaway analysis, combined with further microstructural characterization.

The dimensionless figure of merit, zT, for all the samples is plotted in Fig. 6a. For every composition, zT increases with temperature and reaches a maximum and then declines at higher temperature. Throughout the entire 150–300 K range, the Bi₈₀Sb₂₀/x vol% Fe₃O₄ nanocomposites exhibit substantially higher zT values than pristine Bi₈₀Sb₂₀. The highest zT value of 0.31 at 242 K of the x = 0.4% sample represents an improvement of ∼100% over the matrix (Fig. 6b). Therefore, judicious optimization of the nano-Fe₃O₄ content markedly enhances the TE performance of Bi₈₀Sb₂₀-based composites. The average figure of merit, zT_avg (150 to 300 K), for Bi₈₀Sb₂₀/0.4 vol% Fe₃O₄ and those of typical Bi–Sb based TE materials are presented in Fig. 6c. The zT_avg of 0.29 for Bi₈₀Sb₂₀/0.4 vol% Fe₃O₄ is much higher than that of most Bi–Sb based TE materials and only slightly lower than that of Bi₈₅Sb₁₅/Graphene composites.^31,60–65

Fig. 6 (a) Temperature dependence of the TE figure of merit (zT) for Bi₈₀Sb₂₀/x vol%Fe₃O₄ composites. (b) Relative change rate of (ΔzT/zT₀) of the zT for Bi₈₀Sb₂₀/x vol%Fe₃O₄ composites at 300 K, where zT₀ is the zT value of Bi₈₀Sb₂₀ and ΔzT represents the zT difference after incorporation of Fe₃O₄ composites. (c) Comparison of the average zT (zT_avg) from 150 to 300 K for Bi₈₀Sb₂₀/0.4 vol% Fe₃O₄ and other Bi–Sb based TE materials.^31,60–65 Indentation for Vickers hardness testing of (d) Bi₈₀Sb₂₀ and (e) Bi₈₀Sb₂₀/0.4 vol% Fe₃O₄. (f) Comparison of the Vickers hardness values of Bi₈₀Sb₂₀/0.4 vol% iron tetraoxide and several typical TE materials at 0.2N load and 10s loading time.^66–72

To validate the advantages of the dry preparation process in enhancing the TE performance, this study also subjected Bi₈₀Sb₂₀ and Bi₈₀Sb₂₀/0.2 vol% Fe₃O₄ powders to wet ball milling treatment. As shown in Fig. S8, compared to the dry ball milling samples using stearic acid as a dispersant, the wet-prepared composites exhibited a significant overall reduction in TE performance. Therefore, it can be concluded that combining dry ball milling with stearic acid as a dispersant is more advantageous. Quantitative comparison (Table S3) reveals the Bi₈₀Sb₂₀/0.4 vol% Fe₃O₄ composite achieves a zT of 0.29 at 300 K, which is twice the performance of pristine polycrystalline Bi₈₀Sb₂₀ (zT = 0.14) and surpasses the reported value of polycrystalline Bi₈₅Sb₁₅ (zT ∼0.15).²⁶ This enhancement primarily stems from a striking 107% increase in σ (4220 vs. 1400 S cm⁻¹), yielding a PF of 29.2 μW m⁻¹ K⁻² despite a moderate S reduction (83.2 vs. 89.1 μV K⁻¹). While the thermal conductivity increases to 3.1 W m⁻¹ K⁻¹, the composite closes 34% of the zT gap to single-crystal Bi₈₀Sb₂₀ (zT ∼0.58).³¹ These results demonstrate that magnetic nanoparticle incorporation effectively mitigates the characteristic carrier mobility limitations of polycrystalline Bi–Sb alloys.

Hardness testing of Bi₈₀Sb₂₀/x vol% Fe₃O₄ nanocomposites

The Vickers hardness test was utilized to accurately evaluate the hardness of the materials (Fig. 6d and e). The measured Vickers hardness is (38.6 ± 0.8) HV for the Bi₈₀Sb₂₀ matrix and (47.5 ± 1.0) HV for the Bi₈₀Sb₂₀/0.4 vol% Fe₃O₄ composites. The Vickers hardness of Bi₈₀Sb₂₀/x vol% Fe₃O₄ and several typical TE materials is shown in Fig. 6f. Although the hardness of the composite is lower than that of Ag_0.9Sb_1.1Te_3.1,⁶⁶ GeTe,⁶⁷ p-type Mg₃Sb₂,⁶⁸ Bi₂Te₃-based alloys⁶⁹ and PbSe,⁷⁰ it is significantly higher than that of Cu₂Se⁷¹ and PbTe.⁷² This enhancement in hardness suggests improved resistance to external mechanical stress and vibrations. The Fe₃O₄ nanoparticles act as reinforcement agents within the Bi₈₀Sb₂₀ matrix, which impede dislocation motion during plastic deformation to increase the hardness. In addition, the applied load applied during indentation can be partially transferred to the stiff Fe₃O₄ inclusions,^73,74 reducing the local stress in the Bi₈₀Sb₂₀ matrix and increasing the overall resistance to deformation. These mechanisms collectively enhance the ability of the composite to resist deformation under mechanical stress.

Conclusions

In summary, a series of n-type Bi₈₀Sb₂₀/x vol% Fe₃O₄ nanocomposites were successfully fabricated via a combined process of ball milling of elemental Bi and Sb with stearic acid-assisted dispersion and SPS. Their TE properties were systematically investigated. The incorporation of Fe₃O₄ nanoparticles led to a significant enhancement in TE performance across the entire temperature range of 150–300 K. Among the composites, the sample with 0.4 vol% Fe₃O₄ exhibited the highest zT of 0.31 at 242 K, which represents an ∼100% improvement compared to that of the Bi₈₀Sb₂₀ matrix. Furthermore, the introduction of nano-Fe₃O₄ significantly improved the Vickers hardness of the composites. This study demonstrates that the incorporation of superparamagnetic Fe₃O₄ nanoparticles is an effective strategy to simultaneously enhance both the TE and mechanical performance of n-type Bi₈₀Sb₂₀-based alloys.

Conflicts of interest

The authors declare no competing financial interest.

Data availability

The data that support the findings of this study are available from the corresponding author upon reasonable request.

The supplementary information file contains additional data supporting the main text. See DOI: https://doi.org/10.1039/d5ta04222d.

Acknowledgements

The authors acknowledge financial support from the National Natural Science Foundation of China (NSAF) (No. U2230131 and No. U2141208), JSPS KAKENHI (No. JP24K23069), State Key Laboratory of Powder Metallurgy, Priority Academic Program Development of Jiangsu Higher Education Institutions and Jiangsu Collaborative Innovation Center for Advanced Inorganic Function Composites, Nanjing Tech University. The authors also acknowledge the staff of the BL17B beamline (https://cstr.cn/31129.02.NFPS.BL17B) at the National Facility for Protein Science in Shanghai (NFPS, https://cstr.cn/31129.02.NFPS), Shanghai Advanced Research Institute, Chinese Academy of Sciences, for their technical support in PXRD and GIWAXS data collection and analysis.

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Footnote

† These authors contributed equally.

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