Ultrahigh thermoelectricity obtained in classical BiSbTe alloy processed under super-gravity

Ultrahigh thermoelectricity obtained in classical BiSbTe alloy processed under super-gravity | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article Ultrahigh thermoelectricity obtained in classical BiSbTe alloy processed under super-gravity Min Zhou, Haojian Su, Jun Pei, Li Wang, Hualu Zhuang, Jing-Feng Li, and 6 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-5871932/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted You are reading this latest preprint version Abstract Thermoelectric materials allow direct conversion between heat and electricity and may be useful for power generation or solid-state refrigeration. However, improving thermoelectric performance is challenging because of the strong coupling between the electrical and thermal transport properties. We demonstrate a new super-gravity-field re-melting fabrication technology that synergistically optimizes the thermoelectric performance. Using a super-gravity field, the brittle (Bi,Sb) 2 Te 3 alloy undergoes unusual plastic deformation and forms mounts of microstructure defects, which is rarely observed in common fabrication process. As a result, the microstructure reconstruction and carrier concentration optimization were simultaneously realized, resulting in an ultra-low lattice thermal conductivity of 1.91 in the BiSbTe alloy. The strong enhancement of thermoelectric properties was validated in a thermoelectric module with high conversion efficiency of 6.4% and corresponding output power density of 0.34 W cm 2 when subjected to a temperature difference of 185 K. This work highlights a new super-gravity strategy to achieve a high thermoelectric performance, which may be applicable to other thermoelectric materials. Physical sciences/Materials science/Materials for energy and catalysis/Thermoelectrics Physical sciences/Energy science and technology/Thermoelectric devices and materials Figures Figure 1 Figure 2 Figure 3 Figure 4 Main Text Thermoelectric materials interconvert electrical and thermal energy and have potential applications for waste heat power generation and all-solid-state refrigeration based on the Seebeck effect and Peltier effect, respectively 1,2 . The widespread use of thermoelectric materials is limited by their low thermoelectric conversion efficiencies. These are characterized by the dimensionless figure of merit zT = α 2 σ T /(κ L + κ e ), where α, σ, κ L , κ e , and T are the Seebeck coefficient, electrical conductivity, lattice thermal conductivity, electronic contribution to thermal conductivity, and absolute temperature, respectively. α 2 σ is usually called the power factor (PF). It is difficult to simultaneously manipulate electrical and thermal transport performance due to the complex coupling between these parameters. In recent years, studies have focused on optimizing the thermoelectric properties using band engineering 3,4 , microstructure engineering 5,6 , and by implementing new fabrication technologies 7–9 . These approaches have resulted in higher zT values in some thermoelectric materials. Bi 2 Te 3 -based alloys are the most widely used commercial thermoelectric materials for applications at room temperature 10 . Although a lot of new thermoelectric materials have been discovered and received more attention, Bi 2 Te 3 -based alloys remain at the forefront of thermoelectric research. Commercial Bi 2 Te 3 -based materials are typically prepared by zone melting with peak zT value of around unity for tens of years. This limitation restricts their applications to niche areas because of their low efficiency compared with those of other energy conversion materials, highlighting the need to improve their thermoelectric properties. Innumerable research efforts have focused on improving the thermoelectric performance of Bi 2 Te 3 -based alloys, but the zT value of higher than unity has rarely been obtained. Until 2008, a higher zT of 1.4 was reported 1 , which stimulated a series of following studies. Recent studies have focused on investigating structural modification to enhance the zT values of polycrystalline Bi 2 Te 3 alloys using different processing methods 11–13 , such as ball-milling and hot-pressing 11,14,15 , melt-spinning and spark-plasma-sintering (SPS) 8,16 , hot-forging 17 , low-temperature hydrothermal and hot-pressing treatment 18 . However, no significant increase in zT values was realized until Science published another work, which obtained a high zT of 1.86 in (Bi,Sb) 2 Te 3 compounds via liquid phase sintering with excess Te 19 . It is a pity that this work was controversial and could not be repeated in nearly ten years. Jo 20 and Deng 21 even constructed the similar microstructure in the Te-rich Bi 0.5 Sb 1.5 Te 3 alloys, the obtained maximum zT value was just 1.2–1.3, which was much lower than that reported by Kim 19 . So, high-performance BiTe-based thermoelectric materials are expected. In the present work, we develop a new fabrication technology, super-gravity-field re-melting (SGF-RM), to realize high-performance (Bi,Sb) 2 Te 3 thermoelectric material with record-high figure of merit of > 1.91. Using a super-gravity field, the (Bi,Sb) 2 Te 3 raw material was melted in a “chemical furnace” and then quickly solidified. The equivalent super-gravity field ( G ) is induced by the high-speed rotation of rotors and is expressed as G = ω 2 L , where ω is the angular velocity and L is the distance from the axis of rotation to the point of interest. A self-propagating "chemical furnace" (strong exothermic reaction, Ti + 2B→TiB 2 , 66.8 kcal mol − 1 ) 22 , which replaces the traditional high-temperature melting furnace, is used to melt the raw materials. When the super-gravity reaches a set value, the chemical furnace is ignited. During the burning process, a large amount of heat energy is created, which melts the raw materials. After the combustion reaction is complete, the melts quickly cool and solidify under super-gravity (Fig. 1 A and S1). Compared with traditional melting, the mass and heat transfer of the melts in the super-gravity field were faster than those occurring in the Earth-gravity field. The removal velocity of bubbles in the melt was strongly correlated with the supergravity coefficient ( G / g , g = 9.8 m/s 2 ) and the bubble radius 23,24 (Fig. 1 B and S2). Small bubbles were difficult to remove from the melt during the short solidification process due to their lower removal velocities, which promoted the formation of micropores in the obtained bulks. Under super-gravity, the material underwent a rapid volume change and plastic deformation during solidification. This effect is rarely observed in most brittle thermoelectric materials for conventional deformation processes. The plastic deformation process readily induced high-density dislocations in the alloys, and the super-gravity increased the degree of super-cooling, accelerated the solidification rate, and refined the crystal grains. Thus, the distinctive super-gravity-field re-melting technology facilitates the reconstruction of microstructures via changing the solidification process of (Bi,Sb) 2 Te 3 melts. Furthermore, the SGF-RM is efficient and economical, showing great potential for future industrial applications. In fact, the study on fabrication of metals 25 and ceramics 26,27 under high gravity field has been reported in the past decades. Until recently, highly-dense Cu 2 ZnSnSe 4 28 , SnTe-based 29,30 thermoelectric materials we successfully synthesized under high gravity field. Notably, SGF-RM facilitated microstructure reconstruction by changing the solidification process of the melt (Fig. 1 C). The higher number of grain boundaries and micropore interfaces scattered mid/long-wavelength phonons, which reduced the lattice thermal conductivity. The absence of a conduction medium in the micropores also decreased the thermal conductivity, although it reduced the carrier mobility 6,31 . The introduced high-density dislocations targeted short and medium-wavelength phonons, which reduced the lattice thermal conductivity. Furthermore, the enhanced point defects after SGF-RM (discussed later) targeted short-wavelength phonons. Thus, a full-spectrum strategy targeting a wide spectrum of phonons was realized, resulting in an ultra-low lattice thermal conductivity of <0.25 W/m K at 300 K (Fig. 1 E). However, excess Te tended to evaporate from the melt due to its lower vapor pressure, which generated anti-site defects because Bi(Sb) occupied Te vacancies during the melting process under super-gravity. This increased the carrier concentration and power factor (Fig. 1 D and 1 F). Benefitting from the improved power factor and a significant decrease in the lattice thermal conductivity, the zT value reached >1.91 (375 K) for the re-melted (Bi,Sb) 2 Te 3 alloy under super-gravity (Fig. 1 G); this finding was confirmed and reproducible ( Fig. S6 ). These results suggest that SGF-RM is an efficient method for processing high-performance thermoelectric materials. The (Bi,Sb) 2 Te 3 alloy with a rhombohedral structure showed anisotropic thermoelectric properties (Fig. 2 , S1, and S7), in which greater thermoelectric properties were obtained in the cross-plane direction (Fig. 2 and S1). The electrical conductivity decreased monotonically, indicating a degeneration in the material’s semiconductor characteristic. The Seebeck coefficient exhibited an initial increase and then a decrease with the temperature, which was associated with intrinsic excitation 32,33 . After SGF-RM, the electrical conductivity increased but the Seebeck coefficient decreased. The peak Seebeck coefficient decreased and moved to a higher temperature after SGF-RM. Due to the enhanced electrical conductivity and slightly lower Seebeck coefficient, the power factor increased over the measured temperature range of 300–500 K and reached a maximum of 44.5–48.9 µW/K 2 cm at 300 K; this was about 11–22% higher than that of the (Bi,Sb) 2 Te 3 alloy before SGF-RM (Fig. 2 C). The total thermal conductivity (κ) and lattice thermal conductivity (κ L ) showed similar temperature dependences (Fig. 2 D and 2 E), indicating that the lattice thermal conductivity made a marked contribution to the total thermal conductivity. As the temperature increased, the κ L initially decreased, due to Umklapp scattering, and then increased as intrinsic excitations occurred and dominated the transport process. The thermal conductivity and lattice thermal conductivity decreased after SGF-RM. An ultra-low lattice thermal conductivity of 0.15–0.25 W/m K was obtained, which approached the amorphous limit (Fig. 2 E). Benefiting from the increased power factor and reduced thermal conductivity, the peak zT of 1.91–1.97 (Fig. 1 G) and average zT of 1.63–1.66 (Fig. 2 F) were obtained for the Bi 0.48 Sb 1.52 Te 3.03 alloy after SGF-RM. To further investigate the electrical transport properties of the (Bi,Sb) 2 Te 3 alloys, the carrier concentration and mobility were measured. After SGF-RM, the carrier concentration increased, but the mobility decreased ( Table S2 ). An enhanced carrier concentration has also been reported for (Bi,Sb) 2 Te 3 -based alloys synthesized by melt-spinning compared with those prepared by the traditional melting/quenching/annealing synthesis 34 . The (Bi,Sb) 2 Te 3 alloys were p -type semiconductors whose carrier concentrations were affected by anti-site defects and anion vacancies. During the melting process under super-gravity, excess telluride atoms tended to evaporate from the melt due to their lower vapor pressure, which was confirmed by inductively coupled plasma–optical emission spectroscopy (ICP-OES) ( Table S2 ). Owing to their similar atom radii and physical properties, Bi(Sb) atoms mainly occupied the Te sites to form Bi′ Te or Sb′ Te anti-site defects (Fig. 1 D) 36 , where V •• Te is a Te vacancy, V′″ Bi or V′″ Sb is a Bi or Sb vacancy, Bi′ Te or Sb′ Te is an anti-site defect, and h • is a hole. Thus, the evaporation of excess Te in the Bi 0.48 Sb 1.52 Te 3.03 alloy generated more anti-site defects when Bi(Sb) atoms occupied Te vacancies 37 . These negatively charged anti-site defects formed extra holes in the matrix, which increased the carrier concentration and electrical conductivity after SGF-RM. Moreover, the maximum Seebeck coefficient shifted to a higher temperature after SGF-RM (Fig. 2 B), which was also ascribed to the suppression of the intrinsic conductivity by increasing the carrier concentration. The carrier mobility decreased after SGF-RM, primarily due to increased carrier–carrier scattering and enhanced point defect scattering. In this work, an effective mass model was also used to evaluate the charge carrier transport properties 6,38 . Although bipolar effects easily occur in Bi 2 Te 3 -based alloys, a single-parabolic-band model was used in this work. This model assumed that minor charge carriers contributed little to the electrical conductivity 6,7 . According to the fitted curves with the assumed effective mass m * = 1.05 m 0 ( m 0 is the inertial mass of a free electron) and the drift mobility µ 0 = 420 cm 2 /V s, the predicted Hall-carrier-concentration-dependent Seebeck coefficient and Hall mobility were obtained ( Fig. S8 ). The results confirmed the validity of the single-parabolic-band model. Findings from recent studies 6,7,19,34,39,40 are consistent with those found in this work. The results showed some discrepancies from the fitting lines for the (Bi,Sb) 2 Te 3 materials, which may have been related to the complex electronic structures of the (Bi,Sb) 2 Te 3 alloys. However, the weighted mobility µ w , which characterizes the drift mobility and inherent transport properties, was consistent between the samples before and after SGF-RM ( Fig. S8C ), further confirming that the acoustic phonon scattering mechanism was unchanged. With a combination of the predicted Hall-carrier-concentration-dependent Seebeck and Hall mobility, the thermoelectric power factor was calculated and compared with the experimental data ( Fig. S8D ). The comparison suggested that the improvement in the power factor was mainly due to the optimization of the carrier concentration after SGF-RM. Positrons are sensitive and self-seeking probes for microstructural defects, and positron annihilation measurements provide a way to qualitatively analyze anti-site defects, dislocations, vacancies, and even pores inside materials 41,42 . The measured positron annihilation spectra ( Fig. S9 ) were decomposed into three lifetimes, τ 1 , τ 2 , and τ 3 , with corresponding intensities I 1 , I 2 , and I 3 , respectively, using the LT9.0 software (Table 1 ). The longest-lifetime component τ 3 may have been due to the annihilation of the ortho-positronium formed on the surfaces of the specimens and/or some low-energy positrons annihilated by inner 22 Na 43 . As the values of the relative intensity I 3 of the samples was the weakest (< 2.5%), it will not be discussed in this paper. The positron lifetime τ 1 represents the free positron lifetime originating from anti-site defects, dislocations, and small vacancies, while τ 2 was likely caused by large clusters of vacancies and micropores 44 . Notably, τ 1 and I 1 increased from 0.152 ns and 26.3% to 0.169 ns and 31.1% after SGF-RM, respectively. This suggests the creation of more point defects, including anti-site defects and dislocations that were introduced into the matrix after SGF-RM. The second-lifetime component τ 2 was much longer than τ 1 due to positron trapping and annihilation at several large vacancy clusters or micropores. After SGF-RM, the lifetime τ 2 increased but I 2 decreased. The increased τ 2 indicated that new micropores with larger sizes were formed in the matrix, in addition to the vacancy clusters after SGF-RM. The reduced I 2 may have been related to the decreased density of vacancy clusters caused by the production of more anti-site defects after tellurium evaporation. Positron annihilation measurements showed that more anti-site defects, dislocations, and micropores were introduced in the (Bi,Sb) 2 Te 3 alloys after SGF-RM. Table 1 Positron annihilation lifetime spectroscopy (PALS) data of BST and BST-1. Specimen τ 1 (ns) I 1 (%) τ 2 (ns) I 2 (%) τ 3 (ns) I 3 (%) BST 0.1521 26.3 0.3209 71.6 1.286 2.06 BST-1 0.1685 31.1 0.3344 67.7 1.534 1.25 To analyze the reasons for the reduced thermal conductivity, the microstructure and morphology were further investigated by transmission electron microscopy (TEM). No obvious dislocations were observed in the raw BST samples ( Fig. S10 ), while high-density dislocations were found throughout the melted BST-1 samples (Fig. 3 and S11). The dislocations had diverse morphologies, with many disordered long dislocation lines existing alone or intertwining with each other to form dislocation networks (Fig. 3 B). There were also many shorter dislocation lines inside the grains ( Fig. S11 ). Most dislocations were found inside the grains instead of at the grain boundaries. The (Bi,Sb) 2 Te 3 melt quickly cooled and solidified under super-gravity, which introduced a rapid change in volume and strained the inside of the samples. This caused plastic deformation within the sample, especially inside the grains, leading to the formation of dislocation pile-ups. The high-resolution TEM (HRTEM) image (Fig. 3 B) shows the corresponding fast Fourier transform (FFT) pattern (inset of Fig. 3 B) in the [‾55‾1] direction. The atomically resolved scanning transmission electron microscopy high-angle annular dark field (STEM HAADF) image (Fig. 3 C) shows a dislocation in the BST-1 sample. To further investigate the dislocation characteristics, inverse fast Fourier transform (IFFT) images (Fig. 3 D–F) combined with geometric phase analysis (GPA) were introduced to analyze the HRTEM images for dislocation cores and corresponding strain fields (Fig. 3 G–I). Many dislocation cores existed around dislocations in all three planes. The dislocation density was estimated to be 7 × 10 12 cm − 2 . Strain convergence regions were found around the dislocation cores, which were randomly distributed in all orientations. The high-density dislocations and the associated strain field strongly interfered with the propagation of short/medium-wavelength phonons and in the softening of the lattice 45,46 , which reduced the thermal conductivity. More micropores and finer grains were observed on the fractured surfaces of the melted BST-1 samples ( Fig. S12 ), which also confirmed the above positron annihilation measurements. These micropores and grain boundaries also helped decrease the thermal conductivity. Analogous results were also reported in previous studies 6,47 . The formation of these micropores and smaller grains was also related to the rapid solidification of the melt under the super-gravity field, as discussed above. Based on the above positron annihilation measurements and microstructural characterization results, the presence of pile-ups of microstructural defects, such as dislocations, anti-site defects (Bi(Sb)′ Te ), and micropores, was confirmed, which showed that the microstructures of the (Bi,Sb) 2 Te 3 alloys were reconstructed after SGF-RM. To better understand the main factor responsible for the reduced lattice thermal conductivity, the effective medium theory (EMT) and the Debye–Callaway model were used to analyze the contributions of the absence of thermal conduction within the micropores and the various phonon scattering mechanisms, respectively. According to the classical EMT, the lattice thermal conductivity of a fully dense material (κ L,d ) can be expressed by κ L,d = κ L,p /(1–3ε/2), where κ L,p is the lattice thermal conductivity of the porous material, and ε is the porosity 48 . Based on the experimental lattice thermal conductivity and porosity ( Table S3 ), the corrected κ L,d of the corresponding dense BST-1 sample was obtained (open triangles in Fig. 1 E). The corrected κ L,d can be described using the Debye–Callaway model to analyze the contributions of the various scattering mechanisms to the reduction in the thermal conductivity. The contributions of Umklapp scattering (U), normal scattering (N), and point defect (PD) scattering were accounted for using the Debye–Callaway model to fit the data of the BST sample (black line in Fig. 1 E). Increases in the deviation upon increasing the temperature were due to a bipolar effect. Substantial heat was carried by mid/long-wavelength phonons, which could be scattered more effectively by the interfaces of micropores and grain boundaries. This resulted in a 14–19% reduction of the lattice thermal conductivity in the measured temperature range of 300–500 K (purple solid line in Fig. 1 E). Furthermore, the greater reduction in the lattice thermal conductivity was attributed to the high dislocation density (≈ 7 × 10 12 cm − 2 ), which mainly scattered phonons in the short/mid-wavelength range. The absence of thermal conduction within the micropores also reduced the thermal conductivity based on the above EMT. The micropore structure (including micropores and their interfaces) resulted in about a 24% total reduction in the lattice thermal conductivity at 300 K. As a result, the reconstruction of the microstructures by SGF-RM resulted in an ultra-low lattice thermal conductivity. The thermoelectric power generation is a more direct index used to further confirm the enhanced zT values. Thermoelectric modules with 127 pairs of p - n legs (inset in Fig. 4 A) were fabricated to study the power generation. The measured conversion efficiency and power output of the thermoelectric module (BST-1 module in Fig. 4 ) together with the commercial module (BST module in Fig. 4 ) are shown in Fig. 4 A and 4 C. When the temperature difference across the module increased to 184 K (T cold = 289 K, T hot =473 K), the measured maximum conversion efficiency ( η ) was 6.4%, which was about 52% higher than that of the commercial module (≈ 4.2%). And, high output power of 5.5 W was obtained, representing 83% improvement in comparison to that of commercial module. The corresponding output power density arrived at 0.34 W cm 2 (Fig. 4 D). Although the conversion efficiency and power output the thermoelectric module were lower than the theoretical values, they were higher than many reported values of (Bi,Sb) 2 Te 3 -based devices 7,49–52 (Fig. 4 B and 4 D). These results confirmed the greatly enhanced zT values of the melted (Bi,Sb) 2 Te 3 alloys under super-gravity. The thermoelectric properties of the n -type legs ( Table S5 ) remained much lower than those of the p -type legs. If the thermoelectric properties of the n -type material were improved and the bonding technology of the module were optimized, a higher conversion efficiency might be obtained. The present study highlights the ultrahigh thermoelectricity in the classical BiSbTe alloy obtained by a new super-gravity-field re-melting fabrication technology. Under a super-gravity field, the brittle (Bi,Sb) 2 Te 3 alloy underwent unusual plastic deformation during melt solidification, which reconstructed its microstructure and formed multiple microstructure defects. Together with the carrier concentration optimization, an ultra-low thermal conductivity and a record-high figure of merit ( zT >1.91 at 375 K) were obtained in the BiSbTe alloy. A high-performance thermoelectric device (η max = 6.4%) further demonstrated the enhanced thermoelectric properties and the potential applications in the power generation devices. Declarations Data availability The data that support the findings of this study are available from the corresponding author on request. Acknowledgments This work was supported by the Key Laboratory of Cryogenic Science and Technology (Grant No. CRYO20230203), the National Natural Science Foundation of China (Grant No. 51872299), and the Basic Science Center Project of National Natural Science Foundation of China (Grant No. 52388201). We thank Tsinghua University, Beihang University and Ningbo Institute of Materials Technology & Engineering, CAS for the repeated measurements of the thermoelectric properties. We also thank Huabei Cooling Device Co., Ltd. for fabricating the thermoelectric device modules and the Shenzhen Institute of Advanced Electronic Materials for measuring the thermoelectric conversion efficiency. Author contributions M.Z. and H.J.S. synthesized the samples, designed and carried out the experiments, analyzed the results, and wrote the paper. J.P. conducted theoretical calculations and analyzed the results. L.W. measured the thermoelectric performance. H.L.Z. measured the Hall coefficient. K.S., H.Y.H., and J.J. fabricated the thermoelectric modules. Q.H.Z. helped with TEM measurements and analysis. The experimental design and paper writing were performed under the supervision of J.-F.L. J.J. and L.F.L. All authors contributed to the discussion of the results and commented on the manuscript. Competing interest s The authors declare no competing interests. Additional i nformation Supplementary i nformation is available for this paper. 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Vacancy-induced dislocations within grains for high-performance PbSe thermoelectrics. Nat. Commun. 8 , 13828 (2017). Wang, Y. et al. High Porosity in Nanostructured n-Type Bi 2 Te 3 Obtaining Ultralow Lattice Thermal Conductivity. ACS Appl . Mater . Inter. 11 , 31237–31244 (2019). Hu, H. H. et al. Thermoelectric Cu 12 Sb 4 S 13 -Based Synthetic Minerals with a Sublimation-Derived Porous Network. Adv . Mater . 33 , 2103633 (2021). Zheng, G. et al. High thermoelectric performance of p-BiSbTe compounds prepared by ultra-fast thermally induced reaction. Energ Environ . Sci . 10 , 2638–2652 (2017). Guo, Z. et al. Broadening the optimum thermoelectric power generation range of p-type sintered Bi 0.4 Sb 1.6 Te 3 by suppressing bipolar effect. Chem . Eng . J . 426 , 131853 (2021). Hao, F. et al. High efficiency Bi 2 Te 3 -based materials and devices for thermoelectric power generation between 100 and 300 ℃. Energ Environ . Sci . 9 , 3120–3127 (2016). Wu, G. et al. Optimized Thermoelectric Properties of Bi 0.48 Sb 1.52 Te 3 through AgCuTe Doping for Low-Grade Heat Harvesting. ACS Appl . Mater . Inter . 13 , 57514–57520 (2021). Methods Materials synthesis The zone-melted Te-rich Bi 0.48 Sb 1.52 Te 3.03 ingots (BST) are used as the starting materials. These zone-melted ingots are firstly hand-milled into powders. Some powders are cold pressed into cylindrical compacts with a diameter of 25 mm (BST-1, BST-10). Other powders are sifted. The sieved products with particles between 0.6-1 microns are also cold pressed (BST-S). Each batch of about 0.1 kg powders was cold pressed under a uniaxial pressure of 10 MPa. The compacts are loaded into quartz ampoules, which is then evacuated and sealed. As shown in Fig. S1 , the mixtures of titanium and boron powders are poured into a quartz crucible with an inner diameter of 40 mm and length of 250 mm, into which the sealed (Bi,Sb) 2 Te 3 specimen is placed. A tungsten coil is fixed above the top surface of the (Ti + 2B) mixtures. The quartz crucible is wrapped with carbon felt, and then is loaded into a graphite crucible. A graphite cap is used to close the quartz and graphite crucibles. The graphite crucible is also wrapped with carbon felt and placed into a steel cup, and the cup is horizontally mounted at one side of a rotator in the reaction chamber. A counterweight is mounted at the other side of the rotator to keep balance. After the reaction chamber is evacuated, the rotator is started. By the centrifugal effect, an equivalent super-gravity field ( G ) is induced by high-speed rotation. When the super-gravity reaches set values (for example, G = 100 g , 1000 g ( g = 9.8 m/s 2 )), the top of the (Ti + 2B) mixing powders are ignited by passing an electric current of 10 A in the tungsten coil for 2 s . After being ignited, the (Ti + 2B) powders bed continues to burn in a self-sustained way with the combustion front moving from the top to the bottom of the quartz crucible. During the burning process, a large amount of heat energy is created 20 , which melts the (Bi,Sb) 2 Te 3 compacts. For the exothermic reaction, Ti + 2B→TiB 2 , the flame front velocity was about 15-26.6 mm/s 47 , the combustion reaction lasted for tens of seconds in this work. The peak temperature of the TiB 2 combustion synthesis was over 1200°C 48 , while the melting temperature of Bi 0.48 Sb 1.52 Te 3.03 alloy was about 610°C 49 . So, the high temperature inside of the “chemical furnace” would hold for longer time to melt the (Bi,Sb) 2 Te 3 alloys with the heat insulation layer (Fig. S1 ). In fact, the super-gravity field of 1000 g holds for 1 min (BST-1) and 10 min (BST-10, BST-S) to study the densification process after being ignited. The solidified (Bi,Sb) 2 Te 3 ingots are obtained and then are taken out for later characterizations and measurements. It is worth noting that the density is too low (the relative density is only 80.81%) for the samples fabricated under the super-gravity field of 100 g . So, these samlpes are not discussed in this paper. The simple model is used to analyze the densification process of (Bi,Sb) 2 Te 3 alloys in the melting under super-gravity field without considering the temperature gradient, compositional gradient and melt turbulence. Supergravity can enhance the energy transfer of multiphase flow, thus strengthening the mass transfer, heat transfer and chemical reaction processes. So, it can be recognized that the continuous alloy melt homogenized in a moment under the super-gravity field. But there are still a lot of bubbles in the melt, which determines the density of the final alloy product. Figure 1 B and Fig. S2 briefly show the densification process of (Bi,Sb) 2 Te 3 alloy. Melts and bubbles are separated during the melting, and then cooled under super-gravity. As we know, the lifting velocity of bubbles in melts is closed related to the supergravity coefficients. According to Stokes law 23 , the lifting velocity of bubbles in melts can be calculated ( V B ): $$\:{V}_{B}=\frac{2}{9}({\rho\:}_{M,l}-{\rho\:}_{B,g})\frac{G{R}_{B}^{2}}{{\eta\:}_{M}}$$ 1 where, ρ M,l and ρ B,g are the density of melts and bubble, respectively. G is the super-gravity field, R B is the radius of bubble, η M is the viscosity of melts. The forces of the bubbles in melts include the super-gravity ( F g ), buoyancy of melts ( F b ) and viscous drag of melts ( F v ). The super-gravity: $$\:{F}_{g}=\frac{4}{3}\pi\:{R}_{B}^{3}{\rho\:}_{B,g}G$$ 2 The buoyancy of melts: $$\:{F}_{b}=\frac{4}{3}\pi\:{R}_{B}^{3}{\rho\:}_{M,l}G$$ 3 The viscous drag of melts: $$\:{F}_{v}=6\pi\:{R}_{B}^{3}{}_{M}{V}_{B}$$ 4 when F b = F g + F v , the lifting velocity of bubbles reaches a stabilized value. According to the formula (2–4), the lifting velocity of bubbles at steady state ( V B ): $$\:{V}_{B}=\frac{2}{9}({\rho\:}_{M,l}-{\rho\:}_{B,g})\frac{{R}_{B}^{2}G}{{}_{M}}$$ 5 Because ρ B,g << ρ M,l , formula (5) can be simplified as: $$\:{V}_{B}=\frac{2}{9}{\rho\:}_{M,l}\frac{{R}_{B}^{2}G}{{}_{M}}$$ 6 According to the formula (6), the lifting velocity of bubbles in alloy melts at steady state is calculated (by using the data listed in Table S1 ) and shown in Fig. S2 . The above results show that the lifting velocity of bubbles in alloy melts can be obviously increased by enhancing the supergravity coefficient ( G / g ) and the radius of bubbles. For (Bi,Sb) 2 Te 3 alloy, the super-gravity coefficient ( G / g ) of 1000 is high enough to densify the bulks. However, the bubbles with small radii are hard to clean out of the alloy melts in the short densification process due to the lower lifting velocity of small bubbles. So, a few small pores are observed in the melted bulks. Structural Characterization The phase composition is analyzed by X-ray diffraction (Bruker, Germany) with Cu K α radiation. The typical XRD patterns of the (Bi,Sb) 2 Te 3 samples are shown in Fig. S2 . The microstructures are observed by field-emission scanning electron microscopy (FESEM, S-4800, Hitachi) and transmission electron microscopy (TEM, 2100F, JEOL). Elemental analyses are collected by inductively coupled plasma-optical emission spectroscopy (ICP-OES, Varian 710-ES). Thermoelectric Property Measurements The Seebeck coefficient ( α ) and electrical conductivity ( σ ) are measured by using the Seebeck Coefficient/Electrical Resistance Measuring System (ZEM-3, Ulvac-Riko) under a static helium atmosphere. The Hall coefficient ( R H ) is measured by a Hall measurement system (ResiTest 8340DC, Toyo, Japan) via the van der Pauw method. The hall carrier concentration ( n H ) and mobility ( µ H ) are calculated by n H =1/( eR H ) and µ H = R H / ρ , respectively. The thermal conductivity ( κ ) is calculated using the equation κ = λC p d , where λ is the thermal diffusivity, C p is the heat capacity, and d is bulk density of the sample. The thermal diffusivity is measured by a laser flash technique (Netzsch LFA457) in Ar atmosphere. The heat capacity is measured using Differential Scanning Calorimeter (DSC404-F3). The measured λ and C p values were shown in Fig. S4 and Fig. S5 , respectively. The bulk density is obtained by the Archimedes method. The lattice thermal conductivities ( κ L ) are obtained by subtracting the electrical contribution from the total thermal conductivity using the equation κ L = κ - κ e . Here, the electrical thermal conductivity is expressed by the Wiedemann Franz Law κ e = LσT , where L is estimated by using a Single Parabolic Band (SPB) model 50 . Transport properties are measured in the parallel (cross-plane) (Fig. 2 ) and perpendicular (in-plane) ( Fig. S7 ) to the direction of the super-gravity field. The transport properties in the parallel direction were repeated ( Fig. S6 ). Positron Annihilation Measurement Positron annihilation lifetime spectroscopy (PALS) analysis is performed using a fast-slow coincident ORTEC system with a time resolution of 220 ps for the full width at half maximum. The 22 Na positron source is placed between the two pieces of samples, and then the “sample-source-sample sandwich” is placed between the two BaF 2 detectors to acquire the lifetime spectra. A total of 2×10 6 counts are accumulated for each spectrum to reduce the statistical error in the calculation of lifetimes. The positron lifetime spectra are de-convoluted and analyzed using the LT-9 software. LT-9 is one of the most popular software for PALS analysis. It de-convolutes the experimental curve from the instrument functions to set apart the physical meaning information, i.e. positron annihilation lifetime and intensity. Positron annihilation lifetime and intensity could reflect the defect size and density information. Module fabrication and measurement TE modules with the size of 40×40×2.6 mm 3 and a total 127 pairs of p - n legs were fabricated in Huabei Cooling Device Company. The size for the legs is 1.33×1.33×1.6 mm 3 . The melted Bi 0.48 Sb 1.52 Te 3.03 sample was utilized for the p -type legs. The zone-melted BiSbTe alloys (BST) serve as the references. The n -type counterparts are commercial Bi 2 Te 2.2 Se 0.8 ingots (The measured thermoelectric parameters were shown in Table S5 ). The energy conversion efficiencies and cooling temperature difference of these modules were evaluated by man-made testing system in Shenzhen Institute of Advanced Technology, Chinese Academy of Sciences. The hot-side temperatures were maintained between 423–500 K, while the temperature of the water cooler was kept at 283 K. Methods references 47. Bernert, T. et al. In situ observation of self-propagating high temperature syntheses of Ta 5 Si 3 , Ti 5 Si 3 and TiB 2 by proton and X-ray radiography. Solid State Sci. 22 , 33–42 (2013). 48. Roy, S. K. et al. Combustion Synthesis of TiB and TiB 2 under vacuum. J. Mater. Sci. Lett. 13 , 371–373 (1994). 49. Rowe, D. W. et al. CRC Handbook of Thermoelectrics (CRC press, 1995). 50. Li, Z. Y. et al. Fine-Grained and Nanostructured AgPb m SbTe m+2 Alloys with High Thermoelectric Figure of Merit at Medium Temperature. Adv. Energy Mater . 4 , 1300937 (2014). 51. Hong, M. et al. Rashba Effect Maximizes Thermoelectric Performance of GeTe Derivatives. Joule 4 , 2030–2043 (2020). Additional Declarations There is NO Competing Interest. Supplementary Files ThermoelectricmainmanuscriptsuppNNsubmit.docx Ultrahigh thermoelectricity obtained in classical BiSbTe alloy processed under super-gravity Cite Share Download PDF Status: Under Review Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-5871932","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":410442751,"identity":"9efac722-6028-4d3d-a28a-7119a0b582f1","order_by":0,"name":"Min 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China","correspondingAuthor":false,"prefix":"","firstName":"Jiangtao","middleName":"","lastName":"Li","suffix":""},{"id":410442762,"identity":"2050b0e7-168e-4a72-b3a6-05d27a39495a","order_by":11,"name":"Laifeng Li","email":"","orcid":"","institution":"Technical Institute of Physics and Chemistry, Chinese Academy of Sciences","correspondingAuthor":false,"prefix":"","firstName":"Laifeng","middleName":"","lastName":"Li","suffix":""}],"badges":[],"createdAt":"2025-01-21 09:06:10","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-5871932/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-5871932/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":75580469,"identity":"ba6f4fb5-2917-4748-9412-2f064c0573a1","added_by":"auto","created_at":"2025-02-06 05:33:09","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":814475,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eSynergistically optimizing phonon and electron transport for record-high \u003c/strong\u003e\u003cem\u003e\u003cstrong\u003ezT\u003c/strong\u003e\u003c/em\u003e\u003cstrong\u003e values. \u003c/strong\u003eSchematic illustration of the (\u003cstrong\u003eA\u003c/strong\u003e) super-gravity-field re-melting technology, (\u003cstrong\u003eB\u003c/strong\u003e) movement of bubbles in melts, and (\u003cstrong\u003eC\u003c/strong\u003e) reconstruction of microstructures after super-gravity-field re-melting (SGF-RM). (\u003cstrong\u003eD\u003c/strong\u003e) Process of Te evaporation causing extra holes. (\u003cstrong\u003eE\u003c/strong\u003e) Lattice thermal conductivities (k\u003csub\u003eL\u003c/sub\u003e) of samples before and after SGF-RM. The solid symbols present the experimental results. The black solid line represents the predicted k\u003csub\u003eL\u003c/sub\u003e value considering the scattering of the Umklapp process, normal process, and point defects (U+N+P). The purple solid line represents the predicted k\u003csub\u003eL\u003c/sub\u003e value considering the additional scattering of grain boundaries and micro-pore interfaces (U+N+P+I). The red solid line represents the predicted k\u003csub\u003eL\u003c/sub\u003e values considering the additional scattering of dislocations (U+N+P+I+DS). The effective medium theory (EMT)-corrected values are shown by red empty triangles. (\u003cstrong\u003eF\u003c/strong\u003e) Power factor values as a function of the Hall carrier concentration predicted by the effective mass \u003cem\u003em\u003c/em\u003e* = 1.05m\u003csub\u003e0\u003c/sub\u003e and drift mobility \u003cem\u003eµ\u003c/em\u003e\u003csub\u003ew\u003c/sub\u003e = 420 cm\u003csup\u003e2\u003c/sup\u003e/V s at 300 K. (\u003cstrong\u003eG\u003c/strong\u003e) \u003cem\u003ezT\u003c/em\u003e values of the Bi\u003csub\u003e0.48\u003c/sub\u003eSb\u003csub\u003e1.52\u003c/sub\u003eTe\u003csub\u003e3.03\u003c/sub\u003e alloy before (BST) and after SGF-RM. Note: The sample with hand-milled powders is denoted as BST-1 after re-melting under super-gravity for 1 min. The sample with hand-milled powders is denoted as BST-10 after re-melting under super-gravity for 10 min. The sample with particle sizes between 0.6 and 1 µm is denoted as BST-S after re-melting under super-gravity for 10 min.\u003c/p\u003e","description":"","filename":"image1.png","url":"https://assets-eu.researchsquare.com/files/rs-5871932/v1/5aef899c47ced8dbb8c3aae0.png"},{"id":75580480,"identity":"737f8d65-3451-4b38-8429-dcd4b8f542c6","added_by":"auto","created_at":"2025-02-06 05:33:10","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":433180,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eThermoelectric properties. \u003c/strong\u003eTemperature dependence of (\u003cstrong\u003eA\u003c/strong\u003e) electrical conductivity, (\u003cstrong\u003eB\u003c/strong\u003e) Seebeck coefficient, (\u003cstrong\u003eC\u003c/strong\u003e) power factor, (\u003cstrong\u003eD\u003c/strong\u003e) thermal conductivity, (\u003cstrong\u003eE\u003c/strong\u003e) lattice thermal conductivity, and (\u003cstrong\u003eF\u003c/strong\u003e) average \u003cem\u003ezT\u003c/em\u003e values of the (Bi,Sb)\u003csub\u003e2\u003c/sub\u003eTe\u003csub\u003e3\u003c/sub\u003e alloys before and after SGF-RM. Some data of previously reported typical (Bi,Sb)\u003csub\u003e2\u003c/sub\u003eTe\u003csub\u003e3\u003c/sub\u003e-based materials are also shown in Fig. 2F\u003csup\u003e7,11,19,34,35\u003c/sup\u003e.\u003c/p\u003e","description":"","filename":"image2.png","url":"https://assets-eu.researchsquare.com/files/rs-5871932/v1/59d4db3ae36d9e7e58828aab.png"},{"id":75581517,"identity":"eb64c8dd-0b66-40c7-a6be-2bfdcba03f83","added_by":"auto","created_at":"2025-02-06 05:41:10","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":2192361,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eTransmission electron microscopy (TEM) images of BST-1 samples.\u003c/strong\u003e (\u003cstrong\u003eA\u003c/strong\u003e) Low-magnification TEM Image. (\u003cstrong\u003eB\u003c/strong\u003e) High-resolution TEM (HRTEM) image of a randomly selected region in Fig. 3A. (\u003cstrong\u003eC\u003c/strong\u003e) Atomically resolved scanning transmission electron microscopy high-angle annular dark field (STEM HAADF) image showing a dislocation in a randomly selected region in Fig. 3A. (\u003cstrong\u003eD\u003c/strong\u003e–\u003cstrong\u003eF\u003c/strong\u003e) Inverse fast Fourier transform (IFFT) images in the (015), (10`5) and (110) planes obtained from the area marked by the white rectangle in Fig. 3B. (\u003cstrong\u003eG\u003c/strong\u003e–\u003cstrong\u003eI\u003c/strong\u003e) Strain field maps of e\u003csub\u003exx\u003c/sub\u003e, e\u003csub\u003eyy\u003c/sub\u003e, and shear strain e\u003csub\u003exy\u003c/sub\u003e. The color scale corresponds to strain from −20% to 20% with reference to the average strain of a non-defect area.\u003c/p\u003e","description":"","filename":"image3.png","url":"https://assets-eu.researchsquare.com/files/rs-5871932/v1/8b0de53cb507de026882d029.png"},{"id":75580473,"identity":"456afb91-c9f6-4e23-ae11-0f6668caf72a","added_by":"auto","created_at":"2025-02-06 05:33:10","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":704292,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eMeasured conversion efficiency and output power.\u003c/strong\u003e (\u003cstrong\u003eA\u003c/strong\u003e) Electric current dependence of the conversion efficiency, and the inset shows a photograph of the module. (\u003cstrong\u003eB\u003c/strong\u003e) Maximum conversion efficiency with different temperature differences. (\u003cstrong\u003eC\u003c/strong\u003e) Electric current dependence of output power. (\u003cstrong\u003eD\u003c/strong\u003e) Power density with different temperature differences. The hot-side temperature was set to 423 K or 473K. The corresponding cold-side temperature was 286 K or 289 K. Data from previous studies are shown for comparison\u003csup\u003e7,34, 49-52\u003c/sup\u003e.\u003c/p\u003e","description":"","filename":"image4.png","url":"https://assets-eu.researchsquare.com/files/rs-5871932/v1/b6ff76ead823abe93f1e4294.png"},{"id":75583286,"identity":"ea964309-a282-49c7-a09d-f2754046164c","added_by":"auto","created_at":"2025-02-06 06:05:50","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":5997861,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-5871932/v1/a699b1f3-f0ef-4a0e-a537-9d0c7d6b12b9.pdf"},{"id":75580470,"identity":"20711281-caae-4737-a463-f4f2e80493b6","added_by":"auto","created_at":"2025-02-06 05:33:09","extension":"docx","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":3859116,"visible":true,"origin":"","legend":"Ultrahigh thermoelectricity obtained in classical BiSbTe alloy processed under super-gravity","description":"","filename":"ThermoelectricmainmanuscriptsuppNNsubmit.docx","url":"https://assets-eu.researchsquare.com/files/rs-5871932/v1/fdb33c9a3ce7a3e06b82c568.docx"}],"financialInterests":"There is \u003cb\u003eNO\u003c/b\u003e Competing Interest.","formattedTitle":"Ultrahigh thermoelectricity obtained in classical BiSbTe alloy processed under super-gravity","fulltext":[{"header":"Main Text","content":"\u003cp\u003eThermoelectric materials interconvert electrical and thermal energy and have potential applications for waste heat power generation and all-solid-state refrigeration based on the Seebeck effect and Peltier effect, respectively\u003csup\u003e1,2\u003c/sup\u003e. The widespread use of thermoelectric materials is limited by their low thermoelectric conversion efficiencies. These are characterized by the dimensionless figure of merit \u003cem\u003ezT\u003c/em\u003e\u0026thinsp;=\u0026thinsp;α\u003csup\u003e2\u003c/sup\u003eσ\u003cem\u003eT\u003c/em\u003e/(κ\u003csub\u003eL\u003c/sub\u003e\u0026thinsp;+\u0026thinsp;κ\u003csub\u003ee\u003c/sub\u003e), where α, σ, κ\u003csub\u003eL\u003c/sub\u003e, κ\u003csub\u003ee\u003c/sub\u003e, and \u003cem\u003eT\u003c/em\u003e are the Seebeck coefficient, electrical conductivity, lattice thermal conductivity, electronic contribution to thermal conductivity, and absolute temperature, respectively. α\u003csup\u003e2\u003c/sup\u003eσ is usually called the power factor (PF). It is difficult to simultaneously manipulate electrical and thermal transport performance due to the complex coupling between these parameters. In recent years, studies have focused on optimizing the thermoelectric properties using band engineering\u003csup\u003e3,4\u003c/sup\u003e, microstructure engineering\u003csup\u003e5,6\u003c/sup\u003e, and by implementing new fabrication technologies\u003csup\u003e7\u0026ndash;9\u003c/sup\u003e. These approaches have resulted in higher \u003cem\u003ezT\u003c/em\u003e values in some thermoelectric materials.\u003c/p\u003e \u003cp\u003eBi\u003csub\u003e2\u003c/sub\u003eTe\u003csub\u003e3\u003c/sub\u003e-based alloys are the most widely used commercial thermoelectric materials for applications at room temperature\u003csup\u003e10\u003c/sup\u003e. Although a lot of new thermoelectric materials have been discovered and received more attention, Bi\u003csub\u003e2\u003c/sub\u003eTe\u003csub\u003e3\u003c/sub\u003e-based alloys remain at the forefront of thermoelectric research. Commercial Bi\u003csub\u003e2\u003c/sub\u003eTe\u003csub\u003e3\u003c/sub\u003e-based materials are typically prepared by zone melting with peak \u003cem\u003ezT\u003c/em\u003e value of around unity for tens of years. This limitation restricts their applications to niche areas because of their low efficiency compared with those of other energy conversion materials, highlighting the need to improve their thermoelectric properties. Innumerable research efforts have focused on improving the thermoelectric performance of Bi\u003csub\u003e2\u003c/sub\u003eTe\u003csub\u003e3\u003c/sub\u003e-based alloys, but the \u003cem\u003ezT\u003c/em\u003e value of higher than unity has rarely been obtained. Until 2008, a higher \u003cem\u003ezT\u003c/em\u003e of 1.4 was reported\u003csup\u003e1\u003c/sup\u003e, which stimulated a series of following studies. Recent studies have focused on investigating structural modification to enhance the \u003cem\u003ezT\u003c/em\u003e values of polycrystalline Bi\u003csub\u003e2\u003c/sub\u003eTe\u003csub\u003e3\u003c/sub\u003e alloys using different processing methods\u003csup\u003e11\u0026ndash;13\u003c/sup\u003e, such as ball-milling and hot-pressing\u003csup\u003e11,14,15\u003c/sup\u003e, melt-spinning and spark-plasma-sintering (SPS)\u003csup\u003e8,16\u003c/sup\u003e, hot-forging\u003csup\u003e17\u003c/sup\u003e, low-temperature hydrothermal and hot-pressing treatment\u003csup\u003e18\u003c/sup\u003e. However, no significant increase in \u003cem\u003ezT\u003c/em\u003e values was realized until \u003cb\u003eScience\u003c/b\u003e published another work, which obtained a high \u003cem\u003ezT\u003c/em\u003e of 1.86 in (Bi,Sb)\u003csub\u003e2\u003c/sub\u003eTe\u003csub\u003e3\u003c/sub\u003e compounds via liquid phase sintering with excess \u003cem\u003eTe\u003c/em\u003e\u003csup\u003e19\u003c/sup\u003e. It is a pity that this work was controversial and could not be repeated in nearly ten years. Jo\u003csup\u003e20\u003c/sup\u003e and Deng\u003csup\u003e21\u003c/sup\u003e even constructed the similar microstructure in the Te-rich Bi\u003csub\u003e0.5\u003c/sub\u003eSb\u003csub\u003e1.5\u003c/sub\u003eTe\u003csub\u003e3\u003c/sub\u003e alloys, the obtained maximum \u003cem\u003ezT\u003c/em\u003e value was just 1.2\u0026ndash;1.3, which was much lower than that reported by Kim\u003csup\u003e19\u003c/sup\u003e. So, high-performance BiTe-based thermoelectric materials are expected.\u003c/p\u003e \u003cp\u003eIn the present work, we develop a new fabrication technology, super-gravity-field re-melting (SGF-RM), to realize high-performance (Bi,Sb)\u003csub\u003e2\u003c/sub\u003eTe\u003csub\u003e3\u003c/sub\u003e thermoelectric material with record-high figure of merit of \u0026gt;\u0026thinsp;1.91. Using a super-gravity field, the (Bi,Sb)\u003csub\u003e2\u003c/sub\u003eTe\u003csub\u003e3\u003c/sub\u003e raw material was melted in a \u0026ldquo;chemical furnace\u0026rdquo; and then quickly solidified. The equivalent super-gravity field (\u003cem\u003eG\u003c/em\u003e) is induced by the high-speed rotation of rotors and is expressed as \u003cem\u003eG\u003c/em\u003e\u0026thinsp;=\u0026thinsp;\u003cem\u003eω\u003c/em\u003e\u003csup\u003e2\u003c/sup\u003e\u003cem\u003eL\u003c/em\u003e, where \u003cem\u003eω\u003c/em\u003e is the angular velocity and \u003cem\u003eL\u003c/em\u003e is the distance from the axis of rotation to the point of interest. A self-propagating \"chemical furnace\" (strong exothermic reaction, Ti\u0026thinsp;+\u0026thinsp;2B\u0026rarr;TiB\u003csub\u003e2\u003c/sub\u003e, 66.8 kcal mol\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e)\u003csup\u003e22\u003c/sup\u003e, which replaces the traditional high-temperature melting furnace, is used to melt the raw materials. When the super-gravity reaches a set value, the chemical furnace is ignited. During the burning process, a large amount of heat energy is created, which melts the raw materials. After the combustion reaction is complete, the melts quickly cool and solidify under super-gravity (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003eA and S1).\u003c/p\u003e \u003cp\u003eCompared with traditional melting, the mass and heat transfer of the melts in the super-gravity field were faster than those occurring in the Earth-gravity field. The removal velocity of bubbles in the melt was strongly correlated with the supergravity coefficient (\u003cem\u003eG\u003c/em\u003e/\u003cem\u003eg\u003c/em\u003e, \u003cem\u003eg\u003c/em\u003e\u0026thinsp;=\u0026thinsp;9.8 m/s\u003csup\u003e2\u003c/sup\u003e) and the bubble radius\u003csup\u003e23,24\u003c/sup\u003e (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003eB and S2). Small bubbles were difficult to remove from the melt during the short solidification process due to their lower removal velocities, which promoted the formation of micropores in the obtained bulks. Under super-gravity, the material underwent a rapid volume change and plastic deformation during solidification. This effect is rarely observed in most brittle thermoelectric materials for conventional deformation processes. The plastic deformation process readily induced high-density dislocations in the alloys, and the super-gravity increased the degree of super-cooling, accelerated the solidification rate, and refined the crystal grains. Thus, the distinctive super-gravity-field re-melting technology facilitates the reconstruction of microstructures via changing the solidification process of (Bi,Sb)\u003csub\u003e2\u003c/sub\u003eTe\u003csub\u003e3\u003c/sub\u003e melts. Furthermore, the SGF-RM is efficient and economical, showing great potential for future industrial applications.\u003c/p\u003e \u003cp\u003eIn fact, the study on fabrication of metals\u003csup\u003e25\u003c/sup\u003e and ceramics\u003csup\u003e26,27\u003c/sup\u003e under high gravity field has been reported in the past decades. Until recently, highly-dense Cu\u003csub\u003e2\u003c/sub\u003eZnSnSe\u003csub\u003e4\u003c/sub\u003e\u003csup\u003e28\u003c/sup\u003e, SnTe-based\u003csup\u003e29,30\u003c/sup\u003e thermoelectric materials we successfully synthesized under high gravity field. Notably, SGF-RM facilitated microstructure reconstruction by changing the solidification process of the melt (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003eC). The higher number of grain boundaries and micropore interfaces scattered mid/long-wavelength phonons, which reduced the lattice thermal conductivity. The absence of a conduction medium in the micropores also decreased the thermal conductivity, although it reduced the carrier mobility\u003csup\u003e6,31\u003c/sup\u003e. The introduced high-density dislocations targeted short and medium-wavelength phonons, which reduced the lattice thermal conductivity. Furthermore, the enhanced point defects after SGF-RM (discussed later) targeted short-wavelength phonons. Thus, a full-spectrum strategy targeting a wide spectrum of phonons was realized, resulting in an ultra-low lattice thermal conductivity of \u0026lt;0.25 W/m K at 300 K (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003eE). However, excess Te tended to evaporate from the melt due to its lower vapor pressure, which generated anti-site defects because Bi(Sb) occupied Te vacancies during the melting process under super-gravity. This increased the carrier concentration and power factor (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003eD and \u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003eF). Benefitting from the improved power factor and a significant decrease in the lattice thermal conductivity, the \u003cem\u003ezT\u003c/em\u003e value reached \u0026gt;1.91 (375 K) for the re-melted (Bi,Sb)\u003csub\u003e2\u003c/sub\u003eTe\u003csub\u003e3\u003c/sub\u003e alloy under super-gravity (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003eG); this finding was confirmed and reproducible (\u003cb\u003eFig. S6\u003c/b\u003e). These results suggest that SGF-RM is an efficient method for processing high-performance thermoelectric materials.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe (Bi,Sb)\u003csub\u003e2\u003c/sub\u003eTe\u003csub\u003e3\u003c/sub\u003e alloy with a rhombohedral structure showed anisotropic thermoelectric properties (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e, S1, and S7), in which greater thermoelectric properties were obtained in the cross-plane direction (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e and S1). The electrical conductivity decreased monotonically, indicating a degeneration in the material\u0026rsquo;s semiconductor characteristic. The Seebeck coefficient exhibited an initial increase and then a decrease with the temperature, which was associated with intrinsic excitation\u003csup\u003e32,33\u003c/sup\u003e. After SGF-RM, the electrical conductivity increased but the Seebeck coefficient decreased. The peak Seebeck coefficient decreased and moved to a higher temperature after SGF-RM. Due to the enhanced electrical conductivity and slightly lower Seebeck coefficient, the power factor increased over the measured temperature range of 300\u0026ndash;500 K and reached a maximum of 44.5\u0026ndash;48.9 \u0026micro;W/K\u003csup\u003e2\u003c/sup\u003e cm at 300 K; this was about 11\u0026ndash;22% higher than that of the (Bi,Sb)\u003csub\u003e2\u003c/sub\u003eTe\u003csub\u003e3\u003c/sub\u003e alloy before SGF-RM (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003eC). The total thermal conductivity (κ) and lattice thermal conductivity (κ\u003csub\u003eL\u003c/sub\u003e) showed similar temperature dependences (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003eD and \u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003eE), indicating that the lattice thermal conductivity made a marked contribution to the total thermal conductivity. As the temperature increased, the κ\u003csub\u003eL\u003c/sub\u003e initially decreased, due to Umklapp scattering, and then increased as intrinsic excitations occurred and dominated the transport process. The thermal conductivity and lattice thermal conductivity decreased after SGF-RM. An ultra-low lattice thermal conductivity of 0.15\u0026ndash;0.25 W/m K was obtained, which approached the amorphous limit (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003eE). Benefiting from the increased power factor and reduced thermal conductivity, the peak \u003cem\u003ezT\u003c/em\u003e of 1.91\u0026ndash;1.97 (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003eG) and average \u003cem\u003ezT\u003c/em\u003e of 1.63\u0026ndash;1.66 (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003eF) were obtained for the Bi\u003csub\u003e0.48\u003c/sub\u003eSb\u003csub\u003e1.52\u003c/sub\u003eTe\u003csub\u003e3.03\u003c/sub\u003e alloy after SGF-RM.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eTo further investigate the electrical transport properties of the (Bi,Sb)\u003csub\u003e2\u003c/sub\u003eTe\u003csub\u003e3\u003c/sub\u003e alloys, the carrier concentration and mobility were measured. After SGF-RM, the carrier concentration increased, but the mobility decreased (\u003cb\u003eTable S2\u003c/b\u003e). An enhanced carrier concentration has also been reported for (Bi,Sb)\u003csub\u003e2\u003c/sub\u003eTe\u003csub\u003e3\u003c/sub\u003e-based alloys synthesized by melt-spinning compared with those prepared by the traditional melting/quenching/annealing synthesis\u003csup\u003e34\u003c/sup\u003e. The (Bi,Sb)\u003csub\u003e2\u003c/sub\u003eTe\u003csub\u003e3\u003c/sub\u003e alloys were \u003cem\u003ep\u003c/em\u003e-type semiconductors whose carrier concentrations were affected by anti-site defects and anion vacancies. During the melting process under super-gravity, excess telluride atoms tended to evaporate from the melt due to their lower vapor pressure, which was confirmed by inductively coupled plasma\u0026ndash;optical emission spectroscopy (ICP-OES) (\u003cb\u003eTable S2\u003c/b\u003e). Owing to their similar atom radii and physical properties, Bi(Sb) atoms mainly occupied the Te sites to form Bi\u0026prime;\u003csub\u003eTe\u003c/sub\u003e or Sb\u0026prime;\u003csub\u003eTe\u003c/sub\u003e anti-site defects (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003eD)\u003csup\u003e36\u003c/sup\u003e, where V\u003csup\u003e\u0026bull;\u0026bull;\u003c/sup\u003e\u003csub\u003eTe\u003c/sub\u003e is a Te vacancy, V\u0026prime;\u0026Prime;\u003csub\u003eBi\u003c/sub\u003e or V\u0026prime;\u0026Prime;\u003csub\u003eSb\u003c/sub\u003e is a Bi or Sb vacancy, Bi\u0026prime;\u003csub\u003eTe\u003c/sub\u003e or Sb\u0026prime;\u003csub\u003eTe\u003c/sub\u003e is an anti-site defect, and h\u003csup\u003e\u0026bull;\u003c/sup\u003e is a hole. Thus, the evaporation of excess Te in the Bi\u003csub\u003e0.48\u003c/sub\u003eSb\u003csub\u003e1.52\u003c/sub\u003eTe\u003csub\u003e3.03\u003c/sub\u003e alloy generated more anti-site defects when Bi(Sb) atoms occupied Te vacancies\u003csup\u003e37\u003c/sup\u003e. These negatively charged anti-site defects formed extra holes in the matrix, which increased the carrier concentration and electrical conductivity after SGF-RM. Moreover, the maximum Seebeck coefficient shifted to a higher temperature after SGF-RM (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003eB), which was also ascribed to the suppression of the intrinsic conductivity by increasing the carrier concentration. The carrier mobility decreased after SGF-RM, primarily due to increased carrier\u0026ndash;carrier scattering and enhanced point defect scattering.\u003c/p\u003e \u003cp\u003eIn this work, an effective mass model was also used to evaluate the charge carrier transport properties\u003csup\u003e6,38\u003c/sup\u003e. Although bipolar effects easily occur in Bi\u003csub\u003e2\u003c/sub\u003eTe\u003csub\u003e3\u003c/sub\u003e-based alloys, a single-parabolic-band model was used in this work. This model assumed that minor charge carriers contributed little to the electrical conductivity\u003csup\u003e6,7\u003c/sup\u003e. According to the fitted curves with the assumed effective mass \u003cem\u003em\u003c/em\u003e* = 1.05 \u003cem\u003em\u003c/em\u003e\u003csub\u003e0\u003c/sub\u003e (\u003cem\u003em\u003c/em\u003e\u003csub\u003e0\u003c/sub\u003e is the inertial mass of a free electron) and the drift mobility \u003cem\u003e\u0026micro;\u003c/em\u003e\u003csub\u003e0\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;420 cm\u003csup\u003e2\u003c/sup\u003e/V s, the predicted Hall-carrier-concentration-dependent Seebeck coefficient and Hall mobility were obtained (\u003cb\u003eFig. S8\u003c/b\u003e). The results confirmed the validity of the single-parabolic-band model.\u003c/p\u003e \u003cp\u003eFindings from recent studies\u003csup\u003e6,7,19,34,39,40\u003c/sup\u003e are consistent with those found in this work. The results showed some discrepancies from the fitting lines for the (Bi,Sb)\u003csub\u003e2\u003c/sub\u003eTe\u003csub\u003e3\u003c/sub\u003e materials, which may have been related to the complex electronic structures of the (Bi,Sb)\u003csub\u003e2\u003c/sub\u003eTe\u003csub\u003e3\u003c/sub\u003e alloys. However, the weighted mobility \u0026micro;\u003csub\u003ew\u003c/sub\u003e, which characterizes the drift mobility and inherent transport properties, was consistent between the samples before and after SGF-RM (\u003cb\u003eFig. S8C\u003c/b\u003e), further confirming that the acoustic phonon scattering mechanism was unchanged. With a combination of the predicted Hall-carrier-concentration-dependent Seebeck and Hall mobility, the thermoelectric power factor was calculated and compared with the experimental data (\u003cb\u003eFig. S8D\u003c/b\u003e). The comparison suggested that the improvement in the power factor was mainly due to the optimization of the carrier concentration after SGF-RM.\u003c/p\u003e \u003cp\u003ePositrons are sensitive and self-seeking probes for microstructural defects, and positron annihilation measurements provide a way to qualitatively analyze anti-site defects, dislocations, vacancies, and even pores inside materials\u003csup\u003e41,42\u003c/sup\u003e. The measured positron annihilation spectra (\u003cb\u003eFig. S9\u003c/b\u003e) were decomposed into three lifetimes, τ\u003csub\u003e1\u003c/sub\u003e, τ\u003csub\u003e2\u003c/sub\u003e, and τ\u003csub\u003e3\u003c/sub\u003e, with corresponding intensities \u003cem\u003eI\u003c/em\u003e\u003csub\u003e1\u003c/sub\u003e, \u003cem\u003eI\u003c/em\u003e\u003csub\u003e2\u003c/sub\u003e, and \u003cem\u003eI\u003c/em\u003e\u003csub\u003e3\u003c/sub\u003e, respectively, using the LT9.0 software (Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e). The longest-lifetime component τ\u003csub\u003e3\u003c/sub\u003e may have been due to the annihilation of the ortho-positronium formed on the surfaces of the specimens and/or some low-energy positrons annihilated by inner \u003csup\u003e22\u003c/sup\u003eNa\u003csup\u003e43\u003c/sup\u003e. As the values of the relative intensity \u003cem\u003eI\u003c/em\u003e\u003csub\u003e3\u003c/sub\u003e of the samples was the weakest (\u0026lt;\u0026thinsp;2.5%), it will not be discussed in this paper. The positron lifetime τ\u003csub\u003e1\u003c/sub\u003e represents the free positron lifetime originating from anti-site defects, dislocations, and small vacancies, while τ\u003csub\u003e2\u003c/sub\u003e was likely caused by large clusters of vacancies and micropores\u003csup\u003e44\u003c/sup\u003e. Notably, τ\u003csub\u003e1\u003c/sub\u003e and \u003cem\u003eI\u003c/em\u003e\u003csub\u003e1\u003c/sub\u003e increased from 0.152 ns and 26.3% to 0.169 ns and 31.1% after SGF-RM, respectively. This suggests the creation of more point defects, including anti-site defects and dislocations that were introduced into the matrix after SGF-RM. The second-lifetime component τ\u003csub\u003e2\u003c/sub\u003e was much longer than τ\u003csub\u003e1\u003c/sub\u003e due to positron trapping and annihilation at several large vacancy clusters or micropores. After SGF-RM, the lifetime τ\u003csub\u003e2\u003c/sub\u003e increased but \u003cem\u003eI\u003c/em\u003e\u003csub\u003e2\u003c/sub\u003e decreased. The increased τ\u003csub\u003e2\u003c/sub\u003e indicated that new micropores with larger sizes were formed in the matrix, in addition to the vacancy clusters after SGF-RM. The reduced \u003cem\u003eI\u003c/em\u003e\u003csub\u003e2\u003c/sub\u003e may have been related to the decreased density of vacancy clusters caused by the production of more anti-site defects after tellurium evaporation. Positron annihilation measurements showed that more anti-site defects, dislocations, and micropores were introduced in the (Bi,Sb)\u003csub\u003e2\u003c/sub\u003eTe\u003csub\u003e3\u003c/sub\u003e alloys after SGF-RM.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003ePositron annihilation lifetime spectroscopy (PALS) data of BST and BST-1.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"7\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSpecimen\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eτ\u003csub\u003e1\u003c/sub\u003e (ns)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cem\u003eI\u003c/em\u003e\u003csub\u003e1\u003c/sub\u003e (%)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eτ\u003csub\u003e2\u003c/sub\u003e (ns)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cem\u003eI\u003c/em\u003e\u003csub\u003e2\u003c/sub\u003e (%)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eτ\u003csub\u003e3\u003c/sub\u003e (ns)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u003cem\u003eI\u003c/em\u003e\u003csub\u003e3\u003c/sub\u003e (%)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eBST\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.1521\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e26.3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.3209\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e71.6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e1.286\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e2.06\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eBST-1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.1685\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e31.1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.3344\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e67.7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e1.534\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e1.25\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eTo analyze the reasons for the reduced thermal conductivity, the microstructure and morphology were further investigated by transmission electron microscopy (TEM). No obvious dislocations were observed in the raw BST samples (\u003cb\u003eFig. S10\u003c/b\u003e), while high-density dislocations were found throughout the melted BST-1 samples (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e and S11). The dislocations had diverse morphologies, with many disordered long dislocation lines existing alone or intertwining with each other to form dislocation networks (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003eB). There were also many shorter dislocation lines inside the grains (\u003cb\u003eFig. S11\u003c/b\u003e). Most dislocations were found inside the grains instead of at the grain boundaries. The (Bi,Sb)\u003csub\u003e2\u003c/sub\u003eTe\u003csub\u003e3\u003c/sub\u003e melt quickly cooled and solidified under super-gravity, which introduced a rapid change in volume and strained the inside of the samples. This caused plastic deformation within the sample, especially inside the grains, leading to the formation of dislocation pile-ups.\u003c/p\u003e \u003cp\u003eThe high-resolution TEM (HRTEM) image (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003eB) shows the corresponding fast Fourier transform (FFT) pattern (inset of Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003eB) in the [\u0026oline;55\u0026oline;1] direction. The atomically resolved scanning transmission electron microscopy high-angle annular dark field (STEM HAADF) image (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003eC) shows a dislocation in the BST-1 sample. To further investigate the dislocation characteristics, inverse fast Fourier transform (IFFT) images (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003eD\u0026ndash;F) combined with geometric phase analysis (GPA) were introduced to analyze the HRTEM images for dislocation cores and corresponding strain fields (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003eG\u0026ndash;I). Many dislocation cores existed around dislocations in all three planes. The dislocation density was estimated to be 7 \u0026times; 10\u003csup\u003e12\u003c/sup\u003e cm\u003csup\u003e\u0026minus;\u0026thinsp;2\u003c/sup\u003e. Strain convergence regions were found around the dislocation cores, which were randomly distributed in all orientations. The high-density dislocations and the associated strain field strongly interfered with the propagation of short/medium-wavelength phonons and in the softening of the lattice\u003csup\u003e45,46\u003c/sup\u003e, which reduced the thermal conductivity.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eMore micropores and finer grains were observed on the fractured surfaces of the melted BST-1 samples (\u003cb\u003eFig. S12\u003c/b\u003e), which also confirmed the above positron annihilation measurements. These micropores and grain boundaries also helped decrease the thermal conductivity. Analogous results were also reported in previous studies\u003csup\u003e6,47\u003c/sup\u003e. The formation of these micropores and smaller grains was also related to the rapid solidification of the melt under the super-gravity field, as discussed above.\u003c/p\u003e \u003cp\u003eBased on the above positron annihilation measurements and microstructural characterization results, the presence of pile-ups of microstructural defects, such as dislocations, anti-site defects (Bi(Sb)\u0026prime;\u003csub\u003eTe\u003c/sub\u003e), and micropores, was confirmed, which showed that the microstructures of the (Bi,Sb)\u003csub\u003e2\u003c/sub\u003eTe\u003csub\u003e3\u003c/sub\u003e alloys were reconstructed after SGF-RM. To better understand the main factor responsible for the reduced lattice thermal conductivity, the effective medium theory (EMT) and the Debye\u0026ndash;Callaway model were used to analyze the contributions of the absence of thermal conduction within the micropores and the various phonon scattering mechanisms, respectively. According to the classical EMT, the lattice thermal conductivity of a fully dense material (κ\u003csub\u003eL,d\u003c/sub\u003e) can be expressed by κ\u003csub\u003eL,d\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;κ\u003csub\u003eL,p\u003c/sub\u003e/(1\u0026ndash;3ε/2), where κ\u003csub\u003eL,p\u003c/sub\u003e is the lattice thermal conductivity of the porous material, and ε is the porosity\u003csup\u003e48\u003c/sup\u003e. Based on the experimental lattice thermal conductivity and porosity (\u003cb\u003eTable S3\u003c/b\u003e), the corrected κ\u003csub\u003eL,d\u003c/sub\u003e of the corresponding dense BST-1 sample was obtained (open triangles in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003eE). The corrected κ\u003csub\u003eL,d\u003c/sub\u003e can be described using the Debye\u0026ndash;Callaway model to analyze the contributions of the various scattering mechanisms to the reduction in the thermal conductivity. The contributions of Umklapp scattering (U), normal scattering (N), and point defect (PD) scattering were accounted for using the Debye\u0026ndash;Callaway model to fit the data of the BST sample (black line in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003eE). Increases in the deviation upon increasing the temperature were due to a bipolar effect. Substantial heat was carried by mid/long-wavelength phonons, which could be scattered more effectively by the interfaces of micropores and grain boundaries. This resulted in a 14\u0026ndash;19% reduction of the lattice thermal conductivity in the measured temperature range of 300\u0026ndash;500 K (purple solid line in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003eE). Furthermore, the greater reduction in the lattice thermal conductivity was attributed to the high dislocation density (\u0026asymp;\u0026thinsp;7 \u0026times; 10\u003csup\u003e12\u003c/sup\u003e cm\u003csup\u003e\u0026minus;\u0026thinsp;2\u003c/sup\u003e), which mainly scattered phonons in the short/mid-wavelength range. The absence of thermal conduction within the micropores also reduced the thermal conductivity based on the above EMT. The micropore structure (including micropores and their interfaces) resulted in about a 24% total reduction in the lattice thermal conductivity at 300 K. As a result, the reconstruction of the microstructures by SGF-RM resulted in an ultra-low lattice thermal conductivity.\u003c/p\u003e \u003cp\u003eThe thermoelectric power generation is a more direct index used to further confirm the enhanced \u003cem\u003ezT\u003c/em\u003e values. Thermoelectric modules with 127 pairs of \u003cem\u003ep\u003c/em\u003e-\u003cem\u003en\u003c/em\u003e legs (inset in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003eA) were fabricated to study the power generation. The measured conversion efficiency and power output of the thermoelectric module (BST-1 module in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e) together with the commercial module (BST module in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e) are shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003eA and \u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003eC. When the temperature difference across the module increased to 184 K (T\u003csub\u003ecold\u003c/sub\u003e = 289 K, T\u003csub\u003ehot\u003c/sub\u003e =473 K), the measured maximum conversion efficiency (\u003cem\u003eη\u003c/em\u003e) was 6.4%, which was about 52% higher than that of the commercial module (\u0026asymp;\u0026thinsp;4.2%). And, high output power of 5.5 W was obtained, representing 83% improvement in comparison to that of commercial module. The corresponding output power density arrived at 0.34 W cm\u003csup\u003e2\u003c/sup\u003e (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003eD). Although the conversion efficiency and power output the thermoelectric module were lower than the theoretical values, they were higher than many reported values of (Bi,Sb)\u003csub\u003e2\u003c/sub\u003eTe\u003csub\u003e3\u003c/sub\u003e-based devices\u003csup\u003e7,49\u0026ndash;52\u003c/sup\u003e (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003eB and \u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003eD). These results confirmed the greatly enhanced \u003cem\u003ezT\u003c/em\u003e values of the melted (Bi,Sb)\u003csub\u003e2\u003c/sub\u003eTe\u003csub\u003e3\u003c/sub\u003e alloys under super-gravity. The thermoelectric properties of the \u003cem\u003en\u003c/em\u003e-type legs (\u003cb\u003eTable S5\u003c/b\u003e) remained much lower than those of the \u003cem\u003ep\u003c/em\u003e-type legs. If the thermoelectric properties of the \u003cem\u003en\u003c/em\u003e-type material were improved and the bonding technology of the module were optimized, a higher conversion efficiency might be obtained.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe present study highlights the ultrahigh thermoelectricity in the classical BiSbTe alloy obtained by a new super-gravity-field re-melting fabrication technology. Under a super-gravity field, the brittle (Bi,Sb)\u003csub\u003e2\u003c/sub\u003eTe\u003csub\u003e3\u003c/sub\u003e alloy underwent unusual plastic deformation during melt solidification, which reconstructed its microstructure and formed multiple microstructure defects. Together with the carrier concentration optimization, an ultra-low thermal conductivity and a record-high figure of merit (\u003cem\u003ezT\u003c/em\u003e \u0026gt;1.91 at 375 K) were obtained in the BiSbTe alloy. A high-performance thermoelectric device (η\u003csub\u003emax\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;6.4%) further demonstrated the enhanced thermoelectric properties and the potential applications in the power generation devices.\u003c/p\u003e "},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eData availability\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe data that support the findings of this study are available from the corresponding author on request.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAcknowledgments\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThis work was supported by the Key Laboratory of Cryogenic Science and Technology (Grant No. CRYO20230203), the National Natural Science Foundation of China (Grant No. 51872299), and the Basic Science Center Project of National Natural Science Foundation of China (Grant No. 52388201). We thank Tsinghua University, Beihang University and Ningbo Institute of Materials Technology \u0026amp; Engineering, CAS for the repeated measurements of the thermoelectric properties. We also thank Huabei Cooling Device Co., Ltd. for fabricating the thermoelectric device modules and the Shenzhen Institute of Advanced Electronic Materials for measuring the thermoelectric conversion efficiency.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAuthor contributions\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eM.Z. and H.J.S. synthesized the samples, designed and carried out the experiments, analyzed the results, and wrote the paper. J.P. conducted theoretical calculations and analyzed the results. L.W. measured the thermoelectric performance. H.L.Z. measured the Hall coefficient. K.S., H.Y.H., and J.J. fabricated the thermoelectric modules. Q.H.Z. helped with TEM measurements and analysis. The experimental design and paper writing were performed under the supervision of J.-F.L. J.J. and L.F.L. All authors contributed to the discussion of the results and commented on the manuscript.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCompeting interest\u003c/strong\u003e\u003cstrong\u003es\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe authors declare no competing interests.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAdditional\u0026nbsp;\u003c/strong\u003e\u003cstrong\u003ei\u003c/strong\u003e\u003cstrong\u003enformation\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eSupplementary\u0026nbsp;\u003c/strong\u003e\u003cstrong\u003ei\u003c/strong\u003e\u003cstrong\u003enformation\u003c/strong\u003e is available for this paper.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eReprints and permissions information\u003c/strong\u003e is available online at www.nature.com/reprints.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCorrespondence and requests\u003c/strong\u003e for materials should be addressed to Min Zhou.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eBell, L. 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The sieved products with particles between 0.6-1 microns are also cold pressed (BST-S). Each batch of about 0.1 \u003cem\u003ekg\u003c/em\u003e powders was cold pressed under a uniaxial pressure of 10 MPa. The compacts are loaded into quartz ampoules, which is then evacuated and sealed. As shown in \u003cb\u003eFig. \u003cspan refid=\"MOESM1\" class=\"InternalRef\"\u003eS1\u003c/span\u003e\u003c/b\u003e, the mixtures of titanium and boron powders are poured into a quartz crucible with an inner diameter of 40 mm and length of 250 mm, into which the sealed (Bi,Sb)\u003csub\u003e2\u003c/sub\u003eTe\u003csub\u003e3\u003c/sub\u003e specimen is placed. A tungsten coil is fixed above the top surface of the (Ti\u0026thinsp;+\u0026thinsp;2B) mixtures. The quartz crucible is wrapped with carbon felt, and then is loaded into a graphite crucible. A graphite cap is used to close the quartz and graphite crucibles. The graphite crucible is also wrapped with carbon felt and placed into a steel cup, and the cup is horizontally mounted at one side of a rotator in the reaction chamber. A counterweight is mounted at the other side of the rotator to keep balance. After the reaction chamber is evacuated, the rotator is started. By the centrifugal effect, an equivalent super-gravity field (\u003cem\u003eG\u003c/em\u003e) is induced by high-speed rotation. When the super-gravity reaches set values (for example, \u003cem\u003eG\u003c/em\u003e\u0026thinsp;=\u0026thinsp;100 \u003cem\u003eg\u003c/em\u003e, 1000 \u003cem\u003eg\u003c/em\u003e (\u003cem\u003eg\u003c/em\u003e\u0026thinsp;=\u0026thinsp;9.8 m/s\u003csup\u003e2\u003c/sup\u003e)), the top of the (Ti\u0026thinsp;+\u0026thinsp;2B) mixing powders are ignited by passing an electric current of 10 \u003cem\u003eA\u003c/em\u003e in the tungsten coil for 2 \u003cem\u003es\u003c/em\u003e. After being ignited, the (Ti\u0026thinsp;+\u0026thinsp;2B) powders bed continues to burn in a self-sustained way with the combustion front moving from the top to the bottom of the quartz crucible. During the burning process, a large amount of heat energy is created\u003csup\u003e20\u003c/sup\u003e, which melts the (Bi,Sb)\u003csub\u003e2\u003c/sub\u003eTe\u003csub\u003e3\u003c/sub\u003e compacts. For the exothermic reaction, Ti\u0026thinsp;+\u0026thinsp;2B\u0026rarr;TiB\u003csub\u003e2\u003c/sub\u003e, the flame front velocity was about 15-26.6 mm/s\u003csup\u003e47\u003c/sup\u003e, the combustion reaction lasted for tens of seconds in this work. The peak temperature of the TiB\u003csub\u003e2\u003c/sub\u003e combustion synthesis was over 1200\u0026deg;C\u003csup\u003e48\u003c/sup\u003e, while the melting temperature of Bi\u003csub\u003e0.48\u003c/sub\u003eSb\u003csub\u003e1.52\u003c/sub\u003eTe\u003csub\u003e3.03\u003c/sub\u003e alloy was about 610\u0026deg;C\u003csup\u003e49\u003c/sup\u003e. So, the high temperature inside of the \u0026ldquo;chemical furnace\u0026rdquo; would hold for longer time to melt the (Bi,Sb)\u003csub\u003e2\u003c/sub\u003eTe\u003csub\u003e3\u003c/sub\u003e alloys with the heat insulation layer (Fig. \u003cspan refid=\"MOESM1\" class=\"InternalRef\"\u003eS1\u003c/span\u003e). In fact, the super-gravity field of 1000 \u003cem\u003eg\u003c/em\u003e holds for 1 min (BST-1) and 10 min (BST-10, BST-S) to study the densification process after being ignited. The solidified (Bi,Sb)\u003csub\u003e2\u003c/sub\u003eTe\u003csub\u003e3\u003c/sub\u003e ingots are obtained and then are taken out for later characterizations and measurements. It is worth noting that the density is too low (the relative density is only 80.81%) for the samples fabricated under the super-gravity field of 100 \u003cem\u003eg\u003c/em\u003e. So, these samlpes are not discussed in this paper.\u003c/p\u003e \u003cp\u003eThe simple model is used to analyze the densification process of (Bi,Sb)\u003csub\u003e2\u003c/sub\u003eTe\u003csub\u003e3\u003c/sub\u003e alloys in the melting under super-gravity field without considering the temperature gradient, compositional gradient and melt turbulence. Supergravity can enhance the energy transfer of multiphase flow, thus strengthening the mass transfer, heat transfer and chemical reaction processes. So, it can be recognized that the continuous alloy melt homogenized in a moment under the super-gravity field. But there are still a lot of bubbles in the melt, which determines the density of the final alloy product. Figure\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003eB and \u003cb\u003eFig. S2\u003c/b\u003e briefly show the densification process of (Bi,Sb)\u003csub\u003e2\u003c/sub\u003eTe\u003csub\u003e3\u003c/sub\u003e alloy. Melts and bubbles are separated during the melting, and then cooled under super-gravity.\u003c/p\u003e \u003cp\u003eAs we know, the lifting velocity of bubbles in melts is closed related to the supergravity coefficients. According to Stokes law\u003csup\u003e23\u003c/sup\u003e, the lifting velocity of bubbles in melts can be calculated (\u003cem\u003eV\u003c/em\u003e\u003csub\u003eB\u003c/sub\u003e):\u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ1\" name=\"EquationSource\"\u003e\n$$\\:{V}_{B}=\\frac{2}{9}({\\rho\\:}_{M,l}-{\\rho\\:}_{B,g})\\frac{G{R}_{B}^{2}}{{\\eta\\:}_{M}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e1\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere, \u003cem\u003eρ\u003c/em\u003e\u003csub\u003eM,l\u003c/sub\u003e and \u003cem\u003eρ\u003c/em\u003e\u003csub\u003eB,g\u003c/sub\u003e are the density of melts and bubble, respectively. \u003cem\u003eG\u003c/em\u003e is the super-gravity field, \u003cem\u003eR\u003c/em\u003e\u003csub\u003eB\u003c/sub\u003e is the radius of bubble, \u003cem\u003eη\u003c/em\u003e\u003csub\u003eM\u003c/sub\u003e is the viscosity of melts.\u003c/p\u003e \u003cp\u003eThe forces of the bubbles in melts include the super-gravity (\u003cem\u003eF\u003c/em\u003e\u003csub\u003eg\u003c/sub\u003e), buoyancy of melts (\u003cem\u003eF\u003c/em\u003e\u003csub\u003eb\u003c/sub\u003e) and viscous drag of melts (\u003cem\u003eF\u003c/em\u003e\u003csub\u003ev\u003c/sub\u003e).\u003c/p\u003e \u003cp\u003eThe super-gravity:\u003cdiv id=\"Equ2\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ2\" name=\"EquationSource\"\u003e\n$$\\:{F}_{g}=\\frac{4}{3}\\pi\\:{R}_{B}^{3}{\\rho\\:}_{B,g}G$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e2\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eThe buoyancy of melts:\u003cdiv id=\"Equ3\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ3\" name=\"EquationSource\"\u003e\n$$\\:{F}_{b}=\\frac{4}{3}\\pi\\:{R}_{B}^{3}{\\rho\\:}_{M,l}G$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e3\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eThe viscous drag of melts:\u003cdiv id=\"Equ4\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ4\" name=\"EquationSource\"\u003e\n$$\\:{F}_{v}=6\\pi\\:{R}_{B}^{3}{}_{M}{V}_{B}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e4\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhen \u003cem\u003eF\u003c/em\u003e\u003csub\u003eb\u003c/sub\u003e=\u003cem\u003eF\u003c/em\u003e\u003csub\u003eg\u003c/sub\u003e+\u003cem\u003eF\u003c/em\u003e\u003csub\u003ev\u003c/sub\u003e, the lifting velocity of bubbles reaches a stabilized value. According to the formula (2\u0026ndash;4), the lifting velocity of bubbles at steady state (\u003cem\u003eV\u003c/em\u003e\u003csub\u003eB\u003c/sub\u003e):\u003cdiv id=\"Equ5\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ5\" name=\"EquationSource\"\u003e\n$$\\:{V}_{B}=\\frac{2}{9}({\\rho\\:}_{M,l}-{\\rho\\:}_{B,g})\\frac{{R}_{B}^{2}G}{{}_{M}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e5\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eBecause \u003cem\u003eρ\u003c/em\u003e\u003csub\u003eB,g\u003c/sub\u003e\u0026lt;\u0026lt;\u003cem\u003eρ\u003c/em\u003e\u003csub\u003eM,l\u003c/sub\u003e, formula (5) can be simplified as:\u003cdiv id=\"Equ6\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ6\" name=\"EquationSource\"\u003e\n$$\\:{V}_{B}=\\frac{2}{9}{\\rho\\:}_{M,l}\\frac{{R}_{B}^{2}G}{{}_{M}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e6\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eAccording to the formula (6), the lifting velocity of bubbles in alloy melts at steady state is calculated (by using the data listed in \u003cb\u003eTable \u003cspan refid=\"MOESM1\" class=\"InternalRef\"\u003eS1\u003c/span\u003e\u003c/b\u003e) and shown in \u003cb\u003eFig. S2\u003c/b\u003e.\u003c/p\u003e \u003cp\u003eThe above results show that the lifting velocity of bubbles in alloy melts can be obviously increased by enhancing the supergravity coefficient (\u003cem\u003eG\u003c/em\u003e/\u003cem\u003eg\u003c/em\u003e) and the radius of bubbles. For (Bi,Sb)\u003csub\u003e2\u003c/sub\u003eTe\u003csub\u003e3\u003c/sub\u003e alloy, the super-gravity coefficient (\u003cem\u003eG\u003c/em\u003e/\u003cem\u003eg\u003c/em\u003e) of 1000 is high enough to densify the bulks. However, the bubbles with small radii are hard to clean out of the alloy melts in the short densification process due to the lower lifting velocity of small bubbles. So, a few small pores are observed in the melted bulks.\u003c/p\u003e \u003c/div\u003e\n\u003ch3\u003eStructural Characterization\u003c/h3\u003e\n\u003cp\u003eThe phase composition is analyzed by X-ray diffraction (Bruker, Germany) with \u003cem\u003eCu K\u003c/em\u003eα radiation. The typical XRD patterns of the (Bi,Sb)\u003csub\u003e2\u003c/sub\u003eTe\u003csub\u003e3\u003c/sub\u003e samples are shown in \u003cb\u003eFig. S2\u003c/b\u003e. The microstructures are observed by field-emission scanning electron microscopy (FESEM, S-4800, Hitachi) and transmission electron microscopy (TEM, 2100F, JEOL). Elemental analyses are collected by inductively coupled plasma-optical emission spectroscopy (ICP-OES, Varian 710-ES).\u003c/p\u003e\n\u003ch3\u003eThermoelectric Property Measurements\u003c/h3\u003e\n\u003cp\u003eThe Seebeck coefficient (\u003cem\u003eα\u003c/em\u003e) and electrical conductivity (\u003cem\u003eσ\u003c/em\u003e) are measured by using the Seebeck Coefficient/Electrical Resistance Measuring System (ZEM-3, Ulvac-Riko) under a static helium atmosphere. The Hall coefficient (\u003cem\u003eR\u003c/em\u003e\u003csub\u003eH\u003c/sub\u003e) is measured by a Hall measurement system (ResiTest 8340DC, Toyo, Japan) via the van der Pauw method. The hall carrier concentration (\u003cem\u003en\u003c/em\u003e\u003csub\u003eH\u003c/sub\u003e) and mobility (\u003cem\u003e\u0026micro;\u003c/em\u003e\u003csub\u003eH\u003c/sub\u003e) are calculated by \u003cem\u003en\u003c/em\u003e\u003csub\u003eH\u003c/sub\u003e=1/(\u003cem\u003eeR\u003c/em\u003e\u003csub\u003eH\u003c/sub\u003e) and \u003cem\u003e\u0026micro;\u003c/em\u003e\u003csub\u003eH\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;\u003cem\u003eR\u003c/em\u003e\u003csub\u003eH\u003c/sub\u003e/\u003cem\u003eρ\u003c/em\u003e, respectively. The thermal conductivity (\u003cem\u003eκ\u003c/em\u003e) is calculated using the equation \u003cem\u003eκ\u003c/em\u003e\u0026thinsp;=\u0026thinsp;\u003cem\u003eλC\u003c/em\u003e\u003csub\u003ep\u003c/sub\u003e\u003cem\u003ed\u003c/em\u003e, where \u003cem\u003eλ\u003c/em\u003e is the thermal diffusivity, \u003cem\u003eC\u003c/em\u003e\u003csub\u003ep\u003c/sub\u003e is the heat capacity, and \u003cem\u003ed\u003c/em\u003e is bulk density of the sample. The thermal diffusivity is measured by a laser flash technique (Netzsch LFA457) in \u003cem\u003eAr\u003c/em\u003e atmosphere. The heat capacity is measured using Differential Scanning Calorimeter (DSC404-F3). The measured \u003cem\u003eλ\u003c/em\u003e and \u003cem\u003eC\u003c/em\u003e\u003csub\u003ep\u003c/sub\u003e values were shown in \u003cb\u003eFig. S4\u003c/b\u003e and \u003cb\u003eFig. S5\u003c/b\u003e, respectively. The bulk density is obtained by the Archimedes method. The lattice thermal conductivities (\u003cem\u003eκ\u003c/em\u003e\u003csub\u003eL\u003c/sub\u003e) are obtained by subtracting the electrical contribution from the total thermal conductivity using the equation \u003cem\u003eκ\u003c/em\u003e\u003csub\u003eL\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;\u003cem\u003eκ\u003c/em\u003e-\u003cem\u003eκ\u003c/em\u003e\u003csub\u003ee\u003c/sub\u003e. Here, the electrical thermal conductivity is expressed by the Wiedemann Franz Law \u003cem\u003eκ\u003c/em\u003e\u003csub\u003ee\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;\u003cem\u003eLσT\u003c/em\u003e, where \u003cem\u003eL\u003c/em\u003e is estimated by using a Single Parabolic Band (SPB) model\u003csup\u003e50\u003c/sup\u003e. Transport properties are measured in the parallel (cross-plane) (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e) and perpendicular (in-plane) (\u003cb\u003eFig. S7\u003c/b\u003e) to the direction of the super-gravity field. The transport properties in the parallel direction were repeated (\u003cb\u003eFig. S6\u003c/b\u003e).\u003c/p\u003e\n\u003ch3\u003ePositron Annihilation Measurement\u003c/h3\u003e\n\u003cp\u003ePositron annihilation lifetime spectroscopy (PALS) analysis is performed using a fast-slow coincident ORTEC system with a time resolution of 220 \u003cem\u003eps\u003c/em\u003e for the full width at half maximum. The \u003csup\u003e\u003cem\u003e22\u003c/em\u003e\u003c/sup\u003e\u003cem\u003eNa\u003c/em\u003e positron source is placed between the two pieces of samples, and then the \u0026ldquo;sample-source-sample sandwich\u0026rdquo; is placed between the two \u003cem\u003eBaF\u003c/em\u003e\u003csub\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sub\u003e detectors to acquire the lifetime spectra. A total of 2\u0026times;10\u003csup\u003e6\u003c/sup\u003e counts are accumulated for each spectrum to reduce the statistical error in the calculation of lifetimes. The positron lifetime spectra are de-convoluted and analyzed using the LT-9 software. LT-9 is one of the most popular software for PALS analysis. It de-convolutes the experimental curve from the instrument functions to set apart the physical meaning information, \u003cem\u003ei.e.\u003c/em\u003e positron annihilation lifetime and intensity. Positron annihilation lifetime and intensity could reflect the defect size and density information.\u003c/p\u003e\n\u003ch3\u003eModule fabrication and measurement\u003c/h3\u003e\n\u003cp\u003eTE modules with the size of 40\u0026times;40\u0026times;2.6 mm\u003csup\u003e3\u003c/sup\u003e and a total 127 pairs of \u003cem\u003ep\u003c/em\u003e-\u003cem\u003en\u003c/em\u003e legs were fabricated in Huabei Cooling Device Company. The size for the legs is 1.33\u0026times;1.33\u0026times;1.6 mm\u003csup\u003e3\u003c/sup\u003e. The melted Bi\u003csub\u003e0.48\u003c/sub\u003eSb\u003csub\u003e1.52\u003c/sub\u003eTe\u003csub\u003e3.03\u003c/sub\u003e sample was utilized for the \u003cem\u003ep\u003c/em\u003e-type legs. The zone-melted BiSbTe alloys (BST) serve as the references. The \u003cem\u003en\u003c/em\u003e-type counterparts are commercial Bi\u003csub\u003e2\u003c/sub\u003eTe\u003csub\u003e2.2\u003c/sub\u003eSe\u003csub\u003e0.8\u003c/sub\u003e ingots (The measured thermoelectric parameters were shown in \u003cb\u003eTable S5\u003c/b\u003e). The energy conversion efficiencies and cooling temperature difference of these modules were evaluated by man-made testing system in Shenzhen Institute of Advanced Technology, Chinese Academy of Sciences. The hot-side temperatures were maintained between 423\u0026ndash;500 K, while the temperature of the water cooler was kept at 283 K.\u003c/p\u003e \n\u003cp\u003e\u003cstrong\u003eMethods\u003c/strong\u003e\u003cstrong\u003e\u0026nbsp;\u003c/strong\u003e\u003cstrong\u003ereferences\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e47. Bernert, T. et al. In situ observation of self-propagating high temperature syntheses of Ta\u003csub\u003e5\u003c/sub\u003eSi\u003csub\u003e3\u003c/sub\u003e, Ti\u003csub\u003e5\u003c/sub\u003eSi\u003csub\u003e3\u003c/sub\u003e and TiB\u003csub\u003e2\u003c/sub\u003e by proton and X-ray radiography. \u003cem\u003eSolid State Sci.\u003c/em\u003e \u003cstrong\u003e22\u003c/strong\u003e, 33\u0026ndash;42 (2013).\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e48. Roy, S. K. et al. Combustion Synthesis of TiB and TiB\u003csub\u003e2\u003c/sub\u003e under vacuum. \u003cem\u003eJ. Mater. Sci. Lett.\u003c/em\u003e \u003cstrong\u003e13\u003c/strong\u003e, 371\u0026ndash;373 (1994).\u003c/p\u003e\n\u003cp\u003e49. Rowe, D. W. et al. \u003cem\u003eCRC Handbook of Thermoelectrics\u003c/em\u003e (CRC press, 1995).\u003c/p\u003e\n\u003cp\u003e50. Li, Z. Y. et al. Fine-Grained and Nanostructured AgPb\u003csub\u003em\u003c/sub\u003eSbTe\u003csub\u003em+2\u003c/sub\u003e Alloys with High Thermoelectric Figure of Merit at Medium Temperature. \u003cem\u003eAdv. Energy Mater\u003c/em\u003e. \u003cstrong\u003e4\u003c/strong\u003e, 1300937 (2014).\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e51. \u0026nbsp;\u0026nbsp;Hong, M. et al. Rashba Effect Maximizes Thermoelectric Performance of GeTe Derivatives. \u003cem\u003eJoule\u003c/em\u003e \u003cstrong\u003e4\u003c/strong\u003e, 2030\u0026ndash;2043 (2020).\u0026nbsp;\u003c/p\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"nature-portfolio","isNatureJournal":true,"hasQc":false,"allowDirectSubmit":false,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"","title":"Nature Portfolio","twitterHandle":"","acdcEnabled":false,"dfaEnabled":false,"editorialSystem":"ejp","reportingPortfolio":"","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"","lastPublishedDoi":"10.21203/rs.3.rs-5871932/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-5871932/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThermoelectric materials allow direct conversion between heat and electricity and may be useful for power generation or solid-state refrigeration. However, improving thermoelectric performance is challenging because of the strong coupling between the electrical and thermal transport properties. We demonstrate a new super-gravity-field re-melting fabrication technology that synergistically optimizes the thermoelectric performance. Using a super-gravity field, the brittle (Bi,Sb)\u003csub\u003e2\u003c/sub\u003eTe\u003csub\u003e3\u003c/sub\u003e alloy undergoes unusual plastic deformation and forms mounts of microstructure defects, which is rarely observed in common fabrication process. As a result, the microstructure reconstruction and carrier concentration optimization were simultaneously realized, resulting in an ultra-low lattice thermal conductivity of \u0026lt;\u0026thinsp;0.25 W/m K and a record-high figure of merit of \u0026gt;\u0026thinsp;1.91 in the BiSbTe alloy. The strong enhancement of thermoelectric properties was validated in a thermoelectric module with high conversion efficiency of 6.4% and corresponding output power density of 0.34 W cm\u003csup\u003e2\u003c/sup\u003e when subjected to a temperature difference of 185 K. This work highlights a new super-gravity strategy to achieve a high thermoelectric performance, which may be applicable to other thermoelectric materials.\u003c/p\u003e","manuscriptTitle":"Ultrahigh thermoelectricity obtained in classical BiSbTe alloy processed under super-gravity","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-02-06 05:33:05","doi":"10.21203/rs.3.rs-5871932/v1","editorialEvents":[],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"nature-communications","isNatureJournal":true,"hasQc":false,"allowDirectSubmit":false,"externalIdentity":"NCOMMS","sideBox":"Learn more about [Nature Communications](http://www.nature.com/ncomms/)","snPcode":"","submissionUrl":"https://mts-ncomms.nature.com/","title":"Nature Communications","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"ejp","reportingPortfolio":"Nature Communications","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"a5b99505-92ca-43b0-91ba-6f00bc842d4a","owner":[],"postedDate":"February 6th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[{"id":43756251,"name":"Physical sciences/Materials science/Materials for energy and catalysis/Thermoelectrics"},{"id":43756252,"name":"Physical sciences/Energy science and technology/Thermoelectric devices and materials"}],"tags":[],"updatedAt":"2025-02-06T05:33:05+00:00","versionOfRecord":[],"versionCreatedAt":"2025-02-06 05:33:05","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-5871932","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-5871932","identity":"rs-5871932","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}