Advances and challenges for Mg₃(Sb,Bi)₂-based thermoelectric materials and devices

Abstract

Mg₃(Sb,Bi)₂-based thermoelectric (TE) materials have attracted considerable attention due to their earth-abundant constituent elements, excellent environmental compatibility, and outstanding TE properties in the low- and medium-temperature range. However, optimizing TE properties remains challenging for Mg₃(Sb,Bi)₂, as does device structure design. Given the rapid development of Mg₃(Sb,Bi)₂-based materials and their devices in recent years, there is an urgent need for a systematic and critical review of the progress, challenges, and prospects. We systematically summarize and analyze various current strategies for improving TE properties, including component modulation, defect engineering, band engineering, grain boundary engineering, and mixed scattering optimization of ionized impurities and phonons. In addition, the key challenges for practical applications are comprehensively analyzed, particularly focusing on connection technology, barrier layer material screening, and device structure design. Finally, we outline the significant potential and current challenges of Mg₃(Sb,Bi)₂-based materials in low- and medium-temperature waste heat recovery and solid-state cooling applications, and provide future insights regarding TE properties modulation, preparation scale-up, and novel application prospects.

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1. Introduction

With the rapid development of society and the increasing consumption of fossil fuels, the search for clean, efficient, and renewable energy materials has emerged as a global priority. Thermoelectric (TE) materials have gained widespread attention, attributed to their environmental friendliness and capability for solid-state cooling and power generation.^1,2 Advancements in near-room-temperature TE materials are being critically driven by the demand for energy harvesting and low-grade waste heat recovery.^3–7 The TE conversion efficiency (η) is defined by the dimensionless figure-of-merit, zT = S²σT/κ, where S, σ, κ, and T represent Seebeck coefficient, electrical conductivity, total thermal conductivity, and absolute temperature, respectively.^8,9 Recently, Mg₃(Sb,Bi)₂ has garnered significant research attention because of its benefits such as abundance, low toxicity, and cost-effectiveness.^10–12 Compositional modulation strategies enable Mg₃(Sb,Bi)₂ to demonstrate promising properties for low-grade heat recovery and room-temperature cooling, positioning it as a viable next-generation candidate.^13–16

Mg₃(Sb,Bi)₂ is a typical Zintl compound that crystallizes in a CaAl₂Si₂-type structure, as shown in Fig. 1a. Its crystal structure features a three-dimensional chemical bonding network comprising Mg²⁺ cations in octahedral coordination and (Mg₂Sb₂)²⁻ anionic layers in tetrahedral coordination, establishing a robust basis for excellent TE properties.^17–21 As shown in Fig. 1b, the intrinsic band structure of Mg₃(Sb,Bi)₂ indicates that Mg₃Sb₂ is an indirect bandgap (E_g) semiconductor (0.4–0.8 eV) with relatively low carrier concentration (n_H), whereas Mg₃Bi₂ is a type-II topological nodal-line semimetal characterized by the absence of E_g and high n_H.^22–25Fig. 1c shows the density of states (DOS) for Mg₃Sb₂ and Mg₃Bi₂. The valence band maximum (VBM) of Mg₃Sb₂ and Mg₃Bi₂ is dominated by the Sb/Bi 5p orbitals, while the conduction band minimum (CBM) is dominated by the Mg 3s orbitals.^26,27 This band structure indicates that the electronic states of anions and cations dominate the electrical properties of p-type and n-type conduction samples, respectively. The E_g can be regulated by changing the Bi/Sb ratio through Mg₃Sb₂ and Mg₃Bi₂ alloying, enabling optimization of electrical transport properties.^28–30 However, the volatility and high vapor pressure of Mg during synthesis result in a large number of Mg vacancies, significantly inhibiting electron transport properties.^31,32 The breakthrough came when Tamaki et al.³³ first synthesized n-type Mg_3.2Sb_1.5Bi_0.49Te_0.01 using excess Mg and Te-doping, achieving a remarkable zT of 1.5 at 723 K. This immediately attracted significant research interest. Subsequent studies demonstrated that interstitial Mn doping effectively suppresses the formation of Mg vacancies. This approach led to the first identification of a positive temperature-dependent E_g in Mg_3+δSb_xBi_2−x, directly confirming the suppression of the bipolar effect at medium temperatures. Ultimately, Mg_3+δSb_1.5Bi_0.49Te_0.01Mn_0.01 achieved an average zT (zT_ave) of 1.05 between 323 and 523 K. Notably, its favorable mechanical toughness highlights Mg_3+δSb_xBi_2−x materials as promising candidates for TE applications near-room-temperature.³⁴ Further demonstrating potential, a zT value of 0.9 was achieved at 350 K for the n-type Mg_3.2Bi_1.998−xSb_xTe_0.002 reported by Mao et al.,³⁵ demonstrating its significance as a substitute for Bi₂Te₃ in low-grade waste heat recovery applications. Furthermore, in a cooling device with p-type Bi_0.5Sb_1.5Te₃, it achieved a temperature difference (ΔT) of 91 K at a hot-side temperature (T_h) of 350 K, exceeding the performance of commercial counterparts. A room-temperature analysis of the electronic quality factor (B_ET/κ_l) confirms that n-type Mg₃Sb₂-based alloys exhibit highly competitive TE properties compared to commercial Bi₂Te₃ alloys, solidifying their status as strong contenders for TE cooling and power generation near-room-temperature.³⁶ Given this remarkable progress, a systematic and critical review is essential to summarize the advancements, challenges, and prospects of Mg₃(Sb,Bi)₂.

Fig. 1 (a) The crystal structure and visualization of Mg₃(Sb, Bi)₂ are plate-like [Mg₂(Sb,Bi)₂]²⁻ intercalated with Mg²⁺ cations. (b) Schematic diagrams of the band structures and (c) corresponding DOS for Mg₃Sb₂ and Mg₃Bi₂. Drawn by the authors.

Currently, defect engineering,³⁷ additive manufacturing,³⁸ and device applications^39,40 cover various aspects of TE materials. To facilitate the further development of Mg₃(Sb,Bi)₂, we systematically summarize the past advancements in TE performance regulation and device structure design. In this review, we commence by introducing the fundamental properties of Mg₃(Sb,Bi)₂, including crystal and electronic structures, to elucidate the intrinsic foundations of its transport behavior. Next, we systematically categorize strategies for enhancing properties, including component modulation, band engineering, grain boundary (GB) engineering, composite engineering, and mixed scattering optimization of ionized impurities and phonons. We then discuss connection techniques, the screening of barrier layer materials, and the design of device structures for TE modules of Mg₃(Sb,Bi)₂, addressing critical steps toward practical applications. Ultimately, this review provides valuable insights into the development of Mg₃(Sb,Bi)₂-based materials and promotes their application in low-grade heat recovery and solid-state cooling.

2. Synthesis and progress

2.1. Preparation method

Fabricating advanced Mg₃(Sb,Bi)₂-based materials demands precise control over composition, microstructure, and defect states. Common synthesis techniques encompass melt-based processing, solid-state reactions, single crystal growth, mechanical alloying, and emerging additive manufacturing approaches. Careful selection of the fabrication route is therefore crucial for optimizing TE and mechanical properties, especially considering the volatility of Mg.

High-temperature melting/reaction is a traditional synthesis method valued for its simplicity and suitability for large-scale production.⁴¹ For instance, Y-doped ingots achieving grain sizes > 100 µm and room-temperature carrier mobility (µ_H) > 100 cm² V⁻¹ s⁻¹ were prepared by high-temperature reactive melting with subsequent annealing.⁴² However, significant Mg volatilization during melting remains a challenge. This can be mitigated by adding excess Mg during sintering, which effectively compensates for Mg loss in conventional n-type Mg₃(Bi, Sb)₂ alloys.⁴³ Recently, kilogram-level Mg₃(Sb,Bi)₂ powder was synthesized in merely 5 minutes via the self-propagating high-temperature synthesis method.⁴⁴ This technique also achieves an oxygen content below 0.3%, offering a viable pathway for the industrial-scale production of powder.

As shown in Fig. 2a, solid-state synthesis in sealed tubes suppresses Mg volatilization and impurity formation through high-temperature reactions.^45–47 Using this method, Ponnambalam et al.⁴⁵ synthesized single-phase p-type Mg₃SbBi, achieving a zT value of 0.4 at 825 K. The Mg_3.2Bi_1.4975Sb_0.5Te_0.0025 compound, prepared by sealing in tantalum tubes followed by melt annealing and directional solidification, exhibits record grain sizes larger than 500 µm and room-temperature µ_H of 220 cm² V⁻¹ s⁻¹ among Mg₃(Sb,Bi)₂-based materials.⁴⁸ Although offering low-cost sintering and minimal sintering equipment requirements, the high-temperature synthesis step necessitates specialized equipment and currently lacks scalability for industrial production.

Fig. 2 (a) Mg-flux method using a sealed tantalum tube.⁴⁷ Copyright 2020, Royal Society of Chemistry. (b) Photograph of as-grown Mg₃Bi_1.49Sb_0.5Te_0.01 and Mg_3.1Li_0.003Bi_1.49Sb_0.5Te_0.01 single crystals.^51,52 Copyright 2020, Elsevier. Copyright 2024, American Chemical Society. (c) Synthesis process for mechanical alloying and sintering of Mg₃(Sb,Bi)₂.^66,67 Copyright 2024, American Chemical Society. Copyright 2020, Tsinghua University Press. (d) Schematic diagram of the used 3D printer with a picture of the printed TE legs and their assembly into the device.⁶³ Copyright 2025, The American Association for the Advancement of Science.

Single crystals, with fewer grain boundaries, are expected to exhibit excellent near-room-temperature properties in principle, as GB effects can significantly limit carrier mobility µ_H and TE properties below 500 K.^49,50 As shown in Fig. 2b, the Bridgman method enables the controlled growth of high-quality Mg₃(Sb,Bi)₂ single crystals with precise stoichiometry and low defect densities.^51–53 For example, Mg_3.1Li_0.003Bi_1.49Sb_0.5Te_0.01 achieved an excellent zT of 1.05 at 300 K by suppressing Mg inclusion during single crystal growth, highlighting their competitiveness for cooling applications.⁵² However, compared to polycrystalline synthesis, this method requires precise temperature control and slow growth rates, leading to higher energy consumption and limited productivity.

As illustrated in Fig. 2c, the combination of mechanical alloying (MA) with either hot pressing (HP) or discharge plasma sintering (SPS) offers a relatively simple and controllable approach for synthesizing Mg₃(Sb,Bi)₂.^54–57 Single-phase n-type Mg₃(Sb,Bi)₂ were successfully synthesized using a multi-step ball milling process, achieving a remarkable peak zT value of 1.5 at 716 K.³³ Particularly in Bi-rich compositions, the nanostructures induced by MA promote interface potential scattering of phonons, significantly suppressing the bipolar effect at high-temperatures.⁵⁴ Nevertheless, like other specialized techniques, this method faces challenges for large-scale implementation due to high processing requirements.

Despite the many advantages of these preparation methods, developing novel Mg₃(Sb,Bi)₂-based materials with superior formability and excellent TE performance still faces many obstacles. Given the excellent plasticity of Mg alloys,^58,59 deformation processing (e.g., stretching, rolling) offers a promising strategy to further optimize the microstructure and TE properties. Specifically, rolling refines grain boundaries, reduces porosity, and induces texture. These are critical for improving µ_H and mechanical strength. Furthermore, the enhanced plasticity and mechanical properties of Mg₃Bi₂ provide a solid foundation for exploring its potential in flexible TE device applications.^60–62 Leveraging these properties enables future integration of Mg₃Bi₂ into flexible platforms, boosting η and device flexibility.

Beyond established methods, emerging additive manufacturing methods such as 3D printing (Fig. 2d) may offer significant potential for fabricating complex and gradient structures in future research, as evidenced in the Bi₂(Sb,Te)₃ system.^63,64 This approach uniquely enables the precise construction of complex geometries and facilitates direct multi-material integration of TE materials, electrodes, and substrates, thereby advancing compact, fully integrated device development.⁶⁵

2.2. Progress in thermoelectric figure of merit

As summarized in Fig. 3, the maximum zT values of reported Mg₃(Sb,Bi)₂-based materials since 2018 highlight rapid advancements in the field and underscore their potential for practical applications. The peak zT of Mg₃(Sb,Bi)₂ has remained essentially in the range of 1 to 2 in recent years. While most Mg₃Sb₂-based materials achieve zT values greater than 1, several Mg₃Bi₂-based compositions report lower performance. Among them, the Mg₃Bi_1.49Sb_0.5Te_0.01 single crystals grown by the Bridgman method exhibited a peak zT value of 1.43 at 523 K. The n-type 0.1Nb/Mg₃Sb_1.5Bi_0.49Te_0.01 achieved a peak zT value of 2.04 at 798 K by introducing Nb/Ta impurities at GB modulation of charge carrier and phonon transport.⁶⁸ Similarly, n-type Mg_3.2In_0.02Bi_1.4Sb_0.595Te_0.005 with the homogenizing composition exhibited a zT of 1.27 at 500 K.⁶⁹ Overall, the TE properties of p-type Mg₃(Sb,Bi)₂ are relatively weak due to the lower VB degeneracy.⁷⁰ Despite this, p-type (Mg_3.18Ag_0.02Sb₂)_0.5(YbZn₂Sb₂)_0.5 achieved a zT of 1.17 at 773 K through optimized preparation techniques.⁷¹ A synergistic strategy of band engineering combined with entropy engineering then boosted the peak zT of p-type (Mg_3.07Ag_0.03Sb₂)_0.5(YbZn_1.2Cd_0.8Sb₂)_0.5 to 1.34 and a zT_ave of 0.77 between 323 and 773 K, demonstrating unprecedented performance for p-type Mg₃Sb₂-based materials.⁷² In conclusion, n-type Mg₃(Sb,Bi)₂ demonstrates TE properties nearly twice those of its p-type counterpart, highlighting the need for greater optimization efforts for p-type materials.

Fig. 3 The relationship between the peak zT values of Mg₃(Sb,Bi)₂-based materials and the year of publication.^{35,51,52,68,74–98}

In recent years, the rapid development of Mg₃(Sb,Bi)₂ has made it a promising alternative to Bi₂Te₃. Compared with Bi₂Te₃, Mg₃(Sb,Bi)₂ exhibits a lower cost due to its reduced need for the expensive Te element. Meanwhile, n-type Mg₃(Sb,Bi)₂ shows a good zT value of 0.9 at 300 K,⁷³ making it more promising for solid-state cooling applications compared to Bi₂Te_3−xSe_x. Furthermore, Sb-rich compositions have good potential for power generation at medium temperatures, while Bi-rich compositions hold even more potential for cooling applications. The high cooling performance of Mg₃Bi₂-based alloys motivates future exploration of TE materials for cooling.

3. Optimization strategies for Mg₃(Sb,Bi)₂-based materials thermoelectric properties

Optimizing TE properties of Mg₃(Sb,Bi)₂ requires enhancing the power factor (PF) while suppressing κ. Considering the crystal structure, band structure, fundamental TE properties, and fabrication methods, key strategies include Mg content tuning, band structure engineering, optimizing mixed scattering of ionized impurities and phonons, and complemented are introduced by extensive external element doping. Specifically, TE properties can be improved by optimizing n_H and µ_H to enhance σ, controlling Mg-related defects and tailoring electronic structures to increase the S, and introducing point defects and disordered structures to reduce lattice thermal conductivity (κ_l). These approaches collectively maximize the TE properties of Mg₃Sb_2−xBi_x materials, providing a systematic framework for achieving high η in waste heat recovery and solid-state cooling applications.

3.1. Electrical conductivity

The increase in σ is mainly based on n_H or µ_H.^99,100 The σ can be described as eqn (1):¹⁰¹

σ = neµ (1)

where e is the carrier charge. Mg₃(Sb,Bi)₂ have received significant attention and exploration in the TE field owing to their high band structure degeneracy, ultra-low κ_l, and high µ_H. However, their inherently low n_H limits further improvements in TE properties.^102,103 To overcome this limitation, identifying suitable dopants to regulate n_H and optimize µ_H constitutes a critical strategy for enhancing σ.

3.1.1. Carrier concentration. The coupling between σ and S complicates TE enhancement since both are directly controlled by n_H. Additionally, the bipolar effect simultaneously reduces the S and increases κ by exciting minority carriers, thereby diminishing the high-temperature TE performance.¹⁰⁴ As shown in Fig. 4a, carrier type can be effectively tuned by adjusting initial Mg content.¹⁰⁵ Furthermore, increasing the DOS effective mass (m*) by enhancing the band degeneracy improves the n_H. However, the effect of the E_g on TE properties has received comparatively less attention.²⁸ As shown in Fig. 4b, Bi alloying not only increases the weighted mobility (µ_W) and narrows the E_g, thus optimizing n_H. Nevertheless, excess Bi promotes intrinsic excitation and triggers a bipolar effect, which in turn degrades the performance.^106,107 In Mg₃Sb_2−xBi_x alloys, the conduction bandwidth increases with higher Bi content, which reduces the conduction band m*. Consequently, the S decreases, while σ and µ_W increase.^95,107,108Fig. 4c shows the plot of the TE properties of Mg₃Sb_2−xBi_x with n_H obtained from experimental results and single parabolic band (SPB) model fitting, which indicates that the TE properties of Mg₃Sb_2−xBi_x are significantly enhanced as the Bi content increases to x = 1.¹⁰⁹ To suppress the bipolar effect, deep-level dopants such as Mn and Fe are introduced.^110,111 These deep-level defects act as recombination centers, directly reducing minority n_H and lifetime by facilitating electron–hole pair recombination, thereby mitigating the negative impact of the bipolar effect.

Fig. 4 (a) The n_H as a function of nominal composition Mg_3+xSb_1.5Bi_0.5.¹⁰⁵ (b) Illustration of the reduction in E_g due to alloying with Mg₃Bi₂.¹⁰⁷ Copyright 2020, Elsevier. (c) Schematic n_H dependence of zT for Mg₃Sb_2−xBi_x using the SPB model.¹⁰⁹ Copyright 2020, The American Association for the Advancement of Science. (d) The µ_H and n_H at 300 K as a function of the electronegativity difference |χ_Q − χ_Mg| in n-type Mg₃Sb_1.5Bi_0.5.⁷⁴ Copyright 2018, John Wiley and Sons. (e) Doping atoms versus n_H of Mg₃(Bi,Sb)₂-based compounds at room-temperature. (f) Temperature-dependent σ of Mg₃(Sb,Bi)₂-based materials.^{52,80,86,89,114,115} Band structures of (g) Mg₂₄Sb₁₆, (h) Pr₁Mg₂₃Sb₁₅Se₁, and (i) Nd₁Mg₂₃Sb₁₅Se₁.⁸⁶ Copyright 2022, Elsevier.

Chalcogen element doping (e.g., S, Se, Te) represents a common approach to enhance the properties of n-type Mg₃(Sb,Bi)₂. For example, S-doped Mg₃Sb_1.5Bi_0.5 achieved a peak zT of 1.0 at 725 K, though its properties are inferior to Se- and Te-doped systems due to lower n_H and µ_H, as shown in Fig. 4d.⁷⁴ The decreasing electronegativity difference (|χ_Q − χ_Mg|) from S to Te leads to enhanced n_H and µ_H, ultimately improving TE properties. Subsequent studies revealed that Se doping offers environmental benefits, obtaining a peak zT of 1.24 at 498 K in Mg_3.2Bi_1.4Sb_0.59Se_0.01 and demonstrating its widespread prospect for low-temperature TE applications.⁸⁷ Additionally, the combination of Te doping with defect control and GB optimization significantly enhances TE properties, underscoring the pivotal role of chalcogen doping in improving σ.¹¹²

In addition to anion doping with chalcogen elements, both rare-earth elements doping and single-crystal design enhance the σ of Mg₃(Sb,Bi)₂.^56,78,81,113Fig. 4e demonstrates the higher n_H achievable with rare-earth element doping, underscoring its potential for σ enhancement. Fig. 4f compares the temperature-dependent σ of single crystal and rare-earth elements doping.^{52,80,86,89,114,115} Elements like La and Ce act as promising dopants, enabling n_H to approach the theoretical doping limit.⁸⁹ In addition, the σ of Li–Te co-doped single crystals increased to 13 × 10⁴ S m⁻¹ from 6.2 × 10⁴ S m⁻¹ for Mg_3.1Bi_1.49Sb_0.5Te_0.01 at 300 K.⁵² To further understand the electron transport mechanism, the band structures of Mg₂₄Sb₁₆, Pr₁Mg₂₃Sb₁₅Se₁, and Nd₁Mg₂₃Sb₁₅Se₁ were calculated by first-principles calculation.⁸⁶Fig. 4g shows that the CBM and VBM of pristine Mg₃Sb₂ are at different locations, which corresponds to indirect E_g semiconductors. As shown in Fig. 4h and i, Pr–Se and Nd–Se significantly increase the DOS near the E_F, narrow the E_g, and enhance carrier transport, thereby improving the σ and PF. Ultimately, Mg_3.17Pr_0.03Sb_1.5Bi_0.49Se_0.01 and Mg_3.17Nd_0.03Sb_1.5Bi_0.49Se_0.01 achieved peak zT values of 1.67 and 1.74 at 700 K, which are 38% and 43% higher than that of Se-only doped sample, respectively. In conclusion, the optimized treatment of band engineering, doping, and defect control is crucial for improving n_H and electrical transport properties in Mg₃(Sb,Bi)₂. The trade-off between n_H optimization and bipolar effect suppression remains a key challenge, especially in high-temperature environments. Therefore, introducing deep-level dopants and leveraging energy filtering effects offer strategies to mitigate detrimental bipolar effects.

3.1.2. Carrier mobility. The µ_H is another key factor in optimizing σ. Differences in scattering mechanisms directly affect µ_H and thus significantly influence σ.^116–119 Primary carrier scattering mechanisms include electron-phonon, impurity scattering, and electron–electron scattering.^120–124 This section highlights strategies to effectively mitigate carrier scattering. Generally, transition metals such as Fe, Co, Hf, Ta,⁷⁷ Nb,¹²⁵ and Mn⁷⁵ tend to segregate at GB, forming nanoscale precipitates. These aggregated precipitates effectively passivate GB, thereby transforming the dominant low-temperature scattering mechanism from ionized impurities to mixed scattering, such as ionized impurity and phonon scattering. As shown in Fig. 5a, this strategy enhanced the room-temperature µ_H of Mg_3.1Co_0.1Sb_1.5Bi_0.49Te_0.01 from 16 cm² V⁻¹ s⁻¹ for Mg_3.2Sb_1.5Bi_0.49Te_0.01 to 81 cm² V⁻¹ s⁻¹. The increased µ_H improves the PF, while dopant introduction simultaneously reduces κ_l. As a result, a peak zT of 1.7 was attained in Mg_3.1Co_0.1Sb_1.5Bi_0.49Te_0.01 at 773 K, demonstrating a favorable balance between electrical and thermal transport properties.

Fig. 5 (a) Temperature-dependent µ_H of Mg_3.1A_0.1Sb_1.5Bi_0.49Te_0.01 (A = Fe, Co, Hf, and Ta).⁷⁷ (b) Predicted upper-limit of the zT when grain boundary phase resistance is considered negligible (solid line).⁴⁹ Copyright 2018, Royal Society of Chemistry. (c) SPS displacement as a function of sintering time. (d) Microstructural evolution of Mg_3.2Bi_1.5Sb_0.498Te_0.002Cu_0.01.⁸⁵ Copyright 2022, Springer Nature. (e) The EBSD orientation maps for Mg_3.2Sb_1.5Bi_0.49Te_0.01 samples sintered at 873 K and 1123 K.¹²⁹ Copyright 2018, AIP Publishing. (f) and (g) The APT characterization of Nb_0.1Mg_3.05Sb_1.99Te_0.01.¹³¹ Copyright 2021, John Wiley and Sons.

GB scattering severely limits room-temperature µ_H in Mg₃(Sb,Bi)₂.^126,127 GB resistance reduces µ_H, leading to a decrease in the PF, restricting TE properties. Simulation of GB band offsets indicates that eliminating GB resistance could enhance the room-temperature zT of Mg_3.2Sb_1.5Bi_0.49Te_0.01 by over 60% (Fig. 5b), emphasizing the significance of GB engineering in enhancing zT.⁴⁹ Optimizing sintering temperatures and incorporating a small amount of Cu have proven effective in GB engineering. As shown in Fig. 5c and d, optimal sintering produces dense microstructures with large grains and minimal porosity. Significant increase in grain size at 1073 K compared to 723 K sintering. The room-temperature peak zT of Mg_3.2Bi_1.5Sb_0.48Te_0.002Cu_0.01 increased significantly to 0.9 due to the complete elimination of thermal GB resistance at low temperatures.⁸⁵ Two-dimensional nanomaterials such as graphene have shown remarkable potential as GB additives. The introduction of graphene (G) can effectively regulate the space charge region at grain boundaries, reducing carrier transport barriers. For instance, in Mg_3.24Sb_1.5Bi_0.49Te_0.01/1.0 vol% G, the E_b decreased from 42 meV to 18 meV, enhancing room-temperature µ_H to 68 cm² V⁻¹ s⁻¹.⁹³ Additionally, graphene nanoplatelets (GNPs) have been reported to increase interface thermal resistance, reduce the temperature at grain boundaries, and optimize the interfacial S.¹²⁸ Chemical doping and control of grain size effectively mitigate GB scattering. For example, indium doping significantly suppressed GB scattering and enhanced room-temperature µ_H.⁸⁸ Moreover, the addition of transition metals such as Mo and Nb promotes grain growth via GB segregation, which reduces scattering and increases both µ_H and σ.^68,95 For instance, Mo doping increased the average grain size of Mg_3.16Mo_0.04Sb_1.5Bi_0.49Te_0.01 from 9.46 µm for Mg_3.2Sb_1.5Bi_0.49Te_0.01 to 18.07 µm.⁹⁵ Similarly, introducing Nb impurities into Mg₃Sb_1.5Bi_0.49Te_0.01 improved the room-temperature zT by more than 200%, reaching an unprecedented high zT of 2.04 at 798 K.⁶⁸ Grain size optimization also effectively suppresses GB scattering. As shown in Fig. 5e, the average grain size of Mg_3.2Sb_1.5Bi_0.49Te_0.01 increased from 1.0 µm to 7.8 µm,¹²⁹ significantly reduced GB scattering, enhanced µ_H, and maintained stable κ.

The synergistic effects of grain size and texturing improved the σ of the layered Mg_3.24Sb_1.5Bi_0.49Te_0.01 structure, achieving a maximum zT of 1.71 and a high zT_ave of 1.12 perpendicular to the pressing direction (⊥P).⁹⁴ Increasing the sintering temperature further enlarged grain sizes, reducing GB scattering and increasing the room-temperature σ by over 300%.¹³⁰ Notably, the enhanced µ_H can be attributed to the weakening of GB scattering due to the grain growth and coarsening. Fig. 5f presents the scanning electron microscope (SEM) image of an atom probe tomography (APT) sample. Fig. 5g illustrates the three-dimensional distribution of Mg, Sb, Nb, and Te. These results indicate that the Nb fails to incorporate into the Mg₃Sb₂ matrix after doping but instead segregates along the GB in a metallic state. This segregation leads to the formation of a Nb-rich wetting layer, which promotes grain growth, therefore enhancing σ.¹³¹ Notably, the elimination of GB scattering in single crystals leads to superior TE properties.¹³² Demonstrating this advantage, Imasato et al.¹³³ first synthesized n-type Te-doped Mg₃Sb₂ single crystals by employing a flux method followed by Mg vapor annealing. The elimination of GB resistance led to a remarkable improvement of over 100% in both µ_W and zT near-room-temperature.

While the aforementioned strategies have successfully enhanced the µ_H in Mg₃(Sb,Bi)₂, recent research has shifted toward gaining deeper, atomic-level insights into how defects and carriers interact locally. Fig. 6a–c show high-angle annular dark field (HAADF) and annular bright field (ABF) scanning transmission electron microscopy (STEM) images, along with the integrated differential phase contrast (iDPC) views of Mg₃Sb₂ single crystals. The iDPC imaging visualizes both Mg and Sb atoms in Mg₃Sb₂ single crystals.¹³⁴ Furthermore, Fig. 6f illustrates the Fourier difference electron density maps (F_o − F_c) difference electron density map, confirming the presence of Mg cation vacancy defects and Frenkel defects.¹³⁵ Meanwhile, the origin of the excellent TE properties is further explored by angle-resolved photoelectron spectroscopy (ARPES). Fig. 6g shows the constant energy diagrams of the ARPES of Mg₃Bi₂, Mg₃Bi_1.25Sb_0.75, and Mg₃Sb₂ single crystals. The electronic states close to E_F disappear from Mg₃Bi₂ to Mg₃Sb₂, and the valence band tops move significantly to higher binding energies, leading to a significant widening of the E_g.⁴⁷ To elucidate the effect of doping on the local structure, synchrotron X-ray pair distribution function (X-PDF) was performed on Mg_3.2(Bi_0.7Sb_0.3)_1.99Te_0.01, Mg_3.2(Bi_0.7Sb_0.3)_1.99Te_0.01–Cu₂Se 1.0%, and Mg_3.2(Bi_0.7Sb_0.3)_1.99Te_0.01–Ag₂Se 1.0%, as shown in Fig. 6f–h.¹³⁶ In comparison to Mg_3.2(Bi_0.7Sb_0.3)_1.99Te_0.01, the enhanced short-range ordering in the Cu₂Se and Ag₂Se composites, as evidenced by the narrowing of the characteristic peaks, provides a superior channel for carrier transport. These studies emphasize the crucial role played by GB engineering, defect control, and single-crystal methods in achieving superior µ_H. Since the cost-effective and controllable approach to achieve defect-free single crystals is still a major challenge, GB engineering combined with defect modulation strategies offers a preferred path to balance performance and cost.

Fig. 6 STEM images of Mg₃Sb₂: (a) HAADF, (b) ABF, and (c) iDPC images along [001] direction.¹³⁴ Copyright 2021, Elsevier. (d) The F_o − F_c difference electron density map of n-type Mg₃Sb₂ before refining the interstitial position.¹³⁵ Copyright 2023, American Chemical Society. (e) Series constant energy maps of Mg₃(Sb,Bi)₂.⁴⁷ Copyright 2020, Royal Society of Chemistry Synchrotron X-PDF data as a function of r for (f) Mg_3.2(Bi_0.7Sb_0.3)_1.99Te_0.01, (g) Mg_3.2(Bi_0.7Sb_0.3)_1.99Te_0.01–Cu₂Se 1.0 wt%, and (h) Mg_3.2(Bi_0.7Sb_0.3)_1.99Te_0.01–Ag₂Se 1.0 wt%.¹³⁶ Copyright 2025, Elsevier.

3.2. Seebeck coefficient

In addition to high σ, an excellent S value is essential to achieve excellent PF. The S can be expressed by eqn (2):¹³⁷where k_B and h are the Boltzmann constant and Planck constant, respectively. Band engineering strategies focus on enhancing the DOS near the E_F to improve the S. Key approaches include quantum well, resonant level, band convergence, band curvature, and band anisotropy.^138,139Fig. 7a shows common band convergence and band anisotropy in Mg₃(Sb,Bi)₂. Fig. 7b and c illustrate that the N_v of Mg₃Sb₂ is 6 in the CBM, but only one in the VBM. The VBM exhibits characteristic anisotropic behavior across the Brillouin zone.¹⁴⁰ Additionally, ionic doping (Ca and Yb) can modify the CBM and display anisotropic characteristics. This adjustment increased the band degeneracy to 7, thereby significantly enhancing both S and PF.¹⁴¹

Fig. 7 (a) Schematic diagrams of the band structures and DOS for band convergence and band anisotropy.¹³⁸ Copyright 2021, Springer Nature. Electrical properties of (b) n-type and (c) p-type Mg₃Sb₂.^109,138,140 Copyright 2020, The American Association for the Advancement of Science. Copyright 2021, Springer Nature. (d) Strain-dependent m* at conduction band edge.¹⁴² Copyright 2020, The American Association for the Advancement of Science. (e) Defect formation energies of the lanthanide substitution on the Mg₁ site.¹⁵⁷ Copyright 2020, John Wiley and Sons. (f) Temperature-dependent S of Mg₃(Sb,Bi)₂-based materials.^{52,80,86,89,114,115} (g) Schematic diagram of E_b near the GB and metal–semiconductor interface region.⁶⁸ Copyright 2023, Springer Nature.

3.2.1. P-Type Mg₃(Sb,Bi)₂-based materials. The low band degeneracy and limited hole concentration in p-type Mg₃(Sb,Bi)₂ ^10,29 have limited the commercial development of Mg₃(Sb,Bi)₂ TE devices. Strategies have primarily focused on optimizing the band structure and implementing effective doping to enhance n_H.

As illustrated in Fig. 7d, under the influence of strain, the m* of the DOS at the CBM of Mg₃Sb₂ exhibited a linear decreasing trend.¹⁴² Theoretically, a reduction in m* leads to a lower S. However, when acoustic phonon scattering dominates, the maximum PF is proportional to the ratio of N_v/m*. Thus, a smaller m* corresponds to a higher µ and a higher PF.¹⁰⁷ Meanwhile, biaxial strain can effectively enhance band degeneracy. For example, p-type Mg₃Sb₂ achieved a maximum S in the plane from 375 µV K⁻¹ under unstrained to 623 µV K⁻¹ under 2.5% biaxial strain at 700 K.¹⁴³ Furthermore, in p-type Mg₃(Sb,Bi)₂, the introduction of elements such as Li,¹⁴⁴ Zn,³¹ Cd,³² Ag,¹⁴⁵ and Na¹⁴⁶ at the cationic sites to replace Mg can effectively regulate the n_H and µ_H. Meanwhile, multiple co-doping at the Mg sites simultaneously enhances both carrier transport and phonon scattering.^32,147 For instance, a peak zT value of 0.87 was achieved in Mg_1.95Na_0.01Zn₁Sb₂ at 773 K through Na–Zn co-doping.⁹⁸ First-principles calculations revealed that Ag–Bi co-doping shifts the E_F into the VB and narrows the E_g. This facilitates hole generation, increasing n_H from 3.50 × 10¹⁷ cm⁻³ to 7.88 × 10¹⁹ cm⁻³. As a result, Mg_2.94Ag_0.06Sb_1.9Bi_0.1 achieved an impressive PF of 778.9 µW m⁻¹ K⁻² at 723 K.⁹² Nanostructured bulk materials fabricated using high-energy ball milling combined with SPS exhibit uniform microstructures that enhance S.¹⁴⁸

3.2.2. N-Type Mg₃(Sb,Bi)₂-based materials. Different synthesis methods can lead to significant performance variations.^44,149–152 For instance, Mg₃Sb₂ single crystals prepared using the self-flux method exhibit distinct S for different flux methods. The p-type samples synthesized with Sb-flux achieved a room-temperature S of 764 µV K⁻¹, while n-type samples prepared with Mg-flux reach a high S of −897 µV K⁻¹.¹³⁵ For polycrystalline systems, the combination of MA with HP sintering can effectively inhibit Mg volatilization.¹⁵³ Among compositions, Mg₃Sb_0.6Bi_1.4 achieves an optimal balance for charge transport. Its n-type variants exhibited a larger effective E_g and superior TE properties.²⁸

Band structure modulation via doping effectively enhances the S.^154–156 The calculated formation energies for various dopants are summarized in Fig. 7e. La and Ce act as effective n-type dopants, exhibiting high donor transition energy levels significantly above the CBM.¹⁵⁷Fig. 7f compares the S for single crystals and rare earth element doping.^{52,80,86,89,114,115} The S of all rare-earth doping increases with temperature, indicating degenerate semiconductor behavior. Moreover, the S of single-crystal Mg_3.1Li_0.003Bi_1.49Sb_0.5Te_0.01 decreases with rising temperature owing to the presence of bipolar effect.⁵² The significant enhancement of S in Mn-doped Mg₃Sb_1.5Bi_0.5 was attributed to the presence of multiple conduction bands with high band degeneracy.⁷⁵ Furthermore, the addition of transition metals such as Nb/Ta can scatter low-energy carriers more efficiently by changing the interfacial barrier (E_b). As shown in Fig. 7g, the interfacial barrier decreases from E_b1 to E_b2, improving the tendency for more high-energy carriers to pass through, which leads to an increase in the S.⁶⁸ In summary, achieving an optimal S not only requires precise control of n_H but also demands a comprehensive strategy involving band engineering, defect chemistry, and interface optimization. Future research should further explore the interplay between band structure modulation and microstructural design to achieve an ideal balance between the S and σ.

3.3. Lattice thermal conductivity

The relatively high κ of Mg_3.2Bi₂ limits its TE properties. The minimum value of κ is derived through Cahill and Ball using eqn (3):¹⁵⁸where V, v_t, and v_l represent the average volume of each atom, transverse and longitudinal wave velocities, respectively. The Debye model under the relaxation time approximation (τ(x)) is usually used to describe κ_l, which can be expressed as eqn (4):¹⁵⁹where θ_D is the Debye temperature, and x is defined as hω/k_B.

3.3.1. Phonon dispersion. Fig. 8 illustrates a typical phonon transport mechanism in Mg₃(Sb,Bi)₂, analyzing its physical origins.¹⁶⁰Fig. 8a and b show the powder-averaged dynamic structure factor S(|Q|, ω) for Mg₃Sb₂ and Mg₃Bi₂, respectively. The vertical intensity stripes corresponding to the phonons spread outward from the elastic line (0 meV). The tops of the phonons and the low-energy optical phonons together contributed to the stronger intensity in the range of 6 to 10 meV, which originates from the softened phonon.¹⁶¹ The density of atomic projected phonon states (Fig. 8c) further demonstrated how well the moment tensor potential (MTP) and density functional theory (DFT) results characterize the low-frequency region of the phonon spectrum, which is the main part of phonon transport. The core mechanism underlying the low κ_l lies in its strong lattice anharmonicity. For Mg₃Sb₂, the Grüneisen parameter (Fig. 8d) captured significant positive and negative values in low-frequency acoustic branches from MTP-derived data. These extremes substantially enhanced phonon–phonon scattering through strong anharmonicity (Fig. 8e) and shorten the phonon mean free path (l_ph), thereby reducing the κ_l. To understand the effects of doping on κ_l, the calculated phonon spectra of Mg₂₄Sb₁₆, YMg₂₃Sb₁₅Cl, and YMg₂₃Sb₁₄ClTe were shown in Fig. 8f–h.¹⁶² Importantly, the similarity in the energy and momentum of phonon modes within overlapping branches enables numerous scattering channels. The results demonstrate that the YCl₃ doping induced a “crossover avoidance”¹⁶³ effect between the acoustic and optical branches, leading to a clear separation between the low-frequency acoustic and optical branches (marked by red circles). This effect increased the anharmonicity of the phonon vibrations and significantly reduced the speed of sound (Fig. 8i). Additionally, Te doping further amplifies this separation effect and phonon softening is observed, thus reducing the κ_l. The analysis of the phonon spectrum provides a robust theoretical explanation for the reduction of κ_l from a phonon transport dynamics perspective. Simultaneously, the observed separation between the phonon and optical branches and the phonons softening are typically associated with low κ_l.

Fig. 8 Neutron dynamical structure factor S(|Q|, ω) of (a) Mg₃Sb₂ and (b) Mg₃Bi₂.¹⁶¹ Copyright 2020, The American Association for the Advancement of Science. (c) Atom-projected phonon DOS of Mg₃Sb₂ and Mg₃Bi₂.¹⁶⁰ Copyright 2023, American Chemical Society. (d) The Grüneisen parameter, and (e) scattering rate of anharmonic for 300 K of Mg₃Sb₂.¹⁶⁰ Calculated phonon spectra of (f) Mg₂₄Sb₁₆, (g) YMg₂₃Sb₁₅Cl, (h) YMg₂₃Sb₁₄ClTe, and (i) the sound velocity comparison.¹⁶² Copyright 2025, Elsevier.

3.3.2. Phonon scattering center. Multiscale defects, including point defects, grain boundaries, dislocations, strains, and precipitates, can introduce multiscale scattering centers to scatter phonons of different frequencies.^164–166 Intrinsic point defects comprising vacancies, interstitial atoms, and substitutional atoms are essential determinants of Mg₃(Sb,Bi)₂ TE properties.¹⁶⁷ The strong lattice anharmonicity¹³³ and the small ionic radius of Mg²⁺ cations¹⁶⁸ favor soft vibrational modes, which result in low κ_l.^35,168

In Mg_3.2Bi₂, partial substitution of Bi with Sb effectively reduces κ_l through alloy scattering. The κ_l reduced from 9.6 W m⁻¹ K⁻¹ for Mg_3.2Bi₂ to 3.2 W m⁻¹ K⁻¹ for Mg_3.2Bi_1.298Sb_0.7Te_0.002, leading to a high zT value of 0.9 at 350 K.³⁵ Additionally, alloy scattering induced by compositional variations reduced the κ_l of Mg_3.2Bi_1.4Sb_0.595Se_0.01 to 0.6–0.7 W m⁻¹ K⁻¹ in the low-temperature range, demonstrating excellent room-temperature TE properties.⁸⁷ Furthermore, the Sb–Bi lattice disorder introduced during alloying can further reduce κ_l to 0.44 W m⁻¹ K⁻¹ at 716 K, approaching the Cahill minimum κ_l.³³ Point defects and lattice defects also significantly contribute to κ_l reduction by scattering phonons of different wavelengths. For instance, introducing heavy-mass Co enhanced phonon scattering, enabling Mg_3.15Co_0.05(Sb_0.3Bi_0.7)_1.99Te_0.01 to achieved a minimum κ_l of 0.64 W m⁻¹ K⁻¹ at 450 K and a high peak zT of 1.03 at 525 K.⁷⁹ Furthermore, Mg_3.18Y_0.02Sb_1.5Bi_0.49Se_0.01 leveraged point defects and dense grain boundaries to enhance phonon scattering, achieving a κ_l reduction. This effect yielded a theoretical η of 13.8% and an excellent zT of 1.87 under a 450 K temperature gradient.⁹¹ Doping with rare-earth elements such as Gd and Pr can further optimize n_H and κ. By synergistic tuning the electronegativity difference, mass fluctuations, and point defects, Gd-doped Mg_3.065Sb_1.3Bi_0.7Gd_0.015 achieved a high zT of 1.55 at 700 K.⁸² Similarly, Pr-doping not only increased n_H but also reduced κ_l to 0.42 W m⁻¹ K⁻¹, leading to a peak zT of 1.70 for Mg_3.2Pr_0.02Sb_1.5Bi_0.5 at 725 K.⁷⁶

Nanostructured materials, through the introduction of interfaces and defects, can effectively scatter a wide range of phonons while maintaining favorable electronic transport properties.^148,169,170 For instance, nanostructured Mg₃Sb₂ and Mg₃Sb_1.8Bi_0.2 exhibited respective peak zT enhancements of 54% and 56% at 773 K, primarily due to preferential phonon scattering at interfaces.^81,84Fig. 9a demonstrates a transmission electron microscopy (TEM) image of Mg_2.94Ag_0.06Sb_1.9Bi_0.1, indicating the presence of nano-precipitates and lattice distortion. Furthermore, lattice distortion was verified by high-resolution transmission electron microscopy (HRTEM) (Fig. 9b). The κ_l was effectively decreased to 0.48 W m⁻¹ K⁻¹ by phonon scattering at point defects, distorted lattices, and nanoprecipitates, as illustrated in the schematic diagram Fig. 9c.⁹² Similarly, Bi nanoprecipitation and lattice distortion significantly enhance phonon scattering. Combined with shorter relaxation times, this ultimately reduced κ_l for Mg_3.18Ce_0.02SbBi_0.97Te_0.03 to 0.51 W m⁻¹ K⁻¹ at 673 K.¹⁷¹ In Mg_3.24Sb_1.5Bi_0.49Te_0.01/1 vol% G, an equivalent nanoparticle scattering mechanism resulted in a moderate reduction in κ_l, achieving a peak zT value of 1.30 at 773 K.⁹³ Furthermore, Mn doping suppresses Mg evaporation during the sintering process, helping to decouple the electrical and thermal transport. As shown in Fig. 9d and e, low-magnification TEM imaging reveals the grains fractured along the crystals. Fig. 9f presents an HRTEM image that allows the observation of nanoprecipitates and nanostructured GB grain boundaries, both contributing to lower κ_l.³⁴ Dislocation and strain engineering have shown remarkable success in further optimizing phonon transport mechanisms. The aggregation and evolution of vacancies caused by Bi defects into dislocations enhanced phonon scattering, resulting in a peak zT of 1.82 for Mg_3.16Y_0.01Sb_1.5Bi_0.48 at 473 K.⁹⁰ The presence of dislocations and strains in Mg_3.2Sb_1.5Bi_0.49Te_0.01–4% Mg and Mg_3.2In_0.005Sb_1.5Bi_0.49Te_0.01 reduced the phonon relaxation time, leading to a remarkable decrease in κ_l.^67,172 Phonon transport is further constrained by strain-induced disorder and lattice anharmonicity, which reduce phonon relaxation times. Additionally, as shown in Fig. 9g, dislocation strain and defect-induced mass fluctuations further suppress phonon transport. Mg_3.22Ho_0.03Sb_1.5Bi_0.5 sintered at 1073 K achieved a low κ_l of 0.47 W m⁻¹ K⁻¹ at 750 K.¹³⁰

Fig. 9 HRTEM images of (a) Mg_2.94Ag_0.06Sb_1.9Bi_0.1 and (b) rectangular area indicated in (a). (c) Schematic diagram of point defects strengthening phonon scattering.⁹² Copyright 2025, Elsevier. (d) and (e) Low-magnification TEM image of the sample with Sb content of Mg_3.02Mn_0.01Sb_1.2Bi_0.79Te_0.01, with an inset depicting the electron diffraction patterns along the [12̄13̄] direction. (f) HAADF image of the coarse-grained boundary.³⁴ Copyright 2018, John Wiley and Sons. (g) Schematic diagram demonstrating the combined effect of strain engineering and scattering mechanisms on the modulation of phonon and charge carrier transport.¹³⁰ (h) The l_ph dependence of accumulated κ_l and schematic diagram of all-scale hierarchical structures. Copyright 2024, Elsevier.

Under the Debye model approximation, the l_ph can be expressed as eqn (5):

l_ph = v_sτ(x) (5)

Fig. 9h illustrates the relationship between the l_ph and the accumulated κ_l. Lattice defects of different scales scatter phonons of various frequencies and lead to extremely low κ_l. To effectively employ a multi-scale defects, the dimensions of the introduced scattering centers should be smaller than the κ_l and larger than the carrier mean free path.¹⁷³ These studies reveal the complex mechanism of phonon transport in Mg₃(Sb,Bi)₂ materials and offer a theoretical basis for reducing κ_l by modulating phonon scattering. Future studies should integrate multiscale defect optimization with advanced characterization techniques to simultaneously balance electrical/thermal properties and advance TE performance limits.

4. Mg₃(Sb,Bi)₂-based thermoelectric device

Despite high zT values and promising TE properties of Mg₃(Sb,Bi)₂-based materials, there remain numerous challenges to overcome before achieving large-scale practical applications. A high zT value alone does not ensure outstanding device performance, particularly when sustaining high η over a wide temperature range is required. The η of the device is determined by the zT_ave across the entire operating ΔT, expressed by eqn (6):¹⁷⁴where T_H and T_C are defined as the leg temperatures at the hot and cold sides, respectively. Therefore, maintaining high efficiency and reliability across the entire operating temperature range is essential for maximizing overall η, necessitating strategic structural optimization at the device level.

The manufacture of TE devices entails more intricate scientific and engineering issues than optimization of material properties. Appropriate interface and structural design strategies, including the connection technology, selection of barrier layers, multi-stage optimization, and size matching between n-type and p-type TE legs, are essential for enhancing device performance.^{150,175–178}Fig. 10a illustrates a single-leg structure consisting of a Cu electrode, hot- and cold-side solders, a metal contact layer, a barrier layer, and a TE leg that can be used to test the performance of a single material. The traditional module (Fig. 10b) is suitable for η in terms of a combination of n- and p-type materials over a wide temperature range. However, optimization of leg size matching and interfacial stability between different materials is required. Though thermal expansion compatibility and interfacial contact resistance must be addressed, the segmented module (Fig. 10c) maximizes the η of the device. Additionally, issues such as thermal stability, mechanical properties, device assembly techniques, and manufacturing costs are key obstacles to address for large-scale applications.^{175,179–181}Fig. 10d summarizes the η of Mg₃(Sb,Bi)₂-based TE devices at different ΔT. Mg_3.2Sb_1.5Bi_0.49Te_0.01 + 0.25 vol% TiO_2−n single-leg achieved a η of 15% at ΔT of 470 K, which fully demonstrates its excellent potential for application.^{11,68,182–186}

Fig. 10 Schematic diagram of the structure of (a) single-leg, (b) traditional module, and (c) segmented module. (d) The η of Mg₃(Sb,Bi)₂-based TE devices as a function of ΔT.^{11,68,182–188}

4.1. Connection technology

The advancement of high-performance TE modules critically depends on achieving low-resistance and thermally stable interconnects between TE materials and electrodes.^{183,189–192}Fig. 11a shows the joining of Al–Si–Cu alloys by brazing combined with pressure-assisted sintering under 830 K and 10 MPa. However, high-temperature leads to the volatilization of Mg and Zn, resulting in the formation of cracks in the TE legs. The Mg_3.2Bi_1.497Sb_0.5Te_0.003/Bi_0.4Sb_1.6Te₃ device using SnBi solder retained 98.3% of its original performance after 3000 current cycles, demonstrating the excellent thermal fatigue resistance of the solder.¹⁹³ In a separate case, the Pb-free commercial solder Ag₅₆Cu₂₂Zn₁₇Sn₅ was used to bond Fe₇Mg₂Ti and Fe₇Mg₂Cr to Cu electrodes at approximately 903 K. The resulting joints maintained shear strength greater than 30 MPa and contact resistivity below 10 µΩ cm² after aging at 673 K for 15 days, indicating exceptional high-temperature stability.¹⁹⁴

Fig. 11 (a) Schematic of conventional soldering technique.¹⁹⁷ Copyright 2023, Oxford University Press. (b) Mg₃Sb₂-based modules assembled by Ag composite paste under low-temperature and low-pressure conditions.¹⁹⁷ (c) Mass change and heat flow of Ag composite paste during thermal cycling.¹⁹⁷ (d) Analysis of the resistance changes observed before and after soldering with Ag composite paste.¹⁹⁷ (e) Schematic diagram of TE device assembly by Ag nanoparticle sintered bonding.¹⁸³ Copyright 2024, Springer Nature. (f) and (g) Characterization of the nano-Ag sintered connection layer.¹⁸³

Compared with the traditional soldering technique, the novel composite Ag paste soldering technique effectively avoids the problem of device failure due to TE arm damage caused by pressure and temperature limitations. As shown in Fig. 11b, the Ag paste was uniformly applied to the electrode before heating and heated at 523 K in argon for 1.5 h. The connection between the TE legs and Cu electrode was realized after heating and exhibits good thermal stability (Fig. 11c).^195,196Fig. 11d compares the resistance change before and after soldering of the new Ag composite paste to avoid impairing the TE material and interface, and the resistivity is consistent with the predicted values.¹⁹⁷ This low-temperature, low-pressure connection technique utilizing Ag composite adhesive demonstrates effective performance. In addition, the efficiency of n-type single-leg Mg₃Sb₂-based devices prepared using a low-temperature nano-Ag sintering process is up to 13.3%.¹⁸³ Nano-Ag sintering was performed at 573 K and 10 MPa, as shown in Fig. 11e. The Ag nanoparticles exhibited an almost spherical morphology and were encapsulated by an organic layer that inhibits oxidation and self-adhesion (Fig. 11f). The sintered nano-Ag network structure was homogeneously dispersed and well-connected at the interface (Fig. 11g). Also, this process can be combined with phase diagram engineering, which exhibits great potential for interconnect packaging of a wide range of high-performance TE power generation devices.

4.2. Barrier layer

To maintain the robust operation of TE modules, a stable interface barrier layer with low contact resistance is required.^198–203 However, interface losses and failures between TE materials and electrodes remain significant challenges.¹⁹² In the preparation of cooling modules for Mg₃(Sb,Bi)₂, the selected diffusion barrier materials should exhibit excellent chemical stability, compatible thermal expansion coefficients (CTE), robust bonding strength, low contact resistance, and comparatively low processing temperatures to avoid degradation of Mg₃(Sb,Bi)₂. Wu et al.¹⁹⁴ systematically investigated interfacial reactions and diffusion behavior through high-throughput experiments. Their study identified Fe, Ni, Mo, W, and Co as pure TE interface materials with excellent thermal stability. However, when bonding performance with Mg₃Sb_1.5Bi_0.5 was evaluated after 15 minutes at 773 K, Nb, Mo, W, and Co were excluded due to their tendency to form intermetallic compounds and inert diffusion characteristics, which led to inferior interfaces.

The Fe/Ni layers have been confirmed as proper barrier layers for Mg₃(Sb,Bi)₂.^188,204,205 Taking the Fe contact layer as an example, the microstructure and compositional line scan of the Mg_3.2Sb_1.5Bi_0.49Te_0.01/Fe interface show that the mixed region is primarily enriched with Fe and Mg (Fig. 12a). Due to the minimal solubility of Fe and Mg, the excess Mg in the mixed layer is residual and destabilizing. Aging the Mg_3.2Sb_1.5Bi_0.49Te_0.01/Fe interface at 523 K for 400 h further elucidated its thermal chemical stability. As shown in Fig. 12b, the thickness of the Fe–Sb layer and the Sb-rich Mg₃Sb₂ layer increased to 1 µm and 0.7 µm, respectively. The overall thickness of the reaction layer exhibits a favorable linear relationship with the square root of time (Fig. 12c), indicating that the interface layer growth is governed by diffusion. Subsequent studies found that Mg₂Cu was a suitable barrier layer for Mg₃(Sb,Bi)₂ compared to Ni/Fe electrodes.²⁰⁶ The ternary phase diagram of Cu–Mg–Sb(Bi) indicated that Mg₂Cu is thermodynamically stable within the Mg–Mg₂Cu–Mg₃Bi_1.5Sb_0.5 phase region, as shown in Fig. 12d. Thus, it effectively prevents the diffusion of Cu into Mg₃(Sb,Bi)₂. The contact resistivity (ρ_c) of the Mg_3.2Bi_1.4975Sb_0.5Te_0.0025 legs, measured using the four-probe method, was as low as 12 mΩ cm² (Fig. 12e).²⁰⁷Fig. 12f demonstrates the maximum thermal stress (70 MPa) in the contact layer of Cu/Mg₂Cu/Mg_3.2Bi_1.4975Sb_0.5Te_0.0025 at a constant ΔT and optimized current, indicating that the material is used as an optimal buffer layer to relieve the thermal stresses.

Fig. 12 The composition profile of Mg_3.2Sb_1.5Bi_0.49Te_0.01/Fe interface after an aging treatment of (a) 0 h and (b) 400 h. (c) The thickness of the reaction layer as a function of aging time.²⁰⁶ Copyright 2020, Elsevier. (d) Mg–Mg₂Cu–Mg₃Bi_1.5Sb_0.5 three-phase region. (e) Contact resistance measurement of the interfacial layers. (f) Simulated thermal stress distribution near the barrier layers of the module during operation.²⁰⁷ Copyright 2022, Elsevier. (g) The energy dispersive spectroscopy mapping and line scanning results showing the elemental distribution of Ti foil sintered with Mg₃(Sb,Bi)₂. (h) Changes in power generation performance of a Mg₃Sb₂-based single-leg during thermal cycling testing.²⁰⁸ Copyright 2024, Springer Nature.

Through the dynamical transition from a high-temperature substable phase to a low-temperature stable phase, the limitations of thermodynamic equilibrium can be overcome, and ideal materials for TE barrier layers are identified. By comparing the kinetic properties of the reaction and diffusion behavior of Mg₃(Sb,Bi)₂ and Ti during sintering and operation, the Ti foil/Mg₃(Sb,Bi)₂ connectors present excellent sintering activity and inert behavior.²⁰⁸ As shown in Fig. 12g, the interface reaction product between the Ti foil and Mg₃(Sb,Bi)₂ was a MgTiSb compound with a thickness of 1 µm when held at 1023 K for 15 min. Therefore, it can function effectively as a barrier layer for Mg₃Sb₂-based materials. As illustrated in Fig. 12h, the power generation performance of a Mg₃Sb₂-based single-leg TE device remained stable during 200 thermal cycles lasting 330 h, with the heat source temperature cycling between 473 K and 748 K, exhibiting excellent stability and reliability. The interface ρ_c reduced to below 5 µΩ cm², allowing the Mg₃Sb₂-based module to achieve a high η of 11% at a ΔT of 440 K, surpassing most advanced medium-temperature TE modules. Advances in novel connection techniques and the development of stabilizing barrier layers have greatly improved the reliability, efficiency, and performance of Mg₃(Sb,Bi)₂-based TE devices. These strategies address critical issues related to interfacial loss, contact resistance, and thermal stress.

4.3. Thermoelectric modules

From a device design perspective, output power and reliability are the two core factors influencing practical applications. High output power ensures superior η and expands the applicability of TE modules, while good stability guarantees device reliability and long-term operation under diverse environments.^209–211 One of the main challenges to the thermal stability of Mg₃Sb_2−xBi_x lies in the loss of Mg at elevated temperatures.^212,213 Significant progress has been achieved in enhancing the thermal stability of Mg₃(Sb,Bi)₂ through various thermal treatments, chemical reactions, and surface modification techniques. For instance, BN-coated Mg_3.2Sb_1.5Bi_0.49Te_0.01 achieved a high η of 11.1% under a ΔT of 473 K.¹⁸² Additionally, annealing processes have been demonstrated to significantly mitigate material degradation. Applying Mg vapor annealing, surface coatings, and low-temperature annealing effectively suppresses non-equilibrium defects, thereby enhancing structural stability.^214,215 Traditional TE technology at room temperature has long been dominated by Bi₂Te₃-based materials. However, the scarcity of Te poses significant limitations for future large-scale applications.²¹⁶ Developing the next generation of Te-free materials is therefore crucial to mitigating potential raw material supply bottlenecks and achieving sustainable development. The one-step hot-pressing method has been shown to realize strong bonding between the barrier layers and Mg₃Sb₂-based TE materials, effectively reducing contact resistance, as shown in Fig. 13a. This method enabled a η of 10.6% within a ΔT range of 100 to 500 °C.¹¹ As shown in Fig. 13b, the 0.1Nb/Mg₃Sb_1.5Bi_0.49Te_0.01 single-leg apparatus can run continuously for more than 120 h at ΔT = 470 K with η higher than 14%.⁶⁸ In addition, Mg₃(Sb,Bi)₂ and p-type MgAgSb modules designed by GB engineering, and geometrical optimization achieved η of 7.3% and 8.2%, respectively,^185,217 and the performance remained stable after 32 000 thermal cycles.²¹⁸ These studies further demonstrate the reliability and high η values of the Te-free modules, achieving competitive performance in the low temperature range.

Fig. 13 (a) Single-leg η measurement architecture under high ΔT, with operational setup visualization.¹¹ Copyright 2019, Elsevier. (b) Comparison of the maximum η among the single-leg devices in 0.1Nb/Mg₃Sb_1.5Bi_0.49Te_0.01 with other TE modules.⁶⁸ Copyright 2023, Springer Nature. (c) Module fabrication and cooling measurement setup for n-type Mg_3.2Bi_1.5Sb_0.498Te_0.002Cu_0.01 and p-type α-Mg_0.99Cu_0.01Ag_0.97Sb_0.99.⁸⁵ Copyright 2022, Springer Nature. (d) Cooling performance of p-type MgAg_0.97Sb_0.99 and n-type Mg_3.6Y_0.003Sb_0.6Bi_1.4.²¹⁸ Copyright 2022, Royal Society of Chemistry. (e) Design of the setup used to characterize the cooling performance of the Mg₃Bi₂-based double-stage TEC.⁹ Copyright 2025, Innovation Press. (f) and (g) Solid-state sensor device and applications of Mg_3.19Co_0.01Sb_0.5Bi_1.49Te_0.01.²²⁸ Copyright 2024, Elsevier.

The CTE mismatch between the two TE legs can lead to stress accumulation during repeated thermal cycles, ultimately degrading performance.^219,220 For medium- and high-temperature applications, minimizing the CTE mismatch is an important strategy for improving device performance. For example, p-type MgAgSb and n-type Mg_3.49Y_0.01Sb_1.5Bi_0.5 exhibited a CTE mismatch of only 0.95%, demonstrating good compatibility between the two leg materials within TE modules.²²¹ Furthermore, Peltier modules mediated by ultrafine grains and nanoporous structures in α-MgAgSb and Mg_3.2(Bi,Sb)₂ achieved a maximum ΔT of 52 K and a coefficient of performance (COP) of 8.3 under high-temperature conditions.²²² For medium- and high-temperature modules, using n- and p-type legs from the same material system can reduce CTE mismatches and simplify electrode material selection.²²³ For example, n-type Mg_3.2Sb_1.5Bi_0.49Te_0.01Mn_0.01 and p-type Na_0.005Mg_2.995Sb_1.5Bi_0.5 exhibited comparable thermal expansion properties, achieving a theoretical η of approximately 9.5% under a ΔT of 300 K to 773 K.²²⁴

Besides power generation, TE cooling is equally important.^225–227 Full-scale TE cooling devices with 7 pairs, 31 pairs, and 71 pairs were fabricated by joining an n-type Mg_3.2Bi_1.4975Sb_0.5Te_0.0025 layer with an effective and reliable Mg₂Cu diffusion barrier to a p-type (Sb_0.75Bi_0.25)₂(Te_0.97Se_0.03)₃.²⁰⁷ Nevertheless, despite the progress in high-performance single-pair and full-scale TE coolers, the development of TE devices entirely free of (Bi, Sb)₂Te₃-based TE devices remains limited. Inspired by this, a cooling module was constructed by combining n-type Mg_3.2Bi_1.5Sb_0.5 with p-type α-MgAgSb through microstructure design (Fig. 13c). It achieved an η value of 2.8% (ΔT = 95 K), a maximum cooling ΔT of 56.5 K, and a maximum COP (COP_max) of 2.6 (ΔT = 10 K).⁸⁵ Furthermore, a TE device composed of high-performance n-type Mg_3.6Y_0.003Sb_0.6Bi_1.4 and p-type MgAg_0.97Sb_0.99 compounds exhibits a maximum ΔT of 72 K with T_h of 347 K (Fig. 13d).²¹⁸ A 7-pair TE cooling module fabricated using p-type Bi_0.5Sb_1.5Te₃ and n-type MgAg_0.97Sb_0.99 reached a maximum ΔT of 100 K at T_h = 400 K, exhibiting COP_max of 8.9, 7.5, and 3.2 at T_c of 0 K, 5 K, and 10 K, respectively.⁴⁸ The subsequently developed multistage refrigeration device follows the design of heat distribution where the cooling capacity of the next stage is larger than the heat dissipation of the previous stage for realizing the cooling stage by stage.⁹ The temperature field simulation results show that the seven-stage refrigeration device of Mg_3.1Sb_0.497Bi_1.5Te_0.003/(Bi,Sb)₂Te₃ can realize step-by-step refrigeration by the layer-by-layer stacked “pyramid” configuration. As shown in Fig. 13e, the Mg_3.1Sb_0.497Bi_1.5Te_0.003/(Bi,Sb)₂Te₃ two-stage refrigeration device achieved a maximum cooling capacity of 3.0 W and a maximum ΔT of 103.2 K, which is comparable to the commercial Bi₂Te₃ alloy-based device.

The potential interdisciplinary applications of Mg₃(Sb,Bi)₂ have also been explored. Fig. 13f shows an infrared thermogram of a respiratory mask equipped with Mg_3.19Co_0.01Sb_0.5Bi_1.49Te_0.01-based TE sensor, demonstrating its potential for respiratory monitoring applications. Additionally, Fig. 13g reveals that five common liquids have different contact angles on the polyurethane film, indicating the TE sensor can be used for liquid identification.²²⁸ These advancements suggest that Mg₃(Sb,Bi)₂-based modules have the potential to rival, or even surpass, commercial Bi₂Te₃ systems in performance, offering an environmentally friendly and efficient alternative that represents a significant step forward in the sustainable development of TE technology.

5. Challenge and outlooks

Mg₃(Sb,Bi)₂-based materials, as a resource-abundant and environmentally friendly class of Zintl-phase materials, have attracted widespread focus and discussion owing to their excellent thermoelectric (TE) properties and low cost. Compared to conventional Bi₂(Te,Se)₃-based TE materials, Mg₃(Sb,Bi)₂ exhibits high conversion efficiency (η) near-room-temperature while addressing the scarcity and high cost of Te, presenting great potential for both research and practical applications. We summarize the key factors for Mg₃(Sb,Bi)₂-based materials and devices in Fig. 14. Before large-scale commercialization, Mg₃(Sb,Bi)₂ must overcome several key challenges in practical implementation, as outlined below:

Fig. 14 Challenges and optimization aspects of Mg₃(Sb,Bi)₂.^181,186,215 Copyright 2023, John Wiley and Sons. Copyright 2023, Oxford University Press. Copyright 2024, Springer Nature. Copyright 2023, Elsevier.

(1) In terms of fabrication, methods such as mechanical alloying, discharge plasma sintering, and hot-pressing have been widely employed for producing Mg₃(Sb,Bi)₂ bulk materials. These techniques not only improve material densification but also effectively enhance lattice uniformity and TE properties. Furthermore, advancements in single-crystal fabrication technologies have drastically reduced electrical resistance caused by grain boundary scattering, further improving carrier mobility (µ_H) and η. Current fabrication techniques are mostly limited to laboratory-scale production, which cannot meet the demands of large-scale industrial manufacturing. Developing cost-effective and environmentally friendly synthesis methods is essential for the commercialization of these materials.

(2) By adjusting the Bi/Sb ratio, the bandgap of Mg₃(Sb,Bi)₂ can be flexibly tuned to optimize carrier concentration and µ_H, thereby enhancing electrical transport properties. Additionally, doping with rare-earth elements has further improved the Seebeck coefficient (S) and power factor, with some studies reporting a peak zT exceeding 2.0 across a wide temperature range from room temperature to medium- and high-temperatures. Achieving the ideal balance between electrical conductivity with S and minimizing undesirable effects such as bipolar effects remains a key challenge in realizing the full potential of practical TE applications.

(3) The introduction of multiscale defects significantly reduces lattice thermal conductivity (κ_l) by effectively suppressing thermal conduction through phonon scattering, resulting in outstanding TE properties in the low- and medium-temperature range. Critically, while enhanced phonon scattering reduces κ_l, charge carrier mobility µ_H must be considered to maintain excellent electrical transport properties. Future research should screen Mg₃(Sb,Bi)₂-based compositions with intrinsically low κ_l through combined first-principles calculations and high-throughput methods, while exploring emerging phonon transport mechanisms like liquid-like ionic diffusion and topological phonon states.

(4) Mg₃(Sb,Bi)₂-based TE devices exhibit significant prospects for both power generation and cooling applications. To narrow the gap between theoretical and actual η, researchers have systematically developed interface barrier layer design and connection process optimization strategies. While Fe/Ni, Mg₂Cu, and Ti barrier materials exhibit excellent contact resistance, chemical stability, and thermal expansion coefficient matching, long-term reliability under thermal cycling remains challenging due to interfacial reactions. Novel connection processes like low-temperature Ag sintering and composite Ag paste soldering prevent degradation from temperature-pressure coupling while enabling robust bonding, yet face scalability challenges requiring improved uniformity and long-term thermal cycling reliability.

(5) Enhancing the long-term stability of TE modules and optimizing device structural design are central to the practical utilization of TE devices. By optimizing p-type MgAgSb and n-type Mg₃(Sb,Bi)₂ with matched thermal expansion coefficients, the accumulation of thermal stresses can be significantly reduced. The combination of geometrical optimization and surface coating technology improves the long-term stability of the modules. In addition, emerging manufacturing technologies such as 3D printing are expected to overcome the bottleneck of mass production. With its excellent performance and scalable applications, Mg₃(Sb,Bi)₂ is expected to be a core candidate for the next generation of TE materials, which will support the advancement of clean energy technology.

Author contributions

Yu Yan: writing – original draft, data curation, formal analysis, conceptualization. Wen Zhang: validation, visualization. Huijun Kang: writing – original draft, writing – review & editing, supervision, investigation, conceptualization. Zongning Chen: writing – review & editing, investigation. Enyu Guo: writing – review & editing, investigation. Rongchun Chen: writing – original draft, writing – review & editing, supervision. Tongmin Wang: writing – original draft, writing – review & editing, supervision, investigation, conceptualization.

Conflicts of interest

The authors declare no conflict of interest.

Data availability

No primary research results, software or code have been included and no new data were generated or analysed as part of this review.

Acknowledgements

This work was financially supported by the National Natural Science Foundation of China (Grant No. 52271025, 52501042, U25A20222 and U22A20174), the Postdoctoral Fellowship Program of China Postdoctoral Science Foundation (GZC20240173), the Science and Technology Planning Project of Liaoning Province (2023JH2/101700295 and 2025-BS-0002), and the Innovation Foundation of Science and the Technology of Dalian (No. 2023JJ12GX021).

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