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[Longquan Wang](https://orcid.org/0009-0009-9910-9770), Wenhao Zhang, [Song Yi Back](https://orcid.org/0009-0000-8890-1484), [Naoyuki Kawamoto](https://orcid.org/0000-0002-2022-3987), [Duy Hieu Nguyen](https://orcid.org/0000-0002-6938-6517), [Takao Mori](https://orcid.org/0000-0003-2682-1846)

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[High-performance Mg3Sb2-based thermoelectrics with reduced structural disorder and microstructure evolution](https://mdr.nims.go.jp/datasets/c2ad3b54-c62e-4054-abd7-d9dd1490927c)

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High-performance Mg3Sb2-based thermoelectrics with reduced structural disorder and microstructure evolutionArticle https://doi.org/10.1038/s41467-024-51120-3High-performance Mg3Sb2-basedthermoelectrics with reduced structuraldisorder and microstructure evolutionLongquan Wang1,2, Wenhao Zhang1, Song Yi Back 1, Naoyuki Kawamoto3,Duy Hieu Nguyen3 & Takao Mori 1,2Mg3Sb2-based thermoelectrics show great promise for next-generation ther-moelectric power generators and coolers owing to their excellent figure ofmerit (zT) and earth-abundant composition elements. However, the com-plexity of the defect microstructure hinders the advancement of high per-formance. Here, the defect microstructure is modified via In doping andprolonged sintering time to realize the reduced structural disorder andmicrostructural evolution, synergistically optimizing electron and phonontransport via a delocalization effect. As a result, an excellent carriermobility of~174 cm2V−1 s−1 and anultralow κlat of ~0.42Wm−1 K−1 are realized in this system,leading to an ultrahigh zT of ~2.0 at 723 K. The corresponding single-legmodule demonstrates a high conversion efficiency of ~12.6% with a 425 Ktemperature difference, and the two-pair module of Mg3Sb2/MgAgSb displays~7.1% conversion efficiency with a 276 K temperature difference. This workpaves a pathway to improve the thermoelectric performance of Mg3Sb2-basedmaterials, and represents a significant step forward for the practical applica-tion of Mg3Sb2-based devices.To realize the carbon neutral goal and sustainably developed society,thermoelectric materials represent a potentially helpful technologybased on directly converting the waste heat into electricity via solid-state devices1. The energy conversion efficiency of the thermoelectrictechnology is determined by the performance of the thermoelectricmaterials, a dimensionless figure of merit (zT = S2σT/(κlat + κele), whereS, σ, T, κlat and κele are the Seebeck coefficient, electrical conductivity,absolute temperature, lattice thermal conductivity, and electronicthermal conductivity2, respectively. However, the widespread appli-cation of thermoelectric technology is hindered by the relatively lim-ited thermoelectric performance and scarcity or high cost ofmaterials3,4. Pursuing high thermoelectric performance in a materialrequires optimizing the electrical and phonon transport simulta-neously, following the phonon-glass electron-crystal concept5,6. Gen-erally, high thermoelectric performance in materials can be achievedby low lattice thermal conductivity, attributed to their complexmicrostructure, and high electrical transport properties arising fromthe ordered band structure.Owing to decades of effort across several strategies, includingband structure engineering to enhance electrical transportproperties7–9, and nanostructuring to achieve effective phononscattering10–13, high-performance thermoelectric materials with zTmaxbeyond 2.0 have been gradually revealed, such as GeTe14,15, PbTe16,AgSbTe217, and SnSe18. However, all kinds of disadvantages includingtoxicity, high cost, scarcity, and low stability limit the commercialapplication of these materials. Recently, there has been a surge ofinterest in n-type Mg3Sb2-based thermoelectric materials because oftheir promising thermoelectric performance, abundant compositionalelements, and cost effectiveness19,20, which are significant in advancingthe applications of thermoelectric technology. Since the report byReceived: 1 May 2024Accepted: 31 July 2024Check for updates1Research Center for Materials Nanoarchitectonics (MANA), National Institute for Materials Science (NIMS), Tsukuba, Japan. 2Graduate School of Pure andApplied Sciences, University of Tsukuba, Tsukuba, Japan. 3Center for Basic Research on Materials, National Institute for Materials Science (NIMS), Tsukuba,Ibaraki, Japan. e-mail: MORI.Takao@nims.go.jpNature Communications |         (2024) 15:6800 11234567890():,;1234567890():,;http://orcid.org/0009-0000-8890-1484http://orcid.org/0009-0000-8890-1484http://orcid.org/0009-0000-8890-1484http://orcid.org/0009-0000-8890-1484http://orcid.org/0009-0000-8890-1484http://orcid.org/0000-0003-2682-1846http://orcid.org/0000-0003-2682-1846http://orcid.org/0000-0003-2682-1846http://orcid.org/0000-0003-2682-1846http://orcid.org/0000-0003-2682-1846http://crossmark.crossref.org/dialog/?doi=10.1038/s41467-024-51120-3&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-024-51120-3&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-024-51120-3&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-024-51120-3&domain=pdfmailto:MORI.Takao@nims.go.jpTamaki et al. on n-type Mg3Sb2-based alloys with a zT ~ 1.5 at 716 K21,many of the efforts have been focused on achieving higherperformance22–25, but the progress is limited compared to traditionalthermoelectric materials. Therefore, a novel mechanism to realize thehigh thermoelectric performance in Mg3Sb2-based materials is cove-ted considering the great potential for commercial applications.The inherent disordered structure with high-density defects inMg3Sb2-based materials limits electron transport with highmobility26,27. Recently, the regulation of disorder-induced localizationhas shown great potential for thermoelectric improvement17,28, as aneffective strategy for changing electronmobility. Basedon the relevantphysics of Anderson-like electron localization within the parabolic-band-acoustic-phonon-scattering framework, a quantitative transportmodel predicts that the optimum thermoelectric performance occursin slightly disordered materials29. In the meantime, plentiful micro-structural defects contribute to the scattering of phonon transport,thereby leading to the low κlat in Mg3Sb2-based alloys23,26. Therefore,the intricate defect microstructure in Mg3Sb2-based alloys indicatesthe prospect of improving electron transport and restraining phonontransport by combining disorder-induced localization and nanos-tructuring engineering to advance thermoelectric performance.Herein, the reduced structural disorder inMg3Sb2-based alloys isrealized by introducing In doping, coupled with the synergeticmicrostructure evolution for phonon scattering through prolongedsintering time. The reduced structural disorder promotes electrontransport, benefiting from the transition of electron localization todelocalization, synergistically reducing grain boundary scattering, sothe excellent carrier mobility of ~174 cm2 V−1 s−1 is realized in oursample. Moreover, the reconstructed defect microstructure facil-itates multiple strain fluctuations, thereby restraining phonontransport, leading to an ultralow κlat of ~0.42Wm−1 K−1 in ourMg3.2In0.005Sb1.5Bi0.49Te0.01 sample. The significantly improvedthermoelectric performance shows the zT with ~0.5 at room tem-perature to ~2.0 at 723 K (Fig. 1a), which is one of the best valuesreported in Mg3Sb2-based alloys21–24,30,31. As a result, a high average zTof ~1.36 in the temperature range of 300–723 K is achieved in oursample (Fig. 1b). The excellent thermoelectric performance, espe-cially the high average zT, is the foundation for the application topursue a high conversion efficiency of the modules. Therefore, thecorresponding fabricated single-leg module shows an exceptionallyhigh conversion efficiency of ~12.6% with a temperature difference of425 K, which is the superior value among known n-type single-legmodules in this applicatively important temperature range(Fig. 1c)32–37. Subsequently, the optimized n-type materials are fabri-cated into a two-pair module coupled with a p-type MgAgSb com-pound. The fabricated two-pair module demonstrates a highconversion efficiency of ~7.1% with a temperature difference of 276 Kfor power generation, which is challenging with the low-temperaturemonopoly of Bi2Te3 (Fig. 1d)38–40. Therefore, our Mg3Sb2-based alloysdemonstrate great progressiveness and application potential in awide temperature range due to the simultaneous control of electronand phonon transport.ResultsToexplore theoriginof thehighperformance, the electrical propertiesof our samples were systematically investigated. The thermally acti-vated conductivity normally occurs in the n-type Mg3Sb2-basedmaterials, which limits low-temperature σ and zT. This temperature-dependent tendency of σ was found in the x =0–10min sample(Fig. 2a), which was ascribed to the electron scattering derived fromgrain boundaries and defects27,41,42. Interestingly, the near-room-temperature σ was significantly improved via minor In doping0 100 200 300 400 50002468101214This workT (K)max)%(Mg 3Sb 2Mg2Sn0.75Ge0.25n-type Bi 2Te 3 PbTeMg2Si0.3Sn0.7PbSnS2n-type single-leg modules0.00.40.81.21.6This workZTavMg 3.2Sb1.5Bi 0.49Te0.01Mg 3.065Sb1.3Bi 0.7Gd 0.015Mg 3.05Nb 0.15Sb 1.5Bi0.49Te0.01Mg 3.175Mn 0.025Sb1.5Bi 0.49Te0.01Mg 3.2Sb1.5Bi 0.49Te0.01Cu0.01n-type Mg Sb2-xBixMg 3.16Y0.01Sb1.5Bi 0.48Samples300 400 500 600 700 8000.00.40.81.21.62.0 Mg3.065Sb1.3Bi0.7Gd0.015 Mg3.2Sb1.5Bi0.49Te0.01Cu0.01 Mg3.05Nb0.15Sb1.5Bi0.49Te0.01 Mg3.16Y0.01Sb1.5Bi0.48This work Mg3.175Mn0.025Sb1.5Bi0.49Te0.01Mg3.2Sb1.5Bi0.49Te0.01T (K)ZT50 100 150 200 250 300 35002468 This workmax)%(T (K)Zone melting Bi2Te3Zn-doped Bi2Te3Cu-doped Bi2Te3Bi2Te3-Ag NPsMg3Sb2/MgAgSba bc dFig. 1 | High performance of the Mg3Sb2-based thermoelectric materials andmodules. aTemperature-dependent zT, and (b) average zTwithin300–723 Kof thesample in this work with a comparison to literature results for Mg3Sb2-basedmaterials21–24,30,31. c Maximum conversion efficiency as a function of ΔT for thesingle-leg module in this work, in comparison with known n-type single-legmodules32–37. d Comparison of the maximum conversion efficiency of the two-pairmodule in this work with Bi2Te3-based38–40 and Mg-based22 modules. The error barrepresents the uncertainty of the measurement result.Article https://doi.org/10.1038/s41467-024-51120-3Nature Communications |         (2024) 15:6800 2(x =0.005–10min), as shown in Fig. 2a. Our previous research andrelated literatures have proved the important effect of grain bound-aries on electron transport27,42–44. In addition, defect-dominated elec-tron scattering, such asMgvacancies and interstitials, inMg3Sb2-basedmaterials cannot be completely ignored, and the appreciable role inelectron scattering of the point defects has been recently highlightedby Zhang et al.27. Therefore, the potential possibility for the improvedlow-temperature σ heremay stem from reduced electron scattering bygrain boundaries and defects.We tried applying a prolonged sintering time to our samples,which led to a further improvement of σ in the low-temperature rangeof x = 0.005–20min sample. It can be ascribed to the reduced grainboundary scattering by prolonging the sintering time, because thehigher sintering temperature and longer holding time can promotegrain growth driven by thermodynamics. However, the undopedsample has an apparently deteriorative σ due to the unavoidable Mgloss during high-temperature sintering, which is evident from theporous structure observed in the fracturemorphology of x =0–20minsample (Supplementary Fig. 1). Supplementary Fig. 2 shows the X-raydiffraction (XRD) patterns of our samples with different In doping andsintering time, and all the samples canbe indexed to theMg3Sb2 phase.Additionally, the XRD pattern of the melting phase during high-temperature sintering was detected, confirming the existence of Mgevaporation during the high-temperature spark plasma sintering (SPS)process. According to the phase boundarymapping45, the excessMg iscrucial for achieving the n-type behavior in Mg3Sb2-based alloys andexerts a significant influence on the thermoelectric performance.Therefore, the electrical properties of the x =0–20min sample sharplydeteriorated due to heavily reduced carrier concentration (Fig. 2a, band Supplementary Table 1). However, this adverse Mg loss has beensuppressed after In doping, so the x = 0.005–20min sample shows theimproved σ and also comparable S compared to the x =0–10minsample. To explore this pattern, we prepared samples with different Indoping and sintering time (Supplementary Figs. 3–7), and the ratio of σfor different samples was used to distinguish the degree of perfor-mancedeterioration (Supplementary Fig. 8). The ratio for theundopedsample is significantly lower than that for the In-doped samples. Thetrend in the ratios of σ20/σ10 and σ30/σ10 suggests improved stability inIn-doped samples during high-temperature sintering compared toundoped samples, which might originate from the apparent higheratomic mass and stability of In compared to Mg. Moreover, theinductively coupled plasma atomic emission spectroscopy (ICP-OES)was performed to check the actual composition of our samples, con-firming minor In doping and effectively restrained Mg evaporationduring the sintering after In doping (Supplementary Table 2). As aresult, no noticeable changes in composition were found in our In-doped samples, even with prolonged sintering times. In addition,minor In doping (x =0.005) was applied in further research based onthe optimized weighted mobility, but increased In content wouldcause a slightly decreased low-temperature σ due to additional elec-tron scattering from the Mg-rich phase (Supplementary Fig. 7)46.Therefore, the In-doped samples obtained observably improvedpower factor (PF) owing to increased σ, especially in the low-temperature range (Fig. 2c). The room-temperature PF increasesfrom11.20μWcm−1 K−2 for the x = 0–10min to 17.90μWcm−1 K−2 for thex =0.005–20min sample.To reveal the origin of this extraordinary improvement in elec-trical properties, we measured the low-temperature (2–323 K) elec-trical resistivity of our samples (Fig. 2d). As a result, we observed atransition from insulating behavior to metallic behavior upon In-doping. Apparently, the In-free samples exhibit a sharp increase inresistivity below 50K, which indicates the charge carrier localization,in line with disorder-induced charge localization (i.e., Andersonlocalization)28,29. Conversely, a semiconductor-like transport in theresistivity was found in the In-doped samples. At sufficiently lowtemperatures, in disordered materials, the electronic transport0.50 0.52 0.54 0.56 0.58 0.60-6.4-6.2-6.0-5.8-5.6-5.4y = 2.99 x  7.76 = 166 Å x = 0-10minnl()T-1/4 (K-1/4)0 50 100 150 200 250 300 350051015x = 0-10min x = 0.005-10minx = 0-20min x = 0.005-20min(mm)T (K)1 2 3 4 5 6050100150200(cm2 V-1s-1)n (1019cm-3)This workCu additionTransition metal Te codopingTe dopingMg3Bi1.25Sb0.75Single crystal300 400 500 600 700 80010152025T (K)PF(m cW-1K-2)300 400 500 600 700 8000123456  x = 0-10min x = 0-20min x = 0.005-10min x = 0.005-20minT (K)(104  Sm-1)300 400 500 600 700 800-180-240-300-360-420T (K)S(VK-1)b ce f0 100 200 3000.1110(mm)T (K)Localization - lowDelocalization - high2 3 4 5 60-20-40T1/2 (K1/2)S(V K-1) y = 4.69 xr2 = 0.998Fig. 2 | Electrical transport properties. Temperature-dependent (a) electricalconductivity, (b) Seebeck coefficient, (c) power factor of the Mg3.2InxSb1.5Bi0.49Te0.01samples. d Low-temperature electrical resistivity of the samples, and the inset showsthe enlarged details by the logarithmic axis. e ln ρ versus T−1/4 and S versus T 1/2 plots.The variable-range hopping (VRH) behavior in the sample with the evidences fromelectrical resistivity and Seeebeck coefficient. f The relationship between Hall carrierconcentration and mobility for the samples in this work and reported values in theMg3Sb2-based system22–25,51,52.Article https://doi.org/10.1038/s41467-024-51120-3Nature Communications |         (2024) 15:6800 3mechanism relies on the hopping conduction between localizedelectronic states near the Fermi level. Therefore, the low-temperatureresistivity in the disordered system can be understood via variablerange hopping (VRH) conduction47:ρ Tð Þ= ρ0 expT0T� � 1d + 1" #ð1Þwhere ρ0 and T0 are the pre-factor of electrical resistivity andcharacteristic temperature, respectively. The value of the exponent,1=ðd + 1Þ, is given to be 1/4 by Mott VRH hopping in three-dimensional systems. In the VRH system, the T0 inversely dependson the localization length ξ with the relationship ofkBT0 = 18:1=½D EF� �ξ3�48, which diverges with the insulator-metaltransition. The kB, D EF� �are the Boltzmann constant and densityof states at Fermi level energy, respectively. It is confirmed that theundoped samples experience unavoidable Mg loss, and the induceddefects can play a role as a random source of disorder. Therefore,we have plotted the electrical resistivity of the undoped samples(x = 0–10min, x = 0–20min) by using VRH conduction, which showsgood fitting, as shown in Fig. 2e and Supplementary Fig. 9a.According to the criterion of Mott VRH hopping conduction, theaverage hopping distance RM must be larger than the localizationlength ξ , RM=ξ = ð3=8Þ TM=T� �1=4>1, with the undoped samplefollowing this criterion well. Hence, it can be concluded that theinsulating behavior of undoped samples below 50 K is caused by thecharge carrier localization induced by disorder. T0 was obtained byfitting lnρ versus T −1/4 (Fig. 2e), and D EF� �was estimated using low-temperature specific heat (Supplementary Fig. 10). The detailedphysical parameters for this fitting are listed in SupplementaryTable 3. A localization length of 166 Å was obtained for thex = 0–10min sample. The value of localized length is much largerthan the lattice constant, indicating the Anderson weak localizationin the undoped sample. Strikingly, it can be observed that thelocalized charge carrier is delocalized through In doping, as shownin Fig. 2d. This suggests that In doping successfully prevents theformation of the disordered structure caused by Mg defects duringhigh-temperature sintering, leading to improved electronic trans-port properties. Therefore, the ultra-low carrier mobility has beendemonstrated in the pristine sample compared to the In-dopedsample at low temperatures (10 K and 50 K) due to the chargelocalization, as shown in Supplementary Fig. 9b. Furthermore, thelow-temperature S deviates from the simple linear temperature-dependent behavior, but follows a relationship of S versus T 1/2,consistent with VRH in three-dimensional systems, confirming theMott VRH conduction (Fig. 2e)49,50. Benefiting from the transitionfrom charge localization in undoped samples to delocalization in In-doped samples, coupled with slightly reduced grain boundaryscattering, we achieved a more than 90 % enhancement in carriermobility at room temperature, reaching a record value of174 cm2 V−1 s−1 in x = 0.005–20min sample (Fig. 2f), surpassing thoseof polycrystalline and even single-crystal samples22–25,51,52. In addi-tion, the slightly decreased carrier concentration in the In-dopedsamples may be caused by the charge compensation effect due todifferent substitutional positions53.To trace the source of the disorder-induced localization inMg3Sb2-based alloys, it is possible that, Frenkel defects, consistingof Mg vacancies and interstitials, could be responsible for creatingthe heavily disordered structure. The crystal structure of Mg3Sb2consists of a tetrahedrally coordinated anion [Mg2Sb2]2− layer andan octahedrally coordinated cation Mg2+ layer stacked in the zdirection19. Therefore, the structure contains twoMg positions, andthe refined occupancy parameter at Mg (1) sites (octahedral site)was utilized to validate vacancy generation, as evidenced bysynchrotron powder X-ray diffraction (XRD) measurement in pre-vious literatures26,27. The high-energy and high-sensitive XRD mea-surements were conducted on our samples to confirm this defectstructure (Supplementary Fig. 11), and detailed Rietveld-refinedparameters are shown in Supplementary Tables 4–6. The vacancygeneration was confirmed by the refined occupancy of the Mg (1)site, ~0.928 for the x = 0–10min and ~0.938 for thex = 0.005–20min sample, indicating the existence of the Mgvacancies and interstitial. Moreover, the slightly higher occupancyin the x = 0.005–20min sample demonstrates the effective sup-pression of Mg loss by In doping, consistent with the previous dis-cussion on electrical properties. In addition, the apparent higherelectrical resistivity observed in the x = 0–20min sample at lowtemperatures indicates the stronger disorder-induced localization(Fig. 2d), likely caused by the high-density random defects by Mgevaporation during high-temperature sintering. This reaffirms thepotential relationship between Frenkel defects and disorderedstructure. Therefore, improving electrical properties at low tem-peratures can be achieved by reducing structural disorder, con-firming the appreciable role of defects in the electron transport ofn-type Mg3Sb2-based materials.To investigate the effect of grain boundary scattering in oursamples, electron backscatter diffraction (EBSD) was utilized tomeasure the grain sizes (Fig. 3a, b). A slightly increased averagegrain size, from 4.4 μm for the pristine sample to 5.6 μm for the In-doped sample, was observed (Supplementary Fig. 12), which con-tributes to the enhanced electrical transport. This increase may beattributed to the reduced solute dragging effect from Mg and Bi ongrain boundary migration54,55, resulting in slightly promoted graingrowth. To explore the microstructural evolution, transmissionelectron microscopy (TEM) observations were performed on thex = 0–10min and x = 0.005–20min samples. Random nanoprecipi-tates (blue circle) and Moiré fringes (yellow circle) were observed inthe x = 0–10min sample, as depicted in Fig. 3c and SupplementaryFig. 13. The presence of nanoprecipitates may be associated withcomposition fluctuations in n-type Mg3Sb2, and previous reportshave identified nanometer-scale Bi-rich phases using TEM and atomprobe tomography56,57. In addition, the Moiré fringe, originatingfrom the overlapping of two lattices with comparable periodicspacing, has been demonstrated for qualitative analysis of defectand strain in TEM58,59. The corresponding selected area electrondiffraction (SAED) pattern reveals the misoriented angle betweenthe overlapped lattice grating, allowing for the indication of ran-domly distributed defects in x = 0–10min sample by the Moiréfringe, typically accompanied by high-density lattice defects58. Theapparent lattice distortion has been observed to alleviate the latticestrain caused by existing defect structures in the sample (red rec-tangle). However, the microstructure of x = 0.005–20min sampleexhibits a distinctly different arrangement, characterized by col-lective nanoprecipitates and Moiré fringes, as illustrated in Fig. 3dand Supplementary Fig. 14. The lattice distortion induced bynanoprecipitates and dislocations around the edges of the Moiréfringe serves as scattering centers, impeding phonon propagation(Fig. 3e–h). Simultaneously, strong lattice distortion has been foundin the x = 0.005–20min sample, with corresponding geometricphase analysis (GPA) revealing intense strains in this region (Fig. 3i, jand Supplementary Fig. 14)60. The strain fluctuation region shouldbe caused by the high-concentration defect structures observed inthe x = 0.005–20min sample characterized by TEM images. A typi-cal Williamson-Hall analysis was conducted for quantitative analysisof lattice strain in our samples (Supplementary Fig. 15). It reveals anincreasing trend of lattice strain attributed to the microstructuralevolution following In doping and prolonged sintering time, con-sistent with TEM observations and GPA analysis. ThisArticle https://doi.org/10.1038/s41467-024-51120-3Nature Communications |         (2024) 15:6800 4microstructural evolution results in the apparent higher strainfluctuation in the samples, which is a crucial factor for restrainingphonon transport. Additionally, a high-angle annular dark-fieldscanning TEM (HAADF-STEM) image reveals a neat triple-junction ofthe grain boundary in the x = 0.005–20min sample (Fig. 3k), sup-porting that the In doping does not function via grain boundarysegregation, highlighting a distinction between this work and pre-vious common grain boundary segregation research42,61.Fig. 3 | Microstructural evolution induced by In doping and prolongedsintering time. Electron backscatter diffraction (EBSD) crystal-orientationmaps of(a) x =0–10min, (b) x =0.005–10min samples. Transmission electron microscopy(TEM) lattice image of (c) x =0–10min, (d) x =0.005–20min samples, and the insetof (c) reveals the corresponding selected-area electron diffraction (SEAD) pattern.The high-density nanoprecipitates (blue circle), Moiré fringe (yellow circle) andlattice distortion (red rectangle) are observed in the samples. e, f Fast Fouriertransform (FFT) and inverse FFT images of the selected Moiré fringe regions 1 in d.Inverse FFT images of the (g) nanoprecipitate region 2, (h) perfect-lattice region 3in d. i TEM image with obvious lattice distortion for the x =0.005–20min sampleand (j) corresponding strainmaps along different directions.kHAADF-STEM imageshowing the clean triple-junction of the grain boundary and corresponding EDSelement mapping images.Article https://doi.org/10.1038/s41467-024-51120-3Nature Communications |         (2024) 15:6800 5Figure 4a displays the κ of the samples, and the notably low-er κ happened in the x = 0.005–20min sample. By subtracting theκele from the κ, where the κele is calculated as LσT(L= 1:5 + expð�jSj=116Þ62, the κlat was determined to evaluate pho-non transport (Fig. 4b). The sample with In doping(x = 0.005–10min) demonstrates a lower κlat compared to theundoped sample, and the x = 0.005–20min sample further reducesκlat across the entire temperature range. For instance, the room-temperature κlat reduces from 1.06Wm−1 K−1 for the pristine sampleto 0.78Wm−1 K−1 for the x = 0.005–20min sample. It reaches theminimum value of ~0.42Wm−1 K−1 at 723 K for the x = 0.005–20minsample, which is lower than that of all other doped Mg3Sb2-basedalloys (Fig. 4b)21–23,30,31,51,63–66. Moreover, the high-temperature κlatfalls below the minimum value predicted by the Cahill model andapproaches the diffusion limit proposed by Snyder et al.67,68. Itshould be noted that the abnormally increased κlat in thex = 0–20min sample is attributed to the destructive microstructuredue to theMg evaporation. Therefore, the apparent reduction in κlatin our sample should be ascribed to the microstructural evolutioninduced by In doping and prolonged sintering time as discussedbefore.The low-temperature κlat displays typical characteristics of thepolycrystal materials in the temperature of 5–323 K (Fig. 4c)69. Initially,the κlat increase with temperature as κlat ∼Tn due to the graduallyexcitation of acoustic phonons. Later, themaximum κlat occurs wherethe phononmean free path controlled by defects is comparable to thephonon-phonon scattering processes. The x =0.005–20min samplehas a peak κlat of 3.74Wm−1 K−1 at 15 K, which is similar to the previousreport in polycrystalline Mg3Sb226. With the increase in temperature,κlat decreases due to the stronger phonon-phonon scattering processand shows a different temperature dependence at T > θD. Klemens-Callaway’s model provides a method to analyze the κlat of defect-containing crystalline solids at high temperatures (T > θD)70,71.κlat =kB2π2vs ACTð Þ12tan�1 kBθ_ACT� �12 !=kBffiffiffiffiffivspffiffiffiffiffiffiπ3p 1ffiffiffiffiffiffiffiffiffiffiffiffiffiΩ0CΓp 1ffiffiffiffiTp tan�1 kBθ_Ω0Γ4πv3s CT� �12 ! ð2ÞwhereΩ0 is the unit cell volume, C is the inverse time coefficient forphonon-phonon scattering processes in the pure and perfectmaterials, and Γ is the point defect scattering strength parameterdetermined by the fractions and types of the defects. Theexpression for A is A= Ω0Γ4πv3sgiven by Klemens. In the case of largedefect scattering for solid solutions, the term oftan�1ðkBθ_ ð ACTÞ1=2Þ≈π=2, so the formula can be rewritten asκlat =kB4πvs ðACTÞ1=2. Therefore, the κlat has a temperature dependenceof T−1/2, close to the trend observed for the x = 0–10min sample ofT−0.6 (Fig. 4c). This moderate temperature dependence of κlat wasalso observed in previously reported Mg3Sb2-based alloys26,indicating the presence of disordered structure with high-densitydefects as discussed before. However, the κlat for thex = 0.005–20min sample displays a stronger temperature depen-dence of T−1.1, leading to the lower κlat in the sample compared to thepristine sample. This variation can be understood via the competingmechanism between the phonon-phonon and phone-defect scatter-ing. Point defects show a strong suppressed effect on thetemperature dependence, even for extremely low defect fractions72.Therefore, the plentiful Mg vacancies in pristine sample result in themoderate temperature dependence due to the competitionbetween intrinsic and extrinsic phonon scattering. The reduced10 1001234 x = 0-10min x = 0.005-20minT (K)lat(W m-1K-1)T -0.6D = 213 KT -1.10 2 4 60481216~ 12.6%)%(I (A) Tc ~ 295 KTh = 373 K Th = 473 K Th = 573 K Th = 671 K Th = 720 K 300 400 500 600 7000.20.40.60.81.01.21.4x = 0-10minx = 0.005-20minT (K)lat(Wm-1K-1)diff U + B + MF U + B + MF + SFStrain fluctuation300 400 500 600 700 8000.40.60.81.01.2T (K)lat(Wm-1K-1)min300 400 500 600 700 8000.60.81.01.2  x = 0-10min x = 0.005-10minT (K)(Wm-1K-1) x = 0-20min x = 0.005-20mina300 400 500 600 700 800 900 10000.00.51.01.52.0This workT (K)ZTn-type materialsSiGehalf-HeuslerPbSeskutteruditesce fd0.40.60.8lat(Wm-1K-1)SamplesThis workMg 3.2Pr0.03Sb1.5Bi 0.5Mg 3.2Sb1.5Bi 0.49Te0.01Cu 0.01Mg 3.065Sb1.3Bi 0.7Gd 0.015Mg 3.15Mn 0.05Sb 1.5Bi 0.49Te0.01Mg 3.16Y0.01Sb1.5Bi 0.48Mg 3.5Tm0.03Sb1.97Te0.03Mg 3.5Sc0.04Sb1.97Te0.03Mg 3.07Sb 1.5Bi 0.48Se0.02Mg 3.2Sb1.99Te0.01Mg 3.2Sb1.5Bi 0.49Te0.01Fig. 4 | Thermoelectric properties of the materials and module. Temperature-dependent (a) thermal conductivity, (b) lattice thermal conductivity of theMg3.2InxSb1.5Bi0.49Te0.01 samples. The inset compares the minimum lattice thermalconductivity in this work and reported values forMg3Sb2-based alloys21–23,30,31,51,63–66.c Low-temperature lattice thermal conductivity. d Experimental and calculatedlattice thermal conductivity of the samples, considering Umklapp process (U),grain boundaries (B), mass fluctuation (MF) and strain fluctuation (SF).e Temperature-dependent zT of the samples in this work, in comparison with state-of-the-art n-type thermoelectric materials13,78–80. f Maximum conversion efficiencyas a function of the current under different hot-side temperatures for the single-legmodule.Article https://doi.org/10.1038/s41467-024-51120-3Nature Communications |         (2024) 15:6800 6Mg vacancies and structural disorder via defect evolution in our In-doped sample suppress the phonon-defect scattering effect,leading to an increased temperature dependence of κlat . To betterunderstanding the stronger temperature dependence inx = 0.005–20min sample, the linear thermal expansion of thesamples was explored (Supplementary Fig. 16). The large coefficientof linear thermal expansion in our sample (~21.2 × 10−6K−1), compar-able with anharmonic materials such as PbTe and SnTe73, indicatesstronger phonon anharmonicity. Previous work systematicallyinvestigated the anomalous low thermal conductivity in Mg3Sb2,revealing higher thermal expansion in Mg3Sb2 compared toisostructural compounds (CaMg2Sb2, YbMg2Sb2)74. This suggeststhat highly anharmonic acoustic branches contribute to the lowthermal conductivity. Additionally, the inherently low latticethermal conductivity in Mg3Sb2 has been attributed to phononicorigins75, underscoring the importance of controlling phonon-phonon interaction to reduce lattice thermal conductivity. There-fore, the transition from charge localization to delocalization viadefect regulation in our work may weaken the suppression oftemperature dependence from phonon-defect scattering, thusleading to the lower lattice thermal conductivity based on highphonon anharmonicity. Noticeably, the Klemens-Callaway model islimited in describing the high-temperature κlat , as it suggests thatκlat decreases endlessly with temperature, whereas materialseventually reach saturation at a constant value. Next, the Debye-Callaway model was adopted to fit the high temperature κlat of oursamples76, as shown in Fig. 4d. The detailed calculation andparameters can be found in the supplementary materials. TheUmklapp process (U), grain boundaries (B), mass fluctuation (MF)and strain fluctuation (SF) were considered as the source of phononscattering and their contributions were fitted to our experimentaldata. Figure 4d shows the fitted results for the samples, and theapparent reduction in κlat for the x = 0.005–20min samplecompared to the pristine sample is found to be caused by thestronger strain fluctuation resulting from microstructural evolu-tion, which was verified by previous Williamson-Hall and GPAanalysis. Additionally, it has been reported that lattice strain cansuppress the insulating Mott phase and induce a transition tometallic behavior77. This transition from insulator to metal due tolattice strain further supports our analysis of electrical resistivity atlow temperatures. The introduction of In doping not only promotescharge delocalization, enhancing carrier mobility, but also inducesfluctuations in lattice strain, consequently reducing lattice thermalconductivity. Moreover, the broadening of the Raman spectrumindicates a shorter phonon relaxation time and stronger phononscattering in the x = 0.005–20min sample (Supplementary Fig. 17).Benefiting from the improved electron transport and effec-tively restrained phonon transport, the significantly enhanced zToccurs in our samples in the temperature range of 100–723 K(Fig. 4e and Supplementary Figs. 18 and 19). The improved n-typeMg3Sb2-based alloys demonstrate excellent thermoelectric per-formance across the entire temperature range, outperformingmost state-of-the-art n-type materials and indicating great poten-tial for power generation applications13,78–80. The x = 0–10minsample has a peak zT of 1.55 at 723 K and an average zT of 1.07 in thetemperature range of 300–723 K, consistent with previousreports21,22. Strikingly, the x = 0.005–20min sample reaches amaximum zT of 2.0 at 723 K and an average zT of 1.36 in the tem-perature range of 300–723 K, representing an increase of ~29% and~27% compared to the undoped sample, respectively. High-performance samples were reproduced, and similar propertieswere measured, demonstrating good reproducibility (Supple-mentary Fig. 20). We would like to point out that the heat capacitymeasured by the differential scanning calorimeter (DSC) wasapplied to estimate the κ and zT of our samples (SupplementaryFig. 21). Themaximum zT of our sample could reach ~2.13 at 723 K ifwe calculate κ based on the heat capacity determined by theDulong-Petit law (Supplementary Fig. 21). Motivated by the ultra-high zT in the optimized sample, we successfully fabricated asingle-leg module with an interface prepared using 304 stainlesssteel powder and Mg turning to evaluate the energy conversionefficiency81. Details regarding the module fabrication and mea-surement can be found in the methods part. As shown in Figs. 1cand 4f, and Supplementary Fig. 22, a high conversion efficiency of~12.6% was achieved in the single-leg module with a 425 K tem-perature difference, which is the superior value among Mg3Sb2-based materials. The excellent reproducibility and stability of thesingle-leg module are demonstrated in Supplementary Fig. 23.Importantly, it stands as the optimum choice for the n-type mate-rials in the low- tomid-temperature range, considering its excellentefficiency and comparatively low cost compared to other commonn-type materials. The theoretical efficiency based on finite elementsimulations reaches ~16%, with the disparity displayed in theinternal resistance and heat flow between the measured value andpredicted value, indicating the need for further progress toimprove the contact layer and thermal radiation evaluation (Sup-plementary Figs. 24 and 25). Next, the p-type MgAgSb was selectedto fabricate the two-pair module due to its comparable mechanicaland thermoelectric properties (Supplementary Fig. 26). The con-tact layer information of the n-type and p-type legs was examinedthrough the scanning electron microscope (SEM) images and cor-responding EDS mapping (Supplementary Figs. 27 and 28). Sup-plementary Figure 29 illustrates the output voltage, output power,heat flow from the cold side, and conversion efficiency as functionsof current under various temperature differences. A maximumconversion efficiency of ~7.1% was obtained with a 276 K tempera-ture difference, representing a competing value compared to theBi2Te3-based module38–40. However, it is still notably lower than thesimulated value, close to ~11%, due to the higher internal resistanceand slightly lower open circuit voltage (SupplementaryFigs. 30 and 31). This underscores the importance of interfacecontact to reduce the inevitable contact resistance of electrical andthermal across multiple layers in the device (SupplementaryFig. 32). Additionally, the measured open circuit heat flow is higherthan the theoretical value at high-temperature gradients due to theheat radiation from the unfilled part. Dedicated efforts towardinterfacial layer design and connection technology are required toachieve higher efficiency in future work. The detailed schematicdiagram of the energy conversion efficiency measurement systemof Mini-PEM and the simulated temperature distribution are shownin Supplementary Figs. 33 and 34. It is worth emphasizing that theservicing temperature for our module is limited by the phase-transition temperature in p-type MgAgSb (Supplementary Fig. 35),demonstrating the potential to realize higher efficiency coupledwith mid-temperature p-type materials. Considering the lowermaterials cost, better mechanical properties compared to Bi2Te3-based materials, and higher stability of Sb-rich Mg3Sb2 comparedto Bi-rich Mg3Bi2, our module shows the competing advantages forharvesting abundant low-grade waste heat.DiscussionIn summary, the reduced structural disorder and enhanced strainfluctuation through microstructural evolution were realized in oursample via In doping and prolonged sintering time, leading tosynergistically optimal electron and phonon transport. The excellentcarrier mobility of ~174 cm2 V−1 s−1 and ultralow κlat of ~0.42Wm−1 K−1occurred in the sample, which leads to superior zT values rangingArticle https://doi.org/10.1038/s41467-024-51120-3Nature Communications |         (2024) 15:6800 7from ~0.5 at room temperature to ~2.0 at 723 K in our Mg3Sb2-basedalloys. Consequently, the fabricated single-legmodule demonstrateda high conversion efficiency of ~12.6% with a temperature differenceof 425 K, and the two-pair module reached a maximum efficiencyof ~7.1% with a temperature difference of 276 K coupled with p-typeMgAgSb. Our work would significantly accelerate the progression ofn-type Mg3Sb2-based alloys and highlight the bright applicationpotential for thermoelectrics in low- to mid-temperature energyharvesting.MethodsSynthesis processToprepare the samples ofMg3.2InxSb1.5Bi0.49Te0.01, the high-purity rawmaterials of Mg (99.95%), Te (99.999%), Bi (99.999%), Sb (99.999%),and In (99.99%)were stoichiometricallyweighted and then loaded intothe stainless-steel ball milling jaw in the glovebox for high-energymilling process. The ball-milling process was kept for 5 hours and thenwas consolidated by spark plasma sintering (SPS, SPS-1080 System,SPS SYNTEX INC) under axial pressure of 60MPa at 700 °C. The sin-tering time for SPS is 10min, 20min, and 30min to prepare differentsamples, which are labeled as x–10min, x–20min, and x–30min. Thesample of p-type Mg0.995In0.005Ag0.97Sb0.99 was prepared via a two-step ball-milling process. The raw materials of Mg (99.95%) and Ag(99.99%) were stoichiometrically weighted and then loaded into thestainless-steel ball milling jaw in the glovebox for the high-energymilling process. The first-step ball-milling process is 10 hours and thenadd Sb (99.999%), In (99.99%) to finish the second-step ball-millingwith 5 hours. The obtained powder was consolidated by SPS at 573 Kwith 60MPa for 5min.Properties characterizationThe prepared samples were cut into strips and columns for measuringelectrical and thermal properties. The electrical properties of σ and Swere measured by the ZEM-2 instrument in a helium atmosphere(ADVANCE RIKO, ±5% uncertainty). The thermal conductivity κ wascalculated using the equation κ = λCpd, where the thermal diffusivity λwas measured by a laser flash method (LFA 467, NETZSCH, ±3%uncertainty), the densities dwas measured by an Archimedes method.The heat capacity Cp was measured by the differential scanningcalorimeter (DSC) measurement (Netzsch STA 449F1 Jupiter) in an N2atmosphere at a heating rate of 5 K/min. TheHall carrier concentrationwas measured using a Physical Properties Measuring Systems (PPMS,QuantumDesign). The PPMSwith an AC resistance option was appliedto measure low-temperature (2–323 K) resistivity, a thermal transportoption was also used to measure the low-temperature (5–323 K) ther-moelectric properties of σ, S and κ in the same direction, and a heatcapacity option was used to perform low-temperature (2–300K) heatcapacity.Phase and microstructure characterizationThe XRD patterns were measured using the X-ray diffractometer(MiniFlex600-Cu, Rigaku) with Cu Kα radiation operating at 40 kV ×15mA, and the scanning rate was set as 3°/min. The high-energy andhigh-sensitivity type XRD was performed by SmartLab 9 kW (Rigaku)with Cu Kα radiation operating at 45 kV × 200mA, and the corre-sponding data was used to do Rietveld refinement. Electron back-scattered diffraction (EBSD) measurements were performed using aFE-SEM (JSM-7001F, JEOL Ltd.) operated at 15 kV with a step size of0.2 µm. The samples for EBSD observation were prepared bymechanical polishing to 0.1 μm with diamond paste and then ionmilling. The micro-Raman was carried out using a laser confocalmicroscope (inVia, Renishaw) with a 532 nm excitation laser and anelectron multiplying CCD detector. The fracture structure and com-position were characterized using a scanning electron microscope(FESEM, Hitachi SU8000) equipped with an energy dispersive spec-trometer (EDS, XFlash FlatQUAD 5060 F). The microstructure wascarried out by a transmission electron microscopy (TEM, JEOL JEM-3100FEF) at an acceleration voltage of 300 kV with a STEM modeequipped with an EDS detector. TEM samples were prepared by thefocused ion beam (FIB) method with Ar milling. Longitudinal (vl) andtransverse (vt) sound velocity was measured by using a sing-aroundultrasonic velocity measuring instrument (UVM-2, Ultrasonic Engi-neering Co., Ltd) at room temperature, and corresponding averagesound velocity (ν) was calculated via the equation: ν�3 = 13 ðν�3l +2ν�3t Þ.The linear thermal expansion was measured using a dilatometer in anAr atmosphere at a heating rate of 5 K/min (Netzsch DIL 402c). Theactual composition of the samples was determined by inductivelycoupled plasma atomic emission spectrometer (720 ICP-OES, AgilentTechnologies Japan, Ltd.).Module fabrication and efficiency evaluationTo fabricate the single-leg module, the interface material andMg3.2In0.005Sb1.5Bi0.49Te0.01 bulk were loaded into a graphene die witha sandwich structure, and then sintered at 973K for 10min by SPS. Theinterface material was prepared by the ball-milling process with304 stainless steel powder and Mg turning. The obtained sandwich-structure joints were ground, polished and then cut into dice forenergy efficiency measurement. For the two-pair modules, the n-typelegs were prepared with the same process as the single-leg module.The MgCuSb was selected to be the contact layer to prepare p-typelegs by one-step SPS sintering. The dimension was 3.8mm×3.8mm×6mm of the n-type and p-type legs, and the length of the ther-moelectric materials and contact layer were 5mm and 0.5mm,respectively. The two-couple n-type and p-type legs were alternatelyput onto the Cu substrate with the dimensions of 10mm× 10mm×0.6mm, which has two printed Cu patterns with 0.21mm onto theheat-conducting polymer film. The liquid In-Ga eutectic alloy was usedto connect the legs and Cu electrodes to reduce thermal and electricalresistance. The Cu leading wires were soldered to the cold-side Cuelectrodes to measure the current and voltage.The fabricated module was mounted between ceramic plates,thermal grease and graphite sheets to reduce the thermal contactresistance. The electrical output power and generation perfor-mance of the fabricated module were characterized using a com-mercial apparatus (Mini-PEM, ADVANCE RIKO, Japan). A uniaxialpressure of 0.5 MPa was applied by Mini-PEM to reduce the elec-trical and thermal contact resistances. The hot-side temperature Thof the modules was controlled by a heater, and the cold-side tem-perature Tc was maintained by the flowing water. In order to pre-sent widely comparable results of the performance of the module,we have utilized the Mini-PEM system where the cold-side isactively cooled and thereby the temperature difference can beaccurately controlled, however, in real-world applications, suitableheat sinks need to be used to create temperature difference basedon the specific application situation82,83. The output power (P) andcold-side heat flow (Qc) were measured by Mini-PEM, so the energyconversion efficiency could be calculated by η= PP +Qc. The three-dimensional finite-element simulations of power-generation wasperformed with COMSOL Multiphysics® software in the HeatTransfer Module, and the electrical and thermal contact resistancebetween the multiple interfaces of the module are not consideredin the simulation.Data availabilityAll data generated or analyzed during this study are included in thepublished article and its Supplementary Information. 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Suzuki of NIMS for his tech-nical support with the thermal expansion measurement.Author contributionsL.W. contributed to the sample preparations, characterization, dataanalysis, conceptualization, methodology, writing, and revising themanuscript. W.Z. contributed to data analysis, methodology, writing,and revising the manuscript. S.Y.B. contributed to data analysis,writing, and revising the manuscript. N.K. and D-H.N. contributedto the TEM characterization. T.M. led the project, providing con-ceptualization and supervision, writing-review and editing, andfunding acquisition. All authors contributed to the review of thefinal manuscript.Competing interestsT.M. and L.W. havefiled one Japanesepatent application (2024-082608)on the work described here. The remaining authors declare no com-peting interests.Article https://doi.org/10.1038/s41467-024-51120-3Nature Communications |         (2024) 15:6800 10Additional informationSupplementary information The online version containssupplementary material available athttps://doi.org/10.1038/s41467-024-51120-3.Correspondence and requests for materials should be addressed toTakao Mori.Peer review information Nature Communications thanks the anon-ymous reviewer(s) for their contribution to thepeer reviewof thiswork. 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If material is not included in the article’s Creative Commonslicence and your intended use is not permitted by statutory regulation orexceeds the permitted use, you will need to obtain permission directlyfrom the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by-nc-nd/4.0/.© The Author(s) 2024Article https://doi.org/10.1038/s41467-024-51120-3Nature Communications |         (2024) 15:6800 11https://doi.org/10.1038/s41467-024-51120-3http://www.nature.com/reprintshttp://creativecommons.org/licenses/by-nc-nd/4.0/http://creativecommons.org/licenses/by-nc-nd/4.0/ High-performance Mg3Sb2-based thermoelectrics with reduced structural disorder and microstructure evolution Results Discussion Methods Synthesis process Properties characterization Phase and microstructure characterization Module fabrication and efficiency evaluation Data availability References Acknowledgements Author contributions Competing interests Additional information