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Gang Wu, [Airan Li](https://orcid.org/0009-0004-7318-4821), [Longquan Wang](https://orcid.org/0009-0009-9910-9770), Xinzhi Wu, Xinyuan Wang, [Takao Mori](https://orcid.org/0000-0003-2682-1846)

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[Modulating phonon dynamics: tailoring lattice vibrations to enhance thermoelectric efficiency in Mg3(Sb, Bi)2 alloy](https://mdr.nims.go.jp/datasets/079d137a-12e5-4388-9873-57bf39c497e8)

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Modulating phonon dynamics: tailoring lattice vibrations to enhance thermoelectric efficiency in Mg3(Sb, Bi)2 alloyArticle https://doi.org/10.1038/s41467-025-65325-7Modulating phonon dynamics: tailoringlattice vibrations to enhance thermoelectricefficiency in Mg3(Sb, Bi)2 alloyGang Wu1, Airan Li 1, Longquan Wang 1, Xinzhi Wu 1, Xinyuan Wang1,2 &Takao Mori 1,2Heat in crystalline materials is transported by phonons from lattice vibrations,and lattice thermal conductivity critically determines thermoelectric perfor-mance. Different from conventional approach that reduce thermal con-ductivity via extrinsic additives sacrificing electrical transport, here, wedemonstrate a notable advancement in the n-typeMg3Sb1.5Bi0.5 bymodulatingphonon dynamics through lattice softening and simultaneously suppressingthe phonon mean free path in a more localized manner while remainingcompositionally invariant. Originating from Mg vacancies and derivativedefects, elevated internal strain degrades bonding rigidity and localize pho-nons at the lattice-constant level, yielding an ultra-low thermal conductivity of0.3Wm⁻¹ K⁻¹, close to the theoretical minimum. This intrinsic strategy,combinedwith electron concentration optimization, yields a ZTmax of 2.06 andan extraordinary ZTave of 1.58, exceeding state-of-the-art n-type materials.Furthermore, a single-leg generator and two-pair module deliver conversionefficiencies of 12.5% (ΔT = 440K) and 7.4% (ΔT = 300K), respectively, high-lighting exceptional potential for waste heat recovery.More than half of the energy from fossil fuels is lost as unusableheat during combustion, especially waste heat in the range ofnear room temperature to below 500 °C, for which there is cur-rently no effective method to capture and convert this low-gradeenergy into useful power1,2. Thermoelectric (TE) generators coulddirectly convert heat and electricity via the Seebeck effect,thereby efficiently utilizing waste heat and promoting sustainableenergy development3–5. The crucial factor in enhancing the con-version efficiency (η) of TE generators relies on achieving a highdimensionless figure of merit, ZT = S2σΤ/κtot, where S, σ, Τ and κtotstand for the Seebeck coefficient, electrical conductivity, tem-perature, and total thermal conductivity, containing electronic(κele), lattice (κlat) and bipolar (κbip) thermal conductivity,respectively. Realizing a high ZT hinges on a high power factor(S2σ) and low thermal conductivity, yet these parameters arecoupled together and varied by carrier concentration andmobility6,7.It is, in general, difficult to enhance any individual TE parameterwithout compromising the others8,9. Among S, σ, and κ, the κlat isregarded as the only parameter that can be tuned independently10,11.Thermodynamically, the κlat is basically dominated by the phononpropagation dynamics, quantized lattice vibrations that govern heattransport. Usually, traditional strategies for κlat regulation pre-dominantly rely on introducing nanostructures, including secondaryphases, interfaces, or grain boundaries on the tens to hundreds ofnanometer scale to disrupt vibrational coherence, which reduces thephononmean freepath (l) and lowers the κlat12,13.While these structureseffectively scatter mid- to low-frequency phonons, their comparabledimensions to carrier mean free paths inevitably deteriorate carriermobility. According to the phonon gas model14,15, the κlat could beReceived: 30 July 2025Accepted: 11 October 2025Check for updates1Research Center for Materials Nanoarchitectonics (MANA), National Institute for Materials Science (NIMS), Tsukuba, Japan. 2Graduate School of Pure andApplied Science, University of Tsukuba, Tsukuba, Japan. e-mail: MORI.Takao@nims.go.jpNature Communications |        (2025) 16:10366 11234567890():,;1234567890():,;http://orcid.org/0009-0004-7318-4821http://orcid.org/0009-0004-7318-4821http://orcid.org/0009-0004-7318-4821http://orcid.org/0009-0004-7318-4821http://orcid.org/0009-0004-7318-4821http://orcid.org/0009-0009-9910-9770http://orcid.org/0009-0009-9910-9770http://orcid.org/0009-0009-9910-9770http://orcid.org/0009-0009-9910-9770http://orcid.org/0009-0009-9910-9770http://orcid.org/0000-0002-5545-8460http://orcid.org/0000-0002-5545-8460http://orcid.org/0000-0002-5545-8460http://orcid.org/0000-0002-5545-8460http://orcid.org/0000-0002-5545-8460http://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/s41467-025-65325-7&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-025-65325-7&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-025-65325-7&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-025-65325-7&domain=pdfmailto:MORI.Takao@nims.go.jpwww.nature.com/naturecommunicationsexpressed as16:κlat =13Cvvl ð1Þwhere Cv, v represent heat capacity and the sound velocity, respec-tively. Apart from tailoring lattice vibrations through phonon meanfree path regulation, the modulation of sound velocity is often over-looked. To minimize κlat, two synergistic strategies appear. As illu-strated in Fig. 1b12,17–22, it is crucial to simultaneously lessen the productof the mean free path and sound velocity (υ × l) in a localized manner,to effectively decouple thermal and electronic transport. Whenphonon-phonon interactions are the primary scattering mechanism,the phonon gas model formula could also be written as follows23,24:κlat =ð6π2Þ23 �MV234π2γ2v3gD ETð2ÞwhereV, γ, andM symbolize the atomic volume, Grüneisen parameter,and mean atomic weight, respectively. It can be seen that κlat is moresensitive to lattice bonding stiffness. In other words, reducing theelastic properties, comprising average sound velocity, Shearmodulus,Young’smodulus, or increasing the Grüneisen parameter and loweringthe Debye temperature, weakens the bonding stiffness, which causeslattice softening and loosens up phonon propagation, and minimizesthe effect on electron transport due to the defect-dominated chargescattering. This dual strategy, centered on tailoring lattice vibrationslocally, reduces the adverse correlation between κlat and carriermobility, which is a cornerstone for optimizing TE performance.Bi2Te3 is currently the most widely used TE material25–28, but itsscarce tellurium and poor mechanical properties, especially for itsn-type counterpart, have long plagued the industry29,30. Ever sinceTamaki et al. achieved a high ZT value of 1.5 in n-type Mg3(Sb, Bi)2 byadding excess Mg content to lower the formation energy of Mgvacancies, Mg3(Sb, Bi)2 has attracted widespread attention for its highperformance, low cost and plasticity31–42. Owing to the complex hier-archical structure, Mg3(Sb, Bi)2 naturally exhibits a low intrinsic latticethermal conductivity (κlat ≈ 1Wm−1 K−1 at room temperature)43,44,though it is till sizably larger than the theoretical limit. Due to the highvapor pressure of Mg, many strategies have emerged to refine theelectrical transport properties. For example, increasing the sinteringtemperature, synthesizing single crystals and annealing in the Mgatmosphere to boost grain size45–48, or doping with elements, such asNd, Mn, and Cu to alter electron scattering mechanisms have all beenemployed42,49–53. These efforts primarily focus on electronic conduc-tion. However, the critical dimension of phonon dynamics modulationthrough lattice vibrational tailoring remains insufficiently addressed.In this work, in contrast to the conventional approach thatdepends on substantial fluctuations in chemical makeup by extrinsicadditives to reduce κlat at the price of electrical properties, we proposean atomic-scale localized defect engineering strategy: constructingsub-nanometer point defects, such as vacancies with associated localstrain fields within the lattice, prioritizing atomic-scale phonon scat-teringwhile strategically suppressing electronic degradation. Vacancy-induced strain fields are especially pronounced compared to thosefrom extrinsic dopants. Taking n-typeMg3(Sb, Bi)2-based material as aprototype, its TE properties are known to be highly sensitive to Mgvacancies. However, conventional approaches through crude reduc-tion of initial Mg content fail to precisely control vacancy concentra-tion, with excessive vacancies triggering conductivity type inversion top-type conduction. To address this, we exploit the characteristic ofhigh saturated vapor pressure of Mg at elevated temperatures, dyna-mically tuning vacancy concentration via prolonged sintering time.After carrier concentration tunning byMnTe, intrinsic lattice softeningamplification coupled with selective phonon mean free path restric-tion by leveraging conventional sintering techniques, synergisticallysuppresses phonon propagation. Originating from Mg vacancies andtheir derivative defects, elevated internal strain degrades bondingrigidity and defects suppress phonon mean free path, resulting in anultra-low lattice thermal conductivity. The schematic of the mainmechanism is shown in Fig. 1a. Although a certain number of disloca-tions and nanopores are likely to form due to vacancy clusteringduring prolonged sintering to affect the electrical performance, theirimpact may further mitigate by the carrier concentration and densityof states effective mass decrease. As a result, through fine-tuning theMg vacancy, the carrier concentration and mobility remain at highlevels, maintaining the power factors in the x =0.01 (20min) sample,and the product of phonon velocity and phonon mean free pathdecreases to an extremely low value below previous samples31,51,53–56,displayed in Fig. 1c, lowering the lattice thermal conductivity to0.3Wm−1 K−1, close to the theoretical minimum, achieving a partialdecoupling of electrical and thermal transport. Consequently, one ofthe highest ZTmax of 2.06, notable average ZTave of 1.04 (300–500K)and extraordinary ZTave = 1.58 (300–723K) are obtained, showing itscompetitiveness to any other n-type TE materials near room tem-perature, and superiority in the mid-temperature region, as shown inFig. 1d57–65. Most importantly, we achieve a high conversion efficiencyof 12.5% (ΔT = 440K) and 7.4% (ΔT = 300K) for a single TE-leg gen-erator and a two-pair module in Fig. 1e21,22,29,51,56,58,60,66–71, respectively.Compared to both commercial Bi2Te3 modules or other TE systems,the initial conversion efficiency obtained in this work exhibits strongcompetitiveness, highlighting great potential for waste heat recovery.ResultsModulating thermal properties by tailoring lattice vibrations,including lattice softening and suppressed phonon meanfree pathFirstly, the doped MnTe in Mg3.2Sb1.5Bi0.5 is to optimize the carrierconcentration. As shown in Fig. S1, the electrical conductivity increasesfrom 219 S cm−1 for x = 0.005 to 481 S cm−1 for x =0.02 sample. Theincrease in electrical conductivity is primarily due to the rise in carrierconcentration following MnTe doping. In addition, with the enhance-ment of MnTe content, the carrier-scattering mechanism shifts frombeing dominated by grain boundary scattering to mixed scatteringbefore 400K, which is beneficial for optimizing TE performance in theroom-temperature range. Ultimately, a peak ZT of 1.73 at 723 K isachieved in the x =0.01 sample. So, the subsequent discussion willfocus on the x = 0.01 composition.Tailoring lattice vibrations at the local scale is essential todecouple electrical-thermal performance by weakening the adversecorrelation between κlat and carrier mobility. Unlike conventionalextrinsic doping methods that rely on substantial fluctuations in che-mical composition, we modulate phonon transport locally by creatingsub‑nanometer point defects, such as vacancies with associated strainfields, that weaken bond stiffness and enhance phonon scattering,while strategically minimizing adverse effects on electron transport.However, excess Mg vacancies are believed to be detrimental to theperformance of n-type Mg3(Sb, Bi)2-based materials. It is critical toreconcile this competing effect and tune the vacancy concentration toan optimal range in order to balance electrical and thermal transport.We adopt an initial composition with slight excess Mg and MnTecompound to ensure robust n-type conductivity with an adequatecarrier concentration. Exploiting the characteristic of high saturatedvapor pressure of Mg at elevated temperatures, Mg vacancies aredynamically tuning by extending the sintering time to achievebalanced TE transport, which is further discussed later. To furtherdemonstrate the necessity of such fineMg vacancy regulation, we alsoprepare samples with different initial Mg contents to investigate theeffect of starting composition as shown in Fig. S2. These results showArticle https://doi.org/10.1038/s41467-025-65325-7Nature Communications |        (2025) 16:10366 2www.nature.com/naturecommunicationsthat the conventional approaches through crude reduction of initialMg content fail to precisely control vacancy concentration.Mg3(Sb, Bi)2-based alloys belong to the α-La2O3-type structure. AsFig. S3 shows, the X-ray diffraction (XRD) patterns of (Mg3.2Sb1.5Bi0.5)1-x(MnTe)x samples at room temperature arewell indexed to theMg3Sb2structure (JCPDS#03-0375). There is a single-phase structure withoutany impurity phases within the detection limits of XRD. We have alsoperformed SEM analysis on two representative samples, x = 0.01Phononsfast slowscatteringυgMg1 Bi/Sb Mg2NanoprecipitatesDislocationElectronLattice softening and defect scattering in Mg3(Sb,Bi)2 alloyVMgaSofteningStrainυg300 450 600 750 900 105001230 100 200 300 400 50036912edPbTePbSeMg2Si0.3Sn0.7SnSeZrNiSnSnSSiGeCoSb3This workCommericial Bi2Te3Mid-temp.ZTT (K)n-type TE materialsNear room temp. High-temp.Mg3Sb2+CuMg3Sb2MgAgSbBTSBST+CuBTS+Sb+TeBTS+CuGaTe2PbTeMg2Si0.3Sn0.7MgAgSbPbSe GeTe Single-leg TE generator TE module Single-leg TE generator in this work TE module in this work Commerical Bi2Te3-based module�  (%)�T (K)AgSbTe2Fig. 1 | Lattice softening and defects enhances phonon scattering and enablessuperior thermoelectric (TE) performance in Mg3(Sb, Bi)2-based alloys.a Schematic diagram of the lattice softening and phonon scattering mechanism inthe Mg3(Sb, Bi)2-based alloy. b υ × l vs. κlat at 300K for various TE systems. c Thecomparison of υ × l with other Mg3Sb1.5Bi0.5-based sample. The comparison of (d)ZT value and e conversion efficiency η with other TE systems.Article https://doi.org/10.1038/s41467-025-65325-7Nature Communications |        (2025) 16:10366 3www.nature.com/naturecommunications(10min) and x =0.01 (20min) shown in Figs. S4 and S5. In both sam-ples, the elemental mapping shows that Mg, Sb, Bi, Mn and Te arehomogeneously distributed throughout samples. No obvious segre-gated MnTe compound is observed. To elucidate phonon transportbehavior, the thermal performance parameters are presented in Fig. 2.As shown in Fig. 2a, the κtot near the room temperature graduallydecreases as the sinteringholding time is extended.A relatively low κtotof 0.6Wm−1 K−1 at 623 K is acquired for the x =0.01 (20min) sample.The variations in κtot are associated with fluctuations in κele, shown inFig. S6b, where κele is calculated by the Wiedemann–Franz law,κele = LσT, and L is the Lorenz number estimated by the empiricalformula72 L = 1.5 + exp(–|S|/116) × 10−8V2 K−2 and plotted in Fig. S6a. Theκtot-κele, displayed in Fig. 2b, gradually decreases with rising tempera-ture, while it experiences a slight increase at high temperatures due tothe bipolar effect. It is interesting that a lower value of κlat is acquiredafter extending the sintering holding time, dropping from0.88Wm–1 K–1 for the x = 0.01 (10min) sample to 0.57Wm–1 K–1 for thex =0.01 (20min) sample at room temperature, a reduction of over30%. Notably, the lowest value decreases to 0.3Wm–1 K–1 at 623 K,which is close to the theoretical minimum predicted by the diffusionlimit73. The calculation of the theoretical minimum is provided inthe Supporting Information. The reason for thediminishment of latticethermal conductivity is primarily attributed to the phonon modesoftening and enhanced phonon scattering, which is further dis-cussed later.Elastic properties are commonly used to gauge the inter-atomicbonding strength in a crystal lattice. To further scrutinize the reasonsbehind the reduction in thermal conductivity, we undertake investi-gationof the elastic properties to estimate the chemical bond strength.The calculation method for the elastic properties is provided inthe Supporting Information. As we can see from Fig. 2e, at roomtemperature, the longitudinal (νl), transverse (νt) and mean (νs) soundvelocities decrease obviously when the sintering holding time isextended. Meanwhile, elastic parameters including the Shear andYoung’s modulus, have also noticeably decreased, as shown inTable S1. The lessened elastic properties suggest a weakening of thechemical bonding stiffness in the Mg3.2Sb1.5Bi0.5 material, which com-monly engenders lattice softening and impedes phonon propagation.Besides elastic properties, the Debye temperature can also serve as anindicator of atomic bonding strength. As shown in Fig. 2f, the Debyetemperature steadily decreases with extended sintering holding time,which aligns with the conclusions derived from the elastic properties.According to the ball-and-spring model by Heremans74, weaker inter-atomic bonding strength is associated with stronger anharmonicity,and as shown in Table S1, the sample’s anharmonicity also increases.To gain deeper insights into the reduction in elastic properties,wecalculate the internal strain of powder samples via XRD. Figure 2hFig. 2 | Temperature-dependent thermal transport properties and phononscattering analysis of (Mg3.2Sb1.5Bi0.5)0.99(MnTe)0.01 samples. The temperature-dependent thermoelectric (TE) properties of (Mg3.2Sb1.5Bi0.5)0.99(MnTe)0.01 sam-ples atdifferent sintering condition, a κtot,b κtot-κele, c the sumof κbip and κlat.dThefrequency-dependent κs for the x =0.01 (20min) sample at room temperature onthe basis of the Debye–Callaway model. e Sound velocities. f The comparison ofphonon mean free path, Debye temperature. g Raman spectrum for the(Mg3.2Sb1.5Bi0.5)1−x(MnTe)x samples at room temperature. h The Williamson–Hallstrain analysis of x =0.01 (10, 20, 30min) samples. i The comparison of κlat in thiswork with those of other reports.Article https://doi.org/10.1038/s41467-025-65325-7Nature Communications |        (2025) 16:10366 4www.nature.com/naturecommunicationspresents the measurement of internal strain according to theWilliamson–Hall function75, with the calculation details provided inthe Supporting Information, and ε represents the magnitude of theinternal strain. It is obvious that there exists a significant increase ininternal strain with prolonged sintering holding time, which primarilyoriginates from the stress field induced by the higher density of VMgand their derivative defects, with further discussion later. Typically,defect-induced internal strain fields usually modify phonon fre-quencies, which in turn leads to lattice softening. Therefore, the latticesoftening induced by internal strain leads to a reduction in thermalconductivity. Thepeakpositionsof theRamanspectrum for samples atroom temperature gradually shift to the lower frequency area, shown inFig. 2g, indicating the lattice softening as well. By the way, the phononmean free path of samples decreases significantly with the extendingsintering holding time displayed in Fig. 2f, especially for the x=0.01(20min) sample, which is reduced to 0.57 nm and close to the latticeparameters of the unit cell. This indicates that phonon transport hasbeen nearly suppressed to its limit through scattering, contributing tothe obtained extremely low lattice thermal conductivity.To further quantitatively elucidate the effect in the reduction ofκlat, we employ the Debye–Callaway model to theoretically analyse76:κlat =kB2π2vkBTℏ� �Z θD=T0τtotðxÞx4exðex � 1Þ2dx ð3Þwhere x = ℏω/kBT, kB, ℏ, τtot are the reduced phonon frequency,Boltzmann constant, reduced Plank constant, and phonon relaxationtime, respectively. More details and corresponding parameters can beseen in Supporting Information and Table S2. This model primarilyconsiders phonon-phonon Umklapp process (U), grain boundaryscattering (B), point defect scattering, dislocations scattering, strainscattering (DS), nanoprecipitates (NP) and nanopores (Pore). As shownin Fig. 2c, the experimental data align well with the theoreticalcalculations, confirming that lattice softening anddefect scattering arethe primary reasons for the reduction in lattice thermal conductivity. Itcan be also observed that the bipolar effect becomes morepronounced with the extending sintering holding time, because ofthe decrease in carrier concentration. The frequency-dependent κs forthe x =0.01 (20min) sample at room temperature is plotted in Fig. 2d.The reduction in lattice thermal conductivity originates from Mgvacancies and their derived defects, which act at different levels. Theisolated Mg vacancies contribute at the atomic scale through point-defect scattering. And during prolonged sintering, Mg vacancies tendto aggregate, giving rise to vacancy clusters, dislocations, nanopores77,that act at larger length scales and further enhance phonon scattering.In this sense, the internal strain generated by Mg vacancies and theirderivative defects leads to lattice softening, while these defectssuppress the phononmean free path. Together, they jointly constitutethemain origin of the lattice thermal conductivity reduction. Thus, theobtained κlat is lower than those ofmost reported values, both at roomand the peak ZT temperature, as shown in Fig. 2i51,53–56,78,79.We further explore more microstructure analysis to gain insightsinto phonon transport behavior. A certain of Mg vacancies’ deriveddefects, such as dislocations and nanopores, form due to vacancyclustering during prolonged sintering. Some defects, includingobvious dislocations and NP, have found through the low-magnification transmission electron microscopy images plotted inFig. 3a–c. A certain of nanoscale pores forms from the STEM images inFig. S7, which have the ability to scatter low- and medium frequencyphonons. From the EDS elemental mapping in Fig. 3d, there is a sig-nificant Bi-rich aggregation near the grain boundaries, which is alsoconfirmed through line scanning in Fig. S8. The same phenomenon isalso observed in other regions of the same sample shown in Fig. S9.These NP have a diameter of nearly tens of nanometers, which oftenresults in the formation of stacking faults and induces internal stress.Thehighdensity of latticedistortions, stacking fault andNP canalsobenoticed in the high-resolution transmission electron microscopy ima-ges within the grain and near the grain boundary shown in Fig. 3e, f,which is beneficial to impede phonon propagation. Figure 4g exhibitsthe strain maps by the geometric phase analysis (GPA) along differentdirections, inducing large strain fluctuation near the grains, whichregularly triggers phonon mode softening. Furthermore, comparedwith the x =0.01 (10min) sample, the dislocation density increases bynearly 50% in x = 0.01 (20min) sample from the EBSD analysis seen inFig. 3h, i. All in all, widespread stress fluctuations and numerousdefects are responsible for the lattice softening andphonon scattering,as depicted in the primary phonon scattering mechanisms diagram ofFig. 1a, which results in the obtained ultra-low κlat, and is consistentwith the analysis above. Although the newly introduced dislocationdefects also adversely affect electron transport, the reduced carrierconcentration and density of states effective mass can mitigate thisimpact, as discussed later.In addition, from the SEM images shown in Fig. S10, the number ofmicron-scale pores increases significantly from x = 0.01 (20min) tox =0.01 (30min) samples as the sintering time further increases. Thegradual decrease in sample density listed in the Table S3 withincreasing sintering time also indirectly indicates a corresponding risein pores. In the geometric-scattering regime, large pores scatter pri-marily long-wavelength phonons, which contribute partly to reductionof thermal resistance. Therefore, upon further extension to 30min, thenanoscale pores tend to coarsen and agglomerate into micron-scalepores, resulting in a slight enhancement in the phononmean free pathand κlat compared to the x = 0.01 (20min) sample shown in Fig. 2b, f.High electrical transport maintenance and ZT valueenhancementBesides thermal transport, maintaining high electrical performance isalso crucial. As shown in Fig. 4a, with extending the sintering holdingtime, the carrier-scattering mechanism shifts toward grain boundaryscattering. And the electrical conductivity deteriorates severely whenthe sintering holding time extends to 30min. From the grain sizedistribution in EBSD images shown in Fig. S11, there is no significantchange in the average grain size. So, the carrier-scattering mechanismalteration is attributed to the formation of Mg vacancies during pro-longed holding time, which is also supported by the gradual decreasein carrier concentration, as shown in Fig. 4b. From the XRD refinementresults shown in Figs. S12–S14 and Table S4, the Mg site occupancydecreased markedly, further confirming an increase in Mg vacancyconcentration. Therefore, sustaining high electrical conductivitynecessitates an appropriate sintering holding time, further evidencingthe existence of a critical Mg vacancy concentration and the impera-tive for dynamically regulating vacancy concentration to decouplephonon-electron interactions in Mg3(Sb, Bi)2-based materials. Addi-tionally, with the increase of Mg vacancy concentration, the carriermobility does not deteriorate due to the reduction in carrier con-centration, which mitigates the adverse impact of dislocation defectson carrier scattering.The temperature-dependent Seebeck coefficient of samples isshown in Fig. 4c. The Seebeck coefficient gradually increases withrising temperature, and the negative values denote a typical n-typeconducting behavior. The Seebeck coefficient shows no significantchange in x =0.01 (10min) and x = 0.01 (20min) samples, whereasx =0.01 (30min) sample exhibits a marked increase, primarily due tothe reduction in carrier concentration. The curve between carrierconcentration and Seebeck coefficient is plotted in Fig. 4d to furtherconsider the electronic transport properties on the basis of singleparabolic band model. In samples with extended sintering holdingtime, the density of states effective mass decreases partially. We haveperformed EPMA compositional analysis on samples with differentholding times. As we can see from Figs. S15–S17 and Table S5, allArticle https://doi.org/10.1038/s41467-025-65325-7Nature Communications |        (2025) 16:10366 5www.nature.com/naturecommunicationselements are homogeneously distributed, and no MnTe compound isobserved. By theway, a slight decrease inMg content is detected as theholding time enhancement, indicating an increased concentration ofMg vacancies. This phenomenon is consistent with the decrease ofelectron concentration. The observed decrease of the density of stateseffectivemass canbe related to the formation ofMgvacancies. A lowerelectron concentration shifts the Fermi level downward, away from theregions of higher density of states, thereby reducing the effectivemass. Some similar phenomena have also been reported in previousstudies54. The reduction in density‑of‑states effective mass can alsomitigate the effect of carrier mobility by defect‑induced electronscattering.Fig. 3 | Themicrostructureanalysisofx =0.01 (20min) samplebySTEM. a–c thedifferent microstructure images showing a high density of lattice defects, and thedefects indicated by the yellow arrows corresponding to dislocations, while thosemarked by the red arrows representing nanoprecipitates. d The EDS elementalmapping ofMg, Bi, Sb,Mn andTealong the grain boundary. e, fHigh-magnificationSTEM micrograph of lattice distortions, stacking fault and nanoprecipitates.g Strain mapping in (e) along different directions is confirmed by the geometricphase analysis (GPA). h, i The dislocation density distribution of x =0.01 (10min)and x =0.01 (20min) samples from EBSD analysis.Article https://doi.org/10.1038/s41467-025-65325-7Nature Communications |        (2025) 16:10366 6www.nature.com/naturecommunicationsAs a result, one of the highest ZT value of 2.06 has been achievedat 623 K, as shown in Fig. 4e. Interestingly, theZT curvequickly reachesits peak and then gradually levels off, which is very beneficial behaviorfor obtaining a high average ZT value. This temperature dependence ismainly attributed to the fact that as the temperature increases past theoptimum performance, i.e., peak ZT, the enhanced carrier mobilityscattering slightly weakens the improvement in electrical transport,while the lattice thermal conductivity in this work, already achievingvalues close to its theoretical limit, exhibits a relatively small decreasewith temperature. Excitingly, the ZTave reaches 1.04 and 1.58within thetemperature range of 300–500 and 300–723 K shown in Fig. 4f,respectively. In comparison with previous reports on Mg3(Sb, Bi)2, orany other knownn-type TEs, the ZTave in this work is at the state-of-the-art level and higher than that of commercial Bi2Te3. This indicates thatthe n-type Mg3(Sb, Bi)2 obtained in this work exhibits significantadvantages for waste heat recovery across both the near-room-temperature and mid-temperature ranges. In addition, we reproducemultiple samples of x = 0.01 (20min) and repeatedly test them, and theconsistency of the properties is excellent, as plotted in Figs.S18 and S19.Design, fabrication and assessment of TE moduleBoth a single-leg and a two-pair TEdevice have beendesigned to betterdemonstrate the TE performance across different temperatureranges80–82. Figure 5a illustrates the structure of the single-leg device.To better harness the excellent TE performance and fully exploit thetemperature difference, the finite element simulation is carried out. Asshown in Fig. 5b, only the appropriate height and cross-sectional areacan yield themaximumTEconversion efficiency. Thus, the dimensionsof 3.4 × 3.4 × 6.5mm3 have been adopted to fabricate the single-legdevice. The contact resistance between theMg3(Sb, Bi)2-based leg andthe barrier layer is examined using the four-probe method, shown inFig. S20. The low contact resistance around 10μΩ cm2, plotted inFig. 5c, indicates a good contact. The slight difference in contactresistances at both ends of the TE leg can be attributed to minor var-iations in local thermal-mechanical conditions during sintering, but itremains within the typical experimental uncertainty. In addition, themicroscopic morphology and element distribution of the interfacehave been shown in Fig. S21. The elemental distribution is uniform, andthere is no apparent elemental diffusion or voids at the interface,consistent with the result of low contact resistance.As shown in Fig. 5d for the single-leg device, the open-circuitvoltage slowly improves with the rising temperature difference. Theinternal resistance, obtained by the slope of theV–I curve shown in Fig.S22b, increases gradually, primarily due to the decrease in electricalconductivity as the temperature rises. In addition, as the currentincreases, the output heat flow displayed in Fig. S22a gradually risesdue to the enhanced Jouleheating andPeltier effect.When the externalresistance matches the internal resistance of the device, the outputpower and conversion efficiency reach their maximum, as shown inFig. 5e. Ultimately, the maximum conversion efficiency of the single-leg device realizes a conversion efficiency of 12.5% at the 440K tem-perature difference, competitive with the highest performance pre-vious reports, as plotted in Fig. 5f60,78,83–88. Furthermore, coupledwith MgAgSb, the prepared two-pair module after geometricaldesign, shown in Fig. S23, achieves a high conversion efficiency of 7.4%(ΔT = 300K). It is indicated that this work has great potential for wasteheat recovery, whether in the near-room-temperature or mid-temperature range.DiscussionIn summary, a strategy focusing on modulating phonon dynamics in amore localizedmanner forminimizing the lattice thermal conductivitywithout deterioration of electrical transport and thus promoting TEs isproposed. Particularly, in the n-type Mg3Sb1.5Bi0.5-based alloy, latticevibrations are tailored via dynamically regulating Mg vacancy, pro-nounced internal strain, and defect proliferation, which softeninteratomic bond stiffness and confine phonon propagation to dis-tances comparable to the lattice parameter. These achieve anultra-lowlattice thermal conductivity of 0.3Wm−1 K−1, which is close to thetheoretical minimum. As a result, one of the highest ZTmax of 2.06,ZTave of 1.04 (300–500K) and unprecedented 1.58 (300–723K) areobtained, which achieves a significant competitive edge in the low-to-mid temperature range. Furthermore, as an initial demonstration ofFig. 4 | The temperature-dependentTEproperties of (Mg3.2Sb1.5Bi0.5)0.99(MnTe)0.01samples at different sintering condition. a The electrical conductivity, b the carrierconcentration (n) and carriermobility (μ) at 300K. cThe Seebeck coefficient.dTherelationship between carrier concentration and Seebeck coefficient on the basis ofsingle parabolic band model. e The ZT value. f The comparison of the average ZTwith other n-type thermoelectric materials at the range of 300–500K and300–723K51,54,55,57–60,65,85. Error bars represent ±10% standard deviation relative tothe ZT value.Article https://doi.org/10.1038/s41467-025-65325-7Nature Communications |        (2025) 16:10366 7www.nature.com/naturecommunicationsthe potential of the material, an excellent conversion efficiencyof 12.5% (ΔT = 440K) and 7.4% (ΔT = 300K) for a single TE-leg gen-erator and a two-pair module is achieved, respectively. Our workdemonstrates the great potential for waste heat recovery of theMg3Sb1.5Bi0.5-based alloy, whether in the near-room-temperature ormid-temperature range, and demonstration of enhanced latticevibrations control can enable advancements across various thermalfunctional materials.MethodsSample synthesisHigh-purity raw Mg (4N), Bi (4N), Sb (4N) and MnTe (3N) wereweighed according to the ratio of (Mg3.2Sb1.5Bi0.5)1−x(MnTe)x (x =0,0.005, 0.01, 0.015, 0.02). The elements were loaded into the ball mil-ling jar inside an Ar-filled glovebox with an O2 concentration below0.1 ppm and then ball-milled (SPEX-Sample Prep 8000 Mixer Mill) for5 h. The obtained powders were loaded into a φ10mm graphite dieinside the glovebox. It was then immediately sintered using SPS (SPS-1080 System, SPS SYNTEX INC) at 700 °C under 60MPa for 10, 20,and 30min.Measurement and characterizationThe electrical conductivity and Seebeck coefficient of all samples weresimultaneously measured using ZEM-3 under the He atmosphere. Thethermal conductivity was estimated through κtot =DρCp, where ther-mal diffusivity (D) was measured by Netzsch LFA 467, the density ofsamples (ρ)was calculated by theArchimedesmethod, and the specificheat capacity (Cp) was determined by the formula Cp = 3NR(1 + 1.3 × 10−4 T−4 × 103T−2)/M89. The room temperature electron carrierconcentration (n) was measured by the physical properties measure-ment system, Quantum Design based on the formula n = 1/RHeand μ = σRH.The samples’ phase structure was identified by the XRD (Smar-tLab3, Rigaku) with Cu Kα radiation. The microstructure of sampleswas characterized using electron backscatter diffraction (EBSD, JSM-7001F, JEOL Inc.), scanning electron microscope (SEM, HitachiSU4800) fitted with an energy-dispersive spectroscopy (EDS, HoribaEMAXE volutionX-Max) and electronprobemicro analysis (EPMA, JXA-8500F). The Raman spectroscopy was performed with the 532nmexcitation laser (inVia, Renishaw). The finer microstructure was char-acterized by scanning transmission electron microscopy (STEM, JEM-ARM-200F-B). The room temperature sound velocity wasmeasured bythe Model UVM-2 (Ultrasonic Engineering Co., Ltd).TE module fabrication and stimulation methodTo fabricate the single-leg generator, the sandwiched structure of(Mg3.2Sb1.5Bi0.5)0.99(MnTe)0.01 powder and Fe alloy (304 stainless steel)powder was employed, using the one-step sintering process. Theobtained ingot was cut into dice with dimensions of3.4 × 3.4 × 6.5mm3. The two-pair TEmodulewas fabricatedon thebasisof n-type (Mg3.2Sb1.5Bi0.5)0.99(MnTe)0.01 leg with the height of 5mmand cross-section of 12.25mm2, and p-typeMgAgSb legwith the heightof 5mm and cross-section of 10.89mm2. The MgAgSb leg preparationprocess can be seen from previous work22. The TE module conversionefficiency (η) was measured by Mini-PEM, (ADVANCE RIKO, Japan)90.Thedetails of theTEmodule test andnumericalmodeling areprovidedin the Supporting Information.The numerical simulation of power generation was performedwith COMSOL Multiphysics software, version 6.1. The Heat TransferModule and the ElectricCurrentsModulewere coupled through theTEEffectmultiphysics interface to simulate the coupled temperature andelectrical potential fields. A three-dimensional model was built in thesoftware interface to represent TE legs with a similar geometry anddimension. The temperature-dependent electrical conductivity,Fig. 5 | The performance of the single-leg thermoelectric device. a Schematicdiagram of the single-leg device. b The theoretical η as a function of TE leg heightand cross-sectional area under the temperature difference of 440K. c The mea-sured contact resistance. The data of single-leg device by current dependenced output voltage (V) and output power (P), and e the η under the different tem-peratures. f The comparison of ηmax between the constructed single-leg device inthis work and previous reports.Article https://doi.org/10.1038/s41467-025-65325-7Nature Communications |        (2025) 16:10366 8www.nature.com/naturecommunicationsSeebeck coefficient, and thermal conductivity were taken from actualmeasurement results. Herein, the electrical and thermal contactresistances between interfaces were not considered in our simulationmodel. The material domains were discretized using a physics-controlled mesh, with the element size set to the default (normal)setting, and a fixed temperature difference was applied between thehot and cold ends.Statistical analysisThe electronic and thermal transport measurements are independentof sample dimensions, and the uncertainties mainly reflect theinstrumental deviations. In particular, the systematic errors areapproximately 3% for the Seebeck coefficient and 5% for the electricalconductivity. For the total thermal conductivity, the uncertainty isabout 7% calculated from dκtotκtot =ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffidρρ� �2+dCpCp� �2+ dDD� �2r(1% for thedensity ρ, 5% for the specific heat Cp and 5% for the thermal diffusionD). Consequently, the propagated error for the calculated ZT values isestimated to be approximately 10%. 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L.W. investigated the PPMStest. X.W. (Xinzhi Wu) and X.W. (Xinyuan Wang) played a part in thediscussion. T.M. provided supervision and the funding. All authors havereviewed and approved the final version of the manuscript.Competing interestsThe authors declare no competing interests.Additional informationSupplementary information The online version containssupplementary material available athttps://doi.org/10.1038/s41467-025-65325-7.Correspondence and requests for materials should be addressed toTakao Mori.Peer review information Nature Communications thanks Hanfu Wangand the other anonymous reviewer(s) for their contribution to the peerreview of this work. 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To view a copy of this licence, visit http://creativecommons.org/licenses/by-nc-nd/4.0/.© The Author(s) 2025Article https://doi.org/10.1038/s41467-025-65325-7Nature Communications |        (2025) 16:10366 11https://doi.org/10.1038/s41467-025-65325-7http://www.nature.com/reprintshttp://creativecommons.org/licenses/by-nc-nd/4.0/http://creativecommons.org/licenses/by-nc-nd/4.0/www.nature.com/naturecommunications Modulating phonon dynamics: tailoring lattice vibrations to enhance thermoelectric efficiency in Mg3(Sb, Bi)2 alloy Results Modulating thermal properties by tailoring lattice vibrations, including lattice softening and suppressed phonon mean free path High electrical transport maintenance and ZT value enhancement Design, fabrication and assessment of TE module Discussion Methods Sample synthesis Measurement and characterization TE module fabrication and stimulation method Statistical analysis Reporting summary Data availability References Acknowledgements Author contributions Competing interests Additional information