The optimization of thermoelectric materials involves the decoupling of the transport of electrons and phonons. In this work, an increased Mg1-Mg2 distance, together with the carrier conduction network protection, has been shown as an effective strategy to increase the weighted mobility () and hence thermoelectric power factor of Mg3+δSb2-yBiy family near room temperature. Mg3+δSb0.5Bi1.5 has a high carrier mobility of 247 cm2 V-1 s-1 and a record power factor of 3470 μW m-1 K-2 at room temperature. Considering both efficiency and power density, Mg3+δSb1.0Bi1.0 with a high average ZT of 1.13 and an average power factor of 3184 μW m-1 K-2 in the temperature range of 50-250°C would be a strong candidate to replace the conventional n-type thermoelectric material Bi2Te2.7Se0.3. The protection of the transport channel through Mg sublattice means alloying on Sb sublattice has little effect on electron while it significantly reduces phonon thermal conductivity, providing us an approach to decouple electron and phonon transport for better thermoelectric materials.
Thermoelectric (TE) materials offer the convenience to convert the widely distributed waste heat into electric power directly, which is highly desired for the autonomous operation of the Internet of things (IoT) in recent years. The conventional room temperature (RT) thermoelectric material, Bi2Te3 family, dominates the market of the solid-state refrigeration [1, 2]. However, its mediocre mechanical property and the extremely low abundance of Te element limit its application . The past years have witnessed great progress in developing medium-temperature thermoelectric materials, but not so much in near room temperature TE materials. So far, there is no candidate material that can compete with the Bi2(Te,Se)3 family in terms of near room temperature TE performance. In our previous report, we have shown that the Mn-doped Mg3+δSb1.5Bi0.5 (, ) would be a very promising candidate for substituting the Bi2Te3−xSex family (, ) in the temperature range of 50–250°C because of the comparable average ZT and much higher fracture toughness . It is noted that intensive efforts have been made into searching high ZT composition in the Bi-rich Mg3+δSb2-yBiy with varying doping [5–7]. Imasato et al. researched Bi content-dependent thermoelectric properties and discovered that Mg3+δSb0.6Bi1.4 shows exceptional thermoelectric performance . Ren et al. produced a thermoelectric cooling couple with Mg3+δSb0.5Bi1.5 and Bi0.5Sb1.5Te3, which realized around 90 K at the hot-side of 350 K. Further improvement on the power factor is desirable for power generation applications . However, the power factor of the reported Mg3+δSb1.5Bi0.5 is still lower than that of the Bi2Te3−xSex family, which could lead to a reduced power density of the thermoelectric power generator. Further enhancement in the PF of Mg3+δSb1.5Bi0.5 is thus much desired.
However, it is challenging to decouple the transport of electrons while tuning the thermoelectric properties . Electron-phonon interaction and defects would affect electron and phonon transport at the same time. The material parameter () is commonly used as a guideline to boost thermoelectric performance of materials, where and are the carrier mobility and effective mass, respectively . Usually, a material that has multicarrier valleys and small DOS effective mass for each valley could have a large power factor () , and a material with heavy elements can have low intrinsic . For instance, Bi2Te3 and PbTe are known as conventional thermoelectric materials. Also, alloying has been greatly used to reduce the lattice thermal conductivity after Ioffe’s  and Goldsmid’s  pioneering works. However, the decrease in from alloying is usually offset by the reduction in from alloying . Recently, Liu et al. have found that the small atomic size difference between the period 5 elements (Zr, Nb) and period 6 elements (Hf, Ta) moderates alloying’s negative impact on carrier mobility in the half-Heusler system .
In 2016, Tamaki et al. reported an n-type Mg3+δSb2-based laminar Zintl compound with a high ZT of 1.5 at 442°C , which has attracted much attention in the thermoelectric community to enhance the peak ZT of Mg3+δSb2-based TE materials [19–22]. The most surprising feature of this material family is that the alloy disorder at anionic sites has little effect on carrier mobility. Favorable alloying sites are known in the Bi2Te3 family, i.e., n-type Bi2Te3 has a favorable site at the Te sublattice while the p-type one has a favorable site at the Bi sublattice. Similar favorable doping sites have been observed in the PbTe [23, 24] and Mg2Sn  systems. Wang et al. suggested that the favorable dopants should be on the site that is of less influence on the charge-conducting band . Recently, Yang et al. proposed a conduction network in the real space: the vast majority of atoms formed a conductive framework for charge carriers, while the chief role of the remaining atoms was to scatter phonons . If the alloying elements or dopants get into the sublattice away from the conduction network, they would have little impact on carriers’ transport. Tamaki et al. also pointed out the conduction network, formed by the 3s-like orbitals of Mg2+ and the weakly hybridized atomic orbitals of [Mg2Sb2]2- in Mg3+δSb2-based layered Zintl compound, but not connecting with the feature that alloying has little effect on carrier mobility. We believe that this carrier conductive network forms a favorable carrier transport channel in real space. It was found that the disordering Bi/Sb at the anionic site is “far away” from the electronic transport channel, which explains the fact that the electrical conductivity of Mg3+δSb1.5Bi0.5 is very sensitive to the Mg vacancy but not to the disordering Bi/Sb [18, 27, 28]. Experimentally, excess Mg is necessary to suppress the formation of Mg vacancy and obtain stable n-type samples . However, as suggested by Tamaki et al., Mg vacancy is still a favorable intrinsic defect even in a Mg-rich condition. In our previous work , we have shown that the Mn dopant at Mg4-tetrahedron interstitial site provides an attracting force to suppress the formation of the Mg vacancy.
In this work, we will theoretically show a more unique character of the carrier conduction network: by increasing the Mg1-Mg2 distance, we can increase the weighted mobility and enhance the power factor () through the increased carrier mobility. Experimentally, we found the Bi-rich Mg3+δSb2-yBiy with interstitial dopant Mn and anionic dopant Te has a recorded high carrier mobility of 247 cm2 V-1 s-1 and a high power factor of 3470 μW m-1 K-2 at room temperature in the Mg3+δSb0.5Bi1.5 sample. The Mg3+δSb1.0Bi1.0 possessed a high average ZT of 1.13 and an average PF of 3184 μW m-1 K-2 in the temperature range of 50-250°C.
2. Results and Discussion
Figure 1 shows the effect of increased Mg1-Mg2 distance in real space on the band structure and Hall mobility. Our motivation was to find a way to further tailor the charge conductive network in real space and make it more favorable for the transport of electrons. Mg3Sb2 has a trigonal structure (space group: ) and a layered structure with alternate layers of Mg and [Mg2Sb2] in the ab-plane , as shown in Figure 1(a). Recently, Sun et al. suggested that part of the conduction band minimum (CBM) originates from the covalence-like bonding state of Mg1 3s orbital and Mg2 3s orbital and there was also a small amount of antibonding-like interaction between Mg1 3s and Sb 5s orbitals, where Mg1 represents the Mg at the Sb-octahedral center (0, 0, 0) while Mg2 is the Mg at the tetrahedral center (0.3333, 0.6667, 0.3718(4)) . Figure 1(b) shows the charge density in (011) plane of the trigonal Mg3Sb2. Detailed analysis of the band composition near CBM shows that the states near CBM consist of Mg1 3s orbitals, Mg2 3s orbitals, and Sb 5s orbitals. The most weighted contribution to conductive network comes from the dispersive Mg1 3s orbitals. Furthermore, our first-principles calculations also suggest that an increase of Mg1-Mg2 distance reduces the overlap of Mg1 3s and Mg2 3s orbitals that constitute the Mg1-Mg2 “bond.” As the distance between Mg1 and Mg2 increases with strain, the difference of the squared wave function, between pristine and the one with 4% strain, shows that (i) the overlap of Mg1 3s and Mg2 3s orbitals at CBM reduces and (ii) the released charge would go to Mg1 3s orbitals and enhance the antibonding between Mg1 3s orbitals that is the most pronounced constituent around CBM (see Figure 1(c)). Therefore, it leads to a more dispersive band (i.e., lighter band) (see Figure 1(d)). The red line with solid circles in Figure 1(d) plots the DOS effective mass of conduction band minimum of Mg3Sb2 as a function of the strain along the -axis. An almost linear decline in the band effective mass is observed when the strain increases from 1% to 4%. When acoustic phonon scattering is considered as the dominant scattering mechanism, the maximum power factor is proportional to the ratio (the derivation is given in SI A). A smaller effective mass (lighter band) corresponds to the higher carrier mobility and the increased power factor [27, 30, 31]. Li et al. also suggested an enhanced power factor of Mg3SbBi as a biaxial strain was used in their first-principles calculation .
Figure 2 provides more information on the relation between carrier effective mass of Mg3Sb2 and Mg1-Mg2 distance according to our first-principles calculations. Experimentally, partial substitution of Sb atoms with Bi atoms expands the crystalline lattice, as shown in Figure 2(a). The XRD patterns of Mg3Sb2-yBiy () powders (grinded by SPS bulks) are given in Fig. S1 (SI). All the samples show a single phase with a La2O3-type trigonal structure. The lattice parameters and distance of Mg1-Mg2 are derived from the Rietveld refinement. An almost linear expansion is observed that the lattice parameter varies from 7.296 Å to 7.416 Å (Fig. S2, SI) with increasing Bi content, indicating a complete solid solution of Mg3Sb2 and Mg3Bi2, and the ratio remained around 1.587, which is close to that of pure Mg3Sb2. As a result, the Mg1-Mg2 distance increases from 3.832 Å to 3.891 Å as the Bi content increases from to . The estimated Mg1-Mg2 distances in Mg3Sb2 and Mg3Sb1.5Bi0.5 are 3.761 Å and 3.786 Å, respectively. Figure 2(b) plots the effective mass for the single band () as a function of Mg1-Mg2 distance. Here, both the -axis strain and Bi alloying effect increase the Mg1-Mg2 distance. The DOS effective mass at the conduction band edge decreases with increasing Mg1-Mg2 distance. Bi alloying increases the distance between Mg1 and Mg2 and weakens the covalence-like bonding between Mg1 3s and Mg2 3s orbitals. However, the slopes of the two curves, as shown in Figure 2(b), are slightly different. The change in band effective mass mb from Bi alloying is more complicated because (1) adding Bi into the system expands the lattice not only along the -axis but also in the a-b plane (Fig. S2, SI) and (2) adding Bi leads to the upward shifting of valence bands and the narrowing of band gaps. The upward shifting of valence bands brings hybridization between Bi p orbitals from valence bands and Mg1 3s orbitals from conduction bands. Such hybridization makes bands more dispersive, therefore lighter effective mass. A similar tensile strain-dependent reduction of band DOS effective mass was also reported in the typical semiconductor with well-known covalent bonds, such as Ge  and Si .
A closing band gap of Mg3Sb2-yBiy with increasing Bi content has been theoretically predicted by many researchers [27, 34]. Our previous experiments also proved this . Zhang et al. suggested a transition from semiconductor to semimetal as the Bi content increases and goes higher than (Mg3Sb2-yBiy) . However, in our calculation, the band gap remains as large as 0.17 eV for the sample Mg3Sb0.5Bi1.5 without spin-orbit correction. Our calculations for the Mg3Sb2-yBiy (, 0.5, 0.75, 1, 1.25, 1.5, and 2.0) family give the same trend as shown in Figures 2(c)–2(e) and Table 1. The narrowing of the band gap with increasing Bi concentration is attributed to the upward shift of valence band maximum since the valence band maximum mainly consists of Sb and Bi p orbitals, and Bi p orbitals are more dispersive and lie at higher energy levels than Sb p orbitals. The band shape at CBM does not change much within the calculated Sb/Bi ratio window, but the effective mass at CBM decreases monotonically. Furthermore, the color indicator also shows that all the Mg3Sb2-yBiy family members have a similar CBM between M and L, mainly raised from the Mg3s orbital. This suggests that the alloying disordering at the Sb site might have less impact on the transport of the electron since its transport channel in the real space is around the Mg site.
Figure 3 shows the Hall measurement of the as-fabricated Mg3+δSb2-yBiy, together with reported theoretical and experimental data from literature. The carrier concentrations of as-fabricated Mg3+δSb2-yBiy samples show a weak dependence on Bi content in the range of , with an average Hall carrier concentration of , as shown in Figure 3(a). For the composition of Mg3+δSb1.5Bi0.5 with 1% Te and 1% Mn, our measured Hall carrier concentration () is slightly higher than the reported data [8, 27, 35]. The effective charge carrier per Te was estimated to be 0.30, 0.47, and 0.56 electron/atom as Bi content is , 0.5, and 1.0, respectively. Then, it reached a saturated value of about 0.55 electron/atom when Bi content gets larger than , which indicates that Te is a strong donor in Mg3+δSb2-yBiy that is comparable with Te in CoSb3-xTex (0.4 electron/atom) . Figure 3(b) shows that the Hall mobility of as-fabricated Mg3+δSb2-yBiy increases from 48.0 to 68.8, 169.8, 195.9, 201.8, 247.0, and 247.3 cm2 V-1 s-1 as the Bi content increases from to 0.5, 1, 1.2, 1.4, 1.5, and 1.6, respectively. Based on our measured data together with theoretical and experimental ones from literature, a weak alloying effect was found [4, 5, 7, 8, 18, 35, 37–40], suggesting that the disordering Sb/Bi has a weak coupling effect on the charge transport channel. The Pisarenko curve was also used to analyze the alloying effect (Fig. S3, SI). The charge carrier effective masses were derived from an equivalent single band mode and changed from 1.15 to 1.05, 0.89, 0.89, 0.91, and 0.86 m0 as the Bi content increased from to 1, 1.2, 1.4, 1.5, and 1.6. It is noted that the theoretical carrier effective mass, derived from , is less than the experimental observed value, where and are the degeneration number of the CBM and band effective mass (Figures 1(d) and 2(b)). The extra disagreement between first-principles calculations and experiments could be related to the adaption of theoretical lattice constants at zero Kelvin and the screened hybrid functional HSE06. Furthermore, the conduction network forms a protected electron transport channel, away from the disordering Sb/Bi. Due to the combined effect of the electronic transport channel protection and the increased Mg1-Mg2 distance, a high Hall mobility of ~247 cm2 V-1 s-1 is obtained in Mg3+δSb0.5Bi1.5 and Mg3+δSb0.4Bi1.6 with 1% Te and 1% Mn samples, much higher than that of the conventional composition Mg3+δSb1.5Bi0.5, as shown in Figure 3(c) [36, 38–40]. Figure 3(d) shows the weighted mobility calculated by the carrier effective mass using the equivalent single band model and carrier mobility by Hall measurement. The weighted mobility increases from 85.5 to 183.7, 163.8, 169.7, 217.6, and 195.9 cm2 V-1 s-1 as the Bi content increases from to , 1.2, 1.4, 1.5, and 1.6, respectively. This trend is consistent with our theoretical interpretation of the increasing Mg1-Mg2 distance and decreasing DOS-m at CBM.
Figure 4 shows the temperature-dependent electrical transport properties of as-fabricated Mg3+δSb2-yBiy () with 1% Te and 1% Mn. The data of our previously reported Mg3+δSb1.5Bi0.5 is also shown for comparison . Firstly, a positive correlation between temperature and electrical resistivity is found in all samples without notable abnormal negative near room temperature. It should be resulted from suppressed formation of Mg vacancy by using excess Mg  and interstitial Mn  and less grain boundary scattering  due to a large grain size of 5-10 μm and high carrier concentration. The SEM images of the fracture section of as-fabricated Mg3+δSb2-yBiy samples are shown in Fig. S4, indicating a grain size of 5-10 μm. Secondly, due to the nearly unchanged carrier concentration and increasing carrier mobility with increasing Bi/Sb ratio, the room temperature electrical resistivity decreases from 8.8 to 8.2, 7.6, 6.0, 6.7, 6.2, 5.7, and 5.0 μΩm as the content of Bi increases from to , 1.4, 1.5, 1.6, 1.7, 1.8, and 2.0, respectively (Figure 4(a)). It is noted that the Mg3+δSb0.5Bi1.5 sample has a low electric resistivity that is only half of that of the previously reported Mg3+δSb1.5Bi0.5 because of its high carrier mobility. Furthermore, the room temperature Seebeck coefficient of Mg3+δSb2-yBiy () shows a weak Bi/Sb ratio dependence (staying at almost constant around 145 μV K-1) which is consistent with the trend of carrier concentration. As Bi content increases from to and 2.0, the Seebeck starts to decrease from -145 μV K-1 to -126.7 μV K-1 and -81.4 μV K-1, respectively, shown in Figure 4(b). Figure 4(c) plots the temperature-dependent power factor of Mg3+δSb2-yBiy () calculated from the measured electrical resistivity and Seebeck coefficient. All the as-fabricated Mg3+δSb2-yBiy () samples, except for Mg3+δBi2, have a large power factor over 2500 μW m-1 K-2 near room temperature. The largest room temperature power factor of 3470 μW m-1 K-2 is obtained in Mg3+δSb0.5Bi1.5, which is 50% larger than that of our previously reported Mg3+δSb1.5Bi0.5 and also 17% larger than a recently reported Bi-rich Mg3+δSb0.6Bi1.4 (~2960 μW m-1 K-2) and 26% larger than Mg3.05Sb2-x-yBiy-xTex (~2750 μW m-1 K-2) [7, 8]. More comparisons were included in Fig. S5 (SI). Figure 4(d) plots room temperature power factor as a function of reduced Fermi level under the acoustic phonon dominant scattering (calculation details are given in SI A), suggesting that the sample Mg3+δSb1.0Bi1.0 was very close to the optimized carrier concentration while Mg3+δSb2-yBiy () would be overdoped. The optimized reduced Fermi energy () is estimated to be around 0.67, equal to at room temperature, which corresponds to a Seebeck coefficient of -167 μV K-1.
Figure 4(e) compares the average power factor of Mg3+δSb2-yBiy () in the temperature range of 50-250°C. All the samples (except ) have a value over ~3000 μW m-1 K-2, which is 166% higher than Tamaki’s Mg3+δSb1.5Bi0.5 (1130 μW m-1 K-2) and also about 16% higher than that of previously reported Mg3+δSb1.5Bi0.5 (2590 μW m-1 K-2) [4, 18]. This has already surpassed many polycrystalline n-type Bi2(Te,Se)3, which can be comparable with textured Bi2(Te,Se)3 [41, 42] and commercially available Bi2(Te,Se)3 ingot in the temperature range of 50-250°C. A more accurate relationship between output power density and the power factor is given in equation (1); the engineering power factor (Figure 4(f)) is calculated as equation (2) . where is the temperature difference, is the TE-leg length, and and are temperature-dependent Seebeck coefficient and electrical resistivity. In the temperature range of 50-250°C, all the samples (except ) have an engineering power factor of about 0.6 W m-1 K-1, which is 100% larger than Tamaki’s Mg3+δSb1.5Bi0.5 (0.3 W m-1 K-1) and also 20% larger than that of previously reported Mg3+δSb1.5Bi0.5 (0.5 W m-1 K-1) [4, 18].
Figures 5(a) and 5(b) show the temperature-dependent thermal properties of Mg3+δSb2-yBiy (). At room temperature, the thermal conductivity increases from 1.31 to 1.34, 1.47, 1.64, 1.41, 1.90, 2.13, and 2.18 W m-1 K-2, as the Bi content increases from to 1.2, 1.4, 1.5, 1.6, 1.7, 1.8, and 2.0, respectively. A notable bipolar effect is observed in all the samples which are characterized by an increasing thermal conductivity with temperature at the high temperature end. Furthermore, the samples with more Bi (i.e., larger value in the formula of Mg3+δSb2-yBiy) have a lower starting temperature, which is consistent with narrowing band gap predicated by our theoretical calculations. The lattice thermal conductivity is estimated by subtracting the contribution of electronic part () and bipolar part () from the total thermal conductivity (), i.e., (Figure 5(b)). The details of the calculation relative to the electronic thermal conductivity () and bipolar thermal conductivity () are given in SI B. At room temperature, changes from 0.75 to 0.69, 0.77, 0.76, 0.61, 1.00, 1.12, and 0.82 W m-1 K-2 as the Bi content increases from to 1.2, 1.4, 1.5, 1.6, 1.7, 1.8, and 2.0, respectively. For comparison, of Mg3Sb2 and Mg3Sb1.5Bi0.5 from our previous work are estimated to be 1.46 W m-1 K-2 and 0.73 W m-1 K-2 . of Mg3+δSb1.0Bi1.0 is 48% lower than that of Mg3Sb2 and 12% lower than that of Mg3Bi2. This decrease in lattice thermal conductivity is the result of alloying scattering on the transport of the phonon.
Figure 5(c) compares ZT as a function of temperature of Mg3+δSb2-yBiy (). Mg3+δSb1.0Bi1.0 shows a peak ZT of 1.5 at 300°C, while a room temperature ZT of 0.75, which is 275% higher than that of Tamaki’s Mg3+δSb1.5Bi0.5 () and 20% higher than that of our previously reported Mg3+δSb1.5Bi0.5 (), as shown in Figure 5(c) [4, 18]. This is also comparable with recently reported Mg3.2Bi1.998-xSbxTe0.002 at room temperature  and higher than Mg3+δSb0.6Bi1.4, which behaves and peak ZT of ~1.1 . It is comparable with those of commercially available n-type Bi2Te3 ingot () . Moreover, in the temperature range of 50-250°C, Mg3+δSb1.0Bi1.0 has an engineering ZT of 0.56, which is 16.7% higher than our previously reported Mg3+δSb1.5Bi0.5 () and Bi2Te3-xSex () (data from literatures are plotted on Fig. S7, SI) [4, 44]. Furthermore, the thermoelectric properties of three batches of Mg3+δSb1.0Bi1.0 and circling electrical property test for one of the samples were given in Fig. S6 (SI), which shows that the results are repeatable. Finally, a dual parameter criteria of “ZT versus PF”  are used to select the better thermoelectric materials with a consideration for requirements of efficiency and power density at the same time . Figure 5(d) clearly suggests that Mg3+δSb1.0Bi1.0 in this work surpasses any other Mg3+δSb2-yBiy material in this work and the Bi2Te3-xSex family [4, 6, 7, 18, 19, 27, 38, 39, 41, 44, 46, 47], for its high average ZT of 1.13 and an average power factor of 3184 μW m-1 K-2. (Reference data from literature is plotted on Fig. S8, SI.).
We have successfully enhanced the room temperature thermoelectric performance of Mg3+δSb2-yBiy by the strategy of electronic transport channel protection and tuning in real space. It was found that the increased carrier mobility was closely related to the weakening covalence-like bonding between Mg1 3s and Mg2 3s orbitals and hence the lightening DOS effective mass. Experimentally, our Mg3+δSb0.5Bi1.5 samples reached a high carrier mobility of 247 cm2 V-1 s-1 and high power of 3470 μW m-1 K-2 at room temperature. We also suggest that, in a dual parameter criteria of “ZT versus PF,” Mg3+δSb1.0Bi1.0 would be a promising room temperature thermoelectric material, to replace the classic n-type Bi2Te2.7Se0.3, for its high values of , at room temperature, , and in the temperature range of 50-250°C, which gives an efficiency of 8.5% under ideal adiabatic condition. Furthermore, the electronic transport channel protection and tuning in real space could be a new electronic engineering strategy to increase the carrier mobility.
4. Experimental Procedures
4.1. Sample Synthesis
The samples with nominal compositions of Mg3+δSb2-yBiy-0.01Te0.01:Mn0.01 were synthesized by mechanical alloying and spark plasma sintering (SPS). High-purity magnesium turnings (Mg, >99.9%; Acros Organics), antimony shots (Sb, 99.999%; 5N Plus), bismuth shots (Bi, 99.999%; 5N Plus), tellurium shots (Te, 99.999%; 5N Plus), and manganese powders (Mn, 99.95%; Alfa Aesar) were weighed according to the composition of Mg3+δSb2-yBiy-0.01Te0.01:Mn0.01 (, , 1.2, 1.4, 1.5, 1.6, 1.7, 1.8, and 2.0), simplified as Mg3+δSb2-yBiy in the text, and were then loaded into a stainless steel ball milling jar together with stainless steel balls in a glove box in an argon atmosphere with the . After ball milling for 8 hours in SPEX 8000D, or 8000 M, the ball-milled powders were loaded into a graphite die with an inner diameter of 15 mm in a glove box. Graphite die with loading powder was immediately sintered at 675°C under a pressure of 50 MPa for 5 min in SPS division (SPS-211Lx, Fuji Electronic Industrial Co. LTD). The SPS bulks are ~15 mm in diameter and ~8 mm in thickness. The Seebeck coefficient, electrical resistivity, and thermal diffusivity were measured in the directions perpendicular to pressure.
4.2. Thermoelectric Characterization
Electrical properties, including Seebeck coefficient, electrical resistivity, and power factor, were measured by ZEM-3, ULVAC Riko, under a 0.01 MPa pressure helium atmosphere from RT to 400°C. Measured samples were cut into about pieces. Thermal conductivity was calculated by equation , where is thermal diffusivity measured by laser flash method (LFA 467; Netzsch) using about pieces, is density measured by the Archimedean method, and specific heat () is tested by differential scanning calorimetry (Discovery DSC, Waters LLC), shown in Fig. S9 (SI).
4.2.1. Hall Effect Measurement
Hall coefficient was measured by Physical Property Measurement System (PPMS-14L, Quantum Design) with four-point method in magnetic field from -5 T to 5 T. Tested samples were cut into about pieces and then soldered to Φ0.1 mm enameled wire with In as the solder. Hall carrier concentration was calculated by , and Hall mobility was calculated by , where is elementary charge and is measured electrical resistivity.
4.3. X-Ray Diffraction
SPS bulks were grinded into powder in a glove box, and then, the phase composition was characterized by X-ray diffraction (Rigaku SmartLab) with Cu Kα radiation (, operating at 40 kV/15 mA with Kβ foil filter). XRD patterns were further refined by the Rietveld method to calculate lattice parameter and Mg1-Mg2 distance.
4.4. Calculation Methods
The first-principles calculations are based on density functional theory (DFT) [48, 49] and the screened hybrid functional HSE06 [50, 51] as implemented in the Vienna Ab Initio Simulation Package (VASP) code . Projected augmented wave (PAW) potentials  with plane-wave basis set and an energy cutoff of 550 eV are used. The valence electronic configurations for Mg, Sb, and Bi are 3s2, 5s25p3, and 6s26p3 in the pseudopotentials, respectively. For integrations over the Brillouin zone, we use Monkhorst-Pack k-point mesh  for 40-atom cells (). The atomic positions are fully relaxed until the forces on each atom are less than 0.005 eV/Å and total energy differences between two consecutive steps are less than 10-6 eV. The lowest-energy structural configurations for alloy systems are constructed by Supercell program  and direct energy comparison.
Conflicts of Interest
There are no conflicts to declare.
W.S. Liu and Z.J. Han designed the experiment; Z.J. Han conducted the synthesis and TE transport property measurement; Z.G. Gui contributed to the first-principles calculation; P. Qin and Y.B. Zhu conducted the Hall measurement; Z.J. Han and Z.G. Gui complete the writing of the manuscript; B.P. Zhang, W.Q. Zhang, L. Huang, and W.S. Liu were responsible for the interpretation of the results and revision of the manuscript. All authors discussed the results and gave comments regarding the manuscript. Z.J. Han and Z.G. Gui have equivalent contribution.
The authors would like to thank the support of State’s Key Project of Research and Development Plan No. 2018YFB0703600, NSFC Program No. 51872133, Guangdong Innovative and Entrepreneurial Research Team Program No. 2016ZT06G587, and Shenzhen Basic Research Fund under Grant Nos. JCYJ20170817105132549 and JCYJ20180504165817769. The authors would also like to thank the support of Centers for Mechanical Engineering Research and Education at MIT and SUSTech. The computing time was supported by the Center for Computational Science and Engineering of SUSTech. The authors would like to thank Prof. Gang Chen and Qian Xu of the Department of Mechanical Engineering, MIT, and Prof. Hongtao He, Prof. Liusuo Wu, and Liang Zhou, of the Department of Physics, SUSTech.
Fig. S1: XRD patterns of the Mg3+δSb2-yBiy (, 1.2, 1.4, 1.5, 1.6, 1.7, 1.8, and 2.0) solid solution powder. Fig. S2: lattice parameter and of Mg3+δSb2-yBiy as function of Bi content, and dash lines show Vegard’s law between Mg3Sb2 and Mg3Bi2. Fig. S3: Pisarenko’s plot for Mg3+δSb2-yBiy. It shows a decrease effective mass with higher Bi content. Fig. S4: SEM images of the fractured surface of Mg3+δSb2-yBiy: (a) , (b) , (c) , (d) , and (e) . Fig. S5: comparison of power factor of the Mg3 (Sb, Bi)2 system [1–18]. Fig. S6: reproducibility and circling test of as-fabricated Mg3+δSb1.0Bi0.99Te0.01:Mn0.01. Fig. S7: temperature dependence of (a) power factor and (b) ZT of as-fabricated Mg3+δSb2-yBiy and Bi2(Te,Se)3 from references [8, 9, 12, 15, 17–23]. Fig. S8: engineering ZT of Mg3+δSb2-yBiy-0.01Te0.01:Mn0.01 in the temperature range of 50-250°C. Fig. S9: specific heat of the Mg3+δSb2-yBiy-0.01Te0.01:Mn0.01 solid solution powder. (Supplementary Materials)
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