The Electronic Transport Channel Protection and Tuning in Real Space to Boost the Thermoelectric Performance of Mg3+δSb2-yBiy near Room Temperature

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 (U = μm∗3/2) 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.


Introduction
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, Bi 2 Te 3 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 [3]. 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 Bi 2 (Te,Se) 3 family in terms of near room temperature TE performance. In our previous report, we have shown that the Mn-doped Mg 3+δ Sb 1.5 Bi 0.5 (ðZTÞ avg = 1:05, K IC = 2:2-3:0 MPa m 1/2 ) would be a very promising candidate for substituting the Bi 2 Te 3−x Se x family (ðZTÞ avg = 0:9 -1:0, K IC = 0:6-1:3 MPa m 1/2 ) in the temperature range of 50-250°C because of the comparable average ZT and much higher fracture toughness [4]. It is noted that intensive efforts have been made into searching high ZT composition in the Bi-rich Mg 3+δ Sb 2-y Bi y with varying doping [5][6][7]. Imasato et al. researched Bi contentdependent thermoelectric properties and discovered that Mg 3+δ Sb 0.6 Bi 1.4 shows exceptional thermoelectric performance [8]. Ren et al. produced a thermoelectric cooling couple with Mg 3+δ Sb 0.5 Bi 1.5 and Bi 0.5 Sb 1.5 Te 3 , which realized ΔT around 90 K at the hot-side T of 350 K. Further improvement on the power factor is desirable for power generation applications [9]. However, the power factor of the reported Mg 3+δ Sb 1.5 Bi 0.5 is still lower than that of the Bi 2 Te 3−x Se x family, which could lead to a reduced power density of the thermoelectric power generator. Further enhancement in the PF of Mg 3+δ Sb 1.5 Bi 0.5 is thus much desired.
However, it is challenging to decouple the transport of electrons while tuning the thermoelectric properties [10]. Electron-phonon interaction and defects would affect electron and phonon transport at the same time. The material parameter B (B ∝ μm * 3/2 /κ lat ) is commonly used as a guideline to boost thermoelectric performance of materials, where μ and m * are the carrier mobility and effective mass, respectively [11]. Usually, a material that has multicarrier valleys and small DOS effective mass for each valley could have a large power factor (S 2 σ) [12], and a material with heavy elements can have low intrinsic κ [13]. For instance, Bi 2 Te 3 and PbTe are known as conventional thermoelectric materials. Also, alloying has been greatly used to reduce the lattice thermal conductivity after Ioffe's [14] and Goldsmid's [15] pioneering works. However, the decrease in κ from alloying is usually offset by the reduction in μ from alloying [16]. 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 [17].
In 2016, Tamaki et al. reported an n-type Mg 3+δ Sb 2based laminar Zintl compound with a high ZT of 1.5 at 442°C [18], which has attracted much attention in the thermoelectric community to enhance the peak ZT of Mg 3+δ Sb 2 -based TE materials [19][20][21][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 Bi 2 Te 3 family, i.e., n-type Bi 2 Te 3 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 Mg 2 Sn [25] systems. Wang et al. suggested that the favorable dopants should be on the site that is of less influence on the charge-conducting band [24]. 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 [26]. 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 Mg 2+ and the weakly hybridized atomic orbitals of [Mg 2 Sb 2 ] 2in Mg 3+δ Sb 2 -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 Mg 3+δ Sb 1.5 Bi 0.5 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 [19]. 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 [4], we have shown that the Mn dopant at Mg 4 -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 Mg 1 -Mg 2 distance, we can increase the weighted mobility U and enhance the power factor (S 2 σ) through the increased carrier mobility. Experimentally, we found the Bi-rich Mg 3+δ Sb 2-y Bi y with interstitial dopant Mn and anionic dopant Te has a recorded high carrier mobility of 247 cm 2 V -1 s -1 and a high power factor of 3470 μW m -1 K -2 at room temperature in the Mg 3+δ Sb 0.5 Bi 1.5 sample. The Mg 3+δ Sb 1.0 Bi 1.0 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. Figure 1 shows the effect of increased Mg 1 -Mg 2 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. Mg 3 Sb 2 has a trigonal structure (space group: P 3m1) and a layered structure with alternate layers of Mg and [Mg 2 Sb 2 ] in the ab-plane [18], 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 Mg 1 3s orbital and Mg 2 3s orbital and there was also a small amount of antibondinglike interaction between Mg 1 3s and Sb 5s orbitals, where Mg 1 represents the Mg at the Sb-octahedral center (0, 0, 0) while Mg 2 is the Mg at the tetrahedral center (0.3333, 0.6667, 0.3718(4)) [29]. Figure 1(b) shows the charge density in (011) plane of the trigonal Mg 3 Sb 2 . Detailed analysis of the band composition near CBM shows that the states near CBM consist of Mg 1 3s orbitals, Mg 2 3s orbitals, and Sb 5s orbitals. The most weighted contribution to conductive network comes from the dispersive Mg 1 3s orbitals. Furthermore, our first-principles calculations also suggest that an increase of Mg 1 -Mg 2 distance reduces the overlap of Mg 1 3s and Mg 2 3s orbitals that constitute the Mg 1 -Mg 2 "bond." As the distance between Mg 1 and Mg 2 increases with strain, the difference of the squared wave function, between pristine and the one with 4% strain, shows that (i) the overlap of Mg 1 3s and Mg 2 3s orbitals at CBM reduces and (ii) the released charge would go to Mg 1 3s orbitals and enhance the antibonding between Mg 1 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 Mg 3 Sb 2 as a function of the strain along the c-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 N v /m * (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 Mg 3 SbBi as a biaxial strain was used in their first-principles calculation [28]. Figure 2 provides more information on the relation between carrier effective mass of Mg 3 Sb 2 and Mg 1 -Mg 2 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 Mg 3 Sb 2-y Bi y (y = 1:0~2:0) powders (grinded by SPS bulks) are given in Fig. S1 (SI). All the samples show a single phase with a La 2 O 3 -type trigonal structure. The lattice parameters and distance of Mg 1 -Mg 2 are derived from the Rietveld refinement. An almost linear expansion is observed that the lattice parameter c varies from 7.296 Å to 7.416 Å (Fig. S2, SI) with increasing Bi content, indicating a complete solid solution of Mg 3 Sb 2 and Mg 3 Bi 2 , and the c/a ratio remained around 1.587, which is close to that of pure Mg 3 Sb 2 . As a result, the Mg 1 -Mg 2 distance increases from 3.832 Å to 3.891 Å as the Bi content increases from y = 1:0 to y = 2:0. The estimated Mg 1 -Mg 2 distances in Mg 3 Sb 2 and Mg 3 Sb 1.5 Bi 0.5 are 3.761 Å and 3.786 Å, respectively. Figure 2 distance between Mg 1 and Mg 2 and weakens the covalence-like bonding between Mg 1 3s and Mg 2 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 c-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 Mg 1 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 [32] and Si [33]. A closing band gap of Mg 3 Sb 2-y Bi y with increasing Bi content has been theoretically predicted by many researchers [27,34]. Our previous experiments also proved this [4]. Zhang et al. suggested a transition from semiconductor to semimetal as the Bi content increases and goes higher than y = 1:5 (Mg 3 Sb 2-y Bi y ) [34]. However, in our calculation, the band gap remains as large as 0.17 eV for the sample Mg 3 Sb 0.5 Bi 1.5 without spin-orbit correction. Our calculations for the Mg 3 Sb 2-y Bi y (y = 0, 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 Mg 3 Sb 2-y Bi y 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 asfabricated Mg 3+δ Sb 2-y Bi y , together with reported theoretical   Figure 3(a). For the composition of Mg 3+δ Sb 1.5 Bi 0.5 with 1% Te and 1% Mn, our measured Hall carrier concentration (3:52 × 10 19 cm −3 ) 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 y = 0, 0.5, and 1.0, respectively. Then, it reached a saturated value of about 0.55 electron/atom when Bi content gets larger than y = 1:0, which indicates that Te is a strong donor in Mg 3+δ Sb 2-y Bi y that is comparable with Te in CoSb 3-x Te x (0.4 electron/atom) [36]. Figure 3(b) shows that the Hall mobility of as-fabricated Mg 3+δ Sb 2-y Bi y increases from 48.0 to 68. 8, 169.8, 195.9, 201.8, 247.0, and 247.3 cm 2 V -1 s -1 as the Bi content increases from y = 0 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][38][39][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 m 0 as the Bi content increased from y = 0:5 to 1, 1.2, 1.4, 1.5, and 1.6. It is noted that the theoretical carrier effective mass, derived from m * = N v 2/3 m b * , is less than the experimental observed value, where N v and m b * 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 Mg 1 -Mg 2 distance, a high Hall mobility of~247 cm 2 V -1 s -1 is obtained in Mg 3+δ Sb 0.5 Bi 1.5 and Mg 3+δ Sb 0.4 Bi 1.6 with 1% Te and 1% Mn samples, much higher than that of the conventional composition Mg 3+δ Sb 1.5 Bi 0.5 , as shown in Figure 3(c) [36,[38][39][40].  Figure 4 shows the temperature-dependent electrical transport properties of as-fabricated Mg 3+δ Sb 2-y Bi y (y = 1:0-2:0) with 1% Te and 1% Mn. The data of our previously reported Mg 3+δ Sb 1.5 Bi 0.5 is also shown for comparison [4]. Firstly, a positive correlation between temperature and electrical resistivity is found in all samples without notable abnormal negative dρ/dT near room temperature. It should be resulted from suppressed formation of Mg vacancy by using excess Mg [22] and interstitial Mn [4] and less grain boundary scattering [21] due to a large grain size of 5-10 μm and high carrier concentration. The SEM images of the fracture section of as-fabricated Mg 3+δ Sb 2-y Bi y 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 y = 1:0 to y = 1:2, 1.4, 1.5, 1.6, 1.7, 1.8, and 2.0, respectively (Figure 4(a)). It is noted that the Mg 3+δ Sb 0.5 Bi 1.5 sample has a low electric resistivity that is only half of that of the previously reported Mg 3+δ Sb 1.5 Bi 0.5 because of its high carrier mobility. Furthermore, the room temperature Seebeck coefficient of Mg 3+δ Sb 2-y Bi y (y = 1:0-1:7) 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 y = 1:7 to y = 1:8 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 Mg 3+δ Sb 2-y Bi y (y = 1:0-2:0) calculated from the measured electrical resistivity and Seebeck coefficient. All the as-fabricated Mg 3+δ Sb 2-y Bi y (y = 1:0-2:0) samples, except for Mg 3+δ Bi 2 , 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 Mg 3+δ Sb 0.5 Bi 1.5 , which is 50% larger than that of our previously reported Mg 3+δ Sb 1.5 Bi 0.5 and also 17% larger than a recently reported Bi-rich Mg 3+δ Sb 0.6 Bi 1.4 (~2960 μW m -1 K -2 ) and 26% larger than Mg 3.05 Sb 2-x-y Bi y-x Te x (~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 Mg 3+δ Sb 1.0 Bi 1.0 was very close to the optimized carrier concentration while Mg 3+δ Sb 2-y Bi y (y = 1:2-1:8) would be overdoped. The optimized reduced Fermi energy (E F /k B T) is estimated to be around 0.67, equal to E F = 0:017 eV at room temperature, which corresponds to a Seebeck coefficient of -167 μV K -1 . Figure 4(e) compares the average power factor of Mg 3+δ Sb 2-y Bi y (y = 1:0-2:0) in the temperature range of 50-250°C. All the samples (except y = 2:0) have a value over~3000 μW m -1 K -2 , which is 166% higher than Tamaki's Mg 3+δ Sb 1.5 Bi 0.5 (1130 μW m -1 K -2 ) and also about 16% higher than that of previously reported Mg 3+δ Sb 1.5 Bi 0.5 (2590 μW m -1 K -2 ) [4,18]. This has already surpassed many polycrystalline n-type Bi 2 (Te , Se) 3 , which can be comparable with textured Bi 2 (Te , Se) 3 [41,42] and commercially available Bi 2 (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) [43].  [41].

Results and Discussion
where ΔT is the temperature difference, L is the TE-leg length, and SðTÞ and ρðTÞ are temperature-dependent Seebeck coefficient and electrical resistivity. In the temperature range of 50-250°C, all the samples (except y = 2:0) have an engineering power factor of about 0.6 W m -1 K -1 , which is 100% larger than Tamaki's Mg 3+δ Sb 1.5 Bi 0.5 (0.3 W m -1 K -1 ) and also 20% larger than that of previously reported Mg 3+δ Sb 1.5 Bi 0.5 (0.5 W m -1 K -1 ) [4,18].   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 y value in the formula of Mg 3+δ Sb 2-y Bi y ) 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 (κ ele ) and bipolar part (κ bip ) from the total thermal conductivity (κ tot ), i.e., κ lat = κ tot − κ ele − κ bip (Figure 5(b)). The details of the calculation relative to the electronic thermal conductivity (κ ele ) and bipolar thermal conductivity (κ bip ) are given in SI B. At room temperature, κ lat 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 y = 1:0 to 1.2, 1.4, 1.5, 1.6, 1.7, 1.8, and 2.0, respectively. For comparison, κ lat of Mg 3 Sb 2 and Mg 3 Sb 1.5 Bi 0.5 from our previous work are estimated to be 1.46 W m -1 K -2 and 0.73 W m -1 K -2 [4]. κ lat of Mg 3+δ Sb 1.0 Bi 1.0 is 48% lower than that of Mg 3 Sb 2 and 12% lower than that of Mg 3 Bi 2 . 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 Mg 3+δ Sb 2-y Bi y (y = 1:0-2:0). Mg 3+δ Sb 1.0 Bi 1.0 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 Mg 3+δ Sb 1.5 Bi 0.5 (ZT @RT = 0:2) and 20% higher than that of our previously reported Mg 3+δ Sb 1.5 Bi 0.5 (ZT @RT = 0:62), as shown in Figure 5(c) [4,18]. This is also comparable with recently reported Mg 3.2 Bi 1.998-x Sb x Te 0.002 at room temperature [5] and higher than Mg 3+δ Sb 0.6 Bi 1.4 , which behaves ZT @RT0 :68 and peak ZT of~1.1 [8]. It is comparable with those of commercially available n-type Bi 2 Te 3 ingot (ZT @RT = 0:71) [4]. Moreover, in the temperature range of 50-250°C, Mg 3+δ Sb 1.0 Bi 1.0 has an engineering ZT of 0.56, which is 16.7% higher than our previously reported Mg 3+δ Sb 1.5 Bi 0.5 (ðZTÞ eng = 0:48) and Bi 2 Te 3-x Se x (ðZTÞ eng = 0:47) (data from literatures are plotted on Fig. S7, SI) [4,44]. Furthermore, the thermoelectric properties of three batches of Mg 3+δ Sb 1.0 Bi 1.0 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" [43] are used to select the better thermoelectric materials with a consideration for requirements of efficiency and power density at the same time [45]. Figure 5(d) clearly suggests that Mg 3+δ Sb 1.0 Bi 1.0 in this work surpasses any other Mg 3+δ Sb 2-y Bi y material in this work and the Bi 2 Te 3-x Se x 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.).

Conclusion
We have successfully enhanced the room temperature thermoelectric performance of Mg 3+δ Sb 2-y Bi y 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 Mg 1 3s and Mg 2 3s orbitals and hence the lightening DOS effective mass. Experimentally, our Mg 3+δ Sb 0.5 Bi 1.5 samples reached a high carrier mobility of 247 cm 2 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," Mg 3+δ Sb 1.0 Bi 1.0 would be a promising room temperature thermoelectric material, to replace the classic n-type Bi 2 Te 2.7 Se 0.3 , for its high values of ZT @RT = 0:75, PF @RT = 3100 μW m −1 K −2 at room temperature, ðZTÞ avg = 1:13, and ðPFÞ avg = 3184 μW m −1 K −2 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. Bi y 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 oxygen level < 1 ppm. 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.

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 2:5 mm × 3 mm × 13 mm pieces. Thermal conductivity was calculated by equation κ = DC p ρ, where D is thermal diffusivity measured by laser flash method (LFA 467; Netzsch) using about 6 mm × 6 mm × 1 mm pieces, d is density measured by the Archimedean method, and specific heat (C p ) is tested by differential scanning calorimetry (Discovery DSC, Waters LLC), shown in Fig. S9  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 K α radiation (λ = 1:54 Å, operating at 40 kV/15 mA with K β foil filter). XRD patterns were further refined by the Rietveld method to calculate lattice parameter and Mg 1 -Mg 2 distance.

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 [52]. Projected augmented wave (PAW) potentials [53] with plane-wave basis set and an energy cutoff of 550 eV are used. The valence electronic configurations for Mg, Sb, and Bi are 3s 2 , 5s 2 5p 3 , and 6s 2 6p 3 in the pseudopotentials, respectively. For integrations over the Brillouin zone, we use 5 × 5 × 3 Monkhorst-Pack k-point mesh [54] for 40-atom cells (2 × 2 × 2). 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 [55] and direct energy comparison.