Revealing the Defect-Dominated Electron Scattering in Mg3Sb2-Based Thermoelectric Materials

The thermoelectric parameters are essentially governed by electron and phonon transport. Since the carrier scattering mechanism plays a decisive role in electron transport, it is of great significance for the electrical properties of thermoelectric materials. As a typical example, the defect-dominated carrier scattering mechanism can significantly impact the room-temperature electron mobility of n-type Mg3Sb2-based materials. However, the origin of such a defect scattering mechanism is still controversial. Herein, the existence of the Mg vacancies and Mg interstitials has been identified by synchrotron powder X-ray diffraction. The relationship among the point defects, chemical compositions, and synthesis conditions in Mg3Sb2-based materials has been revealed. By further introducing the point defects without affecting the grain size via neutron irradiation, the thermally activated electrical conductivity can be reproduced. Our results demonstrate that the point defects scattering of electrons is important in the n-type Mg3Sb2-based materials.


Introduction
Thermoelectric materials can realize the direct conversion between thermal energy and electricity and vice versa. Solidstate thermoelectric modules have been applied for power generation and electronic refrigeration [1][2][3][4]. Thermoelectric performance of a single material is evaluated by the figure of merit zT (zT = S 2 σT/κ), where S is the Seebeck coefficient, σ is the electrical conductivity, κ is the thermal conductivity, and T is the absolute temperature [5,6]. Essentially, the thermoelectric parameters (S, σ, and κ) are governed by the transport of elec-trons and phonons. In polycrystalline materials, the existence of crystal defects, e.g., grain boundaries, dislocations, and point defects, is usually unavoidable. Such defects will distort the perfect crystal structure and scatter electrons and phonons [7]. In other words, the defect-dominated (electron and phonon) scattering mechanism will play a pivotal role in the thermoelectric transport properties. It is well known that phonon scattering by defects is quite notable and can substantially reduce the lattice thermal conductivity [8][9][10][11]. As a result, phonon engineering by introducing defects has been widely adopted to improve the zT of thermoelectric materials [12][13][14][15][16][17][18].
Similarly, the defects can significantly impact electron transport in thermoelectric materials. Usually, grain boundary scattering [19,20], ionized impurity scattering (by charged point defects and ionized impurities) [21], and alloying scattering (by neutral substitutional point defects) [22,23] have been regarded as the important defectdominated scattering mechanisms in thermoelectric materials. However, thermoelectric materials are often synthesized in the thermodynamical nonequilibrium methods (e.g., quenching, arc-melting, and mechanical alloying [24]), which unavoidably lead to the coexistence of a high concentration of various defects. In this scenario, it is extremely difficult to distinguish how a specific type of defect scatters the electrons.
In terms of defect characterizations, information regarding the grain size can be easily obtained by optical and electron microscopy. On the contrary, characterizations of point defects are much more challenging [49,50]. Up to now, only a few experimental studies related to point defects in Mg 3 Sb 2 -based materials have been reported [51,52]. In addition, it is well known that different crystal defects are both sensitive to the preparation temperatures and chemical compositions. Therefore, increasing the sintering temperature or preparing the single crystal at equilibrium condition not only reduces or eliminates the grain boundaries but also unavoidably reduces the concentration of other defects. In other words, due to the difficulty of tuning the defects independently, identifying the defect-dominated electron scattering mechanism is quite challenging.
Herein, we revisit the issue of the electron scattering mechanism in n-type Mg 3 Sb 2 -based materials. By carefully characterizing the microstructures and point defects of the n-type Mg 3 Sb 2 -based samples, our results show that the concentrations of Mg vacancies and Mg interstitials are sensitive to the preparation conditions and chemical compositions. In addition, by intentionally introducing the point defects with-out affecting the grain size via neutron irradiation, we can reproduce the thermal activation of electrical conductivity. Our results demonstrate that point defects play an appreciable role in the electrical properties of Mg 3 Sb 2 -based materials.  Figure 1. Distinct differences in the temperature dependence of electrical conductivity near room temperature can be observed (Figure 1(a)). Mg 3.2 Sb 1.5 Bi 0.49 Te 0.01 that is prepared at 923 K shows thermally activated electrical conductivity below 500 K, inconsistent with the acoustic phonon scattering mechanism, resulting in a lower room-temperature electrical conductivity. In contrast, the room-temperature electrical conductivities of Mg 3.175 Co 0.025 Sb 1.5 Bi 0.49 Te 0.01 and Mg 3.2 Sb 1.5 Bi 0.49 Te 0.01 (prepared at 1073 K) are much higher. According to the Hall measurement, the room-temperature electron concentrations of the three samples are comparable ( Figure S1, Supporting Information). Therefore, the disparity in the temperature dependence of electrical conductivity mainly originates from the difference in electron mobilities, as shown in Figure 1(b). The room-temperature electron mobility is as high as 78 cm 2 V -1 s -1 for Mg 3.175 Co 0.025 Sb 1.5 Bi 0.49 Te 0.01 while it is only~48 cm 2 V -1 s -1 for Mg 3.2 Sb 1.5 Bi 0.49 Te 0.01 (prepared at 923 K). A higher room-temperature electron mobility of 97 cm 2 V -1 s -1 is obtained for Mg 3.2 Sb 1.5 Bi 0.49 Te 0.01 (prepared at 1073 K). In principle, the temperature dependence of electron mobility is mainly determined by the electron scattering mechanism. The distinct discrepancy in the temperature dependences of electron mobility reveals the different electron scattering mechanisms. In addition, a similar Seebeck coefficient is observed for all the samples (Figure 1(c)). As a result, noticeably enhanced roomtemperature power factors have been achieved for Mg 3.175 Co 0.025 Sb 1.5 Bi 0.49 Te 0.01 (~14.8 μW cm -1 K -2 ) and Mg 3.2 Sb 1.5 Bi 0.49 Te 0.01 prepared at 1073 K (~19.1 μW cm -1 K -2 ) compared to that of Mg 3.2 Sb 1.5 Bi 0.49 Te 0.01 prepared at 923 K (~9.8 μW cm -1 K -2 ), as shown Figure 1(d). The results obtained in this work are in good agreement with the previous reports [19,[42][43][44]. In other words, doping Co at the Mg site and increasing the preparation temperature are both effective in improving the room-temperature electrical properties of n-type Mg 3 Sb 2 -based materials.

Grain Size and Elemental Distribution.
Since grain boundary scattering has been proposed as the dominant electron scattering mechanism in the Mg 3 Sb 2 -based materials, quantifying the variations in the grain size of these samples is necessary. Therefore, the electron backscatter diffraction (EBSD) characterization has been performed, and the results are shown in Figure 2 and Figure  and 2(f)). In other words, there is a substantial grain size enhancement when the preparation temperature increases from 923 to 1073 K, and it is in good agreement with the previous reports [19,44]. However, Mg 3.175 Co 0.025 Sb 1.5 Bi 0.49 Te 0.01 has an average grain size of~1.9 μm, which is similar to that of the Mg 3.2 Sb 1.5 Bi 0.49 Te 0.01 (prepared at 923 K), as shown in Figures 2(b) and 2(e). Therefore, Codoping at the Mg site does not change the average grain size, and this is different from the report of Nb-doped Mg 3 Sb 2 [53]. This result is reasonable considering that the doping concentration of Co is relatively low (~0.8 at.%), and the hot-pressing temperature is identical to the prepared Mg 3.2 Sb 1.5 Bi 0.49 Te 0.01 . It was speculated that the transition metal element was preferentially segregated at the grain boundary [19]. In this scenario, the potential barrier of the grain boundary will be reduced, which can alleviate the grain boundary scattering and improve electron mobility [20]. To verify this assumption, detailed elemental distribution near the grain boundary region in the Co-doped Mg 3.2 Sb 1.5 Bi 0.5 is further characterized using transmission electron microscopy (TEM). Figure 3(a) displays a selected area electron diffraction (SAED) pattern of the Co-doped Mg 3 Sb 1.5 Bi 0.5 , and it can be indexed as [100] direction with a hexagonal structure of the P 3m1. A clear grain boundary is identified, as shown in Figure 3(b). The elemental composition mapping by energy dispersive spectroscopy (EDS) has been conducted, and the results are shown in Figure 3(c)-3(f). As can be seen, the Co atoms distribute uniformly in the sample without preferential segregation at the grain boundary ( Figure 3(d)). It should be pointed out that the white nanoparticles in Figure 3(b) are Bi-rich (Figure 3(f)) instead of Co-rich. In addition, energy dispersive spectroscopy mapping inside the grain also shows similar results, i.e., the distribution of the Co atoms within the grain is uniform ( Figure S3, Supporting Information). Our results are different from the report of Nb-doped Mg 3 Sb 2 [53], where Nb impurity phases mainly segregate at the grain boundary. The discrepancy can be partially attributed to the notable difference in the doping concentration, i.e., the doping concentration of Nb is as high as~3.33 at.% while that of Co is only~0.8 at.%. The solubility of the transition metal elements in the Mg 3 Sb 2 -based materials is low, so a high doping concentration results in the formation of the impurity phases. In this case, the transition metal impurity phase will be trapped at the grain boundary. However, it should be pointed out that even when the doping concentration of Co is rather low and Co does not segregate at the grain   i.e., controlling the concentration of Mg vacancies, is critical for determining the conduction type (n-type or p-type) of the Mg 3 Sb 2 -based materials [25,57,58]. In addition to the Mg vacancies, the Mg interstitials [25] and also the defect complex (e.g., Frenkel defect) [51,59] in the Mg 3 Sb 2 -based materials have also been reported. However, it is noted that there are controversies on the existence of the Mg interstitials and defect complex [52,60]. Therefore, experimentally  identifying the point defects in the n-type Mg 3 Sb 2 -based materials is necessary. In our study, the synchrotron powder X-ray diffraction (SPXRD) measurements are conducted, and the Rietveld refinements are shown in Figure 4. Details for the atomic sites and the occupancy of Mg atoms at the Mg (1) site, Mg(2) site, and interstitial site Mg I are shown in Table 1. It can be seen that there are appreciable differences in the Mg atom occupancy among the three samples. For Mg 3.2 Sb 1.5 Bi 0.49 Te 0.01 which is prepared at 923 K, the occupancy of the Mg(1) site is only~0.921, and the interstitial site Mg I exhibits an occupancy of 0.058. It demonstrates the existence of the Mg vacancies and Mg interstitials. In comparison, the occupancy of the Mg (1) (1) site is as high as~0.979, and the interstitial site Mg I exhibits an occupancy of 0.047. In other words, the higher preparation temperature can effectively reduce the Mg vacancies and the Mg interstitials in the Mg 3 Sb 2 -based materials. Usually, the point defects concentration in thermodynamical equilibrium increases with the temperatures. In this work, the Mg 3 Sb 2 -based materials are prepared by mechanical alloying and hot pressing. Due to the high mechanical energy during ball-milling, a high concentration of oversaturated point defects can be produced [61]. These point defects will be suppressed after notable atomic diffusion during hot pressing [62]. In this case, it can explain why a higher preparation temperature will result in a lower concentration of Mg vacancies. Combining the results of electrical transport measurements and point defect characterizations, Mg 3.175 Co 0.025 Sb 1.5 Bi 0.49 Te 0.01 and Mg 3.2 Sb 1.5 Bi 0.49 Te 0.01 (prepared at 1073 K) with reduced concentration of point defects exhibit higher electron mobilities.
It is noted that the single-crystalline Mg 3 Sb 2 (prepared in the Mg-rich condition) also exhibits a very high occupancy of 0.993 at the Mg (1) site, indicating the concentration of Mg vacancy is negligible [51]. In other words, the n-type single-crystalline Mg 3 Sb 2-x Bi x is not only free of grain boundary but is also nearly free of Mg vacancies. This can also explain why the room-temperature electrical conductivity of single crystals is dominated by acoustic phonon scattering [32,47,48]. In addition, the single-crystalline Mg 3 Sb 2 that is prepared in the Mg-poor condition shows p-type conduction [63], indicating the existence of Mg vacancies. Later, characterization of the p-type single crystal shows the Mg interstitials are negligible [52]. The results are reasonable considering the crystal is grown in the Mg-poor condition. Again, these results suggest that the point defects in the Mg 3 Sb 2 -based materials are highly sensitive to the chemical compositions and preparation conditions.

Neutron Irradiation.
The challenge to identifying the electron scattering mechanism of specific defects lies in the difficulty of tuning the defects independently. To tackle this issue, we conducted the neutron irradiation experiment on the ntype Mg 3 Sb 2 -based materials. It is well known that neutron irradiation can introduce point defects (i.e., vacancies and intersti-tials) into the specimen but leave the grain size unaffected [64][65][66]. Since the sample of Mg 3.2 Sb 1.5 Bi 0.49 Te 0.01 (prepared at 1073 K) does not show abnormal temperature-dependent electrical conductivity at room temperature, it is chosen for the neutron irradiation experiment. Detailed information for the neutron irradiation experiment can be found in Methods.
A comparison of the electrical properties of the sample prior to and after the neutron irradiation is shown in Figure 5. The electrical conductivity at 300 K of the pristine sample is~4:6 × 10 4 S m −1 , and it reduces significantly to4 :7 × 10 1 S m −1 (the red symbols) after the neutron irradiation, a reduction as large as three orders of magnitude. The neutron-irradiated sample reproduces the thermal activation of electrical conductivity, which resembles that of the sample prepared at 923 K. Since the Seebeck coefficients are comparable ( Figure S4, Supporting Information), the substantial difference in the electrical conductivities should mainly originate from the disparity in electron mobilities. Usually, it is the point defect that will be produced after the neutron irradiation [64,65,[67][68][69]. However, due to safety concerns for radiation, we are unable to perform detailed microstructural and defect characterizations on the neutronirradiated sample.
It should be pointed out that the electrical conductivity is partially restored after the measurement. The blue symbols represent the measurement of electrical conductivity during the cooling down period, and it is higher than that of the heating up period (the red symbols). This indicates that the concentration of the point defects reduces after the measurement, which has a similar effect as the heating treatment. In fact, the reduction of the concentration of point defects after annealing has also been reported previously [65,67]. A similar effect has also been observed for the neutron-irradiated SiGe [70]. In addition, it should be pointed out that the as-prepared Mg 3 Sb 2based samples also show similar restoration of electrical conductivity during the heat and cooling cycles of the measurements [71]. Again, this indicates that the defects are highly temperature-sensitive.
2.5. Electron Scattering Mechanism. At this stage, however, we do not have more detailed information on the point defects, e.g., whether they are charged or not. Therefore, we cannot conclude how the point defect scatters electrons, i.e., whether it is due to the ionized impurity scattering. In case when the point defects are neutral, their effect on the electron scattering should be ascribed to the distortion of the periodic potential. However, the discussion on this topic will be further complicated by the configuration of point defects in the lattice, i.e., if point defects can be regarded as independent single point defects, or if they form complexes among themselves (e.g., defect pairs or defect clusters) [72,73]. Therefore, identifying how the point defect scatters electrons in the n-type Mg 3 Sb 2 -based materials is a daunting task, and concerted efforts in experiments and theoretical calculations are needed to clarify this point.
We need to point out that our results do not disprove the importance of grain boundary scattering on the electrical properties of n-type Mg 3 Sb 2 -based materials [19,20,44]. Again, the complexity of the electron scattering mechanism 5 Research of defects should be highlighted. On the one hand, there are various types of defects (e.g., grain boundaries, dislocations, and point defects) in the prepared materials, and our understanding of their specific effect on electron transport is still limited. Besides, most of the reported results are based on polycrystalline samples, which contain a high concentration of various defects. In addition, since different research groups adopt different approaches and apparatus to synthesize the samples, the type of defects and concentration of the defects can vary significantly. Then, the discussion on the defectrelated phenomena in one case may not be simply applied to the others. In our case, it is more reasonable to limit the discussion on the electron scattering mechanism to the samples that have been synthesized for this work. Therefore, we cannot disapprove of the electron scattering mechanism by other defects. Discouragingly, does it mean that the electron scattering-related research cannot be reproduced and is meaningless? The answer is no. If we can conduct experiments on high-quality samples (e.g., single crystals) by intentionally introducing only one type of defect, then we should be able to clarify the electron scattering effect, and the results should be reproducible. To this end, more dedicated efforts in

Conclusion
In summary, the microstructures and defects have been investigated for the n-type Mg 3.2 Sb 1.5 Bi 0.5 , and the relationship between the electrical transport properties and point defects has been revealed. Our results show that Co-doping does not change the grain size of the Mg 3 Sb 2 -based materials, but it can still impact the electron scattering mechanism near room temperature. The synchrotron powder Xray diffraction characterizations show that Co-doping and preparation temperature can both impact the concentration of the point defects (Mg vacancy and Mg interstitial). Combining the electrical properties and the defect characterization, it can be found that samples with lower point defect concentration exhibit higher electron mobility. In addition, neutron irradiation can significantly reduce the electrical conductivity, and it can also reproduce the thermally activated electrical conductivity that resembles that of the sample prepared at 923 K. Therefore, our results show that the point defect plays an appreciable role in the electron scattering mechanism of the n-type Mg 3 Sb 2 -based materials. Since point defects are widely present in various thermoelectric materials, their potential impact on the electron scattering mechanism deserves to be investigated.

Microstructural Characterization.
To analyze the distribution of grain size, electron back-scattering diffraction (EBSD) was performed. Square-shaped samples with a dimension of 4 mm × 4 mm × 2 mm were prepared. The samples were first ground using SiC paper and then polished by glycol-based diamond slurry and finally washed with alcohol and blown dry. After that, ion-polishing was applied to remove the surface stress. To analyze the microstructures of the samples, scanning transmission electron microscopy was performed. Selected area electron diffraction (SAED) and energy dispersive spectroscopy (STEM-EDS) were performed at 200 kV using a double Cs-corrected transmission electron microscope (JEM-ARM 200F).

Synchrotron Powder X-Ray Diffraction (SPXRD)
Characterization. Synchrotron powder X-ray diffraction measurement was performed at the PD beamline at the Australia Synchrotron using the beamline wavelength of 0.59077 Å. All synchrotron powder X-ray diffraction samples were measured in the Debye-Scherrer geometry under transmission mode in 0.7 mm quartz capillaries sealed under an Ar atmosphere. The analyzed 2θ range was from 3 to 50 degrees. The Rietveld method was used to perform refinement, and the Pseudo-Voigt function was used for peak-shape fitting.

Data Availability
Data associated with the current manuscript is available from the authors at reasonable request.

Conflicts of Interest
The authors declare that they have no competing interests.  Figure S1: Carrier concentration of the prepared samples. Figure S2: Grain size information obtained by the electron backscatter diffraction characterization. Figure S3: Energy dispersive mapping characterization. Figure S4: Comparison of the Seebeck coefficient prior to and after the neutron irradiation experiment. (Supplementary Materials)