Enhancing the zT Value of Bi-Doped Mg2Si0.6Sn0.4 Materials

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Enhancing the zT Value of Bi-doped Mg2Si0.6Sn0.4 Materials through Reduction of Bipolar Thermal Conductivity Wenhao Fan, Shaoping Chen, Bo Zeng, Qiang Zhang, Qingsen Meng, Wenxian Wang, and Zuhair A. Munir ACS Appl. Mater. Interfaces, Just Accepted Manuscript • DOI: 10.1021/acsami.7b09125 • Publication Date (Web): 08 Aug 2017 Downloaded from http://pubs.acs.org on August 9, 2017

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ACS Applied Materials & Interfaces

Enhancing the zT Value of Bi-doped Mg2Si0.6Sn0.4 Materials through Reduction of Bipolar Thermal Conductivity Wenhao Fan‡a,b, Shaoping Chen‡*,b,c, Bo Zengb,c, Qiang Zhangb,c, Qingsen Mengb,c, Wenxian Wangb,c and Zuhair A. Munird

a

College of Physics and Optoelectronics, Taiyuan University of Technology, Taiyuan 030024, China.

b

Key Laboratory of Interface Science and Engineering in Advanced Materials, Ministry of Education, Taiyuan University of Technology, Taiyuan 030024, China.

c

College of Material Science and Engineering, Taiyuan University of Technology, Taiyuan 030024, China.

d

Department of Material Science and Engineering, University of California, Davis, CA 95616, USA.

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ABSTRACT：Solid solutions of Mg2Si0.6Sn0.4-xBix with 0 ≤ x ≤ 0.03 were prepared by a one-step synthesis and consolidation method, using MgH2 as a starting material. The thermoelectric properties of these samples were evaluated over the temperature range 300-775 K. Figure of merit, zT, values were determined over this range for all compositions and found to increase with temperature reaching a value of 1.36 at 775 K for samples with x = 0.02. Examination of the components of the total thermal conductivity showed that the bipolar thermal conductivity is suppressed by an increase in the band gap, resulting from solid solution formation, and by low minority carrier mobility. The suppression of the bipolar thermal conductivity is believed to be the consequence of charged grain boundaries.

KEYWORDS: Thermoelectric properties; Mg2Si0.6Sn0.4-xBix; SPB model; Bipolar thermal conductivity; One-step synthesis; Nano structure; Band gap; Charged grain boundaries.

1. INTRODUCTION According to the recent US Energy Information Administration’s International Energy Outlook 2016, the world energy consumption will grow by 48% between 2012 and 2040.1 This projection, coupled with the growing concern about environmental issues, has been a significant driving force behind the current focus on alternative energy sources that are environmentally benign. A promising approach in this regard is the utilization of waste heat. It has been estimated that between 20 and 50% of the energy consumed by the manufacturing industry in the US ends up as waste heat in various forms.2-3 Therefore, a process that utilizes waste heat is expected to 2 ACS Paragon Plus Environment

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contribute significantly to a more efficient use of current fuels and thus would help ameliorate the overall negative environmental impact of the fuels.4 Thermoelectric (TE) materials are semiconductors that can convert electricity into thermal energy for cooling or heating through the Peltier effect, or convert waste heat into electrical energy through the Seebeck effect. For power generation, the maximum efficiency, η, of a TE device is the ratio of the output electrical power, P, to the input thermal power, Q, i.e.,

= =

( )/

( )/

(1)

where, TH and TC are the temperatures of the hot and cold sides of the sample, and TM is the average temperature. The dimensionless product, zT, referred to as the figure of merit, defines the efficiency of the specific TE material. It is, in turn, defined as, zT= α2σT/κ

(2)

where α is the Seebeck coefficient (µV K-1), σ is electrical conductivity (Ω-1 cm-1), κ is the thermal conductivity (W m-1 K-1) and T is the absolute temperature (K). The product α2σ is commonly referred to as the power factor. Higher zT values result from materials with a high electrical conductivity and a low thermal conductivity, as well as a high Seebeck coefficient. For effective waste heat recovery from, for example, vehicle exhaust to increase the mileage to up to 10%, an efficiency of about 10% is needed, with a corresponding average zT value of about 1.25. An efficiency of about 20% is needed for primary power generation, with an average zT value of 1.5 or higher.4 3 ACS Paragon Plus Environment


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The thermal conductivity term in Eq. (2) contains the lattice thermal conductivity, κl,

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the

electronic conductivity, κe, and the bipolar thermal conductivity κb. Thus κ = κl + κe + κb. Because the bipolar conductivity involves the diffusion of an electron and a hole independently down a temperature gradient (carrying no net charge),5 its increase is detrimental to the zT value. Thus any effort to decrease the value of the bipolar contribution to the thermal conductivity would lead to an increase in the zT value. Magnesium silicide, Mg2Si, and its solid solutions exhibit promising mid-temperature range TE properties. These materials have the added advantage of being made from non-toxic and naturally abundant constituent elements.6-12 They have been reported to have zT values greater than unity, comparing favorably with values of classic TE materials.13-15 For example, in the case of Mg2Si1-xSnx, a combination of both solid solution formation and a decrease in grain size leads to high zT values. These favorable values are the consequence of a lower lattice thermal conductivity, κl. This, in turn, is due to an increase in phonon scattering caused by structural disorder due to alloying, fine grain size,16-17 and the degeneracy of the conduction band that leads to an increase in α2σ by adjusting the Mg2Sn content of the Mg2SixSn1-x materials.10, 14, 18 The formation of MgO during the processing of Mg2Si-based materials is detrimental to their TE performance. Suppression of the formation of MgO has been successfully accomplished by new approaches such as the use of the B2O3 flux method19 or the use of MgH2 as a starting material in a one-step processing method.20-21 In the latter case, pure, nano-structured Mg2Si was formed. 4 ACS Paragon Plus Environment

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In recent work,22-24 however, the bipolar thermal conductivity was not fully separated from the lattice thermal conductivity. To separate the bipolar conductivity from the lattice conductivity a linear fitting of the total thermal conductivity, minus the electric conductivity term κe, is performed as a T-1 relationship. At the intermediate temperature range, the bipolar term is negligible and the lattice conductivity has a T-1 dependence. Thus by extrapolating to high temperatures the bipolar contribution can be determined.25-26 The contribution of the bipolar thermal conductivity can be significant. For example, an analysis of the data for Mg2SnxSi1-x alloys18 by a multi-parabolic band Boltzmann transport model showed that the bipolar thermal conductivity was as high as 1.0 W m-1 K-1 at 800 K.26 As pointed out above, the suppression of the bipolar thermal conductivity enhances the zT value of Mg2Si-based materials at elevated temperatures.27 The bipolar thermal conductivity is defined as diffusion of an electron and a hole independently down a temperature gradient, carrying no net charge. As it is not subject to the Wiedemann-Franz law, it impairs zT value dramatically.28-30 It can be expressed as,

κb =

σ n，σ p （α p − α n）2T σn +σ p

(3)

Where σi and αi (subscript i = n, p) are the partial electrical conductivities and Seebeck coefficients of electrons and holes, respectively.5, 31 These partial properties can be calculated by separating the transport components occurring in the conduction band and the valence band using the Boltzmann transport calculation. Near the intrinsic regime, Eq. (3) is approximated by, 5 ACS Paragon Plus Environment


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κ b ∝ exp(−

Eg 2k BT

)

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(4)

Where Eg is the band gap, and kB is the Boltzmann constant. Thus the bipolar thermal conductivity increases exponentially with increasing temperature at a given doping density, and the smaller the band gap, the larger the bipolar thermal conductivity.32 For a heavily doped semiconductor, the single parabolic band (SPB) model can be utilized to analyze the transport properties of TE materials.33 In the SPB model, the Seebeck coefficient of each carrier (hole or electron) can be written as

αi = ±

kB (λ + 5 / 2) Fλ +3/ 2 (ξi ) [ξi − i ] e (λi + 3 / 2) Fλ +1/ 2 (ξi )

(5)

where kB is the Boltzmann constant, e the free electron charge, ξ the reduced Fermi energy (=Ef/kbT), λ the carrier scattering parameter, and Fx the Fermi integral of the order of x.33 For acoustic phonon scattering (λ = -1/2), κb can be expressed as,

κ b =（

E σ nσ p k 2 F (ξ ) 2 F (ξ ) ） ( B ) 2 [ g + 1 n + 1 p ]2 σ n + σ p e k BT F0 (ξ n ) F0 (ξ p )

As the variation of the term [

Eg k BT

+

(6)

2 F1 (ξ n ) 2 F1 (ξ p ) + ] with ξn or ξp is rather negligible at a F0 (ξ n ) F0 (ξ p )

fixed temperature,34 Eq. (6) can be approximated by,

1/ kb (T ) ∝1/ σn (T ) +1/ σ p (T )

(7)

According to Eq. (7), for a heavily doped semiconductor (n >> p or p >> n), κb is primarily determined by the partial electronic conductivity of the minority carrier. Based on the partial electronic conductivity of the minority carrier and band gap consideration, we synthesized 6 ACS Paragon Plus Environment

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Mg2Si0.6Sn0.4-xBix (0 ≤ x ≤ 0.03) solid solution thermoelectric materials utilizing the field-activated and pressure assisted synthesis (FAPAS) method.35 2. EXPERIMENTAL MATERIALS AND METHODS Powders of MgH2 (-325 mesh, 98% pure, Alfa Aesar, Shanghai), Si (-200 mesh, 99.99% pure, Aladdin, Shanghai), Sn（-325 mesh, 99.8% pure, Alfa Aesar, Shanghai), Bi (-200 mesh, 99.99% pure, Aladdin, Shanghai) were used as the starting materials to prepare Mg2Si0.4Sn0.4-xBix (0 ≤ x ≤ 0.03) solid solutions. All raw materials and processes were handled in an argon-filled glove box. The Si and Bi powders were initially ball-milled for 8 h with 15 min intervals in a high-speed vibration ball-mill (QM-3B, Nanjing Nanda Instrument Factory) to obtain a grain size of less than 100 nm, as determined by scanning electron microscopy (SEM, TESCAN MIRA3 LMH/LMU). The ball-to-powder mass ratio and revolution speed were 10:1 and 1200 rpm, respectively. Then this mixture and powders of MgH2 and Sn were weighed in the prescribed molar ratios, and ball-milled for another 30 min (at 15 min intervals) with a ball-to-powder mass ratio of 4:1 and 1200 rpm. This procedure was done to ensure that the components are well mixed. The powder mixture was then placed inside a 20-mm diameter graphite die with two 19.8 mm diameter graphite plungers. The entire assembly was introduced into the FAPAS apparatus for sintering. Details of the apparatus have been provided in an earlier publication.35 The one-step synthesis of Mg2Si0.6Sn0.4-xBix（(0 ≤ x ≤ 0.03) implies the formation of the solid solution and its densification taking place simultaneously, according to the following steps. The sample was 7 ACS Paragon Plus Environment


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heated to 510 K within 20 min and then held at this temperature for another 20 min (stage 1 in Figure 1), to allow the tin to melt and wet the other powders. Then the temperature was increased to 773 K and held there for another 25 min (stage 2 in Figure 1). During this stage, MgH2, silicon, and tin reacted thoroughly. This was accompanied by an increase in gas pressure in the vacuum system to as high as 30 Pa due to hydrogen evolution. When the pressure decreased to 10 Pa and remained at this value for another 5 min, the heating unit attached to the inner walls of the chamber was turned off and the current was applied to the die to heat the sample to 1023 K in 15 min, and held at that temperature for 15 min (stage 3 in Figure 1). A uniaxial pressure of 60 MPa was applied during this period. A vacuum of less than 10 Pa was maintained throughout the process. The resulting samples, which were discs with a diameter of 20 mm and thickness of 3 mm, were sealed in a vacuum quartz tube and annealed for another 12 h at 673 K. The pellets were then cut into appropriate sizes for thermal and electrical transport property measurements. The process of formation and densification of the samples, through the three stages mentioned above, is shown in Figure 1. In this figure, the solid line and the dashed line represent the temperature and the uniaxial pressure changes, respectively.


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Figure 1. The changes with time of the temperature and uniaxial pressure in the synthesis of Mg2Si0.6Sn0.4-xBix (0 ≤ x ≤ 0.03) thermoelectric materials. The solid line represents temperature and the dashed line represents pressure.

After polishing, the samples were analyzed by X-ray diffraction (Philips X'Pert MPD diffract meter) at 45 kV and 40 mA, to determine the composition and purity of the products. Rietveld analysis was also performed using Philips X'part plus software. A Zeiss 1550 VP scanning electron microscope was used to determine the phase purity and microstructure on fracture surfaces of the consolidated samples. For measuring the thermoelectric properties, the electronic conductivity and Hall coefficient were determined using a 4-point probe by the Van der Pauw technique with a 0.8 T field under high vacuum.36 The Seebeck coefficient was also measured using a light-pipe method with tungsten–niobium thermocouples under high vacuum.37 The thermal conductivity was calculated by κ =DρCp, where D is the measured thermal diffusivity (NETSCH LFA457), ρ is the measured density by the Archimedes method, and Cp is the 9 ACS Paragon Plus Environment


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Dulong-Petit heat capacity, 0.56 J g-1 K-1. This value is in agreement with measured values (0.55-0.60 J g-1 K-1) reported by Gao et al. for Mg2.08Si0.4Sn0.6 for the temperature range 300-800 K, respectively.38 The lattice component plus the bipolar thermal conductivity, κL + κb, of the total thermal conductivity was obtained by subtracting the electronic component, κe (κe = LσT). The Lorenz number, L, calculated as a function of temperature using the SPB model,39 is 1.54×10-8 W Ω K-2. 3. RESULTS AND DISCUSSION:


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Figure 2. Properties of Mg2Si0.6Sn0.4-xBix solid solutions: (a) X-ray diffraction patterns; (b)

Grain orientation image; (c) Grain size distribution histogram; and (d) SEM image of a

fracture surface. Arrow points to region with nano-particles.

Figure 2 (a) shows the XRD patterns of Mg2Si0.6Sn0.4-xBix sintered samples with different Bi contents, 0 ≤ x ≤ 0.03. An important result from these patterns is the absence of peaks corresponding to MgO (its major peak at 2θ ≈ 43°), indicating that the employed synthesis process, using MgH2 as a starting material, suppressed the formation of this oxide. This is a clear advantage over methods in which Mg is used in elemental form. The main diffraction peaks of the patterns of Figure 2 (a) can be indexed to an anti-fluorite type structure (space group, F m 3 m ), and all the peak positions of the solid solutions are located between the peaks of pure Mg2Si and Mg2Sn (also provided in the figure), indicating that pure Mg2Si0.6Sn0.4-xBix solid solutions were synthesized. Figures 2 (b) and 2 (c) show, respectively, the orientation image microscopy (OIM) and the grain diameter distribution from the electron back-scattered diffraction (EBSD) of Mg2Si0.6Sn0.4 after consolidation. The microstructure appears to be very dense and the grain size is less than 10 µm. The total number of grains in Figure 2 (c) is more than 11×103, of which more than 80% has a grain size smaller than 3µm. Figure 2 (d) shows an SEM image of a fracture surface of the sample. The image reveals a dense texture with a typical fine cleavage step pattern, in which nano-particles can be seen at grain boundaries (inside rectangle indicated by arrow). Nano-sized 11 ACS Paragon Plus Environment


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particles are believed to decrease the lattice thermal conductivity by increasing phonon scattering.40-41 A similar surface structure has been reported for Bi-doped Mg2Si.42

Figure 3. (a) The temperature dependence of zT of Mg2Si0.6Sn0.4-xBix (0 ≤ x ≤ 0.03) solid solutions and selected maximum zT values from the literature; (b) The zT value vs. Hall carrier concentration for Mg2Si0.6Sn0.4-xBix (0 ≤ x ≤ 0.03) at 450, 550, and 775 K. The curves were calculated by the SPB model, and the symbols are experimental data.

The temperature dependence of the calculated zT values is shown in Figure 3 (a). For comparison, the highest zT values obtained in other investigations15-17 on Mg2Si1-xSnx-based samples are also included in this figure. The maximum zT obtained in this work is 1.36 at 775 K for Mg2Si0.6Sn0.38Bi0.02 synthesized by our one-step method. The highest zT value from the work of Liu, et al.15 is ~1.4 at ~775K for Mg2.16(Si0.4Sn0.6)0.97Bi0.03 obtained by a two-step synthesis process. Also shown in Figure 3 (a) are results from the work of Zhang et al.17 The highest zT value, ~1.2 at ~550 K, was obtained for melt-spinning formed Mg2(Si0.4Sn0.6)Bi0.03. In this 12 ACS Paragon Plus Environment

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referenced work, the zT values decreased at higher temperatures, being about 0.7 at 775K. In contrast, the zT value for Mg2Si0.6Sn0.38Bi0.02 obtained in this study continued to have an upward trend at the highest temperature, 775 K. As the minority carriers have no significant influence on electron transport, as will be discussed later, the theoretical curves of zT value dependence on Hall carrier concentration calculated by the SPB model, is shown in Figure 3(b) for three selected temperatures. Also included in this figure are experimental values from this work at the selected temperatures. In general, the experimental values are consistent with the calculated curves. The maximum zT value and the corresponding optimum carrier density increase with temperature. At 775 K the optimized zT value is near n ~1.24×1020 cm-3, which is consistent with values reported in the literature.15-17



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Figure 4. The temperature dependence of: (a) the Seebeck coefficient, (b) the electrical conductivity, (c) the Hall carrier concentration, and (d) the Hall mobility.

The temperature dependence of the Seebeck coefficient of samples made in this study is shown in Figure 4 (a). The seebeck coefficient values increased monotonously with temperature, indicating that the minority carrier has no significant effect on electron transport in the extrinsic regime.43 However, the existence of minority carriers can still be inferred by the change in slope with temperature of both the carrier concentration and the Seebeck coefficient, as shown in Figure 4 (c). As the temperature increased beyond about 550K, the carrier concentration increased slowly, and the slope of Seebeck coefficient curves decreased, implying that the excitation of minority carriers plays a role in the change of properties. The Seebeck coefficient can be expressed as,

α=

σ eαe + σ hαh αe µen + αh µh p = σe +σh µen + µh p

(8),


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where, αp is the positive Seebeck coefficient, αn is the negative Seebeck coefficient, σe is the electron conductivity, σp is the hole conductivity, n is the electron concentration, p is the hole concentration, µn is the electron mobility, and µp is the hole mobility.43 As Eq. (8) indicates, α is a combination of the negative Seebeck coefficient, αn, and the positive Seebeck coefficient, αp, weighted by the electron mobility, µn, electron concentration n, hole mobility µp, and the hole concentration p. As seen from the trend of the Seebeck coefficient with temperature, Figure 4 (a), the minority carrier has very small impact on this coefficient, thus the concentration or the mobility of the minority carrier would be limiting. As Figure 4 (b) shows, the electrical conductivity of each sample in this work increased with temperature up to about 475 K, and then decreased as temperature increased beyond this value. This behavior is believed the consequence of different scattering mechanism on mobility at different temperature regimes. This is different from reported observations for the Bi-doped bulk Mg2Si1-xSnx in the literature.10,

44

However, an increase in electrical conductivity at low

temperatures has also been reported previously.13,

20, 42

The genesis of the increase is the

relatively high resistivity of the prepared samples which is the consequence of the high grain boundary density and the presence of nano-particles at grain boundaries. A similar observation was reported for nano-composites and attributed to higher density of grain boundaries.13 Since the carrier concentration is relatively flat with T in this region (300-500K), Figure 4 (c), the incease in conductivity is believed to be due to an increase in mobility. The mobility of 15 ACS Paragon Plus Environment


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samples in this work has been analyzed, Figure 4 (d).

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The carrier mobility of Mg2Si0.6Sn0.4Bi0.1

is proportional to T below 475 K while that of Mg2Si0.6Sn0.4Bi0.2 and Mg2Si0.6Sn0.4Bi0.3 is proportional to T3/2, which indicates that ion scattering is the dominant mechanism.39 Based on the SPB model, only effective mass m* and carrier concentration n are the basic parameters of Seebeck coefficient, so the change in mobility does not have an obvious effect on it. On the basis of the above observations, it can be stated that the minority carrier has a small influence on the electron transport at high temperatures. Thus the SPB model can be used to analyze the thermoelectric transport properties of these samples.39

Figure 5. Temperature dependence of: (a) The thermal conductivity; (b) Lattice plus bipolar thermal conductivity of Mg2Si0.6Sn0.4-xBix

Figure 5 (a) shows the temperature dependence of the thermal conductivity of the samples synthesized in this study. With the exception of values at T < 600K for melt-spinning formed samples,17 the values obtained in this study are lower than those obtained in previous 16 ACS Paragon Plus Environment

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investigations,15-17 including those indicated as nano-structured Mg2Si1-xSnx.17 Figure 5 (b) shows the dependence on temperature of the sum of the lattice thermal conductivity and the bipolar thermal conductivity of our samples and corresponding results from previous studies.15-17 The minimum theoretical lattice thermal conductivity, κl,min, of the Mg2Si0.6Sn0.38Bi0.02 is calculated by, 1

κ L , min =

1 π 3 ( ) k BV 2 6

−

3 2

( 2ν T + ν L )

(9),

Where V, νT, and νL are the average volume per atom, the transverse speed of sound, and longitudinal speed of sound, respectively.39 The lattice parameters, which were used to calculate the average volume per atom, were obtained from XRD results using the Rietveld analysis. The values of νT and νL of this sample are 3630 and 5920 m s-1, respectively, as obtained from ultrasonic measurement carried out in this study. The calculated value of κl,min is shown in Figure 5 (b). As can be seen from Figure 5 (b), the values of κl + κb for the samples of this work approached κl,min as the temperature is increased. For the sample with x = 0.01 (blue curve in Figure 5 (b), the minimum is reached at about 550K. For the sample with x = 0.02, the sample with the highest zT value, the curve approaches κl,min at about 675K. The continued decrease of κl + κb with temperature with no upward tendency at high temperatures indicates that the bipolar thermal conductivity has been suppressed.



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According to Eqs. (4) and (7), the minority carrier effective mass and its mobility as well as Eg will have a strong influence on κb. The band gap Eg of Mg2Si1-xSnx solid solution can be calculated by,

EgAB = xEgA + (1 − x)EgB

（10）

where EgAB is the band gap of the solid solution of A and B, EgA the band gap of solid A, and EgB the band gap of solid B. As the band gap of Mg2Sn (0.36 eV) is smaller than that of Mg2Si (0.7 1eV), the band gap of Mg2Si1-xSnx decreased with an increase in the value of x.45-46 Thus the band gap of Mg2Si0.6Sn0.4 is larger than that of Mg2Si0.4Sn0.6, and therefore, the bipolar thermal conductivity of Mg2Si0.6Sn0.4 is expected to be easier to suppress at higher temperatures. In comparison with Mg2Si0.6Sn0.4 synthesized by other methods,16 κb of Mg2Si0.6Sn0.4 synthesized in this work is smaller. As these samples have the same molecular structure and doping element, their band structure and effective mass of minority carrier are expected to be similar. The suppression of κb in our samples is believed to be the consequence of the reduction of the minority carrier mobility. Due to its preferential residence at grain boundaries, the concentration of Bi dopant is higher than that in grains.20 In this work, fine grain size leads to high density of grain boundaries with positively charged impurity of Bi dopant as donor like defects, which limits the mobility of holes by selective scattering based on Coulomb barriers. 47 Meanwhile, the high density grain boundary scatters more low energy electrons due to interface barrier, which contributes mainly to the temperature dependence of mobility, T3/2 below 475 K. 4. CONCLUSION 18 ACS Paragon Plus Environment

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Employing a one-step synthesis and consolidation method, solid solutions of Mg2Si0.6Sn0.4-xBix with 0 ≤ x ≤ 0.03 were prepared using MgH2 as a starting material. Thermoelectric characterizations of these samples were made over the temperature range 300-775 K. The zT values for all compositions increased with increasing temperature reaching a high value of 1.36 at 775 K for samples with x = 0.02. The results also indicate a continuing upward trend for zT with T for this composition. Analysis of the components of the total thermal conductivity indicated a suppression of the bipolar thermal conductivity by an increase in the band gap, through alloying, and by a limitation of mobility of the minority carriers. The sum of the lattice and bipolar thermal conductivities, κl + κb, approached the minimum, κl,min, as T increased. The suppression of the bipolar thermal conductivity is believed to be the consequence of charged grain boundaries containing Bi.

Corresponding Author

*E-mail: [email protected].

ORCID

Shaoping Chen: 0000-0002-6315-140X

Author Contributions

‡Wenhao Fan and Shaoping Chen contributed equally to this work.

Notes



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The authors declare no competing financial interest.

ACKNOWLEDGEMENTS:

The authors would like to thank Prof. G. Jeffery Snyder and his group from Northwestern University for the measurement and analysis of properties. We gratefully acknowledge the financial support from the National Science Foundation of China through Grant No. 51101111 and 51405328, Shanxi Province Science Foundation through Grant No. 201601D011033. Shanxi Scholarship Council of China No. 2017-050 and 2017-028

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Table of contents:


Enhancing the zT Value of Bi-Doped Mg2Si0.6Sn0.4 Materials

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