Nano- and Microstructure Engineering: An Effective Method for

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Nano- and microstructure engineering: an effective method for creating high efficiency magnesium silicide based thermoelectrics Nader Farahi, Sagar Prabhudev, Gianluigi A. Botton, James R. Salvador, and Holger Kleinke ACS Appl. Mater. Interfaces, Just Accepted Manuscript • DOI: 10.1021/acsami.6b12297 • Publication Date (Web): 24 Nov 2016 Downloaded from http://pubs.acs.org on November 25, 2016

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ACS Applied Materials & Interfaces

ACS Applied Materials and Interfaces

Nano- and microstructure engineering: an effective method for creating high efficiency magnesium silicide based thermoelectrics

Nader Farahi,a Sagar Prabhudev,b Gianluigi A. Botton,b James R. Salvador,c Holger Kleinke* a a

Department of Chemistry and Waterloo Institute for Nanotechnology, University of Waterloo,

Waterloo, ON, Canada N2L 3G1 b

Materials Science and Engineering Department, McMaster University, Hamilton, ON, Canada

L8S 4L8 c

General Motors Research & Development Center, Warren, MI, USA 48154

ABSTRACT: Considering the effect of CO2 emission together with the depletion of fossil fuel resources on future generations, industries in particular the transportation sector are in deep need of a viable solution to follow the environmental regulation to limit the CO2 emission. Thermoelectrics may be a practical choice for recovering the waste heat, provided their conversion energy can be improved. Here, the high temperature thermoelectric properties of high purity Bi doped Mg2(Si,Sn) are presented. The samples Mg2Si1–x–ySnxBiy with x(Sn) ≥ 0.6 and y(Bi) ≥ 0.03 exhibited electrical conductivities and Seebeck coefficients of approximately 1000 Ω–1cm–1 and -200 µV K–1 at 773 K, respectively, attributable to a combination of band convergence and microstructure engineering through ball mill processing. In addition to the high electrical conductivity and Seebeck coefficient, the thermal conductivity of the solid solutions 1

ACS Paragon Plus Environment


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reached values below 2.5 W m–1K–1 due to highly efficient phonon scattering from mass fluctuation and grain boundary effects. These properties combine for zT values of 1.4 at 773 K with an average zT of 0.9 between 400 K and 773 K. The transport properties were both highly reproducible across several measurement systems and are stable with thermal cycling.

KEYWORDS:

Magnesium

silicide,

thermoelectric,

high

microstructure

*: Corresponding author contact information: [email protected]

2


efficiency,

nanostructure,

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1. INTRODUCTION With respect to the visible impact of fossil fuel consumption and greenhouse gas emissions on the climate and environment, we are now, more than ever, in critical need of advanced technologies to reduce their effects in the near future.1 The automotive sector, due to its global ubiquity and large fuel energy usage based on the current engines, has a very high potential to benefit from these emerging technologies to improve overall vehicle efficiency. In addition to enhancing the engine efficiency, developing an efficient and cost effective waste energy recovery mechanism seems to be a reasonable way to proceed.2,3 For the recovery of waste heat, thermoelectric (TE) materials were demonstrated to be a reliable and irreplaceable candidate.4 To be suitable for industrial scale applications, the materials need to be relatively cheap, made from elements that are abundant in nature and also non-toxic to meet the environmental regulations. Last but not least, the materials should have sustained high efficiency to enhance energy recovery as much as possible. The efficiency of a TE material depends on the figure of merit, zT, via zT= TS2σ (κe + κl)–1, where T, S, σ, κe and κl represent absolute temperature, Seebeck coefficient, electrical conductivity, electronic and lattice thermal conductivity, respectively. An ideal, practical TE material should exhibit not only low thermal conductivity to maintain the temperature gradient with low heat flux, but also high electrical conductivity and Seebeck coefficient to facilitate charge transport to attain larger power output.5 Aside from its low efficiency, magnesium silicide fulfills almost all the aforementioned criteria for large scale applications. To find the most feasible strategy to improve the efficiency of this material, it is worth understanding the origin of its low efficiency. Mg2Si has a fairly wide band gap of 0.77 eV 6 with a low room temperature intrinsic carrier concentration of 1014 cm–3,6

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which leads to a low electrical conductivity of around 0.001 Ω–1cm–1 at 300 K. The highly ¯

symmetric anti-fluorite cubic structure with Fm3m space group, and also the absence of heavy elements together with the highly covalent bonds facilitates phonon transport, which results in high thermal conductivity of approximately 10 W m–1K–1 at 300 K.7 To increase the carrier concentration, doping with group 15 elements such as phosphorus (P),8 antimony (Sb)9–16 and bismuth (Bi)17–23 which substitute for silicon (Si), act as electron donors and have been shown to be profoundly effective dopants. Among all the dopants substituting at the Si site, Sb and Bi seemed to be the most effective for improving the electrical conductivity through increasing the carrier concentration by six orders of magnitude to > 1020 cm–3 at 300 K.20 As mentioned above, a significant amount of heat is carried through lattice vibrations in Mg2Si materials; therefore to reduce the thermal conductivity the best approach is to focus on reducing the lattice thermal conductivity (κl). Based on the kinetic theory, lattice thermal conductivity can be estimated as κl = 1/3 l ν Cv where l, ν and Cv designate phonon mean free path, phonon group velocity and specific heat at constant volume, respectively.24 Introducing germanium (Ge) or tin (Sn) into the Mg2Si structure has been shown to reduce the both phonon group velocity and mean free path, due to their heavier mass and larger size compare to Si. This alloying drastically reduced the lattice thermal conductivity of Mg2Si from ~ 10 W m–1K–1 to ~ 2.5 W m–1K–1 for Mg2Si0.3Sn0.7.7,12 The localized atomic scale distortion generated by alloying is more effective for scattering short-wavelength phonons. To scatter a broader range of phonons other techniques such as nanostructuring, nanophase inclusion and grain boundary engineering could be combined with alloying to decrease lattice thermal conductivity beyond the alloy limit. For instance, inclusion of multi-walled carbon nanotubes (MWCNT) into Mg2Si0.877Ge0.1Bi0.023 reduced the low temperature (T < 500 K) by 15%,25 while adding SiC had a similar effect, but only minor 4


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changes to the figure of merit.26 It does, however, enhance the mechanical properties of Sbdoped Mg2(Si,Sn).27 Nanostructuring in Si80Ge20 through ball mill processing decreased the thermal conductivity by around 40%

28,29

and Te coated grain boundaries in Bi0.5Sb1.5Te3.0

reduced κl by 50% as compared to the non-coated sample.30 The

best

performing

Mg2.15Si0.28Sn0.71Sb0.006,31

alloys

in

the

Mg2.16(Si0.4Sn0.6)0.97Bi0.03,21

Mg2(Si,Ge,Sn) and

system

include:

Mg2Si0.53Ge0.05Sn0.4Bi0.02,19

all

demonstrating figures of merit between 1.2 and 1.4 near 800 K.32 The Si/Sn ratios of these phases are around the reported miscibility gap in the Mg2Si – Mg2Sn system, which may lead to inhomogeneous products and irreproducibility of properties. Previously, this gap was believed to occur between 0.4 Sn and 0.6 Sn, but it seems to fluctuate based on the synthesis conditions, and is reported to vary between 0.2 Sn and 0.45 Sn.33,34 In an attempt to overcome the potential kinetic barriers to a completely homogenous solid solution in the materials we report here, we utilize a two stage ball milling assisted synthesis method developed to produce Mg2Si1–xSnx solid solutions with stable micro-structure, that are oxide free, within the postulated forbidden composition range. Although the powder X-ray pattern of all samples were single phase solid solutions, the nano-structure and the composition of grain boundaries were examined to shed more light on possible nanoscale inhomogeneities of the composition that is supposed to be in the so-called miscibility gap. Finally, the reliability and the reproducibility of the presented data were assured through consecutive measurements.

2. EXPERIMENTAL SECTION Bismuth doped Mg2Si1–xSnx samples were synthesized by mixing the stoichiometric ratios of elements in an argon filled glove box. Mg chips (99.98%, Sigma Aldrich, 4-30 mesh),

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Si powder (99.9%, Alfa Aesar, -100 mesh), Sn granules (99.9%, Alfa Aesar, ≤ 2 cm) and Bi granules (99.99%, Sigma Aldrich) were used for the synthesis. The elements were put in tantalum crucibles, which were sealed under argon in an arc melter, and then placed into silica tubes that were then flame sealed under vacuum. The charges were heated in a resistance furnace at 923 K for one week and thereafter for 1223 K for another week. The heat treated samples were ground into powders and dry ball milled for two hours under inert atmosphere by using Fritzsch Pulverisette 7 Premium planetary mill. To consolidate the powders to near full density for physical property measurements, an Oxy-Gon hot press was used to densify the mixtures in an 95% Ar - 5% H2 atmosphere at a maximum temperature of 973 K under 56 MPa. The applied pressure was released during cooling, to mitigate stress and strain on the pellets. The pressed pellets were 2 mm thick and 12.7 mm in diameter, and were 98% of the theoretical densities as determined via the Archimedes method. An Inel powder X-ray diffractometer with Cu-Kα radiation and a position sensitive detector was used to examine the purity of the pressed samples; the diffraction patterns (supplementary Figure S1) revealed no traces of MgO, which is a typical side product in Mg2Si based compounds that is challenging to avoid. The four samples with x(Sn) = 0.4, 0.6, 0.665 and 0.67 and y = 0.03 - 0.035 Bi per formula unit were prepared phase-pure within detection limits of the instrument. Thermal diffusivity (α) was measured, between 300 K and 800 K, under flowing argon using the Anter Flashline FL3000 thermal properties analyzer. The diffusivity values were then multiplied by the density (ߩ) of the pellets, and the specific heat (Cp) of the compounds, as calculated from the Dulong-Petit approximation, to obtain thermal conductivity (κ), κ = α ߩ Cp. The validity of using the Dulong-Petit approximation for the high temperature (above 400 K)

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specific heat of Mg2Si based materials was examined previously,22,35 and it was established to be a reliable approximation for the thermal conductivity calculation in this class of materials. For measuring the electrical conductivity (σ) and Seebeck coefficient (S), the consolidated pellets used in the thermal diffusivity measurements were subsequently cut into rectangular bars with the dimensions of roughly 12 × 2 × 2 mm. The measurements were performed under a helium atmosphere between 300 K and 800 K by using the ULVAC-RIKO ZEM-3 apparatus. To confirm the results, a second set of measurements was performed using a Linseis LRS-3 system. Estimated experimental errors are 3% for the Seebeck coefficient, and 5% both for the electrical and thermal conductivity, which results in an error of about 10% for the figure-of-merit.36 Hall effect measurements and four probe resistivity measurements were made with a cryostat equipped with a 5.0 Tesla magnet and a Linear Research AC resistance bridge. Hall data was collected with both a positive and negative field (-3 to +3 Tesla) to account for probe misalignment. Estimated errors are again 5% for the conductivity, and 3% for the carrier concentration, corresponding to an error of 6% for the mobility. To investigate the homogeneity of the samples at the micron scale, scanning electron microscopic (SEM) analysis was performed on consolidated piecess using a Zeiss ULTRA electron microscope equipped with an EDAX Pegasus 1200E. The transmission electron microscopy (TEM) sample was prepared by focussed ion beam (FIB) using a Zeiss NVision 40 instrument. A FIB liftout was prepared and milled to a final thickness of ~ 20 nm. The sample was cleaned from hydrocarbon using a hydrogen-oxygen plasma for 2 minutes (Gatan Solarus plasma cleaner). The sample was imaged in a FEI Titan 80 - 300 cubed microscope, equipped with a CEOS image and probe corrector. The point resolution of the microscope is < 0.1 nm for

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TEM and STEM mode. High angle annular dark field (HAADF) micrographs were taken in order to show the atomic structure of the sample in different crystal orientations. Additionally ine scans were taken perpendicular to the grain boundaries using an Oxford INCA x-sight spectrometer.

3. RESULTS AND DISCUSSION The scanning electron microscopy mapping of the samples (Figure 1) exhibits a high level of homogeneity at the micron level, which is attributable to the ball milling of the materials prior to consolidation.

Figure 1 here

The composition of the analyzed area is fairly close to the nominal composition with a slight discrepancy in silicon and tin, which could be the result of a Si rich region somewhere else in these samples, as commonly observed in Mg2(Si,Sn) solid solutions:19,34 the analysis of Mg2Si0.3Sn0.665Bi0.035 (corresponding to 66.7 : 10.0 : 22.2 : 1.2 atomic-%) resulted in at-% of Mg : Si : Sn : Bi of 66.8 : 8.2 : 23.7 : 1.3, and the one of Mg2Si0.365Sn0.6Bi0.035 (66.7 : 12.2 : 20.0: 1.2 atomic-%) yielded 67.3 : 10.4 : 20.9 : 1.3. The line scan on the low-magnification STEM imaging of the grain boundaries as shown in Figure 2 unveils the segregation of larger elements such as Sn and Bi around the edges of the grains. Since there is a greater opportunity for lattice distortions at the grain boundaries, these regions are a preferred location for the larger elements.

Figure 2 here

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The electrical conductivity of all samples is shown in Figure 3. Although the values of the electrical conductivity above 500 K are relatively close for all samples, the two samples with 0.035 Bi have higher conductivity at room temperature, compared to the two samples with 0.03 Bi. Among the two samples with 0.035 Bi, the one with more Sn exhibits higher conductivity in part due to band convergence, which is also true for the samples with 0.03 Bi. While the latter differences may be insignificant, larger Bi amounts should lead to higher carrier concentration, and thusly higher conductivity. Of these four samples then, Mg2Si0.3Sn0.665Bi0.035 has the highest conductivity with σ = 2400 Ω–1cm–1 at 320 K, compared to 1950 Ω–1cm–1 for Mg2Si0.57Sn0.4Bi0.03. With experimental errors of 5% (120 Ω–1cm–1 and 100 Ω–1cm–1, respectively), the differences are significant at 320 K, but within error at the highest temperature measured (see error bars in Figure 3). The former sample exhibits higher σ than the known high performance materials in this family, led by Mg2.16(Si0.4Sn0.6)0.97Bi0.03 with 1970 Ω–1cm–1 at 320 K, which was prepared by a solid state reaction, followed by spark-plasma-sintering, and ultimately exhibited a zTmax (800 K) = 1.4.21

Figure 3 here

Hall effect measurements (Figure 4) find a temperature independent carrier concentration n of the order of 3 × 1020 cm–3 for both Mg2Si0.57Sn0.4Bi0.03 and Mg2Si0.3Sn0.665Bi0.035, slightly higher than the n = 2.4 × 1020 cm–3 determined for Mg2.16(Si0.4Sn0.6)0.97Bi0.03. The Hall coefficient was negative (indicative of negative charge carriers) for all samples over the entire temperature range investigated. 9



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Figure 4 here

All the samples show a decrease in electrical conductivity with increasing temperature mainly due to the reduction in mobility (Figure 5), which is caused by acoustic phonon scattering of charge carriers. The Mg2Si0.3Sn0.665Bi0.035 sample exhibits a mobility of around 50 cm2V–1s–1 at 300 K, which is within error (±3 cm2V–1s–1) equal to the 45 cm2V–1s–1 reported for Mg2.24Si0.45Sn0.537Sb0.013

and

the

48

cm2V–1s–1

for

the

high

performance

material

Mg2.2Si0.49Sn0.5Sb0.01 obtained by Liu et al., with a zTmax of 1.25 at 800 K.37,38

Figure 5 here

Figure 6 demonstrates the Seebeck coefficient of all samples. The consistently negative values are indicative of electrons being predominant charge carriers, as expected based on Bi doping for Si and is consistent with the observed sign of the Hall coefficient. This figure illustrates the importance of Sn content on the magnitude of the Seebeck coefficient in Mg2(Si,Sn) solid solutions: the Seebeck value of the sample with the lowest Sn content of 0.4 is 90 µV K–1 at 320 K, compared to ∼ -120 µV K–1 for the samples with 0.60 to 0.67 Sn content at the same temperature, and this difference persists throughout the entire temperature range. With an error of ±3 µV K–1, these differences are significant. The Seebeck value of Mg2Si0.365Sn0.6Bi0.035 (S = -120 µV K–1 at 320 K) is similar to the value achieved for Mg2.2Si0.49Sn0.5Sb0.01, which in turn is higher than the -85 µV K–1 measured for Mg2.24Si0.45Sn0.537Sb0.013 despite the higher dopant concentration, and within error of ±3 µV K–1 10


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equal to S = -125 µV K–1 at 320 K reported for Mg2.16(Si0.4Sn0.6)0.97Bi0.03.21,37,38

Figure 6 here

The influence of Sn content on the Seebeck coefficient can be explained by band structure tuning that is introduced by its incorporation. The conduction band minimum (CBM) around the Γ point, in Mg2Si1–xSnx consists either of a heavy or a light band, depending on the amount of Sn (x). These two bands have the same energetic minima at a certain Sn level (0.625 ≤ x ≤ 0.7),31,39 which then simultaneously causes an equalization of the Si and Sn character of the CBM and the effective mass to reach its maximum value (m* ≈ 2.5 me), therefore leading to an enhanced Seebeck coeficient.39 The degeneracy of CBM was suggested to be facilitated through the hybridization of 4d states of Sn with 3s states of Mg in the conduction band. The combination of band convergence and micro structure engineering manifests itself in the Mg2Si0.3Sn0.665Bi0.035 sample, which not only demonstrates the highest Seebeck effect but also has the highest carrier concentration, mobility and electrical conductivity among the samples investigated. As a result, the sample exhibits the highest power factor (supplementary Figure S2) of P.F. = S2σ = 44 µW cm–1K–2 at 676 K. The other two samples with 0.6 - 0.67 Sn have basically equivalent Seebeck values, and only slightly lower electrical conductivity as above mentioned, ultimately providing three quite comparable materials with respect to their electrical performance: their P.F. values range from 39 µW cm–1K–2 to 43 µW cm–1K–2 at 773 K, which is within the experimental error of 7% (≈ ±3 µW cm–1K–2), while Mg2Si0.57Sn0.4Bi0.03 has only P.F. = 33 µW cm–1K–2. Figure 7 exhibits the thermal conductivity of all solid solutions, which decreases with increasing temperature. Comparing the thermal conductivity of pure Mg2Si and Mg2Sn to the 11



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values presented here (κ ≈ 3 W m–1K–1 at 320 K), it is indisputable that the solid solution reduces the thermal conductivity by a large factor. Generally, the thermal energy in a semiconductor can be transferred by both charge carriers and acoustic phonons. Since reducing the charge carrier concentration directly affects the electrical conductivity, the focus to decrease the thermal conductivity is mainly to reduce the acoustic phonon propagation.

Figure 7 here

The lattice thermal conductivity, κl, of all solid solutions (Figure 8) was obtained from the thermal conductivity, κ, by deducting the electronic part of the thermal conductivity (Figure S3), κe, which was calculated by applying the Wiedemann-Franz law, κe = LσT. The procedure for calculating the temperature dependence Lorenz numbers, L (Figure S4), from the Seebeck coefficient40 was discussed in detail in our previous study.25 Considering the lattice as a springmass system and the phonon as lattice vibration, the vibration can be disturbed whenever there is an inhomogeneity in mass or spring constant (chemical bond) of the lattice.24,41 Adding Sn and Bi can have the following effects on the thermal conductivity of Mg2Si: First, adding Sn atoms, which are four times heavier than Si, introduces mass fluctuation that can disrupt the pathway of phonon transport. Normally, the minimum of lattice thermal conductivity is expected to be at the highest distortion, i.e. at x(Sn) = 0.5. According to Tan et al.,39 at a Sn content of 0.625 Sn the lattice thermal conductivity will be minimized, due to the intense mass fluctuation, defect scattering and increase in average mass compared to the 1 : 1 ratio of Si/Sn. The lowest calculated lattice thermal conductivity (0.625 Sn) was reported to be κl = 1.62 W m–1K–1 at 300 K, comparable with the 1.57 W m–1K–1 at 320 K achieved by Liu after

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spark-plasma-sintering for the Mg2.16(Si0.4Sn0.6)0.97Bi0.03 sample,21 and our value of 1.39 W m– 1

K–1 for Mg2Si0.365Sn0.6Bi0.035 at 320 K (Figure S5). Considering experimental errors of 10%, i.e.

± 1.5 W m–1K–1, all these values are equal within error. The low κl values observed here may, in part, be caused by enhanced grain boundary scattering from the microstructure, which is imparted by the ball milling assisted synthesis. Second, the modulus of elasticity decreases from around 111 GPa for Mg2Si to 62 GPa for Mg2Sn, which lower the phonon group velocity.35 The weaker bonds manifest themselves in a 220 K lower melting point of Mg2Sn in comparison with Mg2Si. The larger molar weight results in the reduction of the specific heat from 0.90 J g–1K–1 for Mg2Si to 0.44 J g–1K–1 for Mg2Sn,42,43 which is partially offset by the increase in density. Finally, the anharmonic thermal motion of atoms,44,45 the lattice strain 46,47 and the increased number of grain boundaries through ball milling could potentially scatter phonons to further reduce the lattice thermal conductivity.

Figure 8 here

The thermoelectric figure of merit zT in the range of 300 K to 800 K is shown in Figure 9. For all samples, zT increases with increasing temperature, culminating in zT values between 1.3 and 1.4 (± 0.1) at 773 K for the three samples with 0.6 to 0.67 Sn per formula unit, while the sample with 0.4 Sn falls behind with its maximum zT = 1.1. These values are consistent with the best performing Mg2SixSn1-x alloys, prepared by spark-plasma-sintering, and are dramatically higher than the values reported for the doped Mg2Si1–xGex, Mg2Si, Mg2Ge and Mg2Sn nanocomposites.

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Figure 9 here

One of the pivotal issues in reporting the high efficiency thermoelectric properties is the reproducibility and reliability of the measured data. To address this issue, the power factor of the best sample was determined twice (Figure S6); it remains well within the estimated experimental error, which confirms the stability of the samples in the designated temperature range and the reproducibility of the transport properties. The reproducibility and stability of the Mg2Si0.57Sn0.4Bi0.03 sample with its zTmax = 1.1, which is supposed to be in the miscibility gap, is shown by comparing the transport properties measured at General Motors with the Linseis LSR device (Figure S7); as anticipated the values are easily within experimental error, which proves the ball milling assisted synthesis as a potent method to eliminate the kinetic barriers to form a phase that was thought to be thermodynamically unstable.

4. CONCLUSIONS The Mg2Si1–x–ySnxBiy samples were synthesized using solid state reaction and ball mill assisted hot pressing synthesis. Although all the samples showed high homogeneity from grain to grain, some heavy element (Sn, Bi) segregation near the grain boundaries was observed on the nanoscale. The Mg2Si0.3Sn0.665Bi0.035 sample exhibited very high electrical conductivity (2400 Ω– 1

cm–1), Seebeck coefficient (-120 µV K–1), mobility (50 cm2V–1s–1) and carrier concentration (~3

× 1020 cm–3), which can be understood as the manifestation of band convergence resulting in an increase in the density of states effective mass to a value of m* ≈ 2.5 me, which is significantly higher than that of the pure Mg2Si (1.1 me) and Mg2Sn (1.2 me) compounds. The thermal conductivity of the solid solutions started around a low value of 3 W m–1K–1,

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and decreased through the whole temperature range reaching a minimum below 2.5 W m–1K–1 at 773 K. This could be due to the combination of alloying, grain boundaries segregation together with micro-nano structuring through ball milling. All in all, Mg2Si0.3Sn0.665Bi0.035 showed a reliable and reproducible figure of merit zT of 1.4 at 773 K, which makes it a prominent candidate for advanced waste heat recovery applications. Aside from Mg2Si0.57Sn0.4Bi0.03 sample, all other samples demonstrated a very high zT close to 1.4 at 773 K which makes our synthesis procedure a very promising approach for large scale industrial synthesis that can tolerate a certain fluctuation of the Si/Sn ratio and the Bi content while still producing a high performance material. It is also noted that zT was still increasing at 773 K, and the zT = 1.4 reported for Mg2Si0.53Ge0.05Sn0.4Bi0.02 was obtained at 800 K, and the materials introduced here lack Ge which will reduce materials cost. Compared to other high performing Mg2Si variants, additional advantages lie in the avoidance of toxic antimony and spark-plasma-sintering, which would be difficult to use for large samples as required by industry. To even further enhance the figure of merit, it could be worthwhile to investigate the effects of in-situ and ex-situ nano-inclusions on thermoelectric properties of these solid solutions.

Acknowledgments The authors would like to thank A. Korinek for performing STEM and EDX work, the Natural Sciences and Engineering Research Council of Canada (NSERC), AUTO21 (Network Centres of Excellence), General Motors and Dana Corporation for financial support of this work. The STEM and EDX work was carried out at the Canadian Centre for Electron Microscopy, a national facility supported by the Canada Foundation for Innovation, NSERC and McMaster University.

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Supporting Information Powder X-ray diffraction patterns of Bi doped Mg2Si1–xSnx samples. Brillouin zone for FCC lattice and CBM movement with respect to tin concentration. Power factor of all solid solutions. Calculated Lorenz numbers between 300 K and 800 K. Electronic thermal conductivity of all samples. Lattice thermal conductivity of all samples with respect to Sn content. Power factor of Mg2Si0.3Sn0.665Bi0.035 sample for two consecutive measurements. Electrical conductivity and Seebeck coefficient of Mg2Si0.57Sn0.4Bi0.03 measured at University of Waterloo and General Motors laboratory to examine the consistency of the data.

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Figure captions Figure 1. SEM / EDX mapping of Mg2Si0.3Sn0.665Bi0.035 and Mg2Si0.365Sn0.6Bi0.035 samples. Figure 2. Low-magnification STEM imaging with the EDX line scans along the grain boundaries, revealing the segregation of Bi (green line) and Sn (red line) near the grain boundary. Figure 3. Electrical conductivity of the Mg2Si1–x–ySnxBiy solid solutions. Figure 4. Carrier concentration of Mg2Si0.3Sn0.665Bi0.035 and Mg2Si0.57Sn0.4Bi0.03. Figure 5. Carrier mobility of Mg2Si0.3Sn0.665Bi0.035 and Mg2Si0.57Sn0.4Bi0.03. Figure 6. Seebeck coefficient of the Mg2Si1–x–ySnxBiy solid solutions. Figure 7. Thermal conductivity of the Mg2Si1–x–ySnxBiy solid solutions. Figure 8. Lattice thermal conductivity of the Mg2Si1–x–ySnxBiy solid solutions extracted by utilizing Wiedemann-Franz law. Figure 9. Dimensionless figure of merit of the Mg2Si1–x–ySnxBiy solid solutions.

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Figure 1. SEM / EDX mapping of Mg2Si0.3Sn0.665Bi0.035 and Mg2Si0.365Sn0.6Bi0.035 samples.

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Figure 2. Low-magnification STEM imaging with the EDX line scans along the grain boundaries, revealing the segregation of Bi (green line) and Sn (red line) near the grain boundary.

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Figure 3. Electrical conductivity of the Mg2Si1–x–ySnxBiy solid solutions.

Figure 4. Carrier concentration of Mg2Si0.3Sn0.665Bi0.035 and Mg2Si0.57Sn0.4Bi0.03.

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Figure 5. Carrier mobility of Mg2Si0.3Sn0.665Bi0.035 and Mg2Si0.57Sn0.4Bi0.03.

Figure 6. Seebeck coefficient of the Mg2Si1–x–ySnxBiy solid solutions.

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Figure 7. Thermal conductivity of the Mg2Si1–x–ySnxBiy solid solutions.

Figure 8. Lattice thermal conductivity of the Mg2Si1–x–ySnxBiy solid solutions extracted by utilizing Wiedemann-Franz law. 28


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Figure 9. Dimensionless figure of merit of the Mg2Si1–x–ySnxBiy solid solutions.

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Nano- and Microstructure Engineering: An Effective Method for

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