Functionally Graded (PbTe)1–x(SnTe)x Thermoelectrics - Chemistry of

Article Cite This: Chem. Mater. 2018, 30, 280−287

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Functionally Graded (PbTe)1−x(SnTe)x Thermoelectrics Ellen M. J. Hedegaard, Aref A. H. Mamakhel, Hazel Reardon, and B. B. Iversen* Center for Materials Crystallography, Department of Chemistry and iNANO, Aarhus University, Langelandsgade 140, Aarhus 8000, Denmark S Supporting Information *

ABSTRACT: Functionally graded (PbTe)1−x(SnTe)x ingots have been prepared by Bridgman crystal growth method for the first time. From SEM-EDX, the composition (x) of the ingot was found to increase smoothly from 10.6 to 25.4 along the direction of the growth. The gradual change in composition is shown to cause a decrease in band gap as crystallization proceeds, and to be accompanied by a change in carrier concentration. By a Potential-Seebeck microprobe (PSM), a smoothly varying Seebeck coefficient was measured along the growth direction of the sample at room temperature. High-temperature properties relevant for thermoelectric performance were measured and used to evaluate the potential of this system as a functionally graded high-temperature thermoelectric material. This study provides insight into understanding the complicated interplays of advanced crystal growth and physical properties, going beyond standard thermoelectric sample preparation approaches.

1. INTRODUCTION

Thermoelectricity is the direct interconversion between thermal and electrical energy through a semiconductor, and offers the opportunity to exploit waste heat in a variety of contexts, including industrial effluent pipelines and vehicle exhausts. To date, thermoelectric materials have been most effectively employed in radioisotope thermoelectric generators (RTGs) for reliable power generation on space exploration missions, including the Cassini (20y) and Voyager (40y) NASA missions. However, thermoelectrics for terrestrial use have been primarily hindered by the need for higher efficiencies over a specific temperature range, and as such have not yet had their major breakthrough, in spite of intense research into many thermoelectric material classes, including silicides,9,10 halfHeuslers,11,12 clathrates,13,14 selenides,15−17 antimonides,18−20 and tellurides (e.g., of Pb and Ge)21,22 in recent years. The efficiency of a thermoelectric material can be estimated from its dimensionless Figure of Merit, zT:23,24

Functionally graded materials (FGMs) exhibit a spatial property distribution along one or more directions, which is related to modifications in composition or structure.1 The grading of properties can generally be achieved by either interconnecting/growth of layers of functional materials, or continuously grading the composition throughout one material. The FGM approach to materials was pioneered by Japanese aerospace scientists in the mid 1980s,2 but has been fruitful in a diverse range of applications, from ceramics used in the defense industry,3 to biomedical composite materials, e.g., for orthopedic prostheses and implants.4 Functionally graded material design allows incorporation (or a combination) of fascinating properties such as shape memory to allow recovery from deformation,5 enhanced robustness/hardness,6 and tuning of electrical properties of advanced energy materials, e.g., semiconductors and cathode materials for fuel cells,7,8 to name but a few. Here, we will explore functionally graded thermoelectric materials, with the aim of highlighting a rapid and facile method for screening, optimizing, and understanding thermoelectric performance by functionally grading a combination of two well-known high-performance thermoelectric systems. First, a short introduction to explain the main drivers for functional grading in thermoelectrics will be given. © 2017 American Chemical Society

zT =

α 2σ T κ

(1)

Received: October 25, 2017 Revised: November 23, 2017 Published: November 28, 2017 280

DOI: 10.1021/acs.chemmater.7b04473 Chem. Mater. 2018, 30, 280−287

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Chemistry of Materials where α is the Seebeck coefficient, σ is the electrical conductivity, κ is the thermal conductivity, and T is the absolute temperature. The maximum zT of a homogeneous material is obtained in a narrow temperature interval. Consequently, a single thermoelectric material exhibits optimal performance only within a specific, typically narrow operating temperature range.25 Segmented modules have recently been investigated to exploit this, in which multiple materials are electrically connected in one leg to exploit the optimum operating capability of more than one material over a specific operational temperature interval.26 For the exploitation of the temperature gradients present in real-life applications more effectively, however, it has long been suggested to employ continuously graded FGMs. This was initially based on theoretical observations that described optimization of the peak zT position along the length of a material as a function of composition or carrier concentration.25,27 As illustrated by the “nkbT”-rule, samples with higher band gaps will generally exhibit optimal performance at higher temperature.28 This originates from the fact that the higher band gap will shift the temperature at which the onset of bipolar carrier behavior reduces the thermoelectric performance of the material. A sample graded in composition should therefore have a band gap gradient orientated in such a way that the higher band gap is positioned at the highest temperature. Similarly increasing the carrier concentration will cause the zT peak to shift to higher temperatures.2 We have previously presented a proof-of-principle FGM study, based on Czochralski pulled Ge1−xSix samples.29 This work demonstrated that simultaneous grading in the band gap and the carrier concentration can be obtained in a one-step directional crystal growth procedure. Herein we explore the Bridgman method, as a more user-friendly alternative to the Czochralski method, for preparation of uniaxial graded thermoelectric materials. Directional solidification by the Bridgman method has proven successful in functional grading of thermoelectrics containing Bi2Te3.30 Kuznetsov et al. demonstrated that the optimum conversion efficiency of a thermocouple comprising FGM (p-type) and segmented (ntype) materials extended over the 223−423 K range, with total efficiencies exceeding that of nongraded/segmented couples (10% versus 8.8%). Their pioneering work on FGM thermoelectrics highlighted the significant opportunities in this approach for broadening the temperature range over which a material can operate efficiently. PbTe based materials have been among the most studied and used thermoelectric systems for decades,31 and are found in the majority of the extraterrestrial RTG modules mentioned previously. Findings that the full potential of PbTe-based generators is higher than so far assumed have in recent years again increased research efforts into this material.31−33 Several factors contribute to the remarkable thermoelectric properties of PbTe: the most important being the low thermal conductivity, and the high electrical valley degeneracy. A range of approaches have been used to influence these properties, including nanostructuring, (co)doping, and alloying to achieve both high-performance p- and n-type PbTe materials.34,35 Of particular note in the recent literature is the Na-doped (PbTe)1−x(PbS)x systems proposed by the group of Kanatzidis, where a zT of ≥2.0 above 800 K was reported.36,37 Thus, on the basis of the tunable nature of PbTe, we have selected this material as the cornerstone of this FGM study.

The low thermal conductivity of PbTe, possessing a seemingly simple NaCl-type cubic structure (space group Fm3̅m),38 has been studied fervently. On the basis of investigations by several different techniques it has been concluded that this phenomenon is likely the result from high disorder on the cation (Pb2+) site.39−41 Other studies suggest a strong anharmonic contribution to the thermal motion of Pb.42,43 Furthermore, it has been shown by several authors that the thermal conductivity of PbTe in an application can be even further reduced through scattering phonons at several length scales, from atomic to micrometer sized, by combinations of disorder over several orders of magnitude.44,45 The high valley degeneracy originating from the convergence of two valence bands located at the L and Σ points is another important factor in the high thermoelectric performance of PbTe and related materials.46,47 The convergence of these bands may be engineered by doping toward the heavier, lower Σ band.48 Further improvements of the electronic contribution to the thermoelectric performance have been achieved through an increase in the Seebeck coefficient by increasing the density of states in the proximity of the Fermi level by Tl doping.49 The positive coefficient in band gap furthermore aids in suppressing the onset of bipolar conduction.47,50 PbTe systems typically operate at much lower temperatures than the GeSi-based thermoelectrics we have studied previously;23 efficiency optimization through grading would broaden the scope of applications that may exploit thermoelectric technology. For the grading of PbTe through composition grading by directional solidification, a suitable PbTe-based system was carefully selected, namely, the pseudobinary PbTe−SnTe system.51,52 There are a number of advantages in using SnTe-based thermoelectrics. First, they are lead free, thereby reducing the amount of toxic elements needed.53 The high similarity between PbTe and SnTe is desirable since most technologies available for PbTe thermoelectric energy conversion should be easily adapted to SnTe.54 As for PbTe the thermal conductivity in SnTe is found to be reduced by disorder on the cation site;55 however, in contrast to PbTe, the thermoelectric performance of SnTe has been found enhanced by doping toward the light L band.56 As shown in Figure 1a, combination of these two binary compounds results in a fully miscible solid solution over the entire composition range. Directional crystal growth, such as Bridgman growth,57 performed at an intermediate composition in this system will have an increasing concentration of SnTe as crystallization proceeds.51 It has previously been reported that, because of the proximity of the liquidus and solidus, no noteworthy grading is found.58 However, this could be due to the pulling rate dependency of segregation effects in combination with the high pulling rates of the Czochralski synthesis performed.51 Compositional segmentation has previously been applied for PbTe by powder processing methods, both by alloying with SnTe and by sintering with, e.g., Bi2Te3.59−61 To the best of our knowledge, no reports have yet been made on compositional grading via one-step directional growth, highlighting the novelty of this study. Figure 1 also shows that the band gap varies smoothly across the entire composition range in the PbTe−SnTe system, emphasizing this as a well-judged system for this study.62 For a balance of the band gap development with both composition and temperature, a composition in the PbTe-rich part of the phase diagram is preferred to ensure an enhancement of the thermoelectric properties. 281

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of 1.97−1.99 mm/h at 850−985 °C. The surfaces of the resulting samples were polished to allow for characterization along the growth direction of the samples. Each sample was then cut into discs perpendicular to the pulling direction. An overview of these discs is provided in Table 1.

Table 1. Pelletsa Cut from the As-Grown Samples pellet name

distance to tip (mm)/thickness of pellet (mm)

PbTe_16

Pure PbTe 16.3/3.1

PbTe_26

25.7/2.9

SnTe_13

Pure SnTe 13.3/2.3

composition from SEM-EDX (mol %) Pb: Te: Pb: Te:

50.3(2) 49.7(2) 50.5(1) 49.5(1)

Sn: 49.0(4) Te: 51.0(4) SnTe_21 20.6/2.4 Sn: 48.91(7) Te: 51.09(7) SnTe_29 29.3/2.2 Sn: 49.0(3) Te: 51.0(3) Graded with Overall Composition (PbTe)0.85(SnTe)0.15 Graded_15 15.3/2.0 Sn: 5.74(4) Pb: 44.8(1) Te: 49.5(1) Graded_23 23.3/2.1 Sn: 6.7(3) Pb: 43.4(7) Te: 49.8(4) Graded_33 33.0/3.1 Sn: 8.0(3) Pb: 42.3(2) Te: 49.7(1)

Figure 1. (a) Phase diagram and (b) band gap across the composition in the pseudobinary PbTe−SnTe system. The broken line in part a marks the overall composition of the prepared sample. Band gaps as functions of composition and temperature are calculated on the basis of Fano.62 The phase diagram is digitally reproduced from Kattner et al.52 Insert: zoom-in of part b incorporating band gap values found by the Arrhenius method for three positions along the graded sample produced in this work. a

Each pellet is named according to the overall composition and the distance to the tip of the sample.

In recent years, it has been shown that a complicated defect structure greatly influences the thermoelectric properties of PbTe−SnTe-based materials, although this is not yet fully understood.40,41 Therefore, the prospect of preparing samples graded with respect to band gap is strongly influenced by the potential grading in carrier concentration, and a thorough investigation is needed to evaluate the potential of FGMs in the PbTe−SnTe system. Bridgman crystal growth is ideally suited for investigating gradient effects in the PbTe−SnTe system, as it has been shown that milling or grinding of these materials may introduce defects through strain-induced compensation.63 Samples prepared directly from the melt by the Bridgman method will not have this further complication when tailoring the properties as this avoids powder metallurgical processing. Founded on the reasoning given above, this study aims to shed light on how optimization of thermoelectric performance in the PbTe−SnTe system can be achieved across a temperature range through a systematic compositional grading study.

2.2. Experimental Methods. X-ray diffraction (XRD) data were collected in the 10° ≤ 2θ ≤ 130° range using a Rigaku Smartlab diffractometer equipped with a Cu Kα source and monochromator (λ = 0.154 056 nm) in Bragg−Brentano optics geometry. Sample compositions throughout the samples were characterized by scanning electron microscopy energy-dispersive X-ray spectroscopy (SEMEDX) on a Nova NanoSEM instrument equipped with an EDAX detector. For each position along the samples, data were measured at three points, and these were averaged to give the composition for the given position. The standard deviation from the averaging was used as the measurement error. Spatially resolved room-temperature Seebeck coefficients were determined both along the entire length and on radial surfaces perpendicular to the growth direction by PSM. Grid point spacings of 0.080 and 0.100 mm were employed. Hall carrier concentrations and resistivities were measured between room temperature and 100 °C on a bespoke setup described by Borup et al. based on the Van der Pauw (VdP) method.65 Furthermore, resistivities and Seebeck coefficients were measured for selected samples between room temperature and 350 °C in steps of 25 °C using a ZEM-3 by ULVAC technologies.

2. EXPERIMENTAL SECTION

3. RESULTS AND DISCUSSION 3.1. XRD. Prior to high-temperature property characterization, XRD data were collected from the surface of the pellets. Data are presented in the Supporting Information along with extracted unit cell parameters. All of the reflections in the diffraction patterns can be assigned to the expected NaCl-type cubic structure (space group Fm3̅m). The influence from defects greatly reduces what further information should be extracted from the XRD data. It has been shown that the

2.1. Sample Preparation. For synthesis of PbTe and SnTe as starting materials, Pb (99.999%), Sn (99.999%), and Te (99.9999%) were mixed in 1:1 stoichiometric ratios and prereacted in evacuated quartz ampules using horizontal tube furnaces. The homogeneity of both materials was checked by a Potential Seebeck microprobe (PSM, Panco Gmbh).64 The prepared PbTe and SnTe were then mixed to give an overall composition of (PbTe)0.85(SnTe)0.15 and packed into an evacuated quartz ampule with a narrow neck approximately 2 cm from the tip. Reference samples of pure PbTe and SnTe were packed in the same way. Bridgman syntheses were performed at pulling rates 282

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precision of the data is within 0.5 mol %; however, the accuracy is not expected to be better than 1 mol %. It is seen that both of the pure end components (i.e., PbTe and SnTe) show a reasonably stable composition along the entire length of the sample, whereas a clear composition gradient is seen for the sample of intermediate composition. For the pure PbTe sample a slight discrepancy is seen in the composition at approximately 25 mm from the tip. From Figure 4, this feature corresponds with the position of a surface change in the Seebeck coefficient map, and it is therefore assessed to be a surface effect only. For the pure SnTe sample, a deviation of approximately 1 mol % from the expected 50 mol % is seen for both Sn and Te. This corresponds well with the high tendency of SnTe to form Sn vacancies.41 For the sample of intermediate composition, the concentration of SnTe increases as the crystallization proceeds, as was expected from the phase diagram. The part of the sample closest to the onset of crystallization was found to contain 5.3(3) mol % Sn which then systematically increases to 12.7(2) mol % along the length of the sample. Returning to the phase diagram (Figure 1a), the composition at the beginning of the crystallization was expected to be 8.2 mol % SnTe. Thus, the experimentally determined value of 5.3(3) mol % Sn at a position 9 mm from the tip of the sample is in reasonable agreement with expected values. For characterization of the influence of the composition gradient on thermoelectric properties, slices were cut perpendicular to the growth direction at three positions along the sample (marked by open rectangles in Figure 2). Among other properties, these slices have been characterized for resistivity, both in the temperature range 25−100 °C by the VdP method, and by ZEM-3 in the temperature interval 20− 350 °C. From these data the band gaps have been found by the Arrhenius method. Since the temperature dependence of the electrical conductivity in semiconductors is mainly determined by the increase in carrier concentration, by excitation over the band gap, it is given by the Arrhenius equation:

influence of defects on the unit cell parameters in SnTe can be the same as a 10% composition change across the PbTe−SnTe phase diagram.66 Therefore, Vegard’s law behavior cannot be assumed in this system.67 Furthermore, it can be challenging to distinguish Pb and Sn on the same crystallographic site with laboratory PXRD data. Since the diffraction data were collected from the surface of cut pellets, grain orientation may also cause the peak intensities to deviate from the theoretical pattern. 3.2. EDX and Band Gap Characterization. The results of the SEM-EDX analysis are shown in Figure 3. It is seen that the

Figure 2. As-grown graded sample with an overall composition of (PbTe)0.85(SnTe)0.15, with positions for EDX data points (◊) and pellets for high-temperature characterization (open rectangles) marked.

σ = σ0e−Eg /2kBT

(2)

where σ is the electrical conductivity, σ0 is a constant, Eg is the band gap energy, kB is the Boltzmann constant, and T is the temperature. The band gaps are shown in the inset in Figure 1, and corresponding Arrhenius plots are given in the Supporting

Figure 3. Compositions determined by SEM-EDX along the lengths of the pure PbTe and SnTe ingot and the (PbTe)0.85(SnTe)0.15 sample. The shaded areas correspond to the positions of the pellets cut for property characterization.

Figure 4. (a−c) PSM scans along the grown samples. (d−f) Plots showing the same data averaged perpendicular to the pulling direction. 283

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crossover to negative values for the Seebeck coefficients at around 300 °C). A clear shift in the temperature at which the α peak is seen is evident from the data collected on the discs cut from the graded sample: from approximately 215 °C to approximately 250 °C with respect to increasing Sn content. However, the “10kbT” rule states that the α peak position should decrease as band gap decreases, which is the opposite trend to that observed in the data for the graded sample. To understand the shift in α peak temperature with respect to the change in composition, investigation of the charge carrier behavior along the sample was necessary. Figure 6 shows the

Information. Along with the band gaps from the entire measured temperature intervals (20−350 °C for ZEM-3, and 25−100 °C for the VdP measurement), band gaps have also been calculated on the basis of the data from the VdP setup between 30 and 60 °C to minimize effects from the change of band gap with temperature. It is seen from the figure that the low-temperature band gaps show a gradient as expected. As the temperature intervals over which the fits have been performed are increased, the band gaps also increase. This is in agreement with band gaps from the literature.62 It is also apparent that as the temperature interval over which the Arrhenius plot is performed is increased, the gradient in band gap is decreased. This originates from the fact that, as a larger temperature interval is probed, the change in band gap from the temperature change exceeds that induced by the composition gradient. 3.3. PSM Scans. Spatially resolved, room-temperature Seebeck coefficients have been measured along the growth direction for all samples (see Figure 4). The data have been averaged perpendicular to the pulling direction to give the development in Seebeck coefficients as crystallization proceeds (Figure 4). The pure end members show constant Seebeck coefficients along the length of the samples except at the very end, where segregation of impurities causes an abrupt change of the Seebeck coefficients. This is in good agreement with the well-known behavior of impurities in directional crystal growth methods.14 The intermediate composition on the other hand shows a very smooth gradient in Seebeck coefficient along the entire length of the sample. This clearly shows that the gradient in composition has resulted in a gradient in the thermoelectric properties. For completeness, the radial homogeneity has also been assessed by radial Seebeck coefficient scans (see the Supporting Information). 3.4. High-Temperature Physical Properties. The Seebeck coefficient, α, has been measured in the 20−350 °C range by ZEM-3, for the three positions along the graded sample as presented in Figure 2 and Table 1. The data are shown in Figure 5 along with the data for the pure end

Figure 6. Hall carrier concentrations for both of the pure end member and the graded sample of overall composition (PbTe)0.85(SnTe)0.15.

carrier concentrations for all discs from Table 1 in the 20−100 °C temperature interval. The carrier concentration is graded along the compositionally graded sample, increasing from 6.328(3) × 1018 to 8.99(2) × 1018 cm−3 as crystallization proceeds. This can be explained by the carrier concentrations of the end members. Inspecting Figure 6, the carrier concentration of the pure SnTe is 2 orders of magnitude greater than that of the pure PbTe, in good agreement with the literature.68 Furthermore, the pure SnTe sample shows a more significant shift of carrier concentration along the sample than the pure PbTe sample. This agrees well with the known tendency of SnTe to have a high concentration of Sn vacancies.41 Figure 5 also shows that the higher tendency of SnTe (compared to PbTe) to form defects causes the carrier concentration of the graded sample to increase as the concentration of SnTe increases. Since higher carrier concentrations are generally known to shift the peak position of the Seebeck coefficient to higher temperatures through a shift in the onset of bipolar carrier behavior,25 this explains the behavior observed in Figure 5. These results highlight that the gradient in carrier concentration has such a strong influence over the gradient in properties that it will dominate over the influence from the band gap. The Seebeck coefficient is inversely dependent on carrier concentration, and the observed gradient in carrier concentrations therefore fits very well with the observed gradient in room-temperature Seebeck coefficients along the sample (Figure 4). The high-temperature resistivity data are shown in Figure 7. Again, the difference between the end members is dominated by the different temperatures at which bipolar behavior sets in. As expected from the carrier concentrations along the graded sample, the resistivity decreases as crystallization proceeds. The resistivity increases with temperature over the entire temper-

Figure 5. Seebeck coefficients for selected positions along the pure end members and the graded sample. The inset shows the peak positions for the Seebeck coefficients for the graded sample of overall composition (PbTe)0.85(SnTe)0.15.

members. The end members show the difference that would be expected between PbTe and SnTe; the latter is known to have the onset of bipolar conduction at a much higher temperature than the former. The SnTe discs show an increasing α over the entire temperature interval. For PbTe, a clear transition to bipolar behavior is seen around 175 °C (with a complete 284

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grading through engineering of these parameters. However, we have shown that an increasing carrier concentration with increasing SnTe concentration is intrinsic to the system. It is therefore suggested that the SnTe-rich part of the phase diagram would be more beneficial toward combining gradients in both band gap and carrier concentration, since the gradient in band gap here is oriented to enhance the inherent gradient in carrier concentrations.

4. CONCLUSIONS In summary, we have shown that a clear gradient in composition, and thereby band gap, can be achieved in the PbTe−SnTe pseudobinary solid solution via a one-step directional solidification. This gradient in composition leads to a gradient in carrier concentration as a consequence of the higher tendency for SnTe to form defects than PbTe. The intrinsic gradients in band gap and carrier concentrations in this study show the significant potential of PbTe−SnTe alloys to be engineered to fit experienced temperature spans in thermoelectric applications through property gradients along one direction. This is especially the case if a dopant can be found that can enhance this behavior. Furthermore, this study highlights the importance of a thorough understanding of the influence of defect structure on thermoelectric properties in the lead and tin chalcogenides. With recent studies showing that SnTe holds a higher potential as a thermoelectric material than so far assumed,70 it may be valuable to investigate combining the increase in carrier concentration with increasing SnTe content, with the correspondingly increasing band gap at the SnTe-rich side of the phase diagram. This study demonstrates that grading through a carrier concentration gradient holds a great and still largely unexploited potential and looks beyond the improvements that can be obtained in homogeneous materials alone.

Figure 7. Resistivities from ZEM-3 for selected positions along the pure end members and the graded sample of overall composition (PbTe)0.85(SnTe)0.15.

ature interval, corresponding to extrinsic semiconductor behavior. 3.5. Power Factor. The power factors were calculated for both the graded samples and the end members on the basis of the data presented in Figures 5 and 7, and are given in Figure 8.

■

Figure 8. Power factors for three positions along the compositional graded sample along with data for the pure end members. The inset shows a zoom-in of the peak positions for the graded sample.

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.chemmater.7b04473.

It is seen that the gradient in properties is only evident as a subtle feature at low temperatures. It can thereby be concluded that even though a clear gradient in band gap, Seebeck coefficients, and carrier concentration is present, the combination only leads to a slight gradient in power factor. Previously, a study on graded quaternary clathrate phases has been published, showing how these present similar effects; a clear gradient in composition is partly counter-acted by a gradient in carrier concentration.69 This demonstrates that the effects of advanced crystal growth are extremely difficult to control or even predict. The data presented here further emphasize an important consideration when synthesizing and reporting on samples grown by, e.g., the Bridgman method. Reporting the nominal stoichiometry as the actual composition when working with phase diagrams such as that of PbTe−SnTe (or other incongruently melting systems) cannot be assumed valid. Unfortunately this is not always a fully appreciated fact.68 We have previously reported the benefits of a combination of gradients in both band gap and carrier concentration for the Ge1−xSix:B system through advanced crystal growth.29 On the basis of the study presented here, the PbTe−SnTe system cannot be ruled out as a candidate for enhanced functionality

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XRD data, PSM scans investigating the radial distributions of Seebeck coefficients, and Arrhenius plots (PDF)

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

B. B. Iversen: 0000-0002-4632-1024 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors thank Christian Zeuthen for fruitful discussions. The work was supported by the Danish National Research Foundation (Center for Materials Crystallography, DNRF93) and Innovation Foundation Denmark (Center for Thermoelectric Energy Conversion). 285

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