Powder Diffraction of Thermoelectrical Materials

Powder Diffraction of Thermoelectrical Materials

Abstract

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Termoelectrical (TE) materials are important for alternative technologies because it can transfer waste heat to electricity directly. As a result, material scientists have done a lot of research for the n-type and p-type TE materials to generate TE devices. The main factor to influence the efficiency of the TE devices is the figure of merit (ZT) which is affected by the Seebeck coefficient (S), electrical conductivity (), and the thermal conductivity (). The crystal structure of materials which could be analyzed by powder diffraction also relates to the ZT value. In order to comprehend the powder diffraction of TE materials, this review article will present the background of TE material and analyze the powder diffraction of three-type TE materials, including Bismuth Chalcogenides, Layered SnSe, and Half-Heusler MgAgSb.

Introduction

Thermoelectrical (TE) materials have ability to convert waste heat to electricity directly, which causes they play an important role in alternative energy technologies to decrease our demand for fossil fuels around the world. Therefore, TE materials have been researched for a few past decades because of its high performance for power generation and electronic refrigeration.¹ From past to now, the main topic of the research about TE materials is to enhance the converted efficiency for waste heat, so material scientists are keep designing new high-efficiency TE materials, especially in solid-state crystal chemistry. Material chemists have found several bulk materials for TE application such as skutterudites, clathrates, half-Heusler alloys, and complex chalcogenides in the research of high-temperature bulk materials.¹ These materials have complex crystal structure and good TE properties.¹ In order to confirm the crystal structure of these TE materials, chemists usually employ powder diffraction to analyze the products, which includes X-ray, neutron, or electron diffraction. In which, the most common analytical method is X-ray diffraction (XRD) because of its low cost and convenient. Thus, the research about TE materials usually accompanies with XRD to know the polycrystal structure. To understand the powder diffraction of TE materials, the literature review will demonstrate the background information of TE materials, the recent researches about TE materials, and comparison of different TE materials’ crystal structure by their powder diffraction analysis.

Thermoelectrical Materials

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TE devices could convert waste heat to useful power, so they are important for alternative energy technologies. There are two types TE Modules, Power-Generation Mode and Refrigeration Mode, which are composed by both n-type and p-type TE materials. Moreover, in order to achieve high-efficiency TE materials, the figure of merit (ZT) should be as high as possible. The following sections will introduce two types TE modules, discuss the basic concept of ZT, and compare ZT of TE materials in current research.

TE Modules. TE materials could be categorized to two types, n-type and p-type. N-type TE materials could provide negative thermopower and be electron carriers; in contrast, p-type TE materials could offer positive thermopower and be hole carriers.¹ We can quickly realize this concept through Bi₂Te₃ alloy system, [(Bi_1-xSb_x)₂(Te_1-xSe_x)₃].¹ For example, Bi₂(Te_0.8Se_0.2)₃ is n-type semiconductor, and (Bi_0.2Sb_0.8)₂Te₃ is p-type semiconductor in this system.² The n-type and p-type semiconductor are determined by the majority and minority of hole diffusion and electron diffusion. In the n-type semiconductor of Bi₂(Te_0.8Se_0.2)₃, the majority is the electron diffusion, in which the electron diffusion form Te and Se sites to Bi site. In contrast, the majority is hole diffusion in p-type semiconductor. N-type and p-type are both used to build two TE Modules, including Power-Generation Mode and Refrigeration Mode. (Fig. 1) In the power-generation mode, a temperature gradient is imposed to the device, which produces a voltage to drive a current pass through a load resistance or device.¹ Therefore, the heat could be converted to electricity directly. This phenomenon is also called “Seebeck Effect”.¹ On the other hand, the refrigeration mode is using a providing current to generate a temperature gradient.¹ The heat is absorbed in the cold side and transferred by TE materials.¹ When the heat pass through the heat-rejection sink, it will be rejected so that the TE device show a refrigeration capability.¹ The phenomenon is also defined as “Peltier Effect”.¹ All in all, TE applications have two modules, Power-Generation Mode and Refrigeration Mode, which are both operated by n-type and p-type TE materials. Therefore, material chemists should design suitable n-type and p-type TE materials to make high-performance TE devices, which is related to a factor, the Figure of Merit (ZT).

The Figure of Merit (ZT). The potential materials for TE application are determined by the figure of merit (ZT) of the materials, which is influenced by the Seebeck coefficient (S), electrical conductivity (), and the total thermal conductivity (,  = _L+_E, the lattice and electronic contributions, respectively).¹ The formula of ZT is shown in the following:

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ZT=S2σTκ=S2Tρκ

Where  is the electrical resistivity, and S² (or S²/) is the power factor as a function of carrier concentration (n) which is usually optimized by narrow-bandgap semiconductor.¹ The Fig. 2 shows the relationship of ZT and the efficiency of TE devices in the different temperature, which indicated the higher ZT could get higher efficiency to convert waste heat. For example, we have the TE device efficiency of 30% at ZT=10 in 300K (Room Temperature).³ As a result, in order to achieve high-efficiency TE applications, scientists should design TE materials that have high ZT as well as possible. However, it is difficult to design a high-ZT TE material because S and  are in inverse proportion through the various n. The Fig. 3 is illustrated the relationship between ZT and its related factors. We can see that high S is dropping down through the decreasing n, but  is increasing through the increasing n. Thus, scientist should find the proper carrier concentration range (10¹⁹~10²⁰ carriers/cm³) to make the maximum S² by balancing S and .⁴ Because of the difficulty for balancing S and , the best TE materials recently that are applied in TE applications have ZT1¹, which has the TE device efficiency of about 10 % (Fig. 2). Therefore, the recent research should focus on increasing the ZT of TE materials to achieve higher efficiency TE applications.

In a TE applications, we have both n-type and p-type TE materials, so the ZT for a single material is meaningless.¹ The Fig. 4 is shown the ZT of n-type and p-type materials through the changed temperature.  In the low temperature (from 200 to 400 K), bismuth telluride (Bi₂Te₃) is preferred TE material.⁵ Nevertheless, lead telluride (PbTe) is recommended to use in the temperature between 600 and 800 K.⁵ At the high temperature (from 800 to 1300 K), silicon germanium would be chosen. These three TE materials all have ZT around 1 in the different range of temperatures.⁵ Moreover, alloys, especially with AgSbTe₂, have shown the ZT >1 for both n-type and p-type materials in the mid-temperature range (from 600 to 800 K).² For instance, AgSbTe₂-GeTe (TAGS) has ZT = 1.2 at about 700 K, which has been successfully applied in long-life thermoelectric application.² Another main point in Fig. 3 is that the defect chemistry in the alloys could help increasing ZT of TE materials, which is extensive research for material chemists currently. In order to achieve high-ZT TE materials, Snyder and Toberer have presented that reducing _L could directly increase the ZT of TE materials, which shown in Fig. 5.² This model system is Bi₂Te₃, in which the point (1) is shown an optimized ZT 0f 0.8 with a  _L of 0.8 Wm^-1K^-1, and _E is a function of the n (purple line).² Decreasing _L to 0.2 Wm^-1K^-1 could directly increase ZT to point (2), accompanied with the n reduces, which leads to reduced _E and larger S.² Therefore, the reoptimized ZT is shown in point (3).² Obviously, reducing the _L of TE materials is a significant way to get high-ZT TE materials. Currently, there are two approaches that have been reported to decrease the _L of TE materials. The first strategy is pointing defects to materials such as interstitials, vacancies, or alloying.² The second strategy is “Ponon-Glass/Electron Crystal” approach, which is making complex crystal structure materials such as crystalline material, amorphous materials, or glass-like materials.¹ Evidently, the crystal structure of TE materials is related to the ZT of materials because the _L could be reduced by changing the crystal structure. Therefore, in the research of TE material, we need to employ XRD to analyze the materials to know the connection between crystal structure and ZT.

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Powder Diffraction of Thermoelectrical Materials

In order to know the crystal structure of TE materials, scientists usually study the product by XRD. The XRD is the cheapest and most convenient way to know the crystal structure. As a result, the following paragraphs will compare the crystal structure of different TE materials which have suitable ZT and their XRD patterns, such as Bismuth Chalcogenides, Layered SnSe, and Half-Heusler MgAgSb.

Bismuth Chalcogenides.  Bismuth telluride (Bi₂Te₃) is a traditional TE material, which belongs to Bismuth Chalcogenides. Bi₂Te₃ has ZT of 1 at room temperature and could be both n-type and p-type TE materials by alloying method. As a result, scientists have done a lot of research about not only Bi₂Te₃ but also its alloy system, [(Bi_1-xSb_x)₂(Te_1-xSe_x)₃]. Bi₂Te₃ shows a layer structure (Fig. 6) with rhombohedral-hexagonal symmetry with space group

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R3̅m

.¹ The hexagonal lattice parameters for Bi₂Te₃ in room temperature are a = b = 4.38 Å and c = 30.5 Å.¹ The Bi and Te layers form a strong covalent bond to connect each other, while the adjacent Te layers are bonded by van der Waals.¹ This weak bonding between Te layers is easy to dissociate through the c-axis, which shows the property of the anisotropic thermal and electrical transportation in the plan perpendicular to the c-axis in Bi₂Te₃.¹ As a result, the plan perpendicular to the c-axis shows higher thermal conductivity of 1.5 Wm^-1K^-1 than the thermal conductivity along the c-axis direction (0.7 Wm^-1K^-1), which displays the ZT value about 0.6 in Bi₂Te₃ near room temperature.¹ Based on the information from previous section, we have known that alloying could reduce the lattice thermal conductivity of Bi₂Te₃, which could get higher ZT in the TE material. Han et al. has presented the research about the n-type TE material of Bi₂Te_3-xSe_x alloy. The powder diffraction patterns of Bi₂Te_3-xSe_x (x = 0.15, 0.3, 0.6) alloy is shown in Fig. 7a.⁶ The peak shifting is demonstrated by enlarged XRD pattern in Fig. 7b. Through the increasing percentage of Se atom in the composition, the peak tends to go the high angle since the radius of Se atom (1.15 Å) is smaller than the radius of Te atom (1.4 Å).⁶ Comparing with their power factor (S²), thermal conductivity (), and figure of merit (ZT), the power factor and thermal conductivity decreases through the increasing Se atoms at 323 K, so we get the highest ZT value about 0.875 at 323 K for the x = 0.15⁶, which is higher than the ZT of single crystal of Bi₂Te₃. In the other research of p-type TE material, Serrano-Sánchez et al. analyzed the crystal structures of Bi_2-xSb_xTe₃ series (0 ≤ x ≤ 2) based on neutron powder diffraction (NPD) and got the highest ZT value of Bi_0.51Sb_1.49Te₃, 1.1, at 395 K which has the thermal conductivity of 0.92 Wm^-1K^-1.⁷ The NPD pattern of Bi_0.5Sb_1.5Te₃ is shown in Fig. 8. After the refinement, the author got the lattice parameter of Bi_0.5Sb_1.5Te₃ that is a = b = 4.3 Å and c = 30.5 Å⁷, in which the lattice parameter a is smaller than Bi₂Te₃ (4.38 Å). This phenomenon is due to the substitution by the smaller ionic size of Sb³⁺ (0.76 Å) to Bi³⁺ (1.03 Å).⁷ Understandably, the research of n-type Bi₂Te_3-xSe_x and p-type Bi_2-xSb_xTe₃ illustrates that the defect chemistry could increase the ZT of TE material because of the decreasing lattice parameter, which also could reduce the thermal conductivity.

Layered SnSe. Layered SnSe has the high recorded ZT value of 2.62 at 923 K along its b-axis recently.⁸ The crystal structure of SnSe is a layered orthorhombic at room temperature, which can be resulted from a three-dimensional distortion of the NaCl structure.⁸ The perspective views of SnSe crystal structure at room temperature along the a,b, and c-axis are shown in Fig. 9 a-c.⁸ SnSe has two-atom-thick SnSe slabs along the b-c plane which includes the strong Sn-Se bonding, then linked with weaker Sn-Se bonding through the a-axis.⁸ (Fig. 9 b) The two-atom-thick SnSe slabs are corrugated and form a zigzag like shape along the b-axis.⁸ The weakest bond of layered SnSe is in the (001) plans so the cleavage is happened along the (001) plans.⁸ At about 750~800 K, there is a phase transition from a higher symmetry, space group Cmcm, to a lower symmetry, space group Pnma, while cooling from high temperature.⁸ The temperature-dependencee XRD pattern of SnSe is shown in Fig. 10 a. The peak shifting through the increasing temperature is indicating the phase transition of SnSe from Cmcm to Pnma.⁹ The Fig. 10 b demonstrates the XRD pattern of Pnma phase for examining dynamic structural behavior of SnSe nanocrystals at thermal cycling. The peaks are obviously reversible in thermal cycle, which indicates the second order phase transition.⁹ The lattice parameter a and b increase through the increasing temperature; however, the lattice parameter c reveals differently changeable tendency, which indicates the lattices shrink in c-axis but extend in the ab plane.⁹ (Fig. 10 c) Furthermore, the cell volume is increased by the rising temperature, which performs the thermal expansion behavior of the material.⁹ (Fig. 10 c) On the other hand, the transmission electron microscopy (TEM) could observe the space group transfer of layered SnSe directly. (Fig. 11) The (100) plan of SnSe is studied to know the space group transfer (Pnma (RT) to Cmcm (HT)). (Fig. 11 a) The crystal structures of SnSe at room temperature and high temperature in the view along the [211] and [121] directions are shown in Fig.11 b. Through the changed temperature cycle, the researchers got the angle between

1 1̅ 1̅

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and

0 1̅ 1

decreases through the raised temperature and reverses approximately original angle when coming back to the room temperature⁸, which indicate the space group transition of SnSe through the changed temperature. (Fig. 11 c) Compared with XRD and TEM analysis method, the TEM could observe that the obvious angle changes, which indicates the crystal structure becomes different directly.

Because of the unusual layered SnSe and its phase transfer through the variable temperature, we can get the different ZT value in its various facets. The research has exhibited that SnSe has ZT = 2.62 along its b-axis and ZT = 2.3 along its caxis at 923 K; however, ZT is significantly lower along it’s a-axis, about 0.8.⁸ (Fig. 12) In summary, layered SnSe has the high ZT value because of its unique crystal structure, which open a way for material scientist to get the ZT of TE materials above 1. As we mentioned before, the defect chemistry could increase the ZT of TE materials so that material chemists could try to use defect chemistry to improve the ZT of layered SnSe.

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Half-Heusler MgAgSb. Scientists have been attracted by the material with Half-Heusler structure as TE materials due to its excellent electrical transport properties.⁴ MgAgSb has been researched because of its crystal structure related to Half-Heusler structure. MgAgSb has three different phases in the multitemperature. In the low temperature, the phase of -MgAgSb (with space group

I4̅c2

) is stable up to 600 K.¹⁰ At 700 K, -MgAgSb (with space group

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P4/nmm

) and -MgAgSb (with space group

F4̅3m

) are coexisted until 800 K.¹⁰ After the temperature over 800 K, there is only -MgAgSb.¹⁰ The Mg and Ag form Mg-Sb rocksalt-type sublattices in these three phases.¹⁰ (Fig. 13 a-c) The XRD patterns of these three phases are shown in Fig. 14 a-c, which displays that -MgAgSb and -MgAgSb have stable single phase in low temperature and high temperature, but -MgAgSb, -MgAgSb, and impurities appear in the intermediate temperature.¹⁰

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Due to the phase transfer and impurities, it is difficult to get a high value of ZT from MgAgSb. For example, -MgAgSb has only ZT about 0.5 at 425 K.⁴ As a result, scientists have done the research about using alloying method in MgAgSb to optimize ZT. The highest optimized ZT is MgAg_0.965Ni_0.005Sb_0.99 which is approximately 1.4.⁴ (Fig. 15) In the case of MgAgSb, we can comprehend that the phase transition and impurities will influence the ZT value, so scientists should try to make a single phase when designing a new TE material.

Through analyzing the crystal structure by powder diffraction and ZT of the Bismuth Chalcogenides, Layered SnSe, and Half-Heusler MgAgSb, we can conclude that ZT has significant correlation with the crystal structure of TE materials. Recently, the alloying method is the main method to increase ZT of TE materials. When we use smaller radius atom to dope on the material, it could reduce the lattice parameter, which will cause impacts on thermal conductivity and ZT. In order to find the suitable doped ratio to ameliorate the ZT of TE materials, the duty for material scientists is continuously doing research in the future.

Conclusion

In conclusion, this review paper is showing the concept of TE materials, the current TE materials, and the crystal structure of TE materials such as Bismuth Chalcogenides, Layered SnSe, and Half-Heusler MgAgSb which analyze by the powder diffraction. TE materials are candidates for alternative technologies to convert waste heat to electricity straightforwardly. As a result, scientists have attributed a lot of efforts to study TE materials in order to get high value of ZT (ZT  1 in current research), which could influence the efficiency of TE devices. In order to get high ZT value, we could use alloying method to change the lattice parameters of the crystal structure. The layered structure materials in different directions also could be high-ZT-material candidates like layered SnSe. In the future, scientists need to keep doing the research of TE materials because ZT do not have limitation. The high-ZT TE material is just waiting for us to explore.

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Reference

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(6)  Han, S. T.; Rimal, P.; Lee, C. H.; Kim, H.-S.; Sohn, Y.; Hong, S.-J. Enhanced Thermoelectric Cooling Properties of Bi2Te3−xSex Alloys Fabricated by Combining Casting, Milling and Spark Plasma Sintering. Intermetallics 2016, 78, 42–49. https://doi.org/10.1016/j.intermet.2016.08.006.

(7)  Serrano-Sánchez, F.; Gharsallah, M.; Nemes, N. M.; Biskup, N.; Varela, M.; Martínez, J. L.; Fernández-Díaz, M. T.; Alonso, J. A. Enhanced Figure of Merit in Nanostructured (Bi,Sb)2Te3 with Optimized Composition, Prepared by a Straightforward Arc-Melting Procedure. Sci. Rep. 2017, 7 (1). https://doi.org/10.1038/s41598-017-05428-4.

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