Performance Analysis of Thermoelectric Generator by Using Lead Telluride, Perovskites, Skutterudites and Tetrahedrites

Home , Lead telluride, Thermoelectric generator, Thermoelectric materials

WEENTECH Proceedings in Energy 5 (2019) 66-78 Page | 66

4th International Conference on Energy, Environment and Economics, ICEEE2019, 20-22 August 2019, Edinburgh Conference Centre, Heriot-Watt University, Edinburgh, EH14 4AS, United Kingdom Performance analysis of thermoelectric generator by using lead telluride, perovskites, skutterudites and tetrahedrites

Pradyumn Manea*, Deepali Atheayab aEngineering Physics Department, School of Engineering and Applied Sciences, Bennett University, Tech Zone – II, Greater Noida 201310, UP, India bMechanical and Aerospace Engineering Department, School of Engineering and Applied Sciences, Bennett University, Tech Zone – II, Greater Noida 201310, UP, India *Corresponding author’s mail: [email protected]

Abstract

In this research paper performance analysis of thermoelectric generator by using lead telluride, perovskites, skutterudites and tetrahedrites has been proposed. The performance of thermoelectric materials and thermoelectric modules has been calculated. These thermoelectric materials were combined to make thermoelectric couple which will be used in thermoelectric generator. The performance analysis of these thermoelectric couples were simulated on COMSOL Multiphysics 5.2 software. The results indicated that Pb1-xMgxTe0.8Se0.2 and n-type PbTe, Pb1-xMgxTe0.8Se0.2 and CoSb3-xTe x, Pb1-xMgxTe0.8Se0.2 and CaMn0.98Nb0.02O3, Cu12Sb4S13 and CoSb3-xTex indicated higher efficiency than other thermoelectric couples. The proposed system can be utilized for varied range of applications for waste heat recovery and renewable power generation in automotive, industrial, power plants and space sector at an excellent efficiency and lower cost.

Keywords: Seebeck effect; Lead telluride; Perovskites; Skutterudites; Tetrahedrites.

Copyright © 2019 Published by WEENTECH Publishers. This is an open access article under the CC BY License (http://creativecommons.org/licenses/BY/4.0/). All Peer-review process under responsibility of the scientific committee of the 4th International Conference on Energy, Environment and Economics, ICEEE2019

https://doi.org/10.32438/WPE.7319 Manuscript History Receipt of completed manuscript: 09 April 2019 Receipt of Revised Manuscript: 10May 2019 Date of Acceptance: 20 August 2019 Online available from: 26 September 2019

Nomenclature

V Voltage output. TC Temperature at the cold terminal. Page | 67 TH Temperature at the hot terminal. ΔT Temperature difference. T Average temperature. S Seebeck coefficient. Sp Seebeck coefficient of the p-type thermoelectric material. Sn Seebeck coefficient of the n-type thermoelectric material. ρp Specific resistance of the p-type thermoelectric material. ρn Specific resistance of the n-type thermoelectric material. σ Electrical conductivity. σp Electrical conductivity of p-type thermoelectric material. σp Electrical conductivity of n-type thermoelectric material. k Thermal conductivity. kp Thermal conductivity of p-type thermoelectric material. kn Thermal conductivity of n-type thermoelectric material. zT Figure of merit of a thermoelectric material. ZT Figure of merit of a thermoelectric module. η Performance efficiency.

1. Introduction

The demand for energy is increasing day by day with increase in population. Also, burning fossil fuels is not a good option as it degrades the environment. Thus, an alternative and renewable sources need to be found out to satisfy the growing demands without harming the environment. One such alternative is thermoelectricity which converts thermal energy directly into electricity without any moving parts. The research on the thermoelectricity or thermoelectric effect is going since many decades and due to the development of nanotechnology, lot of progress has been made in this field. On an average the efficiency of thermoelectric generator is around 5% - 8% and lead telluride (PbTe), bismuth telluride (BiTe), calcium manganese oxide (Ca2Mn3O8) are few common materials used in making thermoelectric materials [1].

There are numerous applications of the thermoelectric effect, few examples are discussed. Thermoelectric effect could be used to recover waste heat and convert them in to electricity. Around 60% of energy is lost in a system, this energy could be utilized further to generate electricity with the help of thermoelectric generator [2]. In automobile this means, reduction of carbon emissions up-to 1.5 tones and saving 400 liters – 800 liters of fuel annually due to increase in fuel efficiency [3]. Thermoelectric effect can also be used in hybrid vehicles by storing electricity generated from the waste heat from the engine and the exhaust pipe into a storing unit like the battery and then using the stored electricity to ride the vehicle, thus, no need of recharging the battery [3]. Thermoelectric effect can also be used in thermal power plants to increase the power plant’s efficiency by 10%. This effect could also be used in military and space exploration [4]. A thermoelectric module comprising of many thermoelectric couples, weighs less than a

battery and occupies 1/20th space of a solar cell. Thermoelectric generators are portable, has no moving parts, no maintenance and has longer lifespan.

The following table compares Seebeck coefficient and electrical conductivity between metals, semiconductors and insulators. Page | 68 Table 1 Average values of thermoelectric parameters of metals, semiconductors and insulators at 300K [5].

Properties Metal Semiconductor Insulator S (μV/K) ~5 ~200 ~1000 σ (Siemen/m) ~108 ~105 ~10-10

From the Table 1, we see that insulators have highest Seebeck coefficient but lowest electrical conductivity, on other hand metal has Seebeck coefficient but highest electrical conductivity. Therefore, semiconductors could give the best performance and could prove themselves to be the best thermoelectric material.

Use of nanotechnology in thermoelectric materials has scaled the performance of thermoelectric module. Using nanotechnology in thermoelectricity, it is possible to decouple the Seebeck coefficient, electrical conductivity and thermal conductivity, thus, improving the figure of merit (ZT) of thermoelectric module and increasing the performance of the thermoelectric module [6]. In this paper, we have also chosen thermoelectric materials which use nanotechnology to give greater performance.

As per Chen [1] the commercial thermoelectric generators have efficiency between 5% - 8% which is far behind commercial engines and photovoltaic power systems. The research also claims that Cu-Sb-S compounds is one of the cheapest thermoelectric materials which could be manufactured. Alphabet energy released E1 in 2014 which uses Cu-Sb-S based thermoelectric compounds to get maximum efficiency and at lower cost.

In 2013, Ma et al. [6] reviewed the then current status of the development of composite thermoelectric materials with embedded nanoparticles. They compared the bulk thermoelectric materials and thermoelectric materials composing nanoparticles by grouping the studies according to optimal temperature operational range. As per their research, most studies have been devoted to materials within the medium temperature range, followed by low temperature materials, whereas high temperature materials have not yet received much attention within this area [6]. Today there’s a need to find a perfect combinations of thermoelectric materials and thermoelectric modules to achieve maximum efficiency in an economically viable manner. Our research claims that with right combinations of thermoelectric materials, thermoelectric couples with 18% efficiency can be achieved. We have simulated our data in COMSOL Multiphysics 5.2 software and analyzed the performance of various thermoelectric modules and thermoelectric couples which could be used in thermoelectric generator.

2. Description of proposed thermoelectric material and thermoelectric couple

So far, five thermoelectric materials and eight thermoelectric couples has been studied. The properties of five thermoelectric materials were already validated. These five thermoelectric materials were combined

to make thermoelectric couple and then these thermoelectric couples were simulated. Out of five thermoelectric material the most prominent thermoelectric material which was observed is a quaternary alloy of Pb1-xMgxTe0.8Se0.2 with a figure of merit (zT) of 2.2 at a temperature (Tmax) of 800K. This quaternary alloy is a lead telluride (PbTe) based compound. Lead telluride (PbTe) and its alloys are well known for their high thermoelectric performance and has played an important role in deep space exploration. The Seebeck coefficient is about 260μV/K with electrical conductivity and thermal Page | 69 conductivity to be 4 x 104 S/m and 1 W/m K respectively [7]. Since the alloy has a positive Seebeck coefficient it’s a p-type thermoelectric material.

Perovskites are a class of materials that has a similar structure like calcium titanium oxide (CaTiO3), which display a myriad of exciting properties like superconductivity, magnetoresistance and many more. The general chemical formula for Perovskites material is ABX3, where A and B are two cations of different sizes and X is an anion which bonds to A and B. The Perovskite structure is generally adopted by many oxides that have the chemical formula ABO3. One of the oxide based Perovskite material is CaMn0.98Nb0.02O3 which has a figure of merit (zT) of 0.2 at a temperature (Tmax) of 800K [8]. This Perovskite material has a Seebeck coefficient of -230μV/K with electrical conductivity and thermal conductivity to be 0.28 x 104 S/m and 2.2 W/m K respectively [8]. Since the alloy has a negative Seebeck coefficient it’s an n-type thermoelectric material.

Skutterudites are another well-known class of material. Skutterudites are a cobalt arsenide mineral containing variable amounts of nickel and iron substituting for cobalt with general formula CoAs3. Materials with a skutterudite structure are studied as a low cost thermoelectric material with low thermal conductivity. CoSb3-xTex is a skutterudite structure material with the Seebeck coefficient of -200μV/K [9], thus, an n-type thermoelectric material with figure of merit (zT) of 1.1 [9, 10]. The electrical conductivity 5 and thermal conductivity of CoSb3-xTex is 10 S/m and 2 W/m K respectively [9].

Tetrahedrite is a natural mineral which share a similar structure like Cu12Sb4S13. This material has high symmetric crystal structure with large unit cell, also has intrinsically low thermal conductivity and is cost efficient and environmental friendly [1]. The Cu12Sb4S13 has a Seebeck coefficient of 200μV/K and shows electrical conductivity and thermal conductivity (k) of 104 S/m and 0.5 W/m K respectively [1]. Therefore, the figure of merit (zT) is 0.6. Other than Cu12Sb4S13, Cu3Sb1-xGexS4 is also a type of Tetrahedrite with figure of merit (zT) of 0.2. Cu3Sb1-xGexS4 has a Seebeck coefficient of 400μV/K and shows electrical conductivity and thermal conductivity of 103 S/m and 0.8 W/m K respectively [1]. Here both the tetrahedrites are p-type thermoelectric materials.

Table 2 Thermoelectric materials and properties [1, 7, 8, 9, 10]

Thermoelectric type Tmax S σ ρ (Ωm) K zT Material (K) (μV/K) (S/m) (W/m K) 4 -4 Pb1-xMgxTe0.8Se0.2 P 800 260 4x10 0.25x10 1 2.2

4 -4 CaMn0.98Nb0.02O3 N 800 -230 0.28 x10 3.6 x10 2.2 0.2 5 -5 CoSb3-xTex N 800 -200 10 10 2 1.1 4 -4 Cu12Sb4S13 P 800 200 10 10 0.5 0.6 3 -3 Cu3Sb1-xGexS4 P 800 400 10 10 0.8 0.2

By applying various combinations of p-type thermoelectric materials and n-type thermoelectric materials, eight thermoelectric couples were further studied and simulated to find the best thermoelectric couple for using in thermoelectric generator. Among eight different thermoelectric couples, four showed an efficiency greater than the average i.e. 10%. These four couples are theorized below and the simulation output of these thermoelectric systems are shown. Page | 70 Table 3 Thermoelectric couples and their properties

p-type n-type ZT η Volt (V) Volt (V) Th Tc (%) calculate simulated (K) (K) d Pb1-xMgxTe0.8Se0.2 CaMn0.98Nb0.02O3 0.1746 11.43 0.245 0.260 800 300 Pb1-xMgxTe0.8Se0.2 CoSb3-xTex 1.0555 15.96 0.230 0.240 800 300 Pb1-xMgxTe0.8Se0.2 n-typePbTe 1.4872 18.48 0.286 0.280 800 300 Cu12Sb4S13 CaMn0.98Nb0.02O3 0.0820 1.78 0.215 0.230 800 300 Cu12Sb4S13 CoSb3-xTex 0.5587 9.57 0.200 0.200 800 300 Cu3Sb1-xGexS4 CaMn0.98Nb0.02O3 0.0688 1.49 0.347 0.330 800 300 Cu3Sb1-xGexS4 CoSb3-xTex 0.1746 3.59 0.300 0.310 800 300 Cu3Sb1-xGexS4 n-typeCu3SbS4 0.0619 1.36 0.375 0.380 800 300

The tabulated data from Table 3 shows that Pb1-xMgxTe0.8Se0.2 and CaMn0.98Nb0.02O3, Pb1- xMgxTe0.8Se0.2 and n-type PbTe, Pb1-xMgxTe0.8Se0.2 and CoSb3-xTex, Cu12Sb4S13 and CoSb3-xTex gives an above average efficiency values. Thus, among eight thermoelectric couples, Pb1-xMgxTe0.8Se0.2 and CaMn0.98Nb0.02O3, Pb1-xMgxTe0.8Se0.2 and n-type PbTe, Pb1-xMgxTe0.8Se0.2 and CoSb3-xTex, Cu12Sb4S13 and CoSb3-xTex shows higher performance and are the best thermoelectric couples.

3. Problem identification and basic principle

The variables which define the performance of a thermoelectric leg and thermoelectric couple are Seebeck coefficient, electrical conductivity, thermal conductivity, carrier concentration, temperature difference, figure of merit, etc. The governing equations are discussed further. The Seebeck coefficient is defined as the measure of the magnitude of an induced thermoelectric voltage in response to a temperature difference across the material [5]. The Seebeck coefficient is measured in μV/K and its numerical expression depends upon the effective mass (m*) and carrier concentration (n) [5]. 푚∗ 푆 훼 (1) 푛2/3

8휋2푘2 휋2/3 푆 = 퐵 푚∗ 푇 (2) 3푒ℎ2 (3푛)2/3

-23 Where kB is Boltzmann constant with a value of 1.38 x 10 J/K, h is Plank’s constant with a value of 6.63 x 10-34 Js and e is electric charge with all entities in S.I. units [5]. Increase and decrease in effective mass and carrier concentration changes the Seebeck coefficient significantly [5]. Positive numerical value of the Seebeck coefficient implies to a p-type thermoelectric material or thermoelectric leg whereas negative numerical value of Seebeck coefficient implies to an n-type thermoelectric material or thermoelectric leg

[5]. The combine of p-type thermoelectric legs and n-type thermoelectric legs forms a thermoelectric couple. The figure of merit for a thermoelectric leg is denoted as zT whereas the figure of merit for a thermoelectric couple is denoted as ZT [5]. The figure of merit is a unit less and dimensionless numerical expression taken as representing the performance of a given thermoelectric device or material. The figure of merit of a thermoelectric leg depends upon the Seebeck coefficient, thermal conductivity, electrical conductivity and the average temperature between two thermoelectric materials [5]. Page | 71

푆2휎푇 푧푇 = (3) 푘

Thus, to have a larger numerical value for zT, the material at a specified temperature range should be chosen such that it has higher value of Seebeck coefficient and electrical conductivity and lower thermal conductivity. The figure of merit for a thermoelectric couple is given as follows [5]. 2 (푆푝 − 푆푛) 푇 푍푇 = (4) 2 (√휌푛푘푛 + √휌푝푘푝) Where Sp and Sn are Seebeck coefficient (μV/K) of p-type and n-type thermoelectric materials respectively, kp and kn are thermal conductivity (W/m K) of p-type thermoelectric materials and n-type thermoelectric materials respectively and ρp and ρn are electrical conductivity (Siemen/m) of p-type thermoelectric materials and n-type thermoelectric materials respectively. When a temperature difference is created between two thermoelectric materials a potential difference is produced causing charges to flow and generate thermoelectric voltage. The thermoelectric voltage is formulated as follows [5].

푉 = (푆푝 − 푆푛)∆푇 (5)

Where ΔT is the temperature difference (Kelvin) between two thermoelectric junctions. The electrical conductivity is defined as the ability of a material to conduct electricity. The electrical conductivity relies upon the carrier concentration, electric charge and mobility of the charge carriers. The mobility of the charge carriers is defined as the drift velocity of the charge carriers per unit of the electric field and is formulated as μ = eτ/m*, where τ is mean scattering time between the collisions of the charge carriers [5]. The electrical conductivity is formulated as follows [5].

휎 = 푛푒휇 (6)

Since in a semiconductor both the electrons and the holes contributes towards current conduction, the electrical conductivity could be given as follows [5].

휎 = 푛푒휇푛 + 푝푒휇푝 (7)

Where n and p are electron and hole carriers respectively and μn and μp are the mobility of electrons and holes respectively. The thermal conductivity is the ability to transfer heat across a material and here it the contributors are lattice thermal conductivity (kL) and electron thermal conductivity (kE). Lattice thermal conductivity (kL) is the heat transfer from the vibration of the lattice, known as phonons. Electron thermal conductivity (kE) is the transfer of heat from the electrons [5]. Therefore, we could formulate the thermal conductivity as follows [5].

푘 = 푘퐸 + 푘퐿 (8)

휋2푛2푇푘2휇 푘 = 퐵 (9) 퐸 푒

퐶푣푙 Page | 72 푘 = (10) 퐿 3

Where C is the phonon heat capacity per unit volume, v is the average phonon velocity and l is phonon mean free path [5]. Here one interesting fact to note is that as you increase the carrier concentration the electrical conductivity as well as thermal conductivity increases. Since thermal conductivity should be minimum for the material to be called as the best thermoelectric material, the carrier concentration should be chosen such that an optimum performance should be achieved by the thermoelectric material. The thermal conductivity and electrical conductivity are related by Weidman Franz law [5].

푘퐸 = 퐿0휎푇 (11)

8 2 -2 -2 Where L0 is a constant called as Lorentz number with a value of 2.4 x 10 J K C . The efficiency of the thermoelectric couple depends mainly upon the figure of merit and the temperature difference which can be formulated as follows [5].

푇 − 푇 √(1 + 푍푇) − 1 휂 = 퐻 퐶 (12) 푇퐶 푇퐻 √(1 + 푍푇) + 푇퐻

Here TC and TH are cold terminal and hot terminal temperatures respectively. Fourier law is the law of heat conduction which determines the heat transfer through unit cross sectional area when temperature differential is applied. It could be formulated as follows [11].

푞 = −푘 ∇푇 (13)

Where q is heat flux density in W/m2. The heat loss could be formulated in terms of heat generation per unit volume (𝑔̇) which could be formulated as follows [11].

𝑔̇ = −푘 ∇2푇 (14)

The above equation is applicable to steady state only and has unit W/m3.

4. Methodology

During the simulation, it was assumed that there are no cracks and impurities in the used thermoelectric materials. Further, ‘heat transfer in solids’ and ‘thermoelectric effect’ multiphysics modules were used to simulate the thermoelectric couples. The simulated outputs are time independent, therefore, lifespan and durability of these thermoelectric couples has not been tested.

Figure 1 displays the flow diagram of the information in the thermoelectric model. After the required multi-physics and time independent modules were chosen, materials were defined to the thermoelectric couple. Input parameters like electrical conductivity, thermal conductivity, Seebeck coefficient, figure of merit, and boundary conditions like the hot temperature at top surface and cold temperature at bottom surface were provided to the simulation software. Further meshing was defined. Meshing is discretization of the designed thermoelectric couple into number of cells and node to compute the results accurately. An Page | 73 extremely fine mesh would give better accuracy but would consume lot of computational time. Therefore, in this simulation, physics controlled (default) meshing was defined for the designed thermoelectric couple geometry. Temperature distribution, voltage output and heat loss were computed using Eqs. (13) (5) and (14) respectively and simulation results were shown.

Fig. 1 Information flow diagram

5. Results and discussions

After uniting thermoelectric legs together, the thermoelectric couples were simulated with COMSOL Multiphysics 5.2 software. The distribution of the temperature along the thermoelectric surface, Page | 74 thermoelectric voltage, heat loss, etc. were investigated using Eqs. (13) (5) and (14) respectively and the best thermoelectric couples were selected. The dimensions of the thermoelectric legs were taken to be of 10mm x 0.5mm x 0.5mm for both p-type and n-type. The thermoelectric legs were attached to an electrical conductive material Copper (Cu) which was then combined with 1mm x 14mm x 7mm of Alumina (Al2O3). While simulating thermoelectric couples in COMSOL Multiphysics, temperatures were set at hot and cold terminals of the designed thermoelectric couples. Simulation of all eight thermoelectric couples and four thermoelectric couples which showed efficiency more than 10% were done.

Fig. 2 Temperature distribution on thermoelectric module surface

The Figure 2 shows the temperature distribution on the surface of the thermoelectric module which includes thermoelectric legs, electrical conductive metal plate and ceramic. Copper (Cu) and Alumina (Al2O3) were utilized as electrical conductive metal plate and ceramic respectively. The temperature of the cold and hot terminal were set at 300K and 800K respectively. Figure 2 illustrates 3D plot group and surface plotting whose expressions were set as temperature in COMSOL Multiphysics 5.2 software. This justifies temperature variation on the surface of the thermoelectric module. For the thermoelectric module to have high performance efficiency the temperature difference has to be large. Here the temperature difference was set at 500K.

(a) (b)

Page | 75

Fig. 3 Thermoelectric voltage output of thermoelectric couples: (a) Pb1-xMgxTe0.8Se0.2 and CaMn0.98Nb0.02O3 based thermoelectric couple. (b) Pb1-xMgxTe0.8Se0.2 and n-type PbTe based thermoelectric couple. (c) Pb1-xMgxTe0.8Se0.2 and CoSb3-xTex based thermoelectric couple. (d) Cu12Sb4S13 and CoSb3-xTex based thermoelectric couple. Figure 3 shows the thermoelectric voltage of various thermoelectric couples. For a given temperature difference and properties of thermoelectric materials, thermoelectric voltage (V) was formulated by Eq. (5). The thermoelectric voltage output was obtained through 3D plot group and multislice with electric potential. Figure 3(a) exhibits voltage output for Pb1-xMgxTe0.8Se0.2 and CaMn0.98Nb0.02O3 based thermoelectric couple, (b) exhibits voltage output for Pb1-xMgxTe0.8Se0.2 and n-type PbTe based thermoelectric couple, (c) exhibits voltage output for Pb1-xMgxTe0.8Se0.2 and CoSb3-xTex based thermoelectric couple, (d) exhibits voltage output for Cu12Sb4S13 and CoSb3-xTex based thermoelectric couple. It has been observed that, Pb1-xMgxTe0.8Se0.2 and n-type PbTe based thermoelectric couple showed maximum thermoelectric voltage output, whereas, for Cu12Sb4S13 and CoSb3-xTex based thermoelectric couple showed lowest thermoelectric voltage output while comparing four efficient thermoelectric couples.

(a) (b)

Page | 76

Fig. 4 Variation of total power dissipation density with respect to temperature of thermoelectric couple: (a) Pb1-xMgxTe0.8Se0.2 and CaMn0.98Nb0.02O3 based thermoelectric couple. (b) Pb1-xMgxTe0.8Se0.2 and n- type PbTe based thermoelectric couple. (c) Pb1-xMgxTe0.8Se0.2 and CoSb3-xTex based thermoelectric couple. (d) Cu12Sb4S13 and CoSb3-xTex based thermoelectric couple. Figure 4 illustrates the total power dissipation density for different thermoelectric couples. The total power dissipation density takes into account the heat loss owing to electrical resistance and surface resistance. The plot was achieved with 1D plot group and line graph. The x-axis denotes the temperature range from 300K to 800K and y-axis denotes the total power dissipation density. From the Figure 4 it has been observed that the magnitude of the total power dissipation density is higher for temperatures at 300K and 800K. Thus, at the contacts of the thermoelectric couple the main heat loss was noted and it affects the efficiency of the thermoelectric couple. Further, efforts have been done to improvise the electrical contacts. Use of nanotechnology in thermoelectric materials will enhance the efficiency of thermoelectric couples [1]. Thus, a perfect combination of thermoelectric legs with efficient electrical contacts will cause an increase in the efficiency of the thermoelectric module. The results are in accordance with the results reported by R. Bjørk et al. [12]. Figure 4(a) exhibits the total power dissipation density for Pb1- xMgxTe0.8Se0.2 and CaMn0.98Nb0.02O3 based thermoelectric couple, (b) exhibits the total power dissipation

density for Pb1-xMgxTe0.8Se0.2 and n-type PbTe based thermoelectric couple, (c) exhibits the total power dissipation density for Pb1-xMgxTe0.8Se0.2 and CoSb3-xTex based thermoelectric couple, (d) exhibits the total power dissipation density for Cu12Sb4S13 and CoSb3-xTex based thermoelectric couple. It has been observed that in Figure 4(b) the magnitude of the total power dissipation density is more for temperature at 300K and 800K however, is relatively less than Figure 4(a). So, the efficiency of Pb1-xMgxTe0.8Se0.2 and CaMn0.98Nb0.02O3 based thermoelectric module has been found to be less than Pb1-xMgxTe0.8Se0.2 and n- Page | 77 type PbTe based thermoelectric module.

6. Conclusions Based on the present studies following conclusions have been made.

 Pb1-xMgxTe0.8Se0.2 and n-type PbTe, Pb1-xMgxTe0.8Se0.2 and CoSb3-xTex, Pb1-xMgxTe0.8Se0.2 and

CaMn0.98Nb0.02O3, Cu12Sb4S13 and CoSb3-xTex thermoelectric couples indicated higher efficiency

than other studied thermoelectric couples.

 Pb1-xMgxTe0.8Se0.2 and n-type PbTe, Pb1-xMgxTe0.8Se0.2 and CoSb3-xTex, Pb1-xMgxTe0.8Se0.2 and

CaMn0.98Nb0.02O3, Cu12Sb4S13 and CoSb3-xTex thermoelectric modules indicated above average

efficiency.

 Pb1-xMgxTe0.8Se0.2 and n-type PbTe, Pb1-xMgxTe0.8Se0.2 and CoSb3-xTex, Pb1-xMgxTe0.8Se0.2 and

CaMn0.98Nb0.02O3, Cu12Sb4S13 and CoSb3-xTex thermoelectric modules were simulated on

COMSOL Multiphysics 5.2 software and thus they could be used for an efficient thermoelectric

generator.

ORCID Id of authors

Mane, Pradyumn: https://orcid.org/0000-0001-5222-2367 Atheaya, Deepali: https://orcid.org/0000-0002-2693-0295

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