Thermoelectricity Properties of Tl_10-x ATe₆ (A = Pb) in Chalcogenide System

Abstract

The different elements are doping in the tellurium telluride to determine the different properties like electrical and thermal properties of nanoparticles. The chalcogenide nanoparticles can be characteristics by the doping of the different metals which are like the holes. We present the effects of Pb doping on the electrical and thermoelectric properties of Tellurium Telluride Tl10-xPbxTe6 (x = 1.000, 1.250, 1.500, 1.750, 2.000) respectively, which were prepared by solid state reactions in an evacuated sealed silica tubes. Structurally, all these compounds were found to be phase pure as confirmed by the x-rays diffractometery (XRD) and energy dispersive X-ray spectroscopy (EDS) analysis. The thermo-power or Seebeck co-efficient (S) was measured for all these compounds which show that S increases with increasing temperature from 295 to 550 K. The Seebeck coefficient is positive for the whole temperature range, showing p-type semiconductor characteristics. Similarly, the electrical conductivity (σ) and the power factors have also complex behavior with Pb and Sn concentrations. The power factor (PF=S2σ) observed for Tl10-xPbxTe6 compounds are increases with increase in the whole temperature range (290 K-550 K) studied here. Telluride’s are narrow band-gap semiconductors, with all elements in common oxidation states, according to (Tl+) 9 (Pb3+)(Te2−)6. Phases range were investigated and determined with different concentration of Pb and Sn with consequents effects on electrical and thermal properties.

1. Introduction

The thermo-electro-materials are now used as the renewable energy. It is used as the place of the coal, water tides, solar cells etc. The thermo electro-materials have more efficiency and reliable. Thermoelectric is one of the most important approaches in the solid state physics which can be converted the heat energy in the electrical energy, help to increase the efficiency, effectiveness and competency. Its importance is increase since last twenty years when the ease of use of fossil fuel is decrease. So there are different thermoelectric materials are used for the different temperatures from 10 K to the 1000 K which are used in the different applications for the cooling and heating [1, 2, 3, 4, 5]. Tellurium telluride is one important compound of the thermoelectric material which is studied, modified and increases the efficiency for the more and more applications for generation of power [1] and solar cells [2].

It is statistical results show that up to 60% of energy is losing in vain worldwide, most in the form of waste heat. High value of performance which is thermoelectric (TE) materials that have directly and inversely changed heat energy to electrical energy has thus drawn growing attentions of governments and research institutes [6]. Thermoelectric system is an environment-friendly energy conversion technology with the advantages of small size, high reliability, no pollutants and feasibility in a wide temperature range. However, the efficiency of thermoelectric devices is not high enough to rival the Carnot efficiency [7, 8]. Tellurium telluride is a basically alloy that is used for the increases the energy conversion efficiency at the any temperature of the heating and cooling in the electrical circuit [9, 10].

Many new thermoelectric materials or new material with which have high performance have been found such as skutterudites with high scattering rates of phonons [11, 12], silicon nanowires [13, 14], TE thin films [15], and nanostructured bismuth antimony telluride bulk alloys [16]. It was thinking that high barriers and extremely degenerately doped superlattices must achieve significant increases in thermos-electric power factor over bulk materials [17, 18]. It was revised that electron transport which are perpendicular to the barrier and investigated that large number of degenerate doped semiconductor or metal super-lattices could achieve which shows the power factors higher than the bulk and determined that non-maintenance of transverse momentum can have a large effect (especially in the case of metal super-lattices) by increasing the number of electrons contributing to conduction by thermionic emission [19].

An electric field provides a potential difference along a wire of electrons, which creates a force,

$$\mathrm{F}=eE$$E1

where ‘e’ is the charge of an electron and ‘E’ is the magnitude of the electric field. That force accelerates the electrons, as expected by Newton’s second law. We get the expression for v_d by equating the above two equations of force,

$$\mathrm{F}={\mathrm{m}}_{\mathrm{e}}\mathrm{a}$$E2

We get the expression for v_d by equating the above two equations of force,

$${\mathrm{m}}_{\mathrm{e}}\mathrm{a}=eE$$E3

As we know that

$$\mathrm{a}=\frac{vd}{\tau }$$E4

$$\frac{\mathit{mevd}}{\tau }=eE$$E5

$$v_d=\frac{Ee\tau }{m_e}$$E6

Plugging this expression into that of conductivity, we get

$$\sigma =\frac{ne{v}_d\mathrm{A}}{AE}$$E7

$$\sigma =\frac{ne{v}_d}{E}$$E8

Using the equation of drift velocity.

$$v_d=\frac{Ee\tau }{m_e}$$E9

We have

$$\sigma =\frac{ne}{E}\frac{Ee\tau }{m_e}$$E10

$$\sigma =\frac{\mathrm{n}{e}^2\tau }{m_e}$$E11

This is the required expression of electrical conductivity.

The figure of merit is

$$ZT=\frac{S^2\sigma T}{k}$$E12

Where is σ is the electrical conductivity,$k$is the thermal conductivity, S is the see-beck coefficient, and T is the absolute temperature which is determined the efficiency of the thermo electric materials applications [8]. The power factors can be determined the electrical and thermal properties. The power factor can be defined as ${\mathrm{S}}^2\sigma$. It can be help the determination of the charge carrier’s concentration, from the doping concentration charges and lay down the free electrons in the system of chalcogenides.

We have investigated the chalcogenide with different materials (lead, tin, bismuth etc.) doped in the thallium tellurides. They have complex composition and structure on the basis of the electronic configurations. These compositions help to increases their properties like thermal, electrical, optical etc. of the thermo-electrical materials. There are many challenges of complex composition to high their electrical conductivity, high see-beck coefficient and low thermal conductivity. Due to this, they can controlled the electronic structures of the system i.e. band gap, shapes and degenerated level which is near the Fermi level, concentration of electrons and charge carriers scattered depend on them [7, 8].

The ideal situation is having high effective mass and high mobility, but this is extremely difficult to tune in a material. One has to compromise one for the other, and there are reports of compounds showing promising thermoelectric material at both ends of the spectrum. Chalcogenides (group 16 10 elements).

2. Experimental section

The Pb doped Tl_10-xA_xTe₆ (A = Pb) is (x = 1.00, 1.25, 1.50, 1.75, 2.00) has been prepared by solid state reactions in evacuated sealed silica tubes. The purpose of this study were mainly for discovering new type of ternary compounds by using Tl⁺¹, Pb⁺³and Te⁻² elements as the starting materials. Direct synthesis of stoichiometric amount of high purity elements i.e. 99.99% of different compositions have been prepared for a preliminary investigation. Since most of these starting materials for solid state reactions are sensitive to oxygen and moistures, they were weighing stoichiometric reactants and transferring to the silica tubes in the glove box which is filled with Argon. Then, all constituents were sealed in a quartz tube. Before putting these samples in the resistance furnace for the heating, the silica tubes was put in vacuum line to evacuate the argon and then sealed it. This sealed power were heated up to 650 C^o at a rate not exceeding 1 k/mint and kept at that temperature for 24 hours. The sample was cooled down with extremely slow rate to avoid quenching, dislocations, and crystals deformation.

Structural analysis of all these samples was carried out by x-rays diffraction, using an Inel powder diffractometer with position-sensitive detector and CuKα radiation at room temperature. No additional peaks were detected in any of the sample discussed here. X-ray powder diffraction patterns confirm the single phase composition of the compounds.

The temperature dependence of Seebeck co-efficient was measured for all these compounds on a cold pressed pellet in rectangular shape, of approximately 5 × 1 × 1 mm³ dimensions. The air sensitivity of these samples was checked (for one sample) by measuring the thermoelectric power and confirmed that these samples are not sensitive to air. This sample exposes to air more than a week, but no appreciable changes observed in the Seebeck values. The pellet for these measurements was annealed at 400°C for 6 hours.

For the electrical transport measurements 4-probe resistivity technique was used and the pellets were cut into rectangular shape with approximate dimension of 5 × 1 × 1 mm³.

3. Result and discussions

3.1 Structural analysis

X-ray diffraction is used for the structural analysis of the materials. It helps to determine the crystal structure and particle size. Several of Tl_10-xATe₆ which have doped Pb and Sn in it. The A is the different doped element. Here, A is Pb and Sn. It has the different concentration of it. The X-ray diffraction of Tl_10-xATe₆ with different concentration of doping of Pb and Sn is shown in Figure 1. Due to the different concentration, their peaks are different shown in Figure 1. Crystal size which prepared samples in the range of (20-24 nm) indicating that Pb & Sn incorporations in TlATe₂ do not affect significantly its crystallite size.

Figure 1.

XRD of doping of Pb in the TlATe (A = Pb).

The average particle size (D) was estimated by Scherrer formula given as

$$\mathrm{D}=\frac{k\lambda }{\mathit{\beta cos\theta }}$$E13

where ‘k’ is the Scherrer’s constant and also known as shape constant having value 0.9 in our case, ‘λ’ is wavelength of x-rays, ‘β’ is full width at half maximum (FWHM) and θ is the Bragg angle.

By using the following equation, lattice parameters ‘a’, b and ‘c’ of cubic Tl_10-xATe₆ were calculated.

$$\frac{1}{d^2}=\frac{h^2+k^2+l^2}{a^2}$$E14

For cubic structure, the volume can be calculated by

$$\mathrm{V}=a^3$$E15

and X-ray density can be calculated by

$$\rho =\frac{nM}{V{N}_A}$$E16

M is the molecular mass of Tl_10-xATe₆, $N_A$ is Avogadro’s number and its value is constant (6.02 × 10 ²³ mol⁻¹). n is the number of atoms per unit cell.

The XRD data are summarized in Table 1.

Sample	Crystallite size, D = 0.9λ/βcosθ (nm)	Lattice constant; a, b, c = (Å)	Volume (Å^3)
Tl9Pb1Te6	32.247	a = b = 8.8931; c = 13.0052	1004.521
Tl8.75Pb1.25Te6	31.795	a = b = 8.84510; c = 13.07515	1023.925
Tl8.50Pb1.50Te6	31.180	a = b = 8.82510; c = 13.00010	1013.429
Tl8.25Pb1.75Te6	31.128	a = b = 8.81010; c = 13.0010	1009.093
Tl8Pb2Te6	31.055	a = b = 8.84814; c = 13.16215	1022.722

Table 1.

Value of crystallite size and crystal system of doped Tl_10-xA_xTe₆ (A = Pb).

Figure 2 shows the EDX of the Tl_10-xXTe₆, have the different concentration of the doping of the Pb in it. The EDX shows the composition of the compounds. It shows the Pb are present in it.

Figure 2.

Comparison of the EDX of doping of Pb in the TlATe (A = Pb).

3.2 Electrical and thermal properties

To determine the different concentration of the doping of the Pb in the compound, there is changing in the charges carries. So the doping is effect on the temperature. Due to this temperature, it is variant in the Seebeck coefficient (S) as shown in Figure 3. The Seebeck coefficient can determined the temperature gradient for 1 K. It shows that the positive Seebeck effect from the 300 K to 500 K, for all p type semiconductors whose have the high charge carrier concentration. The Seebeck is positive due the concentration of doping elements is increase. So the mostly thermoelectric materials are the p type semiconductors materials. Due to increasing the concentration of doping elements, It improves the (i) reducing of grain size (ii) charge mobility and carrier density in thermos electric materials.

Figure 3.

The see-Beck Co-efficient of doping of Pb in the TlATe (A = Pb).

The Seebeck coefficient is varying from 80 to 120 μѴ/K as a function of the temperature. The behavior of the Seebeck coefficient is increasing as the Fermi level energy is decreasing due to the charge carrying density. In Figure 4 shows that there is low level of charge carrier so that the holes are increase in it, so that it shows the high value of thermopower. So the large value of X, the doping elements have the large number of electrons and less number of charges carriers. As electrical conductivity ‘σ’ increases with increases in n according to the equation

Figure 4.

The electrical conductivity of doping of Pb in the TlATe (X = Pb).

$$\sigma =ne\mu$$E17

where

μ = carrier mobility

and

e = charge of carriers

In Figure 4 shows, the electrical conductivity of the quaternary compounds as compared to the temperature while the temperature is varied. The electrical conductivity is decrease as the temperature is increase that is why it is show the p type semiconductor and behave the positive temperature coefficient. It is cause the phonons scattering the charge carriers and effects the grains boundary. As increase the doping of elements, the holes in the compounds are increase, which is cause the phonons scattering. In chalcogenide system, the different elements are doping in the compound has no effect on the electrical conductivity. The low electrical conductivity is due to the effect oxide as the impurity in the compounds.

The Electrical Conductivity data are summarized in Table 2.

Sample	Electrical conductivity(Ω^−1 cm^−1) at 300 K	Electrical conductivity (Ω^−1 cm^−1) at 550 K
Tl9Pb1Te6	1645	890
Tl8.75Pb1.25Te6	1540	750
Tl8.50Pb1.50Te6	1335	610
Tl8.25Pb1.75Te6	1301	585
Tl8Pb2Te6	460	288

Table 2.

The electrical conductivity of Tl_10-xA_xTe₆ (A = Pb) at 300 and 550 K for all samples (1.0 ≤ x ≤ 2.0).

The behavior of temperature is different for the different concentration of the compound. The relationship between the Seebeck, temperature and concentration of doping elements as given below.

$$m^{\ast }$$E18

Where,$\sigma$is the Boltzmann constant, e is the electronic charge, h is the Planck’s constant,$PF={\mathrm{S}}^2\sigma$is the effective mass and n is the charge carrier concentration. The effective mass and concentration are two parameters of the Seebeck coefficient. The samples have low concentration, it increase the thermos-power as well as the temperature.

Figure 4 shows that the electrical conductivity $\sigma$ is decrease as the increase of the temperature of the compounds. Increased, doping concentration causes decrease in ó as expected and inversely affecting their Seebeck counterpart [20]. The Seebeck is inversely effect due to the increasing of the doping of the concentration of the doping.

The Seebeck coefficient data are summarized in Table 3.

Sample	See-beck coefficient(μVK^−1) at 300 K	See-beck coefficient(μVK^−1) at 550 K
Tl9Pb1Te6	32	56
Tl8.75Pb1.25Te6	40	90
Tl8.50Pb1.50Te6	68	100
Tl8.25Pb1.75Te6	73	110
Tl8Pb2Te6	80	160

Table 3.

See-beck Co-efficient of all doped Tl_10-xA_xTe₆ (A = Pb) samples at 300 and 550 K.

The different compounds have enhance the power factor

$$PF={\mathrm{S}}^2\sigma$$E19

is decreases the electrical conductivity as increases the Seebeck coefficient in the given system. The PF is depend on the Seebeck coefficient. To measure the PF by the knowing the electrical conductivity and Seebeck coefficient in Figure 5. As increases the temperature, the power factor is increases for all the compounds. Figure 5 shows that the power factor increase as the doping of the concentration is increases. As increases, the doping of the elements in the compounds is increase the optimization, which can help to increases the Seebeck and power factor.

Figure 5.

The power factor of doping of Pb in the TlATe (A = Pb).

The power factor data are summarized in Table 4.

Sample	Power factor S^2σ; (μWcm^−1 K^−2) at 300 K	Power factor S^2σ; (μWcm^−1 K^−2) at 550 K
Tl9Pb1Te6	1.8	4.7
Tl8.75Pb1.25Te6	2.8	8.5
Tl8.50Pb1.50Te6	6.8	10
Tl8.25Pb1.75Te6	7.9	10.2
Tl8Pb2Te6	3.6	9.7

Table 4.

Power factor of all doped Tl_10-xA_xTe₆ (A = Pb) samples at 300 and 550 K.

4. Conclusion

The different concentration of the doped Pb in the Tl_10-xATe₆ nanoparticles is synthesized by the solid state reaction within evacuated silica sealed tube with the pellet size is 5*1*1 mm³ in the rectangular dimension and then studied the electrical and thermal properties of the nanoparticles. The XRD shows the nanoparticles are the single phase, crystal structure measured by the experimental formula, having the same space group 14/mcm like Tl₅Te_3. The doping of the holes materials it changes its physical properties i.e. thermal, electrical, phase etc. For the electrical transport measurements 4-probe resistivity technique was used and the pellets were cut into rectangular shape with approximate dimension of 5 × 1 × 1 mm³. Due the doping of Pb in the Tl_10-xATe₆ nanoparticles the Seebeck coefficient is increases. The phase of the both nanoparticles is also change. The phase is come to the face centered cubic. It is also shows that the increases temperature decreases the electrical conductivity due to the doping of Pb in the Tl_10-xATe₆ nanoparticles. The power factor is increases because the Seebeck coefficient is increase.