Thermoelectric Nanostructured Perovskite Materials

*Megha Unikoth, George Varghese, Karakat Shijina and Hind Neelamkodan*

### **Abstract**

The global need for energy production from renewable resources and the effect of greenhouse gas, especially carbon dioxide is increasing day by day. Statistical survey shows that about 60% of the energy lost in vain worldwide, in the form of waste heat. The conversion of this waste into useful energy form will certainly play a major role in alternative energy technologies. Thermoelectric materials (TE) can harvest waste heat and convert this into electrical energy and vice versa. The development of highefficiency TE materials for waste-heat-recovery systems is necessary to bring vast economic and environmental benefits. The methods of synthesis,that is, control over particle size play an important role in controlling the properties of thermoelectric materials. The nanostructuring of thermoelectric materials can enhance the efficiency by quantum confinement effect and phonon scattering. Perovskites have a long history of being a potential candidate for thermoelectric applications, due to their fascinating electrical, mechanical, and thermal properties. Compared with other thermoelectric materials perovskites have the advantage of eco-friendliness, less toxicity and are highly elemental abundant. Owing to the high thermal conductivity and low electrical conductivity overall performance of perovskites is relatively poor. The hybrid perovskites overcome this difficulty and started to draw the attention to thermoelectric applications.

**Keywords:** thermoelectric, figure of merit, nanostructuring, power generation, hybrid perovskites

### **1. Introduction**

The imbalance between energy production and demand is increasing day by day. While the conventional resources are being depleted, the challenges of researchers are concentrated on the power generation from renewable energy sources and on the efficient use of available resources. On the other hand, waste heat generation as greenhouse gas especially carbon dioxide is increasing in the environment. In internal combustion engines, only 25% of energy is used for vehicle mobility and accessories, approximately 40% of the fuel energy is wasted as exhaust gas, 30% is dissipated in the engine coolant and 5% is lost as radiation and friction. Here comes the importance of thermoelectric materials! The materials which can harvest heat from combustion of fossil fuels, sunlight, chemical reactions, nuclear decay, vehicles, etc., and convert it

into electrical energy and vice versa are thermoelectric materials. Thermoelectric power generation technology and the fields are now growing steadily due to their ability to convert heat into electricity and to develop cost-effective and pollution-free forms of energy conversion. A wide variety of thermoelectric materials has been identified and their properties have been explored. Among the oxide-based thermoelectric materials, rare earth-based perovskites are considered to be a potential material due to their fascinating electrical, mechanical, and thermal properties and high value of figure of merit. The thermoelectric materials in nanostructured form can enhance the performance of material by phonon scattering and quantum confinement effects [1–4].

### **2. Thermoelectric materials**

Thermoelectric materials have drawn vast attention due to the direct conversion between thermal and electrical energy. These materials can convert the heat energy to electrical energy and vice versa, thus providing an alternative source for power generation and refrigeration. Statistical survey shows that more than 60% of world's energy loss is in the form of heat. The high-performance thermoelectric materials can easily convert this heat into usable electrical energy. The thermoelectric system is an eco-friendly energy conversion technology with the advantages of high reliability, small size, feasibility in a wide temperature range, and no pollutants. The efficiency of the thermoelectric devices is small compared to Carnot's efficiency. The efficiency of these materials is defined in terms of figure of merit, ZT, which determines the thermoelectric performance.

$$ZT = \frac{\mathbb{S}^2 \sigma}{\kappa} T \tag{1}$$

where S is the Seebeck coefficient, σ is the electrical conductivity, κ is the thermal conductivity, and T is the absolute temperature. In order to get good performance, the value of ZT should be high. This can be achieved by increasing both the Seebeck coefficient and electrical conductivity and reducing the thermal conductivity.

The physics behind the thermoelectric power generation and the refrigeration is mainly governed by the three fundamental thermodynamic effects-the Seebeck, Thomson, and Peltier effects. When a temperature gradient is applied, an electrical potential gradient is generated, which is the Seebeck effect and is mainly used in the power generation. The Peltier effect is the reverse of the Seebeck effect in which a temperature gradient is established when a current is passed through the material and is used for refrigeration. Thomson heat is absorbed or released internally in the material if the flow of the Peltier heat is balanced by the temperature-dependent Seebeck coefficient. All the three effects are related to the heat transported by the charge carriers in the material as electrons or holes. Seebeck effect illustrating the working of a thermoelectric generator is given in **Figure 1**.

The thermoelectric efficiency (*ηP*) in the power generation mode as a function of average ZT is given by,

$$\eta\_P = \frac{T\_H - T\_C}{T\_H} \left( \frac{\sqrt{\mathbf{1} + Z T\_M} - \mathbf{1}}{\sqrt{\mathbf{1} + Z T\_M} + \frac{T\_C}{T\_H}} \right) \tag{2}$$

*Thermoelectric Nanostructured Perovskite Materials DOI: http://dx.doi.org/10.5772/intechopen.106614*

#### **Figure 1.**

*Illustration of the Seebeck effect, when heat flows through the junction current is generated.*

where TC, TH, and TM are the cold side, hot side, and average temperature respectively.

$$ZT\_M = \frac{1}{T\_H - T\_C} \int\_{T\_C}^{T\_H} ZTdT\tag{3}$$

A larger temperature difference can produce higher conversion efficiency, if the value of *ZTM*= 3 and *ΔT* = 400 K, *η<sup>P</sup>* can reach 25%, comparable to that of traditional heat engines. The Seebeck effect is the thermoelectric power generation model and has application in advanced scientific fields. The thermoelectric cooling efficiency (*ηC*) is given by,

$$\eta\_C = \frac{T\_H}{T\_H - T\_C} \left( \frac{\sqrt{\mathbf{1} + Z T\_M} - \frac{T\_H}{T\_C}}{\sqrt{\mathbf{1} + Z T\_M} + \mathbf{1}} \right) \tag{4}$$

Similar to thermoelectric power generation, higher *ZTM* will produce a large cooling efficiency (*ηC*). For *ZTM*= 3 and *ΔT* = 20 K, *η<sup>C</sup>* could reach 6%. The Peltier effect is a thermoelectric refrigeration model and is used to cool computer components to keep temperature within the limit or to maintain suitable functioning. The high ZT value is obtained only by increasing the value of S and σ and minimizing the κ. The complex relationship of thermoelectric parameters can be obtained from the Wiedemann-Franz law and Pisarenko relation, which is given by,

$$\mathcal{S} = \frac{8\pi^2 K\_B^2}{3eh^2} m^\* T \left(\frac{\pi}{3n}\right)^{\frac{2}{5}} \tag{5}$$

$$
\sigma = \frac{ne^2\tau}{m^\*} = ne\mu\tag{6}
$$

$$
\kappa\_{\text{total}} = \kappa\_{\text{electronic}} + \kappa\_{\text{lattice}} = L\sigma T + \kappa\_{\text{lattice}} \tag{7}
$$

where *K*<sup>B</sup> is the Boltzmann constant, h is the Planck constant, n is the carrier concentration, T is the absolute temperature, e is the electron charge, m\* is the effective mass, τ is the relaxation time, μ is the carrier mobility, and L is the Lorenz number. The electronic part of thermal conductivity is proportional to the electrical conductivity. Therefore, simultaneous enlargement of S and σ and the minimization of κ for high ZT values are very difficult. Over the past few decades, there is a lot of progress in the field of thermoelectrics to make an ideal material with ZT value greater than 3. There are many strategies for decoupling the relation between these parameters which includes phonon scattering mechanism, mass fluctuation strategy, rattling strategy, band engineering, 2D superlattice, and Panasonic approach. Energy filtering effects were also used in which an energy barrier was introduced by grain boundaries or nanocomposites [5]. According to the optimal working temperature, TE materials are classified into three – Bi2Te3 based low temperature (<400 K) materials, PbTebased material in the temperature range between 600 K and 900 K, and SiGe-based high temperature(>900 K) materials.

The first generation thermoelectric materials have ZT = 1 and the power generation efficiency is about 4–5%. The second generation materials pushed the ZT value up to 1.7 by nanostructuring and the obtained efficiency is 11–15%. The third generation material is under development and the predicted efficiency will be in the range of 15– 20%. The main goal will be to attain ZT ≥3 in future. PbTe is one of the most attractive thermoelectric materials [6].

The Skutterudites, Half-Heuslers, clathrates, and chalcogenides are hightemperature thermoelectric materials. Skutterudites are compounds with general formula MX3 where M = Co, Rh or Ir and X = P, and As or Sb (e.g., is CoSb3). These materials can influence the phonon transport mechanism, thereby reducing the lattice conductivity to very low level. X. Shi et al. reported that, for Ba0.08 La0.05 Yb0.04 Co4 Sb12 skutterudites has ZT = 1.7 at 850 K [7]. Half-Heuslers are alloys of the form ABX where A-Ti, Zr and Hf, B- CoSb, NiSn, etc. It was reported that, for n-type Hf0.5Zr 0.5NiSn0.99Sb0.01,0.8 ≤ ZT ≤ 1 was obtained at 600–700° C and for p-type Hf0.5Zr0.5CoSn0.2Sb0.8,0.5 ≤ ZT ≤ 0.8 due to the remarkable reduction in the lattice thermal conductivity [8].

The clathrates are low thermal conductivity compounds with Type I having X2Y6E46 formula and Type II having X 8Y 16E136 formula, where X and Y are guest atoms, E - Si, Ge, or Sn. Ba8Ga16Ge30 shows a Seebeck coefficient of 45 to -150mVK<sup>1</sup> and electrical conductivity of 1500–600Scm<sup>1</sup> at 300–900 K. The thermal conductivity of this compound is 1.8 WK<sup>1</sup> m<sup>1</sup> at 300 K and is reduced to 1.25 W K<sup>1</sup> m<sup>1</sup> at 900 K which makes ZT = 1.35 [9]. Chalcogenides are compounds with sulfides, selenides, and tellurides present in them (e.g., Bi2Te3, PbTe, SnSe, SiGe, etc). Among the oxide materials, NaCo2O4 has 0.7 ≤ ZT ≤ 0.8 at 1000 K [10]. The other new thermoelectric materials include In4Se3-<sup>δ</sup> (ZT =1.48) [33], In4Se3-xCl0.03 (ZT = 1.53) [34], β-Cu2-xSe (ZT = 1.5) [11] and β-Zn4Sb3 (ZT = 1.35) [12]. Low dimensional thermoelectric materials have higher performance than bulk materials because the density of states near the Fermi level is enhanced due to the quantum confinement effects, thereby increasing the thermopower (S2 σ) and boundary scattering at the interfaces reduces the thermal conductivity more than electrical conductivity. Therefore, by reducing the size of materials to 1D and 2 D, a significant enhancement in the value of ZT is obtained. Hicks and Dresselhaus first improved the value of ZT >1 of 2D Bi2Te3 quantum well [13]. He reported that the enhancement of ZT was achieved by the quantum confinement of electrons and holes, which increases the S2 σ and the reduction in the thermal conductivity was attributed to various effects, such as scattering of phonons at interfaces, defects, or phonon localization. Venkatasubramanian et al. reported, ZT = 2.4 for Bi2Te3-Sb2Te3 quantum well superlatttice of 6 nm periodicity [14]. The quantum dot superlattice of PbTe–PbSeTe system developed by Harman and co-workers has ZT = 1.6, which is higher than the bulk (ZT = 0.34) [15].

*Thermoelectric Nanostructured Perovskite Materials DOI: http://dx.doi.org/10.5772/intechopen.106614*

Hochbaum et.al reported that at room temperature, 50 nm diameter nanowires of Silicon have ZT = 0.6, which is very much higher than the bulk [16]. Boukai et al. noticed that reducing the nanowire's diameter, a significant reduction in thermal conductivity is attained and ZT of 1 at 200 K was reported for nanowires of 20 nm diameter. Nanostructured thermoelectric materials are designed in such a way to introduce nanometer-sized interfaces and polycrystalline into the bulk materials [17]. The lattice thermal conductivity can be reduced by increasing phonon scattering. Nanostructured composites of grain size �5 nm–10 μm can be fabricated by hot pressing or spark plasma sintering of fine powders [18]. In nanostructured material families (PbTe based nanomaterials, Bi2Te3–based and SiGe–based nanocomposites) an enhancement in ZT value is noticed. S. Fan et al. reported that in Bi2Te3–based nanocomposites, Bi0.4 Sb1.6Te3 has a ZT of 1.8 at 316 K [19]. Biswas et.al suggested that 2% SrTe – containing PbTe nanocomposites have a ZT of 1.7 at 800 K and X.W.Wang et al. studied Si80Ge20P2 nanocomposites and reported the ZT value of 1.3 at 1173 K [20, 21]. Perovskites, as well as their hybrids, started to draw attention as a potential candidate for thermoelectric applications.

### **3. Perovskites**

The first perovskite CaTiO3 was discovered by Gustav Rose in 1839 and named in the honor of an eminent mineralogist Count Lev Alexevich von Perovski. Perovskites are compounds having the structure formula ABC3, where A - rare earth, alkaline earth, alkali, or large ions, such as Pb+2, Bi+3, B - transition metal ion, and C - O, Fl, Cl, I, etc., commonly seen as in the form of ABO3. A cation may be monovalent like Li, Na, K, divalent like Ca, Ba, Sr., or trivalent like La, Nd, Pr, which is cubo-octahedrally coordinated with 12 oxygen atoms while B cation as Ti, Ni, Fe, Co, or Mn is octahedrally coordinated with 6 oxygen atoms. The substituted and mixed compounds of the form A1-xA'xB1-yB'yO3 also come under this class with distorted nonstoichiometric oxygen deficient configuration. The pseudo-perovskites are a special class of perovskites with empty A-site and BO3 configurations (e.g., ReO3 and WO3). The most abundant materials in the earth's crust are MgSiO3 and FeSiO3 perovskites [22].

The stability of perovskites is determined by a factor called Goldsmith tolerance factor given by, *<sup>t</sup>* <sup>¼</sup> *rA*þ*r*<sup>0</sup> ffiffi 2 <sup>p</sup> ð Þ *rB*þ*r*<sup>0</sup> , where *rA* – ionic radii of A-cation, *rB* – ionic radii of Bcation, and *r0*-ionic radii of oxygen. The value of t will be unity for an ideal perovskite. For different values of t, these materials have different structures. If t > 1, the crystal structure will be hexagonal in which A ions are too big and B ions are too small (e.g., BaNiO3). If t = 1 the structure will be cubic with A and B ions having ideal size (e.g., SrTiO3, BaTiO3). The materials with 0.71 < t < 1 have orthorhombic/rhombohedral crystal structure where A ions are too small to fit into B ion interstices (e.g., CaTiO3/ GdFeO3) and for t < 0.7 materials have different structures in which A ions and B ions have similar ionic radii (e.g., FeTiO3) [23].

The coexistence of spin, charge, lattice, and orbital interactions in perovskite materials make them applicable in optoelectronics, spintronics, photocatalysis, sensors, piezoelectric devices, electrode in solid oxide fuel cells, and thermoelectrics. They have a lot of fascinating properties, such as multiferroicity (BaTiO3, BiFeO3), colossal magnetoresistance (manganites), superconductivity (cuprates), ferromagnetism (SrRuO3), metal-insulator transition (LaMnO3), thermoelectricity (LaCoO3), etc.
