Thermoelectric Nanostructured Perovskite Materials

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 high-efficiency 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.

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, 2, 3, 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.

$$\mathit{ZT}=\frac{S^2\sigma }{\kappa }T$$E1

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.

Figure 1.

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

The thermoelectric efficiency (${\eta }_P$) in the power generation mode as a function of average ZT is given by,

$${\eta }_P=\frac{T_H-T_C}{T_H}\left(\frac{\sqrt{1+{\mathit{ZT}}_M}-1}{\sqrt{1+{\mathit{ZT}}_M}+\frac{T_C}{T_H}}\right)$$E2

where T_C, T_H, and T_M are the cold side, hot side, and average temperature respectively.

$${\mathit{ZT}}_M=\frac{1}{T_H-T_C}\underset{T_C}{\overset{T_H}{\int }}\mathit{\text{ZTdT}}$$E3

A larger temperature difference can produce higher conversion efficiency, if the value of ${\mathit{ZT}}_M$= 3 and $\mathit{\Delta T}$ = 400 K, ${\eta }_P$ 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 (${\eta }_C$) is given by,

$${\eta }_C=\frac{T_H}{T_H-T_C}\left(\frac{\sqrt{1+{\mathit{ZT}}_M}-\frac{T_H}{T_C}}{\sqrt{1+{\mathit{ZT}}_M}+1}\right)$$E4

Similar to thermoelectric power generation, higher ${\mathit{ZT}}_M$ will produce a large cooling efficiency (${\eta }_C$). For ${\mathit{ZT}}_M$= 3 and $\mathit{\Delta T}$ = 20 K, ${\eta }_C$ 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,

$$S=\frac{8{\pi }^2{K}_B^2}{3{\mathit{eh}}^2}{m}^{\ast }T{\left(\frac{\pi }{3n}\right)}^{\frac{2}{3}}$$E5

$$\sigma =\frac{{\mathit{ne}}^2\tau }{m^{\ast }}=\mathit{ne\mu }$$E6

$${\kappa }_{\mathit{\text{total}}}={\kappa }_{\mathit{\text{electronic}}}+{\kappa }_{\mathit{\text{lattice}}}=\mathit{L\sigma T}+{\kappa }_{\mathit{\text{lattice}}}$$E7

where K_B 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, PbTe- based 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 high-temperature 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 Ba_0.08 La_0.05 Yb_0.04 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 Hf_0.5Zr _0.5NiSn_0.99Sb_0.01,0.8 ≤ ZT ≤ 1 was obtained at 600–700° C and for p-type Hf_0.5Zr_0.5CoSn_0.2Sb_0.8,0.5 ≤ 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⁻¹ and electrical conductivity of 1500–600Scm⁻¹ at 300–900 K. The thermal conductivity of this compound is 1.8 WK⁻¹ m⁻¹ at 300 K and is reduced to 1.25 W K⁻¹ m⁻¹ 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 In₄Se_3-δ (ZT =1.48) [33], In₄Se_3-xCl_0.03 (ZT = 1.53) [34], β-Cu_2-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 (S²σ) 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 S²σ 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].

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, Bi_0.4 Sb_1.6Te₃ 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 A_1-xA’_xB_1-yB’_yO₃ also come under this class with distorted non-stoichiometric 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, $t=\frac{r_A+r_0}{\sqrt{2}\left(r_B+r_0\right)}$, where r_A – ionic radii of A-cation, r_B – ionic radii of B-cation, 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.

3.1 Perovskite oxides (ABO₃) as thermoelectric materials

Oxide perovskites have been used as thermoelectric materials due to their low thermal conductivity, high Seebeck coefficient, and electrical conductivity. There are two approaches to enhance ZT value, one is tuning the carrier concentration and another is engineering structure and material properties to decouple the S, σ, and κ. The further modification methods to enhance ZT value are self-doping, nano-engineering, band engineering, and doping shown in Figure 2. In perovskite oxides the main candidates which show TE properties were titanates, manganates, and colbatates.

Figure 2.

Methods to enhance the ZT of thermoelectric perovskite materials.

The substituted perovskite compounds of titanates (Sr_1-xA_xTi_1-yNb_yO₃, where A- Ca, La, Ba, Eu, etc) are promising classes of thermoelectric materials with high figure of merit. It was reported that SrTi_0.8Nb_0.2O₃ thin films have ZT = 0.37 at 1000 K, which was reduced to 0.35 by hot pressing the sample to a temperature of 1073 K. When the material SrTi_0.8Nb_0.2O₃ is grown in nanostructure as superlattice, where a single layer of this material is sandwiched between the several layers of insulating SrTiO₃ (STO), a remarkable increase in ZT ∼2.4 at 300 K is obtained. In La-doped STO thin films S can be tuned from −120 to -260μVK⁻¹. The La 15% doped STO has a ZT value of 0.28 at 873 K was achieved. Even though the electrical conductivity of STO is increased by La doping, it reduces the lattice thermal conductivity by phonon scattering. It was reported that the substitution of Ce, Ba, Ca, Pr, and Y on A-site and Nb, Ta, Mn, and Co on B-site enhances the electrical conductivity of the sample. The Nb-doped STO(Sr(Nb_xTi_1 − x)O₃,0.01 < x < 0.4), in which substituted Nd⁵⁺ at Ti⁴⁺ site will generate carrier electrons and a ZT of ∼0.35–0.37 at 1000 K was achieved for 20%Nb. While Mn substitution of Sr_1 − xLaxTiO₃ the S was enhanced from −120 to −180 μV·K⁻¹ and the ZT value of 0.07 to 0.15 at 300 K was obtained when the composition changed from Sr_0.95La_0.05TiO₃ to Sr_0.95La_0.05Ti_0.96Mn_0.04O₃. For SrTi_0.9Ta_0.1O₃ the ZT value obtained was 0.17 at 752 K and for SrTi_0.875Co_0.125O₃ was 0.135 at 300 K. The A-site substitution enhances electrical properties while B-site enhances the Seebeck coefficient value. However, the doping of Y, La, Sm, Gd, and Dy in STO reduces the thermal conductivity. For (Sr_0.9Dy_0.1)TiO₃ has a ZT value of 0.22 at 573 K. Mn doped Sr_1 − xLaxTiO₃ can enhance anharmonic lattice vibrations, which result in inelastic phonon-phonon scattering reduces thermal conductivity and offers high electrical conductivity. Compared to ZT of Sr_0.95La_0.05TiO₃ 0.07 Sr_0.95La_0.05Ti_0.98Mn_0.02O₃ has 0.15 at 300 K. The effective way to reduce thermal conductivity is rare earth substitution in A-site and Mn substitution in B-site. The data compounds obtained were tabulated in Table 1 [5].

Materials	Electrical Conductivity (S cm^−1)	Seeback coefficient (μVK^−1)	Thermal conductivity (W m^−1 K^1)	Power Factor (μW m^−1 K^−2)	ZT	Temperature (K)
Sr0.85La0.15TiO3	400	175	3		0.28	873
reducedgrapheneoxide—SrTiO3	30	−380			0.09	760
Sr0.875Pr0.125TiO3	3700	−80			0.4	323
Sr0.9 Dy0.1TiO3 R = (La,Sm,Gd,Dy,Y)	500	−160	2.7		0.22	573
Sr0.95La0.05TiO3	150	250	4.2	800	0.15	780
Sr0.9La0.1TiO3	300	−225	3.2		0.21	750
La-dopedSrTiO3	80	−300	3.1		0.27	1073
Sr(Ti0.8Nb0.2)O3		−200	3.5	1300	0.37	1000
Ba0.3Sr0.6La0.1TiO3		−110	4.4		0.13	420
Sr0.45Ca0.45La0.1TiO3	250	−195	3.7		0.22	850
Sr0.98La0.02TiO3	500	−260	11		0.09	298
SrTiO3/SrTi0.8Nb0.2O3 /SrTiO3	1400	−850	12		2.4	300
SrTi0.9Ta0.1O3	300	−175	4.4		0.17	752
Sr0.95La0.05Ti0.98Mn0.02O3	833	−150	3.9	20	0.15	300
n-typeSrTiO3		300			0.7	1400

Table 1.

Thermoelectric studies of doped ATiO₃ compounds.

The thermoelectric properties of Mn substituted perovskites were summarized in Table 2. In these perovskite oxides multiple elements are used as A-site dopants in AMnO₃ including Yb, Y, La, Ce, Sm, Dy, Tb, Ho, Pr, Ca, Sr, Nd, etc. and for B-site Mo, Ru, Ta, etc. Relatively high ZT values are not achieved in these materials. CaMn_0.98Nb_0.02O₃ shows a significant ZT of 0.32 at 1050 K. It was noticed that the thermal conductivity of Mn-doped samples is low.

Materials	Electrical Conductivity (S cm^−1)	Seeback coefficient (μVK^−1)	Thermal conductivity (W m^−1 K^1)	Power Factor (μW m^−1 K^−2)	ZT	Temperature (K)
Tb0.1Ca0.9MnO3	−0.18	−140			0.13	950
Ho0.1Ca0.9MnO3	−0.18	−110			0.08	950
Y0.1Ca0.9MnO3	−0.2	−130			0.15	950
Ca0.9Bi0.1MnO3	10	80			0.095	1173
Ca0.85Pr0.15MnO2.98	111	−130	1.5		0.17	1100
Ca0.9Yb0.1MnO3	133	−150	1.6		0.16	970
Pr0.3 Sr0.7MnO3	250	−75	1.6		0.085	1073
Ca0.96Bi0.04MnO3	66.7	−170	3.6	300	0.086	1000
CaMn0.96Mo0.04O3		−90	3.4		0.012	270
CaMn0.94Ru0.06O3		−140	5.4		0.0085	330
CaMn0.98Ta0.02O3	29	−190			0.05	1000
CaMn0.98Nb0.02O3	31	−255			0.32	1050
SrMn0.7Ru0.3O3	50	−40			0.01	370
Sr(Mn0.975Mo0.025)O3	0.13	−120	5		0.013	400
Ca0.8Nd0.2MnO3	280	−62	1.3		0.17	873

Table 2.

Thermoelectric studies of doped AMnO₃ compounds.

Rare earth cobalt oxides are compounds having the stoichiometry RCoO₃, R – La, Ce, Pr, Nd, etc. It was also reported that the electrical conductivity of these materials increased with increasing ionic radii of rare earth metals doping (Pr³⁺ > Nd³⁺ > Tb³⁺ >Dy³⁺). The complex spin structure of Co ions in perovskite gives us plenty of opportunities to explore the exotic magnetic phenomenon of these materials. The Co ions in RCoO₃ can exist in three different spin states, low spin LS (t_2g⁶ e_g⁰ for Co³⁺ and t_2g⁵ e_g⁰ for Co⁴⁺), intermediate spin IS (t_2g⁵ e_g¹ for Co³⁺ and t_2g⁴ e_g¹ for Co⁴⁺), and high spin state HS (t_2g⁴, e_g² for Co³⁺ and t_2g³, e_g² for Co⁴⁺), which can induce spin entropic effect to the perovskite structure and can influence all the magneto-transport properties of the materials [24, 25, 26]. It was reported that A- site substituted LaCoO_3, has high ZT value. Sr, Na, Pb, and Ba are usually used elements for substitution. For La_1 − xSr_xCoO₃ the electrical conductivity gets enhanced, and the ZT value of 0.046 to 0.18 was achieved. Pb doped LaCoO₃ has Seebeck coefficient of 110 μV·K⁻¹ and ZT of 0.23 to reported. Thermoelectric measurements of doped ACoO₃ compounds are tabulated in Table 3.

Materials	Electrical Conductivity (S cm^−1)	Seeback coefficient (μVK^−1)	Thermal conductivity (W m^−1 K^1)	Power Factor (μW m^−1 K^−2)	ZT	Temperature (K)
(Pr0.9Ca0.1)CoO3	220	106	1.9		0.047	358
TbCoO3	200	80	1.6		0.05	873
Ho0.9Ca0.1CoO3	20	220	0.75		0.051	573
La0.875Sr0.125CoO3		100	6		0.035	230
La0.95Sr0.05CoO3	20	720	0.037		0.18	300
La0.9Sr0.1CoO3		120	1.5		0.046	300
La0.9Pb0.1CoO3	333	110	0.8		0.23	575
La0.97Ba0.03CoO3	40	80		80	0.08	420

Table 3.

Thermoelectric studies of doped ACoO₃ compounds.

The other B-site cations include iron (Fe), nickel (Ni), tin (Sn), lead (Pb), bismuth (Bi), molybdenum (Mo), ruthenium (Ru), and uranium (U). The thermoelectric measurements are tabulated in Table 4. For Fe doped compounds La_0.95Sr_0.05FeO₃ and Pr_0.9Sr_0.1FeO₃, the ZT value obtained are 0.076 and 0.024, while for Ni-doped LaCo_0.92Ni_0.08O_2.9 the ZT value of 0.2 was achieved. Double perovskite A₂FeMoO₆ (A-Ca,Sr,K,Ba) was also studied. For ZT ranges from 0.1 to 0.99 was reported. For tin substituted compounds BaSnO₃ ZT of 0.65 was theoretically calculated. Sr_1 − xBa_xPbO₃ ZT of 0.13 was observed. There was no significant high ZT value seen when the B-site is doped with Mo, Ru, and U. The thermoelectric measurement parameters are all tabulated in Table 4.

Materials	Electrical Conductivity (S cm^−1)	Seeback coefficient (μVK^−1)	Thermal conductivity (W m^−1 K^1)	Power Factor (μW m^−1 K^−2)	ZT	Temperature (K)
LaCo0.92Ni0.08O2.9	33.3	220	0.35		0.2	300
Pr0.9Sr0.1FeO3		140	0.8		0.024	850
La0.95Sr0.05FeO3		230	1.8		0.076	1273
Ca2FeMoO6	300	−108	3.2		0.14	1250
Ca1.9Sr0.1FeMoO6	250	−110	3		0.14	1250
Ca1.8Sr0.2FeMoO6	260	−100	2.8		0.14	1250
Sr1.6K0.4FeMoO6		−48	3.1	450	0.24	1250
Ba2FeMoO6		−1350			0.995	300
Ba0.998La0.002SnO3	150	−170	4		0.1	1073
Sr0.99La0.01SnO3	1.5	−80	3.6	120	0.05	1073
BaSnO3	300	−130	3.4	1400	0.65	1200
Ba0.4Sr0.6PbO3	250	125	2		0.13	673
Ba0.2Sr0.8PbO3	79	−190	1.8		0.13	680
BaMoO3		−30			0.015	1000
SrRuO3		36	5.3		0.03	1200
(Sr0.95 La0.05)2 RuErO6		−160			0.001	800
K0.991Ba0.009Ta O3	333	200			0.03	300
BaUO6	0.1	−170	0.8		0.0002	880

Table 4.

Thermoelectric studies of other doped perovskite oxide.

3.2 Hybrid perovskites

Compared to other thermoelectric materials hybrid perovskites have high Seebeck coefficient and low thermal and electrical conductivity. For CH₃NH₃PbI₃ at 295 K has S = 700 μV·K⁻¹, κ = 0.5 W·m⁻¹·K^−1, and ZT value is 10⁻⁷ due to the low electrical conductivity. The photo-induced or chemical doping strategies were used in these materials to enhance the electrical conductivity. There are many hybrid perovskite materials that show TE applications, such as ABI₃ (A = CH₃NH₃ (MA), NH₂CHNH₂ (FA), and B = Pb, Sn), CsMI₃, and C₆H₄NH₂CuBr₂I. Theoretical studies on n-type and p-type CH₃NH₃PbI₃ hybrid perovskites show ZT value of 0.9 and 1.25. For (MA)PbI₃, (MA)SnI₃, (FA)PbI₃, and (FA)SnI₃ n-type materials the reported ZT values are 0.44, 0.45, 0.42, and 0.35 respectively. As the carrier concentration increases ZT also increases. The same CH₃NH₃PbI₃ n-type ZT of 2.56 at 800 K can be achieved. The first-principles calculations and semi-classical Boltzmann transport theory showed that the ZT values of 0.63 and 0.64 for CsSnI₃ and CsPb n-type at 1000 K. The thermoelectric properties of hybrid perovskites are tabulated in Table 5.

Materials	Electrical Conductivity (S cm^−1)	Seeback coefficient (μVK^−1)	Thermal conductivity (W m^−1 K^1)	Power Factor (μW m^−1 K^−2)	ZT	Temperature (K)
CsSnl3			0.18		0.63	1000
CsPbl3			0.1		0.64	1000
(FA)Pbl3		100			0.43	298
(FA)Snl3		150			0.35	298
CH3NH3Pbl3-n-type	1.2	80			0.9	330
CH3NH3Pbl3-p-type	1	50			1.25	330
C6H4NH2CuBr2l	2950	−82	3.25		0.21	363
CH3NH3Pbl3-n-type	68	−428	0.151	11.3	2.56	800
p-type	25	358	0.04	3.3	1.08	800
CH3NH3Snl3	0.001	720	0.08		0.01	295
CH3NH3Pbl3	10^−7	700	0.5		10–^7	295
(MA)Pbl3		200			0.44	298
(MA)Snl3		200			0.44	298

Table 5.

Theoretical ZT value of hybrid perovskites from calculations.

4. Nanostructuring of thermoelectric materials

The materials having at least one of the dimensions in the order of 10⁻⁹ m are nanostructured materials. If the dimension of material is in nanometer range its surface-to-volume ratio increases and the properties changes drastically. Nanoparticles are highly reactive because they possess large surface energy. Such an increase in surface area in thin films and coating can enhance the sensing property, catalytic activity of surfaces, light trapping in solar cells, surface reactivity, etc. Nanosystems are classified into three two-dimensional (2D), one-dimensional (1D), and Zero dimensional (0D). Nanosheets and superlattices are 2D nanosystems, nanowires, nanorods, and nanotubes are 1D and nanopowders and quantum dots are 0D nanosystems. There are two approaches for the fabrication of nanostructured materials- top-down method and the bottom-up method. Starting from bulk crystalline material and dividing it into small pieces to obtain fine nanosized particles is the top-down method. Ball milling, spin melting, thermal cycling, lithography, etc. [27]. In bottom-up method, nanoparticles are produced from their constituent elements, which are assembled to form dense solids Figure 3.

Figure 3.

Bottom-up strategies for nanostructuring of TE materials.

When the particle size is decreased to nano, size-dependent quantum confinement effect arises. Generally, in nanostructures, the energy level spacing increases with decreasing size and is the quantum size confinement effect. This effect influences the optical, electronic, magnetic, thermal, and dynamic properties of the material. Another important size reduction effect is the electron-phonon coupling. With decrease in size, the density of states of both phonons and electrons decreases in size and this decreases the overlap. The combination of density of states and the surface phonon frequencies affect the phonon-electron interaction in the nanostructures. The quantum confinement effect and the phonon scattering have a crucial role in enhancing the efficiency of thermoelectric materials. By nanostructuring, the electrical conductivity of thermoelectric materials can be enhanced by quantum confinement effect and the thermal conductivity can be reduced by phonon scattering at the interfaces, thereby increasing the figure of merit.

The nanostructured thermoelectric perovskite compounds have been prepared by many techniques which include co-precipitation, mechanical synthesis, solid-state reactions, solution combustion or thermal decomposition, hydrothermal, Pechini, and sol-gel method. Many new methods and improvements in synthesis conditions have been tried by the researchers as the properties of the end product strongly depend on the method of synthesis technique used. The citrate sol-gel auto-combustion method, which is a modified Pechini method based on the polyesterification of ethylene glycol and citric acid for the synthesis of the perovskite nanopowders. The method involves relatively easy synthesis route when compared to the other conventional processes. The control over the end stoichiometry and low operating temperature are the main advantages of this technique.

Popa et al. have synthesized perovskite – LaMeO₃ (Me - Co, Mn, Fe) compounds by the polymer complex method and elaborated its advantages. Nonuniformity in particle size, compositional inhomogeneity, and high processing temperature are the main disadvantages when the conventional mixed oxide methods are preferred for the synthesis. Perovskite nanopowders developed through wet-chemical method have relatively high product uniformity and reliable reproducibility. By this method, it is possible to reduce the agglomeration of nanoparticles and can control the particle size. In citrate sol-gel auto-combustion method, at relatively low temperature excellent chemical homogeneity can be achieved. The perovskite nanopowders thus obtained have uniform particle size, which allows sintering to give dense well shaped uniformly grained microstructures [28]. The nanopowders were subjected to characterization techniques including XRD, SEM-EDAX, XPS, particle size analyzer, etc. Finally, dc electrical conductivity, thermal conductivity, and the Seebeck coefficient measurements are carried out using thermoelectric measurement setup.

5. Thermoelectric characterization

The simultaneous measurement of electrical resistivity and Seebeck coefficient was done using ULVAC-ZEM 3. The sample is sandwiched between the electrodes and kept in helium atmosphere at low pressure of 10⁻³ Torr. The resistivity is calculated using four probe method.

$$\rho =\frac{\mathit{RA}}{l}$$E8

where ρ is the electrical resistivity, R is the resistance, A is the area of cross section and l is the distance between the probes. High impedance current is supplied through the probes connected to upper and lower blocks. Other two probes measure the voltage produced. Seebeck coefficient is determined by measuring the electromotive force generated at the probes. The sample is kept in such a way that a temperature gradient can exist between the two ends. Let T₁ and T₂ be the temperatures at two ends and the electrical potential difference is $\mathit{dV}$, the Seebeck coefficient can be calculated using the formula,

$$S=\frac{\mathit{dV}}{T_1-T_2}$$E9

The measurement is controlled by a computer. The voltage-current measurement is made to check the correct contact of the sample. The thermal conductivity of the sample can be measured by divider bar method. In this method the sample is sandwiched between two metal blocks, heat flows through the sample by measuring the thermal gradient the thermal conductivity can be measured.

6. Conclusion

It is well known from the literature that, the need for thermoelectric material for power generation and refrigeration is increasing day by day. Nowadays, heat generation from automobiles, factories, combustion of fossil fuels, nuclear decay, etc. is increasing a lot and it is necessary to convert these waste heat into useful form. Therefore, development of thermoelectric material which can convert the waste heat into electricity will be a milestone for the modern technology. Even though the ZT value of perovskite was very small, we can tune the properties of these materials by nanostructuring, band gap engineering, and by doping. In these thermoelectric perovskite materials, SrTiO₃/SrTi_0.8Nb_0.2O₃ /SrTiO₃ was considered to be the best material with a ZT value of 2.4 at 300 K. Therefore, there are many possibilities in perovskite materials to be a replaceable candidate for TE applications. The hybrid perovskites which are low cost and easily synthesized by energy cost methods can be potential TE material in future at room temperature range. In the case of these materials, CH₃NH₃PbI₃-n-type shows a ZT of 2.56 at 800 K, which was only a theoretical calculation. Further in future, we can make all the calculations be true for an alternative energy resource for the world.