Environmentally friendly Ba_xSr_2−xTiFeO₆ double perovskite with enhanced thermopower for high temperature thermoelectric power generation

Abstract

In the present work, the prospects of environmental friendly Ba_xSr_2−xTiFeO₆ complex double perovskites have been evaluated for applications as high temperature thermoelectric materials with properties converging to the ‘phonon-glass electron-crystal’ model. Ba_xSr_2−xTiFeO₆ compositions with 0.0 ≤ x ≤ 0.25 were synthesized by a solid-state reaction method. The oxide samples were then investigated for their crystal structure (single phase) and morphology by XRD and SEM, respectively. Thermo-power or Seebeck coefficient (S) and the electrical conductivity (σ) of these oxide samples were simultaneously measured to calculate the thermoelectric power factor (S²σ). All the Ba_xSr_2−xTiFeO₆ compositions showed p-type non-degenerate semiconductor behavior before semiconductor to metal transition occurred as evident from the temperature dependent Seebeck coefficient of these double perovskites. Conduction mechanisms of these oxides were analyzed using variable range hopping and small polaron hopping conduction models. All these double perovskites exhibited more than 100 μV K⁻¹ thermo-power in the wide range of temperature from 300 K to 1223 K. A very high thermo-power (S) value (∼800 μV K⁻¹) was obtained for Ba_xSr_2−xFeTiO₆ with x = 0.25 at 1123 K.

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1. Introduction

Scavenging the waste heat generated by industries, furnaces, combustion engines, various electronic appliances etc. by converting it into electricity using thermoelectric materials has been considered as one of the cleanest sources of energy generation. Thermoelectric devices use the phenomenon called the ‘Seebeck effect’ to convert thermal energy into electrical energy. Although prospects of thermoelectric power generation were evaluated long ago, a cost effective high efficiency power conversion device is yet to be realized. All the vital parameters involved in the process of effective thermoelectricity generation are manipulated in the single quantity called the ‘Figure of Merit’. The dimensionless figure of merit, ZT is defined as

where σ is the electrical conductivity, k is the thermal conductivity, and S is the Seebeck coefficient. Moreover, thermal conductivity can be divided into electronic thermal conductivity (k_e) and lattice thermal conductivity (k_l) for the heat transport medium of electron and phonon, respectively. A greater ZT indicates a greater thermodynamic efficiency of the device. In order to achieve higher ZT values in thermoelectric devices, large Seebeck coefficient and higher electrical conductivity along with poor thermal conductivity are required. It is quite tough to achieve higher electrical conductivity and poor thermal conductivity in the same material, as both are mutually exclusive properties. Good thermoelectrics should be crystalline materials, which can scatter phonons without significantly disrupting the electrical conductivity. Thermoelectric materials therefore require a rather unusual material in which electrons and holes can be transported in fast, efficient manner like in crystals. However, it should be difficult to transport heat similar to what is generally found in glass where lot of phonon scattering happens due to its disordered amorphous structure. This material's requirement for achieving higher ZT values was summarized well as ‘phonon-glass and electron-crystal’ model, proposed by Slack.¹ All the existing state-of-art thermoelectric materials suffer from several drawbacks such as toxicity, decomposition, vaporization, or melting of the constituents especially at higher temperature (T > 600 K) resulting poor efficiency of energy conversion (heat into electricity) at high temperature. Hence the detailed investigations are required to engineer a novel environmental friendly non-toxic material, which can optimize a variety of conflicting properties like higher electrical conductivity along with lower thermal conductivity besides large Seebeck coefficient resulting improved efficiency of thermoelectric devices.

In this regard, oxide materials with good ZT values can be major breakthrough in the course of searching non-toxic, environment friendly, low-cost thermoelectric materials especially for high temperature applications since they exhibit relatively higher oxidation resistance and better thermal stability. The recent discovery of p-type thermoelectric oxides^2,3 like Na_xCoO₂, Ca₃Co₄O₉ with good figure of merit have generated renewed attention in the scientific community to explore oxide materials for thermoelectric applications. The outstanding thermoelectric performance of these oxides is attributed to its anomalously large thermopower considering their high carrier concentration (h ∼ 10²² cm⁻³) and low thermal conductivity. The coexistence of high thermopower and electrical conductivity has been attributed to the fact that the electron spin and orbital can also carry entropy current^4–6 in these cobaltite oxides. Recently doped SrTiO₃ based materials^7–11 have shown tremendous potential as n-type TE materials, however their ZT values (∼0.2) are needed to be improved to use it in thermoelectric devices. It is proposed in the current investigation that SrTiO₃ based double perovskites will be able to enhance the ZT values by enhancing its power factor (S²σ) and lowering thermal conductivity. In the Sr₂TiB′O₆ double perovskites TiO₆ and B′O₆ octahedras are arranged in the ordering of three-dimensional (3D) checkerboard. In the current investigation, crystal structure of Sr₂TiB′O₆ double perovskites have been engineered by choosing a ferromagnetic transition metal iron (Fe) for B′ sites as shown schematically in Fig. 1. These double perovskites are one of those rare materials having half-metallic^12–14 ground states in which conduction electrons are fully spin polarized. Few research works so far have been reported on double perovskite based thermoelectric materials based on Sr₂(FeMo)O₆ based materials with Ba, Ca substitution in Sr-site of the double perovskite materials.^15–19 Some of these materials have been reported to achieve ZT values of 0.31, which suggests the high potential of these double perovskite compounds for thermoelectric applications.

Fig. 1 Schematic representation of Ba_xSr_2−xTiFeO₆ double perovskite crystal-structure.

In the current investigation, Ba_xSr_2−xTiFeO₆ compositions with 0.0 ≤ x ≤ 0.25 double perovskites were synthesized by solid-state route. Furthermore, potential of these oxides for high temperature thermoelectric applications has been evaluated by measuring their Seebeck coefficient and electrical conductivity. To the best of our knowledge, there are no reports on thermoelectric properties of Ba_xSr_2−xTiFeO₆ compositions.

2. Experimental procedure

Dense samples of Ba_xSr_2−xTiFeO₆ (BSTF) ceramics with compositions 0.0 ≤ x ≤ 0.25 were prepared by the conventional solid-state reaction method.^20–22 Stoichiometric compositions of Ba_xSr_2−xTiFeO₆ (BSTF), were synthesized by mixing the powders of SrCO₃ (Sigma Aldrich ≥99.9%), BaCO₃ (Sigma Aldrich ≥99%), Fe₂O₃ (Sigma Aldrich ≥99.995%), and TiO₂ (Sigma Aldrich ≥99.5%) in appropriate ratios in ball-mill at 350 rpm for 24 h using ethanol as the milling media. Then the mixed BSTF powders were calcined at 1473 K for 10 h. Since the powder obtained after calcination process was agglomerated, powders were milled again to break those agglomerates. Homogeneous nano-powders of calcined BSTF were obtained after milling in a planetary micro mill (Fritsch®, PULVERISETTE 7 premium Line, Rhineland-Palatinate, Germany) for 120 min at 600 rpm using zirconia grinding balls (diameter: 2 mm, 1.5 mm and 1 mm in the 5 : 2 : 1 ratio, respectively). After adding the binder the oxide powders were pressed into pellets. Sintering of the pellets was carried out at 1623 K for 10 h. Microstructural investigation of the polished ceramic samples was performed using scanning electron microscope (SEM, Carl Zeiss NTS GmbH, EV050, Germany). The powder X-ray diffraction (XRD) patterns of annealed oxide powders were measured in the range of 2θ = 20–100° using a PANalytical X'Pert diffractometer. Thermoelectric properties, such as electrical resistivity ρ (Ω m⁻¹), and Seebeck coefficient S (μV K⁻¹) were simultaneously measured in the temperature range from 300 K to 1125 K at the interval of 50 K using a ZEM-3M10 apparatus (ULVAC-RIKO Inc.). In the thermoelectric measurement using ZEM3-M10, a rectangular bar-shaped sample was placed in a vertical position between the upper and lower platinum blocks in the heating furnace. While the sample was heated to, and held, at a specified temperature; one end of the sample was heated by the heater in the lower block to provide a temperature gradient (ΔT). Thermo-power (S) and electrical resistivity (ρ), were simultaneously measured at three temperature gradient (ΔT = 20 K, 30 K and 40 K) for every specified temperature. Final thermoelectric data at the specified temperature was collected by averaging measured values at these three temperature gradients (ΔT). Seebeck coefficients were determined by measuring the temperatures of upper and lower Pt-blocks with the thermocouples, followed by measurement of electromotive force, dE between the same wires on one side of the thermocouple. Electric resistance is measured by the dc four-terminal method. V–I plot measurement was carried out for every sample to judge if the probes or leads were in intimate contact with the sample.

Furthermore the electrical conductivity (σ) and thermoelectric power factor (S²σ) were calculated for all the compositions in the temperature range from 300 K to 1125 K.

3. Results and discussion

3.1 Structural analysis

To determine the existence of any secondary phase in the well-sintered dense pellets of Ba_xSr_2−xTiFeO₆ compositions with 0.0 ≤ x ≤ 0.25, powder X-ray diffraction studies were carried out at room temperature. As shown in the Fig. 2, powder X-ray diffraction pattern verifies the single-phase solid solution for all the Ba_xSr_2−xTiFeO₆ (BSTF) composition with 0.0 ≤ x ≤ 0.25. All the reflections in the XRD patterns were indexed with respect to the perovskite structure as shown in Fig. 2. As no splitting was observed in any of the pseudocubic profiles of the diffraction pattern, the room temperature structure of the Ba_xSr_2−xTiFeO₆ ceramics with 0.0 ≤ x ≤ 0.25 can be regarded as cubic.

Fig. 2 XRD pattern of sintered Ba_xSr_2−xTiFeO₆ ceramics with 0.0 ≤ x ≤ 0.25.

Microstructure has a very critical role to play in determining the performance of the thermoelectric devices measured by the figure of merit, ZT = (S²σ/k)T. It is possible to increase ZT value by decreasing the lattice thermal conductivity (k_l). The lattice thermal conductivity (k_l) of the ceramic materials can be decreased significantly by increasing the phonon scattering from grain boundaries without affecting much the electrical conductivity.

To increase the phonon scattering one must achieve smallest possible grain size in the ceramic materials. Besides one should have dense ceramic pellet without having much porosity to achieve good the electrical conductivity. Microstructural studies were carried out for all the Ba_xSr_2−xTiFeO₆ (BSTF) ceramics with 0.0 ≤ x ≤ 0.25 by Scanning Electron Microscopy (SEM) as shown in Fig. 3. It is evident from the SEM (scanning electron microscope) images of BSTF sintered pellets that all the samples were well-sintered and dense as no such porosity was observed. It is found that with the increase in barium concentration in Ba_xSr_2−xTiFeO₆ (BSTF) ceramics, the grain size increases. BSTF ceramics exhibit average grain size in the range from 4 μm to 8 μm. However, it is proposed to use spark plasma sintering process in order to achieve nm-scale grain size, which is expected considering the fact that particle size of initial calcined powder was reduced to less than 100 nm by nano-scale ball milling.

Fig. 3 SEM images of Ba_xSr_2−xTiFeO₆ ceramics with (a) x = 0.0 (b) x = 0.10 (c) x = 0.15 (d) x = 0.25.

3.2 Thermoelectric measurements of Ba_xSr_2−xTiFeO₆ (BSTF) ceramics with 0.0 ≤ x ≤ 0.25

To evaluate the potential of Ba_xSr_2−xFeTiO₆ (BSTF) ceramics with 0.0 ≤ x ≤ 0.25 for the applications in high temperature thermoelectric power generation, detailed investigation was carried out on well-sintered dense ceramic samples of these compositions. Thermoelectric properties like thermo-power or Seebeck coefficient (S) and electrical conductivity (σ) were measured simultaneously in the temperature range from 300 K to 1273 K as shown in Fig. 4. At room temperature, the value of Seebeck coefficient or thermo-power increases continuously with the increase in barium concentration in Ba_xSr_2−xFeTiO₆ compositions as shown in Fig. 4(a). It is attributed to the higher value of effective mass of holes in barium doped STF compositions. Thermo-power obtained for Ba_xSr_2−xFeTiO₆ with x = 0.25 at room temperature is as high as ∼200 μV K⁻¹ compared to that of pure Sr₂FeTiO₆ (∼150 μV K⁻¹). Very few materials available today which exhibit such a high thermo-power at room temperature which is the major impetus in our attempt to develop thermoelectric devices based on these double perovskites. With the increase in temperature, Seebeck coefficient value gradually decreases for all the BSTF compositions upto a certain temperature after which it started increasing rapidly with increase in temperature. This point of inflection in the temperature dependant Seebeck coefficient graph was found in the temperature range from 840 K to 940 K for all the BSTF compositions. Beyond 940 K, very high thermo-power (S) values were obtained at high temperature for these BSTF compositions. Maximum thermo-power (S) value achieved is ∼800 μV K⁻¹ at 1123 K for Ba_xSr_2−xFeTiO₆ with x = 0.25. This is considered very high since state of the art materials like p-type Bi₂Te₃ exhibits^23,24 maximum thermo-power like 100 to 250 μV K⁻¹ and recently developed one of the best p-type thermoelectric material, Na_xCoO₂ shows^2,25 max thermopower value ∼200 μV K⁻¹.

Fig. 4 Temperature dependence of (a) Seebeck coefficient (S) and (b) electrical conductivity (σ) for Ba_xSr_2−xTiFeO₆ ceramics with x = 0.0, 0.1, 0.15 and 0.25.

On the contrary, conductivity does not change much at room temperature with the doping of isovalent barium in place of strontium in Sr₂FeTiO₆ double perovskites. Conductivity initially increases for all BSTF compositions, but later decreases with increase in temperature showing a distinct diffuse peak in the temperature dependant electrical conductivity (σ) graph as shown in Fig. 4(b). Table 1 shows maximum electrical conductivity (σ) and its corresponding temperature obtained from the temperature dependant conductivity graph for Ba_xSr_2−xTiFeO₆ (BSTF) ceramics with 0.0 ≤ x ≤ 0.25. Among all the BSTF compositions, pure Sr₂FeTiO₆ (STF) exhibits maximum conductivity value of 415.3 S m⁻¹ at 890.1 K. It suggests that as a result of barium doping, the conductivity of STF double perovskites actually diminishes, opposite to the effect of barium doping on Seebeck coefficient. Maximum conductivity obtained for all the compositions is in the temperature range from 840 K to 940 K, which is exactly the same temperature range where the point of inflection was observed in the temperature dependant study of Seebeck coefficient. It suggests that the semiconductor to metal transition was occurred in this temperature range for Ba_xSr_2−xFeTiO₆ double perovskites. For example, in Ba_xSr_2−xTiFeO₆ ceramics with x = 0.15, the metallic-like conductivity (dσ/dT < 0) is observed at temperatures above 892 K whereas, the point of inflection in Seebeck coefficient graph occurred at 894 K after which thermo power increases rapidly with the increase in temperature as shown in Fig. 5.

Table 1 Maximum electrical conductivity (σ) and its corresponding temperature obtained from the temperature dependant conductivity graph for Ba_xSr_2−xTiFeO₆ (BSTF) ceramics with 0.0 ≤ x ≤ 0.25

Composition	Peak temperature (K)	Maximum conductivity (S m^−1)
Sr2FeTiO6	890.1	415.3
Ba0.1Sr1.9FeTiO6	932.9	347.6
Ba0.15Sr1.85FeTiO6	892.0	273.8
Ba0.25Sr1.75FeTiO6	842.4	230.5

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Fig. 5 Variation of Seebeck coefficient (S) and electrical conductivity (σ) with temperature for Ba_xSr_2−xTiFeO₆ ceramics with x = 0.15.

Furthermore, thermoelectric power-factor (S²σ) was calculated for all the BSTF compositions. Higher thermoelectric power factor indicates higher figure of merit, ZT values for thermoelectric devices. Thermoelectric power-factor (S²σ) calculated in the temperature range from 300 K to 1123 K for all the Ba_xSr_2−xTiFeO₆ (BSTF) ceramics with 0.0 ≤ x ≤ 0.25 is shown in Fig. 6. With the increase in temperature, power-factor goes on increasing for all the BSTF compositions in the whole temperature range of measurement as shown in Fig. 6. Maximum power-factor achieved is ∼26 μW m⁻¹ K⁻² at 1123 K for Ba_xSr_2−xTiFeO₆ composition with x = 0.15. This is very much encouraging considering not much electrical conductivity attained in these BSTF double perovskites.

Fig. 6 Variation of thermoelectric power-factor (S²σ) with temperature for Ba_xSr_2−xTiFeO₆ ceramics with x = 0.0, 0.1, 0.15 and 0.25.

3.3 Discussion

All the BSTF compositions exhibit positive Seebeck coefficient indicating it is a p-type material in the whole temperature range of measurement. The source of the positive carriers in STF is due to Fe³⁺ ions, which has 4+ formal valence in Sr₂FeTiO₆ as expressed by using Kröger–Vink notation²⁶ in eqn (2) suggesting holes as the majority charge carriers.

Substitution of isovalent barium in place of strontium in Ba_xSr_2−xFeTiO₆ does not change its p-type behavior as expected. The electrical conductivity of all the BSTF compositions shows a diffuse semiconductor (dσ/dT > 0) to a high temperature metallic (dσ/dT < 0) transition as shown in Fig. 4. However, to understand the conduction mechanism in these double perovskites based semiconductor oxides, the band model may not always be the most appropriate description of conduction. In a system like BSTF, where charge carriers are more or less localized at defect sites, we would expect to see an activation energy, i.e. an energy barrier that a carrier needs to overcome to become delocalized (ionization energy). Moreover, mobile carriers have to cross a barrier when jumping from one site to another (mobility barrier) for proper charge transport in these oxides. Hence a hopping conduction model seems more appropriate to explain the conduction mechanism in these oxides. Hopping conduction occurs when ions of the same type have different valences but occupy equivalent crystallographic sites similar to occupancy of Fe³⁺ and Ti⁴⁺ in the B site of Ba_xSr_2−xFeTiO₆ double perovskites.

To elucidate the conduction mechanism in BSTF oxides, ‘variable-range hopping model’^27,28 was considered where conductivity is given by eqn (3):

where A and T₀ are constants. So the linear fit in the plot of natural logarithm of conductivity vs. T^−1/4 should demonstrate variable-range hopping. However, in case of BSTF ceramics, the linear fit in the plot of ln σ versus T^−1/4 was only found for temperatures below ∼550 K as shown in Fig. 7 for Ba_xSr_2−xTiFeO₆ composition with x = 0.15. Departure from the variable range hopping behavior beyond ∼550 K suggests the small polaron hopping behavior in these oxides. Multivariant degenerate sites in these solids can exchange positions of charge and therefore be transported through the solid as electron accompanying polarization field known as a quasi-particle, polaron. Small polaron hopping conduction involving emission or absorption of optical phonons follows the well-known equation.^28–31where E_Hop is the activation energy for small polaron hopping, σ₀ is the constant and k_B is Boltzmann constant. So the conduction mechanism driven by small polaron hopping model in the temperature dependant conductivity should show a linear relationship between ln(σT) and 1/kT with a slope equal to E_Hop. As shown in Fig. 8 all the BSTF compositions exhibit the linear fit in the ln(σT) vs. (1/kT) plot showing small polaron hopping behavior in the temperature range from room temperature to their semiconductor-to-metal transition temperatures. Calculated activation energy (E_Hop) for small polaron hopping conduction mechanism observed in all the BSTF composition is presented in Table 2. The total activation energy (E_σ) for conduction has generally two contribution: (i) activation energy for mobility (E_μ), and (ii) activation energy associated with carrier generation E_a; E_σ = E_μ + E_a. In small-polaron hopping conduction the activation energy for conduction is generally controlled by the mobility term,³² which can be seen from the Table 2, where values of (E_a) are calculated using p-type non-degenerate semiconductor model in temperature dependence of thermopower (S).

Fig. 7 Electrical conductivity ln σ vs. T^−1/4 for Ba_xSr_2−xTiFeO₆ composition with x = 0.15 showing variable range hopping conduction.

Fig. 8 Natural log of electrical conductivity – temperature product [ln(σT)] plotted against reciprocal thermal energy (1/k_BT) for Ba_xSr_2−xTiFeO₆ composition with (a) x = 0.0 (b) x = 0.10 (c) x = 0.15 (d) x = 0.25.

Table 2 Activation energy calculated for Ba_xSr_2−xTiFeO₆ compositions obtained from p-type non-degenerate semiconductor behavior in thermopower and small polaron hopping conduction behavior in conductivity measurement

BaxSr2−xTiFeO6 composition	EHop in eV (using small polaron hopping conduction)	Ea in eV (using thermopower data)
x = 0	0.3933	4.04 × 10^−5
x = 0.1	0.39681	4.17 × 10^−5
x = 0.15	0.38916	4.82 × 10^−5
x = 0.25	0.3701	5.52 × 10^−5

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Temperature dependence of thermopower (S) can be explained using p-type non-degenerate semiconductor given by the following equation:^29,33

where E_a is the activation energy, A is the constant and k_B is Boltzmann constant. To elucidate the temperature dependant thermopower behavior for BSTF compositions a plot of eS/k_B versus 1/T is shown in Fig. 9 using eqn (5). It can be seen from Fig. 9 that all the BSTF compositions behave like p-type non-degenerate semiconductor before they undergo semiconductor to metal transitions. Activation energy (E_a) calculated from the slopes of eS/k_B versus 1/T plot for all the BSTF compositions can be seen in Table 2. With the increase in barium content in BSTF compositions the activation energy increases. Very low activation energy (E_a) compared to the activation energy (E_Hop) required for small polaron hopping suggests the presence of phonon-drag and local disorder in the structure causing the low mobility of charge carriers. Enhanced thermo-power observed in the metallic region of all the BSTF compositions can be explained using degenerate semiconductor model. Temperature dependence of thermopower for metal-like behavior in a degenerate semiconductor, assuming a temperature independent mean-free path, is typically described using a degenerate Fermi gas model,^33–35

Fig. 9 Plot of eS/k_B versus 1/T showing p-type non-degenerate semiconductor like behavior in temperature dependant thermopower for Ba_xSr_2−xTiFeO₆ composition with (a) x = 0.0 (b) x = 0.10 (c) x = 0.15 (d) x = 0.25.

The constant C_n contains basic fundamental physical parameters, m* is the hole effective mass; n_e is the carrier concentration; and h is Planck's constant. Eqn (6) shows the increase in thermopower with increase in temperature, which was observed in the high temperature range of BSTF compositions as shown in Fig. 4. This is consistent with the metallic like behavior (dσ/dT < 0) observed in the conductivity plot at higher temperature. Similar kind of behavior was observed be Lee et al.¹¹ for reduced SrTiO_3−δ.

4. Conclusion

In conclusion, an environmental friendly, non-toxic, cheap, high-temperature thermoelectric materials, Ba_xSr_2−xTiFeO₆ ceramics with x = 0, 0.1, 0.15, and 0.25 were synthesized by solid-state reaction route with proper stoichiometry. All the compositions were verified to be single-phase solid solution by room temperature X-ray diffraction measurements. SEM images of these oxides confirmed that the samples were well sintered and dense as no such porosity was observed. Seebeck coefficient confirms BSTF as a p-type material in the whole temperature range of measurement from 300 K to 1123 K. All the BSTF compositions exhibit p-type non-degenerate semiconductor behavior in temperature dependence of thermopower (S) and small polaron hopping conduction mechanism till these materials undergo semiconductor to metal transition at very high temperature (∼900 K). All these double perovskites exhibit more than 100 μV K⁻¹ thermo-power in the wide range of temperature from 300 K to 1223 K. Enhanced thermo-power (S) values were obtained at high temperature by inducing a semiconductor to metal transition in these BSTF ceramics. Maximum thermo-power (S) value achieved is ∼800 μV K⁻¹ at 1123 K for Ba_xSr_2−xTiFeO₆ with x = 0.25. Although very high Seebeck coefficient has been achieved in the current research, the electrical conductivity of these oxides needs to be improved. It is further suggested that aliovalent doping in these BSTF double perovskites is necessary to increase the charge carrier concentration for increasing their electrical conductivity.

Acknowledgements

This work is supported by the grant from Science and Engineering Research Board, DST (SERB-DST), India (Grant No. SB/S3/ME/008/2015).

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