Scholarly article on topic 'Thermal energy conversion and temperature-dependent dynamic hysteresis analysis for Ba0.85Ca0.15Ti0.9−xFexZr0.1O3 ceramics'

Thermal energy conversion and temperature-dependent dynamic hysteresis analysis for Ba0.85Ca0.15Ti0.9−xFexZr0.1O3 ceramics Academic research paper on "Materials engineering"

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{"Energy conversion" / "Olsen cycle" / "Dynamic hysteresis scaling" / Ferroelectric}

Abstract of research paper on Materials engineering, author of scientific article — Deepakshi Sharma, Satyanarayan Patel, Anupinder Singh, Rahul Vaish

Abstract Temperature-dependent ferroelectric behavior in Ba0.85Ca0.15Ti0.9−x Fe x Zr0.1O3 (BCT-BZT-Fe) (x =0%, 0.5%, 1%) has been investigated. Olsen cycle is used to estimate the thermal energy conversion potential in the compositions under study. The maximum energy conversion density of 305kJ/m3 per cycle is obtained for BCT-BZT-Fe (0.5% Fe content) when the cycle is operated between 30 and 110°C and an electric field of 0–3MV/m. The obtained energy density is very high for small electric field and temperature gradient as compared to other lead-free ferroelectric materials. A comparison table of previously reported Olsen cycle-based energy conversion in bulk ferroelectric ceramics is presented. Temperature also affects the hysteresis parameters, therefore, scaling relations for coercive field (E c ) and remnant polarization (P r ) as a function of temperature (T) were also observed. The power-law exponents are obtained for all hysteresis parameters in the compositions under study. The scaling relations are found as E c ∝ T −0.658, E c ∝ T −0.687 and E c ∝ T −0.717 for 0%, 0.5% and 1% Fe, respectively. Similarly, P r ∝ T −1.59, P r ∝ T −1.65 and P r ∝ T −1.85 are for 0%, 0.5% and 1% Fe, respectively. Additionally, back-switching polarization (P bc ) behavior as a function of temperature is estimated by well-described Arrhenius law to evaluate the average activation energy for all the compositions.

Academic research paper on topic "Thermal energy conversion and temperature-dependent dynamic hysteresis analysis for Ba0.85Ca0.15Ti0.9−xFexZr0.1O3 ceramics"

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Thermal energy conversion and temperature-dependent dynamic hysteresis analysis for Bao.85Cao.i5Tio.9-xFexZro.iO3 ceramics

qi Deepakshi Sharmaa1, Satyanarayan Patelb1, Anupinder Singha, Rahul Vaishb *

a Department of Physics, Guru Nanak Dev University, Amritsar 143005, Punjab, India

b School of Engineering, Indian Institute of Technology Mandi, 175 001, Himachal Pradesh, India

10 11 12

article info

Article history: Received 21 August 2015 Received in revised form 24 December 2015 Accepted 26 December 2015 Available online xxx

abstract

16 Keywords:

17 Energy conversion

18 Olsen cycle

19 Dynamic hysteresis scaling

20 Ferroelectric

Temperature-dependent ferroelectric behavior in Bao.85 Cao.15Tio.9-xFexZro.1 O3 (BCT-BZT-Fe) (x — 0%, 0.5%, 1%) has been investigated. Olsen cycle is used to estimate the thermal energy conversion potential in the compositions under study. The maximum energy conversion density of 305 kJ/m3 per cycle is obtained for BCT-BZT-Fe (0.5% Fe content) when the cycle is operated between 30 and 110 °C and an electric field of 0-3 MV/m. The obtained energy density is very high for small electric field and temperature gradient as compared to other lead-free ferroelectric materials. A comparison table of previously reported Olsen cycle-based energy conversion in bulk ferroelectric ceramics is presented. Temperature also affects the hysteresis parameters, therefore, scaling relations for coercive field (Ec) and remnant polarization (Pr) as a function of temperature (T) were also observed. The power-law exponents are obtained for all hysteresis parameters in the compositions under study. The scaling relations are found as Ec aT-0 658, Ec aT-0 687 and Ec a T-0 717 for 0%, 0.5% and 1% Fe, respectively. Similarly, Pr a T-159, Pr a T-165 and Pr a T-185 were for 0%, 0.5% and 1% Fe, respectively. Additionally, back-switching polarization (Pbc) behavior as a function of temperature is estimated by well-described Arrhenius law to evaluate the average activation energy for all the compositions.

© 2016 The Ceramic Society of Japan and the Korean Ceramic Society. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/

licenses/by-nc-nd/4.0/).

1. Introduction

Ferroelectric materials are widely used in many areas of science and technology from the last few decades [1-3]. It has wide applications due to its unsurpassed properties, such as hysteresis (non-volatile memory), high piezoelectric effect (actuators), strong electro-optic effect (electro-optic materials for data storage applications), high dielectric constant (capacitors), high pyroelectric coefficient (infrared detectors), high dielectric constant and anomalous temperature coefficient of resistivity [2-15]. Ferroelectric materials are also widely used for ambient energy conversion and scavenging waste energy [16-24]. In this direction, a huge number of studies report their usage for electrical energy harvesting from mechanical vibrations and temperature fluctuations [19-21]. Most of these ferroelectric ceramics are based on

* Corresponding author. Tel.: +91 1905 237921; fax: +91 1905 237945.

E-mail address: rahul@iitmandi.ac.in (R. Vaish).

1 These authors contributed equally to this work. Peer review under responsibility ofThe Ceramic Society ofJapan and the Korean Ceramic Society.

Pb(ZrxTi1-x)O3 (PZT) and Pb(Mg1/3Nb2/3)O3 (PMN) or their solid solutions [1-3,5,11,25]. The main disadvantage of these ceramics is that they contain approximately 60% of lead by weight, which is highly toxic in nature and can cause several unwanted effects, such as cancer, brain damage, atmospheric issues, etc. [23,26-28]. Lead-free ferroelectric materials are currently subject to extensive research activities owing to environmental concerns and corresponding legislation, which point to substitute lead-based ferroelectric material [23,26-28].

In this direction, BaTiO3, Bi0.5Na0.5TiO3 and K0.5Na0.5NbO3-based ferroelectric materials have been extensively studied [23,26-28]. These compositions are fabricated near morphotropic phase boundary (MPB); thus, the system can exhibit high piezoelectric, pyroelectric and ferroelectric properties [29]. However, these materials show saturation at higher electric field. Recently, Ba0.85Ca0.15Ti0.gZr01O3 (BCT-BZT) ceramic is reported for large piezoelectric and pyroelectric properties as compared to other lead-free and lead-based materials at lower electric field. It exhibits optimal properties of d33 — 650 pC/N, d31 — 74 pC/N, kp —0.53, kt — 0.38, k31 —0.309, SE1 = 14.0 x 10-12m2/N, Sr — 4500 and Pr — 11.69 |iC/cm2 [30]. Further, BCT-BZT also shows electric field tunable dielectric properties; the tenability is 82% under

http://dx.doi.0rg/10.10i6/j.jascer.2015.12.005

2187-0764 © 2016 The Ceramic Society ofJapan and the Korean Ceramic Society. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

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DC field of 40kV/cm [31,32]. Moreover, it has low dielectric loss of 0.001, which is very small as compared to other ferroelectric materials [32]. Furthermore, it consists of high pyroelectric coefficient of 5.84 x 10-8 C/(cm2 K) at room temperature, which is larger than those reported for other BaTiO3-based materials [33]. These enhanced piezoelectric, pyroelectric and ferroelectric properties are achieved due to the existence of MPB near room temperature of ferroelectric rhombohedral and tetragonal phases [32,34,35]. A detailed analysis of elastic, dielectric, and piezoelectric constants in BCT-BZT ceramic is performed by a resonance method and measured the temperature dependence of electrical properties [36]. BCT-BZT has also received attention in energy conversion and refrigeration (electrocaloric) because it shows low electric field saturation. A large EC requires a large AS and AT change with applied electric field (AE). However, requirements for generation of high voltage are bulky, costly and tend to be unsafe. Hence, it is preferred that cooling devices should be operated at low voltage. Therefore, an EC material with a large EC induced under small electric fields is also an important parameter. EC responsivity is quantifiable, which can be defined as AT/AE and serves as a good figure of merit as reported by number of researchers [37-40]. Hence, for practical designs, development of dielectric materials, capable of generating giant EC at relatively low applied electric field change AE, is required [39,40]. Further, Olsen cycle-based energy conversion capabilities in BCT-BZT are reported, which is comparable with other lead-based materials [41]. This energy conversion also requires small electric field. Therefore, it can be a potential material for energy conversion.

Recent investigation reveals that BCT-BZT is one of the most studied lead-free piezoelectric ceramics having high dielectric and ferroelectric properties. Therefore, the present work deals with the energy conversion capability of Ba0.85Ca015Ti0.9_xFexZr01O3 (BCT-BZT-Fe) bulk ferroelectric ceramics through Olsen cycle. In order to understand ferroelectric properties, hysteresis scaling relations of coercive field (Ec) and remnant polarization (Pr) as a function of temperature (T) are systematically investigated. Additionally, back-switching polarization (P¡,c) behavior as a function of temperature is estimated by well-described Arrhenius law to evaluate the average activation energy for all the compositions.

2. Experimental method

In the present work, Bao.85Cao.15Tio.9-xFexZro.1O3 (BCT-BZT-Fe) was synthesized by the solid-state reaction route. The ceramics samples were fabricated by differing the iron (Fe) (x = 0%, 0.5%, 1%, 1.5%) composition. The starting raw powders barium carbonate (BaCO3), calcium oxide (CaO), titanium oxide (TiO2), zirconium oxide (ZrO2) and iron (Fe) were mixed in stoichiomet-ric ratio and milled in acetone to obtain physical homogeneity using mortar and pestle. The mixtures were calcined twice at 1325 °C and 1350 °C for 6 h with intermediate grinding. In the calcined powder, PVA (2% by weight) was mixed to improve the green strength of the compacts. Green samples of 12 mm (diameter) x 1 mm (thickness) were prepared using cold hydraulic press. Finally, all the samples were sintered at 1400 °C for 4h. The crystal structure was confirmed by using powder X-ray diffraction (XRD) technique employing Cu-Ka radiations. Density of the sintered pellets was measured using Archimedes principle. To confirm the topology of the sintered specimen, scanning electron microscope (SEM) was used. For making specimen electrical conducting, silver paste was electrodes on both the sides of the given specimen. Polarization-electric field (P-E) hysteresis loops were measured at different temperature by using P-E loop tracer.

3. Results and discussion

The XRD patterns of sintered samples for BCT-BZT-Fe ceramics are shown in Fig. 1(a). All the XRD peaks are indexed, which indicate the existence of both rhombohedral and tetragonal structures. The square mark indicates peaks split (200), which can be reflections of the coexistence of rhombohedral and tetragonal phases. Similarly, other researchers also reported coexisting of rhombohedral (R3m) and tetragonal (P4mm) phases in BCT-BZT ceramics [42-45]. It shows that the addition of Fe does not affect crystal structure. Further, Fig. 1(b)-(d) presented SEM micrographs of all the compositions under study. It indicates good density of all samples due to closely packed grains (lack of porosity), which is also confirmed by the Archimedes principle and found to be ~93% of the theoretical density. P-E hysteresis loops of BCT-BZT-Fe for the compositions (0%, 0.5%, 1%, 1.5%) under study are represented in Fig. 2. Fig. 2(a) shows a comparison of P-E loop for all compositions, with a fixed electric field and temperature. It can be said that as the Fe content increases, polarization also increases up to 1%. However, P-E loop parameters are decreased with addition of 1.5% Fe content in BCT-BZT. It is well known that typical aliova-lent dopants in PZT are Nb5+ and Fe3+ acting as donor and acceptor, which significantly alter the domain stability [1]. Similarly, Humburg et al. discussed that Fe3+ doping in (Ba0.865Ca0.135 XZr0.11 Ti0.89) enhances the defect dipole model; this can be attributed to aging due to the formation of charged defect complexes in the material [46]. It is very sensitive to the Zr/Ti ratio and is only observed in compositions fabricated close to their MPB [46,47]. Incorporation of Fe3+ ion as a b-site dopant disrupts the phase formation. It can be said that the Fe addition (up to 1%) enhanced ferroelectric properties. Moreover, addition of more than 1% Fe decreases ferroelectric properties, which can be attributed to losses in material due to difference in Fe3+ and Ti4+ atomic radius. Furthermore, this phenomenon is attributed to the influence of local compositional fluctuations and random charge introduced by the dopants that locally reduce the tetragonal symmetry and the ferroelectric state [46]. However, at this point, a complete explanation for this effect is not available. Notwithstanding, the optimum Fe doping concentration is revealed to be 1%. Therefore, the present work deals with only three compositions of x = 0%, x = 0.5% and x =1.0%. Furthermore, Fig. 2(b)-(d) shows the hysteresis loops forx = 0%, x = 0.5% and x = 1.0% Fe, respectively at different temperatures under constant electric field of 20 kV/cm. All these hysteresis loops are measured at a constant frequency of 50 Hz. Frequency can also affect the P-E loop parameters; however, the present work does not deal with such effect. Further, at a given temperature, if the applied electric field is small, it shows unsaturated minor loop. However, as the electric field increases, minor loop (unsaturated loop) starts converting into major loop (saturated loop) due to increase in coercive field (Ec), saturation polarization (Ps) and remnant polarization (Pr). On the other hand, Ec, Ps and Pr decrease with increase in temperature as shown in Fig. 2(b)-(d). Moreover, ferroelectric materials are a subclass of pyroelectric materials [24]. Therefore, it produces electric current/voltage due to temporal temperature gradient; this can be used as a means of energy conversion [24]. From Fig. 2, it is clear that there is huge possibility of pyroelectric energy conversion in these materials. Hence, we have to put light on the energy conversion capability of the material through Olsen cycle.

Ferroelectric materials show hysteresis behavior on polarization versus electric field graph (P-E). The hysteresis represents the difference in the energy required to polarize and depolarize the ferroelectric material in the form of heat. The material becomes capable to absorb the heat and generate electricity. It is reported that the reversible polarization can be made to trace a clockwise loop between two different temperatures. This cycle is known as

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Olsen cycle, which basically is used to convert thermal energy into electricity. This cycle mainly consists of two isothermal and two isoelectric field processes [17,18,48-50]. The schematic of the Olsen cycle for energy conversion is shown in Fig. 3. The processes 1'-2-3-4-1' represent the electric analog of the Olsen cycle, whereas corresponding enclosed area shows the electric energy produced per unit volume per cycle [23]. The area enclosed (1-2-1'-1) represents the hysteresis loss when Olsen cycle is operated in bipolar P-E loop [17,18,38-40]. However, in the unipolar P-E loop, hystere-isQ4 sis loss is very small. Therefore, for unipolar condition hysteresis loss, these can be neglected and the improved energy conversion is represented by the shifted loop (1-2-3-4-1), which is considered in the present work. Process 1-2 is performed at a constant lower temperature (TL) as electric field increases from lower limit (El) to higher limit (EH), and correspondingly material polarization also increases. In process 2-3, heat (Qs) is supplied to the material, which increases the temperature and produces lattice vibration. Hence, material depolarizes at constant electrical field EH. This generates a large depolarization current, which can be used or stored for powering electronic equipment using suitable circuit. Further, temperature of the material increases from lower temperature (TL) to higher temperature (TH). In the process 3-4, the electric field reduces from EH to EL at constant temperature TH. The polarization also decreases due to lack of electric field, which generates a weak depolarization current. Finally, in process 4-1, extraction of heat from the system at constant electric field (EL) is done so that the material reaches to its initial state and completes the cycle. A detailed discussion on Olsen cycle is available in a number of articles [16-18,22,23,49-51]. This process is known as isoelectric heat

rejection. Energy density (ND) per unit volume of the material can be estimated by [19,23]:

Nd = é E dP

where E and P represent the electric field and polarization, respectively. Eq. (1) represents the surface integral of E with respect to change in polarization. This cycle was employed on the BCT-BZT-Fe compositions and results are shown in Fig. 4. In this work, EL and TL are considered as zero electric field and 30 °C, respectively. Fig. 4(a) presents Olsen cycle-based energy conversion in BCT-BZT as a function of applied higher electric field (EH) at various higher temperatures (TH). It indicates that as the temperature and electric field span are increased, energy also increases. The maximum energy, 80kJ/m3, is observed when the cycle is operated between 30-110°C and 0-21.5 kV/cm. Similarly, Fig. 4(b) and (c) shows energy conversion for BCT-BZT-Fe having 0.5% and 1% Fe content, respectively. It has also similar behavior as observed in BCT-BZT. Further, it is interesting to note that the slope of energy conversion differs from each other in the compositions under study. This is due to fact that the addition of the Fe can lower the ferroelectric-paraelectric transition. Fe3+ plays the role of a B-site acceptor dopant in BCZTO-Fe. Fe doping has been reported to reduce remnant polarization, coercive field value and ferro-para transition temperature [46]. However, an increase in the maximum polarization has been achieved as compared to undoped ceramics. Hence, addition of the Fe in BCT-BZT can increase energy conversion, which is also clear from the comparison graph as shown in Fig. 4(d).

220 221 222

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Fig. 2. (a) Polarization versus electric field (P-E) hysteresis loops for BCT-BZT-xFe bulk ceramic for all the compositions under study. P-E loop under different temperature and fixed magnitude of electric field for (b) 0%, (c) 0.5% and (d) 1% Fe content.

The maximum energy conversion in 0.5% Fe content ceramics is 305kJ/m3 when the cycle is operated between 30-110°C and 0-30 kV/cm. In Fig. 4(d) at 30 kV/cm, energy conversion is predicted for the BCT-BZT composition. The maximum energy conversion

density of the Pb[(MnxNb1_x)1/2(MnxSb1_x)1/2]y(ZrzTi1_z)1_yO3 (PMN-PMS-PZT) based on pyroelectric effect was found as 69kJ/cm3 per cycle [52]. However, we found that BCT-BZT has almost five times larger energy conversion potential than

Table 1

Comparison of energy density for various bulk ferroelectric materials.

Material name Energy conversion, AW (kJ/m3) Tl-Th (°C) AT (°C) El-Eh (MV/m) AE (MV/m) Reference

PZT (soft) 92 25-160 135 0.1-2 1.9 [19]

PZST ioo i46-i59 i3 o.o-2.9 2.9 [17]

PMN-32PT 100 80-170 90 0.2-0.9 0.7 [54]

PZST i3i i57-i77 2o o.4-3.2 2.8 [16]

PZN-5.5PT 150 100-190 90 0.0-1.2 1.2 [49]

PMN-10PT 186 30-80 50 0.0-3.5 3.5 [55]

PZT (hard) 189 25-160 135 0.1-2 1.9 [19]

PZN-4.5PT 2i7 ioo-i6o 6o o.o-2 2 [56]

8/65/35 PLZT (thick films) 888 25-i6o i35 o.2-7.5 7.3 [50]

60/40 P(VDF-TrFE) 52i 25-iio 85 2o-5o 3o [48]

61.3/29.7/9 P(VDF-TrFE-CFE) 9oo 25-i2o 95 2o-6o 4o [18]

0.5Ba(Zr0.2Ti0.s)03-0.5(Ba0.yCa0.3)Ti03 87 20-120 100 0.1-1 0.9 [41]

Ba0.85Ca0.15Ti0.895Fe0.005Zr0.1O3 101 30-110 80 0-1 1 Present work

Ba0.85Ca0.15Ti0.895Fe0.005Zr0.1O3 305 30-110 80 0-3 3 Present work

K[(Nbo.9oTao.io)o.99Mno.oi ]O3 629 i2o-i6o 4o o.i-5 4.9 [41]

Bio.5Nao.35Lo.i5TiO3 ii46 25-i2o 95 o.i-ii.2 ii.i [23]

(Bi0.5 Na0.5 )0.915(Bi0.5 K0.5 )0.05 Ba0.02 Sr0.015TiO3 1523 20-160 140 0.1-4 3.9 [24]

Bio.5Nao.38Ko.i2TiO3 i986 25-iio 85 o.i-5.2 5.i [23]

o.88Bio.5Nao.5TiO3-o.o2SrTiO3-o.1Bio.5Lio.5TiO3 2i3o 2o-i4o i2o o.i-6 5.9 [53]

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p2 N^ = iE.dP~ pi Isothermal process 2

1 , Work gain 3

Polarization (P) * ¿yj3 j ' y m. M "

4 V Isoelectric process

High temperature (TH) SI y \ K \ / ' / EL Eh Electric field (E) ' \ \ Low temperature (TL)

Fig. 3. Schematic of the electrical energy conversion using Olsen cycle.

249 PMN-PMS-PZT. Here, it is important to note that PMN-PMS-PZT

250 has actual energy output; however, our estimation is based on

251 only material energy conversion potential. A comparison of Olsen

252 cycle-based energy conversion potential in bulk ferroelectric mate-

253 rials has been given in Table 1. Further, a number of researches

254 has applied Olsen cycle on ferroelectric thin film and shown huge

amount of energy conversion [24,48,50,53]. However, thin film 255

contains very small volume; hence, for practical purpose, it can- 256

not fulfill the energy requirements. Therefore, we have considered 257

only bulk ferroelectric for comparison. From Table 1, it can be 258

said that the present work has small energy conversion poten- 259

tial as compared to others. However, according to temperature 260

difference AT (TH - TL), it indicates that the present work is in 261

the second position after PMN-10PT. It is important to note that 262

we have not considered AT of bold materials (Table 1) because 263

they have very high value of 100°C<TL. Similarly, according to 264

applied electric field AE (EH - EL), it indicates that the present 265

work is in the third position. In the same fashion, we have not 266

considered bold materials (Table 1) because they have very high 267 value of 5MV/m< AE. Further, Gaurav et al. [41] have reported q5 268

87 kJ/m3 as given in Table 1 considering lower electric field-based 269

large energy conversion potential in BCT-BZT. However, the present 270

work reported 25% improvement in previously reported energy 271

conversion due to addition of 0.5% Fe in same compositions. In sum- 272

mary, it can be said that for small electric field and temperature 273

change, BCT-BZT-Fe is fairly a good candidate for thermal energy 274

conversion. 275

In order to further study the temperature effect on the hys- 276

teresis loop parameters, we have studied the scaling behavior of 277

hysteresis parameter. Therefore, we have plotted logarithmic form 278

of Ec and Pr versus T under different values of electric fields, as pre- 279

sented in Figs. 5 and 6. Fig. 5(a)-(c) shows ln Ec versus ln Tfor all the 280

Fig. 4. Energy conversion versus electric field plots of Ba0.85Ca0.i5Ti0.9_xFexZr0.iO3 (BCT-BZT-Fe) bulk ceramics for (a) x = 0%, (b) x = 0.5%, (c) x = 1% Fe content at EL = 0 kV/cm and (d) comparison of energy conversion capacity in compositions under study.

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Fig. 5. Logarithmic plot of coercive field (Ec) versus temperature (T) under different magnitude of electric field for (a) 0%, (b) 0.5% and (c) 1% Fe content. Inset indicates corresponding slope versus electric field.

compositions under study. The linear least square-fitting methods (with R2 ~ 0.96-0.98) were used to explain the dependence of ln Ec on ln T. The scaling relation between Ec and T can be determined from the slope of ln Ec versus ln T. Further, effect of electric field (E) on the slope of ln Ec versus ln T are also plotted in the inset of the corresponding figures. Hence dependence of Ec on T can be written as:

ln Ec = Y ln T + YEc

where y is the slope and YEc is Y-intercept. For BCT-BZT compositions, it can be written as,

ln Ec = Y1 ln T + YEc = (0.0013E - 0.658) ln T + YEc

where y 1=0.0013E-0.658. Here, Y-intercept (YEc) plays a role only at zero temperature. In the above equation, YEc can be determined when temperature approaches to zero, and its estimated value can be different from practical values. However, at the zero temperature, ferroelectric domains are freezed; hence, the ferroelectric properties dramatically vary and are entirely different for the domains at high temperature [25,57,28,58]. Therefore, we can safely neglect the effect of Y-intercept because we are not dealing with the effect on Ec at T = 0°C. This assumption is used in the present work. Hence, Eq. (3) can be written as:

ln Ec = (0.0013E - 0.658) ln T

Further, it can be said that Ec versus T relation moderately depend on E. For the constant electric field (E), effect of E is very small, as

the magnitude of E is small. This assumption is also used in the present work. Therefore, effect of E can be also ignored and Eq. (4) can be rewritten as:

ln Ec = -0.658 ln T

The scaling relation between Ec and T can be written as, Ec a Ty1 or Ec a T-0 658, where y1 = 0.658 is a dimensionless number. In the same fashion, scaling relations between Ec and T have been established for BCT-BZT-Fe x = 0.5% and x =1.0% as shown in Fig. 5(b) and (c), respectively. The scaling relation between Ec and T can be written as Ec a Ty2 and Ec a Ty3 for x = 0.5% and x = 1.0% Fe content, respectively. Scaling relations for x = 0.5% and x =1.0% Fe content are found as Ec a T-0 687 and Ec a T-0 717.

Further, we have neglected the effect of applied electric field on the scaling relations. However, the slight difference in the scaling exponent can be observed due to the difference in switching behavior at constant electric field [25,57,28,58]. The scaling relation can be also estimated on the domain switching behavior as a function of E and T as reported [25,57,59,60]. In ferroelectric material, domain is a region where all the dipoles are aligned in the same direction and the direction of the dipoles depends on temperature, electric field and crystallographic structure [25,57,59,60]. The phenomena of the rotation of dipoles are known as ferroelectric domain switching. Due to these domain switching, there is a change in the shape of the unit cell, but the volume remains the same [25,57,59,60]. The whole process takes place in two steps; firstly, domain growth and

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Fig. 6. Logarithmic plot of remnant polarization (Pr ) versus temperature (T) at various electric fields for (a) 0%, (b) 0.5% and (c)1%Fe compositions. Inset indicates corresponding slope versus electric field.

secondly, rotation of domains. When the external field is less than Ec, domains growth will take place. Secondly, when electric field is greater than Ec, the rotation of domains will take place in the direction of electric field. During this process, hysteresis loop goes on increasing. When the electric field goes above the threshold value, it is unable to produce increment in polarization, which is known as saturation [25,57,28,58-60]. Any further increase in the electric field leads to its dielectric breakdown. Therefore, to avoid the effect of electric field, we have considered saturated P-E loop only.

In order to further investigate similar scaling relation for Pr versus T represented in Fig. 6 at different magnitude of electric field, Fig. 6(a) shows ln Pr versus ln T graph for BCT-BZT at four different electric fields. Therefore, Ec dependence on T can be written as:

ln Pr =<$! ln T + Yp,

343 where <5i is the slope and Ypr is Y-intercept. Further, it can be written

344 as

345 lnPr =1jln T + Ypr = (0.0052E-1.59)ln T + Ypr (7)

346 Similar assumptions are considered and Eq. (7) can be written as:

347 Pr «T'2 or Pr aT-159 (8)

348 In the similar fashion, scaling relations between Pr and T have

349 been established for BCT-BZT-Fe x = 0.5% and x =1.0%, as shown in

350 Fig. 6(b) and (c), respectively. The scaling relation between Pr and

351 T can be written as Pr a Ts2 or Pr a T-165 and Pr a Ts2 or Pr a T-185

352 for x = 0.5% and x = 1.0% Fe content, respectively. The sharp change

in the Pr shows the phase transition in BCT-BZT and shows the diffused ferroelectric-paraelectric phase transition at temperature 80 °C [29,31]. Similar systematic shift in Pr can also be observed by addition of Fe content. Additionally, scaling relation of Ec, Pr versus T for previously reported bulk ferroelectric ceramics are given in Table 2. It indicates that the lead-free ferroelectric has not been given much attention for analysis of the scaling behavior. Therefore, this study can provide a significant contribution in this direction to understand the hysteresis behaviors of BCT-BZT based lead-free composition.

Temperature also affects the domain wall motion; this is due to the fact that as the temperature increases, lattice vibration increases, which enhance the rotation of the domains and reduce the stability of the polarization [25,57,58,60]. Therefore, hysteresis loop area also decreases with increase in the temperature. The temperature dependence on the polarization can be explained in terms of back-switching. Generally, domain polarization takes place in two steps; firstly, switchable polarization in domain, which is known as Ps, and another is back-switched polarization, known as Pr [61,62]. When the external electric field is applied, polarization reaches to Ps, whereas when electric field is removed, it again comes to stable polarization Pr. Such phenomenon is known as back-switching polarization. Back-switching polarization (P^c) can be calculated as [28,61,62]:

Pbc = Ps-Pr

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8 D. Sharma et al. / Journal of Asian Ceramic Societies xxx (2016) xxx-xxx

Table 2

Dynamic scaling exponents for different bulk ferroelectric ceramics.

Material y (Ec aTy ) 1 (Pr aT1) Temperature range (K) Electric field (kV/cm) References

Ba0.85Ca0.15Ti0.89Zr0.11Fe0.01O3 -0.717 -1.85 303-383 18-29 Present work

Ba0.85Ca0.15Ti0.895Zr0.1Fe0.005O3 -0.687 -1.65 303-383 18-29 Present work

Ba0.85Ca0.15Ti0.9Zr0.! O3 -0.658 -1.59 298-388 10-21.5 Present work

0.715Bi0.5Na0.5Ti03-0.065BaTi03 -0.22SrTi03 -0.6396 -0.6849 298-398 17.5-34.5 [28]

Soft PbZr1-xTix03 (APC-855, APC International, Ltd., USA) 1 -1.2332 298-453 10-40 [57]

Soft PbZr1-xTix03 (PKI-552, Piezo Kinetics Inc., USA) 1 -1.2332 298-453 10-40 [59]

PbZr0 95Ti0 05 03 at low T -1.867 -0.617 288-313 20-35 [60]

PbZr0.95Ti0.0503 at high T -2.649 -0.313 329-393 20-35 [60]

Hard PbZr1-xTix03 (APC-840, APC International, Ltd., USA) -0.882 -0.026 298-453 10-40 [25]

378 Fig. 7 shows the back-switching polarization versus temperature

379 plots at various electric fields. Fig. 7(a) shows that as the tem-

380 perature increases, the back-switching polarization increases; but

381 after 355 K, it starts to decrease with temperature. It shows that

382 the Ps have more dependence on the T as compared to Pr. Simi-

383 lar behavior is obtained in Fig. 7(b) and (c) for BCT-BZT 0.5% and

384 1% Fe composition, respectively. From Fig. 7(b) and (c), it can be

385 seen that Pbc data have been varied above 345 K and 335 K, which

386 indicates that there must be a phase transition. It is also evident

387 that the addition of Fe can decrease phase transition from 355 K to

388 335 K. Therfore, it can be said that addition of Fe can reduce the

389 ferroelectric-paraelectric transition by approximately 20 K. In the

high-field ranges, the relationship between Ps - Pr and T obeys the 390

Arrhenius law [28,61,62]: 391

Ps -Pr = Po exp ^ —f) (10) 392

where EA is the average activation energy of trapped charge defect 393

such as oxygen vacancy, and P0 is a constant. The slope of ln(Ps - Pr) 394

versus 1/T can be used to estimate the activation energy of the 395

domain switching. Therefore, ln(Ps - Pr) versus 1000/T are plotted 396

in Fig. 8(a)-(c) for all the compositions under study. It is impor- 397

tant to note that the slope of ln(Ps -Pr) versus 1000/T is positive; 398

12 11 10

- (a)0 0%

• • ▲

X ▼ _

■ ■ • ▲ ▼ • ▼ ▼

■ • • ▲ ▼

■ ■ • ▼

• ▲

■ 10.0 kV/cm ■ •

- • 14.5 kV/cm ■

▲ 18.0 kV/cm

1 ▼ 21.5 kV/cm 1.1. 1 ■ 1

290 300 310 320 330 340 350 360 370 380 390 Temperature (K) 14

E 11 o

(b) 0.5%

■ 18.0 kV/cm

• 20.5 kV/cm

A 24.5 kV/cm

▼ 29.0 kV/cm

290 300 310 320 330 340 350 360 370 380 390 Temperature (K)

(C) 1.0%

▼ ▲

18.0 kV/cm 20.5 kV/cm 24.5 kV/cm 29.0 kV/cm

290 300 310 320 330 340 350 360 370 380 390 Temperature (K)

Fig. 7. Plots for back-switching polarization (Ps - Pr ) versus temperature (T) at various electric fields for (a) 0%, (b) 0.5% and (c) 1% Fe compositions.

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D. Sharma et al. / Journal of Asian Ceramic Societies xxx (2016) xxx-xxx

Fig. 8. ln(Ps -Pr) versus 1/T plots under different magnitude of electric fields for (a) 0%, (b) 0.5% and (c) 1% Fe. Correspondingly, inset indicates average activation energy EA versus applied electric field E.

therefore, the activation energy is negative. However, energy cannot be negative; therefore, we considered it positive. Further, field dependence of the activation energy for the BCT-BZT-Fe fits well to a simple exponential decay function, and activation energy dependence versus electric field plots are shown in insets of corresponding figure (Fig. 8(a)-(c)).

= 0 095 О^ЫУ +0.

Eq. (11) represents the composition having 0% of Fe. Similar calculation is performed for the other compositions, and relations are found as EA = 0.0229 x exp((-E)/9.978)+ 0.043 and Ea = 0.3009 x exp((-E)/9.067) +0.0711 for 0.5% and 1.0% Fe content, respectively. Activation energy decreases with increase in electric field, as shown in insets of Fig. 8. It has been suggested that the lower value of the activation energy obtained at low temperatures is associated mainly with the creation of a large number of space charge carriers in oxidation-reduction processes [61,62]. This work can help to understand the temperature-dependent dynamic hysteresis phenomenon in lead-free ferroelectrics.

4. Conclusions 4i8

In the present work, Ba0.85Ca015Ti0.9-xFexZr01O3 (BCT-BZT- 419

Fe) (x = 0%, 0.5%, 1%) are studied. It is found that Fe doping is a 420

significantly lower ferroelectric-paraelectric phase transition tem- 421

perature close to room temperature. Temperature-dependence 422

hysteresis characteristics of BCT-BZT-Fe bulk ceramics were also 423

studied. Olsen cycle is applied to investigate thermal energy 424

conversion capability of BCT-BZT-Fe ceramics. Maximum energy 425

densities of 210kJ/m3, 305kJ/m3 and 298kJ/m3 per cycle for 426

BCT-BZT-Fe containing 0%, 0.5%, and 1% Fe, respectively under oper- 427

ating condition of 30-100 °C and an electric field 0-3 MV/m were 428

observed. The estimated energy density is comparatively high from 429

most of the bulk ferroelectric ceramics when cycle operated at 430

lower electric field and temperature. Results indicate that BCT- 431

BZT-Fe ceramics can be successfully used for scavenging of waste 432

thermal energy. Additionally, the ferroelectric scaling relations for 433

coercive field (Ec), remnant polarization (Pr), and as a function 434

of temperature (T) are also estimated. The power-law exponents 435

are obtained for all hysteresis parameter and it was in the form 436

of Ec aT-a658, Ec aT-a687 and Ec aT-0J17 for 0%, 0.5% and 1% Fe, 437

respectively. Similarly, Pr aT-1.59, Pr aT-1.65 and Pr aT-1.85 were 438

for 0%, 0.5% and 1% Fe, respectively. The temperature-dependence 439

back-switching kinetics are also estimated and the relation follows 440

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10 D. Sharma et al. / Journal of Asian Ceramic Societies xxx (2016) xxx-xxx

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