Structural, dielectric, impedance, and modulus spectroscopy of BaSnO3-Modified BiFeO3

Journal Pre-proof Structural, dielectric, impedance, and modulus spectroscopy of BaSnO3-Modified BiFeO3 Prabhasini Gupta, P.K. Mahapatra, R.N.P. Choudhary PII:

S0022-3697(19)31205-3

DOI:

https://doi.org/10.1016/j.jpcs.2019.109217

Reference:

PCS 109217

To appear in:

Journal of Physics and Chemistry of Solids

Received Date: 27 May 2019 Revised Date:

27 September 2019

Accepted Date: 28 September 2019

Please cite this article as: P. Gupta, P.K. Mahapatra, R.N.P. Choudhary, Structural, dielectric, impedance, and modulus spectroscopy of BaSnO3-Modified BiFeO3, Journal of Physics and Chemistry of Solids (2019), doi: https://doi.org/10.1016/j.jpcs.2019.109217. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Published by Elsevier Ltd.

Structural, Dielectric, Impedance, and Modulus Spectroscopy of BaSnO3-Modified BiFeO3 *

Prabhasini Gupta, P. K. Mahapatra, R. N. P. Choudhary Multifunctional Laboratory, Department of Physics

Siksha ‘O’ Anusandhan (Deemed to be University), Bhubaneswar-751030, Odisha, India

Abstract A BaSnO3-modified BiFeO3 compound (i.e., Bi0.95Ba0.05Fe0.95Sn0.05O3) was synthesized by a cost-effective mixed-oxide reaction method at 850°C. The solubility of 5% BaSnO3 in BiFeO3 (BFO) and the formation of a single-phase compound in the rhombohedral structure was checked by the Rietveld refinement method using the X-ray diffraction data. The analysis of Fourier transform infrared (FTIR) spectra reconfirmed the formation of the compound. The temperature-dependent dielectric spectrum for the sample exhibits a broad anomaly at 190°C, which seems to be the superposition of three Gaussian peaks corresponding to the Maxwell–Wagner effect, as well as the oxygen-vacancy-induced Fe2+/Fe3+ and Sn2+/Sn4+ redox mechanism. A sharp peak at 350°C corresponds to the magnetic reordering around the Neel temperature. Complex impedance spectroscopy along with modulus analysis confirmed the deviation from Debye-type behavior. The Cole–Cole model was used to resolve the components contributing to the loss tangent. Different models of electrical conduction were used to explain the conduction mechanism in the material. The existence of ferroelectricity in the sample was confirmed from the study of the room-temperature P–E loop. The addition of 5% BaSnO3 to BFO resulted in a 10-fold increase in the dielectric constant and the polarization accompanied by reduced tangent loss, making it attractive for device applications. Keywords: XRD; Dielectric; FTIR; Electrical; Cole–Cole

*Corresponding author: Prabhasini Gupta; E-mail: [email protected]

1. Introduction In the present technology-driven century, there is a quest for new material with improved material properties tailored for various device applications [1]. Perovskites, which have the general formula ABO3, have the flexibility in providing the A and B sites for substitution/doping with iso- and non-isovalent elements; they therefore have the attention of many material scientists synthesizing new materials for promising technological applications [2–5]. Bismuth ferrite (BFO) is an interesting multiferroic compound among all the perovskites, in which the 6s lone pair electrons of bismuth induce ferroelectricity in the compound, and the exchange interaction between Fe3+ ions through O2− induces anti-ferromagnetic ordering [6–7]. Its high Curie temperature (TC = 830°C) makes it a promising candidate for actuators, data storage, and sensor applications [8]. However, the presence of oxygen vacancies and leakage current, which arises because of the volatile nature of bismuth and variable oxidation states of Fe, limits its potential as a material of choice for device applications. Further, the synthesis of single phase BFO via the conventional mixed-oxide reaction method is very difficult because of the formation of secondary phases such as Bi2Fe4O9, Bi25FeO40, or Bi46Fe2O72. Therefore, there is a necessity to remove these impurity phases or to minimize the percentage of these phases in BFO. To address these problems, several methods have been adopted, for example, (i) using a different synthesis method, (ii) substitution at the A or/and B site by rare-earth and other elements, and (iii) making a solid solution with other perovskite ferroelectrics [9–11]. As regards to the substitution/doping at the A and B sites, some of the reported works pertain to the substitution of La3+ and Nb5+ [12], La3+

and Zr4+ [13], Na+ and Nb5+ [14], etc. However, the substitution of an alkaline-earth element at the A site and a tetravalent atom at the B site seems to be a better option for substitution in BFO. In this regard, the addition of alkaline-earth stannate is a potential candidate. Alkaline-earth stannates have wide applications in the scientific and industrial sectors, such as a signal sensors for detecting humidity, temperature, and gas; glass enamels for enhancing the resistance of alkali; the fabrication of ceramic boundary-layer capacitors; as well as photo catalysis, batteries, etc. [15–18]. Of all the stannates (MSnO3, M = Ba, Ca, Sr, etc.), BaSnO3 is the most promising candidate from both elemental and technological points of view because of its semi-conducting and dielectric properties [1921]. Addition of BaSnO3 in BFO is likely to enhance the dielectric constant because of the ionic character of the Ba–O bond, with an electronegative difference of 2.55, greater than that of the covalent Bi–O bond, with an electronegative difference of 1.42. Furthermore, both Fe and Sn have two stable oxidation states, +2 and +3, and +2 and +4, respectively. The oxygen vacancy created during high-temperature synthesis forces some of the Sn and Fe ions to +2 states. Thus, the addition of Sn at Fe sites reduces the number of Fe2+ ions by compensating through a small number of Sn2+ ions. Such a process is expected to reduce the loss tangent in the compound. Keeping all these points in mind, we were motivated to synthesize a compound of BFO with the addition of BaSnO3. For this purpose, we synthesized compounds with 5%, 10%, and 15% added BaSnO3 to BiFeO3 using a standard and cost-effective mixed-oxide reaction method. The X-ray diffraction spectrum of the compound with 10% and 15% addition exhibits many relatively intense impurity peaks, indicating that the compound did not form in the single phase. However, the X-ray diffraction spectrum and the Rietveld refinement of the X-ray

diffraction spectrum of the compound with 5% addition (i.e., Bi0.95Ba0.05Fe0.95Sn0.05O3) indicate the single-phase formation of the compound. As such, we studied the structural and electrical characteristics of Bi0.95Ba0.05Fe0.95Sn0.05O3 only. The present work covers structural and micro structural analyses, compositional confirmation, analysis of dielectric parameters on the basis of the Cole–Cole model, detailed studies of impedance and modulus spectroscopy, as well as conduction mechanism associated with different models and polarization of the prepared sample.

2. Synthesis and Characterization BaSnO3-modified BiFeO3 was synthesized through a mixed-oxide reaction method using AR-grade ingredients Bi2O3 (99.0%, CDH), Fe2O3 (98.0%, Loba Chemie), BaCO3 (99.0%, CDH), and SnO2 (99.9%, Loba Chemie). All of these raw materials (in stoichiometric ratio) were mixed homogenously for 3 h in an agate mortar and pestle under dry conditions. To achieve better uniformity of the mixture, we added ethanol to this mixture and mixed it thoroughly for another 3 h. The obtained mixture was then calcined in an alumina crucible for 4 h at an optimized temperature of 850°C in a muffle furnace. Ethanol, the boiling point of which is 78.24 ± 0.09°C, completely vaporized during the high-temperature calcination conducted at 850°C for 4 h. The lump formed on calcination was powdered. X-ray diffraction (XRD) using a Rigaku Ultima IV diffractometer with CuKα incident radiation (λ = 1.5406 Å) was carried out on the calcined powder to check the phase formation of the compound. After the formation of the compound was confirmed, the calcined powder was sieved into green pellets of 12 mm diameter using a KBR hydraulic press under a pressure of 4 MPa. To reduce the brittleness of the pellet, we used polyvinyl alcohol as the binding agent [22]. The green

pellets were sintered in an alumina boat at 900°C (optimized) for 4 h. During the hightemperature sintering, the binding agent evaporated. The surface morphology and the composition of the sample were studied by field emission scanning electron microscopy (FESEM) using a Zeiss Supra 40. For different characterizations, both sides of the pellet were then polished with fine emery paper followed by silver coating and then subjected to heat treatment at 100°C for 45 min in an oven [23]. The data for the electrical properties (dielectric, impedance, modulus, and conductivity) were taken from an impedance analyzer (PSM 1735, N4L; UK) connected to a laboratory-made sample holder. To determine the temperature of the furnace, a K-type thermocouple was inserted into the sample holder. The infrared absorption and emission spectra was obtained on a Perkin Elmer Fourier transform infrared spectrometer. The ferroelectricity of the sample was measured with a Marine India P–E loop tracer.

3. Results and Discussion 3.1 Compositional, Structural, and Morphological Studies In Fig. 1(a), we have stacked the JCPDS data of the BiFeO3 compound with our studied compound. We analyzed the impurity peak between 20° and 30°. The studied compound matches well the JCPDS data for the compound BiFeO3 (JCPDS: 01-071-2494). The two impurity peaks with nominal intensity in this region correspond to Bi2Fe4O9 and Bi25FeO40 confirmed from the JCPDS file numbers 00-025-0090 and 01-078-1543, respectively. Fig. 1(b) represents the Rietveld refinement plot of our room-temperature XRD data recorded for the final calcined powder. In the refinement graph, the blue line and the black line represent the experimental and the computed data, respectively. The Bragg

positions are marked by the red lines, and the graph within the bottom box with the black solid line represent the difference between the observed and the calculated intensities. The Rietveld refinement was done by using the software MAUD. It is observed that all of the diffracted peaks are different from its constituent compounds and match very well the CIF data of BiFeO3 (ICSD 186955). The lattice parameters and the Rietveld scale factors were refined by using the various options of Refinement Wizard. The refined lattice parameters are found to be a = b = 5.582 Å, c = 13.858 Å. These values are consistent with those of reported ones, i.e., a = b = 5.604 Å, c = 13.952 Å. The Rietveld parameters goodness of fit (2.066), reliability factor (Rw = 5.166%), and pattern R factor (Rexp, % = 2.501%) indicate that the addition of 5% BaSnO3 (which crystallizes in the cubic structure with the space group Pm3m) to BiFeO3 (which crystallizes in the rhombohedral structure with the space group R3c) does not affect the structural properties of the host material. It also shows that it is completely soluble in the structure of BiFeO3, with the formation of single-phase compound (Bi0.95Ba0.05)(Fe0.95Sn0.05)O3 in the rhombohedral structure with the space group R3c. To gain a better idea of the strain due to doping with BaSnO3, we constructed a Williamson–Hall plot (βcos θ ≈ 4sin θ) in Fig. 1(c). The lattice strain, є, and the crystallite size, D, were calculated by using the relation = є4

+

, where

and

respectively represent the Bragg angle and the

full width at half maxima of the corresponding XRD peak. The obtained values of є and D are as 0.003 and 45.9 nm, respectively. The microstructure of the sample is presented in Fig. 1(d). As visualized by the graph, grains of different shapes and sizes confirm the polycrystalline nature of the compound. Further, the grains are densely packed and have an average grain size of 5.83 µm.

Fig. 1(a) XRD pattern of the compound (Bi0.95Ba0.05)(Fe0.95Sn0.05)O3 and (b) Rietveld refinement fitting.

Fig. 1(c) Williamson–Hall plot of the compound (Bi0.95Ba0.05)(Fe0.95Sn0.05)O3.

The elemental analysis and compositional purity of the sample were confirmed by the EDAX spectra shown in Fig. 1(e). The EDAX spectra confirm the emission count rates of the constituent elements (Bi, Ba, Fe, Sn, and O) of our compound. To obtain better insight, we also calculated the elemental atomic ratio of each element using the data obtained from the EDAX spectra; the findings are given in Table 1. It is observed that the each element atomic ratio obtained from EDAX data matches well the stoichiometric ratio of the desired compound.

Fig. 1(d, e) Microstructure and EDAX spectrum of the compound (Bi0.95Ba0.05)(Fe0.95Sn0.05)O3.

Table 1. Element, wt%, at%, and elemental atomic ratio. Element

Wt%

At%

Elemental atomic ratio

Expected

O/(Fe+ Sn +Ba+Bi)

elemental atomic ratio

O

21.94

68.79

2.2034

1.5

Fe

17.99

16.17

0.5179

0.475

Sn

1.72

0.73

0.0234

0.025

Ba

2.46

0.90

0.0288

0.025

Bi

55.89

13.42

0.4298

0.475

3.2 FTIR Study The room-temperature FTIR pattern of the sample is depicted in Fig. 2. The absorbance modes within the range 400–600 cm−1 are the characteristic modes of the compound bismuth ferrite. The three peaks at 443, 537, and 576 cm−1 are consistent with earlier reported data [24, 25]. The modes at 443 and 576 cm−1 are due to the bending vibration of the O–Fe–O bond and stretching vibration of Fe–O bond, respectively. Because of the presence of Bi/Ba–O in the Bi/BaO6 octahedral unit, there exists an absorbance band at 537 cm−1 [24, 26, 27]. As the precursor sample contains carbonate, we obtained the small absorbance peak at 814, 1085, 1119, and 1180 cm−1, as well as a broad peak at around 1429–1507 cm−1. The presence of these carbonate phases cannot be detected in the XRD spectrum. The presence of these organic impurities has a significant effect on the nanosample, whereas it gradually vanishes for the bulk samples [25]. All of these peaks

correspond to the coupling motion of the C=O and C–O bonds [28]. It may be predicted that during FTIR characterization, a small amount of CO2 might have been absorbed from the atmosphere, which gives rise to these vibration modes. At 1629 cm−1, a small peak arises, and at 3334–3436 cm−1, a broad peak arises; these peaks are due to the vibration of an O–H bond [28]. The presence of water may be due to the adsorption by the pellets formed by the KBR hydraulic press.

Fig. 2 FTIR spectra of the synthesized compound (Bi0.95Ba0.05)(Fe0.95Sn0.05)O3.

3.3 Analysis of Dielectric Parameters The variation of dielectric parameters with temperature and frequency is discussed in this section. As depicted in Fig. 3(a), the dielectric constant for all of the studied frequencies exhibits a broad anomaly at around 190°C and a sharp one at 350°C [9]. For better resolution, the variation of dielectric constant with temperature at the two higher frequencies of 500 kHz and 1 MHz is shown as an inset in Fig. 3(a). The dielectric maxima at 350°C in the vicinity of the Neel temperature correspond to the dipole ordering induced by magnetic reordering [29]. The broad anomaly at 190°C seems to be

the superposition of three Gaussian peaks. The multi-peak (three peaks) Gaussian fitting of the broad peak corresponding to six frequencies in the range 500 Hz–1 MHz is presented in Fig. 3(b). The multiple-peak Gaussian fitting (software Origin) was used to deconvolute the apparently overlapped peak into three peaks. The superposed Gaussian peaks are represented by ε ′ = ∑2

1

exp[−

(

$%!

!) #

#

], where Ai is the amplitude, Bi is the

centroid, and Ci is the width of the peaks.

Fig. 3(a) Variation of the dielectric constant with temperature at different frequencies.

The peak position (temperature) and the amplitude of the three peaks corresponding to the various frequencies as obtained from Fig. 3(b) are provided in Table 2. The three peaks are centered at 124, 174, and 199°C. For better comprehension, the variation of peak temperature and the amplitude of the peaks with frequency are depicted in Fig. 3(c) and 3(d), respectively.

Fig. 3(b) Gaussian fitting of dielectric peaks at different frequencies.

While the peak temperature corresponding to the first peak increases up to 10 kHz, the amplitude of the peak continuously decreases with the increase in frequency. The origin of this dielectric peak can be explained using Maxwell–Wagner mechanism, which suggests a more resistive grain boundary than that of the grain/bulk. This contribution is at low frequency [30-31]. The effective temperature of exciting the grain boundary contribution increases with the increase in frequency up to 10 kHz. The Maxwell– Wagner contribution (amplitude) drastically decreased between 10 kHz and 100 kHz. We may infer that the contribution from the electrode and grain boundary decreases fast with the increase in frequency from around 10 kHz. At 100 kHz, this peak corresponding to the Maxwell–Wagner mechanism becomes very broad with a decrease in amplitude and shows a left shift of the centroid. Table 2. Amplitude and centroid of the three Gaussian peaks. Frequency (kHz) 0.5

A1

A2

A3

B1

B2

B3

14656

15432

17666

123.10

178.06

201.51 ±

± 1418.0

± 6.20

± 3.50

0.35

± 1004.38 ± 1431.51 1

10

100

500

1000

Centroid (OC)

Amplitude of the peak

14657

9697.3

13071

127.04

175.88

200.33 ±

± 1254.40

± 786.74

± 985.50

± 9.51

± 18.10

2.48

9513.5

7143.4

8395.4

134.17

174.13 ±

200.41 ±

± 1090.40

± 905.38

± 1098.85

± 10.92

7.15

0.67

2566.0

5081.5

3962.4

112.10

171.30 ±

196.33 ±

± 65.57

± 611.57

± 443.43

± 4.74

3.99

0.62

1676.8

1534.0

1398.9

122.04

173.74 ±

198.11 ±

± 41.48

± 164.18

± 415.47

± 3.10

4.45

0.94

1378.4

1023.6

893.69

128.02

173.42 ±

198.12 ±

± 59.18

± 122.65

± 74.82

± 3.65

4.37

0.80

In Fig. 3(c) and 3(d), the variation of peak temperature and the amplitude with frequency for the second and third peaks follow the same trend, indicating similar reasons behind their occurrence. It is worth mentioning here that Fe and Sn both have stable multiple valence states. The stable oxidation states of Fe are +2 and +3, and those of Sn are +2 and +4. A chemical formula of the compound favors Fe3+ and Sn4+ at the B site, but during synthesis of the compound at 900°C, some oxygen vacancies form; thus, for charge balance, some of the Fe and Sn ions shift to the lower oxidation state of +2. Furthermore, the substitution of Ba is likely to promote oxygen vacancies. The vacancies serve as donors, and Fe3+ captures the electron released in the process, forming Fe2+ and converting Sn4+ to Sn2+ ions. The second and third peaks centered at 174 and 199°C most likely correspond to the transient interaction between oxygen ion vacancies and the Fe2+/Fe3+ and Sn2+/ Sn4+ redox mechanism [32, 33]. Fig. 3(d) shows the steep decrease in the peak value of the dielectric constant for both these cases with the increase in frequency. The dielectric constant vs. frequency graph in Fig. 3(e) depicts the usual trend of decrease in dielectric constant with the increase in frequency due to cessation of some space charge, as well as dipolar modes of polarization owing to the inertia in the subsequent field variation. This aspect is evident in Fig. 3(d). It is worth pointing out here that the space charge polarization, which arises because of the presence of oxygen vacancies and defects and the Maxwell–Wagner effect, is most effective in the temperature range of 90 to 215°C (represented by the width at half maximum of the broad combined peaks in Fig. 3(b)). As such, the dielectric constant in this temperature range is higher than those at other temperatures. In this temperature range, the dielectric constant for the low

frequencies, i.e., up to 1 kHz, is much higher since the amplitude of the peaks corresponding to the Maxwell–Wagner mechanism and the redox mechanism involving Fe and Sn ions due to oxygen vacancies are dominant. From 25 to 100°C, the dielectric constant gradually decreases with frequency, for which there are two regions with different slopes corresponding to the grain boundary and the grain effect. Further, the 100°C curves exhibit a small contribution for the electrode effect. However, for temperatures between 150 and 200°C, we observed that the dielectric curves can be broadly divided into three regions, with each one exhibiting a different slope (dispersion). Variation of the dielectric constant in these three regions corresponds to the electrode effect, grain boundary effect, and the grain effect. At higher temperature (≥250°C), the dielectric constant decreases. It may be recalled that a plateau region is observed between 240 and 300°C in the dielectric constant-temperature graph of Fig. 3(a). To compare our results with those of pure BFO, we present in the inset of Fig. 3(e) the dielectric constant of our compound with that of pure BFO synthesized under similar conditions. As can be ascertained from the inset of Fig. 3(e), the studied compound exhibits a dielectric constant of 5360 at 25°C and 100 Hz, which is very much higher than that of pure BFO (ε ′ = 1076) prepared and measured under identical conditions. It is worth pointing here that for the same temperature and frequency, the reported values of the maximum dielectric constant of BFO based on fabrication methods vary widely, between 81 [9, 34] and 1000 [35]. Moreover, at the higher frequency of 1 MHz, the sample possessed a dielectric constant of 366 at room temperature, which is also higher than that of pure BFO, which has a value of 312.

To confirm our experimental data, we constructed a Cole–Cole plot and used the modified Debye model to explain its characteristics. The room-temperature experimental complex relative permittivity plot, which is also known as the Cole–Cole plot with the semicircular fittings, is depicted in Fig. 3(f). For this purpose, the value of ε′′ was obtained by using the relation &′ = ()* + +,′′. The value of Gdc was obtained from the intercept of the Y′–ω graph (plotted from the data taken from the phase-sensitive meter) [36]. The values of ε′ were obtained from the relation &′′ = +,′. The Cole–Cole plot for the sample at room temperature is found to possess two semicircular arcs, which indicate the presence of both grain and grain boundary contributions to the polarization process in the sample.

Fig. 3(c, d) Frequency variation of peak temperature and amplitude of the three Gaussian peaks of the broad dielectric anomaly.

Fig. 3(e) Frequency variation of the dielectric constant at different temperatures. The inset depicts the dielectric constant curves at 25°C for pure BiFeO3 and the studied compound.

Fig. 3(f) Cole–Cole plot and its inset representing the verification of our experimental data at room temperature.

These semicircles are depressed (Fig. 3(f)), indicating a distribution of the relaxation time for the ceramic sample. In an ideal Debye case with single relaxation time, the complex permittivity can be written as -(+) − -. =

/0 /1

………… (1)

23( 45)

where -6 and -. are the dielectric constant at ω = 0 and ω = ∞ respectively, and τ represents the characteristic relaxation time. However, in our sample, the complex permittivity appears as follows because of the inhomogenous distribution of grain, leading to a distribution of the relaxation time [37]: -(+) − -. =

/0 /1

23( 45)789

… … … … ……… (2)

where (1 − α) is the relaxation distribution parameter. The relaxation distribution parameter is equal to the ratio of the angle made by the tangent to the semicircle at the position corresponding to ε∞ with the real axis and π/2. This parameter bears an inverse relation with grain inhomogeneity. Thus, the tilted angle below the real axis, φ, is related $φ

to the relaxation distribution parameter by the relation (1 − α) = 1 − . Circular arcs <

were obtained for the experimental permittivity data by taking three pairs of ε′ and ε′′ and fitted with the equation of the circle. This process was done frequently in Mathematica software to find the best fit of the semicircle. The fitting provides the radius of the circle, the values of -6 and -. from the intersection of the circle on the real axis, and the depression angle, φ, which is a measure of deviation from the Debye behavior. It is observed that in our sample, the grain and grain boundary are respectively tilted at angles of φg = 22.53° and φgb = 22.90° to the real axis. On the basis of eqn. (2), the real

(εr′) and imaginary part (εr′′) of the permittivity for the sample exhibiting both grain and grain boundary effect can be written as

ε ′ = -.= +

78α?

>/0? /1? @A23>4τ? @ #8#α?

23>4τ? @

BCD φ? E

78α?

3$>4τ? @

+

78α?F

>/0?F /1?F @A23>4τ?F @ #8#α?F

BCD φ? 23>4τ?F @

BCD φ?F E

78α?F

3$>4τ?F @

BCD φ?F

………(3)

and

ε ′′ =

78α?

>/0? /1? @>4τ? @ #8#α?

23>4τ? @

cos φ?

78α?

3$>4τ? @

+

78α?F

>/0?F /1?F @>4τ?F @ #8#α?F

BCD φ? 23>4τ?F @

cos φ?F

78α?F

3$>4τ?F @

BCD φ?F

………………. (4) Where the subscript G and GH stand for the grain and grain boundary effect respectively.

The values of -6= , -.= , -6=J , -.=J determined from the Cole–Cole plot are 2599.2, 254.867, 8586.27, and 2145.87 respectively. The angular frequency ωp, which

corresponds to the peak of both grain and grain boundary in the Cole–Cole plot is found to be 307079.445 and 976.664 rad/s respectively. The relaxation time τ corresponding to the Debye-type relaxation process is the inverse of the angular frequency ωp of the corresponding peak and amounts to 3.26 × 10−6 and 1.03 × 10−3 s for the grain and grain boundary contributions, respectively. Putting all of these values into eqn. (3) and (4), we calculated the values of ε ′ and ε ′′ . In the inset of Fig. 3(f), we have plotted the experimental data for ε ′

and ε ′′

and the theoretically calculated values of the

corresponding quantities. The graphs in the inset of Fig. 3(f) exhibit excellent agreement between the experimental and calculated data and thus confirm the contribution of both grain and grain boundary to the polarization mechanism and the diffusion of thermally excited charge carriers across the barrier [38].

The loss tangent, which is the ratio of the energy dissipated to the energy stored in the capacitor, is one of the important factors that determine the application potential of the ceramic dielectrics. Mathematically, it can be expressed in terms of ()* , as KL M =

4 % NN 3OPQ 4% N

. In terms of dielectric constant, it is expressed as KL M =

ε′′R ε′R

+

SPQ

4ε0 ε′R

……………. (5)

where the first term represents the Debye-type dipolar relaxation, and the second term represents the DC conductivity contribution to the tangent loss. As visualized from the graph (Fig. 3(g)), the loss tangent follows the usual trend of dielectrics. To verify our experimental data, we have calculated the value of loss tangent at room temperature (Fig. 3(h)) by substituting the data obtained from the Cole–Cole plot and eqns. (3) and (4) in eqn. (5). It is observed that the experimental value (black dots) matches very well with the calculated value (red dots) in Fig. 3(h). We also resolved the components of loss tangent in Fig. 3(h) for the Debye contribution of grain (green dots), which is effective at high frequency, the Debye contribution of the grain boundary (blue dots) dominant at lower frequency, and the DC-conductivity-based loss component (pink dots), which decreases rapidly with frequency. All of these curves together with the Cole–Cole analysis confirm the modified Debye response for the sample.

Fig. 3(g, h) Frequency variation of tan δ at different temperatures and the resolution of components of loss tangent at room temperature.

The temperature dependence of the loss tangent is depicted in Fig. 3(i). For all the frequencies, the general trend in the variation of tanδ is that it increases with the rise in temperature. The feature is more visible at low frequencies because of enhancement of the conductivity of the sample with the increase in temperature, which is the major contributor to the tangent loss at low frequencies. However, a broad peak like the anomaly at around 190°C and another sharp peak at 350°C are observed in the tanδ vs. temperature variation for all the frequencies. This feature is akin to that observed in the dielectric constant vs.

temperature graph presented in Fig. 3(a) and 3(b). The broad peak seems to be the superposition of the three peaks corresponding to the three mechanisms mentioned and explains the dielectric vs. temperature variation. For better resolution of the broad peak, the variation of tan δ is shown for the temperature range of 20 to 260°C for some frequencies between 500 Hz and 1 MHz. The tangent loss of the sample for frequencies above 100 kHz in the temperature range of 240 to 320°C is found to be extremely small.

Fig. 3(i) and its inset represents the temperature dependence of loss tangent at different frequencies.

For the studied sample, the value of loss tangent at 25°C in the frequency range of 100 Hz to 10 kHz is found to remain between 1.28–0.28, which is smaller than that of 2.9–0.62 reported for BFO under similar conditions [35]. This reduction in the value is most likely due to the fact that with the addition of BaSnO3, there is a reduction of Fe2+ ions (Fe3+ → Fe2+). This is despite the creation of a relatively small number of Sn2+ ions

(Sn4+ → Sn2+) induced by oxygen vacancies produced during high-temperature synthesis of the compound, which ultimately reduces the value of conductivity and loss tangent. 3.4 Impedance Studies

Impedance studies are a promising non-destructive testing method for analyzing the electrical response of the ceramic compound to the AC signal. In polycrystalline compounds such as the one under study, impedance studies help to identify the grain/bulk, grain boundary, and electrode interface contribution to the circuit elements such as the resistance, capacitance, and the relaxation distribution parameter. The equivalent electrical circuit for the sample having all three contributions is generally represented by the series combination of three parallel RC circuits:

The complex impedance (Z) for the equivalent circuit takes the form [39] 1 T = T + T = V + X+,Y W U

UU

2

2

1 = V + X+,J Y WJ

where T U =

]F

234# %F # ]F #

T = −_ UU

+

]?F

234# %?F # ]?F #

+WJ $ ,J

1 + + $ ,J $ WJ $

+

+

1 +Z + X+,=J [ W=J

2

1 + V + X+,\ Y W\

]^

234 # %^ # ]^ #

+W=J $ ,=J

1 + + $ ,=J $ W=J $

W represents the DC resistance for the concerned effect.

+

+W\ $ ,\

1 + + $ ,\ $ W\ $

`

2

The variation of the reactive part with the resistive part of impedance represents the Nyquist plot. In our ceramic sample, each of the grain, grain boundary, and electrode interface contributions to the impedance plot appears as successive depressed semicircular arcs. The depressed semicircles point at the distribution of relaxation times due to inhomogeneity in size and distribution of grains in the ceramic sample [40]. To take account of this effect, one needs to introduce a constant-phase element (CPE) Q along with the elements R and C in the equivalent circuit for each of the contributions. We have plotted the Nyquist plot for different temperatures in Fig. 4(a). All of the experimental data are fitted with the equivalent electrical circuit by ZSIMPWIN software. All of the parameters obtained from this fitting are listed in Table 3. It is observed that at 25°C, only grain and grain boundary effect contributes to the electrical response. At higher temperatures (≥100°C), the electrode interface effect also contributes in addition to the other two effects.

Fig. 4(a) and its inset representing Nyquist plots at different temperatures.

Fig. 4(b) and its inset represents the disparity of the resistive part, Z', with frequency at selected temperatures. From the graphical representation, it is observed that for all the temperatures, the graphs exhibit inverse dependence on frequency until 100 kHz and then merge to a constant value. This is due to the inertial reluctance of the space charge and progressive cessation of modes of dipolar polarization with increasing frequency of the applied field. On increasing the temperature, Z′ decreases to 200°C and then increases at 250°C, and then again decreases with further rise in temperature. It is worth pointing out here that the sample exhibits a dielectric peak at around 190°C, and there is a decrement in the dielectric constant in the range between 200 and 250°C. Table 3. Values of the resistance, constant-phase element, and the capacitance of grain (g), grain boundary (gb), and electrode effect (e). Temper-

Rg

-ature

(Ω)

n

Cg

Rgb

(F)

(Ω)

n

Cgb (F)

Re

n

Ce

(Ω)

(F)

(°C) 25

1.990

4.491

1.170

4.532

3.059

5.100

5

−1

-9

5

−1

−9

× 10 100

150

300

× 10

× 10

× 10

-

3.474

1.355

9.652

9.541

6.534

1.156

1.300

7.706

× 103

× 10−1

× 10−9

× 103

× 10−1

× 10−9

× 106

× 10−1

× 10−9

6.129

1.995

1.580

8.231

1.775

7.647

4.548

1.415*

1.146

2

−1

−9

3

−1

−9

5

× 10

× 10

× 10

× 10

× 10

× 10

10

−1

× 10−8

3.529

6.550

2.351

3.550

5.358

2.433

4.427

1.143

3.163

2

−1

−8

2

−1

−8

4

−1

× 10−8

× 10 250

× 10

-

2.723

× 10 200

× 10

-

× 10

× 10

× 10

× 10

× 10

× 10

× 10

7.718

1.664

1.884

4.270

6.422

1.516

1.025

1.231

1.163

× 104

× 10−1

× 10−9

× 104

× 10−1

× 10−9

× 105

× 10−1

× 10−9

7.881

9.318

4.180

6.556

7.987

6.967

1.612

2.142

8.439

3

−1

−8

3

−1

−8

4

−1

× 10−8

× 10

× 10

× 10

× 10

× 10

× 10

× 10

× 10

To have a clear picture of the relaxation mechanism associated with the material, we have plotted Z′′ as a function of frequency for different temperatures in Fig. 4(c). The inset of this figure represents a close view of Z′′ at higher temperature. A single relaxation peak is observed in our experimental range of frequency variation. The relaxation peak shifts to a higher frequency with the rise in temperature except for the one at 200°C. This feature points to relaxor behavior in the sample. The left shift of the peak at 200°C can be explained by the dielectric peak at around 190°C. At each temperature, there exists a particular frequency, ωabc , called the relaxation frequency,

where the reactive component achieves the maximum value, i.e., T′′abc . It is observed that the peak value decreases to 200°C and then increases at 250°C and again decreases with further rise in temperature.

Fig. 4(b, c) and their inset represent the frequency variation of Z' and Z'' at different temperatures.

Fig. 4(d) Calculation of activation energy for the relaxation process at different temperatures.

The presence of asymmetry in the characteristic broad peak at all of the temperatures indicates non-Debye-type relaxation process [41]. The process of broadening and shifting of peak with increasing temperature is different in the temperature zones ≤ 200°C and ≥ 200°C, indicating the existence of two types of relaxation mechanism in the material. To confirm these mechanisms of relaxation, we plotted the relaxation frequency (+abc (d)) with respect to temperature in Fig. 4(d) and calculated the activation energy of the relaxation process using the relation +abc (d) = +6 e

εf gh

. All of the symbols used

in this relation have their usual definitions. The slope obtained from the linear fitting of the plot gives the activation energy for the relaxation process [42]; for our sample, it amounts to 0.23 eV at low temperature and 0.85 eV at high temperature. The different activation energies also have their imprint on the conduction process of the grain, which is discussed in the conductivity section.

3.5 Modulus Studies

In addition to complex impedance, analysis of modulus formalism was also emphasized by Hodge to study the properties of solid electrolytes [43]. Modulus spectroscopy has its own significance, enabling the differentiation of components having the same resistance and different capacitances [44]. It is defined through the relation, i = iU + X i" = X+,6 T =

2

/R

where all of the symbols have the usual meanings. Thus, it is specifically

advantageous in analyzing the electrical properties associated with very small capacitance for the material. This also distinguishes the electrode polarization and the grain boundary conduction in a better aspect [45].

The behaviors of M' and M" with frequency are presented in Fig. 5(a) and 5(b) respectively. As visualized from the graph, the value of M' for all of the temperatures increases with the increase in frequency. The negligible or zero value of M' in the lowfrequency region indicates that the ions vibrate within the confinement of their potential energy wells and do not diffuse to the boundary. In addition, the inertial reluctance of ions follow the rapid variation of the electric field at high frequency, leading to the convergence of M' curves for temperatures beyond 240°C [46]. The corresponding curves in the low-temperature region (25 to 75°C) exhibit an increase with frequency and a tendency to merge with those of high-temperature curves (250 and 300°C) at a frequency greater than 1 MHz. However, the curves between 100 and 240°C, which correspond to the temperature range wherein the dielectric constant in Fig. 3(a) exhibits a hump due to the three polarization mechanisms (explained in §3.3), exhibit an anomaly at 1 MHz and above. Keeping all of these behaviors in mind, we can predict that the conduction mechanism in our sample is due to the short-range motion of charge carriers. Furthermore, the value of M' decreases with the increase in temperature; however, at a temperature of ≥250°C, it first increases and then again decreases.

Fig. 5(a, b) Frequency variation of M' and M'' at different temperatures.

The imaginary component of the modulus has a direct dependence on the resistive part of impedance through the relation M" = ωCoZ'. The presence of an asymmetric peak for all of the temperatures supports the deviation of the relaxation process in the sample from the Debye type, as discussed in the impedance section. To examine the short-range mobility of charge carriers, we have plotted the imaginary components of impedance and modulus with frequency in Fig. 5(c). It has been reported that if the peaks of both the components Z′′ and M" occur at the same frequency, long-range-type charge carriers are involved; if it does not occur, then it is due to short-range-type charge carriers [47].

As seen from the graph, both peaks slightly depart from each other, indicating shortrange motion of charge carriers in the sample.

Fig. 5(c) Variation of Z'' and M'' with frequency at 250°C.

3.6 Conductivity Studies

The behavior of AC conductivity as a function of inverse temperature is depicted in Fig. 6(a). Mathematically, AC conductivity is expressed as σac = ωε′tan δ = σdc + ωε′′, where the first and second terms respectively represent the DC conductivity and the absorptive component of displacement current. As is evident from the curves in Fig. 6(a), the conductivity curves in the temperature range of 25 to 190°C exhibit negativetemperature coefficient-of-resistance (NTCR) behavior, with the values increasing with the increase in frequency, a characteristic of hopping conduction. This temperature region corresponds to the increasing portion of the broad dielectric anomaly in Fig. 3(a), which includes the peak excitation temperature for all of the three dielectric polarization processes discussed in the dielectric section. In the temperature range of 190 to 240°C, the conductivity curve decreases, exhibiting positive-temperature coefficient-of-

resistance (PTCR) behavior, and the range of temperature corresponds to the decreasing side of the dielectric anomaly in Fig. 3(a). PTCR behavior implies no more excitation of charge carriers in this temperature range. The temperature range of 240 to 300°C, which corresponds to the plateau-like region in Fig. 3(a), is characterized by a small increase in conductivity with the increase in temperature. Beyond 300°C, the conductivity exhibits a steep increase with temperature mainly due to high-temperature DC conductivity and reordering of charge carriers induced by magnetic reordering at around the Neel temperature of 350°C, as seen in Fig. 3(a). For ready reference, we provide Table 4, which shows the conductivity at different temperatures and frequencies.

Table 4. Values of the AC conductivity at different temperatures corresponding to different frequencies. σac (Ω−1 m−1)

Temperature (°C)

1 kHz

10 kHz

100 kHz

500 kHz

1 MHz

25

0.00010

0.00040

0.00418

0.00935

0.01185

100

0.00155

0.00377

0.00937

0.02828

0.05377

200

0.00463

0.00717

0.03294

0.07916

0.11207

240

0.00023

0.00035

0.00051

0.00081

0.00103

300

0.00125

0.00151

0.00198

0.00255

0.00299

347

0.28248

0.29580

0.31381

0.34870

0.37864

It can be seen from the graph of Fig. 6(a) that the activation energy decreases with the increase in frequency, i.e., from 0.72 eV at 1 kHz to 0.48 eV at 1 MHz. The decrease in activation energy with frequency in the experimental range is due to increased hopping probability with increasing frequency. Fig. 6(b) represents the alteration of AC conductivity with frequency at selected temperatures. These conductivity curves can be analyzed by the Jonscher’s equation: σ (ω) = σ)* +

ωa , where all the symbols have

their usual meanings. For a non-Debye case, the value of the frequency exponent (m) lies between 0 and 1. The value of m was calculated from the slope of log σac ≈ log ν graph. As visualized from the graph, there appear two different regions having different slopes corresponding to different values of m for a particular temperature.

Fig. 6(a, b) Variation of AC conductivity with inverse temperature and frequency at different temperatures.

The conductivity curves in the entire frequency range increases with temperature up to 190°C and then decreases up to 240°C. For temperatures more than 240°C, the conductivity again increases. The different values of m suggest two different conduction

mechanisms in the sample, one in the lower frequency, associated with the grain boundary, and another with grain at higher frequency. To have a detailed illustration about the charge carriers, which are involved in the conduction process, we have plotted the variation of the frequency exponent (m) of both grain boundary and grain effect with temperature in Fig. 6(c) and its inset, respectively. These curves explain the conduction mechanism associated with different models [48]. The frequency exponent corresponding to the grain boundary effect exhibits an overlapping large-polaron tunneling (OLPT) model, where the exponent m first decreases with the increase in temperature, attains a minimum, and then increases again. Here, the overlapping of potential wells of the neighboring sites takes place because of the longrange nature of the Coulombic interaction exhibited by the large polarons [49]. As a result, the polaron hopping energy is reduced and is given by kl = klm (1 − ), where n

]

klm =

\#

oεp n

,α is the inverse localization length, qr is the polaron radius, and klm is the

activation energy. Mathematically,

σb* = [πo e $ s d

{u(vw )}# 2$

]*[

ω]y ω {

Rn

$α z 3 |} ~# ω

]

……………… (6)

Where •(€• ) is the energy level density of the Fermi level, Wω is the tunneling distance,

and s is the Boltzmann constant.

Fig. 6(c) Temperature variation of the frequency exponent (m) for grain boundary effect. Its inset represents the grain effect.

The conduction mechanism associated with the grain effect follows the correlated barrier hopping (CBH) model. It may be worth mentioning here that our sample possesses two different values of activation energy for the relaxation process of grain in the two temperature ranges, the first being room temperature to 190°C and the second being a temperature higher than 240°C. It can be seen that the value of m decreases with the increase in temperature [50]. Here, the transfer of electrons is possible via thermal excitation over the barrier between the two sites. Mathematically, it can be written as [51] ‚b* (ω) =

πƒ

$o

• $ εε6 ωWω „

…………….(7)

where N is the concentration of pure states, Wω is the hopping distance, and the rest of the

symbols have their usual definitions. The hopping distance Wω at frequency + can be

expressed as Wω =

πεε0 […†

\#

z

‡ˆA

7 E] ‰Š‹

…………….(8)

where e is the electronic charge, s is the Boltzmann constant, k• is the barrier height,

and Ž• is the relaxation time. The frequency exponent m in this case is given by

• =1−

…†

„ z z ‡ˆ(2/45‹ )

………………(9)

For large values of k• /s d, the above equation reduces to [52] • =1−

6s d k•

Using the above relation and the linear fitting of the experimental data, we found the values of k• for both temperature ranges to be 97 and 87 meV. We also calculated the hopping distance and the concentration of pure states at 20 kHz, 4.02 Å and 1.71 × 1028 m−3, respectively. 3.7 Polarization Study

To show the ferroelectric behavior of the compound, we have plotted the room temperature polarization data as a function of electric field in Fig. 7. It is observed that the sample shows a saturated loop with a remnant polarization (Pr) of 1.14 µC/cm2 and coercivity (Ec) of 3.58 kV/cm. The reported values of BFO by Deng et al. for Pr and Ec are 0.3 µC/cm2 and 3 kV/cm [36], respectively; and 0.1 µC/cm2 and 4 kV/cm, respectively, as reported by Zhang et al. [35]. The measured value of Pr for our sample (Bi0.95Ba0.05)(Fe0.95Sn0.05)O3 is quite high in comparison to that of the reported values of BFO. The ferroelectricity of the sample was enhanced by doping with 5% BaSnO3 as the dielectric constant increases very drastically because of addition of BaSnO3. It may be recalled here that the studied compound exhibits a dielectric constant of 5360 at 25°C and 100 Hz, which is very much higher than that of pure BFO (ε ′ = 1076) prepared and

measured under identical conditions. It is worth mentioning here that the P–E

measurement was carried out with a field frequency of 100 Hz. The Ba2+ ions at Bi3+ sites act as acceptor centers and are associated with the hardening effect with the increase in coercive field [53, 54]. The higher-valence Sn4+ ion can act as donor center and may even cause some cation vacancies, leading to dipolar defects and helping to suppress oxygen vacancies. The random field around these defects is expected to lower the barrier required for nucleation of new domains, which thus lower the value of the coercive field and help domain motion and consequently increase the ferroelectric properties [55, 56].

Fig. 7 Room-temperature hysteresis loop.

4. Summary and Conclusion (Bi0.95Ba0.05)(Fe0.95Sn0.05)O3 compound was successfully synthesized through the conventional mixed-oxide reaction method. The composition of the compound was confirmed from the EDAX spectrum. Rietveld refinement of the room-temperature XRD data confirmed the formation of single-phase compound that crystallizes in the rhombohedral structure with a crystallite size of 45.9 nm. FESEM confirmed densely

packed grains in the sample with an average grain size of 5.83 µm. The occurrence of characteristic modes in the FTIR spectrum supports the formation of the compound. In the studied range of temperature and frequency, the sample exhibited a broad anomaly at around 190°C and a sharp one at 350°C. By Gaussian fitting, we found the broad peak at 190°C to be the superposition of three peaks centered around 124, 174, and 199°C. These had their origin in the Maxwell–Wagner effect, and the oxygen vacancy mediated transient interaction between the Fe2+/Fe3+ and Sn2+/Sn4+ redox mechanisms. The sharp peak of the dielectric at 350°C corresponds to magnetic ordering around the known Neel temperature. A Cole–Cole plot and the modified Debye model were used to verify our experimental dielectric data and to resolve the components of loss tangent to the Debyelike contribution of the grain and grain boundary and the DC-conductivity-based loss component. The room-temperature Cole–Cole plot confirms the contributions of grain and grain boundary effect in the sample. The Nyquist plot reveals that at high temperature (≥100°C), the electrode interface effect also contributes in addition to the grain and grain boundary effects. The frequency dependence of Z′′ suggests that the grain itself follows two types of relaxation mechanism in the temperature range of ≤200°C and ≥200°C, with activation energies of 0.23 and 0.85 eV, respectively. These relaxation

mechanisms were supported by the conduction mechanism of the grain associated with the CBH model with different barrier height. OLPT model was used to explain the conduction mechanism associated with the grain boundary. The P–E loop confirms the room-temperature ferroelectricity of the sample. The addition of 5% BaSnO3 to BFO resulted in a nearly 10-fold increase in the dielectric constant, and the remnant polarization accompanied a reduction in the loss tangent. The effect might have been

caused by a relatively large reduction in the oxygen-vacancy-mediated Fe2+/Fe3+ redox mechanism compensated by a smaller number of Sn2+/Sn4+ redox mechanisms. The increased dielectric constant, the broad dielectric peak with significantly higher half width, and the reduced loss tangent of the (Bi0.95Ba0.05)(Fe0.95Sn0.05)O3 compound give it more potential for device application as compared with BFO and hosts of other known dielectric materials.

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Figure Captions 1. Fig. 1(a) XRD pattern of the compound (Bi0.95Ba0.05)(Fe0.95Sn0.05)O3 and (b) Rietveld refinement fitting. (c) Williamson–Hall plot of the compound (Bi0.95Ba0.05)(Fe0.95Sn0.05)O3. (d, e) Microstructure and EDAX spectrum of the compound (Bi0.95Ba0.05)(Fe0.95Sn0.05)O3. 2. Fig. 2 FTIR spectra of the synthesized compound (Bi0.95Ba0.05)(Fe0.95Sn0.05)O3.

3. Fig. 3(a) Variation of the dielectric constant with temperature at different frequencies. (b) Gaussian fitting of dielectric peaks at different frequencies. (c, d) Frequency variation of peak temperature and amplitude of the three Gaussian peaks of the broad dielectric anomaly. (e) Frequency variation of the dielectric constant at different temperatures. Its inset depicts the dielectric constant curves at 25°C for pure BiFeO3 and the studied compound. (f) Cole–Cole plot and its inset representing the verification of our experimental data at room temperature. (g, h) Frequency variation of tan δ at different temperatures and the resolution of components of loss tangent at room temperature. (i) Temperature dependence of loss tangent at different frequencies. 4. Fig. 4(a) Nyquist plots at different temperatures. (b, c) Frequency variation of Z' and Z'' at different temperatures. (d) Calculation of activation energy for the relaxation process at different temperatures. 5. Fig. 5 (a, b) Frequency variation of M' and M'' at different temperatures. (c) Variation of Z'' and M'' with frequency at 250°C. 6. Fig. 6(a, b) Variation of AC conductivity with inverse temperature and frequency at different temperatures. 6(c) Temperature variation of the frequency exponent (m) for grain boundary effect. Its inset represents the grain effect. 7. Fig. 7 Room-temperature hysteresis loop.

Tabulation 1. Table 1. Element, wt%, at%, and elemental atomic ratio. 2. Table 2. Amplitude and centroid of the three Gaussian peaks.

3. Table 3. Values of the resistance, constant-phase element, and the capacitance of grain (g), grain boundary (gb), and electrode effect (e). 4. Table 4. Values of the AC conductivity at different temperatures corresponding to different frequencies.

1. The addition of 5% BaSnO3 to BFO results in a nearly 10-fold increase in the dielectric constant with a reduction of the loss tangent. 2. By employing Cole–Cole model, the loss tangent is resolved to identify the contributions from the Debye-type relaxation for both grain and grain boundary effects and that of the DC conductivity. 3. The impedance and modulus analysis confirms the non-Debye response of the sample. 4. Nyquist plot reveals that at high temperature (≥100°C), the electrode interface effect also

contributes in addition to the grain and grain boundary effects.

All the authors have read and approved the manuscript and have agreed for submission to this journal.