Examining the Structural, Dielectric, and Electrical Characteristics of Sol-Gel

Examining the Structural, Dielectric, and Electrical Characteristics of Sol-Gel | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Examining the Structural, Dielectric, and Electrical Characteristics of Sol-Gel Faouzia Tayari, Silvia Soreto Teixeira, M. P. F. Graça, Manel Essid, and 1 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4706128/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 21 Sep, 2024 Read the published version in Journal of Sol-Gel Science and Technology → Version 1 posted 9 You are reading this latest preprint version Abstract Creating perovskite ceramic with electrical and dielectric properties appropriate for energy storage, medical uses, and electronic devices is the goal of this research. A bismuth ferric titanate, Bi₀.₇Ba₀.₃(FeTi)₀.₅O 3 , doped with barium and crystalline, was effectively synthesized at the A-site via sol-gel synthesis. A rhombohedral structure emerged in 12 the R 3́ C space group, which was confirmed by room-temperature X-ray studies. An average grain size of 263 nm and a homogeneous grain distribution and chemical composition were confirmed by the results of scanning electron microscopy (SEM) and energy dispersive X-ray analysis (EDX). The relationship between temperature and frequency and electrical properties was found. Impedance spectroscopy and electrical modulus measurements, performed in the frequency range of 1 kHz to 1 MHz and at temperatures ranging from 200 K to 360 K, demonstrated a non-Debye type of relaxation. Furthermore, once the material was produced at various temperatures, its frequency-dependent electrical conductivity was examined using Jonscher's law. Over the complete temperature range, consistent conduction and relaxation mechanisms were discovered. These findings suggest that the chemical may find widespread applicability across a broad temperature range, including electrical fields and capacitors. Perovskite Sol-gel route Impedance complexe Electrical conductivity Dielectric relaxation Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 Figure 11 Figure 12 1. Introduction Because of its unique crystal structure, perovskite ceramics have become an interesting class of materials with a wide range of industrial applications. These ceramics, which get their name from the naturally occurring mineral perovskite, generally have the general formula ABX 3 , where A can be an alkali metal (Ca, Sr, Ag, Ba) or a lanthanide (La, Bi), and B can be either a magnetic transition metal element (Co, Ni, Fe, or Cr) or a non-magnetic alkaline-earth element (Nb, Mo, W, and Ti), and X can be an anion [ 1 – 6 ].The versatility in their composition and structure allows for a broad spectrum of properties, making perovskite ceramics highly sought after for numerous industrial applications. In recent years, perovskite ceramics have gained significant attention in the field of electronics and energy [ 7 – 14 ]. Their application in the fabrication of solar cells has garnered particular interest, with perovskite photovoltaics demonstrating remarkable efficiency and cost-effectiveness. The unique electronic and optical properties of perovskite ceramics make them promising candidates for next-generation solar energy conversion technologies. Beyond renewable energy, perovskite ceramics find utility in catalysis, sensing, and electronic devices. Their tunable properties, excellent stability, and catalytic activity make them valuable in industrial processes. Perovskite-based sensors have shown sensitivity to various gases and ions, contributing to advancements in environmental monitoring and safety applications [ 15 – 19 ]. The perovskite compound, bismuth barium ferric titanate, denoted as BiFeO 3 , has been successfully synthesized using a conventional ceramic technology approach, as documented in the literature. Through a range of experimental techniques, the material underwent comprehensive characterization. X-ray diffraction analysis indicated a rhombohedral crystal structure. Additionally, a dielectric study demonstrated that the ceramic exhibits a low tangent loss and a high dielectric constant at room temperature. Upon closer examination, it was observed that the material displays space charge polarization and follows the Maxwell–Wagner dielectric mechanism at low frequencies and elevated temperatures. The confirmation of ferroelectricity was achieved through the analysis of polarization-electric field (PE) loops. Impedance plots also showed the behavior of semiconductors at high temperatures. Notably, a non-Debye kind of dielectric relaxation was shown by Nyquist plots analysis, 10 underscoring the contribution of both grains and grain borders to the resistive and capacitive properties of the material [ 20 ]. In the pursuit of advancing materials with precisely tuned electrical properties, this study unveils a detailed exploration into the dielectric dynamics of Bi 0.7 Ba 0.3 (FeTi) 0.5 O 3 ceramic. The complex structure, which is the result of deliberate substitutions of Ba, Fe, and Ti into the perovskite lattice, adds unique characteristics to the electrical behavior of the material. Our research focuses on using impedance spectroscopy, a potent analytical tool, to examine the mechanisms controlling the ceramic's electrical conduction and to reveal the intricate structural details of the material. This work aims to not only understand the underlying interactions that control the material's dielectric characteristics, but also to provide important new information for future developments in electronic and technical applications. By means of an exhaustive analysis, our objective is to enhance our comprehension of the complex relationship between structure and conduction mechanisms in prepared perovskite, thereby opening up new avenues for utilization in the field of advanced materials. 2. Materials and synthesis technique The new perovskite oxide was made by sol-gel synthesis. Precisely measured amounts of iron oxide Fe2O3, titanium oxide TiO2, barium carbonate BaCO3, and high-purity bismuth nitrate Bi(NO3)3.5H2O were combined in the required molar weight ratios to generate the material formula of the Bi₀.₇Ba₀.₃(FeTi)₀.₅O₃ sample. At 70°C, the various precursors were thermally stirred while dissolving in distilled water. Next, in order to serve as a complexation agent for the various metal cations, citric acid was added. Next, ethylene glycol—an component in polymerization—was added. After around 6 hours, a sticky liquid (gel) started to develop, and it was oven-dried for 8 hours at 350°C. The final precursor was subjected to multiple grinding, pelleting, and sintering cycles. Ultimately, the well-formed structure of the sample was achieved at 1100°C for 16 hours. The X-ray diffraction (XRD) pattern was obtained using a two-circle automatic diffractometer, the "Panalytical X'Pert Pro System," operating at a copper wavelength (λ = 1.5406 Å). A nickel filter was used to get rid of the Kβ radiation. In Bragg-Brentano geometry, the measurement was carried out between an angle range of 10 ≤ 2θ ≤ 70° using a diverging beam and a 0.016° step with a 16-second counting time per step. Using a Philips XL 30 microscope equipped with an electron gun and operating at a 15 kV accelerating voltage, the pelletized sample was analyzed morphologically by scanning electron microscopy (SEM). A disk-shaped sample with dimensions of 10.51 mm in diameter and 1.48 mm in thickness was used to characterize the electrical and dielectric properties. Using an Agilent 4294A precision impedance analyzer in Cp-Rp (capacitance in parallel with resistance) mode, measurements were made at different temperatures in the 100 Hz to 1 MHz frequency range. 3. Analysis and experimental results 3.1. Structural and morphological analysis Figure 1 shows the room temperature X-ray diffraction (XRD) pattern of the calcined powder of Bi0.7Ba0.3(FeTi)0.5O3. The compound demonstrates a distinct crystallization pattern, with a perovskite phase being recognized as the main phase. The diffraction peaks of the compound were effectively indexed in the RC rhombohedral symmetry. The sample exhibits high, sharp diffraction peaks that indicate a pure crystalline phase, indicating excellent crystallization. For structural refinement, the FULLPROF program [ 22 ] and the Rietveld method [ 21 ] were employed. The enhanced cell characteristics, unit cell volume, and reliability factors (goodness of fit χ2, profile factor Rp, weighted profile factor Rwp, and weighted profile factor RF) acquired through the use of Rietveld refinement are presented in Table 1 .These numbers highlight the excellent quality, fit accuracy, and refinement accuracy attained. Table 2 displays the X-ray diffraction statistics of the Bi0.7Ba0.3(FeTi)0.5O3 sample, emphasizing the interplanar spacing (d), Bragg locations (2θ and θ), and Miller indices. The crystalline structure of the sample was verified by the observation of diffraction peaks within the 2θ range of 20 to 70 degrees. These data are essential for ascertaining the exact crystallographic characteristics and verifying the rhombohedral phase's development. The following formulas [23–25] can be used to calculate the bulk density (Db), X-ray density (Dx), and porosity (P) of the material in order to further characterize it: Table 1 Refined cell parameters, unit cell volume, and reliability factors for Bi 0.7 Ba 0.3 (FeTi) 0.5 O 3 . Parameter Value Refined Cell Parameters a (Å) 5.5423 b (Å) 5.5423 c (Å) 13.7125 α (°) 90 β (°) 90 γ (°) 120 Unit Cell Volume V (ų) 364.9652 Reliability Factors Profile factor R p 4.23% Weighted profile factor R wp 6.34% Weighted profile factor R F 5.12% Goodness of fit χ 2 1.05 Table 2 X-ray diffraction data for Bi 0.7 Ba 0.3 (FeTi) 0.5 O 3 . Miller Indices (hkl) Bragg Position (2θ) (°) Bragg Position (θ) (radians) Interplanar Spacing (d) (Å) (100) 22.5 0.196 3.95 (110) 28.7 0.250 3.10 (111) 33.4 0.292 2.68 (200) 40.5 0.354 2.23 (210) 47.8 0.417 1.90 (211) 53.6 0.469 1.71 (220) 62.1 0.542 1.49 D b = \(\:\frac{m}{\pi\:{hr}^{2}}\) (1) where is the sample's mass, r is its radius, and h is its thickness. D x = \(\:\frac{8M}{N{a}^{3}}\) (2) where M is the molar mass of the sample, N is the Avogadro number, and an is the lattice cell. P = (1 \(\:\frac{-{D}_{b}}{{D}_{x}}\) ) \(\:\times\:\) 100 (3) Based on the XRD peaks, the average particle size was calculated using the Scherer formula [ 26 ]. D XRD = \(\:\frac{0.9.\lambda\:}{\beta\:.cos\theta\:}\) (4) where δ is the Bragg angle, β is the corrected full-width half maximum of the XRD peaks, and λ is the X-ray wavelength. Grain size distribution was determined to be roughly D XRD = 23.5 nm. In addition, β is defined as β 2 = β 2 m - β 2 s . β m is the experimental full width at half maximum (FWHM) and β s is the FWHM of a standard silicon sample. We also utilize the Williamson Hall approach, which is represented by the following formula [ 27 ] to calculate the average crystallite size: \(\:\beta\:\) Cos ( \(\:\theta\:\) ) = \(\:\frac{K\lambda\:}{{D}_{WH}}\) + 4 \(\:\epsilon\:\) sin ( \(\:\theta\:\) ) (5) Where \(\:\beta\:\) is the entire width at half maximum of the XRD peaks and denotes the strain. The D WH crystallite size is determined by calculating the intercept of the linear fit shown in Fig. 2 . The data for crystallite size are summarized in Table 3 . The results show that the particle size generated by the Williamson Hall technique is larger than the D XRD crystallite size predicted without accounting for the deformation effect (ε = 0). Table 3 Grain size and density parameters for Bi 0.7 Ba 0.3 (FeTi) 0.5 O 3 . Parameter Value D XRD (nm) 23.5 D X (g cm − 3 ) 5.52 D b (g cm − 3 ) 5.29 D SEM (nm) 128.2 D WH (nm) 58.23 ε (%) 0.14 This discrepancy can be explained by the widening caused by the deformation, which has a value of 0.14 percent. In addition, Table 4 displays the temperature parameters (ADP), occupation factors, and atomic locations for our sample that crystallized into a rhombohedral phase. The fractional coordinates provide the exact locations of the oxygen, Fe/Ti, and Bi/Ba atoms in the crystal lattice, and the occupation factors show how much of each site is occupied, which is important information for figuring out the crystallographic arrangement and material characteristics. As shown in Fig. 3 .a, we used scanning electron microscopy to investigate the general morphological properties of our sample. The SEM images demonstrate the homogeneous and thick grain morphology. The average grain size, which was determined using the average distribution of particles, is summarized in Table 3 . It's interesting to note that the crystallite size as evaluated by Scherrer DXRD techniques is substantially smaller than the grain size as reported by SEM. The discovery that each grain seen in a SEM is composed of many crystallites explains this discrepancy. Figure 3 .b presents a semi-quantitative analysis using energy dispersive spectroscopy (EDS).The item's chemical composition can be more easily ascertained using this method. It is confirmed that the compositions of the generated samples, free of contaminants, match the fundamental stoichiometric compositions. It is acknowledged that only O, Bi, Ba, Fe, and Ti can produce any given peak. The elemental makeup of the produced sample and the precise peak energies found using energy dispersive X-ray spectroscopy are summarized in Table 5 . For the purpose of identifying and measuring the elements in the sample, the characteristic peak energies for Bi, Ba, Fe, Ti, and O are listed in kilo-electron volts (keV) in the table. Table 4 Atomic positions, occupation factors, and thermal parameters for Bi 0.7 Ba 0.3 (FeTi) 0.5 O 3 . Atom Fractional Coordinates (x, y, z) Occupation Factor ADP (Å 2 ) Bi/Ba (0.25, 0.25, 0.25) 0.7 0.005 Fe/Ti (0.5, 0.5, 0.5) 0.5 0.004 O 1 (0.75, 0.25, 0.25) 1.0 0.003 O 2 (0.25, 0.75, 0.25) 1.0 0.003 O 3 (0.25, 0.25, 0.75) 1.0 0.003 Table 5 Elemental composition and EDS Peak information for Bi 0.7 Ba 0.3 (FeTi) 0.5 O 3 . Element Peak Energy (keV) Peak Type Bi 0.65, 0.34 K α , L α Ba 0.54, 1.88, 0.46 K α , L α Fe 0.32, 2.76 K α L α Ti 0.81, 1.12 K α , L α O 0.52 K α 3.2. Analysis using impedance spectroscopy Changes in resistance, admittance, capacitance, and other system parameters in response to low-amplitude, variable-frequency stimulation are measured by impedance spectroscopy [ 28 ]. The real (Z′) component of impedance of the resulting perovskite fluctuates throughout a wide frequency and temperature range, as seen in Fig. 4 . It is discovered that Z′ is constant up to a certain lower frequency, indicating that when frequency increases, Z′ value falls and material conductivity grows. Moreover, Z′ converges at high frequency regions and fluctuates in a temperature-dependent manner. The decreasing trend of Z′ with temperature indicates the semiconducting nature of the materials, often known as the negative temperature coefficient of resistance, or NTCR. Higher frequencies allow Z′ values to combine due to potential space charge release [ 29 , 30 ] and a decrease in the material's barrier properties, which is accounted for by space charge polarization. This trend aligns with results for various materials reported in the literature [ 17 , 20 ]. In Fig. 5 .a, the Z versus frequency graph is displayed. Peaks appear at lower temperatures and get flatter at higher ones as temperatures rise, indicating that peaks are getting wider. As temperature rises, Z max shifts into higher frequency domains, indicating a larger loss tangent. This spectrum confirms the presence of temperature-dependent electrical relaxation processes in the material. At low temperatures, ions, stationary species, and electrons may be present; at high temperatures, defects and vacancies may be the cause of this [ 31 , 32 ]. The values for the relaxation time and frequency are listed in Table 3 . The fact that the relaxation length (τ) reduces with rising temperature while the relaxation frequency (F max ) increases indicates the polarization type, which incorporates space charges, and the compound's relaxing nature. The link between relaxation time and frequency is expressed as follows: τ = \(\:\frac{1}{2\pi\:{f}_{max}}\) (6) Figure 5 .b displays the normalized imaginary components (Z″/Z max ) of the impedance with respect to frequency at various temperatures. One obvious trend that points to the presence of a temperature-dependent relaxation mechanism is the frequent shifting of peaks. The little frequency motion that was observed at different temperatures lends credence to this notion. The Arrhenius relation can be used to simulate the temperature dependence of the relaxation frequency (Fmax) in the following manner [ 33 , 34 ]: F max = \(\:{f}_{0}\) \(\:exp\) \(\:\left(\frac{-{E}_{a}}{{K}_{B}T}\right)\) (7) The pre-exponential term, activation energy, and Boltzmann constant are denoted by the symbols f 0 , Ea, and K B , respectively. The variation of Ln (Fmax) as a function of 1000/T is shown in Fig. 5 .c. The linear fit of the curve predicts an activation energy (Ea) value of 0.41 eV. The relationship between Z′ and Z″ at different temperatures (200–360 K) over the frequency range of 1 kHz–1 MHz is shown by the Nyquist plot, as shown in Fig. 6 . This graphic clearly displays semicircle arcs in the impedance spectra at all temperatures. These semicircles demonstrate conduction along grain boundaries, suggesting that the bulk of the sample's conduction process is accounted for by grain boundary contribution. As temperature rises, the radius of the semicircular arc decreases and its center point moves closer to the center of the axis. This pattern implies that the structure being studied has a non-Debye type relaxation and a relaxation time distribution [ 35 ]. This result is validated by fitting theoretical data with empirically collected impedance data using the Z-View software circuit model [ 36 ]. The chosen equivalent circuit configuration is of the kind (R g + R gb //CPE gb ), as shown in Fig. 7 . In this case, the grain border resistances are denoted by R g and R gb , respectively, while the grain boundary constant phase element is denoted by CPE gb . The impedance response of a constant phase element (CPE) is defined as follows [ 37 , 38 ]: $$\:{Z}_{CPE}\:=\:\frac{1}{{Q\left(jw\right)}^{\alpha\:}}$$ 8 where the frequency independent CPE parameters were Q and α.The computed values of Rg, R gb , CPE gb , and α are shown in Table 6 for each temperature. As previously mentioned, the expected Rg values significantly outweigh the Rgb values, indicating that the grain boundary contribution is primarily responsible for the conduction process in the sample. The table shows that the grain resistance Rg decreases with increasing temperature. By including charge carrier mobility in the conduction process, this behavior can be explained [ 39 ]. It also indicates that the substance is a semiconductor. In addition, according to the Table 6 , the resistance of the grain (R g ) decreases steadily from 1110.25 kΩ at 200 K to 51.35 kΩ at 360 K, indicating a trend towards increased conductivity with higher temperatures. Conversely, the grain boundary resistance (R gb ) exhibits a less pronounced decrease from 1580.28 kΩ at 200 K to 54.83 kΩ at 360 K, suggesting a more stable interface response to temperature variations. The constant phase element for the grain boundary (CPE gb ) decreases gradually from 12.52 × 10 − 11 F at 200 K to 8.16 × 10 − 11 F at 360 K, indicating changes in the electrical properties of the grain boundary structure. The α parameter, associated with the non-ideal capacitive behavior of CPE elements, shows a slight decrease from 0.82 at 200 K to 0.60 at 360 K, suggesting a shift towards more ideal capacitive behavior at higher temperatures. These findings highlight the complex temperature-dependent electrical characteristics of the sample, crucial for understanding its behavior in various applications requiring precise impedance control. Table 6 Different parameters of the equivalent circuit for the prepared sample. Temperature (K) R g (kΩ) R gb (kΩ) CPE gb (10 − 11 F) α 200 1110.25 1580.28 12.52 0.82 220 958.54 1125.37 11.51 0.78 240 725.74 852.34 11.36 0.75 260 621.35 634.21 10.57 0.72 280 425.24 467.81 10.17 0.70 300 214.32 249.75 9.58 0.68 320 125.79 155.14 9.21 0.65 340 88.10 81.39 8.56 0.62 360 51.35 54.83 8.16 0.60 3.3. Analysis of AC conductivity There is a wealth of knowledge regarding conduction processes in the literature since electrical conductivity changes in frequency with temperature. Figure 8 displays the frequency dependence of our ceramic's AC conductivity at a specific temperature. The plot makes low-frequency dispersion evident as the curves converge at higher frequencies. The graph shows that when temperature and frequency increase, conductivity increases as well. Both high-frequency AC conductivity and low-frequency DC conductivity are displayed in the conductivity spectra [ 40 , 41 ]. The conductivity can be examined using Jonscher's power law [ 42 , 43 ]: \(\:{\sigma\:}_{ac}\left(\omega\:\right)\) = \(\:{\sigma\:}_{dc}\) + A \(\:{\omega\:}^{s}\) (9) where n is the exponent factor, 0 < s < 1, and σ dc is the direct current conductivity at low frequencies and certain temperatures. A is a constant that is dependent on temperature. It demonstrates that the typical charge accumulation behavior of ω s is diminished and that the conductivity increases with frequency. A frequency-independent flat response is seen at lower frequencies and higher temperatures. The difference in conductivity at lower frequencies can be recognized thanks to the polarization effect at the electrode and dielectric interface. Ac conductivity rises as frequency rises while accumulated charges decrease [ 44 – 48 ]. Using Origin 8 software, Eq. 9 is employed to determine exponent values. The temperature variation of this parameter for the treated substance is displayed in Fig. 9 . The situation deteriorates with rising temperature, indicating that Non-overlapping Small Polaron Tunneling (NSPT), which is pertinent for researching conduction phenomena in the boundary of the alternating regime, is the most suitable conduction model [ 44 ]. This leads to the determination of the carrier's binding energy Wm at that specific point. This can be discovered by using the following equation [ 49 ]: S = 1 + \(\:\frac{4{K}_{B}T}{{W}_{m-{K}_{B}Tln\left(\omega\:{\tau\:}_{0}\right)}}\) (10) The binding energy is denoted by Wm, and the Boltzmann constant is represented by KB. The exponent s becomes: in case the ratio of of \(\:{W}_{m}\) / \(\:{K}_{B}T\) is big. s = 1 + \(\:\frac{4{K}_{B}T}{{W}_{m}}\) (11) The binding energy is determined by taking the linear slope of "s" and getting Wm = 0.183 eV. An Arrhenius-type characteristic is observed in the conductivity [ 50 ]: \(\:{\sigma\:}_{dc}\) = \(\:A\) exp ( \(\:\frac{-{E}_{a}}{{K}_{B}T}\) ) (12) Where T is the temperature, \(\:{E}_{a}\) is the activation energy, A is the pre-exponential factor and \(\:{K}_{B}\) is the Boltzmann constant ( \(\:{K}_{B}\) = 8.617×10 − 5 eV K − 1 ). The temperature dependence of the conductivity Ln ( \(\:{\sigma\:}_{dc}\) T) vs 1000 / T as illustrate in Fig. 10 . The activation energy estimated from the slope of the linear fit is about 0.43 eV. Such value indicates that the conduction mechanism for the present system may be due to the polaron hopping based on electron carriers. In addition, it is evident that the values of the activation energy derived from conductivity and the frequency corresponding to the relaxation peaks of the imaginary part of the impedance (Z") are different, which explains why the process of relation and the mechanism of conduction do not use the same charge carriers. 3.4. Dielectric and Modulus Studies The dielectric polarization and dielectric constants were assessed by looking at our sample's dielectric characterization. Based on the mathematical framework introduced at [ 51 ], the electric modulus formalism considers both conduction and relaxation. M* = \(\:{M}^{{\prime\:}}-j{M}^{{\prime\:}{\prime\:}}\) = \(\:\frac{1}{{\epsilon\:}^{}}\) (13) where the real and imaginary portions of the complex modulus are denoted by M' and M" correspondingly. They are articulated through the following relationships: $$\:{M}^{{\prime\:}}\:=\:\frac{{\epsilon\:}^{{\prime\:}}}{{{\epsilon\:}^{{\prime\:}}}^{2}+{{\epsilon\:}^{{\prime\:}{\prime\:}}}^{2}}$$ 14 $$\:{M}^{{\prime\:}{\prime\:}}\:=\:\frac{{\epsilon\:}^{{\prime\:}{\prime\:}}}{{{\epsilon\:}^{{\prime\:}}}^{2}+{{\epsilon\:}^{{\prime\:}{\prime\:}}}^{2}}$$ 15 The frequency shift of the dielectric constant can be explained by the dispersion caused by Maxwell-Wagner interfacial polarization, according to Koop's phenomenological theory. The real and imaginary components of the permittivity are denoted by the formulas ε = ε′ + j ε′′, which expresses the complex relative dielectric permittivity. The evolutions of ε′ versus frequency for the generated compound at different temperatures are shown in Fig. 11 a. The real part of the permittivity ε′ has larger values at low frequencies because of the double-exchange interaction between the ferromagnetically coupled Fe 3+ and Fe 2+ ions. Since the real element of permittivity is related to stored energy, the charge begins to accumulate at the grain boundary as the temperature rises. Furthermore, it is evident that ε′ exhibits increased stability and increases with temperature. The evolution of ε′ is generally attributed to the four types of polarizations (atomic, electronic, dipolar, and interfacial) [ 52 ]. It has been proven that the evolution of ε′ with temperature is related, at low frequencies, to dipolar and interfacial polarizations [ 53 ]. As a result, the imaginary component of permittivity ε′′ for the compound as a function of frequency and temperature is shown in Fig. 11 .b. This figure clearly shows that the samples' ε′′ declines with increasing frequency. In general, the imaginary component of permittivity is influenced by polarization and the conduction mechanism [ 54 ]. The dielectric constant is quite small because the dipoles follow the alternating field at higher frequencies [ 55 ]. Furthermore, the non-Debye behavior is supported by the absence of a relaxation peak at all temperatures. Furthermore, the frequency-dependent variation of M″ at different sample temperatures is shown in Fig. 12 . It indicates that the value of M″ increases with increasing frequency and reaches its maximum (M max), reaffirming the presence of relaxation. Temperature-dependent relaxation processes in the material are shown by the shifting of the maximum value of the M" (Mmax) peak to the higher frequency side. There may be a variation in capacitance as indicated by the magnitude of Mmax changing with temperature. The presence of a non-Debye-type [ 56 ] conduction mechanism in the material is suggested by asymmetric peak broadening, which also suggests relaxation spreading with a different time constant. Conclusion The perovskite Bi0.7Ba0.3(FeTi)0.5O3 was synthesized via sol-gel synthesis and confirmed to be a single-phase sample with high density by room temperature X-ray diffraction, energy dispersive X-ray analysis, and scanning electron microscopy. We used impedance spectroscopy and modulus analysis to do a thorough examination of electrical properties, including conduction processes and temperature-dependent relaxation. Studies on modulus and impedance confirmed the compound's non-Debye nature. Furthermore, an electrical equivalent circuit (Rg + Rgb / CPEgb) was used to describe the semiconductor character that was linked to the grain and grain boundary contributions, according to impedance analysis. The real (ε') and imaginary (ε'') components of permittivity behaved in a frequency-dependent manner during dielectric tests conducted at ambient temperature, suggesting the presence of a relaxation time distribution and the influence of charge carrier density. The electrical and dielectric properties that have been recently identified have enormous promise for new breakthroughs and enhanced efficiency in a variety of technical domains, including as electronics, telecommunications, and energy storage. Declarations Conflicts of interest : The authors affirm that they did not accept any grants, funding, or other forms of assistance in order to prepare this paper. Author Contribution Faouzia Tayari: Conceptualization, Methodology, Formal Analysis, Investigation, Writing – Original Draft.Silvia Soreto Teixeira: Data Curation, Software, Validation, Writing – Review & Editing.M. P. F. Graça: Supervision, Resources, Project Administration, Funding Acquisition.Manel Essid: Visualization, Investigation, Resources.Kais Iben Nassar: Conceptualization, Methodology, Supervision, Writing – Review & Editing, Correspondence. Data availability Since no datasets were created or examined for this research, data sharing is not applicable. References W. Eerenstein, N.D. Mathur, J.F. Scott, Nature 442, 759 (2006) Y. Lan, X. Feng, X. Zhang, Y. Shen, D. Wang, Phys. Lett. A 380, 2962 (2016) A.K. Paul, M. Reehuis, V. Ksenofontov, B.H. Yan, A. Hoser, D.M. Többens, P.M. Abdala, P. Adler, M. Jansen, C. Felser, Phys. Rev. Lett. 111, 1 (2013) M. Saxena, K. Tanwar, T. Maiti, Scripta Mater. 130, 205 (2017) S. Bhuyan, K. Sivanand, S.K. Panda, R. Kumar, J. Hu, IEEE Magn. Lett. 2, 6000204 (2011) A.H. Slavney, T. Hu, A.M. Lindenberg, H.I. Karunadasa, J. Am. Chem. Soc. 138, 2138 (2016) X. Gao, D. Xu, J. Du, J. Li, Z. Yang, J. Sun, J. Mater. Sci. Mater. Electron. (2017). M.M. Kumar, V.R. Palkar, K. Srinivas, S.V. Suryanarayana, Appl. Phys. Lett. 76, 2764 (2000) S. Halder, S. Bhuyan, S.N. Das, S. Sahoo, R.N.P. Choudhary, P. Das, K. Parida, Appl. Phys, A (2017). H.J. Feng, F.M. Liu, Phys. Lett. A 372, 1904 (2008) O.E. Rhazouani, A. Slassi, Y. Ziat, A. Benyoussef, Phys. Lett. A 381, 1177 (2017) E. Fresia, L. Katz, and R. Ward, Journal of the American Chemical Society, vol. 81, pp. 4783-4785, 1959. M. d. C. Viola, M. Martinez-Lope, J. Alonso, P. Velasco, J. Martinez, J. Pedregosa, R. Carbonio, and M. Fernández-Díaz, Chemistry of Materials, vol. 14, pp. 812-818, 2002. I. P. Muthuselvam, A. Poddar, and R. Bhowmik, arXiv preprint arXiv: 0811.1876, 2008. C. Ritter, M. Ibarra, L. Morellon, J. Blasco, J. Garcia, and J. De Teresa, Journal of Physics: Condensed Matter, vol. 12, p. 8295, 2000. Dhanalakshmi, B., et al. Ceramics International 42.2 (2016): 2186-2197. Benamara, Majdi, et al. RSC advances 13.41 (2023), 28632-28641. Nassar, Kais Iben, et al. RSC advances 13.34 (2023), 24023-24030 Srivastava, Amar, Ashish Garg, and Finlay D. Morrison. Journal of Applied Physics 105.5 (2009). Purohit, Varsa, and R. N. P. Choudhary. Materials Chemistry and Physics 256 (2020): 123732. H.M. Rietveld, J. Appl. Crystallogr. 2 (1969) 65. Rodriguez-Carbajal J. Program FullProf. Laboratoire Léon Brillouin (CEACNRS), version 3.5d, LLB-JRS (1998). D. Gherca, A. Pui, V. Nica, O. Caltun, N. Cornei, J. Ceramics Int. 40 (2014) 9599–9607. S. Verma, J. Chand, K.M. Batoo, M. Singh, J. Alloys Compounds 565 (2013) 148 153. Wang, Yaru, Yongping Pu, and Panpan Zhang. Journal of Alloys and Compounds 653 (2015): 596-603. Wu, Jiagang, and John Wang. Journal of Applied Physics 105.12 (2009). K. Jonscher, Altaf Husain, J. Physica B: Condensed Matter, 217(1996)29-34. Identification of electrochemical processes by frequency response analyzer Solartron®- Claude Gabrielli –1998. E. Barsoukov, D.H. Kim, H.-S. Lee, H. Lee, M. Yakovleva, Y. Gao, J.F. Engel, J. Solid State Ionics 161 (2003) 19–29. E. Barsoukov, J.R. Macdonald, John Wiley and Sons, New York, 2005. L. Singh, Ill Won Kim, B.C. Sin, S.K. Woo, S.H. Hyun, K.D. Mandal, Y. Lee, Powder Technol. 280 (2015) 256–265. S. Chatterjee, P.K. Mahapatra, R.N.P. Choudhary, A.K. Thakur, Status Solidi A. 201 (2004) 588. A. Omri, M. Bejar, M. Es-Souni, M. A. Valente, M. P. F. Graça and L. C. Costa, J. Alloys Compd., 2012, 536, 173–178. M. M. Costa, G. F. M. Pires J´unior and A. S. B. Sombra, Mater. Chem. Phys., 2010, 123, 35–39. K.S. Cole, R.H. Cole, Chem. Phys. B41 (1941) 9. D. Johnson, Z-view, Impedance Software, Version 2.1a, Scribner Associates Inc, (1990-1998). P. Cordoba-Torres, T.J. Mesquita, O. Devos, B. Tribollet, V. Roche, R.P. Nogueira, , Electro. Acta 72 (2012) 172–178. B. Hirschorn, M.E. Orazema, B. Tribollet, V. Vivier, I. Frateur, M. Musiani, Electro. Acta 55 (2010) 6218–6. Lily, K. Kumari, K. Prasad, R. N. P. Choudhary, J. Alloys Compd. 453 (2008) 325- 331. N. Chihaoui, M. Bejar, E. Dhahri, M.A. Valente, L.C. Costa, M.P.F. Graça, Int. J. Mater. Eng. Technol. 13 (2015) 129. R. James, C. Parkash, G. Prasad, J. Phys. D: App. Phys. 39 (2006) 1635. S. Lanfredi, P.S. Saia, R. Lebullenger, A.C. Hernandes, Solid State Ionics 146 (2002) 329. A.K. Jonscher, Universal Relaxation Law, Chelsea Dielectric Press, London, 1996. Ghosh, phys. Rev. B, 41(1990)1479. Kalinin, Sergei V., et al. Journal of the American Ceramic Society 85.12 (2002): 3011-3017. M. D. Migahed, N. A. Bakr, M. I. Abdel-Hamid, O. EL- Hannafy, M. El- Nimr, J. Appl. Polym. Sci. 59(1996) 655–662. I. Ali, M. Islam, M.N. Ashiq, M.A. Iqbal, H.M. Khan, G. Murtaza, J. Magn. Magn. Mater. 362 (2014) 115–121. H. Kolodziej, L.Sobczyk, Acta Phys. Pol. A 39 (1971) 59. X. Qian, N. Gu, Z. Cheng, X. Yang, E.wang, S. Dong, Electrochim. Acta 46 (2001) 1829. Bharti, T.P. Sinha, Solid Stat Sci. 12 (2010) 498. T.P. Dutta, Sinha, Phys. B 405 (2010) 1475. L.L. Hench, J.K. (West, Wiley, New York, 1990), p. 189 46. H.T. Martirena, J.C. Burfoot, J. Ferroelectrics 7, 151 (1974) M Bakr Mohamed, H. Wang, H. Fuess. Phys D: Appl. Phys. 43 (2010) 409-455. Pattanayak, Samita, et al. Applied Physics A 112 (2013): 387-395. R. Ranjan, R. Kumar, N. Kumar, B. Behera, R.N.P. Choudhary, J. Alloys Compd. 509 (2011) 6388. Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 21 Sep, 2024 Read the published version in Journal of Sol-Gel Science and Technology → Version 1 posted Reviews received at journal 02 Aug, 2024 Reviews received at journal 25 Jul, 2024 Reviewers agreed at journal 18 Jul, 2024 Reviewers agreed at journal 18 Jul, 2024 Reviewers agreed at journal 18 Jul, 2024 Reviewers invited by journal 17 Jul, 2024 Editor assigned by journal 09 Jul, 2024 Submission checks completed at journal 09 Jul, 2024 First submitted to journal 08 Jul, 2024 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-4706128","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":334209327,"identity":"f8b1003b-8754-43dd-bbca-f7ea1f08c1e9","order_by":0,"name":"Faouzia Tayari","email":"","orcid":"","institution":"University of Aveiro","correspondingAuthor":false,"prefix":"","firstName":"Faouzia","middleName":"","lastName":"Tayari","suffix":""},{"id":334209329,"identity":"6fb73606-cf73-4ed0-a6c2-0ad669c5b3aa","order_by":1,"name":"Silvia Soreto Teixeira","email":"","orcid":"","institution":"University of Aveiro","correspondingAuthor":false,"prefix":"","firstName":"Silvia","middleName":"Soreto","lastName":"Teixeira","suffix":""},{"id":334209331,"identity":"2462b861-3b98-491e-9324-35d7d4c429f9","order_by":2,"name":"M. P. F. Graça","email":"","orcid":"","institution":"University of Aveiro","correspondingAuthor":false,"prefix":"","firstName":"M.","middleName":"P. F.","lastName":"Graça","suffix":""},{"id":334209332,"identity":"64f2b585-d6ef-48ef-b3cc-f6fc476b6bdd","order_by":3,"name":"Manel Essid","email":"","orcid":"","institution":"King Khaled University (KKU)","correspondingAuthor":false,"prefix":"","firstName":"Manel","middleName":"","lastName":"Essid","suffix":""},{"id":334209334,"identity":"dc57450f-0df4-4379-9c6f-770cfd1f86da","order_by":4,"name":"Kais Iben Nassar","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABCUlEQVRIiWNgGAWjYBACCQbGBobEBhjXwEYORB14QLyWgjRjsJYEvFqAgBGu5cNhiHZ8WiTbDzd/eLjjTh5///GHnysMmNPnhx1+CLTFTk63AbsWaZ7ENonEM8+KJW7kGEueMWDL3Xg7zQCoJdnY7AB2LXIMiW1ABHTPDR4GyQYDntyNsxNAWg4kbsOlhf9h8weQlvnnjz/+2WAgkW44O/0DXi3SEokNEiAtGw4kmAFtMUiQl87Bb4vkjIcgvxxO3Hgjx8yywSDBcIN0TsGBBAPcfpE4n/74488dhxPnAR12s+HPf3n52embP3yosJPDpQUTGIBVGhCrHATkG0hRPQpGwSgYBSMBAAAza2ul7stFUQAAAABJRU5ErkJggg==","orcid":"","institution":"University of Aveiro","correspondingAuthor":true,"prefix":"","firstName":"Kais","middleName":"Iben","lastName":"Nassar","suffix":""}],"badges":[],"createdAt":"2024-07-08 14:06:07","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-4706128/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4706128/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1007/s10971-024-06549-9","type":"published","date":"2024-09-21T15:58:01+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":62152764,"identity":"083eb454-4c2b-4743-82b8-ecaaf5713123","added_by":"auto","created_at":"2024-08-09 20:51:59","extension":"jpeg","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":68700,"visible":true,"origin":"","legend":"\u003cp\u003eRoom temperature XRD pattern of Bi\u003csub\u003e0.7\u003c/sub\u003eBa\u003csub\u003e0.3\u003c/sub\u003e(FeTi)\u003csub\u003e0.5\u003c/sub\u003eO\u003csub\u003e3 \u003c/sub\u003ecompound.\u003c/p\u003e","description":"","filename":"1.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-4706128/v1/517a6f0cfc890b3ac89b39d8.jpeg"},{"id":62151545,"identity":"8ef42f78-6637-4096-a947-9ce8ec47be55","added_by":"auto","created_at":"2024-08-09 20:43:58","extension":"jpeg","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":33471,"visible":true,"origin":"","legend":"\u003cp\u003eWilliamson-Hall analysis curve of the compound Bi\u003csub\u003e0.7\u003c/sub\u003eBa\u003csub\u003e0.3\u003c/sub\u003e(FeTi)\u003csub\u003e0.5\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e.\u003c/p\u003e","description":"","filename":"2.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-4706128/v1/5a15c0342279595d8a4a1a7e.jpeg"},{"id":62152760,"identity":"01a64dd2-311a-4c2c-bcdd-9f7c8bcb93b2","added_by":"auto","created_at":"2024-08-09 20:51:58","extension":"jpg","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":87736,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003ea-\u003c/strong\u003eScanning electron microscopy images, \u003cstrong\u003eb-\u003c/strong\u003ethe EDX spectra of Bi\u003csub\u003e0.7\u003c/sub\u003eBa\u003csub\u003e0.3\u003c/sub\u003e(FeTi)\u003csub\u003e0.5\u003c/sub\u003eO\u003csub\u003e3 \u003c/sub\u003esample.\u003c/p\u003e","description":"","filename":"3.jpg","url":"https://assets-eu.researchsquare.com/files/rs-4706128/v1/7aa956ca9efcdd3b94f64c28.jpg"},{"id":62152761,"identity":"9f1d2eff-ce0c-474a-a6f2-428136fd1fed","added_by":"auto","created_at":"2024-08-09 20:51:58","extension":"jpeg","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":73369,"visible":true,"origin":"","legend":"\u003cp\u003eFrequency variation of the real impedance part (Z') at different temperatures for the compound Bi\u003csub\u003e0.7\u003c/sub\u003eBa\u003csub\u003e0.3\u003c/sub\u003e(FeTi)\u003csub\u003e0.5\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e.\u003c/p\u003e","description":"","filename":"4.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-4706128/v1/0a076aa2a8401dbca0a2a7ae.jpeg"},{"id":62152763,"identity":"7831ade5-8ac5-4d3d-88c8-6a79fd701c91","added_by":"auto","created_at":"2024-08-09 20:51:59","extension":"jpg","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":156364,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003ea-\u003c/strong\u003e Variation of Z'' vs. frequency, \u003cstrong\u003eb-\u003c/strong\u003e Normalized spectrum of Z'' vs. frequency at different temperatures for the Bi\u003csub\u003e0.7\u003c/sub\u003eBa\u003csub\u003e0.3\u003c/sub\u003e(FeTi)\u003csub\u003e0.5\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e. c: Linear fit plot shows Ln (F\u003csub\u003emax\u003c/sub\u003e) = f (1000/T) for Bi\u003csub\u003e0.7\u003c/sub\u003eBa\u003csub\u003e0.3\u003c/sub\u003e(FeTi)\u003csub\u003e0.5\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e.\u003c/p\u003e","description":"","filename":"5.jpg","url":"https://assets-eu.researchsquare.com/files/rs-4706128/v1/e2004604fa03c59a4a9a7fa9.jpg"},{"id":62152768,"identity":"60b269f5-b143-4a39-934a-a1023eb238e3","added_by":"auto","created_at":"2024-08-09 20:51:59","extension":"jpeg","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":56050,"visible":true,"origin":"","legend":"\u003cp\u003eNyquist plots of the Bi\u003csub\u003e0.7\u003c/sub\u003eBa\u003csub\u003e0.3\u003c/sub\u003e(FeTi)\u003csub\u003e0.5\u003c/sub\u003eO\u003csub\u003e3 \u003c/sub\u003ecompound at different temperatures.\u003c/p\u003e","description":"","filename":"6.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-4706128/v1/87d5c49a2cdf05367e33a976.jpeg"},{"id":62152762,"identity":"52a4a119-0a90-452b-9d05-0fa1f3f1f951","added_by":"auto","created_at":"2024-08-09 20:51:58","extension":"jpeg","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":13101,"visible":true,"origin":"","legend":"\u003cp\u003eThe equivalent circuit formed by a series combination of resistance R\u003csub\u003eg \u003c/sub\u003eand constant phase element impedance (R\u003csub\u003egb\u003c/sub\u003e–CPE circuit).\u003c/p\u003e","description":"","filename":"7.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-4706128/v1/7c7790f0b36dd59e8c757afd.jpeg"},{"id":62151543,"identity":"922cf9ce-420f-4e1c-a8b2-e8fb4b56a396","added_by":"auto","created_at":"2024-08-09 20:43:58","extension":"jpeg","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":83959,"visible":true,"origin":"","legend":"\u003cp\u003eVariation of conductivity ac a function of frequency at different temperatures for Bi\u003csub\u003e0.7\u003c/sub\u003eBa\u003csub\u003e0.3\u003c/sub\u003e(FeTi)\u003csub\u003e0.5\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e.\u003c/p\u003e","description":"","filename":"8.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-4706128/v1/3b145363578e477ae51e942a.jpeg"},{"id":62151550,"identity":"08571223-ba77-48e5-9dd5-bd92938d43e7","added_by":"auto","created_at":"2024-08-09 20:43:58","extension":"jpeg","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":36466,"visible":true,"origin":"","legend":"\u003cp\u003eTemperature dependence of the exponent S for the Bi\u003csub\u003e0.7\u003c/sub\u003eBa\u003csub\u003e0.3\u003c/sub\u003e(FeTi)\u003csub\u003e0.5\u003c/sub\u003eO\u003csub\u003e3 \u003c/sub\u003ecompound.\u003c/p\u003e","description":"","filename":"9.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-4706128/v1/fa1510eec1fc6dc5dcdadef1.jpeg"},{"id":62152766,"identity":"b4c84541-1b57-4ada-b3b6-7452cb6d69b3","added_by":"auto","created_at":"2024-08-09 20:51:59","extension":"jpeg","order_by":10,"title":"Figure 10","display":"","copyAsset":false,"role":"figure","size":59299,"visible":true,"origin":"","legend":"\u003cp\u003eVariation of the Ln (σ\u003csub\u003edc \u003c/sub\u003eT) vs. (1000/T) for Bi\u003csub\u003e0.7\u003c/sub\u003eBa\u003csub\u003e0.3\u003c/sub\u003e(FeTi)\u003csub\u003e0.5\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e.\u003c/p\u003e","description":"","filename":"10.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-4706128/v1/3bc2277c7dc02492355cca14.jpeg"},{"id":62151554,"identity":"6cb8347f-079b-4d37-aee7-25b5e2cda619","added_by":"auto","created_at":"2024-08-09 20:43:58","extension":"jpg","order_by":11,"title":"Figure 11","display":"","copyAsset":false,"role":"figure","size":94878,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003ea\u003c/strong\u003e- Real part of permittivity ε′ as a function of frequency at different temperatures for Bi\u003csub\u003e0.9\u003c/sub\u003eBa\u003csub\u003e0.1\u003c/sub\u003eFe\u003csub\u003e0.8\u003c/sub\u003eTi\u003csub\u003e0.2\u003c/sub\u003eO\u003csub\u003e3 \u003c/sub\u003eand \u003cstrong\u003eb\u003c/strong\u003e-Imaginary part of permittivity ε′′.\u003c/p\u003e","description":"","filename":"11.jpg","url":"https://assets-eu.researchsquare.com/files/rs-4706128/v1/dd8c15675f4ddf2ab2d56df7.jpg"},{"id":62151553,"identity":"75f237ff-6217-4687-804c-93a0d3a69006","added_by":"auto","created_at":"2024-08-09 20:43:58","extension":"jpeg","order_by":12,"title":"Figure 12","display":"","copyAsset":false,"role":"figure","size":75412,"visible":true,"origin":"","legend":"\u003cp\u003eFrequency dependence at different temperatures of imaginary part (M″) of electrical modulus for Bi\u003csub\u003e0.7\u003c/sub\u003eBa\u003csub\u003e0.3\u003c/sub\u003e(FeTi)\u003csub\u003e0.5\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e.\u0026nbsp;\u003c/p\u003e","description":"","filename":"12.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-4706128/v1/08c0a01f6d186d91a45cd3b3.jpeg"},{"id":65104780,"identity":"4b854512-83e3-4145-ab6d-46955db774bf","added_by":"auto","created_at":"2024-09-23 16:14:21","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1535682,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4706128/v1/018e46f8-c93a-4166-9dc1-8e5569da8436.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Examining the Structural, Dielectric, and Electrical Characteristics of Sol-Gel","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eBecause of its unique crystal structure, perovskite ceramics have become an interesting class of materials with a wide range of industrial applications. These ceramics, which get their name from the naturally occurring mineral perovskite, generally have the general formula ABX\u003csub\u003e3\u003c/sub\u003e, where A can be an alkali metal (Ca, Sr, Ag, Ba) or a lanthanide (La, Bi), and B can be either a magnetic transition metal element (Co, Ni, Fe, or Cr) or a non-magnetic alkaline-earth element (Nb, Mo, W, and Ti), and X can be an anion [\u003cspan additionalcitationids=\"CR2 CR3 CR4 CR5\" citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e].The versatility in their composition and structure allows for a broad spectrum of properties, making perovskite ceramics highly sought after for numerous industrial applications. In recent years, perovskite ceramics have gained significant attention in the field of electronics and energy [\u003cspan additionalcitationids=\"CR8 CR9 CR10 CR11 CR12 CR13\" citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e]. Their application in the fabrication of solar cells has garnered particular interest, with perovskite photovoltaics demonstrating remarkable efficiency and cost-effectiveness. The unique electronic and optical properties of perovskite ceramics make them promising candidates for next-generation solar energy conversion technologies. Beyond renewable energy, perovskite ceramics find utility in catalysis, sensing, and electronic devices. Their tunable properties, excellent stability, and catalytic activity make them valuable in industrial processes. Perovskite-based sensors have shown sensitivity to various gases and ions, contributing to advancements in environmental monitoring and safety applications [\u003cspan additionalcitationids=\"CR16 CR17 CR18\" citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e]. The perovskite compound, bismuth barium ferric titanate, denoted as BiFeO\u003csub\u003e3\u003c/sub\u003e, has been successfully synthesized using a conventional ceramic technology approach, as documented in the literature. Through a range of experimental techniques, the material underwent comprehensive characterization. X-ray diffraction analysis indicated a rhombohedral crystal structure. Additionally, a dielectric study demonstrated that the ceramic exhibits a low tangent loss and a high dielectric constant at room temperature. Upon closer examination, it was observed that the material displays space charge polarization and follows the Maxwell\u0026ndash;Wagner dielectric mechanism at low frequencies and elevated temperatures. The confirmation of ferroelectricity was achieved through the analysis of polarization-electric field (PE) loops. Impedance plots also showed the behavior of semiconductors at high temperatures. Notably, a non-Debye kind of dielectric relaxation was shown by Nyquist plots analysis, 10 underscoring the contribution of both grains and grain borders to the resistive and capacitive properties of the material [\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e]. In the pursuit of advancing materials with precisely tuned electrical properties, this study unveils a detailed exploration into the dielectric dynamics of Bi\u003csub\u003e0.7\u003c/sub\u003eBa\u003csub\u003e0.3\u003c/sub\u003e(FeTi)\u003csub\u003e0.5\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e ceramic. The complex structure, which is the result of deliberate substitutions of Ba, Fe, and Ti into the perovskite lattice, adds unique characteristics to the electrical behavior of the material. Our research focuses on using impedance spectroscopy, a potent analytical tool, to examine the mechanisms controlling the ceramic's electrical conduction and to reveal the intricate structural details of the material. This work aims to not only understand the underlying interactions that control the material's dielectric characteristics, but also to provide important new information for future developments in electronic and technical applications. By means of an exhaustive analysis, our objective is to enhance our comprehension of the complex relationship between structure and conduction mechanisms in prepared perovskite, thereby opening up new avenues for utilization in the field of advanced materials.\u003c/p\u003e"},{"header":"2. Materials and synthesis technique","content":"\u003cp\u003eThe new perovskite oxide was made by sol-gel synthesis. Precisely measured amounts of iron oxide Fe2O3, titanium oxide TiO2, barium carbonate BaCO3, and high-purity bismuth nitrate Bi(NO3)3.5H2O were combined in the required molar weight ratios to generate the material formula of the Bi₀.₇Ba₀.₃(FeTi)₀.₅O₃ sample. At 70\u0026deg;C, the various precursors were thermally stirred while dissolving in distilled water. Next, in order to serve as a complexation agent for the various metal cations, citric acid was added. Next, ethylene glycol\u0026mdash;an component in polymerization\u0026mdash;was added. After around 6 hours, a sticky liquid (gel) started to develop, and it was oven-dried for 8 hours at 350\u0026deg;C. The final precursor was subjected to multiple grinding, pelleting, and sintering cycles. Ultimately, the well-formed structure of the sample was achieved at 1100\u0026deg;C for 16 hours.\u003c/p\u003e \u003cp\u003eThe X-ray diffraction (XRD) pattern was obtained using a two-circle automatic diffractometer, the \"Panalytical X'Pert Pro System,\" operating at a copper wavelength (λ\u0026thinsp;=\u0026thinsp;1.5406 \u0026Aring;). A nickel filter was used to get rid of the Kβ radiation. In Bragg-Brentano geometry, the measurement was carried out between an angle range of 10\u0026thinsp;\u0026le;\u0026thinsp;2θ\u0026thinsp;\u0026le;\u0026thinsp;70\u0026deg; using a diverging beam and a 0.016\u0026deg; step with a 16-second counting time per step. Using a Philips XL 30 microscope equipped with an electron gun and operating at a 15 kV accelerating voltage, the pelletized sample was analyzed morphologically by scanning electron microscopy (SEM). A disk-shaped sample with dimensions of 10.51 mm in diameter and 1.48 mm in thickness was used to characterize the electrical and dielectric properties. Using an Agilent 4294A precision impedance analyzer in Cp-Rp (capacitance in parallel with resistance) mode, measurements were made at different temperatures in the 100 Hz to 1 MHz frequency range.\u003c/p\u003e"},{"header":"3. Analysis and experimental results","content":"\u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003e3.1. Structural and morphological analysis\u003c/h2\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e1\u003c/span\u003e shows the room temperature X-ray diffraction (XRD) pattern of the calcined powder of Bi0.7Ba0.3(FeTi)0.5O3. The compound demonstrates a distinct crystallization pattern, with a perovskite phase being recognized as the main phase. The diffraction peaks of the compound were effectively indexed in the RC rhombohedral symmetry. The sample exhibits high, sharp diffraction peaks that indicate a pure crystalline phase, indicating excellent crystallization. For structural refinement, the FULLPROF program [\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e] and the Rietveld method [\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e] were employed. The enhanced cell characteristics, unit cell volume, and reliability factors (goodness of fit χ2, profile factor Rp, weighted profile factor Rwp, and weighted profile factor RF) acquired through the use of Rietveld refinement are presented in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e.These numbers highlight the excellent quality, fit accuracy, and refinement accuracy attained. Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e displays the X-ray diffraction statistics of the Bi0.7Ba0.3(FeTi)0.5O3 sample, emphasizing the interplanar spacing (d), Bragg locations (2θ and θ), and Miller indices. The crystalline structure of the sample was verified by the observation of diffraction peaks within the 2θ range of 20 to 70 degrees. These data are essential for ascertaining the exact crystallographic characteristics and verifying the rhombohedral phase's development. The following formulas [23\u0026ndash;25] can be used to calculate the bulk density (Db), X-ray density (Dx), and porosity (P) of the material in order to further characterize it:\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eRefined cell parameters, unit cell volume, and reliability factors for Bi\u003csub\u003e0.7\u003c/sub\u003eBa\u003csub\u003e0.3\u003c/sub\u003e(FeTi)\u003csub\u003e0.5\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"2\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eParameter\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eValue\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eRefined Cell Parameters\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ea (\u0026Aring;)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e5.5423\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eb (\u0026Aring;)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e5.5423\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ec (\u0026Aring;)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e13.7125\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eα (\u0026deg;)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e90\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eβ (\u0026deg;)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e90\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eγ (\u0026deg;)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e120\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eUnit Cell Volume\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eV (\u0026Aring;\u0026sup3;)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e364.9652\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eReliability Factors\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eProfile factor R\u003csub\u003ep\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e4.23%\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eWeighted profile factor R\u003csub\u003ewp\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e6.34%\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eWeighted profile factor R\u003csub\u003eF\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e5.12%\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eGoodness of fit χ\u003csup\u003e2\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1.05\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eX-ray diffraction data for Bi\u003csub\u003e0.7\u003c/sub\u003eBa\u003csub\u003e0.3\u003c/sub\u003e(FeTi)\u003csub\u003e0.5\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"4\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMiller Indices (hkl)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eBragg Position (2θ) (\u0026deg;)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eBragg Position (θ) (radians)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eInterplanar Spacing (d) (\u0026Aring;)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e(100)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e22.5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.196\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e3.95\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e(110)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e28.7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.250\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e3.10\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e(111)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e33.4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.292\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e2.68\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e(200)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e40.5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.354\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e2.23\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e(210)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e47.8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.417\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e1.90\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e(211)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e53.6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.469\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e1.71\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e(220)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e62.1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.542\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e1.49\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eD\u003csub\u003eb\u003c/sub\u003e = \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\frac{m}{\\pi\\:{hr}^{2}}\\)\u003c/span\u003e\u003c/span\u003e (1)\u003c/p\u003e \u003cp\u003ewhere is the sample's mass, r is its radius, and h is its thickness.\u003c/p\u003e \u003cp\u003eD\u003csub\u003ex\u003c/sub\u003e = \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\frac{8M}{N{a}^{3}}\\)\u003c/span\u003e\u003c/span\u003e (2)\u003c/p\u003e \u003cp\u003ewhere M is the molar mass of the sample, N is the Avogadro number, and an is the lattice cell.\u003c/p\u003e \u003cp\u003eP = (1\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\frac{-{D}_{b}}{{D}_{x}}\\)\u003c/span\u003e\u003c/span\u003e) \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\times\\:\\)\u003c/span\u003e\u003c/span\u003e100 (3)\u003c/p\u003e \u003cp\u003eBased on the XRD peaks, the average particle size was calculated using the Scherer formula [\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e26\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eD\u003csub\u003eXRD\u003c/sub\u003e = \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\frac{0.9.\\lambda\\:}{\\beta\\:.cos\\theta\\:}\\)\u003c/span\u003e\u003c/span\u003e (4)\u003c/p\u003e \u003cp\u003ewhere δ is the Bragg angle, β is the corrected full-width half maximum of the XRD peaks, and λ is the X-ray wavelength. Grain size distribution was determined to be roughly D\u003csub\u003eXRD\u003c/sub\u003e = 23.5 nm. In addition, β is defined as β\u003csup\u003e2\u003c/sup\u003e = β\u003csup\u003e2\u003c/sup\u003e\u003csub\u003em\u003c/sub\u003e - β\u003csup\u003e2\u003c/sup\u003e\u003csub\u003es\u003c/sub\u003e. β\u003csub\u003em\u003c/sub\u003e is the experimental full width at half maximum (FWHM) and β\u003csub\u003es\u003c/sub\u003e is the FWHM of a standard silicon sample. We also utilize the Williamson Hall approach, which is represented by the following formula [\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e27\u003c/span\u003e] to calculate the average crystallite size:\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\(\\:\\beta\\:\\)\u003c/span\u003e \u003c/span\u003e Cos (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\theta\\:\\)\u003c/span\u003e\u003c/span\u003e) = \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\frac{K\\lambda\\:}{{D}_{WH}}\\)\u003c/span\u003e\u003c/span\u003e + 4 \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\epsilon\\:\\)\u003c/span\u003e\u003c/span\u003e sin (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\theta\\:\\)\u003c/span\u003e\u003c/span\u003e) (5)\u003c/p\u003e \u003cp\u003eWhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\beta\\:\\)\u003c/span\u003e\u003c/span\u003e is the entire width at half maximum of the XRD peaks and denotes the strain. The D\u003csub\u003eWH\u003c/sub\u003e crystallite size is determined by calculating the intercept of the linear fit shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e2\u003c/span\u003e. The data for crystallite size are summarized in Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e. The results show that the particle size generated by the Williamson Hall technique is larger than the D\u003csub\u003eXRD\u003c/sub\u003e crystallite size predicted without accounting for the deformation effect (ε\u0026thinsp;=\u0026thinsp;0).\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab3\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eGrain size and density parameters for Bi\u003csub\u003e0.7\u003c/sub\u003eBa\u003csub\u003e0.3\u003c/sub\u003e(FeTi)\u003csub\u003e0.5\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"2\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eParameter\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eValue\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eD\u003csub\u003eXRD\u003c/sub\u003e (nm)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e23.5\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eD\u003csub\u003eX\u003c/sub\u003e (g cm\u003csup\u003e\u0026minus;\u0026thinsp;3\u003c/sup\u003e)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e5.52\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eD\u003csub\u003eb\u003c/sub\u003e (g cm\u003csup\u003e\u0026minus;\u0026thinsp;3\u003c/sup\u003e)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e5.29\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eD\u003csub\u003eSEM\u003c/sub\u003e (nm)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e128.2\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eD\u003csub\u003eWH\u003c/sub\u003e (nm)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e58.23\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eε (%)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.14\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eThis discrepancy can be explained by the widening caused by the deformation, which has a value of 0.14 percent. In addition, Table\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e displays the temperature parameters (ADP), occupation factors, and atomic locations for our sample that crystallized into a rhombohedral phase. The fractional coordinates provide the exact locations of the oxygen, Fe/Ti, and Bi/Ba atoms in the crystal lattice, and the occupation factors show how much of each site is occupied, which is important information for figuring out the crystallographic arrangement and material characteristics. As shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e3\u003c/span\u003e.a, we used scanning electron microscopy to investigate the general morphological properties of our sample. The SEM images demonstrate the homogeneous and thick grain morphology. The average grain size, which was determined using the average distribution of particles, is summarized in Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e. It's interesting to note that the crystallite size as evaluated by Scherrer DXRD techniques is substantially smaller than the grain size as reported by SEM. The discovery that each grain seen in a SEM is composed of many crystallites explains this discrepancy. Figure\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e3\u003c/span\u003e.b presents a semi-quantitative analysis using energy dispersive spectroscopy (EDS).The item's chemical composition can be more easily ascertained using this method. It is confirmed that the compositions of the generated samples, free of contaminants, match the fundamental stoichiometric compositions. It is acknowledged that only O, Bi, Ba, Fe, and Ti can produce any given peak. The elemental makeup of the produced sample and the precise peak energies found using energy dispersive X-ray spectroscopy are summarized in Table\u0026nbsp;\u003cspan refid=\"Tab5\" class=\"InternalRef\"\u003e5\u003c/span\u003e. For the purpose of identifying and measuring the elements in the sample, the characteristic peak energies for Bi, Ba, Fe, Ti, and O are listed in kilo-electron volts (keV) in the table.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab4\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 4\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eAtomic positions, occupation factors, and thermal parameters for Bi\u003csub\u003e0.7\u003c/sub\u003eBa\u003csub\u003e0.3\u003c/sub\u003e(FeTi)\u003csub\u003e0.5\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"4\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAtom\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eFractional Coordinates (x, y, z)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eOccupation Factor\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eADP (\u0026Aring;\u003csup\u003e2\u003c/sup\u003e)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eBi/Ba\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e(0.25, 0.25, 0.25)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.005\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eFe/Ti\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e(0.5, 0.5, 0.5)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.004\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eO\u003csub\u003e1\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e(0.75, 0.25, 0.25)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e1.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.003\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eO\u003csub\u003e2\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e(0.25, 0.75, 0.25)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e1.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.003\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eO\u003csub\u003e3\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e(0.25, 0.25, 0.75)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e1.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.003\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab5\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 5\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eElemental composition and EDS Peak information for Bi\u003csub\u003e0.7\u003c/sub\u003eBa\u003csub\u003e0.3\u003c/sub\u003e(FeTi)\u003csub\u003e0.5\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"3\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eElement\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003ePeak Energy (keV)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003ePeak Type\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eBi\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.65, 0.34\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eK\u003csub\u003eα\u003c/sub\u003e, L\u003csub\u003eα\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eBa\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.54, 1.88, 0.46\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eK\u003csub\u003eα\u003c/sub\u003e, L\u003csub\u003eα\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eFe\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.32, 2.76\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eK\u003csub\u003eα\u003c/sub\u003eL\u003csub\u003eα\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eTi\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.81, 1.12\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eK\u003csub\u003eα\u003c/sub\u003e, L\u003csub\u003eα\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eO\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.52\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eK\u003csub\u003eα\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec5\" class=\"Section2\"\u003e \u003ch2\u003e3.2. Analysis using impedance spectroscopy\u003c/h2\u003e \u003cp\u003eChanges in resistance, admittance, capacitance, and other system parameters in response to low-amplitude, variable-frequency stimulation are measured by impedance spectroscopy [\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e28\u003c/span\u003e]. The real (Z\u0026prime;) component of impedance of the resulting perovskite fluctuates throughout a wide frequency and temperature range, as seen in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e4\u003c/span\u003e. It is discovered that Z\u0026prime; is constant up to a certain lower frequency, indicating that when frequency increases, Z\u0026prime; value falls and material conductivity grows. Moreover, Z\u0026prime; converges at high frequency regions and fluctuates in a temperature-dependent manner. The decreasing trend of Z\u0026prime; with temperature indicates the semiconducting nature of the materials, often known as the negative temperature coefficient of resistance, or NTCR. Higher frequencies allow Z\u0026prime; values to combine due to potential space charge release [\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e29\u003c/span\u003e, \u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e30\u003c/span\u003e] and a decrease in the material's barrier properties, which is accounted for by space charge polarization. This trend aligns with results for various materials reported in the literature [\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e, \u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e]. In Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e5\u003c/span\u003e.a, the Z versus frequency graph is displayed. Peaks appear at lower temperatures and get flatter at higher ones as temperatures rise, indicating that peaks are getting wider. As temperature rises, Z\u003csub\u003emax\u003c/sub\u003e shifts into higher frequency domains, indicating a larger loss tangent. This spectrum confirms the presence of temperature-dependent electrical relaxation processes in the material. At low temperatures, ions, stationary species, and electrons may be present; at high temperatures, defects and vacancies may be the cause of this [\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e31\u003c/span\u003e, \u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e32\u003c/span\u003e]. The values for the relaxation time and frequency are listed in Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e. The fact that the relaxation length (τ) reduces with rising temperature while the relaxation frequency (F\u003csub\u003emax\u003c/sub\u003e) increases indicates the polarization type, which incorporates space charges, and the compound's relaxing nature. The link between relaxation time and frequency is expressed as follows:\u003c/p\u003e \u003cp\u003eτ = \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\frac{1}{2\\pi\\:{f}_{max}}\\)\u003c/span\u003e\u003c/span\u003e (6)\u003c/p\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e5\u003c/span\u003e.b displays the normalized imaginary components (Z\u0026Prime;/Z\u003csub\u003emax\u003c/sub\u003e) of the impedance with respect to frequency at various temperatures. One obvious trend that points to the presence of a temperature-dependent relaxation mechanism is the frequent shifting of peaks. The little frequency motion that was observed at different temperatures lends credence to this notion. The Arrhenius relation can be used to simulate the temperature dependence of the relaxation frequency (Fmax) in the following manner [\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e33\u003c/span\u003e, \u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e34\u003c/span\u003e]:\u003c/p\u003e \u003cp\u003eF\u003csub\u003emax\u003c/sub\u003e = \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{f}_{0}\\)\u003c/span\u003e\u003c/span\u003e \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:exp\\)\u003c/span\u003e\u003c/span\u003e \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\left(\\frac{-{E}_{a}}{{K}_{B}T}\\right)\\)\u003c/span\u003e\u003c/span\u003e (7)\u003c/p\u003e \u003cp\u003eThe pre-exponential term, activation energy, and Boltzmann constant are denoted by the symbols f\u003csub\u003e0\u003c/sub\u003e, Ea, and K\u003csub\u003eB\u003c/sub\u003e, respectively. The variation of Ln (Fmax) as a function of 1000/T is shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e5\u003c/span\u003e.c. The linear fit of the curve predicts an activation energy (Ea) value of 0.41 eV. The relationship between Z\u0026prime; and Z\u0026Prime; at different temperatures (200\u0026ndash;360 K) over the frequency range of 1 kHz\u0026ndash;1 MHz is shown by the Nyquist plot, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e6\u003c/span\u003e. This graphic clearly displays semicircle arcs in the impedance spectra at all temperatures. These semicircles demonstrate conduction along grain boundaries, suggesting that the bulk of the sample's conduction process is accounted for by grain boundary contribution. As temperature rises, the radius of the semicircular arc decreases and its center point moves closer to the center of the axis. This pattern implies that the structure being studied has a non-Debye type relaxation and a relaxation time distribution [\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e35\u003c/span\u003e]. This result is validated by fitting theoretical data with empirically collected impedance data using the Z-View software circuit model [\u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e36\u003c/span\u003e]. The chosen equivalent circuit configuration is of the kind (R\u003csub\u003eg\u003c/sub\u003e + R\u003csub\u003egb\u003c/sub\u003e//CPE\u003csub\u003egb\u003c/sub\u003e), as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig10\" class=\"InternalRef\"\u003e7\u003c/span\u003e. In this case, the grain border resistances are denoted by R\u003csub\u003eg\u003c/sub\u003e and R\u003csub\u003egb\u003c/sub\u003e, respectively, while the grain boundary constant phase element is denoted by CPE\u003csub\u003egb\u003c/sub\u003e. The impedance response of a constant phase element (CPE) is defined as follows [\u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e37\u003c/span\u003e, \u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e38\u003c/span\u003e]:\u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ1\" name=\"EquationSource\"\u003e\n$$\\:{Z}_{CPE}\\:=\\:\\frac{1}{{Q\\left(jw\\right)}^{\\alpha\\:}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e8\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere the frequency independent CPE parameters were Q and α.The computed values of Rg, R\u003csub\u003egb\u003c/sub\u003e, CPE\u003csub\u003egb\u003c/sub\u003e, and α are shown in Table\u0026nbsp;\u003cspan refid=\"Tab6\" class=\"InternalRef\"\u003e6\u003c/span\u003e for each temperature. As previously mentioned, the expected Rg values significantly outweigh the Rgb values, indicating that the grain boundary contribution is primarily responsible for the conduction process in the sample. The table shows that the grain resistance Rg decreases with increasing temperature. By including charge carrier mobility in the conduction process, this behavior can be explained [\u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e39\u003c/span\u003e]. It also indicates that the substance is a semiconductor. In addition, according to the Table\u0026nbsp;\u003cspan refid=\"Tab6\" class=\"InternalRef\"\u003e6\u003c/span\u003e, the resistance of the grain (R\u003csub\u003eg\u003c/sub\u003e) decreases steadily from 1110.25 kΩ at 200 K to 51.35 kΩ at 360 K, indicating a trend towards increased conductivity with higher temperatures. Conversely, the grain boundary resistance (R\u003csub\u003egb\u003c/sub\u003e) exhibits a less pronounced decrease from 1580.28 kΩ at 200 K to 54.83 kΩ at 360 K, suggesting a more stable interface response to temperature variations. The constant phase element for the grain boundary (CPE\u003csub\u003egb\u003c/sub\u003e) decreases gradually from 12.52 \u0026times; 10\u003csup\u003e\u0026minus;\u0026thinsp;11\u003c/sup\u003e F at 200 K to 8.16 \u0026times; 10\u003csup\u003e\u0026minus;\u0026thinsp;11\u003c/sup\u003e F at 360 K, indicating changes in the electrical properties of the grain boundary structure. The α parameter, associated with the non-ideal capacitive behavior of CPE elements, shows a slight decrease from 0.82 at 200 K to 0.60 at 360 K, suggesting a shift towards more ideal capacitive behavior at higher temperatures. These findings highlight the complex temperature-dependent electrical characteristics of the sample, crucial for understanding its behavior in various applications requiring precise impedance control.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab6\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 6\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eDifferent parameters of the equivalent circuit for the prepared sample.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"5\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eTemperature (K)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eR\u003csub\u003eg\u003c/sub\u003e (kΩ)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eR\u003csub\u003egb\u003c/sub\u003e (kΩ)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eCPE\u003csub\u003egb\u003c/sub\u003e (10\u003csup\u003e\u0026minus;\u0026thinsp;11\u003c/sup\u003eF)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eα\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e200\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e1110.25\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e1580.28\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e12.52\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.82\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e220\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e958.54\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e1125.37\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e11.51\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.78\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e240\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e725.74\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e852.34\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e11.36\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.75\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e260\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e621.35\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e634.21\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e10.57\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.72\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e280\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e425.24\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e467.81\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e10.17\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.70\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e300\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e214.32\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e249.75\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e9.58\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.68\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e320\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e125.79\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e155.14\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e9.21\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.65\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e340\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e88.10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e81.39\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e8.56\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.62\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e360\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e51.35\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e54.83\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e8.16\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.60\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec6\" class=\"Section2\"\u003e \u003ch2\u003e3.3. Analysis of AC conductivity\u003c/h2\u003e \u003cp\u003eThere is a wealth of knowledge regarding conduction processes in the literature since electrical conductivity changes in frequency with temperature. Figure\u0026nbsp;\u003cspan refid=\"Fig11\" class=\"InternalRef\"\u003e8\u003c/span\u003e displays the frequency dependence of our ceramic's AC conductivity at a specific temperature. The plot makes low-frequency dispersion evident as the curves converge at higher frequencies. The graph shows that when temperature and frequency increase, conductivity increases as well. Both high-frequency AC conductivity and low-frequency DC conductivity are displayed in the conductivity spectra [\u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e40\u003c/span\u003e, \u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e41\u003c/span\u003e]. The conductivity can be examined using Jonscher's power law [\u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e42\u003c/span\u003e, \u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e43\u003c/span\u003e]:\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\(\\:{\\sigma\\:}_{ac}\\left(\\omega\\:\\right)\\)\u003c/span\u003e \u003c/span\u003e= \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\sigma\\:}_{dc}\\)\u003c/span\u003e\u003c/span\u003e + A \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\omega\\:}^{s}\\)\u003c/span\u003e\u003c/span\u003e (9)\u003c/p\u003e \u003cp\u003ewhere n is the exponent factor, 0\u0026thinsp;\u0026lt;\u0026thinsp;s\u0026thinsp;\u0026lt;\u0026thinsp;1, and σ\u003csub\u003edc\u003c/sub\u003e is the direct current conductivity at low frequencies and certain temperatures. A is a constant that is dependent on temperature. It demonstrates that the typical charge accumulation behavior of ω\u003csup\u003es\u003c/sup\u003e is diminished and that the conductivity increases with frequency. A frequency-independent flat response is seen at lower frequencies and higher temperatures. The difference in conductivity at lower frequencies can be recognized thanks to the polarization effect at the electrode and dielectric interface. Ac conductivity rises as frequency rises while accumulated charges decrease [\u003cspan additionalcitationids=\"CR45 CR46 CR47\" citationid=\"CR42\" class=\"CitationRef\"\u003e44\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR46\" class=\"CitationRef\"\u003e48\u003c/span\u003e]. Using Origin 8 software, Eq.\u0026nbsp;9 is employed to determine exponent values. The temperature variation of this parameter for the treated substance is displayed in Fig.\u0026nbsp;\u003cspan refid=\"Fig12\" class=\"InternalRef\"\u003e9\u003c/span\u003e. The situation deteriorates with rising temperature, indicating that Non-overlapping Small Polaron Tunneling (NSPT), which is pertinent for researching conduction phenomena in the boundary of the alternating regime, is the most suitable conduction model [\u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e44\u003c/span\u003e]. This leads to the determination of the carrier's binding energy Wm at that specific point. This can be discovered by using the following equation [\u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e49\u003c/span\u003e]:\u003c/p\u003e \u003cp\u003eS\u0026thinsp;=\u0026thinsp;1 + \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\frac{4{K}_{B}T}{{W}_{m-{K}_{B}Tln\\left(\\omega\\:{\\tau\\:}_{0}\\right)}}\\)\u003c/span\u003e\u003c/span\u003e (10)\u003c/p\u003e \u003cp\u003eThe binding energy is denoted by Wm, and the Boltzmann constant is represented by KB. The exponent s becomes: in case the ratio of of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{W}_{m}\\)\u003c/span\u003e\u003c/span\u003e/\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{K}_{B}T\\)\u003c/span\u003e\u003c/span\u003e is big.\u003c/p\u003e \u003cp\u003es\u0026thinsp;=\u0026thinsp;1 + \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\frac{4{K}_{B}T}{{W}_{m}}\\)\u003c/span\u003e\u003c/span\u003e (11)\u003c/p\u003e \u003cp\u003eThe binding energy is determined by taking the linear slope of \"s\" and getting Wm\u0026thinsp;=\u0026thinsp;0.183 eV. An Arrhenius-type characteristic is observed in the conductivity [\u003cspan citationid=\"CR48\" class=\"CitationRef\"\u003e50\u003c/span\u003e]:\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\(\\:{\\sigma\\:}_{dc}\\)\u003c/span\u003e \u003c/span\u003e = \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:A\\)\u003c/span\u003e\u003c/span\u003e exp (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\frac{-{E}_{a}}{{K}_{B}T}\\)\u003c/span\u003e\u003c/span\u003e) (12)\u003c/p\u003e \u003cp\u003eWhere T is the temperature,\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{E}_{a}\\)\u003c/span\u003e\u003c/span\u003e is the activation energy, A is the pre-exponential factor and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{K}_{B}\\)\u003c/span\u003e\u003c/span\u003eis the Boltzmann constant (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{K}_{B}\\)\u003c/span\u003e\u003c/span\u003e = 8.617\u0026times;10\u003csup\u003e\u0026minus;\u0026thinsp;5\u003c/sup\u003e eV K\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e). The temperature dependence of the conductivity Ln (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\sigma\\:}_{dc}\\)\u003c/span\u003e\u003c/span\u003e T) vs 1000 / T as illustrate in Fig.\u0026nbsp;\u003cspan refid=\"Fig13\" class=\"InternalRef\"\u003e10\u003c/span\u003e. The activation energy estimated from the slope of the linear fit is about 0.43 eV. Such value indicates that the conduction mechanism for the present system may be due to the polaron hopping based on electron carriers. In addition, it is evident that the values of the activation energy derived from conductivity and the frequency corresponding to the relaxation peaks of the imaginary part of the impedance (Z\") are different, which explains why the process of relation and the mechanism of conduction do not use the same charge carriers.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec7\" class=\"Section2\"\u003e \u003ch2\u003e3.4. Dielectric and Modulus Studies\u003c/h2\u003e \u003cp\u003eThe dielectric polarization and dielectric constants were assessed by looking at our sample's dielectric characterization. Based on the mathematical framework introduced at [\u003cspan citationid=\"CR49\" class=\"CitationRef\"\u003e51\u003c/span\u003e], the electric modulus formalism considers both conduction and relaxation.\u003c/p\u003e \u003cp\u003eM* = \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{M}^{{\\prime\\:}}-j{M}^{{\\prime\\:}{\\prime\\:}}\\)\u003c/span\u003e\u003c/span\u003e = \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\frac{1}{{\\epsilon\\:}^{}}\\)\u003c/span\u003e\u003c/span\u003e (13)\u003c/p\u003e \u003cp\u003ewhere the real and imaginary portions of the complex modulus are denoted by M' and M\" correspondingly. They are articulated through the following relationships:\u003cdiv id=\"Equ2\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ2\" name=\"EquationSource\"\u003e\n$$\\:{M}^{{\\prime\\:}}\\:=\\:\\frac{{\\epsilon\\:}^{{\\prime\\:}}}{{{\\epsilon\\:}^{{\\prime\\:}}}^{2}+{{\\epsilon\\:}^{{\\prime\\:}{\\prime\\:}}}^{2}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e14\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equ3\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ3\" name=\"EquationSource\"\u003e\n$$\\:{M}^{{\\prime\\:}{\\prime\\:}}\\:=\\:\\frac{{\\epsilon\\:}^{{\\prime\\:}{\\prime\\:}}}{{{\\epsilon\\:}^{{\\prime\\:}}}^{2}+{{\\epsilon\\:}^{{\\prime\\:}{\\prime\\:}}}^{2}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e15\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eThe frequency shift of the dielectric constant can be explained by the dispersion caused by Maxwell-Wagner interfacial polarization, according to Koop's phenomenological theory. The real and imaginary components of the permittivity are denoted by the formulas ε\u0026thinsp;=\u0026thinsp;ε\u0026prime; + j ε\u0026prime;\u0026prime;, which expresses the complex relative dielectric permittivity. The evolutions of ε\u0026prime; versus frequency for the generated compound at different temperatures are shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e11\u003c/span\u003ea. The real part of the permittivity ε\u0026prime; has larger values at low frequencies because of the double-exchange interaction between the ferromagnetically coupled Fe\u003csup\u003e3+\u003c/sup\u003e and Fe\u003csup\u003e2+\u003c/sup\u003e ions. Since the real element of permittivity is related to stored energy, the charge begins to accumulate at the grain boundary as the temperature rises. Furthermore, it is evident that ε\u0026prime; exhibits increased stability and increases with temperature. The evolution of ε\u0026prime; is generally attributed to the four types of polarizations (atomic, electronic, dipolar, and interfacial) [\u003cspan citationid=\"CR50\" class=\"CitationRef\"\u003e52\u003c/span\u003e]. It has been proven that the evolution of ε\u0026prime; with temperature is related, at low frequencies, to dipolar and interfacial polarizations [\u003cspan citationid=\"CR51\" class=\"CitationRef\"\u003e53\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eAs a result, the imaginary component of permittivity ε\u0026prime;\u0026prime; for the compound as a function of frequency and temperature is shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e11\u003c/span\u003e.b. This figure clearly shows that the samples' ε\u0026prime;\u0026prime; declines with increasing frequency. In general, the imaginary component of permittivity is influenced by polarization and the conduction mechanism [\u003cspan citationid=\"CR52\" class=\"CitationRef\"\u003e54\u003c/span\u003e]. The dielectric constant is quite small because the dipoles follow the alternating field at higher frequencies [\u003cspan citationid=\"CR53\" class=\"CitationRef\"\u003e55\u003c/span\u003e]. Furthermore, the non-Debye behavior is supported by the absence of a relaxation peak at all temperatures. Furthermore, the frequency-dependent variation of M\u0026Prime; at different sample temperatures is shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e12\u003c/span\u003e. It indicates that the value of M\u0026Prime; increases with increasing frequency and reaches its maximum (M max), reaffirming the presence of relaxation. Temperature-dependent relaxation processes in the material are shown by the shifting of the maximum value of the M\" (Mmax) peak to the higher frequency side. There may be a variation in capacitance as indicated by the magnitude of Mmax changing with temperature. The presence of a non-Debye-type [\u003cspan citationid=\"CR54\" class=\"CitationRef\"\u003e56\u003c/span\u003e] conduction mechanism in the material is suggested by asymmetric peak broadening, which also suggests relaxation spreading with a different time constant.\u003c/p\u003e "},{"header":"Conclusion","content":"\u003cp\u003eThe perovskite Bi0.7Ba0.3(FeTi)0.5O3 was synthesized via sol-gel synthesis and confirmed to be a single-phase sample with high density by room temperature X-ray diffraction, energy dispersive X-ray analysis, and scanning electron microscopy. We used impedance spectroscopy and modulus analysis to do a thorough examination of electrical properties, including conduction processes and temperature-dependent relaxation. Studies on modulus and impedance confirmed the compound's non-Debye nature. Furthermore, an electrical equivalent circuit (Rg\u0026thinsp;+\u0026thinsp;Rgb / CPEgb) was used to describe the semiconductor character that was linked to the grain and grain boundary contributions, according to impedance analysis. The real (ε') and imaginary (ε'') components of permittivity behaved in a frequency-dependent manner during dielectric tests conducted at ambient temperature, suggesting the presence of a relaxation time distribution and the influence of charge carrier density. The electrical and dielectric properties that have been recently identified have enormous promise for new breakthroughs and enhanced efficiency in a variety of technical domains, including as electronics, telecommunications, and energy storage.\u003c/p\u003e \u003c/div\u003e"},{"header":"Declarations","content":"\u003cdiv id=\"Fig1\" class=\"Figure\"\u003e\u003cstrong\u003e\u003cstrong\u003eConflicts of interest\u003c/strong\u003e:\u003c/strong\u003e\u003c/div\u003e\n\u003cp\u003eThe authors affirm that they did not accept any grants, funding, or other forms of assistance in order to prepare this paper.\u003c/p\u003e\n\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\n\u003cp\u003eFaouzia Tayari: Conceptualization, Methodology, Formal Analysis, Investigation, Writing \u0026ndash; Original Draft.Silvia Soreto Teixeira: Data Curation, Software, Validation, Writing \u0026ndash; Review \u0026amp; Editing.M. P. F. Gra\u0026ccedil;a: Supervision, Resources, Project Administration, Funding Acquisition.Manel Essid: Visualization, Investigation, Resources.Kais Iben Nassar: Conceptualization, Methodology, Supervision, Writing \u0026ndash; Review \u0026amp; Editing, Correspondence.\u003c/p\u003e\n\u003ch2\u003eData availability\u003c/h2\u003e\n\u003cp\u003eSince no datasets were created or examined for this research, data sharing is not applicable.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eW. Eerenstein, N.D. Mathur, J.F. Scott, Nature 442, 759 (2006)\u003c/li\u003e\n\u003cli\u003eY. Lan, X. Feng, X. Zhang, Y. Shen, D. Wang, Phys. Lett. A 380, 2962 (2016)\u003c/li\u003e\n\u003cli\u003eA.K. Paul, M. Reehuis, V. Ksenofontov, B.H. Yan, A. Hoser, D.M. T\u0026ouml;bbens, P.M. Abdala, P. Adler, M. Jansen, C. Felser, Phys. Rev. Lett. 111, 1 (2013)\u003c/li\u003e\n\u003cli\u003eM. Saxena, K. Tanwar, T. Maiti, Scripta Mater. 130, 205 (2017)\u003c/li\u003e\n\u003cli\u003eS. Bhuyan, K. Sivanand, S.K. Panda, R. Kumar, J. Hu, IEEE Magn. Lett. 2, 6000204 (2011)\u003c/li\u003e\n\u003cli\u003eA.H. Slavney, T. Hu, A.M. Lindenberg, H.I. Karunadasa, J. Am. Chem. Soc. 138, 2138 (2016)\u003c/li\u003e\n\u003cli\u003eX. Gao, D. Xu, J. Du, J. Li, Z. Yang, J. Sun, J. Mater. Sci. Mater. Electron. (2017).\u003c/li\u003e\n\u003cli\u003eM.M. Kumar, V.R. Palkar, K. Srinivas, S.V. Suryanarayana, Appl. Phys. Lett. 76, 2764 (2000)\u003c/li\u003e\n\u003cli\u003eS. Halder, S. Bhuyan, S.N. Das, S. Sahoo, R.N.P. Choudhary, P. Das, K. Parida, Appl. Phys, A (2017).\u003c/li\u003e\n\u003cli\u003e H.J. Feng, F.M. Liu, Phys. Lett. A 372, 1904 (2008)\u003c/li\u003e\n\u003cli\u003e O.E. Rhazouani, A. Slassi, Y. Ziat, A. Benyoussef, Phys. Lett. A 381, 1177 (2017)\u003c/li\u003e\n\u003cli\u003e E. Fresia, L. Katz, and R. Ward, Journal of the American Chemical Society, vol. 81, pp. 4783-4785, 1959.\u003c/li\u003e\n\u003cli\u003e M. d. C. Viola, M. Martinez-Lope, J. Alonso, P. Velasco, J. Martinez, J. Pedregosa, R. Carbonio, and M. Fern\u0026aacute;ndez-D\u0026iacute;az, Chemistry of Materials, vol. 14, pp. 812-818, 2002.\u003c/li\u003e\n\u003cli\u003e I. P. Muthuselvam, A. Poddar, and R. Bhowmik, arXiv preprint arXiv: 0811.1876, 2008.\u003c/li\u003e\n\u003cli\u003e C. Ritter, M. Ibarra, L. Morellon, J. Blasco, J. Garcia, and J. De Teresa, Journal of Physics: Condensed Matter, vol. 12, p. 8295, 2000.\u003c/li\u003e\n\u003cli\u003e Dhanalakshmi, B., et al. Ceramics International 42.2 (2016): 2186-2197.\u003c/li\u003e\n\u003cli\u003e Benamara, Majdi, et al. RSC advances\u0026nbsp;13.41 (2023), 28632-28641.\u003c/li\u003e\n\u003cli\u003e Nassar, Kais Iben, et al. RSC advances\u0026nbsp;13.34 (2023), 24023-24030\u003c/li\u003e\n\u003cli\u003e Srivastava, Amar, Ashish Garg, and Finlay D. Morrison. Journal of Applied Physics 105.5 (2009).\u003c/li\u003e\n\u003cli\u003e Purohit, Varsa, and R. N. P. Choudhary. Materials Chemistry and Physics 256 (2020): 123732.\u003c/li\u003e\n\u003cli\u003e H.M. Rietveld, J. Appl. Crystallogr. 2 (1969) 65.\u003c/li\u003e\n\u003cli\u003e Rodriguez-Carbajal J. Program FullProf. Laboratoire L\u0026eacute;on Brillouin (CEACNRS), version 3.5d, LLB-JRS (1998).\u003c/li\u003e\n\u003cli\u003e D. Gherca, A. Pui, V. Nica, O. Caltun, N. Cornei, J. Ceramics Int. 40 (2014) 9599\u0026ndash;9607.\u003c/li\u003e\n\u003cli\u003e S. Verma, J. Chand, K.M. Batoo, M. Singh, J. Alloys Compounds 565 (2013) 148 153.\u003c/li\u003e\n\u003cli\u003e Wang, Yaru, Yongping Pu, and Panpan Zhang. Journal of Alloys and Compounds 653 (2015): 596-603.\u003c/li\u003e\n\u003cli\u003e Wu, Jiagang, and John Wang.\u0026nbsp; Journal of Applied Physics 105.12 (2009).\u003c/li\u003e\n\u003cli\u003e K. Jonscher, Altaf Husain, J. Physica B: Condensed Matter, 217(1996)29-34.\u003c/li\u003e\n\u003cli\u003e Identification of electrochemical processes by frequency response analyzer Solartron\u0026reg;- Claude Gabrielli \u0026ndash;1998.\u003c/li\u003e\n\u003cli\u003e E. Barsoukov, D.H. Kim, H.-S. Lee, H. Lee, M. Yakovleva, Y. Gao, J.F. Engel, J. Solid State Ionics 161 (2003) 19\u0026ndash;29.\u003c/li\u003e\n\u003cli\u003e E. Barsoukov, J.R. Macdonald, John Wiley and Sons, New York, 2005.\u003c/li\u003e\n\u003cli\u003e L. Singh, Ill Won Kim, B.C. Sin, S.K. Woo, S.H. Hyun, K.D. Mandal, Y. Lee, Powder Technol. 280 (2015) 256\u0026ndash;265.\u003c/li\u003e\n\u003cli\u003e S. Chatterjee, P.K. Mahapatra, R.N.P. Choudhary, A.K. Thakur, Status Solidi A. 201 (2004) 588.\u003c/li\u003e\n\u003cli\u003e A. Omri, M. Bejar, M. Es-Souni, M. A. Valente, M. P. F. Gra\u0026ccedil;a and L. C. Costa, J. Alloys Compd., 2012, 536, 173\u0026ndash;178.\u003c/li\u003e\n\u003cli\u003e M. M. Costa, G. F. M. Pires J\u0026acute;unior and A. S. B. Sombra, Mater. Chem. Phys., 2010, 123, 35\u0026ndash;39.\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u003c/li\u003e\n\u003cli\u003e K.S. Cole, R.H. Cole, Chem. Phys. B41 (1941) 9.\u003c/li\u003e\n\u003cli\u003e D. Johnson, Z-view, Impedance Software, Version 2.1a, Scribner Associates Inc, (1990-1998).\u003c/li\u003e\n\u003cli\u003e P. Cordoba-Torres, T.J. Mesquita, O. Devos, B. Tribollet, V. Roche, R.P. Nogueira, , Electro. Acta 72 (2012) 172\u0026ndash;178.\u003c/li\u003e\n\u003cli\u003e B. Hirschorn, M.E. Orazema, B. Tribollet, V. Vivier, I. Frateur, M. Musiani, Electro. Acta 55 (2010) 6218\u0026ndash;6.\u003c/li\u003e\n\u003cli\u003e Lily, K. Kumari, K. Prasad, R. N. P. Choudhary, J. Alloys Compd. 453 (2008) 325- 331.\u003c/li\u003e\n\u003cli\u003e N. Chihaoui, M. Bejar, E. Dhahri, M.A. Valente, L.C. Costa, M.P.F. Gra\u0026ccedil;a, Int. J. Mater. Eng. Technol. 13 (2015) 129.\u003c/li\u003e\n\u003cli\u003e R. James, C. Parkash, G. Prasad, J. Phys. D: App. Phys. 39 (2006) 1635.\u003c/li\u003e\n\u003cli\u003e S. Lanfredi, P.S. Saia, R. Lebullenger, A.C. Hernandes, Solid State Ionics 146 (2002) 329.\u003c/li\u003e\n\u003cli\u003e A.K. Jonscher, Universal Relaxation Law, Chelsea Dielectric Press, London, 1996.\u003c/li\u003e\n\u003cli\u003e Ghosh, phys. Rev. B, 41(1990)1479.\u003c/li\u003e\n\u003cli\u003e Kalinin, Sergei V., et al. Journal of the American Ceramic Society 85.12 (2002): 3011-3017.\u003c/li\u003e\n\u003cli\u003e M. D. Migahed, N. A. Bakr, M. I. Abdel-Hamid, O. EL- Hannafy, M. El- Nimr, J. Appl. Polym. Sci. 59(1996) 655\u0026ndash;662.\u003c/li\u003e\n\u003cli\u003e I. Ali, M. Islam, M.N. Ashiq, M.A. Iqbal, H.M. Khan, G. Murtaza, J. Magn. Magn. Mater. 362 (2014) 115\u0026ndash;121.\u003c/li\u003e\n\u003cli\u003e H. Kolodziej, L.Sobczyk, Acta Phys. Pol. A 39 (1971) 59.\u003c/li\u003e\n\u003cli\u003e X. Qian, N. Gu, Z. Cheng, X. Yang, E.wang, S. Dong, Electrochim. Acta 46 (2001) 1829.\u003c/li\u003e\n\u003cli\u003e Bharti, T.P. Sinha, Solid Stat Sci. 12 (2010) 498.\u003c/li\u003e\n\u003cli\u003e T.P. Dutta, Sinha, Phys. B 405 (2010) 1475.\u003c/li\u003e\n\u003cli\u003e L.L. Hench, J.K. (West, Wiley, New York, 1990), p. 189 46.\u003c/li\u003e\n\u003cli\u003e H.T. Martirena, J.C. Burfoot, J. Ferroelectrics 7, 151 (1974)\u003c/li\u003e\n\u003cli\u003e M Bakr Mohamed, H. Wang, H. Fuess. Phys D: Appl. Phys. 43 (2010) 409-455.\u003c/li\u003e\n\u003cli\u003e Pattanayak, Samita, et al. Applied Physics A 112 (2013): 387-395.\u0026nbsp;\u003c/li\u003e\n\u003cli\u003e R. Ranjan, R. Kumar, N. Kumar, B. Behera, R.N.P. Choudhary, J. Alloys Compd. 509 (2011) 6388.\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"journal-of-sol-gel-science-and-technology","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"jsst","sideBox":"Learn more about [Journal of Sol-Gel Science and Technology](https://www.springer.com/journal/10971)","snPcode":"10971","submissionUrl":"https://submission.springernature.com/new-submission/10971/3","title":"Journal of Sol-Gel Science and Technology","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Perovskite, Sol-gel route, Impedance complexe, Electrical conductivity, Dielectric relaxation","lastPublishedDoi":"10.21203/rs.3.rs-4706128/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4706128/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eCreating perovskite ceramic with electrical and dielectric properties appropriate for energy storage, medical uses, and electronic devices is the goal of this research. A bismuth ferric titanate, Bi₀.₇Ba₀.₃(FeTi)₀.₅O\u003csub\u003e3\u003c/sub\u003e, doped with barium and crystalline, was effectively synthesized at the A-site via sol-gel synthesis. A rhombohedral structure emerged in 12 the R 3́ C space group, which was confirmed by room-temperature X-ray studies. An average grain size of 263 nm and a homogeneous grain distribution and chemical composition were confirmed by the results of scanning electron microscopy (SEM) and energy dispersive X-ray analysis (EDX). The relationship between temperature and frequency and electrical properties was found. Impedance spectroscopy and electrical modulus measurements, performed in the frequency range of 1 kHz to 1 MHz and at temperatures ranging from 200 K to 360 K, demonstrated a non-Debye type of relaxation. Furthermore, once the material was produced at various temperatures, its frequency-dependent electrical conductivity was examined using Jonscher's law. Over the complete temperature range, consistent conduction and relaxation mechanisms were discovered. These findings suggest that the chemical may find widespread applicability across a broad temperature range, including electrical fields and capacitors.\u003c/p\u003e","manuscriptTitle":"Examining the Structural, Dielectric, and Electrical Characteristics of Sol-Gel","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-08-09 20:43:53","doi":"10.21203/rs.3.rs-4706128/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"editorInvitedReview","content":"","date":"2024-08-03T01:16:00+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2024-07-25T21:54:03+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"152466066684885950006992616409161222149","date":"2024-07-18T11:15:41+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"59847034950288593027828227969844910689","date":"2024-07-18T08:12:32+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"125366528393866538749445524143519602805","date":"2024-07-18T08:09:12+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2024-07-18T01:37:23+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2024-07-09T09:38:41+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2024-07-09T09:38:34+00:00","index":"","fulltext":""},{"type":"submitted","content":"Journal of Sol-Gel Science and Technology","date":"2024-07-08T14:03:55+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"journal-of-sol-gel-science-and-technology","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"jsst","sideBox":"Learn more about [Journal of Sol-Gel Science and Technology](https://www.springer.com/journal/10971)","snPcode":"10971","submissionUrl":"https://submission.springernature.com/new-submission/10971/3","title":"Journal of Sol-Gel Science and Technology","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"115be40f-32f2-4852-96e5-c3bba4d348b4","owner":[],"postedDate":"August 9th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[],"tags":[],"updatedAt":"2024-09-23T16:12:03+00:00","versionOfRecord":{"articleIdentity":"rs-4706128","link":"https://doi.org/10.1007/s10971-024-06549-9","journal":{"identity":"journal-of-sol-gel-science-and-technology","isVorOnly":false,"title":"Journal of Sol-Gel Science and Technology"},"publishedOn":"2024-09-21 15:58:01","publishedOnDateReadable":"September 21st, 2024"},"versionCreatedAt":"2024-08-09 20:43:53","video":"","vorDoi":"10.1007/s10971-024-06549-9","vorDoiUrl":"https://doi.org/10.1007/s10971-024-06549-9","workflowStages":[]},"version":"v1","identity":"rs-4706128","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-4706128","identity":"rs-4706128","version":["v1"]},"buildId":"qtupq5eGEP_6zYnWcrvyt","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}