Unraveling dielectric abnormality based on the effect of defect dipoles in Cr ion doped multipurpose properties of BCT ceramics

With the motive of unraveling the effect of Cr incorporation on the structural, microstructural, dielectric, ferroelectric, energy storage, and magnetic properties of BCT (Barium Calcium Titanate) ceramics have been investigated. Ba 0.80 Ca 0.20 powder samples have been prepared using classical solid-state reaction method. Cr doped BCT ceramics showed a single phase perovskite structure having a tetragonal phase without phase transformation from P4mm to Pm-3m after the addition of Cr. With increased Cr content, the tolerance factor, lattice parameters, unit cell volume, c\a ratio, and grain size have been found to decrease. Both Debye-Scherrer and Williamson-Hall plot methods confirmed the reduction of crystallite size on increased Cr doping in BCT lattice. A dielectric anomaly “hump” (̴ 447 K) has been observed at low frequencies in the paraelectric region due to the presence of acceptor induced defect dipoles. The temperature-dependent dielectric properties of prepared BCT ceramic with Cr compositions possess diffused phase transition (DPT) and the width of DPT is increased. Room temperature energy storage density achieved the maximum value of 190.35 mJ/cm 3 for the composition x = 0.005 at an electric field magnetic fields. These results suggest prepared ceramics as a suitable lead-free material for X8R multilayer ceramic capacitor devices and energy applications.


Introduction
With the functionality of ferroelectric materials, they can be adapted to wide-ranging applications, including multilayer ceramic capacitors (MLCCs), sensors, transducers, actuators, and energy storage devices [1][2][3][4][5]. The rapidly growing demands of energy storage technologies have promoted the development of materials with high energy storage density and high energy storage efficiency [6][7][8][9]. The usage of ferroelectric ceramic materials in electrical and electronic devices is fast blooming as a potential material for energy storage applications [6,[9][10][11]. The majority of ferroelectric ceramic capacitors employ Lead (Pb) containing materials such as PbTiO3 (lead titanate oxide), PZT (lead zirconate titanate), and their derivative compositions [12]. Leadbased compositions of ferroelectric ceramic capacitors offered outstanding energy storage properties. But the presence of highly precarious Lead (Pb) raised concerns regarding detrimental effects on human health and the environment, and forbid their usefulness [3,13,14]. New ceramic compositions need to be designed to replace Pb and derive the improved performance of Lead-free materials in a variety of achievable properties [13,15,16]. For the last few decades, the enthralling research into Lead-free ceramics has been conducted [17]. Currently, the search for Lead-free dielectric ceramics with ergonomic properties is focused on the compositions of BaTiO3, which is a well-studied perovskite ferroelectric material due to its enormous practical applications [13, [18][19][20][21]. Modification in the structure and properties of BaTiO3 can be made by doping with a variety of dopant ions (dopant engineering) for fetching multiple applications from doped ceramic materials [5,15,20,[22][23][24][25][26][27]. The properties of ceramic materials are highly dependent on final crystal symmetry, choice of dopant, the disparity in ionic radii between host/parent and dopant cations, doping concentration, and preparation conditions [28] The A-site substitution of smaller ionic radii Ca 2+ (1.34 Å) in BaTiO3 is caused by replacing Ba 2+ ions with larger ionic radii (1.61 Å) within its solid solution limit. BCT (Ca doping in BaTiO3) ceramics support the diffused temperature dependence of dielectric constant, provide higher breakdown strength, and better piezoelectric properties [2,14,[29][30][31][32]. Moreover, doping effect of at 1100 ˚C for 4 hrs in a high-temperature muffle furnace. The calcined powders were ball milled, dried, and Calcined again following the above-mentioned procedure. After calcination, powders were uniaxially pressed into disk pellets of 1-2 mm thickness and a diameter of 10 mm under a pressure of 0.5 ton/sq. in. for 2 minutes. The pelletized calcined products have been sintered at 1350 ˚C for 4 hrs. All the characterizations have been carried out on the sintered samples. The crystallographic structure of prepared compositions has been examined using Rigaku Miniflex-II X-ray diffractometer over the angular range (2θ) 20 -80˚. The CuKα radiations (λ ̴ 1.540560 Å) from the copper tube has been used for investigation. The phase identification and lattice parameters were calculated by Rietveld refinement of XRD data performed employing Full Prof software 2015. The morphology and microstructure images from the fractured surface of sintered samples have been observed using Scanning Electron Microscope (FE-SEM, Carl Zeiss Supra 55).
For dielectric and ferroelectric measurements, the polished surfaces of disk pellets were coated with a silver paste to make electrodes. The dielectric measurements have been performed using impedance analyzer (Keysight -E4990A) in the frequency range of 500 Hz to 100 kHz. The ferroelectric (P-E) measurements have been carried out using a P-E loop tracer (Marine, India).
The room temperature maganetization vs. magnetic field (M-H) loops have been measured using a Microscence E-29 Vibrating Sample Magnetometer (VSM).

Analysis of crystal structure
The XRD diffraction pattern of Ba0.80Ca0.20Ti1-3x/4CrxO3 (x = 0.000, 0.005, 0.010, 0.015 and 0.020) ceramics have been recorded on crushed powder samples at room temperature, are displayed in Fig. 1 (a). In Fig. 1 (a), XRD patterns evidence the well-defined single-phase perovskite tetragonal structure. Obtained XRD patterns are also free from any impurity phase of oxides and show no structural transformation from the tetragonal (P4mm) phase after Cr doping in the BCT lattice at room temperature. It indicates that samples are well crystallized and diffusion of Cr and Ca ions at Ti and Ba lattice positions into the BCT host matrix, respectively, suggesting the formation of a solid-solution. All the peaks in XRD diffraction patterns of BCT samples doped with Cr ions have been identified to tetragonal phase using JCPDS card number 81-2205 (BaTiO3).
The characteristic peaks located at diffraction angle 2θ ̴ 45.5˚ corresponds to the (002) and (200) crystalline planes of tetragonal (P4mm) symmetry of unit cell. The enlarged part of characteristic tetragonal diffraction peaks is shown in Fig 1 (b). It is also visible from Fig. 1 (b) that no significant change in diffraction peak intensities was observed with increasing the incorporation of Cr contents (x) which verified the prevailing of tetragonal structure for all prepared samples. All the diffraction peaks show a shift towards higher 2θ with respect to bare (x = 0.000) BCT sample for increasing incorporation of Cr. This shifting of diffraction peaks indicates that lattice parameters (a, c) and unit cell volume (a 2 c) decreases with doping of Cr ions at the lattice site of Ti in BCT ceramics. As the shifting of diffraction peaks towards the higher angle side is a clear indication of a decrease in unit cell volume and lattice parameters. This is due to the incorporation of lower size Cr 3+ ions (0.615 Å) in the Ti 4+ (0.62 Å) site of the BCT lattice.
Goldsmith's tolerance (t) factor has been determined for the estimation of degree of distortion of host perovskite structure on the basis of ionic radii in BCT perovskite doped with Cr ions. The t for x mol Cr-doped BCT (doping level dependence of t) was calculated using chemical formula Ba0.80Ca0.20Ti1-3x/4CrxO3, considering Cr 3+ in the lattice is given by [1] (2) and (3,4) respectively [1,37]. Lattice strain values were obtained only from the W-H plot (βcosθ vs.4sinθ).
where, D is average crystallite size, λ ̴ 1.54056 Å (wavelength of Cu (Kα) radiation), k ̴ (0.89) is shape factor, β is FWHM (full width at half maxima), θ is the diffraction angle and η is lattice strain. Fig. 2 shows the graph of the W-H plot, which is plotted between βcosθ (along y-axis) and 4sinθ (along x-axis there would be shrinkage of the lattice which results in the variation of lattice strain [38]. The decrease in crystallite size is an indication of increase in structural defects which would restrict grain growth.

Rietveld Refinement
Rietveld refinement method has been used to determine the precise lattice parameters and  Table 3. From the perusal of data presented in Table 2, refined lattice parameters as well as unit cell volume have been found to decrease with increasing doping content of Cr 3+ at Ti 4+ sites due to the lower ionic radii of Cr. The refined structural parameters are in accordance with the shifting of diffraction peaks. It has also been found that c/a ratio decreases on replacement of larger size Ti ions by Cr ions of smaller size with increasing doping content in the BCT matrix. The reduction in c/a ratio implies a decrease in tetragonality and the emergence of crystal structure towards stable perovskite structure [2]. The refined 3D tetragonal structure model for Ba0.80Ca0.20Ti1-3x/4CrxO3 ceramics was constructed using a CIF file with the help of VESTA software. Data presented in Table 3, shows the variation in bond length values on the incorporation of Cr ions implies lattice deformation due to the induced strain in the BCT lattice.

Density measurement
Archimedes Principle has been utilized for the calculation of experimental density (dexp.) of samples. X-ray density (dxrd) has been calculated using lattice parameters (obtained from Rietveld refinement). Porosity has been determined for prepared samples using the following relation [39] exp (%) 1 100 For all prepared compositions, the density and porosity values as a function of Cr content are summarized in Table 2. From the perusal of data presented in Table 2, it has been observed that density increases for x = 0.005 and then gradually decreases with increasing incorporation of Cr at Ti sites. It has also been observed that experimental density (dexp.) values are smaller than those of x-ray density (dxrd) for all prepared samples. This could be ascribed to the existence of pores which can develop during the sintering process. Opposite variation trend has been found for porosity, sample with composition x = 0.005 shows low porosity whereas other samples show increased porosity with increased Cr doping. This might be due to the incorporation of Cr ions having smaller ionic radii in comparison to Ti ions (larger size), results in the displacement of neighboring atoms from their position and causes the shrinkage of lattice [39]. Thus, increased compositional fluctuations would lead to increased porosity.

Analysis of structural morphology
The SEM micrographs of Ba0.80Ca0.20Ti1-3x/4CrxO3 for all compositions varying from x = 0.000 to 0.020 are presented in Fig. 5 to probe their morphology and average grain size. The SEM images of BCT samples doped with Cr ions reveal that grains appear in polyhedral form/shape with varying sizes and have been heterogeneously distributed with certain voids. Heterogeneous distribution of grain size indicates the nucleation rate is much rapid than grain growth rate [40].
Grain boundaries of all Cr doped BCT samples are clearly visible in the SEM images. The average grain size was calculated from Image J software using SEM micrographs. It has been observed that average grain size firstly increases from 5.  Table 1. This decrease in grain size is due to the adhesion of Cr 3+ ions onto the surface and grain boundaries with increased Cr content [41]. These Cr 3+ ions attached to the surface hinders the grain growth and results in the reduction of grain size.

Temperature dependence of dielectric constant
In order to check the dielectric response of prepared ceramic samples, temperaturedependent dielectric studies have been carried out. The temperature-dependent dielectric constant behavior of all Cr compositions as a parameter of frequency ranging from 500 Hz -100 kHz has been carefully examined (presented in Fig. 6). The temperature-dependent εʹ of Cr doped BCT ceramics at 10 kHz are shown in Fig. 7. It can be seen from the εʹ vs. T plots that there is a gradual increase in εʹ up to tetragonal (P4mm) to cubic (Pm-3m) phase transition temperature (Tc), and then drop in εʹ is clearly visible in the paraelectric region. An additional dielectric anomaly "hump" (located around 447 K) at low frequencies in the paraelectric region has been observed for Cr content (x = 0.005 -0.020). However, no such anomaly is observed in the dielectric curve of BCT sample with composition x = 0.000. This appeared anomaly in acceptor (Cr 3+ ) doped samples could be associated with the dielectric relaxation mechanism induced by orientation polarization of defect dipoles [42,43] Furthermore, the external electric field would orientationally polarize ( (can change their orientation), results in net polarization and creates a hump in the dielectric curve [44]. In addition, the orientation polarization of these oxygen vacancies are associated with defect dipoles typically occurs at high temperatures and low frequencies due to higher volume and lower mobility of oxygen vacancies [43]. This dielectric anomaly almost disappeared at higher frequencies. Therefore, a relaxed hump is formed in εʹ vs. T curve due to thermal fluctuation to the polarization response of prepared samples. The hump size is found to be related to the concentration of oxygen vacancy that accumulates on grain surface, grain boundaries, and domain walls of the ceramics [42]. The transition temperature (Tc) of the prepared ceramic compositions have been determined from the dielectric peak at higher frequencies to discern circumvent the polarization effect of defect dipoles. From the perusal of data presented in Fig. 7, Tc has been observed to shift to a lower temperature (from 404 K to 413 K) and also a lower values of εʹmax at Tc with increased Cr content (x) in BCT ceramics. While the observed change in Tc seems to be quite small, this is reasonable from the perspective of low Cr doping content (up to 2 mol %). The variation in Tc is also directly related to the number of oxygen vacancies ( V o  ) in the acceptor doped ceramics. Additionally, dopant Cr 3+ ions for Ti 4+ ions are highly compatible with the lattice structure of BCT because of their resemblance to ionic radii and electronegativity, which establishes a stable transition temperature for prepared ceramics. With increased Cr doping, the reduction in maximum of dielectric constant (εʹmax) at Tc may be attributed to decrease in grain size as observed by SEM micrographs analysis. Furthermore, the effect of decreasing εʹmax is probable due to formation of oxygen vacancies that usually pin the ferroelectric domain walls motion at higher Cr doping level. The values of εʹRT, εʹmax at 10 kHz and Tc are summarized in Table 4.

Frequency dependence of dielectric constant
From Fig. 6 (a-e), the dielectric constant analysis shows that phase transition temperature (Tc) does not shift as a function of frequency. Thus, Tc value is independent from the frequency effect which is an indication of the classical ferroelectric nature of studied ceramic samples. But, εʹ -T plot shows a decrease of εʹmax along with the disappearance of anomaly peak with increasing frequency from 500 Hz to 100 kHz. Thus, it can be inferred that the intensity of both dielectric peaks in εʹ -T plot decreases but does not show position shift and retains a broad shape around phase transition temperature with increased frequency.

Diffused phase transition behavior
Dielectric constant (εʹ) has been found to be independent of temperature and frequency at low temperatures (below Tc). On careful observation of εʹ vs. T curve above Tc, the phase transition is broadened over a certain temperature interval and seemed to have frequency dependence. To examine the characteristic of ferroelectric phase transition in prepared ceramics, εʹ -T curves were fitted with Power Law at various frequencies. Bare and Cr doped BCT ceramics may obey Power law in the paraelectric region. The Power law is described by the following relation [1]  where, δc is the broadening parameter, γ is the degree of relaxation which is expected to be 1 for ideal ferroelectrics, 1 < γ < 2 for diffused phase transition (DPT) and 2 for relaxor ferroelectrics, Tc is transition temperature and εʹc is a maximum dielectric constant value. To elucidate the dielectric phenomenon in bare and Cr doped BCT solid solution by Power law, εʹ vs. T plot at different frequencies is presented in Fig. 6 (a -e). Fig. 8 (a -e) shows the experimental dielectric constant data along with curves above Tc generated by fitting the data to Power law for all prepared ceramic compositions. The Power law curve excellently fits the presented εʹ vs. T data with best fit parameter R 2 in the range 0.9982 -0.9994. Two parameters γ and δc obtained by fitting the experimental εʹ data to equation (7) and the graph [ Fig. 9 (a) Table 4. It is apparent from Fig. 10 and the values presented in Table that   curve. The behavior of the first dielectric loss peak is corresponding to the tetragonal-cubic phase transition but at a slightly lower temperature than Tc. Additional loss peak (located in paraelectric regime) behavior is also associated with dielectric losses caused due to the existence of defect dipoles. By examining the shape of the Tanδ -T curve, it has been observed that dielectric loss anomaly (related to defect dipoles) is present at the higher temperature side of tetragonal to cubic phase transition. However, the occurrence of hump around 447 K in Tanδ vs. T curve is more pronounced as compared to εʹ -T curve. The intensity of dielectric loss peaks corresponding to tetragonal -cubic phase and anomaly due to the formation of defect dipoles varies as a function of increasing frequency. It can also be noticed that at higher frequencies the effect of defect dipoles weakens and thus a reduction in the intensity of anomaly loss peak. This could be ascribed to the fact that the contribution of orientation polarization of defect dipoles decreases with an increase in the frequency of applied field, resulting in low dielectric loss [46]. An overall reduction in dielectric losses near Tc has been observed with an increase in Cr content. This may be linked with the diminution of average grain size in prepared samples. The dielectric loss (TanδDD) occurred at high temperatures is due to the presence of defect dipoles, which might be because oxygen vacancies begin to move and lead to electric conduction in samples [46]. Also, increasing the doping level of Cr content often induces an increased concentration of oxygen vacancy, resulting in a gradual increase in dielectric loss with Cr content at a higher temperature. Thus giving rise to defect dipole induced dielectric losses. Further, in higher temperature region and at low frequencies, the larger values of dielectric losses may be due to conduction losses that decline as the frequency of applied field rises [2]. A summary of dielectric loss values such as TanδRT, TanδTc, and TanδDD at a frequency of 10 kHz for all prepared Cr doped BCT samples is presented in Table 4.

Temperature coefficient of capacitance
Temperature coefficient of capacitance (TCC) of bare and Cr doped BCT ceramics have been evaluated in the temperature range 303 K to 523 K, using the following formula [1] where, CT is capacitance value at operating temperature T and the CT-1 corresponds to capacitance value at T-1 temperature. Fig. 12 displays the fashion of variation of Tcc with temperature at a frequency of 10 kHz. Looking at a plot of TCC vs. T for all Cr doped samples, it was found that variance of Tcc is initially positive up to 363 K then becomes highly positive around Tc and appears negative above 423 K. The overall variance of Tcc in the prescribed temperature range is within ± 10 %. In the temperature range near Tc, a higher Cr (x = 0.020) doped sample possesses the lowest TCC about ± 7.65 %. This implies that the incorporation of Cr content can enhance the temperature stability of dielectric properties of BCT ceramics. The prepared material yields room temperature εʹ ̴ 629 -793 and εʹ at Tc ̴ 2915 -4368, with low dielectric loss (< 0.07) and temperature coefficient of capacitance (Tcc) of ± 15 % from 303 K to 523 K. Thus the system of Cr doped BCT MLCCs could be a possible contender for the future generation of X8R devices [47].

Electric field induced ferroelectric evolution
The measurement of hysteresis loops (P-E) directly depends on the electric field. To access its influence on ferroelectric properties at room temperature, the electric field has been increased.

Composition induced ferroelectric evolution
The in polarizability [48]. The ferroelectric parameters namely remnant polarization (Pr), maximum polarization (Pmax), and coercive field (Ec) with Cr content at 50 kV/cm are presented in Table 5.
From the data presented in Table 5, it is observed that Ec of ceramic samples continuously increases with increase Cr (up to x = 0.015) content. This increase in Ec can be attributed to the formation of oxygen vacancies on Cr 3+ doping for Ti 4+ ions of BCT. These oxygen vacancies diffused into the domain boundaries and induce a pinning effect on boundaries and reduce the domain wall movement. Thus coercive field increases and prepared material behave as hard ferroelectrics.
However, a drop in Ec for higher Cr doping content (x = 0.020) is due to the dominance of the effect of defect dipoles on the ferroelectric domains. The defect dipoles and oxygen vacancies migrate into domain boundaries because of their moderate mobility, even at lower temperature than phase transition temperature. Such defect dipoles can pin the movement of the domain and may result in the formation of small wavy domains, rather than large domain structures [49]. As a Consequence, the coupling effect between domain walls and grain boundaries gets reduced and would weaken the pining of domain wall motion which contributes to the reduction of Ec [43].

Temperature induced ferroelectric evolution
The temperature-dependent hysteresis loops of prepared ceramic compositions were measured at an applied field of 50 -60 kV/cm with a frequency of 50 Hz. The typical hysteresis loops for Cr doped BCT compositions with x = 0.000, x = 0.010 and x = 0.020 at different temperatures (room temperature to 383 K) are presented in Fig. 15 (a -c). From the perusal of data presented in Fig. 15, it can be observed that P-E loops are well saturated indicating normal ferroelectrics, and are highly temperature-dependent showing evidence of soft ceramics. As the temperature rises, P-E hysteresis loops of Cr doped BCT ceramics tend to be thinner and thinner, accompanied by a gradual decrease of both Pr and Ec, suggesting deterioration of ferroelectric properties. This variation trend of Pr and Ec usually occurs in most of the ferroelectric materials.
The decrease in Pr and Ec is ascribed to energy barrier reduction for the reorientation of domains and to maintain poled state at higher temperatures.

Effect of Cr doping on energy storage properties of BCT ceramics
For the overview of energy storage performance of Cr doped BCT ceramics, P-E loops have been used to determine the energy storage density (Wrec), loss density (Wloss), and also energy storage efficiency (η) with variation of electric field and temperature. P-E loop diagram shown in Fig. 16 (a), demonstrates the Wrec, Wloss enclosed by purple and sky blue colored area respectively. 20 The Wrec, Wloss, and η have been calculated from the hysteresis area in 1 st quadrant using relations [50] where, rec W , loss W , η, E, Pmax, and Pr represents the energy storage density, energy loss density, energy storage efficiency, electric field, maximum polarization and remnant polarization respectively.

Effect of electric field on energy storage properties
The room temperature evolution of energy storage properties ( rec W , loss W and η) with an applied electric field (50 -60 kV/cm) for different compositions of Cr doped BCT has been shown in Fig. 16 (b -d). From the perusal of data presented in Fig. 16 (b -d), it has been found that Wrec, Wloss, and η are increasing overall with an increase in the applied electric field. Table 5 summarizes the values of Wrec, Wloss, and η obtained at a 50 kV/cm as a function of Cr content. The Wrec, Wloss, and η found to be varying from 107.20 to 177.88 mJ/cm 3 , 138.51 to 228.77 mJ/cm 3 , and 35.87 to 56.22 % respectively with Cr (x) content. The variation of Wrec has been observed to be similar to the difference between Pmax and Pr with increased Cr content. The Wrec decreases up to x = 0.010 and then increases. Since there is a large difference between Pmax and Pr, energy storage density would be high. An overall decrease in energy storage efficiency (η) has been observed with Cr content due to the increase in energy loss density (Wloss). The maximum energy storage density at room temperature has been achieved to be 190.35 mJ/cm 3 for x = 0.005 at an applied electric field of 55 kV/cm. The highest efficiency of about 60.5 % has been obtained for Cr content "x = 0.015" at 10 kV/cm.

Effect of temperature on energy storage properties
Temperature-dependent stability is a significant feature that needs to be considered for the practical applications of prepared ceramics for energy storage. For this, temperature-induced ferroelectric hysteresis loops have been used to study the variation of energy storage properties with temperature. Fig. 17 (a -c) is a plot of energy storage density (Wrec), energy loss density (Wloss), and efficiency (η) versus temperature change for BCT samples of different Cr contents (x).
It can be seen from Fig. 17 (a -c) that Wrec and η increases with an increase in temperature because of a decrease in Wloss (as P-E loops become thinner with temperature). Table 5

Magnetic Measurements
M-H loops have been analyzed to observe the doping effect of Cr (d n -electrons) on the ferromagnetic property of parent BCT ceramics. The room temperature magnetic field dependence of magnetization for bare and Cr doped BCT ceramic samples is displayed in Fig. 18 (a -e), with an inset of partial amplification at low magnetic fields. Results of the M-H loop reveal that bare BCT sample exhibits diamagnetic behavior with an applied magnetic field, suggesting Ti ions are in 4+ oxidation state with d 0 electrons (empty d-orbitals). In Cr doped BCT samples, M-H loops show both diamagnetism and ferromagnetism at room temperature [51]. At low applied magnetic fields, the feeble ferromagnetic character of ceramic samples is dominant. At a higher magnetic field, the diamagnetic contribution is dominating the magnetic signal in Cr doped BCT samples.
When acceptor Cr 3+ ions are incorporated at the Ti 4+ site of BCT lattice, charge compensation occurs and results in the creation of oxygen vacancies and defect dipoles. The oxygen vacancies or defects in doped BCT ceramics serve as a medium for magnetic interactions and are assumed to induce ferromagnetism [1]. The observed ferromagnetic behavior of prepared ceramic samples at low applied fields revealed that oxygen vacancies provide short-range ferromagnetic exchange interactions and increases with an increase in Cr content [40]. However, at higher fields, high magnetic energy overcomes the short-range exchange interaction energy which is dominated by diamagnetism [40]. Moreover, for the subtraction of sample holder's diamagnetic contribution, the diamagnetic correction has been done to the obtained M-H loops as shown in Fig. 19 (a -d)

Conclusions
The present research focuses on unraveling the effect of Cr doping on structural, morphological, dielectric, ferroelectric, energy storage, and magnetic properties of BCT ceramics.
The XRD patterns confirm that a single-phase tetragonal structure has been formed in all prepared samples. Rietveld analysis of XRD indicates that lattice parameters and unit cell volume decrease with increasing content of Cr. XRD analysis also shows that tolerance factor and crystallite size calculated using Debye-Scherrer and W-H plot methods decreases by increasing the Cr doping content. SEM micrographs display the presence of well-developed polyhedral shaped grains. The grain size of samples decreased with an increase in the concentration of Cr content. For doped samples, temperature-dependent dielectric constant and dielectric loss curves show the presence of defect dipole induced anomaly at lower frequencies in the paraelectric region. All the prepared ceramic samples have been found to exhibit DPT and also the width of DPT has been observed to increase with increased Cr content in BCT lattice. The TCC values lie within ± 15 % along with low dielectric losses (Tanδ < 0.07), which presents the Cr doped BCT ceramics as a potential material for X8R MLCCs. The ferroelectric hysteresis loops show an increasing trend of Pr and Ec with an electric field and a decreasing trend with an increase in temperature. P-E loops reveal the presence of defect dipole effect on the variation of Pr and Ec with Cr content. An overall increase in energy storage parameters such as Wrec, Wloss, and η has been observed with an increasing function of applied electric field and temperature. For ceramic sample with x = 0.005 composition, the highest Wrec ̴ 190.35 mJ/cm 3 at 55 kV/cm has been attained, and maximum storage efficiency of about 60.5 % has been achieved at 10 kV/cm for the sample x = 0.015 at room temperature.
However, ceramic composition with x = 0.015 also presents better temperature-dependent energy storage properties (Wrec ̴ 238.25 mJ/cm 3 , η ̴ 56.01 % at 353 K). Room temperature M-H loop of Cr doped samples shows the ferromagnetism at low magnetic fields and diamagnetism at high magnetic fields. The diamagnetic correction has been applied to the M-H loops to obtain the magnetic parameters such as remnant magnetization (Mr), saturation magnetization (Ms), and coercivity (Hc). The prepared ceramic compositions in this study could be used for possible future multipurpose systems in X8R MLCCs, energy storage applications, and as a multiferroic material.
This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.