Impedance Spectroscopy and AC Conductivity Analysis of (Ba1−kCak)(Zr0.1Ti0.9)O3, (0.140 ≤ k ≤ 0.160), Ceramics

Ceramic pellets of (Ba1−kCak)(Zr1−zTiz)O3, (k = 0.140–0.160, z = 0.9) were prepared via solid-state reaction technique followed by double sintering. The impedance measurements were carried out at different temperatures and frequencies (12–1000 kHz). The NTCR nature exhibits the semiconducting behavior of the prepared BCZT ceramics in the measured temperature range. The temperature also has a considerable impact on the relaxing process. The characteristics of Nyquist plots show that bulk and grain boundary effects exist in BCZT ceramics. The bulk conductivity indicates an Arrhenius-type thermally activated process. The observed impedance spectra, relaxation behavior, and AC conductivity of the prepared compositions of BCZT ceramics will extend the possibilities for using this compound in various optoelectronic applications.

An AC impedance method has been widely used to characterize the electrical properties of the compounds or materials.Extensive research on some ferroelectric materials belonging to the ABO 3 structural family has revealed that they have a high dielectric constant (K) and low dielectric loss, 1 which are useful for piezoelectric transducers, thermally stable ceramic capacitors, PTC devices, sensors, and actuators, microwave applications etc. [1][2][3][4] Physical qualities such as tangent loss/dielectric constant, piezoelectric and pyroelectric properties, which are dependent on the type and class of materials as well as their synthesis technique, determine the applicability of materials for devices.Because of their strong dielectric characteristics and minimum tangent loss, various ceramic compounds have been investigated as potential compounds for RT applications.][7][8][9][10] One of the important compound is barium calcium zirconate titanate (Ba 1−k Ca k )(Zr 1−z Ti z )O 3 .They were used extensively owing to their large dielectric and piezoelectric constant.Optimizing these materials necessitates a thorough understanding of grain boundary behavior and the impact of microstructural characteristics. 1,11The electrical and structural properties in various oxides can be characterized using impedance spectroscopy method.This makes it easier to distinguish between the contributions of electro-active areas like bulk and grain boundary effects.Impedance spectroscopy provides an explanation for the electrical actions that take place in a system when an AC signal is applied as an input signal.The output response is shown as a series of semicircles on a complex plane plot, indicating electrical phenomena introduced by the bulk material, grain boundary effect, and interfacial polarization.Sen and Choudhary investigated the Sr doped BaZr 1−z Ti 0.95 O 3 (z = 0.95) ceramics which exhibits Debye-like relaxation. 12The relaxation process significantly depends on temperature.Computation of the relaxation time, relaxation frequency and activation energy from the imaginary portion of the impedance spectra was made using the Arrhenius plot (ln(τ p ) vs 1000/T). 13lso, the possible reason behind the relaxation process may be the existence of defects in the higher temperature region and electrons/ immobile species at low temperatures.Badapanda et al. observed the relaxor-like characteristics in BaZr 0.25 TiO 3 ceramic. 14The applied stresses on the grains or the inhomogeneous distribution of Zr 4+ ions at the B-site may be the reason for this kind of relaxation characteristic.A review of the literature reveals that Pb-based compounds, such as PbTiO 3 (ferroelectric), PbZrO 3 (antiferroelectric), and others, have been the subject of extensive research because they are useful for a variety of device applications. 12However, small work was done on the analysis of spectroscopy of (Ba 1−k Ca k )(Zr 1−z Ti z )O 3 ceramics.6][17][18] Also, optoelectronic properties of perovskites with various A-site and Bsite dopants have already been investigated. 11,15Moreover, the optical properties such as band-gap, refractive index, absorbance and transmittance etc. can be significantly changed by varying the annealing temperature of the prepared films of (Ba 1−k Ca k )(Zr 1−z Ti z )O 3, (k = 0.155, z = 0.9) ceramic. 19Also, improved dielectric constant and low leakage current density were observed for higher annealing temperatures. 19Comparatively leadfree perovskite ferroelectric (Ba 1−k Ca k )(Zr 1−z Ti z )O 3 may be a promising material for optoelectronic and other applications like optical coatings, band-gap engineering, memory devices, etc.
Currently, samples of (Ba 1−k Ca k )(Zr 1−z Ti z )O 3, (k = 0.140--0.160,z = 0.9), ceramics have been made using the solid-state reaction method with double sintering at 1300 °C for 4 h per cycle.A sophisticated impedance spectroscopy approach was used to investigate the electrical characteristics of (Ba 1−k Ca k )(Zr 1−z Ti z )O 3 ceramics with the help of bulk and grain boundary effects.The preparation methodology of BCZT ceramics and their dielectric properties, structure, SEM images, piezoelectric properties has been described in a previous communication. 6

Impedance Spectroscopy
The variation of the real part of impedance (Z′) with frequency for the prepared samples of (Ba 1−k Ca k )(Zr 0.1 Ti 0.9 )O 3, (0.140 ⩽ k ⩽ 0.160), ceramics is presented in Figs.1a-1e.The magnitude of Z′ is large at low frequencies, and it decreases with increasing frequency for all temperatures.The magnitude of Z′ was found to decrease with an increase in temperature indicating that the material has a typical negative temperature coefficient of resistance (NTCR). 20The variation of Z′ exhibits a small plateau nature at the lower frequency side.Generally, two plateau zones, one at high frequency and the other at low frequency, should be used to represent the compound's bulk reaction and grain boundary, respectively.The bulk and grain boundary significantly affect the electro-ceramic properties of the BCZT ceramics.In this current study, only one small plateau in the lower z E-mail: d.biswas@hnbgu.ac.in; jhinkwan.surendra@gmail.com;prolay28sharma@gmail.com frequency region was observed.Moreover, the grain boundary response of the BCZT ceramics is usually attributed to the observed low frequency plateau.Furthermore, the grain boundary resistance is increased significantly as the Ca concentration increases.The value of Z′ drops as the trapped charge density lowers and the mobility of charge carriers increases as temperature rises.This sort of behaviour is often attributed to the combined action of dipolar, electrical, and orientation polarization. 21The graphs tend to blend at a higher frequency.After a specific frequency in the upper frequency zone, the values of Z′ are almost similar for all temperatures, which might be due to the probable release of space charge.It represents a larger value of AC conductivity in the high frequency domain for higher temperatures owing to changing barrier characteristics and the release of space charge. 22igures 2a-2e exhibits the variation of the loss spectrum (Z′) with frequency.From the observed impedance loss spectrum, a single peak was examined at the lower frequency side.The observed magnitudes of loss spectra were found to decrease gradually with the rise in frequency ECS Advances, 2023 2 042001 and, hence, merge in the high frequency domain.For the prepared compositions, the loss spectra of the BCZT ceramics exhibit constant value in the high-frequency region.The peak positions have been shifted towards the high frequency side.Also, a decrease in the peak height was observed with the increase in temperature.The broadening and shifting of the peak position exhibit the behavior of relaxation peak, which is associated with the spread of relaxation time with the different time constants. 23The relaxation time is a temperature-dependent entity.The peaks were shifting towards the higher frequency side, and the decrease in peak height may be attributed to the total area conservation.This indicates thermally activated electrical response of charge carriers within the material.The observed broadening of the peaks shifts towards the high frequency region with increasing temperature, exhibiting that there is a distribution of relaxation time.The relaxing ECS Advances, 2023 2 042001 process is influenced by the temperature.Variation of relaxation frequency with temperature confirms it, which means relaxation time is not constant over the entire temperature range.The mean relaxation is temperature-dependent.The contribution of localized relaxation is mostly assigned by relaxation time. 24A non-Debye type dielectric relaxation was observed due to the broadening of the peak results and the spreading of relaxation time over a wide frequency range. 25The time interval between the applied field and polarization in the material is often characterized as relaxation time (τ p ), which may be determined using the equation ω p τ p = 1, where ω p (=2πf p ) signifies relaxation frequency.In this study, the relaxation frequency was selected corresponding to the peak location in the loss spectrum plot at various temperatures, and τ p was computed using the equation ω p τ p = 1.The Arrhenius relation τ p = τ o exp(−E a /k b T) describes the variation of relaxation time with temperature, where T, K, E a , τ o stand for absolute temperature, Boltzmann constant, activation energy, and pre-exponential factor, respectively.Moreover, the observed relaxation peak is mainly attributed to the grain boundary response at low frequencies.It is discovered that as the Ca content increases, the peak height corresponding to the grain boundary also increases at a given temperature.
Figure 3 exhibits the variation of τ p with 1000/T for the compositions of the prepared (Ba 1−x Ca x )(Zr 0.1 Ti 0.9 )O 3 samples.For the prepared compositions, the activation energy (E a ) is calculated from the linearly fitted graph.It has been given in Table I.The presence of some relaxation species in the conduction process is indicated by the modest value of E a , which also confirms the participation of ionic conduction and perhaps ion hopping (Ca 2+ ) in relaxation.
Figure 4 indicates the complex impedance spectra for the prepared compositions of (Ba 1−k Ca k )(Zr 0.1 Ti 0.9 )O 3 ceramics.A complete and symmetric semicircular arc is not always produced by the Cole-Cole plot.It may deviate from ideal Debye type relaxation if relaxation mechanism differs.Here, two semicircular arcswereobserved with their centre underthe real axis, which indicates relaxation process does not follow Debye-type relaxation.Furthermore, the bulk effect may be the responsible factor. 26The radii of these semi-circles indicate the grain resistance (R g ) and grain boundary resistance (R gb ) values, respectively.In comparison to grain resistance, a higher radii value for the second semi-circle (Fig. 4) clearly indicates a larger grain boundary resistance (R gb ).The radius of the semicircles was found decreasing with an increase in temperature, indicating the semiconducting behavior of the material.It also indicates an increase in conductivity due to easier space charge mobility. 27Such characteristics clearly show that the charge transportation process is thermally activated and corroborate the material's semiconducting behavior throughout a wide temperature range.To investigate the complex impedance spectra, an equivalent circuit is required.Further, the impedance data was fitted by using Zview software to characterize the response from the different regions separately.Two parallel resistance-capacitor (RC) elements connected in series yielded an equivalent circuit. 27Each combination of RC elements is associated with grains and grain boundaries, respectively.To overcome dispersion and non-linearity, the CPE (constant phase element) is usually used. 28,29or the prepared compositions, the bulk and grain boundary responses can be represented by two semicircular arcs on the Nyquist plot.The bulk's electrical characteristics reflect the higher frequency semicircle, while the grain boundary responsecharacterizes the lower frequency semicircle. 27The bulk and grain boundary effects significantly dominate the electro-ceramic properties of the BCZT samples.As the intercept points on the Z′ axis migrate closer to the origin with rising temperature, the resistive characteristic decreases for the prepared compositions.Grain boundary and bulk contribute significantly to the impedance spectra at lower and higher order frequencies, respectively.
For all the prepared compositions, the AC electrical conductivity has been shown in Figs.5a-5e.The electrical conductivity is frequency independent in the low frequency zone at a given temperature, and the value increases as the temperature rises, which is related to the DC conductivity of semiconducting materials. 6At low frequencies, the electric field is unable to disrupt the hopping process, and the long-range mobilizations of charge carriers are responsible for such a plateau region.At higher temperatures, this effect is more pronounced.This recommends that BCZT ceramics are semiconducting in nature.Transportation of charge carriers between different localized states increases with frequency, which results in an increase in AC conductivity at high frequencies. 30or the prepared compositions, the real and imaginary values of electric modulus were observed at various frequencies.The variation of the real (M′) and imaginary (M″) parts with frequency was shown in Figs.6a-6e and 7a-7e, respectively.The magnitude of M′ becomes nearly constant at higher frequencies, while the value of M′ is very low at low frequencies.The variation of M′ exhibits a "step-like" increase that gradually moves with a positive slope towards the high frequency side as temperature rises.The imaginary portion of electric modulus was discussed.For the prepared compositions, an increase in the peak height of M″ was observed with the increase in temperature.The decrease in capacitance with rising temperature reflects an increase in the peak height of M″.As the temperature increases, the peaks were moved to the side of higher frequency.The shifting and widening of the peak position demonstrate the behavior of the relaxation peak, which is connected to the variation in relaxation time constants. 31he ions, or charge carriers, cannot follow the path at the high frequency of the input signal, while they can easily follow it at low frequency.The charge carriers' mobility is constrained, and they cannot go longer distances at frequencies above the peak, but they may travel vast distances at frequencies below the relaxation peak.The observed electric modulus spectrum exhibits a difference in the motion of charge carriers, which may suggest a hopping mechanism exists in the samples.][34] Ca doping appears to reduce the magnitude of the relaxation peaks.

Conclusions
The impedance spectroscopy analysis of (Ba 1−k Ca k )(Zr 1−z Ti z )O 3, (k = 0.140-0.160,z = 0.9) ceramics have been systematically observed.According to the electrical properties, the compound displays bulk and grain boundary effects, negative temperature coefficient of resistance (NTCR) nature, and temperature-dependent relaxation phenomena.The activation energies derived from the relaxation time pattern show that the conduction mechanism contains some relaxation species.

Figure 3 .
Figure 3.An Arrhenius plot was used to activation energy (E a ) of (Ba 1−k Ca k )(Zr 0.1 Ti 0.9 )O 3 ceramics, for different compositions (k).

Table I .
Activation energy of the prepared (Ba 1−k Ca k )(Zr 0.1 Ti 0.9 )O 3 samples.