## 3 Results and Discussion
### Electrical Properties
A single peak represents a single relaxation process. Our material also showed a single peak at lower temperatures. If a peak is narrow, it represents a narrow relaxation time distribution. Our material demonstrated a relatively narrow peak at 25 \({}^{\circ}\)C, indicating a narrow distribution of relaxation times at this temperature. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**T** (\({}^{\circ}\)**C**) & \(R_{g}\) **(\(\Omega\))** & \(R_{gb}\) **(\(\Omega\))** & \(R_{el}\) **(\(\Omega\))** \\ \hline
25 & 2364 & 605,910 & 190,730 \\ \hline
100 & 217,070 & 2443 & 568,380 \\ \hline
200 & 13,771 & 203 & 73,776 \\ \hline
300 & 14.22 & 13.26 & 4.48 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Grain (\(R_{g}\)), grain boundary (\(R_{gb}\)), and electrode–material interface (\(\mathrm{R_{el}}\)) contributions at different temperatures. The relaxation peaks were due to the presence of immobile species or electrons at low temperatures and defect vacancies at high temperatures [32]. The progressive widening of this peak with the increase in temperature revealed a gradual widening of the distribution, suggesting the various electrical processes during the distribution of relaxation times [34]. From Figure 6, we can observe that the \(Z^{\prime\prime}\) max values decreased with the increase in temperature, indicating a semiconductor behavior of Ca\({}_{2}\)Fe\({}_{2}\)O\({}_{5}\). Except at 25 \({}^{\circ}\)C, the peaks in \(Z^{\prime\prime}\) were found to shift toward a higher frequency as the temperature decreased. This result is opposite to those of other reports, which mentioned a decrease in the relaxation time [35]. The shifting of the peaks with the temperature variation was considered to be due to electrical processes such as conductivities and relaxations at the peak frequencies [36]. Figure 8 shows the variation of the real part (\(Z^{\prime}\)) of impedance with the frequency at the temperature range of 25-300 \({}^{\circ}\)C for Ca\({}_{2}\)Fe\({}_{2}\)O\({}_{5}\). It can be clearly observed from Figure 8 that the \(Z^{\prime}\) value in the low-frequency region was higher at lower temperatures and decreased gradually with an increasing temperature, indicating an increase in the AC conductivity with the increase in temperature. This displays the semiconductive behavior of the material as described in Figure 4. This type of behavior has been reported in several other perovskite oxides and has been regarded as a result of reducing the grains, grain boundaries, and electrode-interface resistance. This is a result of the negative temperature coefficient of the sample resistance [37]. The \(Z^{\prime}\) values started sloping down at a certain frequency (near 1 kHz), and the sloping continued for all temperatures with the increase in frequency. This type of result (i.e., lower values of \(Z^{\prime}\) at higher frequencies) has been seen in many perovskite oxides and has been regarded as a result of the release of space charge polarization. This phenomenon has been considered to be responsible for the enhancement of conductance at high frequencies. As the \(Z^{\prime}\) curve shifts toward a higher frequency, the \(Z^{\prime}\) curves of all the temperatures start merging [36; 37]. The merger of the \(Z^{\prime}\) curves at the higher frequency region is considered to be due to the release of space charges or polarization and due to the reduction in the material's barrier properties with an increasing temperature. It can also be interpreted by the presence of space charge polarization [36; 37]. The positions which were frequency independent in the \(Z^{\prime}\) curves were found to shift toward the higher frequency side at higher temperatures. This type of phenomenon has  
Figure 7: Frequency-dependent imaginary part of impedance (\(Z^{\prime\prime}\)) at various temperatures. already been reported in several other perovskite oxides [32; 38]. It is considered to be due to the frequency relaxation process in the material [32].