# Electrophysical Properties of PZT-Type Ceramics Obtained by Two Sintering Methods
## 3 Results and Discussion
The values of all parameters describing the hysteresis loop, i.e., the coercive field (\(E_{\mathrm{c}}\)), residual polarization (\(P_{\mathrm{r}}\)), and maximum polarization (\(P_{\mathrm{m}}\)), increase with increasing temperature in the whole measuring range. In the 50-110 \({}^{\circ}\)C temperature range, the S-PS ceramic sample shows the best saturation of the hysteresis loop compared to the sample obtained with hot pressing (S-HP). The ferroelectric parameters \(P_{\mathrm{m}}\), \(P_{\mathrm{r}}\), and \(E_{\mathrm{c}}\) (Figure 7c) are similar for both ceramic samples. However, above 50 \({}^{\circ}\)C, the S-PS ceramic sample has slightly higher values of the set parameters mentioned above, and the \(P\)-\(E\) hysteresis loops show high saturation. Figure 7d shows the hysteresis loops of the obtained ceramic materials at room temperature (with low \(P_{\mathrm{m}}\) maximum polarization of 12.24 \(\mu\)C/cm\({}^{2}\) for S-PS and 13.47 \(\mu\)C/cm\({}^{2}\) for S-HP). These \(P\)-\(E\) loops are typical for dielectric materials with losses and medium ferroelectric hardness. The saturation of the ferroelectric hysteresis loops \(P\)-\(E\) is achieved only by increasing the temperature. At the same time, the maximum polarization increases almost threefold, and, at the temperature of 110 \({}^{\circ}\)C, \(P_{\mathrm{m}}\) is 28.02 \(\mu\)C/cm\({}^{2}\) for S-HP and 30.83 \(\mu\)C/cm\({}^{2}\) for S-PS. The maximum polarization \(P_{\mathrm{m}}\), residual polarization \(P_{\mathrm{r}}\), and coercive field \(E_{\mathrm{c}}\) parameter values of the tested ceramic samples are listed in Table 1.  
Figure 6: Frequency dependencies of real \(\varepsilon^{\prime}\) (**a**,**c**) and imaginary \(\varepsilon^{\prime\prime}\) (**b**,**d**) parts of the dielectric constant at different temperatures for the S-PS and S-HP ceramic samples. Figure 7: _Cont._  
The S-PS and S-HP samples at room temperature show high \(\rho_{\text{DC}}\) resistivity values of 1.20 \(\times\) 10\({}^{9}\)\(\Omega\)m and 1.51 \(\times\) 10\({}^{9}\)\(\Omega\)m, accordingly. Figure 8 shows the relationship \(\ln\)\(\sigma_{\text{DC}}\)(1000/\(T\)) for the analyzed ceramic samples. During the heating cycle, the DC conductivity \(\sigma_{\text{DC}}\) values of the ceramic samples systematically increase, which is related to the increased drift mobility of thermally activated charge carriers [57]. Changes in the slope occurring in the \(\ln\)\(\sigma_{\text{DC}}\)(1000/\(T\)) diagram are caused by a change like the electrical conductivity of the ceramic samples. The DC conductivity in ferroelectrics is predominantly associated with oxygen vacancies, cation vacancies, and defect dipolar effects [58]. At low temperatures, the dominant factor is the ionization process, for which electrons and holes are responsible. In turn, the mobility of extrinsic defects at higher temperatures is responsible for electrical conductivity, which increases at higher temperatures [59]. The activation energy (\(E_{\text{a}}\)) values were calculated according to the Arrhenius law (1) and from the slope of the \(\ln\)\(\sigma_{\text{DC}}\)(1000/\(T\)) plot. \[\sigma_{\text{DC}}=\sigma_{0}e^{-\frac{E_{\text{a}}}{E_{\text{B}}T}} \tag{1}\]  
where: \(\sigma_{0}\)--pre-exponential factor, \(k_{\text{B}}\)--Boltzmann constant, \(E_{\text{a}}\)--activation energy, \(T\)--absolute temperature [60]. The calculated activation energy (\(E_{\text{a}}\)) values are shown in Figure 8 and Table 1. The calculated \(E_{\text{a}}\) values for the ceramic samples indicate mainly electric conductivity dominated by oxygen vacancies [58], which may be related to the loss of oxygen during the sintering process at high temperatures. Figure 8: The \(\ln\)\(\sigma_{\text{DC}}\)(1000/\(T\)) relationship for S-PS and S-HP.