# Electrophysical Properties of PZT-Type Ceramics Obtained by Two Sintering Methods
## 3 Results and Discussion
On the other hand, hot sintering (HP) carried out under the assumed technological conditions reduced the value of the maximum permittivity (\(\varepsilon_{\text{m}}\)), increased the blurring of the phase transition (phase transition occurs in a broader range of temperatures), and shifted the temperature phase transition  
Figure 3: The EDS analysis of the S-PS (**a**) and S-HP (**b**) ceramic samples. towards higher temperatures (by 33 \({}^{\circ}\)C). The grain size and microstructure of the ceramic sample influence the permittivity values. This phenomenon in ferroelectric materials was investigated in several studies [52; 53], which showed a decrease in permittivity with a decrease in the average grain size in the microstructure. Table 1 lists the characteristic dielectric parameters for the tested ceramic samples. Figure 4: Temperature dependencies of the permittivity (**a**,**c**) and dielectric loss factor tan\(\delta\) (**b**,**d**) for the S-PS and S-HP samples. Figure 5: Temperature dependences of the permittivity (**a**) and dielectric loss factor (**b**) for the S-PS and S-HP samples measured at 1 kHz. Figure 6 depicts the frequency dependences of \(\varepsilon^{\prime}\) real and \(\varepsilon^{\prime\prime}\) imaginary parts of the dielectric constant for the S-PS and S-HP ceramic samples measured at selected temperatures from the range of 25 to 400 \({}^{\circ}\)C. For both ceramic samples, \(\varepsilon^{\prime}\) (permittivity) and \(\varepsilon^{\prime\prime}\) (dielectric loss) parameters show high values at lower frequencies, and then their values decrease as the frequency increases. In the case of the \(\varepsilon^{\prime}\), this phenomenon is described by the Maxwell-Wager two-layer model for space charge [54], according to which dielectric materials consist of good conducting grains and separated grain boundaries (with poor conductivity). After applying the electric field, the electrons can easily move from inside the grains and accumulate on their boundaries, contributing to the growth of the polarization (dielectric constant increase) [55; 56]. At higher frequencies, electrons from inside the grains change their migration direction much more often, making it difficult to reach the inter-grain boundaries. This results in lower polarization and the dielectric constant of the material decreases [56; 57]. The behavior of the dielectric loss \(\varepsilon^{\prime\prime}\) (Figure 6b,d) is similar to \(\varepsilon^{\prime}\), but the decline of \(\varepsilon^{\prime\prime}\) with increasing frequency is more rapid, which is described in [PERSON]'s double-layer model [57]. Due to the higher resistance of grain boundaries in low frequency, significantly more energy is required for the motion of charge carriers, resulting in higher dielectric loss values. By contrast, in high frequency, due to the lower resistance grain boundaries, less energy is required for the motion of charge carriers, which reduces the dielectric loss values [57]. \begin{table}
\begin{tabular}{c c c} \hline
**Parameter** & **S-PS** & **S-HP** \\ \hline \(T_{\mathrm{m}}\) (\({}^{\circ}\)C) a  & 316 & 349 \\ \(\varepsilon\) a,b  & 959 & 1245 \\ \(\varepsilon_{\mathrm{m}}\) a  & 14,018 & 10,516 \\ tan\(\delta\) a,b  & 0.004 & 0.011 \\ tan\(\delta\) at T\({}_{\mathrm{m}}\) a  & 0.095 & 0.191 \\ \(\rho_{\mathrm{DC}}\) (\(\mathrm{\Omega m}\)) b  & 1.20 \(\times\) 109  & 1.51 \(\times\) 109  \\ \(E_{\mathrm{a}}\) in 1 (eV) & 0.13 & 0.15 \\ \(E_{\mathrm{a}}\) in 1 (eV) & 0.71 & 0.82 \\ \(P_{\mathrm{r}}\) (\(\mu\)C/cm\({}^{2}\)) b  & 3.93 & 3.63 \\ \(P_{\mathrm{m}}\) (\(\mu\)C/cm\({}^{2}\)) b  & 12.24 & 13.47 \\ \(E_{\mathrm{c}}\) (\(\mathrm{kV/mm}\)) b  & 0.83 & 0.79 \\ \hline \end{tabular}
\end{table} 
Table 1: Electrophysical properties of the PZT-type ceramics. Figure 6: _Cont._  
Temperature tests of the \(P\)-\(E\) hysteresis loop of the S-PS and S-HP ceramic samples were recorded at 22-110 \({}^{\circ}\)C (Figure 7a,b).