## 3 Results and Discussion
### The Piezoelectric and Dielectric Properties of PZT-BYS(\(x\)) Ceramics
Therefore, in the present work, A-site vacancies reduce the concentration of intrinsic oxygen vacancies during sintering and introduce lead vacancies to maintain the charge neutrality. These cation vacancies would, therefore, increase the mobility of the domain wall [26]. The change in the mobility of the domain wall by cation vacancies improves the \(d_{33}\), because displacement is sufficient. Therefore, \(d_{33}\) increases with increasing Sb\({}_{2}\)O\({}_{3}\) content due to the increased concentration of the second phase in the PZT-BYS(\(x\)) system. This increase in \(d_{33}\) by doping was also observed in a typical soft type of PZT system [26; 27]. On the contrary, the value of \(k_{\rm p}\) reached the maximum value of 66.0% at \(x=0.1\), whereby it decreased slightly on further addition of Sb\({}_{2}\)O\({}_{3}\). The grain size effect could be the predominant factor in this case. [PERSON] and [PERSON] [28] reported that Nb and partially substituted Sb-doped PZT shows the maximum electrical properties at a grain size of 2-3 \(\upmu\)m. The deterioration of \(k_{\rm p}\) with decreasing grain size is probably related to the fewer domains and less mobile domain walls. As a result, a slight decrease in \(k_{\rm p}\) was observed at higher Sb\({}_{2}\)O\({}_{3}\) (\(x>0.1\)) contents. Figure 6b shows the variation of \(\varepsilon_{33}\)T and grain size as a function of Sb\({}_{2}\)O\({}_{3}\) contents. It is clear that \(\varepsilon_{33}\)T varies from those of the piezoelectric properties. The \(\varepsilon_{33}\)T sharply decreases as the grain size decreases from \(\sim\)2.5 \(\upmu\)m (at \(x=0\)) to 2.2 \(\upmu\)m (at \(x=0.1\)), while it increases slightly with a decreasing grain size of \(\sim\)1.7 \(\upmu\)m at \(x=0.2\). A further increase in the Sb\({}_{2}\)O\({}_{3}\) content decreases the grain size to \(\sim\)1.4 \(\upmu\)m, and dielectric constants increased sharply. This type of dielectric anomaly was previously explained by the effect of grain sizes [13; 29; 30; 31; 32; 33; 34]. [PERSON] et al. [29] reported that the dielectric constant of BaTiO\({}_{3}\) and PZT could be varied at different ranges of grain size. [PERSON] and [PERSON] [34; 35] reported that \(\varepsilon_{33}\)T at room temperature increases within a critical range of grain size. Similar behavior was also explained by many earlier investigations of grain size effects [35; 36]. They reported that there was a microstructure transition region between 1.3 \(\upmu\)m and 2.7 \(\upmu\)m. Within this range, \(\varepsilon_{33}\)T decreases with decreasing grain size and increases with increasing grain size [36]. Therefore, in the present work, \(\varepsilon_{33}\)T decreases with the PZT-BYS(0.1) composition because grain size decreases from \(\sim\)2.5 \(\upmu\)m to 2.2 \(\upmu\)m. As the grain size decreases below critical values, the structure is changed, and the internal stress would be expected to increase. This in turn suggests that the dielectric constant increases with decreasing grain size for higher Sb\({}_{2}\)O\({}_{3}\) content. Further evidence for the Sb\({}_{2}\)O\({}_{3}\) doping and grain size effects are obtained by examining the polarization-electric field (\(P\)-\(E\)) curve at room temperature and shown in Figure 7a. The values of \(P_{\rm r}\) and \(E_{\rm c}\) are determined from the measured \(P\)-\(E\) loops. The variation of \(P_{\rm r}\) and \(E_{\rm c}\) for undoped and Sb\({}_{2}\)O\({}_{3}\)-doped PZT-BYS(\(x\)) samples sintered at optimum temperatures are shown in Figure 7b. At 0.1 moles of Sb\({}_{2}\)O\({}_{3}\) content, a relatively higher \(P_{\rm r}\), and lower \(E_{\rm c}\) were observed. The relatively higher \(P_{\rm r}\) and lower \(E_{\rm c}\) at \(x=0.1\) could be explained by high mobility of domain walls achieved by suppression of the oxygen vacancies. Upon further increase of Sb\({}_{2}\)O\({}_{3}\) content, \(E_{\rm c}\) and \(P_{\rm r}\) increases sharply.