## 3 Results and Discussion  
To determine the best composition of the host \((1-x)\)BaTiO\({}_{3}\)-\(x\)(Bi\({}_{0.5}\)Na\({}_{0.5}\))TiO\({}_{3}\) ceramic, formulations with an \(x\) value of 0.05, 0.1, or 0.2 were prepared and characterized. While the sinteringtemperature of BaTiO\({}_{3}\) is typically above 1300 \({}^{\circ}\)C, the addition of (Bi\({}_{0.5}\)Na\({}_{0.5}\))TiO\({}_{3}\) significantly reduced the sintering temperature to 1230 \({}^{\circ}\)C for an \(x\) value of 0.05 and to 1215 \({}^{\circ}\)C for \(x\) values of 0.1 and 0.2, which was caused by the formation of the liquid phase [14,25]. XRD results indicated the presence of the tetragonal BaTiO\({}_{3}\) perovskite phase (tetragonal, P4/mmm; JCPDF 75-0462) with trace amounts of second-phase Ba\({}_{6}\)Ti\({}_{17}\)O\({}_{40}\) (monoclinic, C2/c; JCPDF 77-1566), which increased with the (Bi\({}_{0.5}\)Na\({}_{0.5}\))TiO\({}_{3}\) content. This observation is in accord with those reported in the literature [25,26]. In addition, the peaks corresponding to BaTiO\({}_{3}\) in the XRD patterns shifted to lower angles due to the incorporation of the smaller ions Na\({}^{+}\) (VI; 1.02 A) and Bi\({}^{3+}\) (VI; 1.03 A) in the Ba\({}^{2+}\) (VI; 1.35 A) sites. The lattice constants calculated from XRD patterns appeared to be a = 3.991 A and c = 4.025 A. The dielectric properties of the (\(1-x\))BaTiO\({}_{3}\)-\(x\)(Bi\({}_{0.5}\)Na\({}_{0.5}\))TiO\({}_{3}\) at the maximum density, measured at a frequency of 1 KHz, are listed in Table 1. The Curie point of the (\(1-x\))BaTiO\({}_{3}\)-\(x\)(Bi\({}_{0.5}\)Na\({}_{0.5}\))TiO\({}_{3}\) increased with the (Bi\({}_{0.5}\)Na\({}_{0.5}\))TiO\({}_{3}\) content and was 145 \({}^{\circ}\)C, 170 \({}^{\circ}\)C, and \(>\)200 \({}^{\circ}\)C for \(x\) values of 0.05, 0.1, and 0.2, respectively. This increase occurred because Bi-O bonds are weaker than Ba-O bonds, the substitution of Bi\({}^{3+}\) into Ba sites leads to strengthened Ti-O bonds, and more energy is needed to maintain the balance of Ti\({}^{4+}\) displacement in the TiO\({}_{6}\) octahedrons; thus, \(T_{\rm c}\) increased [14,15,19]. The dielectric constant of (\(1-x\))BaTiO\({}_{3}\)-\(x\)(Bi\({}_{0.5}\)Na\({}_{0.5}\))TiO\({}_{3}\) at 25 \({}^{\circ}\)C decreased from 2066 to 677 while the tan\(\delta\) value increased from 2.9% to 3.5% as the \(x\) value increased from 0.05 to 0.2. The TCC at the cold end (\(-\)55 \({}^{\circ}\)C) decreased slightly from \(-\)20.8% to \(-\)24.6%, whereas the TCC at the hot end (200 \({}^{\circ}\)C) significantly increased from 27.0% to 641.0%, which was simply due to the increase in \(T\)c. Because a high dielectric constant, a low tan\(\delta\) value, and a stable TCC areneeeded for X9R materials, the 0.9 BaTiO\({}_{3}\)-0.1(Bi\({}_{0.5}\)Na\({}_{0.5}\))TiO\({}_{3}\) ceramic was selected as the host material to incorporate the Ta\(\alpha\)s and Nb\({}_{2}\)O\({}_{5}\) additives in this study. Figure 1a shows the sintered densities of 0.9 BaTiO\({}_{3}\)-0.1(Bi\({}_{0.5}\)Na\({}_{0.5}\))TiO\({}_{3}\) ceramics with 1.0%, 1.5%, and 2.0% Ta\(\alpha\)s sintered at different temperatures. In all cases, the sintered density increased the sintering temperature, and the maximum densification was reached at 1215 \({}^{\circ}\)C. With further increases in sintering temperature, the sintered density gradually declined because of the trapped porosities associated with the fast grain growth and partly the evaporation of the volatile species such as bismuth and sodium. The weight losses of the Ta\(\alpha\)O\({}_{5}\)-doped 0.9 BaTiO\({}_{3}\)-0.1(Bi\({}_{0.5}\)Na\({}_{0.5}\))TiO\({}_{3}\) ceramics during sintering were found to be less than 1.5 wt% through careful monitoring in this study, suggesting that the deviations of the sintered compositions from the nominal composition were only slight. The sintered density of the ceramics decreased slightly with an increase in Ta\(\alpha\)O\({}_{5}\) content, though Ta has a high molecular weight than the substituted Ti.