## 3 Results and Discussion  
Figure 2 shows the X-ray diffraction patterns of Pb\({}_{0.88}\)(La\({}_{0.6}\) Sm\({}_{0.4}\))\({}_{0.08}\)(Mn\({}_{1/3}\) Sb\({}_{2/3}\))\({}_{0.02}\) Ti\({}_{0.98}\) O\({}_{3}\) ceramics sintered at 1200 \({}^{\circ}\)C and 1230 \({}^{\circ}\)C. The fabricated samples exhibited a pure perovskite phase, and a few secondary phases are observed in the XRD measurement range. Additional studies on the secondary phases are necessary. The ceramic specimens possess a tetragonal phase, which is characterized by the tetragonal (002) and (200) peaks between 40\({}^{\circ}\) and 50\({}^{\circ}\). Figure 2 shows the microstructure of PbTiO\({}_{3}\) system ceramics sintered at 1200 \({}^{\circ}\)C and 1230 \({}^{\circ}\)C. At the 1180 \({}^{\circ}\)C temperature, which is less than 1200 \({}^{\circ}\)C, the ceramics was not poled. So, two sintering temperature were only selected. The average grain size of the ceramics sintered at 1200 \({}^{\circ}\)C and 1230 \({}^{\circ}\)C was 2.83 m and 1.26 m, respectively. As the La\({}^{3+}\) and Sm\({}^{3+}\) ions are substituted for the Pb site, one Pb ion is removed for two La\({}^{3+}\) and Sm\({}^{3+}\) ions, creating a vacancy at the A site in the ABO\({}_{3}\) structure, increasing diffusion flux and promoting the sintering of the ceramics. In addition, the density and the mechanical strength increase. As can be seen in Figure 3, the densified grain appeared at the ceramics sintered at 1200 \({}^{\circ}\)C. In case of the ceramic specimens sintered at 1230 \({}^{\circ}\)C, the grain growth was more restrained on account of the over-firing condition. The specimens sintered at 1200 [\({}^{\circ}\)C] had a dielectric constant (\(\varepsilon_{\rm r}\)) of 202, piezoelectric constant (d\({}_{33}\)) of 56 [pC/N], first and third overtone electromechanical coupling factors k\({}_{\rm t1}\) of 0.548 and k\({}_{\rm t3}\) of 0.219, and then first and third overtone mechanical quality factors Qmt1 of 345 and Qm\({}_{\rm t3}\) of 292, making it more suitable than the specimens sintered at 1230 \({}^{\circ}\)C for device application as an ultrasonic transducer. The specimens sintered at 1230 \({}^{\circ}\)C had a dielectric constant (\(\varepsilon_{\rm r}\)) of 229, first and third overtone electromechanical coupling factors k\({}_{\rm t1}\) of 0.544 and k\({}_{\rm t3}\) of 0.29, and then first and third overtone mechanical quality factors Qm of 94.3 and Qm\({}_{\rm t3}\) of 67.8. In this study, the piezoelectric and resonant properties of the ultrasonic device are important in the first and third vibration modes. Figure 4 shows the resonant properties with sintering temperature in the piezoelectric device. A vibrator using PbTiO\({}_{3}\)-based ceramics generates 1 st, 3 rd, and 5 th order resonance modes in the thickness direction vibration mode, and it is possible to manufacture a resonator using a higher-order vibration mode. For the specimens sintered at 1200 \({}^{\circ}\)C, the excellent resonant properties appeared because of the high Qmt1 of 345 and high D.R of 74.1 dB in the first vibration mode around 3 MHz and the high Qmt3 of 292 and high D.R of 38.11 dB in the third vibration mode around 9.8 MHz, respectively. Figure 5 shows the resonant properties with the side length of the piezoelectric device. The ultrasonic energy is very effective at enhancing microcirculation and improving the metabolism by increasing the tissue temperature through the generation of its thermal energy. And ultrasonic energy can be delivered to the subcutaneous fat cells to break down the fat's cells, reducing the amount of subcutaneous fats [27]. Accordingly, various kinds of ultrasonic transducers can be used for the piezoelectric device mounted with an ultrasonic physical therapy machine and facial massage. The requirement for an ultrasonic transducer is that the dynamic ratio (D.R), which is a measure of the impedance difference between resonance and anti-resonance, must be large [16].