## 1 Introduction
The requirements for an ultrasonic device are that the electromechanical coupling coefficient \(\mathbf{k}_{\mathrm{t}}\) in the thickness direction must be large, the loss at high frequencies must be small, and the thickness mode mechanical quality coefficient \(\mathrm{Q}_{\mathrm{mt}}\) must be large to increase selectivity. And also, the requirement for an ultrasonic transducer is that the dynamic ratio (D.R) showing a measure of the impedance difference between resonance and anti-resonance must be large to sustain its stable driving condition. A composition with a high anisotropy (kt/kp) of the electromechanical coupling coefficient of piezoelectric materials is advantageous for transformers, filters, and resonators that operate in the thickness direction. Conventional piezoelectric Pb (Zr,Ti)O\({}_{3}\) system ceramics have been widely used as the application devices such as piezoelectric actuators, piezoelectric transformers, and ultrasonic transducers for ultrasonic physical therapy machines [9; 10; 11; 12; 13; 14; 15]. Particularly, ultrasonic transducers for nondestructive testing and ultrasonic physical therapy machines require a higher kp for further increasing the electromechanical conversion efficiency in case of using the radial vibration mode. In the conventional Pb (Zr,Ti)O\({}_{3}\) system ceramics, the radial vibration mode electromechanical coupling factor (kp) and thickness vibration mode electromechanical coupling factor (kt) are almost the same; accordingly, unwanted vibration in the radial vibration mode can occur in case of using a high-frequency ultrasonic device. Therefore, the PbTiO\({}_{3}\) system ceramics with a high anisotropy of kt/kp is good for making a high-frequency thickness vibration mode ultrasonic device [16; 17; 18; 19; 20; 21; 22; 23; 24; 25]. In particular, as presented in [PERSON]'s paper [25], PZT composition ceramics in case of using a low-frequency transducer have high values of d\({}_{31}\),d\({}_{33}\), kp, and kt in the length and thickness vibration mode, simultaneously. However, PbTiO\({}_{3}\)-based ceramics have a high Curie temperature due to the large anisotropy of the electromechanical coupling coefficient, and cracks occur when the Curie temperature falls, making it difficult to sinter. To alleviate the anisotropy, the substituent La\({}^{3+}\) and Sm\({}^{3+}\) ions can be substituted for the Pb\({}^{2+}\) site, taking into consideration the ion radius [26]. To decrease the sintering temperature of PNN-PMN-PZT, PMW-PNN-PZT and PNN-PZT ceramics, sintering aids such as CuO, CaCO\({}_{3}\), PbO, Sb\({}_{2}\)Oand Li\({}_{2}\)CO\({}_{3}\) can be added to the main compositions [21; 22; 23; 24; 25; 26; 27]. In this study, to develop the composition ceramics for the applications of an ultrasonic transducer device for alleviating temporomandibular joint disorder pain, PbTiO\({}_{3}\) system ceramics for removing unwanted vibration in the radial vibration mode were manufactured using CuO as sintering aids, and their piezoelectric and resonant properties were investigated. Also, ultrasonic piezoelectric devices were designed with different dimensions. Resonant and piezoelectric characteristics were measured by varying the side length of the piezoelectric device to 3.5, 4.9, 6.3, 7.7 and 9.1 mm, respectively.