Electrical Characteristics of Ultrasonic Piezoelectric Devices Using Pb_0.88 (La_0.6 Sm_0.4)_0.08 (Mn_1/3 Sb_2/3)_0.02 Ti_0.98 O₃ Ceramics for Alleviating Temporomandibular Joint Disorder Pain

Abstract

In this study, to develop the composition ceramics for the application of an ultrasonic transducer device for alleviating temporomandibular joint disorder pain, Pb_0.88 (La_0.6 Sm_0.4)_0.08(Mn_1/3 Sb_2/3)_0.02Ti_0.98 O₃ ceramics were manufactured using CuO as sintering aids, and their piezoelectric and resonant properties were investigated. For the specimen sintered at 1200 °C, excellent values of piezoelectric properties appeared: the dielectric constant (εr) of 202, piezoelectric constant (d₃₃) of 56 pC/N, first and third overtone electromechanical coupling factors k_t of 0.548 and k_t3 of 0.219, and first and third overtone mechanical quality factors Q_mt1 of 345 and Q_mt3 of 292, respectively, made the device suitable for application as an ultrasonic transducer. When the length of the piezoelectric device was 7.7 mm, the first and third overtone electromechanical coupling factors k_t1 of 0.555 and k_t3 of 0.196, first and third overtone mechanical quality factors Q_mt1 of 381 and Q_mt3 of 393, and first and third overtone dynamic ratios (D.Rs) of 63.7 (dB) and 37.7 (dB) were suitable for device applications as an ultrasonic transducer and facial skin massage, respectively.

1. Introduction

Temporomandibular joint disorder is defined as a comprehensive term that includes several clinical problems occurring in the temporomandibular joint capsule and tissues within the joint capsule. Temporomandibular joint disorder includes jaw pain during mandibular movement, restriction, and incoordination of mandibular movement. It is accompanied by various symptoms such as joint noise and joint dislocation [1].

Temporomandibular joint (TMJ) disorder is known to be one of the main causes of tooth pain in the orofacial region, and in severe cases, it is highly likely that it will ultimately have a negative impact on quality of life by reducing the ability to chew, which is a basic human need [2]. Although the actual prevalence of temporomandibular joint disorder is not low, patients often do not recognize it and just overlook it, so the timing of accurate evaluation and treatment is missed, leading to chronic pain [3]. Patients with pain in the TMJ area complain about the pain and functional limitations in the temporomandibular joint area during chewing and mouth opening. If the pain is severe, the opening of the mouth may be restricted [4].

The treatment method for temporomandibular joint disorder includes various methods such as physical therapy, psychological therapy, drug therapy, and surgical therapy.

The primary goal of physical therapy in the patients with temporomandibular joint disorder is to relieve the pain of patients. Heat therapy is a method of relieving pain and promoting healing by applying heat to the painful area using a heating device or ultrasound. Heat therapy is divided into ‘superficial heat therapy’ and ‘deep heat therapy’. Surface heat therapy includes warm compresses and infrared therapy, but the disadvantages are that it is difficult to maintain heat for a long time and that a specific posture must be maintained. On the other hand, ultrasound, which is commonly used among deep heat therapies, increases the temperature inside the tissue and has a deeper effect than surface heat. While moist heat packs or infrared rays cannot penetrate deeper than 1 cm of the skin surface and only increase the temperature of the superficial layer, ultrasound has the advantage of being able to transfer heat up to 5 cm deep under the skin [1,5].

Ultrasound using the piezoelectric phenomenon can control vibration from 1 million to 100 million times per second. The subtle vibration effect can provide a micro-massage effect deep into the human body, and in addition, it promotes the flow of blood and lymphs, activating cell activity and activating the immune system [6].

In a previous study about the thermal effect depending on the material of the transducer of an ultrasonic therapy device [7], there were differences in the surface temperature and core temperature measurements depending on the material of the ultrasonic transducer, and the average temperature rise rate also differed. Therefore, even if an ultrasonic piezoelectric vibrator of the same size is used in the same ultrasonic therapy machine, the actual irradiated output value may differ depending on the transducer material. This suggests that there are various considerations when performing ultrasound treatment.

In general, a temporomandibular joint ultrasound therapy device uses ultrasound waves with wavelengths of 1 MHz and 3 MHz to generate the heat inside the tissue, thereby promoting blood circulation and increasing cell regeneration. So, the ultrasound therapy method can help heal the temporomandibular joint.

In particular, for application as an ultrasonic facial massager, their operating frequency can be increased up to 10 MHz to infiltrate into the surface of skin. In order to increase the operating frequency of the ultrasonic transducer device to MHz, the thickness vibration mode of the piezoelectric ceramics must be used. Their thickness vibration modes include the 1st, 3rd, and 5th order vibration modes, and the higher order vibration mode can be used to further increase the frequency [8]. The requirements for an ultrasonic device are that the electromechanical coupling coefficient k_t in the thickness direction must be large, the loss at high frequencies must be small, and the thickness mode mechanical quality coefficient Q_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)O₃ 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)O₃ 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 PbTiO₃ 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 Antiopi-Malvina Stamatellou’s paper [25], PZT composition ceramics in case of using a low-frequency transducer have high values of d₃₁,d₃₃, kp, and kt in the length and thickness vibration mode, simultaneously. However, PbTiO₃-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 La³⁺ and Sm³⁺ ions can be substituted for the Pb²⁺ 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, CaCO₃, PbO, Sb₂O₅ and Li₂CO₃ 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, PbTiO₃ 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.

2. Experimental Section

The specimens were manufactured using a conventional mixed oxide process. The compositions used in this study were as follows.

Pb_0.88(La_0.6 Sm_0.4)_0.08(Mn_1/3 Sb_2/3)_0.02 Ti_0.98O₃₊ sintering aids (0.25 wt% CuO) were used. The raw materials above 99% purity such as PbO, La₂O₃, Sm₂O₃, MnO₂, Sb₂O₅, and TiO₂ for the given composition were weighted by mole ratio, and the powders were ball-milled for 24 h. After drying, they were calcined at 850 °C for 2 h. Thereafter, 0.25 wt% CuO was added, ball-milled, and dried again. A polyvinyl alcohol (PVA: 5%) was added to the dried powders. The powders were molded by the pressure of 1000 kg/cm² in a mold, which has a diameter of 17 mm, burned out at 600 °C for 3 h, and then sintered at 1200 °C and 1230 °C for 2 h. Density was measured using the Archimedes method. For measuring the piezoelectric and dielectric characteristics, the specimens were polished to 1 mm thickness and then electrodeposited with Ag paste. Poling was carried out at 120 °C in a silicon oil bath by applying DC fields of 40 kV/cm for 30 min. All samples were aged for 24 h prior to measuring the piezoelectric and dielectric properties. The microstructure and crystal structure of specimens were investigated with the aids of a scanning electron microscope (SEM: Model Hitachi, S-2400, Hitachi High-Technologies Corporation, Tokyo, Japan) and X-ray diffractometer (XRD: BRUKER D8 ADVANCE, Bruker, Billerica, MA, USA), respectively. The operation conditions for the X-ray diffractometer are as follows: 0.25 sec time/step (step size: 0.019443897°), scan mode: continuous scan. For investigating the dielectric properties, capacitance was measured at 1 kHz using an LCR meter (ANDO AG-4034, Yokogawa, Japan), and dielectric constant was calculated. For investigating the piezoelectric properties, the resonant and anti-resonant frequencies were measured by an Impedance Analyzer (Agilent 4294A, Keysight Technologies, Santa Rosa, CA, USA) according to the IRE standard [26], and then the electromechanical coupling factor and mechanical quality factor were calculated. Dynamic range (D.R.) was calculated as 20 Log (Za/Zr). Here, Zr is the impedance at the anti-resonant frequency, and Za is the impedance at the resonant frequency. Using the ceramics sintered at 1200 °C and 1230 °C for 2 h, ultrasonic piezoelectric devices were manufactured by circular type (14 Ø × 0.7 mm), using the ceramics sintered at 1200 °C for 2 h. Ultrasonic piezoelectric devices a the fixed thickness of 0.7 mm were manufactured by square type (length × width, length = width). The ultrasonic piezoelectric devices were fabricated by varying the length of the piezoelectric device to 3.5, 4.9, 6.3, 7.7 and 9.1 mm, respectively. Resonant and piezoelectric characteristics were analyzed. Figure 1 show a photograph of the fabricated ultrasonic piezoelectric samples where the side length of each piezoelectric device is apparent against the length scale.

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 O₃ ceramics sintered at 1200 °C and 1230 °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° and 50°. Figure 2 shows the microstructure of PbTiO₃ system ceramics sintered at 1200 °C and 1230 °C. At the 1180 °C temperature, which is less than 1200 °C, the ceramics was not poled. So, two sintering temperature were only selected. The average grain size of the ceramics sintered at 1200 °C and 1230 °C was 2.83 m and 1.26 m, respectively. As the La³⁺ and Sm³⁺ ions are substituted for the Pb site, one Pb ion is removed for two La³⁺ and Sm³⁺ ions, creating a vacancy at the A site in the ABO₃ 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 °C. In case of the ceramic specimens sintered at 1230 °C, the grain growth was more restrained on account of the over-firing condition. The specimens sintered at 1200 [°C] had a dielectric constant (ε_r) of 202, piezoelectric constant (d₃₃) of 56 [pC/N], first and third overtone electromechanical coupling factors k_t1 of 0.548 and k_t3 of 0.219, and then first and third overtone mechanical quality factors Qmt1 of 345 and Qm_t3 of 292, making it more suitable than the specimens sintered at 1230 °C for device application as an ultrasonic transducer. The specimens sintered at 1230 [°C] had a dielectric constant (ε_r) of 229, first and third overtone electromechanical coupling factors k_t1 of 0.544 and k_t3 of 0.29, and then first and third overtone mechanical quality factors Qm of 94.3 and Qm_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 PbTiO₃-based ceramics generates 1st, 3rd, and 5th 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 °C, the excellent resonant properties appeared because of the high Q_mt1 of 345 and high D.R of 74.1 dB in the first vibration mode around 3 MHz and the high Q_mt3 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]. Then, the mechanical quality factor (Q_mt) at the thickness vibration mode is high, and the impedance at the resonance frequency is low, which is advantageous when driven at low voltage. For the treatment of temporomandibular joint disorders, 3 MHz can be utilized for the deep penetration of tissue. Because 10 MHz has a high frequency, it can be used for facial skin massages with slightly less tissue penetration. As can be seen in Figure 4, the resonance peak was large at around 3 MHz, which is the first resonance, and the phase value showing the efficiency of polarization was also over 67°, presenting excellent characteristics. When the side length of the piezoelectric device was 7.7 mm, the highest phase of 83.82° appeared. Figure 6 and Figure 7 show electromechanical coupling factors k_t1 and k_t3 with the side length of the piezoelectric device, respectively. The maximum electromechanical coupling factors k_t1 and k_t3 were increased up to 0.555 and 0.1967 when the side length of the piezoelectric device was 7.7 mm and then decreased, while they slightly decreased at the side length = 6.3 mm. These phenomena are because the optimal condition was found at L/T (length/thickness) = 11, which is like the thickness vibration mode, which corresponds to a thickness-to-diameter ratio of about 10 in the IRE standard.

Figure 8 and Figure 9 show mechanical quality factors Qm_t1 and Qm_t3 with the varying side length of the piezoelectric device, respectively. When the side length of the piezoelectric device was 7.7 mm (L/T = 11), excellent properties appeared. As the size of the ceramic substrate increases, its electrode area expands, which reduces resonance resistance at the resonant frequency and can increase the mechanical quality factor Q_mt.

Figure 10 shows the change in dynamic ratio (D.R) in the first and third vibration modes as the side length of the piezoelectric device changes. As the length of the piezoelectric device increased, the dynamic ratio (D.R) increased up to the side length = 7.7 mm and then decreased.

Their highest values were 63.7 and 37.7 dB at 7.7 mm in the 1st and 3rd vibration modes, respectively, when the length of the piezoelectric device was 7.7 mm (L/T = 11). These results are also because the optimal condition in the thickness vibration mode is a thickness-to-diameter ratio of about 10.

Figure 10. Dynamic ratio (D.R) with varying piezoelectric device side lengths.

Figure 10. Dynamic ratio (D.R) with varying piezoelectric device side lengths.

Here, it can be illustrated that as the high-order mode of the area vibration mode disappeared, unnecessary noise was removed.

Finally, when the side length of the piezoelectric device was 7.7 mm, the parameters were suitable for device application as an ultrasonic transducer, with first and third overtone electromechanical coupling factors k_t of 0.555 and k_t3 of 0.196, first and third overtone mechanical quality factors Q_mt1 of 381 and Qm_t3 of 3938, and first and third overtone dynamic ratios (D.Rs) of 63.7 and 37.7 (dB), respectively.

Table 1. The physical properties of PbTiO₃ system ceramics with sintering temperature.

Sintering Temp.(°C)	Density [g/cm3]	Vibration Mode	fr (MHz)	Fa (MHz)	Zr (Ω)	Za (Ω)	kt	Dielectric Constant	Qmt	D.R. (dB)
1200	7.8	First	3.035	3.315	2.18	11,060	0.5486	202	345	74.1
		Third	9.830	9.955	5.16	419	0.219		292	38.19
1230	7.72	First	3.090	3.370	7.749	2943	0.544	229	94.3	51.59
		Third	9.850	10.090	11.452	99.3	0.299		67.8	18.76

and

Table 2. Pb_0.88(La_0.6 Sm_0.40)_0.08(Mn_1/3 Sb_2/3)_0.02 Ti_0.98O₃ ceramics with varying piezoelectric device side lengths.

The Side Length of Piezoelectric Device (mm)	Vibration Mode	fr (MHz)	Fa (MHz)	Zr (Ω)	Za (Ω)	kt	Qmt	D.R (dB)
3.5	First	3.035	3.260	105.79	25,835	0.499	116	47.7
	Third	9.875	9.935	199.72	2425	0.152	210	21.6
4.9	First	3.005	3.290	80.66	9712	0.555	58.7	41.6
	Third	9.845	9.935	57.30	1500	0.186	232	28.3
6.3	First	3.020	3.275	13.44	2705	0.528	276	46.07
	Third	9.840	9.920	25.19	1545	0.175	422	35.7
7.7	First	3.005	3.290	4.95	7603	0.555	381	63.7
	Third	9.820	9.920	12.145	941	0.196	393	37.7
9.1	First	3.020	3.290	5.89	600	0.541	294	40.1
	Third	9.840	9.920	12.49	584	0.175	417	33.3

show the physical properties of PbTiO₃ system ceramics with sintering temperature and the variation of the side length of the piezoelectric device, respectively.

4. Conclusions

In this experiment, in order to develop the composition ceramics for the application of a thickness vibration mode ultrasonic transducer device with a high k_t, high Q_mt, and high D.R for alleviating temporomandibular joint disorder pain, Pb_0.88(La_0.6 Sm_0.4)_0.08(Mn_1/3 Sb_2/3)_0.02 Ti_0.98 O₃ ceramics were manufactured using CuO as sintering aids, and their piezoelectric and resonant properties were investigated.

• The specimens sintered at 1200 °C and 1230 °C exhibited pure perovskite phase, and few secondary phases were observed.
• For the specimens sintered at 1200 °C, the dielectric constant (ε_r) of 202, piezoelectric constant (d₃₃) of 56 pC/N, first and third overtone electromechanical coupling factors k_{t 1} of 0.548 and k_t3 of 0.219, and first and third overtone mechanical quality factors Q_mt1 of 345 and Qm_t3 of 292 were suitable for the device application as an ultrasonic transducer, respectively.
• When the side length of the piezoelectric device was 7.7 mm, the first and third overtone electromechanical coupling factors k_t of 0.555 and k_t3 of 0.196, first and third overtone mechanical quality factors Qm of 381 and Qm_t3 of 393, and first and third overtone dynamic ratios (D.Rs) of 63.7 and 37.7 dB were suitable for the device applications as an ultrasonic transducer for temporomandibular joint disorder pain relief and facial skin massage, respectively.
• Finally, it is considered that the first vibration mode near 3 MHz was very suitable for device application as an ultrasonic transducer for alleviating temporomandibular joint disorder. In particular, the third vibration mode at 9.8 MHz can be utilized for device application as an ultrasonic transducer for an ultrasonic facial massager. Accordingly, the fabricated piezoelectric device can be simultaneously utilized as 3 MHz and 9.8 MHz ultrasonic generating devices.