Bolted Langevin transducers with leadfree piezoelectric ceramics - Scheidemann, Claus; Bornmann, Peter; Littmann, Walter; Hemsel, Tobias
Lead-containing piezoelectric ceramics are still the base for today’s ultrasonic transducers used in broad applications. This is partly due to missing powerful lead-free piezoelectric ceramic parts in the commercial market. There has been much research on lead-free materials but developing them into marketable parts seems to be an ongoing process. The actual exemption of ROHS has expired, but as the new exemption has already been requested, ceramic suppliers keep on selling lead containing products. Nevertheless, these should be replaced by lead-free alternatives for environmental and health issues. This contribution focuses on exploring the technological readiness level of lead-free hard piezoceramics for prestressed ultrasonic transducers. A small series of bolted Langevin transducers was set up with standard PZT material and three commercial lead-free variants. Results of the building process from individual ring ceramic characteristics to transducer load tests are presented. The main finding of this study is that the lead-free materials technically can compete with the standard PZT for medium-power applications. Some adaptations in the ultrasonic system must be done: the geometry must be altered to fit resonance frequency, and higher voltages or thinner ceramics are needed to achieve the same vibration level at low load. For reaching same power, the volume of lead-free ceramics must be 1.5 to 3 times larger. As already promoted in literature, mechanical losses at high vibration levels are smaller for the lead-free materials. This might help to argument lead-free piezoelectric materials in some applications. References 1. Directive 2011/65/EU of the European Parliament and of the Council of 8 June 2011 on the Restriction of the Use of Certain Hazardous Substances in Electrical and Electronic Equipment. EUR-Lex Document 02011L0065-20240801. Available online: http://data.europa.eu/eli/dir/2011/65/2024-08-01 (accessed on 24 January 2025). 2. Langevin, P. (1918) Method and Apparatus for Transmitting and Receiving Submarine Elastic Waves Using the Piezoelectric Properties of Quartz. French Patent Office; Patent No. FR505703. 3. Hemsel, T.; Twiefel, J. (2023) Piezoelectric Ultrasonic Power Transducers. In Encyclopedia of Materials: Electronics; Academic Press: Oxford, UK; pp. 276–285. https://doi.org/10.1016/b978-0-12-819728-8.00047-4. 4. ATHENA Technologie Beratung GmbH (2025) Description of Ultrasound Generator. Available online: http://shop.myathena.de/epages/12074748.sf/de_DE/?ObjectPath=/Shops/12074748/Products/AM200 (accessed on 13 January 2025). 5. Littmann, W.; Hemsel, T.; Kauczor, C.; Wallaschek, J.; Sinha, W. (2003) Load-adaptive phase-controller for resonant driven piezoelectric devices. Proc. World Congr. Ultrason. 2003, 48, 547–550. 6. Scheidemann, C., Bornmann, P., Littmann, W., & Hemsel, T. (2025). Lead-Free Ceramics in Prestressed Ultrasonic Transducers. Actuators, 14(2), 55. https://doi.org/10.3390/act14020055
Keywords: lead free piezoelectric ceramics; bolted Langevin transducer; medium power ultrasound.

Diagnostics of Piezoelectric Bending Actuators Subjected to Varying Operating Conditions - Aimiyekagbon, Osarenren Kennedy; Bender, Amelie; Hemsel, Tobias; Sextro, Walter (Electronics)
In applications of piezoelectric actuators and sensors, the dependability and particularly the reliability throughout their lifetime are vital to manufacturers and end-users and are enabled through condition-monitoring approaches. Existing approaches often utilize impedance measurements over a range of frequencies or velocity measurements and require additional equipment or sensors, such as a laser Doppler vibrometer. Furthermore, the non-negligible effects of varying operating conditions are often unconsidered. To minimize the need for additional sensors while maintaining the dependability of piezoelectric bending actuators irrespective of varying operating conditions, an online diagnostics approach is proposed. To this end, time- and frequency-domain features are extracted from monitored current signals to reflect hairline crack development in bending actuators. For validation of applicability, the presented analysis method was evaluated on piezoelectric bending actuators subjected to accelerated lifetime tests at varying voltage amplitudes and under external damping conditions. In the presence of a crack and due to a diminished stiffness, the resonance frequency decreases and the root-mean-square amplitude of the current signal simultaneously abruptly drops during the lifetime tests. Furthermore, the piezoelectric crack surfaces clapping is reflected in higher harmonics of the current signal. Thus, time-domain features and harmonics of the current signals are sufficient to diagnose hairline cracks in the actuators.
Keywords: piezoelectric transducer; self-sensing; fault detection; diagnostics; hairline crack; condition monitoring

Model-based condition monitoring of piezoelectric bending actuators - Bender, Amelie (Sensors and Actuators A: Physical)
With enhancing digitalization, condition monitoring is used in an increasing number of application fields across various industrial sectors. By its application, increased reliability as well as reduced risks and costs can be achieved. Based on different approaches, technical systems are monitored and measured data is analyzed to enable condition-based or predictive maintenance. To this end, machine learning approaches are usually implemented to diagnose the health states or predict the health index of the monitored system. However, these trained models are often black-box models, not intuitively explainable for a human. To overcome this shortcoming, a model-based approach based on physics is developed for piezoelectric bending actuators. Such a model enables a transparent representation of the system. Moreover, the model-based approach is extended by a parameter-estimation to account for sudden changes in behavior e. g. caused by occurring cracks.
Keywords: Condition Monitoring; Model-based approach Diagnostics; Varying conditions; Explainability; Piezoelectric bending actuators

Piezoelectric Ultrasonic Power Transducers - Hemsel, Tobias; Twiefel, Jens (Reference Module in Materials Science and Materials Engineering)
This article is dedicated to piezoelectric ultrasonic power transducers that differ to well known medical ultrasonic diagnostic apparatus or non destructive testing devices by the level of power in use; typically several tens of up to more than thousand watts are used in a multitude of different applications. After a short introduction including historical development, the first focus is on theoretical background of the operating principle, design and mechanical modeling. As piezoelectric elements transform electrical to mechanical energy and vice versa, equivalent circuit modeling is also described. After that, sample applications are delineated by the matter wherein ultrasound generates unique effects: incredible high pressure level as well in air as in water, micro-bubbles generating temperature peaks for very short time instances in fluids, acoustoplastic effect, enhancement of diffusion and recrystallization in solids, friction manipulation, incremental deformation and micro-cracking of surfaces, or even generation of macroscopic movements in motors. At the end, some future directions ranging from novel modeling approaches to advanced control and new materials are addressed.
Keywords: Equivalent circuit model; Langevin transducer; Lumped parameter model; Piezoelectric transducer; Ultrasonic processes; Ultrasound

A DC bias approach to the characterisation of non-linear material parameters of piezoelectric ceramics - Dreiling, Dmitrij; Feldmann, Nadine; Henning, Bernd
Keywords: piezoelectric materials; piezoelectric properties; DC bias field; non-linear material parameters

Estimation of Remaining Useful Lifetime of Piezoelectric Transducers Based on Self-Sensing - Kimotho, James Kuria; Sextro, Walter; Hemsel, Tobias (IEEE Transactions on Reliability)
Piezoelectric transducers are used in a wide range of applications. Reliability of these transducers is an important aspect in their application. Prognostics, which involve continuous monitoring of the health of technical systems and using this information to estimate the current health state and consequently predict the remaining useful lifetime (RUL), can be used to increase the reliability, safety, and availability of the transducers. This is achieved by utilizing the health state and RUL predictions to adaptively control the usage of the components or to schedule appropriate maintenance without interrupting operation. In this work, a prognostic approach utilizing self-sensing, where electric signals of a piezoelectric transducer are used as the condition monitoring data, is proposed. The approach involves training machine learning algorithms to model the degradation of the transducers through a health index and the use of the learned model to estimate the health index of similar transducers. The current health index is then used to estimate RUL of test components. The feasibility of the approach is demonstrated using piezoelectric bimorphs and the results show that the method is accurate in predicting the health index and RUL.
Keywords: Estimation of Remaining Useful Lifetime of Piezoelectric Transducers Based on Self-Sensing

Improving the bond quality of copper wire bonds using a friction model approach - Althoff, Simon; Neuhaus, Jan; Hemsel, Tobias; Sextro, Walter (Electronic Components and Technology Conference (ECTC), 2014 IEEE 64th)
In order to increase mechanical strength, heat dissipation and ampacity and to decrease failure through fatigue fracture, wedge copper wire bonding is being introduced as a standard interconnection method for mass production. To achieve the same process stability when using copper wire instead of aluminum wire a profound understanding of the bonding process is needed. Due to the higher hardness of copper compared to aluminum wire it is more difficult to approach the surfaces of wire and substrate to a level where van der Waals forces are able to arise between atoms. Also, enough friction energy referred to the total contact area has to be generated to activate the surfaces. Therefore, a friction model is used to simulate the joining process. This model calculates the resulting energy of partial areas in the contact surface and provides information about the adhesion process of each area. The focus here is on the arising of micro joints in the contact area depending on the location in the contact and time. To validate the model, different touchdown forces are used to vary the initial contact areas of wire and substrate. Additionally, a piezoelectric tri-axial force sensor is built up to identify the known phases of pre-deforming, cleaning, adhering and diffusing for the real bonding process to map with the model. Test substrates as DBC and copper plate are used to show the different formations of a wedge bond connection due to hardness and reaction propensity. The experiments were done by using 500 $μ$m copper wire and a standard V-groove tool.
Keywords: adhesion; circuit reliability; deformation; diffusion; fatigue cracks; friction; interconnections; lead bonding; van der Waals forces; Cu; adhering process; adhesion process; ampacity improvement; bond quality improvement; cleaning process; diffusing process; fatigue fracture failure; friction energy; friction model; heat dissipation; mechanical strength; piezoelectric triaxial force sensor; predeforming process; size 500 mum; total contact area; van der Waals forces; wedge copper wire bonding; Bonding; Copper; Finite element analysis; Force; Friction; Substrates; Wires

Synthesis of lead-free piezoelectric powders by ultrasonic-assisted hydrothermal method and properties of sintered (K0.48Na0.52)NBO3 ceramics - Isobe, G.; Maeda, Takafumi; Bornmann, Peter; Hemsel, Tobias; Morita, Takeshi (Ultrasonics, Ferroelectrics, and Frequency Control, IEEE Transactions on)
(K,Na)NbO3 ceramics have attracted much attention as lead-free piezoelectric materials with high piezoelectric properties. High-quality (K,Na)NbO3 ceramics can be sintered using KNbO3 and NaNbO3 powders synthesized by a hydrothermal method. In this study, to enhance the quality factor of the ceramics, high-power ultrasonic irradiation was employed during the hydrothermal method, which led to a reduction in the particle size of the resultant powders.
Keywords: Q-factor; ceramics; crystal growth from solution; particle size; piezoelectric materials; potassium compounds; powders; sintering; sodium compounds; ultrasonic effects; (K0.48Na0.52)NbO3; KNbO3 powders; NaNbO3 powders; high-power ultrasonic irradiation; lead-free piezoelectric materials; lead-free piezoelectric powders; particle size reduction; piezoelectric properties; quality factor; sintered (K0.48Na0.52)NbO3 ceramics; sintering; ultrasonic-assisted hydrothermal method; Acoustics; Ceramics; Lead; Piezoelectric materials; Powders; Radiation effects; Transducers

High-Velocity Slip-Slip Operation of Piezoelectric Inertia Motors - Experimental Validation - Hunstig, Matthias; Hemsel, Tobias; Sextro, Walter (Proceedings of 10th International Workshop on Piezoelectric Materials and Applications and 8th Energy Harvesting Workshop)
It has been shown previously that ``slip-slip'' operation of piezoelectric inertia motors allows higher velocities and smoother movements than classic ``stick-slip'' operation. One very promising driving option is to use a superposition of multiple sinusoidal signals. In this contribution, previous theoretical results are validated experimentally. The results confirm the theoretical result that for a given maximum frequency, usually defined by the actuator characteristics, a signal with high fundamental frequency and consisting of two superposed sine waves leads to the highest velocity and the smoothest motion. This result is of fundamental importance for the further development of high-velocity piezoelectric inertia motors.
Keywords: Piezoelectric inertia motor; stick-slip motor; driving signal; velocity; smoothness

Modelling the friction contact in an inertia motor - Hunstig, Matthias; Hemsel, Tobias; Sextro, Walter (Journal of Intelligent Material Systems and Structures)
Piezoelectric inertia motors, also known as stickslip drives or (smooth) impact drives, use the inertia of a body to drive it by a friction contact in small steps, in the majority of motors composed of a stick phase and a slip phase between the friction partners. For optimizing inertia motors, it is important to understand the friction contact correctly and to measure its properties appropriately. This contribution presents experimental set-ups for measuring the contact force, friction force and relative displacement in an actual inertia motor with a dry friction contact and numerical simulations of the motor operation. The motor uses a pre-stressed multilayer actuator with a displacement in the range of 20 $μ$ m. It is shown that a previously postulated condition for the applicability of simple kinetic friction models is well fulfilled for the investigated motor. The friction contact in the motor is simulated using different kinetic friction models. The input for the friction models is the measured motion of the rod. The models qualitatively reproduce the measured motion but show quantitative deviations varying with frequency. These can be explained by vibrations of the driving rod that are experimentally investigated.
Keywords: Actuator; friction; motor; piezoelectric

Study on optimizing ultrasonic irradiation period for thick polycrystalline PZT film by hydrothermal method - Ohta, Kanako; Isobe, Gaku; Bornmann, Peter; Hemsel, Tobias; Morita, Takeshi (Ultrasonics)
The hydrothermal method utilizes a solution-based chemical reaction to synthesize piezoelectric thin films and powders. This method has a number of advantages, such as low-temperature synthesis, and high purity and high quality of the product. In order to promote hydrothermal reactions, we developed an ultrasonic assisted hydrothermal method and confirmed that it produces dense and thick lead--zirconate--titanate (PZT) films. In the hydrothermal method, a crystal growth process follows the nucleation process. In this study, we verified that ultrasonic irradiation is effective for the nucleation process, and there is an optimum irradiation period to obtain thicker PZT films. With this optimization, a 9.2-$μ$ m-thick PZT polycrystalline film was obtained in a single deposition process. For this film, ultrasonic irradiation was carried out from the beginning of the reaction for 18 h, followed by a 6 h deposition without ultrasonic irradiation. These results indicate that the ultrasonic irradiation mainly promotes the nucleation process.
Keywords: Piezoelectric material

An efficient simulation technique for high-frequency piezoelectric inertia motors - Hunstig, Matthias; Hemsel, Tobias; Sextro, Walter (Ultrasonics Symposium (IUS), 2012 IEEE International)
Piezoelectric inertia motors use the inertia of a body to drive it by means of a friction contact in a series of small steps. These motors can operate in ``stick-slip'' or ``slip-slip'' mode, with the fundamental frequency of the driving signal ranging from several Hertz to more than 100 kHz. To predict the motor characteristics, a Coulomb friction model is sufficient in many cases, but numerical simulation requires microscopic time steps. This contribution proposes a much faster simulation technique using one evaluation per period of the excitation signal. The proposed technique produces results very close to those of timestep simulation for ultrasonics inertia motors and allows direct determination of the steady-state velocity of an inertia motor from the motion profile of the driving part. Thus it is a useful simulation technique which can be applied in both analysis and design of inertia motors, especially for parameter studies and optimisation.
Keywords: friction; ultrasonic motors; Coulomb friction model; efficient simulation technique; friction contact; high-frequency piezoelectric inertia motor; motor characteristics prediction; numerical simulation; slip-slip mode; stick-slip mode; time-step simulation; ultrasonic inertia motor; Acceleration; Acoustics; Actuators; Computational modeling; Friction; Numerical models; Steady-state

Synthesis of piezoelectric materials by ultrasonic assisted hydrothermal method - Isobe, Gaku; Ageba, Ryo; Maeda, Takafumi; Bornmann, Peter; Hemsel, Tobias; Morita, Takeshi (AIP Conference Proceedings)
Hydrothermal method enables to synthesize high quality piezoelectric materials. To shorten the reaction time and to get higher quality materials, we propose an ultrasonic irradiation to the solution during the hydrothermal method. We named it ultrasonic assisted hydrothermal method (UAHTM). We have synthesized lead-free piezoelectric material and PZT thin film and the effect of UAHTM have been confirmed. In this study, we tried to improve UAHTM. First, to generate powerful and stable ultrasonic irradiation at high temperature on UAHTM, we developed a new transducer using LiNbO3 single crystal. Second, to prevent contamination to the materials, A Teflon cover on the tip of transducer was attached.
Keywords: contamination; lead compounds; piezoelectric materials; piezoelectric thin films; piezoelectric transducers; ultrasonic effects

Piezoelectric applications of hydrothermal lead-free (K0.48Na0.52)NbO3 ceramics - Maeda, Takafumi; Bornmann, Peter; Hemsel, Tobias; Morita, Takeshi (Ultrasonics Symposium (IUS), 2012 IEEE International)
A hydrothermal method utilizes a crystallization process in the solution so that the pure and high-quality powders can be realized. Sintering from the hydrothermal KNbO3 and NaNbO3 powders, a high-dense lead-free piezoelectric (K,Na)NbO3 ceramics could be obtained (density: 98.8%). Concerning about the g33 constant, high value as large as commercial PZT ceramics was measured. Therefore, the hydrothermal (K,Na)NbO3 ceramics is usable for the sensors and the energy harvesting devices. To demonstrate the (K,Na)NbO3 ceramics, a hydrophone sensor was fabricated and evaluated.
Keywords: crystallisation; hydrophones; piezoceramics; potassium compounds; powder technology; powders; sensors; sintering; sodium compounds; (K0.48Na0.52)NbO3; KNbO3 powder; NaNbO3 powder; crystallization; energy harvesting devices; g33 constant; hydrophone sensor; hydrothermal lead-free (K0.48Na0.52)NbO3 ceramics; hydrothermal method; piezoelectric applications; sintering; Materials; Transducers

Analysis of different operation modes for inertia motors - Hunstig, Matthias; Hemsel, Tobias; Sextro, Walter (ACTUATOR 2012 Conference Proceedings)
Piezoelectric inertia motors, also known as ``stick-slip-drives'', use the inertia of a body to drive it by means of a friction contact in small steps. While these steps normally involve stiction and sliding, the motors can also operate in ``slip-slip'' mode without any phase of static friction. In this contribution, a one degree of freedom model of an inertia motor driven by an ideal actuator is analysed. Start-up and constant velocity operation of the motor are investigated and appropriate quantities to compare ``stick-slip'' and ``slip-slip'' operation are determined. Different aspects such as velocity, uniformity of motion, load capacity, robustness, efficiency, and wear are considered. The analysis allows both modes to be applied advantageously in different applications and can widen the field of application of piezoelectric inertia motors. Motor designers are enabled to choose the appropriate mode of operation and the best drive parameters for their individual applications.
Keywords: Piezoelectric Inertia Motors; Drive Signals; Stick-slip; Slip-slip

Multi-DOF cylindrical piezoelectric actuator with radial polarization - Lucinskis, Raimundas; Mazeika, Dalius; Hemsel, Tobias; Bansevicius, Ramutis (AIP Conference Proceedings)
The paper presents the results of numerical and experimental investigation of cylindrical piezoelectric actuator used for achieving independent three degrees of freedom oscillations of the contact point. The design of actuator based on a hollow piezoelectric cylinder mounted on a metal rod. The piezoceramic cylinder has a radial polarization and special configuration of the electrodes that cover inner and outer surface of the cylinder. The main advantage of actuator's design is that solid metallic rod operates as a part of inner electrode of the cylinder and a stator of actuator. The geometry of piezoelectric actuator was adopted to reach resonance of oscillations for the first longitudinal mode and the third flexural mode at same frequency. The actuator is designed to move positioned object through contact point which is located on the top of the rod. The optimal topology of electrodes was found to achieve longitudinal and flexural oscillations of the actuator in two perpendicular planes. Three degrees of freedom of the positioning object can be achieved and control of the system can be implemented by applying different excitation schemes and regimes. The numerical simulation and experimental study of piezoelectric actuator was performed. Impedance of actuator was analyzed under different excitation regimes. The results of numerical modeling and experimental study were compared. Recommendations for the further development of this type of actuator are given.
Keywords: dielectric polarisation; piezoceramics; piezoelectric actuators

Ultrasonically-assisted Hydrothermal Method for Ferroelectric Material Synthesis - Ageba, Ryo; Kadota, Yoichi; Maeda, Takafumi; Takiguchi, Norihito; Morita, Takeshi; Ishikawa, Mutsuo; Bornmann, Peter; Hemsel, Tobias (Journal of Korean Physical Society)
The hydrothermal method enables the production of high-quality piezoelectric materials. In this study, we propose to irradiate the reaction solutions with ultrasonic power during the hydrothermal method to obtain a shorter reaction time and a smooth film surface. A high-pressure reaction container for the ultrasonic transducer was newly developed, and the ultrasonically-assisted hydrothermal method was examined by using this container. The effect of ultrasonic assist on the synthesis of lead-zirconate-titanate (PZT) thin films and (K,Na)NbO$_{3}$ powders was verified. Thicker PZT film, thickness around 10 ${μ}$m, could be obtained in one process, and (K,Na)NbO$_{3}$ powder was synthesized in half the previous reaction time.
Keywords: Hydrothermal method; High-power ultrasonic; PZT thin film; Lead-free piezoelectric materials

Modeling of Piezoelectric Langevin Transducers by Using Mixed Transfer Matrix Methods - Fu, Bo; Li, Chao; Zhang, Jianming; Huang, Zhenwei; Hemsel, Tobias (Journal of Korean Physical Society)
In the modeling of piezoelectric Langevin transducers using usual transfer matrix methods, some simplifications have been adopted. This leads to reduction of the model quality. A mixed transfer matrix method is employed in the modeling of Langevin transducers, where the pre-stressed bolt is modeled as a separate four-pole element, which is connected to other elements in parallel. Based on the mixed transfer matrix method, the four (six)-pole element description of the piezoelectric Langevin transducer is built up and the total transfer matrix relation is derived. The resonance frequencies of the transducer are calculated and then measured using the impedance analyzer (HP4192). Experimental result shows that the mixed transfer matrix method has better modeling quality than the usual transfer matrix method for the vibration analysis of piezoelectric Langevin transducers.
Keywords: Piezoelectric langevin transducer; Transfer matrix method; Four (six)-pole element description; Pre-stressed bolt

Various Aspects of the Placement of a Piezoelectric Material in Composite Actuators, Motors, and Transducers - Hemsel, Tobias; Lierk, Ernst Günther; Littmann, Walter; Morita, Takeshi (Journal of Korean Physical Society)
Piezoelectric materials find wide application in technical systems. Most often, a combination of piezoelectric and other materials is advantageous. The position and the amount of the piezoelectric material within the overall system depends on various aspects like maximum mechanical output to the load, maximum electromechanical efficiency of the system, maximum utilization of the piezoelectric material, minimum self-heating of the piezoelectric material, and controllability of the system, which might be key aspects for the optimisation of the system design. For a composite longitudinal vibrator (bolted Langevin transducer), which is a base for many technical applications, this contribution shows in detail, how above mentioned aspects depend on the position and volume of the piezoelectric material related to the mode shape.
Keywords: Bolted Langevin transducer; Optimum placement of piezoelectric ceramics

Hydrothermal (K1-xNax)NbO3 Lead-free Piezoelectric Ceramics - Maeda, Takafumi; Takiguchi, Norihito; Morita, Takeshi; Ishikawa, Mutsuo; Hemsel, Tobias (Journal of Korean Physical Society)
As a lead-free piezoelectric ceramics, (K,Na)NbO$_{3}$ is a promising material because of its good piezoelectric properties. In this study, (K$_{1-x}$Na$_{x}$)NbO$_{3}$ ceramics were synthesized from a KNbO$_{3}$ and NaNbO$_{3}$ mixture powder prepared by the hydrothermal reaction. The hydrothermal reaction enables the production of high quality powder for the ceramics fabrication process. To obtain (K$_{1-x}$Na$_{x}$)NbO$_{3}$ ceramics, these two powders KNbO$_{3}$ and NaNbO$_{3}$ were mixed and then sintered together. X-Ray diffraction analysis revealed that the solid solution ceramics (K$_{1-x}$Na$_{x}$)NbO$_{3}$ was produced by the sintering process. The K/Na ratio in (K$_{1-x}$Na$_{x}$)NbO$_{3}$ ceramics was optimized for the best piezoelectric properties. The optimized forms was (K$_{0.48}$Na$_{0.52}$)NbO$_{3}$, which showed the following piezoelectric properties; k$_{33}$=0.56, d$_{33}$=114pC/N. In addition, the ferroelectric properties, P$_{r}$=7.72mC/cm$^{2}$, E$_{c}$=857V/mm, and the Curie temperature T$_{c}$=420$_{o}$C were also measured.
Keywords: Lead-free piezoelectric material; KNN; Hydrothermal method