Electromechanical Coupling Coefficient Research Articles

Boosting piezoelectric response and electric-field induced strain in PMN-PT relaxor ferroelectrics

High-performance piezoelectric materials are essential for diverse electromechanical devices, from actuators to sensors and transducers. Here, we synthesized Ce2O3-doped Pb(Mg1/3Nb2/3)O3-0.29PbTiO3 (xCe-PMNT29) solid solutions via conventional solid-state methods. In the x = 2.5 % modified composition, we achieved a notable electrostrain-hysteresis trade-off, enhancing electrostrain (0.2 %), equivalent piezoelectric coefficient d33* (1701 pm V–1 at 3 kV cm–1), and reducing strain hysteresis to 8.1 %. Additionally, direct high-temperature piezoelectric characterizations revealed real-time variations in piezoelectric coefficient (d33) and the actual depolarization temperature, with d33 reaching 859 pC N−1 at 53 °C and planar electromechanical coupling coefficient (kp) exceeding 70 % within 30−85 °C. Leveraging x-ray diffraction (XRD) and piezoelectric force microscopy (PFM), we elucidated synergistic effects between complex nanodomains and local structural heterogeneity, enhancing piezoelectric activity. This study presents a promising approach for improving electromechanical performance and electrostrain in ferroelectrics, with significant potential for practical piezoelectric applications.

Adjustable effective electromechanical coupling of Lamb wave resonator using AlN/Sc0.096Al0.904N composite films

With the rapid development of fifth-generation communication technology, there are more and more 5 G frequency bands and their bandwidths differ. Therefore, many researchers devote themselves to the study of resonators with adjustable electromechanical coupling coefficient. In this paper, we apply composite films to the Lamb wave resonator with a double-IDT configuration to achieve adjustable effective electromechanical coupling coefficient (Keff 2) of the first symmetric mode. The experimental results show that with the increase of the thickness ratio, the series resonant frequency ( fs ) of the resonator decreases from 2.567 GHz to 2.333 GHz; and the parallel resonant frequency ( fp ) of the resonator decreases from 2.608 GHz to 2.396 GHz. The Keff 2 is adjusted from 3.82% to 6.32% and the Δf ( fp−fs ) is adjusted from 41 to 63 MHz by using the AlN/Sc0.096Al0.904N composite films with different thickness ratios. This method may be an efficient way to adjust the bandwidth of the filter to meet the needs of different frequency bands.

0.36BiScO3-0.64PbTiO3/Epoxy 1-3-2 High-Temperature Composite Ultrasonic Transducer for Non-destructive Testing Applications.

The development of high-temperature nondestructive testing (NDT) requires ultrasonic transducers with good temperature resistance and high sensitivity for improved detection efficiency. Piezoelectric composite can improve the performance of transducers because of its high electromechanical coupling coefficient and adjustable acoustic impedance. In this study, 1-3-2 composites and 1-3-2 high-temperature composite ultrasonic transducers (HTCUTs) based on 0.36BiScO3-0.64PbTiO3 (BSPT), which are preferred piezoelectric materials at 200°C-300°C, and high-temperature epoxy with a center frequency of 6 MHz were designed and fabricated. From 25°C to 250°C, 1-3-2 composites show a higher electromechanical coupling coefficient kt especially at high temperatures (~0.53 at 25°C, and ~0.64 at 250°C) than monolithic BSPT (~0.5). The signal of the pulse-echo response of 1-3-2 HTCUTs is distinguishable up to 250 °C and remains stable (Vpp~500 mV) below 150°C, exhibiting higher sensitivity (improved by 7 dB) than that of monolithic BSPT high-temperature ultrasonic transducers (HTUTs). Bandwidth has been greatly enhanced especially at high temperatures (~103250°C) compared with that of monolithic BSPT HTUTs(~30250°C). To verify the excellent performance, B-mode scanning imaging measurement of a stepped steel block and defect location detection of a steel block were performed, showing the potential for high-temperature NDT applications.

Miniaturized Multi-Cantilever MEMS Resonators with Low Motional Impedance.

Microelectromechanical system (MEMS) cantilever resonators suffer from high motional impedance (Rm). This paper investigates the use of mechanically coupled multi-cantilever piezoelectric MEMS resonators in the resolution of this issue. A double-sided actuating design, which utilizes a resonator with a 2.5 μm thick AlN film as the passive layer, is employed to reduce Rm. The results of experimental and finite element analysis (FEA) show agreement regarding single- to sextuple-cantilever resonators. Compared with a standalone cantilever resonator, the multi-cantilever resonator significantly reduces Rm; meanwhile, the high quality factor (Q) and effective electromechanical coupling coefficient (Kteff2) are maintained. The 30 μm wide quadruple-cantilever resonator achieves a resonance frequency (fs) of 55.8 kHz, a Q value of 10,300, and a series impedance (Rs) as low as 28.6 kΩ at a pressure of 0.02 Pa; meanwhile, the smaller size of this resonator compared to the existing multi-cantilever resonators is preserved. This represents a significant advancement in MEMS resonators for miniaturized ultra-low-power oscillator applications.

Structural Optimization Study on a Three-Degree-of-Freedom Piezoelectric Ultrasonic Transducer

A three-degree-of-freedom (3-DOF) piezoelectric ultrasonic transducer is a critical component in elliptical and longitudinal ultrasonic vibration-assisted cutting processes, with its geometric structure directly influencing its performance. This paper proposes a structural optimization method based on a convolutional neural network (CNN) and non-dominated sorting genetic algorithm II (NSGA2). This method establishes a transducer lumped model to obtain the electromechanical coupling coefficients (X-ke and Z-ke) and thermal power (X-P) indicators, evaluating the bending and longitudinal vibration performance of the transducer. By creating a finite element model of the transducer with mechanical losses, a dataset of different transducer performance parameters, including the tail mass, piezoelectric stack, and dimensions of the horn, is obtained. Training a CNN model with this dataset yields objective functions for the relationship between different transducer geometric structures and performance parameters. The NSGA2 algorithm solves the X-ke and Z-ke objective functions, obtaining the Pareto set of the transducer geometric dimensions and determining the optimal transducer geometry in conjunction with X-P. This method achieves simultaneous improvements in X-ke and Z-ke of the transducer by 22.33% and 25.89% post-optimization and reduces X-P to 18.97 W. Furthermore, the finite element simulation experiments of the transducer validate the effectiveness of this method.

Design and Fabrication of a Film Bulk Acoustic Wave Filter for 3.0 GHz-3.2 GHz S-Band.

Film bulk acoustic-wave resonators (FBARs) are widely utilized in the field of radio frequency (RF) filters due to their excellent performance, such as high operation frequency and high quality. In this paper, we present the design, fabrication, and characterization of an FBAR filter for the 3.0 GHz-3.2 GHz S-band. Using a scandium-doped aluminum nitride (Sc0.2Al0.8N) film, the filter is designed through a combined acoustic-electromagnetic simulation method, and the FBAR and filter are fabricated using an eight-step lithographic process. The measured FBAR presents an effective electromechanical coupling coefficient (keff2) value up to 13.3%, and the measured filter demonstrates a -3 dB bandwidth of 115 MHz (from 3.013 GHz to 3.128 GHz), a low insertion loss of -2.4 dB, and good out-of-band rejection of -30 dB. The measured 1 dB compression point of the fabricated filter is 30.5 dBm, and the first series resonator burns out first as the input power increases. This work paves the way for research on high-power RF filters in mobile communication.

LiNbO3-induced phase structure evolution and improved piezoelectric properties in BiFeO3–BaTiO3 ceramics

Eco-friendly (0.73-x)Bi1.05FeO3-xLiNbO3-0.27BaTiO3 ternary ceramics were designed and prepared via a solid-state sintering route. Based on the X-ray diffraction results and Rietveld refinement, it was found that the structure of the ceramics transformed from rhombohedral to tetragonal symmetry with the addition of LiNbO3, and at x = 0.003, there existed a morphotropic phase boundary separating the two phases. Near the phase boundary, the largest values were achieved for the piezoelectric constant d33 and planar electromechanical coupling coefficient kp, being 180 pC/N and 0.27, respectively. Due to the addition of LiNbO3, the grain size tended to become smaller. Additionally, the ceramics were transitioned from normal to relaxor ferroelectrics with increasing x. Despite the fact that the LiNbO3 addition would result in a gradual decrease of Curie temperature, a relatively high Curie temperature (535 °C) was still maintained at x = 0.003, the phase boundary composition, which also showed good temperature stability of piezoelectric properties. These experimental results can provide a reference for the practical applications of high-temperature lead-free ceramics.

Electro-Mechanical Characterization and Modeling of a Broadband Piezoelectric Microgenerator Based on Lithium Niobate.

Vibration energy harvesting based on piezoelectric transducers is an attractive choice to replace single-use batteries in powering Wireless Sensor Nodes (WSNs). As of today, their widespread application is hindered due to low operational bandwidth and the conventional use of lead-based materials. The Restriction of Hazardous Substances legislation (RoHS) implemented in the European Union restricts the use of lead-based piezoelectric materials in future electronic devices. This paper investigates lithium niobate (LiNbO3) as a lead-free material for a high-performance broadband Piezoelectric Energy Harvester (PEH). A single-clamped, cantilever beam-based piezoelectric microgenerator with a mechanical footprint of 1 cm2, working at a low resonant frequency of 200 Hz, with a high piezoelectric coupling coefficient and broad bandwidth, was designed and microfabricated, and its performance was evaluated. The PEH device, with an acceleration of 1 g delivers a maximum output RMS power of nearly 35 μW/cm2 and a peak voltage of 6 V for an optimal load resistance at resonance. Thanks to a high squared piezoelectric electro-mechanical coupling coefficient (k2), the device offers a broadband operating frequency range above 10% of the central frequency. The Mason electro-mechanical equivalent circuit was derived, and a SPICE model of the device was compared with experimental results. Finally, the output voltage of the harvester was rectified to provide a DC output stored on a capacitor, and it was regulated and used to power an IoT node at an acceleration of as low as 0.5 g.

3D printing of CaBi4Ti3.925(Nb2/3Mn1/3)0.075O15 ceramics for high temperature ultrasound transducer

Bismuth layer-structured CaBi4Ti3.925(Nb2/3Mn1/3)0.075O15 (CBTNM) piezoelectric ceramics have been prepared using stereolithography (SL) technology. The effects of various solid contents (76–82 wt%) of CBTNM ceramics on the slurry viscosity, phase structure, microstructure, and electric performance were studied in detail. At a solid content of 82 wt%, the ceramic exhibits good piezoelectric properties. The piezoelectric constant d 33, thickness-mode electromechanical coupling coefficient k t, and Curie temperature Tc were 21 pC/N, 47%, and 790 °C, respectively. The piezoelectric constant of the ceramic has a good stability up to 500 °C. Furthermore, a high-temperature ultrasound transducer was designed and fabricated based on the CBTNM ceramic, and its pulse-echo performance was characterized from room temperature to 250 °C. The pulse-echo performance indicates that the −6 dB bandwidth and echo amplitude of the transducer decrease slightly, but still work normally up to 250 °C. These results indicate that the transducer fabricated based on CBTNM ceramics has potential in high-temperature testing applications.

Precise evaluation of the material constants of [011]-poled mangan-doped 0.32Pb(In1/2Nb1/2)O3-0.39Pb(Mg1/3Nb2/3)O3-0.29PbTiO3 single crystals

Recently, there has been a surge of interest in [011]-poled Mn: PIN-PMN-PT piezoelectric single crystals for high-power transducers. These crystals boast impressive electromechanical coupling coefficients, piezoelectric constants in the transverse mode, and excellent heat resistance due to their high mechanical quality factor. To effectively design transducers using these crystals, understanding their material constants is crucial. Our study focused on determining these constants by employing the resonance method. We created eleven different resonators, analyzed their impedance spectra, and derived seventeen elastic compliance, piezoelectric, and dielectric constants. The precision of the obtained material constants was enhanced by minimizing the difference between the impedance spectra found through finite element analyses and actual measurements of each resonator. The accuracy of these derived constants was validated by comparing the impedance spectra obtained from analysis with those measured experimentally. This novel approach demonstrated a capability to derive more precise material constants than prior studies. These refined material constants hold the potential to enable more precise and effective design of acoustic transducers constructed from the single crystals.

Coupled Shear SAW Resonator With High Electromechanical Coupling Coefficient of 34% Using X-Cut LiNbO₃-on-SiC Substrate

Coupled Shear SAW Resonator With High Electromechanical Coupling Coefficient of 34% Using X-Cut LiNbO₃-on-SiC Substrate

Highly improved quality factor of the film bulk acoustic wave resonator by introducing a high quality ZnO buffer layer

The inferior film quality of sputtered AlN has hindered the further development of high-performance film bulk acoustic wave resonators (FBAR). In this work, the ZnO buffer layer was introduced into the FBAR to improve the performance of FBAR for the first time. Compared with its counterpart without the buffer layer, the devices with a buffer layer exhibited a far higher average quality factor (2π times the maximum energy stored in the FBAR/energy dissipated per period) of 2575 ± 136, which was about 64 % larger than that without a buffer layer. Benefiting from the enhanced crystalline quality of AlN, the device also showed an improved effective electromechanical coupling coefficient.

Spurious-Free Shear Horizontal Wave Resonators Based on 36Y-Cut LiNbO3 Thin Film.

This article presents lithium niobate (LiNbO3) based on shear horizontal (SH0) resonators, utilizing a suspended structure, for radio frequency (RF) applications. It demonstrates the design, analysis, and fabrication of SH0 resonators based on a 36Y-cut LiNbO3 thin film. The spurious-free SH0 resonator achieves an electromechanical coupling coefficient (kt2) of 42.67% and a quality factor (Qr) of 254 at the wave-propagating orientation of 0° in the 36Y-cut plane.

Harmonic oscillations of a piezoceramic functional-graded sectional cylinders with account of energy dissipation

Harmonic oscillations of piezoceramic functional-gradient sectioned hollow cylinders are studied, taking into account energy dissipation. A cylinder of finite length is considered, consisting of an even number of sections polarized in the circular direction, which are connected to each other by similar sides. The material is considered to be functionally heterogeneous in the direction of the previous polarization. The cylinder is loaded by the potential difference applied to the flat faces of the sections. The calculation is performed by the finite element method. The forming of damping matrix and determining the coefficients corresponding to the four ways of introducing Rayleigh damping into the FEM is described. Amplitude-frequency responses taking into account damping are built for displacements, charge on the electrodes, electrical admittance and its logarithm. The consideration of energy dissipation according to the Rayleigh damping model is related to the experimental data due to the Q factor of the piezo element. The frequencies of electrical resonances, anti-resonances and the corresponding electromechanical coupling coefficients for functionally inhomogeneous and homogeneous cylinders are determined. For the functional-gradient piezoelectric element of the considered configuration, the maximum CEMC occurs at the frequency of the second electrical resonance. At this frequency, the dynamic stress-strain state of the cylinder is investigated. Forms of oscillations and distribution of stress amplitude values are constructed. The largest normal stresses according to the Coulomb-Mohr strength theory are determined and compared with the von Mises strength theory. FEA allows three-dimensional calculation of harmonic oscillations of functional-gradient piezo elements of complicated geometry. The determined frequencies of electrical resonance and anti-resonance and the corresponding CEMC make it possible to choose the most effective operating mode of the piezo element. The FEM mathematical apparatus makes it possible to quickly and qualitatively evaluate the strength, determine the charge on the electrodes, the current in the circuit, build the amplitude-frequency characteristics of admittance and impedance, and evaluate the efficiency of energy conversion.

Giant Flexoelectric Effect in Snapping Surfaces Enhanced by Graded Stiffness

Flexoelectricity is present in nonuniformly deformed dielectric materials and has size-dependent properties, making it useful for microelectromechanical systems. Flexoelectricity is small compared to piezoelectricity; therefore, producing a large-scale flexoelectric effect is of great interest. In this paper, we explore a way to enhance the flexoelectric effect by utilizing the snap-through instability and a stiffness gradient present along the length of a curved dielectric plate. To analyze the effect of stiffness profiles on the plate, we employ numerical parameter continuation. Our analysis reveals a nonlinear relationship between the effective electromechanical coupling coefficient and the gradient of Young’s modulus. Moreover, we demonstrate that the quadratic profile is more advantageous than the linear profile. For a dielectric plate with a quadratic profile and a modulus gradient of − 0.9, the effective coefficient can reach as high as 15.74 pC/N, which is over three times the conventional coupling coefficient of piezoelectric material. This paper contributes to our understanding of the amplification of flexoelectric effects by harnessing snapping surfaces and stiffness gradient design.

Extension of the fixed point theory to tuned mass dampers with piezoelectric stack energy harvester

A tuned mass damper with a piezoelectric stack energy harvester (TMD-PSEH) is a passive vibration control device for the dual purpose of absorbing vibration and harvesting energy. This paper develops the fixed point theory for the optimal design of a TMD-PSEH attached to an undamped primary structure under harmonic external excitation. It has been proven that the existence of two fixed points of the amplitude-frequency curve doest not depend on the damping of the primary structure. Based on the requirements for suppressing the vibration of the primary structure and enlarging the harvested power, the analytical expressions for the optimal tuning, damping, and resistance ratios are determined. It is found that the minimum damping ratio occurs in the vicinity of the electrical resistance ratio α=1 for various values of the electromechanical coupling coefficient. Power flow analysis is carried out resulting in closed-form expressions of instantaneous and average powers. Numerical examinations of the system with the obtained optimal parameters are performed demonstrating a very good compatibility between theory and computation. In addition, the effect of damping in the primary structure is also investigated. It is shown that not only the vibration of the primary structure effectively reduces, but also a large amount of the harvested energy can be captured in the main resonance region.

Theoretical Analysis of the Power Performance of a Monostable Galloping-Based Piezoelectric Energy Harvester

In the past few years, different kinds of structural nonlinearities, such as external magnetic interaction and multistable structures, have been introduced into galloping energy harvesters to enhance energy harvesting efficiency. However, since the galloping-based piezoelectric energy harvester (GPEH) is a self-excited system, the conventional impedance matching method that is widely used in vibration energy harvesters is no longer valid for it. Therefore, the power characteristics of the nonlinear GPEH are still an open question to be solved. To this end, this paper is motivated to derive the approximate analytical solution of a monostable galloping-based piezoelectric energy harvester through the harmonic balance method and impedance matching theory. The analytical maximum power, power limit, and critical electromechanical coupling are studied from the perspective of the influence of structural nonlinearity on the power performance. Firstly, the approximate analytical solutions of output power, power limit, optimal resistance, and critical electromechanical coupling coefficient are derived. The accuracy of the analytical solution is verified by numerical simulation. It is found that the influence of structural nonlinearity on the power characteristics of the nonlinear GPEH is quite different under different wind speeds. After that, the power characteristics of the system under different wind speeds and different coupling conditions are investigated. The results showed that the maximum power of the system can be increased by introducing stiffness nonlinearity under low wind speed and weakly coupled configuration. Even more, the system can be shifted into a strongly coupled system when the nonlinearity is enhanced to a certain level. Reasonable design of stiffness nonlinearity can effectively reduce the critical electromechanical coupling, which indicates that stiffness nonlinearity is a feasible and effective way to improve the power performance of low-speed wind energy harvesting.

Energy generation through a hybrid energy harvester under random excitation

This manuscript analyses a multi-frequency based coupled piezo-electromagnetic hybrid vibration energy harvester. Most of the energy harvesting devices discussed in the literature are based on the assumption that the base excitation is harmonic. However, in general, energy harvesting devices are deployed in an ambient environment, which is random in nature. Hence, in this regard, the manuscript discusses the power harvesting capabilities of the hybrid energy harvester under random base excitation using analytical and experimental studies. Acceleration with band limited Gaussian noise has been provided as an input to the base of the harvester. Comparative studies are also made to understand the performance of the hybrid harvester over conventional standalone piezoelectric and electromagnetic harvesters under the same support excitation. Thus, the novelty of the present work is to analyse a novel design of a hybrid harvester to improve harvesting performance across a wide range of frequencies under random base excitation compared to conventional harvesters. The results demonstrate that the proposed hybrid energy harvester can yield sufficient power over a wide range of frequencies. In addition, parametric studies have also been performed to characterize the system parameters in order to enhance the performance of the harvester. Studies show that the harvested power can be enhanced by maximizing the values of mass ratio, frequency ratio, non-dimensional electromechanical coupling coefficient and minimizing the values of structural damping ratios. Finally, practical applications of the proposed device have also been reported.

Enhanced soft piezoelectric properties of Sb2O3 doped 0.5Ba(Zr0.2Ti0.8)O3-0.5(Ba0.7Ca0.3)TiO3 materials

In this paper, we have studied the soft piezoelectric properties of 0.5Ba(Zr0.2Ti0.8)O3-0.5(Ba0.7Ca0.3)TiO3 doped with Sb2O3. The optimal piezoelectric charge constant and dielectric permittivity of the calcined and sintered 0.5Ba(Zr0.2Ti0.8)O3–0.5(Ba0.7Ca0.3)TiO3 were determined by varying the Sb2O3 content. The mol% of Sb2O3 was set to 0, 0.05, 0.1, 0.15, and 0.2, and the doped ceramics were sintered at a temperature of 1475 °C. The piezoelectric charge constant d33, electromechanical coupling coefficient kp, and dielectric permittivity εr of the doped ceramics increased with the increasing Sb2O3 content, whereas their Curie temperature Tc slightly decreased. At 0.1 mol% of Sb2O3, the highest piezoelectric charge constant, electromechanical coupling coefficient, and dielectric permittivity values were obtained. Although the Curie temperature was slightly lowered, the dielectric permittivity improved. 0.5BZT-0.5BCT doped with Sb2O3 exhibited a high remnant polarization Pr even when a weak coercive electric field Ec was applied, resulting in an easy polarization. It can be seen that the improved electrical properties and the behavior of the P-E hysteresis loop through the dopant addition of Sb2O3 are close to the soft piezoelectric characteristics. Thus, the synthesized lead-free and Sb2O3-doped ceramics, with excellent piezoelectric properties and depolarization behaviors, are expected to replace lead-based ceramics and will be useful in energy converters, such as piezoelectric transformers.

Effects of heterovalent ions doping-induced oxygen octahedral distortion and defect chemical change on piezoelectric characteristics and thermal stability of PHT-PIN ceramics

Electromechanical devices require functional materials possessing excellent piezoelectric properties, good thermal stability, and high electromechanical coupling coefficients. To modulate the piezoelectric, dielectric, and electromechanical characteristics of 0.89Pb(Hf0.47Ti0.53)O3-0.11Pb(In1/2Nb1/2)O3 (PHT-PIN) piezoelectric ceramics, heterovalent ions of lithium (Li) and tungsten (W) were doped through a traditional solid-phase reaction approach. On the one hand, large lattice distortions caused by the doped W6+ resulted in the shortening of BO bonds while an increase in the local displacement of B-site ions. Moreover, a mismatch occurred for the oxygen octahedral dimensions, and a subsequent disruption of the long-ranged ordered ferroelectric domains was observed, which resulted in the formation of microdomains. On the other hand, the changes in the concentration of oxygen vacancy defects induced by the Li and W doping inside the ceramic were comprehensively analyzed. The decrease in the concentration of oxygen vacancies was found to be accompanied by the enhancement of piezoelectric properties of the material. Excellent comprehensive performance (piezoelectric coefficient d33 = 655 pC N−1, Curie temperature Tc = 321.1 °C, dielectric constantεr = 3352.31, electromechanical coupling coefficient kp = 0.67, and residual polarization strength Pr = 55 μC cm−2) was obtained for 0.2 mol % doping amount of Li+ and W6+ ions. This work, therefore, proposes a novel strategy for the origin of piezoelectric properties and inspires doping of other heterovalent ions to improve the piezoelectric properties of ceramics. It further promotes the development of Pb-based piezoelectric ceramics for electromechanical devices that can efficiently operate under high-temperature environments.