Piezoelectric Coupling Coefficient Research Articles

A rotational hybrid energy harvester utilizing bistability for low-frequency applications: Modelling and experimental validation

Rotational energy harvesting is one of the promising approaches for realizing self-powered wireless sensor networks. Incorporation of hybrid energy sources and geometric bistable nonlinearity can be a solution to enhance the energy harvesting performance under low-frequency excitations. This paper proposes a gravity-based rotational hybrid energy harvester by using the bistable mechanism for low-frequency applications. A comprehensive theoretical model considering the newly introduced piezoelectric stack and force magnification frame is derived for the first time based on the extended Hamilton’s principle. The piezoelectric and electromagnetic coupling coefficients are explicitly expressed and analysed. Both numerical and experimental results show that increasing the spring stiffness can amplify the harvested energy at a higher excitation frequency, and narrowing the impact gap can broaden the effective working bandwidth. Furthermore, the maximum power usually occurs with the impact inter-well phenomenon, after which the chaotic and intra-well oscillations appear successively. Besides, the maximum total power output of 2.98 mW is generated at 7.5 Hz with spring stiffness of 4200 N m−1, which is at least one order of magnitude higher than the other state-of-the-art energy harvesters under the same excitation. Based on the validated theoretical model, parametric studies are further performed to investigate the effects of the proof mass and the initial prestress on the piezoelectric stack. It is found that the hybrid rotational energy harvesting system can possess high tunability and adaptability to the frequency-variant environment by adjusting multiple structural parameters.

Optimizing Piezoelectric Nanocomposites by High-Throughput Phase-Field Simulation and Machine Learning.

Piezoelectric nanocomposites with oxide fillers in a polymer matrix combine the merit of high piezoelectric response of the oxides and flexibility as well as biocompatibility of the polymers. Understanding the role of the choice of materials and the filler‐matrix architecture is critical to achieving desired functionality of a composite towards applications in flexible electronics and energy harvest devices. Herein, a high‐throughput phase‐field simulation is conducted to systematically reveal the influence of morphology and spatial orientation of an oxide filler on the piezoelectric, mechanical, and dielectric properties of the piezoelectric nanocomposites. It is discovered that with a constant filler volume fraction, a composite composed of vertical pillars exhibits superior piezoelectric response and electromechanical coupling coefficient as compared to the other geometric configurations. An analytical regression is established from a linear regression‐based machine learning model, which can be employed to predict the performance of nanocomposites filled with oxides with a given set of piezoelectric coefficient, dielectric permittivity, and stiffness. This work not only sheds light on the fundamental mechanism of piezoelectric nanocomposites, but also offers a promising material design strategy for developing high‐performance polymer/inorganic oxide composite‐based wearable electronics.

Thin films of the alpha-quartz Si_xGe_{1-x}O_2 solid solution

SiO_2 with the alpha-quartz structure is one of the most popular piezoelectrics. It is widely used in crystal oscillators, bulk acoustic wave (BAW) devices, surface acoustic wave (SAW) devices, and so on. GeO_2 can also be crystallized into the alpha-quartz structure and it has better piezoelectric properties, with higher piezoelectric coefficient and electromechanical coupling coefficients, than SiO_2. Experiments on bulk crystals and theoretical studies have shown that these properties can be tuned by varying the Si/Ge ratio in the Si_xGe_{1-x}O_2 solid solution. However, to the best of our knowledge, thin films of Si_xGe_{1-x}O_2 quartz have never been reported. Here we present the successful crystallization of Si_xGe_{1-x}O_2 thin films in the alpha-quartz phase on quartz substrates (SiO_2) with x up to 0.75. Generally, the films grow semi-epitaxially, with the same orientation as the substrates. Interestingly, the Si_{0.75}Ge_{0.25}O_2 composition grows fully strained by the quartz substrates and this leads to the formation of circular quartz domains with an ordered Dauphiné twin structure. These studies represent a first step towards the optimization of piezoelectric quartz thin films for high frequency (> 5 GHz) applications.

Significant performance enhancement of Nd-doped Pb(In0.5Nb0.5)O3–PbTiO3 ferroelectric crystals

This study presents Nd-doped PIN-0.33PT single crystals. The enhanced piezoelectric d33 and electromechanical coupling coefficient k33 are 2100 pC/N and 91%, which are 80% and 5.8% higher than those of the virgin PIN-0.33PT single crystals (1160 pC/N and 86%).

Response of a stochastic multiple attractors wind-induced vibration energy harvesting system with impacts

Focusing on multiple attractors wind-induced vibration energy harvesting system with unilateral impact under the excitation of Gaussian white noise, the stochastic response characteristics, and energy harvesting performance of the systems are presented and discussed. The stochastic averaging of the energy envelope and a conversion mechanism for decoupling the electromechanical equations are introduced to derive the theoretical probability density functions. Numerical simulation results are given to verify the correctness of such theoretical methods. Effects of the noise intensity, restitution coefficient, time constant ratio and coupling coefficient on the mean square voltage are analyzed. It is found that increments of the restitution coefficient and the piezoelectric coupling coefficient of the electrical part have a positive effect on the output voltage of the system, while other factors are opposite. Analysis can help explain the physical mechanisms of the system and provide ideas for optimizing energy harvesting performance by properly tuning the coefficients.

Homogenous Sn-doped K(Ta,Nb)O3 single crystals and its high piezoelectric response

Perovskite K(Ta,Nb)O3 (KTN) single crystal has drawn great interests for its outstanding electro-optic performance and excellent piezoelectric response. However, growth of compositionally uniform KTN single crystals has always been a great challenge for the great segregation difference between Nb and Ta. In this work, we propose a thermal field optimization strategy to resolve this challenge. Homogenous Sn doped KTN (Sn:KTN) single crystal with significantly reduced composition gradient (0.003 mol/mm, 1/4–1/8 of other KTN system), minimal TC variation (13 °C) and excellent piezoelectric and dielectric response (d33 = 373 pC/N and ε33T = 5206) has been successfully achieved. We found that the functional properties of Sn:KTN were greatly affected by the near-room temperature tetragonal-cubic phase transition. From the intrinsic aspect, longitudinal lattice deformation becomes much easier, resulting in maximum piezoelectric (d33∗), dielectric (ε33T∗), elastic (s33E∗)and electromechanical coupling (k33∗) coefficients along polar direction [001]C. From the extrinsic aspect, both domain wall density and domain wall mobility are greatly improved for the reduced lattice distortion, which also contribute a lot to the functional properties. This work provides a simple and practical route for designing and growing high quality crystals, and more importantly, reveals the fundamental mechanism of the phase transitions/boundaries on the functional properties.

Effect of neodymium and zirconium substitution on electrical properties of SrBi4Ti4O15

Neodymium and zirconium modified strontium bismuth titanate ceramics with content changing from 2.5 to 10 at% Nd and a 2.5 at% Zr of SrBi4Ti4O15 (SrNdxBi4-xZryTi4-yO15, (x = 0.00, 0.025, 0.05, 0.075, and 0.1, y = 0.00 and 0.025) have been prepared by solid state reaction method and analyzed by X-ray diffraction (XRD), dielectric response, ferroelectric hysteresis, electromechanical coupling coefficient, and piezoelectric charge coefficient. From hysteresis loop, the remnant polarization and coercive field were calculated and explained. Dielectric analysis explained the sample behavior. Piezoelectric charge and electromechanical coupling coefficients were found to be increased with the addition of Zr and Nd.

Ce and Y Co-Doping Effects for (Ba0.85Ca0.15)(Zr0.1Ti0.9)O3 Lead-Free Ceramics

CeO2 and Y2O3 were co-doped to (Ba0.85Ca0.15)(Zr0.1Ti0.9)O3 ceramics and sintered by conventional solid-state reaction process to form x wt.% CeO2-y wt.% Y2O3 doped (Ba0.85Ca0.15)(Zr0.1Ti0.9)O3 (CexYy-BCZT) ceramics. The effects of different contents of CeO2-Y2O3 dopants to the (Ba0.85Ca0.15) (Zr0.1Ti0.9)O3 composition were analyzed by studying the phase, surface microstructure, piezoelectric and ferroelectric properties of BCZT ceramics. In this study, we have shown that co-doping a small amount of CeO2 and Y2O3 will not change the phase structure of (Ba0.85Ca0.15)(Zr0.1Ti0.9)O3 ceramics. However, the proper introduction of CeO2 and Y2O3 can improve the piezoelectric constant and electromechanical coupling coefficient of BCZT ceramic samples. Moreover, these dopants can promote the grain growth process in (Ba0.85Ca0.15) (Zr0.1Ti0.9)O3 ceramics. C0.04Y0.02 doped (Ba0.85Ca0.15)(Zr0.1Ti0.9)O3 ceramic has the best piezoelectric properties compared with other composition, the results are as follows: Relative density = 96.9%, Kp = 0.583, and d33 = 678 pC/N, V = 8.9 V. It means that this Ce0.04Y0.02 doped (Ba0.85Ca0.15)(Zr0.1Ti0.9)O3 ceramic is a desired material in the application of lead-free ceramics.

“Generation III” Piezoelectric Single Crystals Developed by Solid-State Single Crystal Growth Method

Crystallographically engineered Relaxor-PT single crystals, specifically PMN-PT (Generation I) and PIN-PMN-PT/PMN-PZT (Generation II), offer much higher piezoelectric and electromechanical coupling coefficients (d33>1,500 pC/N, k33>0.9), when compared to polycrystalline PZT-5H ceramics (d33>600 pC/N, k33>0.75). Recently Ceracomp Co., Ltd. (www.ceracomp.com) has developed the solid-state single crystal growth (SSCG) technique and successfully fabricated Gen III PMN-PZT single crystals modified with acceptors or donors. The piezoelectric constants (d33) of (001) Gen III PMN-PZT single crystals were measured to be higher than 4,000 pC/N and thus about two times higher than those of PMN-PT/PZN-PT (Gen I) and PIN-PMN-PT/PMN-PZT (Gen II) single crystals. The Gen III PMN-PZT single crystals have been firstly applied to single crystal-epoxy composites, ultrasonic transducers, piezoelectric sensors, and piezoelectric actuators. In this paper we introduce the development of Gen III PMN-PZT single crystals, piezoelectric composites and multilayer single crystal actuators.

Engineered hard piezoelectric materials of MnO2 doped PZT-PSN ceramics for sensors applications

ABSTRACT In this study, MnO2-doped 0.96Pb(Zr0.515,Ti0.485)O3-0.04Pb(Sb0.5,Nb0.5)O3 (0.96PZT-0.04PSN) hard piezoelectric ceramics were fabricated by employing a conventional mixed-oxide process. Hard piezoelectric materials are suitable for mechanical device applications such as transducers or piezoelectric ultrasonic motors owing to their high mechanical quality factor. To improve the hard piezoelectric properties, MnO2 was selected and doped into 0.96PZT-0.04PSN ceramics in this study. When MnO2 was introduced into piezoelectric lead zirconate titanate (PZT) ceramics, the resistivity and dielectric permittivity decreased, leading to an increase in the mechanical quality factor. MnO2-doped 0.96PZT-0.04PSN ceramics have a lower piezoelectric charge coefficient and dielectric permittivity compared to those of 0.96PZT-0.04PSN ceramics. However, an enhanced mechanical quality factor of 1600 was obtained for the 0.96PZT-0.04PSN ceramics doped with 0.5 wt% of MnO2. In contrast to other hard piezoelectric materials, MnO2 doped 0.96Pb(Zr0.515,Ti0.485)O3-0.04Pb(Sb0.5,Nb0.5)O3 ceramics have a high Qm value while having an appropriate piezoelectric charge coefficient d33 and electromechanical coupling coefficient kp.

Electromechanical modelling of piezoelectrically actuated MEMS tunable lenses with geometric nonlinearity

This article presents a variational model for the geometrically nonlinear behaviour of the piezoelectrically actuated MEMS tunable lenses. Residual stresses during fabrication and larger actuation voltages cause large deflections such that a linear model would provide less accurate approximation. This presses the need for a nonlinear model that can explain the softening and hardening effects exhibited by the lens during its operation and affect its optical performance. Thus, in the view of von Kármán’s plate theory, the presented nonlinear model predicts the lens displacement after solving a cubic nonlinear system of equations. The chosen displacement ansatz fits the problem under study by satisfying the mechanical boundary conditions, and simplifying calculation of the variational integrals and optical representation of the lens’ sag. The model also shows good agreement with FEM simulations over various combinations of tensile and compressive residual stresses. Moreover, it succeeds in fitting measurements when used in a constrained optimization scheme in which the layers’ residual stresses and the e-form piezoelectric coupling coefficient are the fitting parameters.

Quantitative probe for in-plane piezoelectric coupling in 2D materials

Piezoelectric response in two-dimensional (2D) materials has evoked immense interest in using them for various applications involving electromechanical coupling. In most of the 2D materials, piezoelectricity is coupled along the in-plane direction. Here, we propose a technique to probe the in-plane piezoelectric coupling strength in layered nanomaterials quantitively. The method involves a novel approach for in-plane field excitation in lateral Piezoresponse force microscopy (PFM) for 2D materials. Operating near contact resonance has enabled the measurement of the piezoelectric coupling coefficients in the sub pm/V range. Detailed methodology for the signal calibration and the background subtraction when PFM is operated near the contact resonance of the cantilever is also provided. The technique is verified by estimating the in-plane piezoelectric coupling coefficients (d11) for freely suspended MoS2 of one to five atomic layers. For 2D-MoS2 with the odd number of atomic layers, which are non-centrosymmetric, finite d11 is measured. The measurements also indicate that the coupling strength decreases with an increase in the number of layers. The techniques presented would be an effective tool to study the in-plane piezoelectricity quantitatively in various materials along with emerging 2D-materials.

Piezoelectrically induced nonlinear resonances for dynamic morphing of lightweight panels

A rich variety of resonance scenarios induced in thin elastic plates by periodic axial strains is investigated to describe the morphing capability of flexible, ultra-lightweight panels. The strain-induced excitation is provided by embedded piezoelectric strips actuated by time-varying voltages. The study deals with plates characterized by geometric and mechanical symmetry entailing cylindrical motions so that an ad hoc approximate nonlinear model of elastic beams is adopted to formulate the incremental equation of motion about the nonlinear equilibrium under dead loads. An asymptotic approach based on the method of multiple scales is employed to study the plate dynamics and, primarily, to investigate the effect of the plate slenderness on the nonlinearity of the lowest normal modes. A bifurcation analysis is carried out to investigate the wide array of resonances induced by the harmonic axial excitation, acting in nontrivial equilibrium states, which include primary, super-harmonic, sub-harmonic, and principal parametric resonances, respectively. For selected slendernesses of the plate, corresponding to nonlinear softening, hardening and quasi-linear behaviors, respectively, comprehensive parametric studies on the effect of the PZT cross-sectional size, the plate damping, and the piezoelectric coupling coefficient are carried out to identify the threshold voltages triggering the different resonances.

Nonlinear Response of PZT-Actuated Resonant Micromirrors

In this work, we address the modelling of piezo-micromirrors with large opening angles. We focus on various sources of nonlinearites induced by the interaction with the surrounding fluid and by occurrence of geometric large transformations. Specific attention is also devoted to the piezoelectric coupling coefficient. Piezoelectric thin films have gained attention as key materials for the actuation of micro devices since they provide high drive forces, enabling devices with higher performances compared to electrostatic actuation. However they also induce material nonlinearities that cannot be neglected. The model is validated using experimental data obtained for various excitation levels.

Piezoelectricity as a mechanism on generation of electromagnetic precursors before earthquakes

SUMMARYTo produce the electromagnetic (E&M) precursors of an earthquake, the existence of electric field due to stress-induced charges on the ground surface or in shallow depths of upper crust inside the fault zone is a basic condition. Here, we consider the piezoelectric effect or the elastic–electric coupling as a major mechanism on generating such an electric field. A 1-D model based on the elastic mechanics and electromagnetic Maxwell equations is built up to formulate the relationship between electric field and slip as well as stress on a fault before an earthquake. From the model, we may estimate the low-bound values of stress and slip to yield the critical electric field, Ec, for generation of electromagnetic signals. The normal and shear stresses on the fault planes for three faulting types are constructed. The normal stress is stronger than the shear stress to result in piezoelectricity. The depth ranges for yielding an average normal stress being able to generate Ec are similar for thrust and strike-slip faults and deep for normal faults. The possibility of generating Ec is almost the same for thrust and strike-slip faults and low for normal faults. The pre-earthquake slip could be related to nucleation phases or microfractures. The possible occurrence time of E&M signals may be several 10 min to few hours before impending earthquakes. The major factor in yielding a piezoelectric field to generate the TEC anomalies before an earthquake is the existence of fault gouges composed mainly of clays. A thick gouge layer with low electric resistivity and a piezoelectric coupling coefficient ≥0.67 × 10−12 coul nt–1 is an important condition for yielding piezoelectricity.

Design of spatially varying electrical poling for enhanced piezoelectricity in Pb(Mg1/3Nb2/3)O3–0.35PbTiO3

Improvement in operating characteristics of piezoelectric materials, one of the most extensively used dielectric materials, is a major focus of research among materials scientists. Present work puts forward, a novel approach for achieving enhanced piezoelectricity in ferroelectric materials by manipulating electrode placement during poling. Three unique poling configurations, abbreviated as PC1, PC2, and PC3 are developed for exploiting the dependence of effective piezoelectric properties on spatially varying poling direction. Finite element method based numerical simulations are performed to evaluate the electric field distribution, poling direction, and their effect on effective piezoelectric coupling coefficients of PMN–0.35PT (Pb(Mg1/3Nb2/3)O3–0.35PbTiO3) piezoelectric ceramic. A two-phase solution process is developed to evaluate the local orientation of dipoles for each poling configuration and subsequently computing effective piezoelectric properties of the material in an average sense. Parametric studies are carried out to analyze the effect of aspect ratio R of sample and electrode to sample length ratio, r on effective piezoelectric properties. PC1 yields an increase of up to 135% in the magnitude of the transverse coupling coefficient $$({e}_{31}^{eff})$$ and an 8% increase in effective longitudinal coupling coefficient $$({e}_{33}^{eff})$$ while PC2 is observed to exhibit a maximum enhancement of 164% in the magnitude of $${e}_{31}^{eff}$$ and 11.2% in the magnitude of $${e}_{33}^{eff}$$ . PC3, presented as a special case, yields zero values of piezoelectric coefficients in an average sense but can result in a highly elevated net output for bending applications, owing to favorable spatial variation in stresses and associated piezoelectric coefficients.

Acousto-optic modulation in lithium niobate on sapphire

We demonstrate the first acousto-optic modulators in lithium niobate films on sapphire, detailing the dependence of the piezoelectric and optomechanical coupling coefficients on the crystal orientation. This platform supports highly confined, strongly piezoelectric mechanical waves without suspensions, making it a promising candidate for broadband and efficient integrated acousto-optic devices, circuits, and systems.

Analytical and Experimental Studies of Double Elastic Steel Sheet (DESS) Vibration Energy Harvester System

This study provides a double elastic steel sheet (DESS) piezoelectric energy harvester system, in which the vibration generated by the deformation and clap of two elastic steel sheets is assisted by a piezo patch to generate electric energy. The system is combined with energy storage equipment to propose a complete solution forgreen energy integration. This study buildsexperimentallyon the model of the proposed system to explore its voltage, power output and energy collection efficiency. This study also builds atheoretical model of a nonlinear beam with the piezo patch, including the piezoelectric coupling coefficient and current equation. This nonlinear problem is analyzed by the method of multiple scales (MOMS). The system frequency response wasobserved using fixed points plots. The perturbation technique and numerical method wereused to mutually validate the experimental results; the concept of DESS vibration energy harvester (DESS VEH) is proved feasible. In order to prolong the lifetime of the clapping of DESS piezo patch, a camber protector design is proposed. The findings show that the power-generating effect is best when the piezo patch is placed at the peak of the third mode of the DESS system, and the high camber protector is used to generate electric energy.

S-band delay lines in suspended lithium niobate

Thin-film lithium niobate is an attractive platform for GHz-frequency applications in low-power RF analog signal processing, optomechanics, and quantum devices due to its high coupling, low loss, excellent optical properties, and compatibility with superconducting quantum circuits. We demonstrate aluminum interdigitated transducers (IDTs) in this platform for horizontal shear (SH) waves between 1.2 and 3.3 GHz and longitudinal waves between 2.1 and 5.4 GHz. For the SH waves, we measure a piezoelectric coupling coefficient of 13% and 6.0 dB/mm propagation losses in delay lines up to 1.2 mm with a 300 ns delay in air at room temperature. In these high keff2 transducers, electrical loading gives rise to large reflections and resonances. Finite element method models and an experimental finger-pair sweep are used to characterize the role of resonance in these transducers, illuminating the physics behind the large motional admittances of these small-footprint IDTs.

Investigation of Electrical Properties in Antimony Doped Ba0.9Ca0.1Zr0.07Ti(0.93−x)SbxO3 Lead-Free Ceramics

Lead-free piezoceramics have constantly been gaining attention as candidates for replacing the lead-based hazardous piezoelectric materials. In the present study the electrical properties of Ba0.9Ca0.1Zr0.0.7Ti(0.93−x)SbxO3 (x = 0, 0.005, 0.010, 0.015 and 0.020) lead-free piezoceramics, prepared via solid-state synthesis route, have been investigated. The study of crystalline structure reveals that all the ceramics are in the orthorhombic phase with no secondary phase. The study of surface morphology of the ceramics reveals that the grains become smaller and inhomogeneous with the simultaneous decrease in density, as x increases. Dielectric constant at room temperature increases significantly from 1670 for the un-doped sample to 8200 for the sample with x = 0.02. But, the remnant polarization (Pr), piezoelectric charge coefficient (d33) and electromechanical coupling coefficient (kp) degrade as x increases.