Piezoelectric ceramics

Linearconstitutiveequationsofa thermopiezomagneticmedium involving mechanical, electrical, magnetic, and thermal e elds are presented with the aid of a thermodynamic potential. A thermopiezomagnetic medium can be formed by bonding together a piezoelectric and magnetostrictive composite. Two energy functionals are dee ned. It is shown via Hamilton’ s principle that these functionals yield the equations of motion for the mechanical e eld, Maxwell’ s equilibrium equations for the electrical and magnetic e elds, and the generalized heat equation for the thermal e eld. Finite element equations for the thermopiezomagnetic media are obtained by using the linear constitutive equations in Hamilton’ s principle together with the e nite element approximations. The e nite element equations are utilized on an example two-layer smartstructure, which consistsof a piezoceramic (barium titanate ) layer at the bottom and a magnetoceramic (cobalt ferrite ) layer at the top. An electrostatic e eld appl...

With the decrease in energy consumption of portable electronic devices, the concept of harvesting renewable energy in human surrounding arouses a renewed interest. This technical paper focusses on one such advanced method of energy harvesting using piezoelectric material.

Flat glass is produced by the "float glass process" where molten glass is poured onto a bath of molten tin. The glass floats on the tin and levels out as it spreads along the bath. Consequently, it gives a smooth face to both sides which is then cooled and solidified into flat sheet of glass. Investigators have studied different aspects of tin bath such as fluid dynamics, thermal behavior, tin depth profiles, and diffusion of tin in glass [1-5].

Book Description This monograph covers the fundamentals, fabrication, testing, and modeling of ambient energy harvesters based on three main streams of energy-harvesting mechanisms: piezoelectrics, ferroelectrics, and pyroelectrics. It addresses their commercial and biomedical applications, as well as the latest research results. Graduate students, scientists, engineers, researchers, and those new to the field will find this book a handy and crucial reference because it provides a comprehensive perspective on the basic concepts and recent developments in this rapidly expanding field.

Pulse detonation is a propulsion technology that involves detonation of fuel to produce thrust more efficiently than current engine systems. By literature survey and library research it is shown that Pulse Detonation Engine (PDE) technology is more efficient than current engine types by virtue of its mechanical simplicity and thermodynamic efficiency. As the PDE produces a higher specific thrust than comparable ramjet, scramjet engines at speeds of up to approximately Mach 2.3 to Mach 5, it is suitable for use as part of a multi-stage propulsion system. The PDE can provide static thrust for a ramjet or scramjet engine, or operate in combination with turbofan systems. As such, it sees potential applications in many sectors of the aerospace, aeronautic, and military industries. However, there remain engineering challenges that must be overcome before the PDE can see practical use. Current methods for initiating the detonation process need refinement. To this end, many government research bodies and a few private organizations around the world are working on PDS research & further development.

Piezoelectric actuators are popularly applied as actuators in high precision systems due to their small displacement resolution, fast response and simple construction. However, the hysteresis nonlinear behavior limits the dynamic modeling and tracking control of piezoelectric actuators. This thesis studies a dynamic model of a moving stage driven by piezoelectric stack actuator. The Bouc-Wen model is introduced and analyzed to express the nonlinear hysteresis term of the piezoelectric stack actuator, where the values of the parameters of the model have been taken from a previous work. The simulated results using MATLAB/Simulink demonstrate the existence of the hysteresis phenomenon between the input voltage and the output displacement of the piezoelectric stack actuator, and validate the correctness of the model. Moreover, a Luenberger observer is designed to estimate the hysteresis nonlinearity of the system, and then combined with the voltage input signal to form a Luenberger-based feedforward controller to control the displacement of the system. Furthermore, a Proportional-Integral-Derivative (PID) feedback controller is integrated with the feedforward controller to achieve more accurate output displacement, where the gains of the PID controller are optimized using Particle Swarm Optimization. Several performance index formulas have been studied to get the best solution of the PID’s gains. An Integral Time Squared Error plus Absolute Error performance index formula has been proposed to achieve zero overshoot and steady-state error. The simulated results accomplished using MATLAB/Simulink show the ability of the designed controllers to vastly reduce the amount of error of the output displacement and the response time of the system.

The recent advent of highly durable engineering materials and the advancement of latest structural design theories have made possible the fabrication of more efficient engineering structures. However, the safety and reliability of these structures remains the primary challenge and concern for engineers. Especially, for those structures which involve human traffic and huge investments such as the aerospace structures and bridges. Therefore, there is a compelling need to have high quality online structural health monitoring (SHM) of such structures. The development of a real-time, in-service and smart material based SHM method has recently attracted the interest of a large number of academic and industrial researchers. In the recent past, piezoceramic (PZT) transducer has evolved as an efficient smart material which is usually employed in electro mechanical impedance (EMI) and guided ultrasonic wave propagation techniques. In EMI technique, a PZT transducer interact with the host structure to result in unique health signature, as an inverse function of structural impedance, when it is subjected to high frequency structural excitations in the presence of electric field. Using the self actuating and sensing capabilities of PZT transducers, the EMI models attempted to detect loadings on, and damages in, the structures to be monitored. This paper reviews some of the advancements in the field of PZT based SHM made over the past two decades in engineering structures. This paper also provides an insight into the possible future work and improvements required for PZT based EMI technique.

This paper focuses on the primary development of novel numerical and analytical techniques of the modal damped vibration energy harvesters with arbitrary proof mass offset. The key equations of electromechanical finite element discretisation using the extended Lagrangian principle are revealed and simplified to give matrix and scalar forms of the coupled system equations, indicating the most relevant numerical technique for the power harvester research. To evaluate the performance of the numerical study, the analytical closed-form boundary value equations have been developed using the extended Hamiltonian principle. The results from the electromechanical frequency response functions (EFRFs) derived from two theoretical studies show excellent agreement with experimental studies. The benefit of the numerical technique is in providing effective and quick predictions for analysing parametric designs and physical properties of piezoelectric materials. Although analytical technique provides a challenging process for analysing the complex smart structure, it shows complementary study for validating the numerical technique.

Relaxor ferroelectricity is one of the most widely investigated but the least understood material classes in the condensed matter physics. This is largely due to the lack of experimental tools that decisively confirm the existing theoretical models. In spite of the diversity in the models, they share the core idea that the observed features in relaxors are closely related to localized chemical heterogeneity. Given this, this review attempts to overview the existing models of importance chronologically, from the diffuse phase transition model to the random-field model and to show how the core idea has been reflected in them to better shape our insight into the nature of relaxor-related phenomena. Then, the discussion will be directed to how the models of a common consensus, developed with the so-called canonical relaxors such as Pb(Mg 1/3 Nb 2/3)O3 (PMN) and (Pb, La)(Zr, Ti)O3 (PLZT), are compatible with phenomenological explanations for the recently identified re-laxors such as (Bi 1/2 Na 1/2)TiO3 (BNT)-based lead-free ferroelectrics. This review will be finalized with a discussion on the theoretical aspects of recently introduced 0−3 and 2−2 ferroelectric/relaxor composites as a practical tool for strain engineering.

A small-signal model that describes the energy exchange between surface micromachined beams and bulk-lead zirconium titanate (PZT) actuators attached to the silicon substrate is presented. The model includes detection of acoustic waves launched from electrostatically actuated structures on the surface of the die, as well as their actuation by bulk waves generated by piezoelectric ceramics. The interaction is modeled via an empirical equivalent circuit, which is substantiated by experiments designed to extract the model parameters. The equivalent model is valid for cases where the beam resonance frequency is much smaller than the thickness mode resonance of the PZT/silicon stack. In this paper, the resonance frequency of the beams ranges between 200 and 300 kHz. As energy transfer between bulk-PZT and electrostatic actuated beam resonators must be reciprocal for small signals, this paper uses the extracted equivalent model to describe the physical sources of error that account for discrepancies in reciprocity.

CuO as a sintering additive was utilized to explore a low-temperature sintering of 0.92(Bi 1/2 Na 1/2 )TiO 3 -0.06BaTiO 3 -0.02(K 0.5 Na 0.5 )NbO 3 lead-free piezoceramic which has shown a promise for actuator applications due to its large strain. The sintering temperature guaranteeing the relative density of greater than 98% is drastically decreased with CuO addition, and saturates at a temperature as low as ∼930 • C when the addition level exceeds ca. 1 mol.%. Two distinguished features induced by the addition of CuO were noted. Firstly, the initially existing two-phase mixture gradually evolves into a rhombohedral single phase with an extremely small non-cubic distortion. Secondly, a liquid phase induced by the addition of CuO causes an abnormal grain growth, which can be attributed to the grain boundary reentrant edge mechanism. Based on these two observations, it is concluded that the added CuO not only forms a liquid phase but also diffuses into the lattice. In the meantime, temperature dependent permittivity measurements both on unpoled and poled samples suggest that the phase stability of the system is greatly influenced by the addition of CuO. Polarization and strain hysteresis measurements relate the changes in the phase stability closely to the stabilization of ferroelectric order, as exemplified by a significant increase in both the remanent strain and polarization values. Electron paramagnetic resonance (EPR) spectroscopic analysis revealed that the stabilization of ferroelectric order originates from a significant amount of Cu 2+ diffusing into the lattice on B-site. There, it acts as an acceptor and forms a defect dipole in association with a charge balancing oxygen vacancy.

The PZT/polyvinyl chloride (PVC) composites are prepared by hot-pressing technique using a novel nanocrystalline PVC. The d33 value observed in this work for the 0.5PZT/0.5PVC composite is close to the 0.5PZT/0.5PVDF composite reported in the literature, but PVC is much cheaper than PVDF. The three-phase fgC/0.5PZT/(0.5 − fg)PVC composites are obtained by adding a small content of graphite particles to the 0.5PZT/0.5PVC composite. The measured dielectric properties demonstrate that a percolation transition occurs in the three-phase composites as in normal two-phase metal–insulator continuum media. An optimum piezoelectric property is obtained by adding fg = 0.005 before the percolation threshold in the fgC/0.5PZT/(0.5 − fg)PVC composites, which is 50% higher than that of the 0.5PZT/0.5PVC composite. X-ray powder diffraction (XRD) patterns show domain rotation is easy in this three-phase composite, and P–E hysteresis loops conform that a small amount of graphite particles adding in the composite break the polymer seclusion, and considerably decrease coercive field of the composite.

This paper presents an electromechanical impedance (EMI) model for health monitoring of cylindrical shell structures. By investigating the interaction between the piezoceramic (PZT) transducers and a typical cylindrical shell structure, the EMI of the PZT transducers is obtained. In this study, a generic two-dimensional impedance modeling approach is adopted to obtain the admittance (inverse of impedance) of the PZT transducers. The p-Ritz method, due to its effectiveness and common utility for various boundary conditions, is employed to calculate the mechanical impedance of the cylindrical shell structure. An experimental test is carried out on an aluminum cylindrical shell specimen and the PZT admittance signatures are measured by an impedance analyzer. The experimental results are compared with the theoretical ones to verify the developed EMI model for the PZT-shell system under undamaged and damaged conditions. The feasibility of EMI method for damage detection of cylindrical shell structures is also discussed.

A detailed systematic study of the effect of Li2CO3 addition on the structural, dielectric and piezoelectric properties of the PZT(Zr/Ti =50/50) ceramics in the morphotropic phase boundary (MPB) region was carried out. The addition of Li2CO3 in the PZT system resulted in the improved sinterability and densification of the ceramics. 0.2 wt% Li2CO3 addition is found to be optimum for obtaining better dielectric and piezoelectric
properties in the PZT ceramics. It was further seen that the addition of Li2CO3 shifted the MPB of the ceramics towards the tetragonal phase.The Zr/Ti ratio was hence, varied to regain the MPB in the PZT ceramics with an intention to obtain superior dielectric and piezoelectric properties.

Recently, a new family of piezoelectric perovskite materials based on the solid solution (1−x)BiScO3–xPbTiO3 was developed. This system was found to have a Curie temperature higher than 450°C and excellent piezoelectric properties near the MPB composition. Niobium, as a donor dopant in the piezoelectric system Pb(Zr,Ti)O3 and other lead-based perovskite materials, has commonly been used to increase the electrical resistivity, dielectric, and piezoelectric properties. In the current work, the effect of niobium substitution in the BS–PT system has been reported. The results of niobium additions in the BS–PT system showed no large enhancement of the piezoelectric properties. Niobium doping also led to lower Curie temperatures and higher dielectric loss. Further grain size effects in niobium-doped BS–PT compositions provided experimental evidence of significant extrinsic contributions to the piezoelectric properties in this system.

Lead-free 0.96[Bi 1/2 (Na 0.84 K 0.16 ) 1/2 ] (1Àx) La x TiO 3 -0.04SrTiO 3 (BNKTLax-ST, with x = 0.00, 0.01, 0.02, 0.03, 0.04, and 0.05) ceramics have been synthesized using a conventional solid-state reaction method and their phase transition, dielectric, ferroelectric, and strain properties investigated. X-ray diffraction patterns revealed formation of pure perovskite phase. A phase transition from coexistence of rhombohedral and tetragonal to a pseudocubic phase was observed at x = 0.02. Polarization and bipolar strain hysteresis loops indicated that the ferroelectric order (FE) of BNKT-ST is significantly disrupted by lanthanum doping. The destabilization of the FE order results in degradation of the remanent polarization, coercive field, depolarization temperature (T d ), electromechanical coupling factor (k p ), and static d 33 , accompanied by large electric-field-induced strain of 0.34% at 60 kV/cm with normalized strain of d 33 * = S max /E max = 600 pm/V at a critical composition of around x = 0.02.

This work focuses on an ultrasonic guided wave structural health monitoring (SHM) system development for aircraft wing inspection. In part I of the study, a detailed description of a real aluminum wing specimen and some preliminary wave propagation tests on the wing panel are presented. Unfortunately, strong attenuation and scattering impede guided waves for large-area inspection. Nevertheless, small, low-cost and light-weight piezoelectric (PZT) discs were bonded to various parts of the aircraft wing, in a form of relatively sparse arrays, for simulated cracks and corrosion monitoring. The PZT discs take turns generating and receiving ultrasonic guided waves. Pair-wise through-transmission waveforms collected at normal conditions served as baselines, and subsequent signals collected at defected conditions such as rivet cracks or corrosion detected the presence of a defect and its location with a novel correlation analysis based technique called RAPID (reconstruction algorithm for probabilistic inspection of defects). The effectiveness of the algorithm was tested with several case studies in a laboratory environment. It showed good performance for defect detection, size estimation and localization in complex aircraft wing structures.

Piezo-actuated stages are composed of a piezoelectric actuator (PEA) and a positioning mechanism. Hysteresis behavior of PEAs limits the position accuracy of the piezo-actuated stages. This paper presents a hybrid control approach for precise positioning of a piezo-actuated stage, where Bouc-Wen hysteresis model is used to represent the hysteresis behavior of the PEA. A Luenberger observer-based feedforward controller is designed, and then integrated with a Particle Swarm Optimization (PSO)-based Proportional-Integral-Derivative (PID) controller to form a hybrid controller. Optimal PID gains are obtained based on a fitness function proposed to reduce the displacement error and achieve fast response time. The results show that using the proposed hybrid controller reduces the hysteresis effect significantly, and thus the maximum error is minimized to 0.127 11m, which is 0.17 % of the maximum displacement of 72.1 μm.

This paper, the second in a two-part series, presents various finite element simulations on the interaction between piezo-impedance transducer (Lead Zirconate Titanate, PZT) and structure, inclusive of the bonding layer in the application of electromechanical impedance (EMI) technique with varying temperature. Simulation of the PZT-structure interaction at high frequency range (up to 1000 kHz) using the commercially available Finite Element Method (FEM) software, ANSYS version 8.1 was successfully performed. Promising results were found when compared to the experimental results.

This paper demonstrates a multi-source energy harvester that is able to utilize simultaneously both piezoelectric and pyroelectric effects in lead magnesium niobate-lead titanate (PMN-PT) single crystal. The paper presents a study of PMN-PT single crystal with a (67:33) composition grown in our laboratory via a vertical gradient freeze method without any flux. The performance of the piezoelectric and pyroelectric energy harvester using uni-morph device structure was evaluated via modeling and experiment. The theoretical study was implemented based on a distributed parameter electromechanical model and the modelling procedure was approximated using finite element analysis to predict the electromechanical behavior of the harvester. The maximum power density at a resonance frequency of 50 Hz and optimum resistance of 2 MX was 16.7 nW/(g 2 cm 3) under a 1 g acceleration of vibration. The measured values of electrical output parameters were in good agreement with theoretical and modelling results using MATLAB and COMSOL Multiphysics, respectively. By using the pyroelectric effect along with the piezoelectric effect, the output voltage of the energy harvester was found to be enhanced at the optimum resistance and specific frequency values. It was noticed that the output voltage was increased monotonically with temperature difference (DT) and reaches up to 180 % of its original value under temperature difference of 1.7 °C at a frequency value of 49 Hz.

Relaxor ferroelectric single-crystal materials PMN-PT and PZN-PT are currently of interest to the scientific community due to their enhanced properties and possible role as next-generation piezoelectric transducers in applications such as sonar and medical ultrasound. One key phenomenon affecting both the properties and the mechanical integrity of these materials is the ferroelectric domain structure within the material. In this work we examine the morphology and behavior of domain structures in PMN-29%PT. In order to do this we first present details of the construction and testing of a working piezo-response force microscope (PFM), and then use the PFM to verify a new domain observation technique called “relief polishing”. Relief polishing is shown to reveal surface domains in the same manner as acid etching, preserving domain details as small as 0.5um.

Using these two techniques, we then determine that cutting and polishing strongly affect the surface and subsurface ferroelectric domain structures in PMN-29%PT. Specifically, we show that saw cutting can create characteristic striated domain structures as deep as 130um within a sample, while straight polishing creates a characteristic domain structure known as the “fingerprint” pattern to a depth proportional to the size of the polishing grit, on the order of 0--12um for grits as large as 15um. We hypothesize that most samples contain these “skin effect” domain structures. In consequence, it is suggested that researchers presenting experimental results on domain structures should report the physical treatment history of the samples along with the experimental data.

Potassium sodium niobate (KNN) is a potential candidate to replace lead zirconate titanate in sensor and ac-tuator applications but there are many fundamental science and materials processing issues to be understood before it can be used commercially, including the influence of composition and processing atmosphere on the conduction mechanisms and functional properties. Consequently, KNN pellets with different K/Na ratios were sintered to 95% relative density in air and N 2 using a conventional mixed oxide route. Oxygen vacancies (V O ••) played a major role in the semi-conduction mechanism in low p(O 2) for all compositions. Impedance spectro-scopy and thermo-power data confirmed KNN to be n-type in low p(O 2) in contradiction to previous reports of p-type behaviour. The best piezoelectric properties were observed for air-rather than N 2-sintered samples with d 33 = 125 pC/N and k p = 0.38 obtained for K 0.51 Na 0.49 NbO 3 .

Sodium bismuth titanates Na 1/2 Bi 1/2 TiO 3 (NBT) doped with 0-3 wt% Er 2 O 3 were prepared by the conventional solid-state reaction method. The X-ray diffraction results revealed that the sintered Er-doped NBT ceramics exhibited a pure perovskite structure with Er 31 concentrations ranging from 0 to 1 wt%. At a low Er 2 O 3 concentration, the Er-doped NBT ceramics showed enhanced electrical properties with dielectric constant e 33 T / e 0 5 636, a low dielectric dissipation factor (tan d 5 3.3%), a low coercive field (E c 5 4.56 kV/mm), and a high piezoelectric constant (d 33 5 75 pC/N). The relationship between the composition and properties of Er-doped NBT ceramics has been discussed.

The free strain during unipolar electrical activation and the blocking stress are important figures of merit for actuator applications. The lead-free (1 À x)Ba(Zr 0.2 Ti 0.8 )O 3 Àx(Ba 0.7 Ca 0.3 )TiO 3 (BZT-xBCT) system has been shown to display exceptional unipolar strain at room temperature, making it very attractive as an electroactive material for large displacement, low frequency actuation systems. In this work, the temperature-and composition-dependent blocking stress is measured with the proportional loading method. It was found that BZT-xBCT outperformed Pb(Zr 1Àx Ti x )O 3 and Bi 1/2 Na 1/2 TiO 3 -based ceramics for electric fields up to 2 kV/mm. V C 2014 AIP Publishing LLC.

： In order to study acoustic radiation from the spherical cap transducer, a theoretical model was used by solving the wave equation in spherical coordinates using the method of separation of variables, based on the spherical harmonic Fourier transform and boundary condition. The calculation formulas for far field radiated pressure and directivity of spherical cap are derived. Some theoretical results are presented in the form of far-field directivity patterns of the spherical cap transducer for various polar angle of spherical cap, radius of sphere baffle and operating frequency. The diameter of sphere baffle and wavelength in the media determine the directivity of acoustic radiation from a spherical cap. When the frequency is low or the wavelength is longer than the diameter of the sphere baffle, the acoustic radiation from a spherical cap is omnidirectional. With the increasing of the frequency or the diameter of the sphere baffle, the acoustic radiation from a spherical cap is more directional and the beamwidth more tends to spherical cap angle, furthermore the ripple in the beam is more obvious. Finally, the high frequency spherical cap transducer was fabricated and the directivity pattern were tested. As a result, the measurement data coincides with the theoretical calculation results and at the same time it verifies the correctness of theoretical formulas. This research can provide a guideline for designing the spherical cap transducers and arrays.

Articles from different areas which are closely related to the modelling of the stator of travelling wave ultrasonic motors (TWUMs) are reviewed in this work. Thus, important issues relevant to this problem are identified from the areas of vibration of annular plates, laminated plate theories, and modelling of piezoelectric transducers. From this integrated point of view, it becomes clear that there are some very important issues yet to be addressed in the modelling of TWUMs. Firstly, the influence of material properties and stator dimensions on output efficiency, electromechanical coupling coefficients (EMCC) and maximum output energy is to be investigated in more detail. Secondly, the modelling of the electric potential field (by explicitly including the charge equation) for TWUMs seems to be a must for better prediction of displacements and electric fields close to the resonance, as suggested by some recent works . Moreover, the improvement of current models by using shear deformation (or higher order) laminated plate theories (LPTs) in conjunction with approximated methods of solution are discussed. In addition to analytical models, those works using Finite Element and Finite difference Methods (FEM and FDM) for the modelling and simulation of the TWUM stator dynamics are reviewed.

This paper reports the development of a lead free Ba 0.8 Ca 0.2 Ti 0.8 Ge 0.2 O 3 (BCTG) ceramics elaborated by a conventional sintering process. The BCTG exhibits interesting ferroelectric and dielectric properties. The XRD analysis showed that 20 at.% of Ge doping can be fully incorporated into the perovskite lattice of Ba 1Àx Ca x TiO 3 . Dielectric properties revealed that the BCTG ceramic undergone a second order phase transition type at around 120°C independently of the used frequency and behaves as displacive ferroelectric. Ferroelectric investigation showed that P-E hysteresis loop could be obtained at low applied electrical field. The BCTG compound may be highly promising for applications as lead-free ferroelectric materials to reduce environmental damages.

This paper describes the implementation of LabVIEW software to control instruments and acquire data from a piezoelectric energy harvesting test station which is based on a cantilever structure. The experiment is run in the Clean Energy Laboratory on the Ambient Energy Harvester Test Station. A digital multimeter, a programmable resistance selector, an arbitrary waveform generator, a shaker table, an accelerometer and a laser displacement sensor are used to control and acquire data in terms of harvested energy as a function of vibration frequency and load resistance. LabVIEW software is used to control the test station which makes near real-time data measurements, displays waveforms on a PC screen, and stores data for later analysis. Acquired waveforms are presented in terms of frequency versus voltage of the vibrating cantilever at preselected ranges of load resistances in terms of either AC or DC voltages. The vibration of the cantilever beam is measured with an accelerometer and b...