Electromechanical Coefficient Research Articles

Multi-physics interpolation for the topology optimization of piezoelectric systems

Unlike single-physics static structural problems, the topology optimization of piezoelectric systems involves three different material coefficient groups, such as the mechanical, electrical, and electromechanical coefficient groups, which correspondingly necessitate three values of penalty exponents. Earlier investigations have shown that stable convergence cannot be ensured if the exponents are selected arbitrarily or based simply on typical rules used for static structural problems. Here, stable convergence implies that the use of more materials can yield better system performance and a distinct void–solid distribution is favored over an intermediate material distribution during the optimization process. However, no rule for choosing the values of penalty exponents has yet been studied for piezoelectric systems and in fact, they have been chosen mainly by trial and error. In this work, two conditions that the three penalty exponents must satisfy for stable convergence are derived for one-dimensional problems and their effectiveness for two-dimensional problems is investigated. The first condition is an intrinsic condition ensuring better energy conversion efficiency between mechanical and electric energy for more piezoelectric material usage and the second one is an objective-dependent condition favoring a distinct void–solid distribution over an intermediate material distribution for the same amount of piezoelectric material used. In this study, we consider the design of piezoelectric actuators, sensors and energy harvesters that can be analyzed by static analysis. Several numerical examples are solved to check the validity of the proposed conditions.

Designing Piezoelectric Interdigitated Microactuators Using Finite Element Analysis

This paper presents a methodology toward designing, analyzing, and optimizing piezoelectric interdigitated microactuators using multiphysics finite element analysis. The models used in this paper were based on a circularly interdigitated design that takes advantage of primarily the d33 electromechanical piezoelectric constant coefficient. Because of the symmetric nature of the devices, a small number of 2D axisymmetric parametric models were developed to characterize the behavior of the diaphragms. The parametric models offered a large range of possible results from a very small number of models. The variations in the design parameters and their effects on deflection were captured using these models. The models also showed that several of the design parameters were naturally coupled. Discrete models were then used to capture the variations in the key design parameters during fabrication. The numerical models correlate well to the maximum deflection of the experimental devices.

Microstructure and piezoelectric properties of Na 0.5K 0.5NbO 3–BiNiO 3–LiSbO 3 lead-free ceramics

Lead-free (0.94 − x)Na 0.5K 0.5NbO 3– xBiNiO 3–0.06LiSbO 3 piezoelectric ceramics have been sintered at 1105 °C by ordinary solid mixed oxide method. The phase transitional behavior and various electrical properties were investigated. All samples are typical ABO 3 style perovskite structure. A morphotropic phase boundary between orthorhombic and tetragonal ferroelectric phases has been identified in the composition range of 0.002 ≤ x ≤ 0.004. Main piezoelectric parameters of these ceramics were optimized around x = 0.002 with an enhanced piezoelectric constant d 33 of 240 pC N −1, a planar electromechanical coefficient k p of 44%, a mechanical factor Q m of 38, and a Curie temperature T c of 360 °C. These results indicate the materials studied have a promising future in a wide range of applications.

Investigation of the structure, physical properties, and phase transition in SrAlF5

Crystals of SrAlF5 have been grown by the Bridgman method from the melt and by sintering of the components. Optical polarization studies and measurements of the thermal expansion and birefringence coefficients have been carried out over a wide temperature range. The electromechanical coefficient d 33 has been measured, and the optical second harmonic, dielectric hysteresis loop, and optical quality of the crystal have been assessed. X-ray diffraction investigations have been performed to identify the revealed compounds. It has been demonstrated that the SrAlF5 crystals obtained under the growth conditions chosen have I41/a symmetry and do not undergo structural phase transitions in the temperature range 100–800 K. Crystalline inclusions of the AlOF oxyfluoride have been revealed in crystals grown with an AlF3 excess. The birefringence of the AlOF crystal is an order of magnitude higher than that of SrAlF5, does not depend on temperature, and has no anomalies up to 800 K.

Ferroelectric and electromechanical property characterization of single Pb(ZrTi)O3 fiber resonator

Piezoelectric fibers and fiber composites have attracted much attention for anisotropic sensing and actuation applications in recent year. Complete property characterization for piezoelectric fibers is essential for material and device design and fabrication. In this work, ferroelectric and electromechanical properties of single piezoelectric Pb(ZrTi)O3 (PZT) fiber were characterized by polarization–electric field hysteresis loop measurement using single PZT fiber/polymer 1–3 composite approach, and by direct measurement of the complex impedance spectrum of single PZT fiber resonator. A normalized electrical impedance spectrum method developed recently was used to determine the complex piezoelectric, elastic, and dielectric coefficients, mechanical quality factor and electromechanical coefficient from the complex electrical impedance-frequency spectrum measurement. The results were compared with those determined by the IEEE standard method for the pure length extensional resonator. The permittivity of PZT fiber was found larger than PZT bulk materials, which was attributed for the core-shell structure of the fibers.

Contributions of domain wall motion to complex electromechanical coefficients of 0.62Pb(Mg1/3Nb2/3)O3–0.38PbTiO3 crystals

The loss behavior of 0.62Pb(Mg(13)Nb(23))O(3)-0.38PbTiO(3) (PMN-38%PT) ferroelectric single crystal poled along [001](c) was investigated. It was found that the complex electromechanical coefficients and loss factors change dramatically at the coercive field E(c) around 250 Vmm, representing the intrinsic switching barrier. Since the energy loss is related to the domain wall motion, the imaginary parts of the electromechanical coefficients can be used to study the degree of domain wall motions in relaxor-based ferroelectric single crystals. Experimental results indicate that for this system, domain wall motion contributes significantly to the imaginary parts of electromechanical coefficients. In addition, [001](c) poled PMN-38%PT single crystals have much larger mechanical loss factor compared to that of conventional single crystal like LiNbO(3). This phenomenon is proved to be closely related to 90 degrees domain wall motion in this crystal system.

Enhanced temperature stability of modified (K0.5Na0.5)0.94Li0.06NbO3 lead-free piezoelectric ceramics

To improve both the temperature stability and the mechanical quality factor of (K0.5Na0.5)0.94Li0.06NbO3 (KNLN6) ceramics, dense (K4CuNb8O23, Bi2O3)-modified KNLN6 lead-free ceramics were prepared. Results showed that the (K4CuNb8O23, Bi2O3)-modified ceramics exhibited a flat, temperature-stable behavior over the range of 20–120 °C. K4CuNb8O23 (KCN) and Bi2O3-codoping changed the KNLN6 to “hard” ceramics with a significant improvement of mechanical quality factor, Qm, from 82 to 756. Meanwhile, the piezoelectric constant, d33, and the planar electromechanical coefficient, kp, still maintained relatively high levels (d33 ~118 pC/N, kp ~35.6%). These results indicate that the modified KNLN6 ceramics are promising lead-free piezoelectric candidates for practical applications.

Cathodoluminescence investigation of relaxor-based ferroelectrics Pb(Mg1/3Nb2/3)O3–0.3PbTiO3 (PMN–0.3PT) single-crystal

Abstract Relaxor-based ferroelectric lead magnesium niobate–lead titanate Pb(Mg1/3Nb2/3)O3–PbTiO3 (PMN–PT) possesses ultrahigh electromechanical coefficients near the morphotropic phase boundary (MPB). In this paper, the electro-stimulated emission characteristics of a [0 0 1]-oriented PMN-0.3PTsingle-crystal were studied using high resolution cathodoluminescence (CL) spectroscopy at room temperature. Four luminescence bands were observed in the range of 200–900 nm and they were assigned to polaron, nanometre cluster emission, interband emission and structure-related emission. Besides, it was found that the residual stress field ahead of a crack tip of a Vickers indentation had a considerable influence on these luminescence bands. The relationship between the intensities of CL bands and the residual stress field has been investigated and discussed in this paper.

Effects of MnO 2 on phase structure, microstructure and electrical properties of (K 0.5Na 0.5) 0.94Li 0.06NbO 3 lead-free ceramics

The effects of a small amount MnO 2 (0–1.20 mol%) doping on the phase transition behavior, microstructure and electrical properties of (K 0.5Na 0.5) 0.94Li 0.06NbO 3 (KNLN6) ceramics have been investigated. X-ray diffraction analysis showed that the ceramics underwent a perovskite structure transition from tetragonal to orthorhombic symmetry with increasing the MnO 2 content, which is similar to the morphtropic phase boundary (MPB). SEM and density studies revealed that a small amount of MnO 2 improved effectively the densification of the KNLN6 ceramics. Because of the high densification, the mechanical quality factor Q m of the KNLN6 ceramics were significantly enhanced by MnO 2 addition which meant MnO 2-doping changed the KNLN6 to “hard” ceramics. For 1.20 mol% MnO 2-doped KNLN6 ceramics, the mechanical quality factor Q m reached up to 301, which increased by four times as compared with KNLN6. The piezoelectric constant d 33 and the planar electromechanical coefficient k p still maintained relatively high levels, which were about 141 pC/N and 32.0%, respectively.

ELECTRO MECHANICAL AND IMPEDANCE STUDIES OF (Na1-xKx)1/2Bi1/2TiO3

Ceramic samples of [( Na 1-x K x)1/2 Bi 1/2 TiO 3] (NKBT) (x = 0.1, 0.15, 0.2, 0.3, 0.45) were prepared by double sintering method. The admittance measurements were carried out in the frequency range of 1 KHz to 10 MHz in the temperature range of 30°C–600°C. The dielectric nature as deduced from admittance data shows a strong temperature and frequency dependence, apart from the relaxor behavior. The admittance data was analyzed by complex plane diagrams i.e., Y′ versus Y′′ at different temperature. The frequency explicit plots of imaginary component of electric modulus (M′′) at various temperatures show peaks shifting to higher frequencies with temperature (> 400° C ). The relaxation peaks were effected by the doping. The activation energies are obtained from the data. The electromechanical coefficients KP, K31 were calculated from the resonant and anti-resonant frequencies obtained from vector admittance plots. The temperature dependence of electromechanical coefficients is studied. The solid solution samples show higher KP, K31 values as compared to pure sodium bismuth titanate.

Phase transitional behavior and piezoelectric properties of BiYbO 3–Pb(Ti 0.5Zr 0.5)O 3–LiNbO 3 ceramics

Perovskite (1 − x)(0.06BiYbO 3–0.94Pb(Ti 0.5Zr 0.5)O 3)– xLiNbO 3 (BYPTZ-LN) ceramics were synthesized by the conventional ceramic processing. The effect of LiNbO 3 on the microstructure and piezoelectric properties was investigated. The perovskite phase and the Yb 2Ti 2O 7 pyrochlore phase are coexisting in the BYPTZ-LN ceramics sintered at 1140 °C. The material with perovskite structure is tetragonal at x ≤ 0.04 and becomes single rhombohedral at x ≥ 0.08. A morphotropic phase boundary between rhombohedral and tetragonal phases is found in the composition range 0.04 ≤ x ≤ 0.08. Analogous to Pb(Zr,Ti)O 3, the piezoelectric and electromechanical properties are enhanced for compositions near the morphotropic phase boundary. Piezoelectric constant d 33 values reach 290–360 pC/N. Electromechanical coefficients k p reach 0.38–0.55. The maximum values of d 33, k p and P r are obstained as x = 0.08, accompanying with the minimum values of Q m and E c. The Curie temperature T c and the maximum value of dielectric constant decrease with increasing LiNbO 3 content. BYPTZ-LN ceramics with the high d 33 value and the high thermal-depoling temperatures of >320 °C are obtained.

A new piezoelectric single crystal obtained by Ge doping in the SiO2 structure

AbstractThe interest of Si1–xGexO2 single crystals with alpha‐quartz structure is connected to improvement of electromechanical coefficients and rise of α – β phase transition of quartz one. Growth of an α‐SixGe1–xO2 crystal was realized by a hydrothermal method of temperature gradient in autoclaves, made from Cr–Ni alloys. Nutrient material was prepared from synthetic quartz as crashed rods and placed in the bottom of autoclaves. There was loaded GeO2 powder additive in proportions to quartz nutrient. Single crystals were investigated by electron microprobe analysis, X‐ray diffraction and atomic force microscopy. The most important result, which was obtained during the investigations, is an experimental proof of growth of α‐SixGe1–xO2 single crystals under the hydrothermal conditions. The present results thus open the possibility to tune the piezoelectric properties of these materials by varying the chemical composition. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Dielectric and ferroelectric properties of (1-x)Na0.5Bi0.5TiO3-xSrTiO3 lead-free piezoceramics system

Lead-free piezoelectric ceramics (1-x)Na0.5Bi0.5TiO3-xSrTiO3 (NBST100x), where x=0.02-0.90, were prepared by the fine ceramic sintering technique in air. It was found that all compositions showed single perovskite phase and the crystal structure changed from rhombohedral to cubic at 0.20<x<0.50. The experiment results showed that with the increasing of ST content, the piezoelectric parameters d33, electromechanical coefficient kP and coercive field Ec both decreased. When x=0.25, Tc of 210°C, Ec of 1.26 kV/mm, em of 4984.84 and d33 of 60 pC/N were obtained, respectively. In addition, the samples with lower ST content experienced two phase transitions, the diffuse phase transition had typical relaxor-ferroelectric characteristic. While, with the increasing of ST content (=40%), the samples had only one phase transition peak, the temperature dependence curve of dielectric constant moved towards lower temperature, which could be mostly ascribed to the function of paraelectric ST, and explained by the micro-macro domain transition theory.

Phase transition and electrical properties of lead free (Na 0.5K 0.5)NbO 3–BiAlO 3 ceramics

Lead free (1− x)(Na 0.5K 0.5)NbO 3– xBiAlO 3 (NKN–BA) piezoelectric ceramics have been prepared by a solid-state reaction method. The phase transitional behavior and various electrical properties were investigated. A pure perovskite structure can be achieved when the content of BA is less than 5%. A morphotropic phase boundary between orthorhombic and tetragonal ferroelectric phases has been identified in the composition range of 0.005 ≤ x ≤ 0.01. The enhanced ferroelectric and piezoelectric properties of a piezoelectric constant d 33 of 202 pC/N, a planar electromechanical coefficient k p of 46%, a remanent polarization P r of 23.6 μC/cm 2 and a Curie temperature of 372 °C appear in the composition with x = 0.01. These results indicate that the materials studied have potential as a candidate of lead free piezoelectric ceramics.

Optimized orientation of 0.71Pb(Mg1/3Nb2/3)O3–0.29PbTiO3 single crystal for applications in medical ultrasonic arrays

In order to extend the potential applications of medical ultrasonic array transducers, two optimized directions with the maximal electromechanical coefficient k33′ and minimal k31 are determined for [001] and [110] poled 0.71Pb(Mg1/3Nb2/3)O3-0.29PbTiO3 single crystals using the experimental method. The maximum values of k33′ can reach 92.8% and 93.3%, respectively, corresponding to [001]W/[110]L and [110]W/[1–11]L cuts. Furthermore, we simulate the performances of three 3.5 MHz linear array transducers based on the determined directions by PIEZOCAD. Results indicate that under the [001]W/[110]L direction, 25% broader bandwidth, 40% shorter pulse length, and 3 dB higher sensitivity can be obtained compared to the traditional Pb(Zr1−xTix)O3 transducers.

Dynamic Bone Quality-A Non-Invasive Measure of Bone's Biomechanical Property

Carbon-based electroactive polymers (EAPs) are core materials for actuator applications. Introducing conductive fillers into EAPs is considered an effective method to improve the actuating performance, due to the enhanced dielectric properties achieved. This work describes the elaboration and characterization of polyurethane (PU)/oxygen-functionalized graphene (OFG) composite films. Results revealed that for the nanocomposites, a large increase in dielectric constant was obtained without a great mechanical reinforcement, whereas there was no improvement in electromechanical performance as compared to pure polyurethane. The possible reasons for these discordant results were thus investigated with the help of multiscale studies. The importance of measuring the dielectric and mechanical properties under the same conditions as those used to drive actuators could be pointed out. Using high electric field values led to a better prediction of the electromechanical coefficient M31 for pure PU at low frequency, but did not completely explain the decreasing M31 found for the composites. The discrepancy could be due to the moderate adhesion between the polymer and the graphene nanoplatelets, but also to the competition between the increased dielectric constant and the decreased electric field seen by the polymer, induced by MWS interfacial polarization.

Effective properties of thermo-electro-mechanically coupled piezoelectric fiber reinforced composites

In the present work, strength of materials based approach has been used for determination of effective coupled thermo-electro-mechanical (TEM) properties of piezoelectric fiber reinforced composite (PFRC). Rectangular representative volume element (RVE) with rectangular fibers has been considered and dependencies of effective coupled thermo-electro-mechanical coefficients of PFRC on fiber volume fraction have been studied. Results obtained for electro-mechanical coefficients have been compared with already published results [Mallik N, Ray MC. Effective coefficients of piezoelectric fiber reinforced composites. AIAA J 2003;41:704–10. Ray MC. Micromechanics of piezoelectric composites with improved effective piezoelectric constant. Int Mech Mater Des 2006;3:361–71] and show an excellent agreement. Results also show that effective thermal coefficients are reduced and the effective pyroelectric coefficients for PFRC are increased (for some fiber volume fraction range) compared to that in bulk piezoelectric materials. Model predicts strong dependence of the effective coefficients of the PFRC on the fiber volume fraction as well as elastic properties of matrix.

Manganese and Antimony Doped Lead Zirconate Titanate Ceramic Fibers and Fiber/Epoxy 1—3 Composites

Manganese and antimony doped lead zirconate titanate [Pb(Sb2/3 Mn1/3)0.08(Zr0.52Ti0.48) 0.92O3, PSM—PZT] fibers were prepared by the sol-gel method. The micrographs obtained using a scanning electron microscope (SEM) show that the diameter of the fibers was about 50 μm. The crystalline grains size was 3 ~ 12 μm depending on the sintering temperature. X-ray diffraction patterns show that PSM-PZT ceramic fibers sintered at 1285°C have a pure perovskite structure. The ceramic fiber/epoxy 1—3 composites were fabricated by filling the ceramic fiber bundle with epoxy. The dielectric permittivity ε, electromechanical coefficient kt and the piezoelectric constant d33 of 1—3 composites with 50% fiber loading were 760, 0.67, and 178pC/N, respectively. The hysteresis loop of the composites was measured by a Radiant ferroelectric test system. The results show that the composites could withstand an electric field of 8 kV/mm at room temperature. The effect of pre-poling on symmetry of the hysteresis loop was investigated.

A PZT Based Material for Bimorph Type Transducers and a New Optical Method to Evaluate the Bimorph Performance

The displacement devices using piezoceramic sensors play an important role in many fields. Soft type piezoelectric materials used for such sensors are more appealing because of their lower coercive field, relatively low modulus of elasticity, high electromechanical coupling factors and piezoelectric strain coefficients. We designed a PZT type material doped with niobium and nickel to increase the strain coefficient and still retaining a high coupling coefficient. The chemical formula was Pb0.97Ba0.08Nb0.03Ni0.06Zr0.46Ti0.40O3. The main piezoelectric parameters were: d33=680 pm/V, d31=-235 pm/V, kp=0.64 and k31=0.42. A unimorph transducer was made from a thin sheet of such a piezoceramic material, tightly bonded on a thin optically polished glass plate and mounted as a cantilever. The performance of this transducer was evaluated by means of a new optical method which makes use of the Moiré deflectometry and provides high precision. The method is rather simply and consists mainly in the following: the Moiré fringes rotate when the bimorph bends under the influence of the electric field and by measuring the rotating angle of the fringes one can easily determine the bimorph curvature and the free end displacement.

Thin film piezoelectric response characterisation using atomic force microscopy with standard contact mode imaging

This article introduces a technique for observing and quantifying the piezoelectric response of thin films, using standard atomic force microscopes (AFMs). The technique has been developed and verified using strontium-doped lead zirconate titanate (PSZT) thin films, which are known for their high piezoelectric response. Quantification of the electro-mechanical voltage coefficient d 33 (pm/V) is made directly based on the applied peak-to-peak voltage and the corresponding peak-to-peak displacement in the obtained scan image. Under the proposed technique the AFM is configured in contact mode, where the silicon nitride tip is set to follow the film displacement at a single point. A known sinusoidal voltage is applied across the film and the displacement determined as a function of time, rather than the typical AFM measurement of displacement versus tip position. The resulting raster image contains several bands, which are directly related to the AFM scan frequency and the applied sinusoidal voltage and its frequency. Different combinations of the AFM scan frequency and the applied sinusoid frequency have been used to characterise the PSZT thin films, with estimated values of d 33 between 109 and 205 pm/V.