Hydrostatic Piezoelectric Coefficient Research Articles

Towards advanced piezoelectric metamaterial design via combined topology and shape optimization

Metamaterials open up a spectrum of artificially engineered properties otherwise unreachable in conventional bulk materials. For electromechanical energy conversion systems, lightweight materials with high hydrostatic piezoelectric coupling coefficients and negative Poisson’s ratio can be obtained. Thus, in this contribution, we explore the possibilities of piezoelectric metamaterials design by employing structural optimization. More specifically, we apply a sequential framework of topology and shape optimization to design piezoelectric metamaterials with negative Poisson’s ratio for electromechanical energy conversion under uniform pressure. Topology optimization is employed to generate the initial layout, whereas shape optimization fine tunes the design and improves durability and manufacturability of the structures with the help of a curvature constraint. An embedding domain discretization (EDD) method with adaptive domain and shape refinement is utilized for an efficient and accurate computation of the state problem in the shape optimization stage. Multiple case studies are conducted to determine the importance of desired stiffness characteristics, symmetry conditions and objective formulations on the design of piezoelectric metamaterials. Results show that the obtained designs are highly dependent on the desired stiffness characteristics. Moreover, the addition of the EDD-based shape optimization step introduces significant changes to the designs, confirming the usability of the sequential framework.

Novel Piezo-active 2–1–2 Composites with Sets of Large Hydrostatic Parameters

A 2–1–2 composite with two single-crystal components is studied for the first time to highlight large hydrostatic piezoelectric coefficients dh * and gh *, figure of merit dh *gh *, and electromechanical coupling factor kh *. Each 2–1–2 composite contains layers of domain-engineered [011]-poled relaxor-ferroelectric (1–x)Pb(Zn1/3Nb2/3)O3 – xPbTiO3 single crystal (x = 0.0475–0.09) and heterogeneous layers being systems of aligned piezoelectric Li2B4O7 single crystal rods in polyethylene, and these rods have an elliptic cylindrical shape. New diagrams show the volume-fraction ranges wherein large values of dh *> 10−9 C/N, dh *gh *> 2.10−10 Pa−1 and kh *≈ 0.5–0.6 are observed.

Orientation effects, hydrostatic response, and figures of merit in 2–2-type composites based on relaxor-ferroelectric single crystals

The article reports new results on the hydrostatic performance of laminar piezo-active composites based on domain-engineered relaxor-ferroelectric single crystals (SCs) with the perovskite-type structure. Layers of the composites are either single-crystal poled along [011] (where rotations of the main crystallographic axes around two co-ordinate axes are considered) or porous polymer, with aligned spheroidal pores. These composites are described by 2–2–0 connectivity. An influence of the rotation of the main crystallographic axes and porosity is analyzed, and maxima of the hydrostatic piezoelectric coefficient figure of merit and electromechanical coupling factor of the composites are found as functions of a few parameters. New diagrams are built to show regions of the large (over 1000 pC/N) at variations of two rotation angles in the single-crystal layers. Large values of the hydrostatic figure of merit ∼ (10−10 – 10−9) Pa−1 and electromechanical coupling factor are achieved in specific volume-fraction and rotation-angle ranges. These and other large values of the hydrostatic parameters of the studied 2–2-type composites are important for effective hydroacoustic applications.

Novel lead-free 2–1–2 composite: predicted high piezoelectric sensitivity and significant hydrostatic response

A parallel-connected composite with 2–1–2 connectivity and two lead-free single-crystal (SC) components is proposed. Its high piezoelectric sensitivity is highlighted and its large hydrostatic parameters are described. The first type of composite layer represents a ferroelectric domain-engineered [001]-poled [Li, (K, Na)](Nb, Ta)O3 SC. In the second type of composite layer, piezoelectric Li2B4O7 SC rods in the form of an elliptic cylinder are regularly aligned in a large polymer matrix. The effective electromechanical properties of the composite were found in three stages, using the effective field and matrix methods that are applicable to piezoelectric media. A new orientation effect was studied, linked with rotations of SC rod bases in the polymer medium that forms the second type of layer. Since these rotations are in a Li2B4O7 SC with a unique elastic and piezoelectric anisotropy, the second type of layer exhibits a noticeable influence on the piezoelectric performance and hydrostatic response of the composite. A variation of the aspect ratio of the Li2B4O7 rod base becomes another important factor that can improve the hydrostatic parameters of the composite. Some effective parameters of related 2–1–2 composites were compared for different polymer components. Three diagrams were first constructed for the high-performance 2–1–2 [Li, (K, Na)](Nb, Ta)O3/Li2B4O7/polyethylene composite to show the ranges of rotation angles and volume fractions that correspond to the longitudinal piezoelectric voltage coefficient > 500 mV m N−1, hydrostatic piezoelectric coefficient > 200 mVm N−1 and hydrostatic figure of merit >10−11 Pa−1. These effective parameters are important in piezoelectric sensors and hydroacoustic and other applications of novel lead-free composites.

Threadlike Piezoelectric Sensors Based on Ferroelectrets and Their Application in Washable and Breathable Smart Clothing

AbstractFerroelectrets, featuring strong piezoelectric activity, flexibility, lightweight, and low cost, are advanced material and have attractive prospects for various sensors and actuators. However, large‐scale production of ferroelectret‐based devices and their straightforward implementation in complicated structures remain difficult tasks. In this study, a novel self‐shielding threadlike piezoelectric pressure sensor based on irradiation cross‐linked polypropylene (IXPP) ferroelectrets with a symmetric coaxial structure, named Ferroelectret Coaxial Sensor (FCS), is designed, prepared, and characterized. Besides, such sensors with a length of up to 300 m are successfully produced by an industrial continuous production line, confirming that the fabrication procedure is compatible with it and that the FCS can be mass‐produced in the future. The results show that the hydrostatic piezoelectric coefficient up to 55 pC/N is achieved in the FCS, which is around four times of magnitude higher than those of commercially available piezo‐cables made of poly (vinylidene fluoride). Smart carpets and wristers weaved with an integrated FCS, that can be produced by an industrial production line, are sensitive, flexible/stretchable, washable, and breathable, demonstrating great potential in motion recognition for health care. A laboratory prototype of traffic sensors based on the FCS indicates its capability in speed meauring and dynamic weighing for vehicles. This study will greatly promote applications of ferroelectrets in wearable devices, smart housing, intelligent transportation, etc.

Large piezoelectric anisotropy and high hydrostatic piezoelectric activity due to an appreciable orientation effect and porosity in novel 2–2–0 composites

The polarization orientation effect and porosity effect on the piezoelectric properties and related parameters are studied in 2–2-type composites based on domain-engineered relaxor-ferroelectric [011]-poled single crystals. The parameters, which are of great interest, are an anisotropy of the piezoelectric coefficients [Formula: see text], an anisotropy of the energy-harvesting figures of merit [Formula: see text] and the hydrostatic piezoelectric coefficient [Formula: see text]. An orientation of the main crystallographic axes in each polydomain single-crystal layer is described by angles [Formula: see text] and [Formula: see text]. Diagrams built for the first time show the ([Formula: see text]) regions, where a large anisotropy of [Formula: see text] (or [Formula: see text]) is achieved, and where inequality [Formula: see text] 1000 pC/N holds. A large local max [Formula: see text] = 1930 pC/N is achieved in a 2–2–0 PZN–0.065PT-based composite at the longitudinal piezoelectric coefficient [Formula: see text] = 2290 pC/N and figure of merit [Formula: see text] = 1.02[Formula: see text]10[Formula: see text] Pa[Formula: see text]. The aforementioned large parameters are to be of value in piezoelectric sensing, energy harvesting and hydroacoustics.

Quasi-laminate and quasi-columnate modeling of dielectric and piezoelectric properties of cubic-cell metamaterials

Dielectric and piezoelectric properties of closed-cell or open-cell metamaterials with cubic cells are predicted analytically via quasi-laminate / Q-lam and quasi-columnate / Q-col models. For dielectric properties also numerical results are given. Model predictions of relative permittivity are within the Wiener bounds. Q-lam model predictions are higher than Q-col model predictions (and even exceed the Hashin-Shtrikman upper bound), but the numerical results are in between these two predictions. Closed-cell metamaterials exhibit higher permittivity than open-cell metamaterials. The classical predictions by Rittenmyer et al. and Banno correspond to the Q-col model predictions for open-cell and closed-cell metamaterials, respectively. Model predictions for longitudinal piezoelectric charge coefficients are close to Newnham’s parallel model, i.e. relatively constant over a wide range of porosity, with a steep decrease as the porosity approaches 100 %. Brief comments are given on the transverse piezoelectric charge coefficient, the hydrostatic piezoelectric charge coefficient and the piezoelectric voltage coefficient.

Freeze casting of lamellar-structured porous lead-free (Na0.52K0.48)(Nb0.95Sb0.05)O3 piezoceramic with remarkable enhancement in piezoelectric voltage constant and hydrostatic figure of merit

The study reports the development of lamellar-structured, porous lead-free (Na0.52K0.48)(Nb0.95Sb0.05)O3 ceramics, abbreviated as NKNS, using the freeze-casting method with water as pore-forming agent. The effect of directional porosity on the microstructure, dielectric, and piezoelectric properties of the lead-free porous material is investigated. Furthermore, the effects of conventional and microwave sintering on microstructure and piezoelectric properties have also been analyzed. In addition, the study compares conventional and corona poling too. The results depicted no deterioration of piezoelectric properties (d33:130 pC/N), despite being ~ 50% porosity, along with reasonably good hydrostatic piezoelectric strain coefficient (dh: 60pC/N). The samples exhibited hydrostatic piezoelectric voltage coefficient (gh) of 58.70 mV.m/N providing a significant value of the hydrostatic figure of merit (HFOM = dh∙gh: 3522 × 10–15 Pa−1) for the porous NKNS ceramic which is nearly 39 times more than the dense ceramic. Considering its unique advantages such as environmental friendly, less dense, wide performance range with enhanced figure of merit, the lamellar-structured NKNS ceramic is a promising material for sensor and transducer applications.

Improved piezoelectric performance and hydrostatic parameters of a novel 2–0–2–0 composite

A composite containing parallel-connected layers of a porous ferroelectric PZT-type ceramic and porous polymer is manufactured, and effective piezoelectric properties and hydrostatic parameters are first studied for 2–0–2–0 connectivity. An influence of air pores in different layers on the longitudinal (d33∗) and hydrostatic (dh∗ and gh∗) piezoelectric coefficients, and squared hydrostatic figure of merit dh∗gh∗ of the composite is analysed. Large values of d33∗ ≈ 400–600 pC/N, dh∗ ≈ 300–500 pC/N, gh∗ ≈ 100–150 mV m/N, and dh∗gh∗ ≈ (30–60)·10-12 Pa−1 suggest that this material has no analogs among ceramic-based composites and is suitable for piezoelectric sensor and hydroacoustic applications.

Effect of poling direction and porosity on piezoelectric figures of merit: A numerical study

Piezoelectric materials are at front of scientific research when it comes to sensing, actuation and energy harvesting from smart materials and structures. Crucial to such materials is their output power and performance in terms of figure of merit (FOM). In the present paper, we have compared the effect of two approaches, namely, introducing porosity and poling tuning on different figures of merit. Here, two material systems, 0.3BaTiO3-0.7NaNbO3 (BT-NNb) and Pb[ZrxTi1-x]O3 (PZT-5A), have been considered and the effective piezoelectric properties for different porosity levels (upto 25% volume fraction) and at different poling orientations were computed using representative volume element (RVE). It was observed that for BT-NNb the effective properties get optimised at a given poling orientation unlike in PZT-5A. For BT-NNb, without poling tuning, the maximum change in FOM31, FOM33 and FOMh (associated with transverse (d31), longitudinal (d33) and hydrostatic (dh) piezoelectric strain coefficients) was found to be 14.3%, 14.1% and 14.4% for 25% porous (by volume) system. On the other hand, for the same system, at optimum poling orientation all the FOMs were found to be ∼ 1000 times higher than their corresponding initial values. However, in PZT-5A, no optimum poling orientation was observed and thus it was concluded that FOMs can only be improved by introducing porosity in the system.

Effective piezoelectric coefficients of cement-based 2–2 type piezoelectric composites based on a multiscale homogenization model

The effective piezoelectric properties of the cement-based 2–2 type piezoelectric composites have been investigated both experimentally and theoretically. The two-scale asymptotic expansion method is employed to develop a homogenized model for the effective properties calculation. The validity of the theoretical solution is confirmed through the comparison with the experimental results. The influence of the volume fraction of the piezoelectric phase on the effective piezoelectric coefficients is then examined. It is found that higher volume fraction will induce obvious increment of the magnitude of the effective piezoelectric strain coefficients d31Eff, d32Eff, and d33Eff, however, the hydrostatic piezoelectric strain coefficient dhEff will reach a maximum value at a lower volume fraction.

Enhanced performance of ferroelectric materials under hydrostatic pressure

Mechanical confinement or restricted degrees of freedom have been explored for its potential to enhance the performance of ferroelectric devices. It presents an easy and reversible method to tune the response for specific applications. However, such studies have been mainly limited to uni- or bi-axial stress. This study investigates the effect of hydrostatic pressure on the ferroelectric behavior of bulk polycrystalline Pb0.99Nb0.02(Zr0.95Ti0.05)0.98O3. Polarization versus electric field hysteresis plots were generated as a function of hydrostatic pressure for a range of operating temperatures (298–398 K). The application of hydrostatic pressure was observed to induce anti-ferroelectric like double hysteresis loops. This in turn enhances the piezoelectric, energy storage, energy harvesting, and electrocaloric effects. The hydrostatic piezoelectric coefficient (dh) was increased from 50 pCN−1 (0 MPa) to ∼900 pC N−1 (265 MPa) and ∼3200 pCN−1 (330 MPa) at 298 K. Energy storage density was observed to improve by more than 4 times under pressure, in the whole temperature range. The relative change in entropy was also observed to shift from ∼0 to 4.8 J kg−1 K−1 under an applied pressure of 325 MPa. This behavior can be attributed to the evolution of pinched hysteresis loops that have been explained using a phenomenological model. All values represent an improvement of several hundred percent compared to unbiased performance, indicating the potential benefits of the proposed methodology.

Piezoelectric anisotropy and energy-harvesting characteristics of novel sandwich layer BaTiO3 structures

This paper presents a detailed modelling and experimental study of the piezoelectric and dielectric properties of novel ferroelectric sandwich layer BaTiO3 structures that consist of an inner porous layer and dense outer layers. The dependencies of the piezoelectric coefficients and dielectric permittivity of the sandwich structure on the bulk relative density α are analysed by taking into account an inner layer with a porosity volume fraction of 0.5–0.6. The observed changes in and are interpreted within the framework of a model of a laminar structure whereby the electromechanical interaction of the inner porous layer and outer dense layers have an important role in determining the effective properties of the system. The porous layer is represented as a piezocomposite with a 1–3–0 connectivity pattern, and the composite is considered as a system of long poled ceramic rods with 1–3 connectivity which are surrounded by an unpoled ceramic matrix that contains a system of oblate air pores (3–0 connectivity). The outer monolithic is considered as a dense poled ceramic, however its electromechanical properties differ from those of the ceramic rods in the porous layer due to different levels of mobility of 90° domain walls in ceramic grains. A large anisotropy of at α = 0.64–0.86 is achieved due to the difference in the properties of the porous and monolithic layers and the presence of highly oblate air pores. As a consequence, high energy-harvesting figures of merit are achieved that obey the condition at and values of the hydrostatic piezoelectric coefficients and are achieved at α= 0.64–0.70. The studied BaTiO3-based sandwich structures has advantages over highly anisotropic PbTiO3-type ceramics as a result of the higher piezoelectric activity of ceramic BaTiO3 and can be used in piezoelectric sensor, energy-harvesting and related applications.

Piezoelectric sensitivity and hydrostatic response of novel lead-free 2–0–2 composites with two single-crystal components

This paper reports the piezoelectric performance and important related hydrostatic parameters of 2–0–2 composites based on lead-free ferroelectric and piezoelectric single crystals with 4mm symmetry. We demonstrate that ferroelectric domain-engineered alkali niobate-tantalate based single crystals provide large values of the piezoelectric coefficients g3j∗ and related parameters when used in a 2–0–2 composite system with a relatively wide range of volume fractions of single-crystal components. An ‘aspect-ratio effect’ as a result of the presence of inclusions of a piezoelectric Li2B4O7 single crystal in a polymer medium is studied for the first time for a case where the elastic compliance s12 in the single crystal/polymer layer of the composite passes through zero. It is observed that changes in the aspect ratio and volume fraction of the Li2B4O7 inclusions influence the hydrostatic piezoelectric coefficient gh∗, squared figure of merit dh∗gh∗ and electromechanical coupling factor kh∗ of the composite, and large values of gh∗∼102 mV·m/N, dh∗gh∗∼ (10−11–10−10) Pa−1 and kh∗≈ 0.6–0.7 are achieved. A link between max kh∗ and a change in sgns12 is first described for the 2–2-type composite, and a comparison of the hydrostatic parameters of the novel and related composites is made. The present results show the potential of lead-free 2–0–2 composites that are suitable for piezoelectric sensor, energy-harvesting and hydroacoustic applications.

Piezoelectric Performance and Hydrostatic Parameters of Novel 2–2-Type Composites

This paper provides a detailed study of the structure-piezoelectric property relationships and the hydrostatic response of 2-2-Type composites based on relaxor-ferroelectric 0.72 Pb (Mg1/3Nb2/3)O3-0.28PbTiO3 single crystal (SC) material. Type I layers in the composite system are represented by a single-domain [111]-poled SC. Changes in the orientation of the crystallographic axes in the Type I layer are undertaken to determine the maximum values of the hydrostatic piezoelectric coefficients dh∗ , gh∗ , and eh∗ , and squared figure of merit dh∗ gh∗ of the composite. The Type II layers are a 0-3 composite whereby inclusions of modified PbTiO3 ceramic are distributed in a polymer matrix. A new effect is described for the first time due to the impact of anisotropic elastic properties of the Type II layers on the hydrostatic piezoelectric response that is coupled with the polarization orientation effect in the Type I layers. Large hydrostatic parameters gh∗ ≈ 300 -400 mV · m/N, eh∗ ≈ 40 -45 C/ [Formula: see text], and dh∗ gh∗ ∼10-11 Pa -1 are achieved in the composite based on the 0.72 Pb(Mg1/3Nb2/3)O3-0.28PbTiO3 SC. Examples of the large piezoelectric anisotropy ( |d33∗ /d3f∗ | ≥ 5 or | g33∗ /g3f∗ | ≥ 5 ) are discussed. The hydrostatic parameters of this novel compositesystem are compared to those of conventional 2-2 piezocomposites.

Inter-relations of domain orientations and piezoelectric properties in composites based on relaxor-ferroelectric single crystals

ABSTRACTThis paper presents results on a detailed comparative study of 2–2 relaxor-ferroelectric single crystal / polymer composites. Examples of the hydrostatic piezoelectric performance are discussed for 2–2 composites based on [011]-poled Mn-modified 0.26Pb(In1/2Nb1/2)·O3−0.42Pb(Mg1/3Nb2/3)O3−0.32PbTiO3 single crystals at a molar Mn concentration in the range of 1–5 mol. %. The high piezoelectric activity of these single crystals and rotations of the main crystallographic axes in the single-crystal layers of the composite lead to large values of hydrostatic piezoelectric coefficients , and , squared figure of merit , and electromechanical coupling factor . A rotation mode that leads to a weakening the piezoelectric activity related to the piezoelectric coefficient d32 < 0 is important to achieve composites with a range of large hydrostatic parameters, e.g., ≈ (300–350) pC / N, ∼ 100 mV·m / N, ≈ (21–23) C / m2, ∼ (24–30)·10−12 Pa−1, and ≈ 0.30. In contrast to , higher values of ∼ 10−10 Pa−1 are achieved due to the longitudinal piezoelectric effect. The results obtained in this piezoelectric composite system are interpreted by taking into account the orientation of 71° ferroelectric domains in the single-crystal layers and provide a route to form novel high-performance piezoelectric composites.

Effect of the matrix subsystem on hydrostatic parameters of a novel 1–3-type piezo-composite

The influence of the aspect ratio and volume fraction of ferroelectric ceramic inclusions in a 0–3 matrix on the hydrostatic parameters of a three-component 1–3-type composite is studied to demonstrate the important role of the elastic properties of the two-component matrix on the composite performance. Differences in the elastic properties of the 0–3 matrix and single-crystal rods lead to a considerable dependence of the hydrostatic response of the composite on the anisotropy of the matrix elastic properties. The performance of a 1–0–3 0.92 Pb ( Zn 1/3 Nb 2/3) O 3–0.08 PbTiO 3 SC/modified PbTiO 3 ceramic/polyurethane composite suggests that this composite system is of interest for hydroacoustic applications due to its high hydrostatic piezoelectric coefficients [Formula: see text] and [Formula: see text], squared figure of merit [Formula: see text], and electromechanical coupling factor [Formula: see text].

High-performance 1–3-type lead-free piezo-composites with auxetic polyethylene matrices

High piezoelectric sensitivity and large hydrostatic parameters are discussed for two 1–3-type single crystal/auxetic polymer composites. The single crystal components selected are based on lead-free (K,Na)(Nb,Ta)O3 and (Li,K,Na)(Nb,Ta)O3 solid solutions, and the auxetic polymers are characterised by Poisson’s ratios –0.83≤ ν ≤–0.29. The composites examined exhibit advantageous properties over conventional lead-based piezo-active composites and ceramics such as high longitudinal piezoelectric coefficient g33⁎~(102–103) mV·m/N, squared figure of merit (Q33⁎)2~10–11 Pa−1, hydrostatic piezoelectric coefficient gh⁎~(102–103) mV·m/N and squared figure of merit (Qh⁎)2~(10–11–10−10) Pa−1. The composites also demonstrate an infinitely large anisotropy of piezoelectric coefficients d3j⁎.

New orientation effect in piezo-active 1–3-type composites

This paper demonstrates the influence of the mutual orientation of the poling direction of single-crystal and ceramic components on the properties of 1–0–3 composites containing two ferroelectric components and a piezo-passive polymer. Effective properties to be considered are hydrostatic piezoelectric performance, anisotropy of squared figures of merit and electromechanical coupling factors. We demonstrate that the elastic and piezoelectric anisotropy of the 0–3 connectivity ferroelectric ceramic/polymer matrix with prolate inclusions leads to large hydrostatic piezoelectric coefficients (dh∗ and gh∗) and squared figure of merit (dh∗gh∗) in a 1–0–3 0.67Pb(Mg1/3Nb2/3)O3–0.33PbTiO3 single crystal/(Pb1–xCax)TiO3 ceramic/araldite composite with x = 0.20–0.25. In this type of composite values of maxgh∗ ∼102 mV m/N and max(dh∗gh∗) ∼10−11 Pa−1 are achieved at specific volume-fraction and rotation-angle ranges due to a new orientation effect in the presence of a highly anisotropic 0–3 matrix. Such composites are of interest for sensor, actuator and energy-harvesting applications.

Microgeometry, piezoelectric sensitivity and anisotropy of properties in porous materials based on Pb(Zr, Ti)O3

Relations between the microgeometry, piezoelectric sensitivity and piezoelectric anisotropy are studied in porous composite materials based on Pb ( Zr , Ti ) O 3 ceramics. Systems of micrographs of cuts being parallel and perpendicular to the polarization direction are first shown for the porosity range v p = 0.05 - 0.57, and examples of microcracking at v p = 0.57 are considered. Experimental data on longitudinal and hydrostatic piezoelectric coefficients and squared figures of merit are represented as functions of v p , and nonmonotonic behavior of the piezoelectric anisotropy factor with increasing v p is analyzed in the context of changes in the microgeometry. Experimental results are compared to those derived from approximation formulae for the related porous ceramic.