Hydrostatic Figure Research Articles

Fabrication of Ceramic-Polymer Piezo-Composites with Triply Periodic Minimal Interfaces via Digital Light Processing

The geometry of the phase interface in co-continuous piezoelectric composites is critical in improving their piezoelectric properties. However, conventional co-continuous piezoelectric composites are mostly simple structures such as wood stacks or honeycombs, which are prone to stress concentrations at the joints, thus reducing the fatigue service performance and force–electric conversion efficiency of piezoelectric composites. Such simple structures limit further improvements in the overall performance of co-continuous piezoelectric composites. In this study, based on the digital light processing 3D printing method, we investigated the influence of three different structures–the gyroid, diamond, and woodpile interfaces–on the piezoelectric and mechanical properties of co-continuous ceramic/polymer piezoelectric composites. These findings demonstrate that the gyroid and diamond interfaces outperformed the ceramic skeleton of the woodpile interface in terms of both mechanical and electrical properties. When the ceramic volume percentage was 50%, the piezo-composite of the gyroid surface exhibited the greatest hydrostatic figure of merit (HFOM), reaching 4.23×10−12 Pa−1, and its piezoelectric coefficient (d33) and relative dielectric constant (εr) reached 115 pC/N and 748, respectively. The research results lay the foundation for the application of co-continuous piezoelectric composites in underwater communication and detection.

Ultra-high d31 anti-chiral negative Poisson’s ratio BaTiO3 ceramics fabricated by vat photopolymerization 3D printing

In this study, the anti-chiral negative Poisson's ratio structure BaTiO3 piezoelectric ceramics were fabricated by vat photopolymerization 3D printing technology, which obtained an ultra-high transverse piezoelectric coefficient d31. Here, we performed uniaxial compressive load simulations and electric field-driven lattice in-plane strain response simulations, which showed an in-plane negative Poisson's ratio of −1 for the BaTiO3 ceramics. Its strain amplification is about 10 times that of BaTiO3 bulk material. Using the principle of positive and negative piezoelectric effects, we measured effective transverse piezoelectric coefficients d31 for different dimensional parameters. The effective transverse piezoelectric coefficient d31 with a maximum of 599 pm/V was detected at a ligament aspect ratio of 3.6 for the negative Poisson's ratio BaTiO3 piezoelectric ceramics, which is 7.7 times higher than that of the bulk material. For the prepared hydrophone, test results show that the effective hydrostatic strain constant dh and Hydrostatic Figure of Merit (HFOM) of BaTiO3 piezoelectric ceramics with a negative Poisson's ratio structure are 29.6 and 808 times higher than those of bulk BaTiO3.

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.

Large main-belt asteroids are generally not Maclaurin or Jacobi ellipsoids

Aims.A recent major high-angular-resolution imaging survey of 42 large main-belt asteroids (D > 100 km) with VLT/SPHERE has provided shape models of these bodies with an unprecedented accuracy. We ask whether the shapes of these bodies correspond to Maclaurin or Jacobi hydrostatic equilibrium figures.Methods.To address this question, we compared the aspect ratios and rotation rates of these asteroids with Maclaurin or Jacobi equilibrium figures.Results.The rotation rates and polar flattenings of the 42 asteroids globally do not match those of Maclaurin or Jacobi ellipsoids. Moreover, the equatorial axes of the asteroids are not compatible with an axial symmetry as for Maclaurin figures. Only a very few of them could be compatible with a known hydrostatic figure such as Maclaurin, Jacobi, or Clairaut ellipsoids.

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.

Electromechanical behavior of 3-3 piezoelectric star-shaped metamaterial with four types of connection

This study presents the complete electromechanical properties of 3-3 piezoelectric metamaterial based on variants of star-shaped cellular structure. Four types of three-dimensional piezoelectric star-shaped metamaterial (3D PSSM) with different connection modes (with symmetric interconnects, with asymmetric horizontal interconnects, with asymmetric vertical interconnects and without any interconnects) are introduced. Periodic boundary conditions are applied to unit cell of 3D PSSM. And the finite element analysis is implemented to investigate the effect of different structural parameters and poling directions (longitudinal and transverse) on the effective electromechanical response. Compared with the monolithic piezoelectric materials, different connection modes of the 3D PSSM show different combinations of enhanced electromechanical response and figures of merit. For example, longitudinally poled 3D PSSM with symmetric interconnects has both higher hydrostatic strain coefficient (dh) and hydrostatic figure of merit (dh•gh), and lower acoustic impedance (Z), indicating it is more suitable for the design of hydrophones; longitudinally poled 3D PSSM with asymmetric interconnects has higher piezoelectric coupling constant (kt), indicating that this structure is more suitable for the design of energy harvesters.

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.

Piezoelectric properties of 3-1 type porous PMN-PZT ceramics doped with strodium

In this work, 3-1 type porous lead magnesium niobate-lead zirconate titanate (PMN-PZT) ceramics with one-dimensional ordered pore channels and strontium oxides (SrO) doping on a molecular level have been fabricated by the ionotropic gelation of sodium alginate/PMN-PZT suspensions with SrCl2 solution. By adjusting the concentration of SrCl2 (0.5–2.5 mol/L), the doping amount of SrO in 3-1 type PMN-PZT ceramics increased from 1.954 wt% to 4.052 wt%, making the morphotropic phase boundary (MPB) deviate from rhombohedral (R3m) to tetragonal (P4mm) phase with the decrease in the ratio of the lattice parameters c/a. Increase in the concentration of SrCl2 led to a reduction in the tanδ, an increase in the d33 and ε33. As a result, the prepared samples possessed a maximal hydrostatic figure of merit (HFOM) value of 5045 × 10−15 Pa−1, and a low acoustic impedance (Z) value of 5.88 MRayls, making them promising candidates for application in ultrasonic transformers.

Earth\u2019s gravity from space

Satellite gravimetry began with the launch of the satellites Sputnik 1 and 2 in 1957. During the following 43 years, more and more details were discovered and the models of the Earth’s gravity could be refined. Methods improved and more and more satellite orbits and ground stations were added in the analysis, employing more advanced and precise measuring techniques. A new era started with the dedicated gravimetry missions CHAMP (2000–2010), GRACE (2002–2017), and GOCE (2009–2013). The methods of satellite-to-satellite tracking and satellite gradiometry resulted in a substantial improvement of our knowledge of the Earth’s gravity field in terms of accuracy and its spatial and temporal variations. There are three basic ways of using gravity and geoid models in Earth sciences and geodesy. First, in solid Earth physics, the highs and lows of the field are investigated in comparison with an idealized Earth, e.g., a hydrostatic equilibrium figure. In particular, in South America, Africa, Himalaya and Antarctica the gravity field is known much better now, due to GOCE and lead to an improved understanding of the continental crust and lithosphere. Second, in oceanography, the geoid serves as surface in equilibrium, a hypothetical ocean at rest. The ocean topography is the deviation of the actual ocean surface, measured by satellite altimetry, from this reference. The ocean topography serves as a new and independent input to ocean circulation modeling and leads to an improved understanding of ocean transport of mass, heat, and nutrients. Similarly, geodetic heights of the land surface will soon be referred to the geoid, leading to globally consistent heights and enabling the removal of existent systematic deformations and offsets of national and continental height systems. Third, the GRACE time series of monthly gravity models, reflecting seasonal, inter-annual and long-term gravity changes, became one of the most valuable data sources of climate change studies.

Effect of surface modification of ferroelectric ceramic component on the properties of PZT-type/epoxy piezoelectric composite with spiral structure

A PZT-type ceramic/epoxy resin piezoelectric composite with spiral structure was fabricated by a roll forming-curling method. The ceramic component surface was modified by silane coupling agent KH560 or titanate coupling agent NDZ201 before the spiral ceramic ring was compounded with epoxy matrix. Interface defects are reduced after some time of surface modification. The effects of the two coupling agents on the properties of composites were discussed and compared. The d33 and the hydrostatic figure of merit (FOM) of the composites with KH560 are 7.5% and 29.5% higher than those prepared without the coupling agent. However, the d33 and FOM of the composites treated by NDZ201 are lower than those prepared without the coupling agent. The different structures of the molecular layer at the interface of silane coupling agents and titanate coupling agents play a key role in the different effects on the properties.

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.

Preparation of porous barium titanate ceramics and enhancement of piezoelectric sensitivity

Porous piezoelectric ceramic shows some advantages, such as high hydrostatic figure of merit, low acoustic impedance, and excellent piezoelectric sensitivity, compared with its compact counterpart. These merits make it used widely in various electronic devices, such as underwater acoustic transducer, ultrasonic transducer, and sensor. Currently, the researches of porous piezoelectric ceramics mainly focus on the Pb(Zr, Ti)O<sub>3</sub> ceramic, which is harmful to environment and human health. In this paper, the lead-free porous barium titanate (BaTiO<sub>3</sub>) ceramic doped with dextrin is prepared by using the conventional solid-state method. The effects of sintered temperature and dextrin content on the structure, porosity, and morphology of the pores are studied experimentally and theoretically. Also, the relationship between porosity and dielectric, piezoelectricity, electro-mechanical coupling factor, acoustic impedance, and hydrostatic figure of merit are explored. The X-ray diffraction pattern shows that the lattice constants of ceramic are not affected by dextrin. The BaTiO<sub>3</sub> ceramic demonstrates single perovskite structure with P4mm space group. The SEM micrograph reveals that the porous ceramic has three-dimensional open pores with the size of 1−7 <inline-formula><tex-math id="M2">\begin{document}${\text{μ}}{\rm m}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20181790_M2.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20181790_M2.png"/></alternatives></inline-formula>. Sintering temperature plays a key role in porosity in the BaTiO<sub>3</sub> ceramic. The porosity of ceramic gradually declines with sintered temperature increasing from 1250 to 1300 °C. The max porosity of up to 58% is obtained in 10% dextrin-doped BaTiO<sub>3</sub> ceramic sintered at 1250 °C. The porosity of 5% dextrin-doped ceramic is smaller than that of the undoped one when the sintering temperature is 1250 °C or 1280 °C, indicating that a small amount of dextrin is beneficial to the densification of BaTiO<sub>3</sub> ceramic. Both the dielectric and piezoelectric property gradually decrease with dextrin content increasing. For the BaTiO<sub>3</sub> ceramic, high sintering temperature contributes to better dielectric and piezoelectric property than low temperature. Here, the ceramic with 10% of dextrin sintered at 1250 °C exhibits the highest hydrostatic figure of merit (8376 × 10<sup>–15</sup> Pa<sup>–1</sup>) and the lowest acoustic impedance (~ 2.84 Mrayls). The binding force between grains is also obviously enhanced in the ceramic sintered at 1280 °C, which is very helpful for their mechanical strength improvement. The excellent properties of the BaTiO<sub>3</sub> ceramic doped with dextrin indicate its potential applications in sensor and hydrophone.

3-3 piezoelectric metamaterial with negative and zero Poisson’s ratio for hydrophones applications

This study presents the electromechanical properties of the 3-3 piezoelectric metamaterial based on variants of honeycomb (HC) structure. Three kinds of three-dimensional (3D) elastically anisotropic and piezoelectrically active HC structures were introduced, namely, conventional HC (3D-CHC), a re-entrant HC (3D-RE) and a semi-re-entrant HC (3D-SRE). Highly porous 3D finite element models of the mentioned three kinds of metamaterials were developed and the role of ligament orientation on their effective elastic, piezoelectric and dielectric properties was completely characterized. The intrinsic symmetry of HC structure was utilized and simplified mixed boundary conditions equivalent to periodic boundary conditions were recognized. In comparison to their bulk constituent, all the 3-3 type piezoelectric HC networks exhibited an enhanced response, especially for the longitudinal poling. The normalized figures of merit show a mild dependence on the angle θ and the underlying deformation mechanisms associated with the zero, positive and negative Poisson’s ratios. Figures of merit such as hydrostatic strain coefficient (dh), the hydrostatic figure of merit (dh.gh) and the acoustic impedance (Z) reached their best values at small angles, i.e., θ = 30°. Longitudinally poled networks exhibited four order of magnitude increase in their hydrostatic figure of merit (foam to solid ratio >10,000) and one order of magnitude decrease in the acoustic impedance indicating their applicability for the design of hydrophones.

Architected cellular piezoelectric metamaterials: Thermo-electro-mechanical properties

Advances in additive manufacturing have recently made possible the manufacturing of smart materials with arbitrary microarchitectures, which leads to developing lightweight smart metamaterials with unprecedented multifunctional properties. In this paper, asymptotic homogenization (AH) method is developed for predicting the effective thermo-electro-mechanical properties of architected cellular piezoelectric metamaterials. The effect of pore microarchitecture (relative density and cell topology) and polarization direction on elastic, dielectric, piezoelectric, pyroelectric and thermal properties of periodic cellular piezoelectric metamaterials is explored. The pore topology is determined by Fourier series expansion. Alternative pore microarchitectures are considered by tailoring shape parameters, scaling factor, and rotation angle of the constitutive pore. Smart cellular metamaterials made of both single-phase (BaTiO3) and bi-phase (BaTiO3-expoy) piezoelectric materials are considered. Apart from effective thermo-electro-mechanical properties, a series of figures of merit for the cellular piezoelectric metamaterials, i.e. piezoelectric coupling constant, acoustic impedance, piezoelectric charge coefficient, hydrostatic figure of merit, current responsivity, voltage responsivity and pyroelectric energy harvesting figures of merit, are presented and the reason for difference between the figures of merit of different types of piezoelectric metamaterials is discussed. The figures of merit shed lights on the effect of microarchitecture on optimizing the multifunctional performance of smart cellular metamaterials for applications as structurally efficient multifunctional energy harvesters. It is found that the piezoelectric and pyroelectric figures of merit of cellular piezoelectric metamaterials can be significantly improved compared to the commonly used honeycomb cellular materials and composite materials with solid circular inclusion if an appropriate microarchitecture is selected for the pore. For example, piezoelectric charge coefficient (dh) for a transversely polarized single-phase cellular piezoelectric metamaterial with a solid volume fraction of 0.4 can be 350% higher than the corresponding figures of merit of honeycomb piezoelectric material; voltage responsivity of transversely polarized bi-phase cellular piezoelectric metamaterials with an inclusion volume fraction of 0.3 can be also 249% higher than the corresponding value of composite materials with a solid circular inclusion.

Characterization of High Porous PZT Piezoelectric Ceramics by different Techniques

Ultimate properties of a porous ceramic is highly process dependent. In this study, prevalent porous ceramics fabrication methods (Freeze casting, Foam reticulation and Burnable Plastic Sphere (BURPS) method) have been compared by fabricating the porous lead zirconate titanate (PZT) based piezoelectric ceramics. Field Emission Scanning electron microscopy (FESEM) studies were carried out to study the pore size and distribution of the ceramics. Hydrostatic co-efficients increased tremendously on incorporation of porosity which led to Hydrostatic Figure of Merit of 7480 in Foam reticulation samples (porosity 86%). The three dimensionally interconnected networks in the freeze casted samples led to lowest acoustic impedance (6 MRayls) despite not having the lowest density.

Dielectric and piezoelectric properties of porous lead-free 0.5Ba(Ca0.8Zr0.2)O3-0.5(Ba0.7Ca 0.3)TiO3 ceramics

Porous barium calcium zirconate titanate 0.5Ba(Ca0.8Zr0.2)O3-0.5(Ba0.7Ca0.3)TiO3 (BCZT) lead-free ferroelectric ceramics were fabricated via a burnt polymer spheres (BURPS) technique by introducing corn starch as the pore-forming agent. The effect of porosity on the microstructure, dielectric, and piezoelectric properties of the porous materials were investigated. An increase in porosity volume fraction from 10% to 25% resulted in an increase in the hydrostatic charge coefficient (dh), which was 140 to 560% higher than that of the dense BCZT material. An increase in porosity fraction from 10% to 25% also lead to a decrease in relative permittivity that was 16.7% to 60.4% lower than the dense material. These two changes in properties provided a significant enhancement of the hydrostatic figure of merit (dh∙gh) for the porous ceramic; for example the dh∙gh of the 25 vol.% porous BCZT ceramic was 158 times more than the dense ceramic and demonstrates the potential of porous lead-free ferroelectrics for piezoelectric transducer devices. Reasons for the significant enhancement in piezoelectric performance of the porous ceramics are discussed.

High piezoelectric sensitivity and hydrostatic figures of merit in unidirectional porous ferroelectric ceramics fabricated by freeze casting

High performance lead zirconate titanate (PZT) ceramics with aligned porosity for sensing applications were fabricated by an ice-templating method. To demonstrate the enhanced properties of these materials and their potential for sensor and hydrophone applications, the piezoelectric voltage constants (g33 and g31), hydrostatic parameters (dh, gh, −d33/d31, dh·gh and dh·gh/tanδ) and AC conductivity as a function of the porosity in directions both parallel and perpendicular to the freezing temperature gradient were studied. As the porosity level was increased, PZT poled parallel to the freezing direction exhibited the highest dh, −d33/d31 and figures of merit dh·gh, dh·gh/tanδ compared to the dense and PZT poled perpendicular to the freezing direction. The gh, g33 and g31 coefficients were highest for the PZT poled perpendicular to the freezing direction; the gh was 150%–850% times higher than dense PZT, and was attributed to the high piezoelectric activity and reduced permittivity in this orientation. This work demonstrates that piezoelectric ceramics produced with aligned pores by freeze casting are a promising candidate for a range of sensor applications and the polarisation orientation relative to the freezing direction can be used to tailor the microstructure and optimise sensitivity for sensor and hydrostatic transducer applications.

Structural phase transition and electrical properties of Sr2+ substituted porous PMN‐PZT ceramics

AbstractIn this study, Sr2+ modified porous PMN‐PZT ceramics with one‐dimensional pore channels were produced by the ionotropic gelation process of alginate/PMN‐PZT suspensions. The ion‐exchange method was employed during the fabrication procedure to adjust the content of SrO addition. With the SrO addition increasing from 1.653 wt.% to 2.957 wt.%, the structural phase of porous PMN‐PZT ceramics transformed from rhombohedral (R) to tetragonal (T) perovskite phase. Accordingly, the electromechanical coupling coefficient (kt) value of porous PMN‐PZT ceramics decreased from 64.7% to 58.7%, while the hydrostatic figure of merit (HFOM) value increased from 1510 to 5547 × 10−15 m2/N, and acoustic impedance Z value ranged from 4.59 to 7.55 MRayls, which helped for applications in underwater transducers or hydrophones.

Effect of Meso‐Scale Geometry on Piezoelectric Performances of Additively Manufactured Flexible Polymer‐Pb(ZrxTi1−x)O3 Composites

By integrating phase-field model and finite element calculations, we demonstrate that the additively manufactured 3-3 polymer-Pb(ZrxTi1-x)O3 composite can attain superb d33 and significantly outperform its 0–3, 1–3, and 2–2 counterparts in terms of hydrostatic figure of merit (HFOM), showing great potential in underwater acoustic applications. As a service to our authors and readers, this journal provides supporting information supplied by the authors. Such materials are peer reviewed and may be re-organized for online delivery, but are not copy-edited or typeset. Technical support issues arising from supporting information (other than missing files) should be addressed to the authors. Please note: The publisher is not responsible for the content or functionality of any supporting information supplied by the authors. Any queries (other than missing content) should be directed to the corresponding author for the article.

Effects of pore sizes on the electrical properties for porous 0.36BS–0.64PT ceramics

Porous BiScO3–0.64PbTiO3 (0.36BS–0.64PT) ceramics were fabricated by using burnable plastic sphere technique. Self-synthesized polystyrene microsphere (PS, φ0.36 μm) and poly methyl methacrylate (PMMA, φ2, 10 and 18 μm) micro-balls were selected as PFA. The porosity, microstructure and electrical properties were investigated for porous 0.36BS–0.64PT ceramics fabricated with different particle sizes of pore forming agents (PFA). With increasing particle sizes of PFA, the pore size and porosity increased. Meanwhile relative permittivity (e r), piezoelectric coefficient (d 33, −d 31) and electromechanical coupling coefficients (k p, k t) decreased. The mechanical quality factor (Q m), elastic coefficient (s 11), hydrostatic voltage coefficient (g h) and hydrostatic figure of merit increased accordingly. Finally, the effects of particle sizes of PFA on the microstructure and electrical properties were discussed.