Hydrostatic Figure Research Articles

Effects of sintering behavior on piezoelectric properties of porous PZT ceramics

Porous lead zirconate titanate (PZT) ceramics were fabricated by the gel-casting process of particle-stabilized wet foams and sintered at different temperatures. The bulk density and grain size of porous PZT ceramics increased with the increase of sintering temperature from 1150 to 1250 °C, which exerted remarkable influence on the value of relative permittivity (εr) and piezoelectric strain coefficient (d31 and d33). The relationship between microstructure and electric properties was explained by the space-charge theory reasonably. Under the joint effects of bulk density and grain size, the value of dh and gh decreased with the increase of sintering temperature, resulting in the decrease of hydrostatic figure of merit (HFOM) values from 12633 to 3427×10–15 Pa−1.

Effects of foam composition on the microstructure and piezoelectric properties of macroporous PZT ceramics from ultrastable particle-stabilized foams

Abstract Porous lead zirconate titanate (PZT) ceramics could be produced by combining the particle-stabilized foams and the gelcasting technique. In this study, the foaming capacity of particle-stabilized wet foams was tailored by changing the concentration of valeric acid and pH values of suspension. Accordingly, porous PZT ceramics with different porosity, microstructure, dielectric and piezoelectric properties were prepared with the respective wet foam. Increase in the porosity led to a reduction in the relative permittivity ( e r ), a moderate decline in the longitudinal piezoelectric strain coefficient ( d 33 ) and a rapid decline in the transverse piezoelectric strain coefficient ( d 31 ), which endowed porous PZT ceramics with a high value of hydrostatic strain coefficient ( d h ) and hydrostatic figure of merit (HFOM). As a result, the prepared samples possessed a maximal HFOM value of 19,520×10 −15 Pa −1 with the porosity of 76.3%. The acoustic impedance ( Z ) of specimens had the lowest value of 1.35 Mrayl, which could match well with those of water or biological tissue; accordingly, the material would be beneficial in underwater sonar detectors or medical ultrasonic imaging.

Out-of-plane equilibrium points and their stability in the Robe’s problem with oblateness and triaxiality

This paper examines the existence and stability of the out-of-plane equilibrium points of a third body of infinitesimal mass when the equations of motion are written in the three dimensional form under the set up of the Robe’s circular restricted three-body problem, in which the hydrostatic equilibrium figure of the first primary is an oblate spheroid and the second one is a triaxial rigid body under the full buoyancy force of the fluid. The existence of the out of orbital plane equilibrium points lying on the xz-plane is noticed. These points are however unstable in the linear sense.

Processing and Properties of Porous PZT Ceramics from Particle‐Stabilized Foams via Gel Casting

In the present work, porous lead zirconate titanate (PZT) ceramics with porosity ranging from 27.8% to 72.4% were fabricated by the gel‐casting process of particle‐stabilized wet foams with the initial solid loading of 10–30 vol%. The phase, the microstructure, the dielectric property, and the piezoelectric property were characterized. The relative permittivity (εr) and longitudinal piezoelectric strain coefficient (d33) of the investigated samples decreased with increasing porosity. Both the values of hydrostatic strain coefficient (dh) and hydrostatic voltage coefficient (gh) increased moderately with the increase in porosity, which was beneficial for enhancing the value of hydrostatic figure of merit (HFOM). As a result, the prepared sample possessed a maximal HFOM value of 15236 × 10−15 Pa−1 with the porosity of 72.4%. The acoustic impedance (Z) of specimens decreased linearly with increasing porosity, and had the lowest value of 1.95 MRayls, making them promising candidates for application of medical ultrasonic imaging or underwater sonar detectors.

Role of Domain Orientations in Forming the Hydrostatic Performance of Novel 2–2 Single Crystal/Polymer Composites

This paper reports results of a detailed study of the effects of the crystallographic orientation on the performance of the 2–2 parallel-connected composites based on relaxor-ferroelectric single crystals of 0.72Pb(Mg1/3Nb2/3)O3-0.28PbTiO3. These single crystals are poled along one of the following directions in the perovskite unit cell: [111] (single-domain state), [001] and [011] (polydomain states). The effect of the orientation of the main crystallographic axes in the single-crystal component on the hydrostatic piezoelectric coefficients d* h , e* h and g* h , squared hydrostatic figure of merit d* h g* h and hydrostatic electromechanical coupling factor k* h of the composites is studied for three cases of the poling direction of 0.72Pb(Mg1/3Nb2/3)O3-0.28PbTiO3. Maximum values of the hydrostatic parameters in the 2–2 0.72Pb(Mg1/3Nb2/3)O3-0.28PbTiO3 / polyvinylidene fluoride composites are d* h = 372 pC / N, g* h = 284 mV.m/N, d* h g* h = 33.8.10−12 Pa−1, and k* h = 0.361 (in the presence of the [011]-poled single crystal), and e* h = 45.1 C/m2 (in the presence of the [111]-poled single crystal). The inequality k*33/|k*3j | ≥ 5 (j = 1 and 2) is valid for the composite based on the [111]-poled single crystal under specific conditions. The composites exhibit remarkable properties, and the elastic and piezoelectric anisotropy of the single-crystal component (either [111]- or [011]-poled) plays an important role in achieving the large hydrostatic parameters.

Computational Modeling of Piezoelectric Foams

Piezoelectric materials, by virtue of their unique electromechanical characteristics, have been recognized for their potential utility in many applications as sensors and actuators. However, the sensing or actuating functionality of monolithic piezoelectric materials is generally limited. The composite approach to piezoelectric materials provides a unique opportunity to access a new design space with optimal mechanical and coupled characteristics. The properties of monolithic piezoelectric materials can be enhanced via the additive approach by adding two or more constituents to create several types of piezoelectric composites or via the subtractive approach by introducing controlled porosity in the matrix materials to create porous piezoelectric materials. Such porous piezoelectrics can be tailored to demonstrate improved signal-to-noise ratio, impedance matching, and sensitivity, and thus, they can be optimized for applications such as hydrophone devices. This article captures key results from the recent developments in the field of computational modeling of novel piezoelectric foam structures. It is demonstrated that the fundamental elastic, dielectric, and piezoelectric properties of piezoelectric foam are strongly dependent on the internal structure of the foams and the material volume fraction. The highest piezoelectric coupling constants and the highest acoustic impedance are obtained in the [3-3] interconnect-free piezoelectric foam structures, while the corresponding figures of merit for the [3-1] type long-porous structure are marginally higher. Among the [3-3] type foam structures, the sparsely-packed foam structures (with longer and thicker interconnects) display higher coupling constants and acoustic impedance as compared to closepacked foam structures (with shorter and thinner interconnects). The piezoelectric charge coefficients (d h), the hydrostatic voltage coefficients (g h), and the hydrostatic figures of merit (d hgh) are observed to be significantly higher for the [3-3] type piezoelectric foam structures as compared to the [3-1] type long-porous materials, and these can be enhanced significantly by modifying the aspect ratio of the porosity in the foam structures as well.

Effects of foam shape and porosity aspect ratio on the electromechanical properties of 3-3 piezoelectric foams

Three-dimensional finite element models are developed to completely characterize the role of microstructural features such as foam shape and porosity shape in determining the elastic, piezoelectric and dielectric properties of 3-3 type piezoelectric foam structures. Upon identifying 35 characteristic foam structures that capture a wide range of microstructures, the influence of foam shape, porosity aspect ratio and volume fraction on the effective properties of foam structures is examined. The material properties of the foam structures and their corresponding figures of merit are shown to be strongly dependent on the microstructural features. For foam structures with a particular shape, the principal electromechanical properties in the longitudinal direction (i.e. along the poling direction), such as C22, κ22 and e22, are lower for the piezoelectric foam structures with flat porosity with lower aspect ratios as compared to other foam structures with elongated porosity with higher aspect ratios. The piezoelectric figures of merit such as the piezoelectric charge coefficient (dh), the piezoelectric voltage coefficient (gh) and the hydrostatic figure of merit (dhgh) of the foam structures can be enhanced significantly by modifying the shape of the porosity. For example, in the equiaxed foam structure of PZT-7A with 30% porosity, dh, gh and dhgh are, respectively, increased by 175, 1000 and 1800%, by changing the shape of the porosity from a cuboidal shape (with aspect ratio of 1) to a flat-cuboidal shape (with an aspect ratio of 0.25).

Robe’s Circular Restricted Three-Body Problem Under Oblate and Triaxial Primaries

This paper analyzes Robe’s circular restricted three-body problem when the hydrostatic equilibrium figure of the first primary is assumed to be an oblate spheroid, the shape of the second primary is considered as a triaxial rigid body, and the full buoyancy force of the fluid is taken into account. It is found that there is an equilibrium point near the center of the first primary, another equilibrium point exists on the line joining the centers of the primaries and there exist infinite number of equilibrium points on an ellipse in the orbital plane of the second primary. It is also observed that under certain conditions, all these equilibrium points can be stable. The most interesting and distinguishable results of this study are the existence of elliptical points and their stability.

Electromechanical response of piezoelectric foams

A three-dimensional finite element model is developed to completely characterize the elastic, dielectric, and piezoelectric properties of piezoelectric foam structures. Three kinds of 3-3 type piezoelectric foam structures (i.e. with asymmetric interconnects, with symmetric interconnects, and without any interconnects) are identified and their electromechanical properties are characterized as a function of the interconnect geometry and architecture and benchmarked with that of long porous 3-1 type piezoelectric materials over a range of volume fractions/foam densities. In general, at a particular volume fraction a majority of the elasticity constants (with the exception of C55 and C13) of the 3-3 type open foam structures are lower than that of the 3-1 type long porous structure. Amongst the 3-3 type foam structures the sparsely packed foam structures (with longer and thicker interconnects) display higher coupling constants and acoustic impedance as compared to close-packed foam structures (with shorter and thinner interconnects). The piezoelectric charge coefficients (dh), the hydrostatic voltage coefficients (gh) and the hydrostatic figures of merit (dhgh) are observed to be significantly higher for the 3-3 type (PZT-7A) piezoelectric foam structures as compared with that of the 3-1 type (PZT-7A) long porous materials. For example, at about 3% volume fraction, the dh, gh, and dhgh figures of merit are 360%, 1000% and 5000% higher, respectively, for the interconnect-free foam structure compared with the 3-1 type long porous materials. Amongst the 3-3 type piezoelectric foam structures those that are close packed exhibit higher piezoelectric charge coefficients, while the sparsely packed structures exhibit higher hydrostatic voltage coefficients and hydrostatic figures of merit.

Existence and Linear Stability of Equilibrium Points in the Robe’s Restricted Three-Body Problem with Oblateness

This paper investigates the positions and linear stability of an infinitesimal body around the equilibrium points in the framework of the Robe’s circular restricted three-body problem, with assumptions that the hydrostatic equilibrium figure of the first primary is an oblate spheroid and the second primary is an oblate body as well. It is found that equilibrium point exists near the centre of the first primary. Further, there can be one more equilibrium point on the line joining the centers of both primaries. Points on the circle within the first primary are also equilibrium points under certain conditions and the existence of two out-of-plane points is also observed. The linear stability of this configuration is examined and it is found that points near the center of the first primary are conditionally stable, while the circular and out of plane equilibrium points are unstable.

Effect of Shape Parameter on the Performance of 1-3 Piezoelectric Composites

1-3 polymer-based piezoelectric composites were fabricated using epoxy as matrix by the cut-filling method. The influences of shape parameter on properties of the piezoelectric composite, which include the unit cross-sectional area and the aspect ratio w/t were analyzed. The results indicate that with the increasing of the unit cross-sectional area, the quality factor valueQmincreases and the hydrostatic piezoelectric voltageghincreases and then goes down rapidly while the PMN volume fractionφ(PMN) is kept under the 50%. When theφ(PMN) is 60%,ghis decreased. The trend of the hydrostatic figures of meritdh·ghis similar withghas the change of the unit cross-sectional area, but the value is different. In the 60% PMN volume fraction, the optimal value of thedh·ghis chosen. With the increasing of thew/t, the hydrostatic pressure sensitivityMh, thedh·ghvalues and theQmvalues are all decreased rapidly, and the thickness electromechanical coupling factorktis increased. In other words, the test results show that the smaller of unit cross-sectional area and thinner of thickness, the more helpful for frequency bandwidth and sensitivity when it is used in transducer.

Electromechanical response of (3-0) porous piezoelectric materials: Effects of porosity shape

A three-dimensional finite element model is developed to accurately predict the complete electromechanical properties of porous piezoelectric materials with four geometric configurations of porosity, i.e., 3-0 type flat-cuboidal, 3-0 type spherical, 3-0 type short-cylindrical, and 3-1 type long-cylindrical porosity. The three-dimensional finite element model characterizes the complete electromechanical response of materials that belong to several symmetry classes, i.e., barium titanate (6mm), barium sodium niobate (mm2), and lithium niobate (3m). In general, the elastic, piezoelectric, and dielectric properties vary monotonically with increase in porosity volume fraction with the material properties in the longitudinal direction being the highest for the case of the materials with the 3-1 type long-cylindrical porosity for all three symmetry classes. The piezoelectric charge coefficient (dh) and the hydrostatic figure of merit (dh·gh) of the porous piezoelectric materials with the 3-0 type flat-cuboidal porosity are found to be significantly higher than those of the piezoelectric materials with spherical or short-cylindrical porosity. For example, in the barium titanate system, the differences in the dh and dh·gh values between the materials with the 3-0 type flat-cuboidal porosity and the materials with the 3-1 type long-cylindrical porosity are observed to be 223% and 1818% respectively, at 30% porosity volume fraction. Hence, piezoelectric materials with the 3-0 type flat-cuboidal porosity (that exhibit low aspect ratios with respect to the poling direction) could be better suited for hydrophone applications.

Microstructural modelling of the polarization and properties of porous ferroelectrics

Micromechanical models of porous ferroelectric ceramics have often assumed that thematerial is fully polarized in a particular direction and/or consists of a single isolated pore.In this work the polarization state in three-dimensional porous polycrystalline ferroelectricnetworks has been modelled to eradicate the oversimplification of these idealized unit cells.This work reveals that microstructural network models more closely represent a porousferroelectric microstructure since they are able to take into account the complexpolarization distribution in the material due to the presence of high and low permittivityregions. The modelling approach enables the prediction of the distribution ofpoled and unpoled material within the structure. The hydrostatic figures of meritand permittivity were determined for a variety of porous lead zirconate titanatemicrostructures and found to be in good agreement with experimental data. The decreasein piezoelectric activity with porosity was observed to be associated with thecomplex polarization state within the material. Model results were shown to bemuch improved when compared to a model assuming a fully polarized model.

Performance Analysis of the 1-3 Piezoelectric Composites and Transducer Fabrication

1-3 polymer-based piezoelectric composites were fabricated using epoxy as the matrix by the cut-filling method. The influences of PMN volume fraction on the piezoelectric and dielectric properties of the composite were analyzed, and then the piezoelectric composite was fabricated to transducer whose properties were also analyzed. The results indicate that with increasing the PMN volume fraction, both the hydrostatic piezoelectric voltage gh and hydrostatic figures of merit dh·gh of the composite decrease, while the relative dielectric constant εr increases. The hydrostatic piezoelectric strain dh has the optimum value in the PMN volume fraction range of 40%-60%. The resonant frequency of transducer in water is 306.5 kHz and anti-resonant frequency is 352.6 kHz.

Effects of porosity on dielectric and piezoelectric properties of porous lead zirconate titanate ceramics

We report porous lead zirconate titanate ceramics fabricated by tert-butyl alcohol-based gel-casting process which show a very high thickness electromechanical coupling coefficient (0.77), high hydrostatic figure of merit (9594×10−15 m2/N), and low acoustic impedance (3.7 Mrayls). We show that the porosity effectively affects the performance of the samples in two ways: (1) a higher porosity simplifies the resonance behavior, leading to more efficient energy transduction; (2) its replacement of active ceramic phase leads to low relative permittivity, high hydrostatic figure of merit, and low acoustic impedance. It was confirmed the properties could be tailored by controlling the porosity.

Piezoelectric Properties of the 1-3 Type Porous Lead Zirconate Titanate Ceramics

Porous lead zirconate titanate (PZT) ceramics are of great interest for hydrophones and medical imaging applications. The 0–3 type and 3–3 type porous PZT ceramics have been extensively discussed these years but the 1–3 type PZT ceramics have seldom been reported. This paper describes the fabrication process to obtain such 1–3 type porous PZT ceramics with one-dimensional pore channels by using tert-butyl alcohol-based directional freeze-casting method, and presents analysis of both microstructure and functional properties. The 1–3 type porous PZT ceramics with porosity ranging from 28.1% to 68.7% were fabricated by adjusting initial solid loading. With the increase of porosity, relative permittivity (ɛr) decreased slightly and longitude piezoelectric coefficient (d33) exhibited only a small decline, which could be attributed to the special 1–3 type porous structure. The resultant samples with 61.3% porosity possessed a high value of hydrostatic figure of merit, >100 times higher than that of dense materials. The acoustic impedance (Z) showed a linear dependence on porosity with the lowest magnitude reaching 1.3 MRayls (106 kg·(m2·s)−1), matching very well with biological tissue or water.

Electromechanical response of porous piezoelectric materials: Effects of porosity connectivity

A three-dimensional finite element model is developed to completely characterize the electromechanical response of a general piezoelectric material with spherical or cylindrical porosity, respectively, with zero-dimensional (3–0) or one-dimensional (3–1) connectivity and to obtain a quantitative assessment of the effects of porosity connectivity on the effective performance characteristics of porous piezoelectric materials. By considering materials with different crystal symmetries, it is demonstrated that piezoelectric materials designed with spherical porosity (with 3–0 connectivity) exhibit enhanced hydrostatic figure of merit and are more suitable for hydrophone applications, as compared to materials engineered with cylindrical porosity (with 3–1 connectivity).

Enhanced Pyroelectric and Piezoelectric Figure of Merit of Porous Bi0.5(Na0.82K0.18)0.5TiO3 Lead‐Free Ferroelectric Thick Films

Bi0.5(Na0.82K0.18)0.5TiO3(NKBT) lead‐free ferroelectric thick films with various porosities have been produced by screen printing. Their microstructures, pyroelectric and piezoelectric properties were investigated with variation of porosity. The results show that the relative dielectric constant of the resulting 90 μm NKBT thick films with 19% and 32% porosity was down to 161 and 56, respectively. The pyroelectric voltage figure of merit (Fv) and detectivity figure of merit (FD) of NKBT thick films were increased from 10.2 × 10−13 to 19.7 × 10−13 Cm/J and 1.1 × 10−5 to 3.8 × 10−5 Pa−0.5. Moreover, the hydrostatic voltage constant and hydrostatic figure of merit of the NKBT thick films with 32% porosity reached 81 × 10−3 V/mPa and 8200 × 10−15 Pa−1 respectively. The decreasing of relative dielectric constant, volume specific heat, and piezoelectric coefficient with increasing porosity was responsible for the improved pyroelectric and piezoelectric figures of merit of the NKBT thick films. Furthermore, screen printing with the addition of controlled fraction of organic vehicle in pastes has been proved to be an alternative method for fabrication of porous pyroelectric and piezoelectric thick films. Our work demonstrates that introduction of pores in ferroelectric thick films creates a matrix void composite resulting in high figures of merit for pyroelectric and piezoelectric applications.

Porous PZT Ceramics with High Hydrostatic Figure of Merit and Low Acoustic Impedance by TBA‐Based Gel‐Casting Process

Porous lead zirconate titanate (PZT) ceramics with three‐dimensionally interconnected pores were prepared using a novel tert‐butyl alcohol‐based gel‐casting process, an unconventional technique in acquiring high‐porosity ceramics. In the present work, PZT ceramics with porosity ranging from 31.3% to 58.6% were fabricated by adjusting the initial solid loading and sintering temperature. The fabricated samples were characterized in terms of both porous structure and functional properties to clarify the underlying correlation. With the increase of porosity, relative permittivity (ɛr) decreased to a significantly low value compared with dense PZT ceramics while the longitude piezoelectric coefficient (d33) exhibited a moderate decline, which could be attributed to the unique structure with homogeneous pore distribution. As a result, the resultant samples possessed a high value of hydrostatic figure of merit, >100 times higher than that of dense materials. The acoustic impedance (Z) showed a linear dependence on porosity with the lowest magnitude reaching 3.0 MRayls (106 kg·(m2·s)–1), hopefully leading to enhanced coupling with biological tissue or water.

A New Reference Equipotential Surface, and Reference Ellipsoid for the Planet Mars

Using the shape model of Mars GTM090AA in terms of spherical harmonics complete to degree and order 90 and gravitational field model of Mars GGM2BC80 in terms of spherical harmonics complete to degree and order 80, both from Mars Global Surveyor (MGS) mission, the geometry (shape) and gravity potential value of reference equipotential surface of Mars (Areoid) are computed based on a constrained optimization problem. In this paper, the Areoid is defined as a reference equipotential surface, which best fits to the shape of Mars in least squares sense. The estimated gravity potential value of the Areoid from this study, i.e. W0 = (12,654,875 ± 69) (m2/s2), is used as one of the four fundamental gravity parameters of Mars namely, {W0, GM, ω, J20}, i.e. {Areoid’s gravity potential, gravitational constant of Mars, angular velocity of Mars, second zonal spherical harmonic of gravitational field expansion of Mars}, to compute a bi-axial reference ellipsoid of Somigliana-Pizzetti type as the hydrostatic approximate figure of Mars. The estimated values of semi-major and semi-minor axis of the computed reference ellipsoid of Mars are (3,395,428 ± 19) (m), and (3,377,678 ± 19) (m), respectively. Finally the computed Areoid is presented with respect to the computed reference ellipsoid.