Hydrostatic Figure Of Merit Research Articles

Electromechanical Response of Piezoelectric Honeycomb Foam Structures

A finite element model is developed to characterize the complete electromechanical properties of the most general form of elastically anisotropic and piezoelectrically active foams with honeycomb structures. Four classes of piezoelectric honeycomb structures are identified depending on the relative orientation of the poling direction with the porosity direction (longitudinal and transverse) and the geometry of the honeycombs (isotropic and anisotropic). It is observed that: (i) Most of the elastic, dielectric, and piezoelectric constants of the longitudinally porous honeycomb foams exhibit linear dependence on the volume fraction (or relative density) of the material; (ii) The electromechanical properties of transversely porous foam structures (with the exception of C22 and κ22) exhibit significant dependence on the shape of the porosity; (iii) The piezoelectric figures of merit of the longitudinally porous foams do not exhibit significant dependence on the shape of the porosity; (iv) The piezoelectric figures of merit of the transversely porous foams exhibit a strong dependence on the shape of the porosity with the hexagonal foams exhibiting enhanced hydrostatic strain coefficient and lower acoustic impedance while the square foams exhibiting enhanced piezoelectric coupling constant and hydrostatic figure of merit; (v) In transversely porous anisotropic honeycomb structures, the shear elastic constants such as C12 and C66 and some figures of merit are enhanced significantly when compared to their isotropic counterparts. For example, in the PZT–7A transversely porous anisotropic honeycomb structures with 10% relative density, the hydrostatic figure of merit is expected to be 2485% greater than that predicted for the transversely porous isotropic honeycomb structures.

Electromechanical properties of relaxor ferroelectric foams

Three-dimensional finite element models are developed to characterize the complete electromechanical properties of relaxor ferroelectric-based foams. It is demonstrated that microstructural features such as porosity volume fraction and connectivity play significant roles in determining the elastic, dielectric, and piezoelectric properties of relaxor foams. Furthermore, piezoelectric figures of merit such as the coupling constant (Kt), the hydrostatic strain coefficient (dh), and the hydrostatic figure of merit (dhgh) of (PMN-PT based) relaxor foams are significantly higher (by 40%, 900%, and 3000%, respectively, for 3-3 type foams with 50% porosity) than those observed in equivalent (PZT-7A based) traditional piezoelectric foams.

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.

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).

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.

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.

Piezoelectric Properties of PZT‐Based Ceramic with Highly Aligned Pores

Porous lead zirconate titanate–lead zinc niobate (PZT–PZN) piezoelectric ceramics with a high degree of pore alignment were fabricated using directional freeze casting of a ceramic/camphene slurry. Well‐aligned pores were formed as the replica of the camphene dendrites that grew in a preferential orientation, while a high porosity of 90% was achieved by employing a low initial solid loading of 5 vol%. As the orientation angle of the pores to the poling direction was decreased, the hydrostatic piezoelectric properties, such as hydrostatic piezoelectric strain coefficient (dh), the hydrostatic piezoelectric voltage coefficient (gh), and the hydrostatic figure of merit, increased significantly. The sample containing pores aligned parallel to the poling direction showed an extremely high HFOM of 161019 × 10−15 Pa−1, which was ∼1300 times higher than that (124 × 10−15 Pa−1) of the dense sample, owing to the presence of aligned pores.

Piezoelectric Multilayer Ceramic/Polymer Composite Transducer with 2–2 Connectivity

A multilayer piezoelectric ceramic/polymer composite with 2–2 connectivity was fabricated by thermoplastic green machining after co‐extrusion. The multilayer ceramic body was composed of piezoelectrically active lead zirconate titanate (PZN)–lead zinc niobate (PZN)‐lead zirconate titanate (PZT) layers and electrically conducting PZN–PZT/Ag layers. After co‐extruding the thermoplastic body, which consisted of five piezoelectric layers interspersed with four conducting layers, it was computer numeric‐controlled machined to create periodic channels within it. Following binder burnout and sintering, an 18 vol% array of 190 μm thin PZT slabs with a channel size of 880 μm was fabricated. The channels were filled with epoxy in order to fabricate a PZN–PZT/epoxy composite with 2–2 connectivity. The piezoelectric coefficient (effective d33) and hydrostatic figure of merit (dh×gh) of the PZN–PZT/epoxy composite were 1200 pC/N and 20 130 × 10−15 m2/N, respectively. These excellent piezoelectric characteristics as well as the relatively simple fabrication procedure will contribute in widening the application range of the piezoelectric transducers.

Processing and piezoelectric properties of porous PZT ceramics

5–45% porous lead zirconate titanate (PZT) ceramics were fabricated by adding pore formers such as polymethyl methacrylate (PMMA) and dextrin and sintering at 1200 °C for 2 h. The optimum heating procedure was decided according to the thermogravimetric analysis of pore formers. The effects of different pore formers and their content on the microstructure and piezoelectric properties were investigated. With an increase in the content of pore formers, the porosity of sintered ceramics increased, which led to reduced dielectric constant ( ɛ 33) and longitudinal piezoelectric coefficient ( d 33) as well as enhanced hydrostatic piezoelectric voltage coefficient ( g h) and hydrostatic figures of merit ( d h g h). The hydrostatic figures of merit ( d h g h) of 41% porous PZT were 10 times more than that of 95% dense PZT.

Effects of porosity and grain sizes on the dielectric and piezoelectric properties of porous PZT ceramics and their mechanism

Porous lead zirconate titanate (PZT) ceramics were prepared by adding pore formers, and the effects of pore structure and grain sizes on the dielectric and piezoelectric properties of samples were investigated. The research showed that an increase in the porosity led to reduced dielectric constant as well as enhanced hydrostatic figures of merit (dh·gh). The effect of porosity on dielectric constant can be predicted by the Okazaki experiential formula and Banno model under certain conditions. An increase in grain size increases the dielectric constant, piezoelectric coefficient and hydrostatic figures of merit, which can be explained by the Okazaki space-charge theory. For the sample with 10 wt% PMMA additions sintered at 1300℃, the porosity is 34% and the longitudinal piezoelectric coefficient (d33) is very close to that of dense PZT ceramics, while the hydrostatic figures of merit (dh·gh) is about fifteen times greater than that of dense PZT ceramics. Compared with PZT-polymer composites, the dielectric constant and piezoelectric coefficient of 34% porous PZT sintered at 1300℃ is much higher and can be more efficient in resisting the interference from the ambient medium.

Piezoelectric sensitivity of PbTiO 3-based ceramic/polymer composites with 0–3 and 3–3 connectivity

This paper describes the modelling and comparison of piezoactive composites of 0–3 and 3–3 geometry. Algorithms for the evaluation of effective elastic, piezoelectric and dielectric constants are proposed which can be used for the prediction of piezoelectric sensitivity and optimisation of properties. The hydrostatic piezoelectric voltage coefficient g h, figure of merit d 33· g 33 and hydrostatic figure of merit d h· g h are calculated for PbTiO 3 based piezocomposites in which the anisotropy factor − d 33/ d 31 of the piezoelectric phase can be varied from small to infinitely large values. Maxima of these parameters are determined and factors influencing piezoelectric sensitivity of the composites are analysed.

Porous PZT ceramics for receiving transducers

PZT-air (porous PZT) and PZT-polymer (polymer impregnated porous PZT) piezocomposites with varying porosity/polymer volume fractions have been manufactured. The composites were characterized in terms of hydrostatic charge (dh) and voltage (gh) coefficients, permittivity, hydrostatic figure of merit (dh.gh), and absolute sensitivity (M). With decreasing PZT ceramic volume, gh increased, and dh.gh had a broad maximum around 80 to 90% porosity/polymer content. The absolute sensitivity was also increased. In each case, PZT-air piezocomposites performed better than PZT-polymer piezocomposites. Hydrophones constructed from piezocomposites showed slightly lower measured receiving sensitivities than calculated values for piezocomposite materials, which was due to the loading effect of the cable and the low permittivity associated with the piezocomposites.

Characterization Techniques for Porous Piezoelectric Materials

The applicability of characterization techniques of ferroelectric dense materials to porous ferroelectric materials has been investigated. In fact nonlinearity effects are highly increased in porous materials, due to the discontinuities at the internal boundaries. Resonant and quasi-static techniques, based on direct or converse piezoelectric effect, were employed to obtain the physical properties of various types of ferroelectric porous materials. Soft PZT materials, obtained through the “starch consolidation method,” with porosities ranging from ≈30% to ≈45% and high hydrostatic figure of merit, acoustical matching and mechanical resistance, as requested in many applications, were characterized. The properties of the dense and porous materials were measured and compared and it was evidenced that the same characterization techniques used for dense ferroelectric materials can be safely and reliably employed, with just slight modifications, for porous ferroelectric materials with porosities as high as 45%.

Modelling of 3–3 piezocomposites for hydrophones

Three-dimensional modelling of a 3-3 piezoelectric structure was carried out using finite element modelling software. Hydrostatic figures of merit were calculated for structures with increasing amounts of interconnecting porosity. In addition to using air as the second phase, polymer fillers were added to the three-dimensional model in order to observe the effect of polymer Young's modulus on the piezoelectric properties of the bulk material. Results show that increasing the porosity has the effect of improving the hydrostatic piezoelectric properties for applications such as low frequency hydrophones.

Processing of Porous PZT Materials for Underwater Acoustics

Porous PZT materials are developed for hydrostatic sensing applications, owing to their lowered acoustic impedance that leads to a good acoustic coupling with water and to a high hydrostatic figure of merit. Porous PZT materials with different pore volumes and pore size distributions were obtained by starch consolidation technique. The differnt morphologies, pore volumes and pore size distributions are correlated with the processing parameters and piezoelectric properties and will be discussed in terms of the influence of the peorosity agent properties and reproducibility.

On increasing the hydrostatic sensitivity of three-component piezocomposites

A 1-0-3 composite model of the “ferroelectricpiezoceramic-polymer 1-polymer 2” type is proposed. It is demonstrated that the square hydrostatic figure of merit (HFOM) in this system may reach a level of (Qh*)2∼10−11 Pa−1, which exceeds by approximately one order of magnitude the known estimates for 1–3 composites. Factors favoring an increase in the (Qh*)2 value in three-component piezocomposites are discussed.