Longitudinal Piezoelectric Coefficient D33 Research Articles

Orthorhombic-tetragonal phase coexistence and enhanced piezo-response at room temperature in Zr, Sn, and Hf modified BaTiO3

The effect of Zr, Hf, and Sn in BaTiO3 has been investigated at close composition intervals in the dilute concentration limit. Detailed structural analysis by x-ray and neutron powder diffraction revealed that merely 2 mol. % of Zr, Sn, and Hf stabilizes a coexistence of orthorhombic (Amm2) and tetragonal (P4mm) phases at room temperature. As a consequence, all the three systems show substantial enhancement in the longitudinal piezoelectric coefficient (d33), with Sn modification exhibiting the highest value ∼425 pC/N.

Fabrication and properties of PZT piezoelectric ceramic tubes with large length–diameter ratio

Lead zirconate titanate (PZT) ceramic tubes with large length–diameter ratio were fabricated by a viscous plastic processing-extrusion method at different sintering temperatures and holding times. The phase composition, microstructure, dielectric and piezoelectric properties of the tubes were investigated by XRD, SEM, precision impedance analyzer and d33 measuring instruments. A typical perovskite phase without other impurities was obtained for the tubes sintered at 1290°C for 2h. A homogeneous and compact structure with 2–5μm grain sizes was also observed. The relative dielectric constant (εr) and dielectric loss (tanδ) of PZT piezoelectric ceramic tubes were 2734 and 0.35, respectively. The longitudinal piezoelectric coefficient (d33) of PZT ceramic tubes was 528pCN−1.

Ferroelectric and Piezoelectric properties of (111) oriented lanthanum modified lead zirconate titanate film

Lanthanum modified lead zirconate titanate (PLZT) thick film with molecular formula of Pb0.92La0.08(Zr0.52Ti0.48)0.98O3 was grown preferentially along (111) direction on Pt/SiO2/Si (platinum/silicon oxide/silicon) substrate by spin coating of chemical solution. The directional growth of the film was facilitated by platinum (Pt) (111) template and rapid thermal annealing. X-ray diffraction pattern and atomic force microscopy revealed the preferential growth of the PLZT film. The film was characterized for ferroelectric and detailed piezoelectric properties in a parallel plate capacitor (metal–PLZT–metal) configuration. Ferroelectric characterization of the film showed saturated hysteresis loop with remanent polarization and coercive electric field values of 10.14μC/cm2 and 42kV/cm, respectively, at an applied field of 300kV/cm. Longitudinal piezoelectric coefficient (d33,f) was measured by employing converse piezoelectric effect where electrical charge response and displacement were measured with electrical voltage excitation on the sample electrodes. The effective transverse piezoelectric coefficient (e31,f) was derived from charge measurement with an applied mechanical excitation strain by using the four point bending method. d33,f and e31,f coefficients of PLZT films were found to be 380pm/V and −0.831C/m2 respectively.

Minimization of pyroelectric effects in relaxor-PbTiO3 crystals for piezoelectric sensors

To minimize pyroelectric effects while keeping high piezoelectric effects in relaxor-PbTiO3 single crystals, the crystallographic orientation dependence of the pyroelectric and piezoelectric coefficients were investigated for binary (1 − x)Pb(Mg1/3Nb2/3)O3–xPbTiO3 (PMN–PT), ternary (1 − x − y)Pb(In1/2Nb1/2)O3–yPb(Mg1/3Nb2/3)O3–xPbTiO3 (PIN–PMN–PT) and Mn-doped PIN–PMN–PT single crystals with the “4R” multidomain state. The secondary pyroelectric coefficients were calculated from the thermodynamic inter-relationship between the piezoelectric, elastic, and thermal expansion coefficients, being on the order of (1.16–1.23) × 10−4 C m−2 K−1 for binary crystals and (0.97–2.03) × 10−4 C m−2 K−1 for ternary ones. The primary pyroelectric coefficients were –(6.73–6.84) × 10−4 C m−2 K−1 and −(5.44–6.43) × 10−4 C m−2 K−1 for binary and ternary crystals, respectively. The pyroelectric coefficients could be reduced by matrix rotation, but at the cost of decreasing longitudinal piezoelectric coefficients d33. Of particular interest is that the maximum piezoelectric coefficients d24∗ at θ = ±55o and d34∗ at θ = ±35o by a counterclockwise rotation of θ about the X axis (θ is the rotation angle about the coordinate axes), or d15∗ at θ = ±55o, and d35∗ at θ = ±35o by a counterclockwise rotation the Y axis, were found on the order of 3000 pC N−1. The corresponding pyroelectric coefficients could be reduced by ∼20%. The reduced pyroelectric coefficients that can contribute to decrease undesirable output signals, together with the high piezoelectric coefficients, enable relaxor-PT crystals as favorable candidates for high-sensitivity piezoelectric sensors.

Enhanced piezoelectric activity and temperature stability of [1 1 1]-oriented orthorhombic 0.68Pb(Mg1/3Nb2/3)O3–0.32PbTiO3 single crystals by domain size engineering

The dielectric and piezoelectric properties of [1 1 1]-oriented orthorhombic Pb(Mg1/3Nb2/3)O3–PbTiO3 (PMN–PT) single crystals (3O multi-domain state) with various domain sizes were investigated by poling control. The free dielectric permittivity (e33T/e0) and longitudinal piezoelectric coefficient (d33) were 6400 and 900 pC N−1, respectively, for samples with domain sizes of ∼2 μm, nearly twice that of ∼20 μm. Together with good temperature stability (Δd33/d33(25°C)Δd33/d33(25°C) <8%) up to the orthorhombic–tetragonal phase transition temperature, the “3O” PMN–PT crystals with fine domain structures are promising candidate for sensors and transducers.

Continuum modeling of charging process and piezoelectricity of ferroelectrets

Ferroelectrets in the form of electrically charged micro-porous foams exhibit a very large longitudinal piezoelectric coefficient d33. The structure has hence received wide application interests as sensors particularly in acoustic devices. During charging process, electrical breakdown (Paschen breakdown) takes place in the air pores of the foam and introduces free charge pairs. These charges are separated by electrostatic forces and relocated at the interfaces between the polymer and the electrically broken-down medium, where they are trapped quasistatically. The development of this trapped charge density along the interfaces is key for enabling the piezoelectricity of ferroelectrets. In this article, an internal variable based continuum model is proposed to calculate the charge density development at the interfaces, whereas a Maxwell stress based electromechanical model is used for the bulk behavior, i.e., of the polymer and of the medium where the Paschen breakdown takes place. In the modeling, the electrostatic forces between the separated charge pairs are included, as well as the influence of deformation of the solid layers. The material models are implemented in a nonlinear finite element scheme, which allows a detailed analysis of different geometries. A ferroelectret unit with porous expanded polytetrafluoroethylene (ePTFE) surrounded by fluorinated ethylene propylene is studied first. The simulated hysteresis curves of charge density at the surfaces and the calculated longitudinal piezoelectric constant are in good agreement with experimental results. Simulations show a strong dependency of the interface charge development and thus the remnant charges on the thicknesses of the layers and the permittivity of the materials. According to the calculated relation between d33 and the Young's modulus of ePTFE, the value of the Young's modulus of ePTFE is identified to be around 0.75 MPa, which lies well in the predicted range of 0.45 to 0.80 MPa, determined from the dielectric resonance spectra in the work of Zhang et al. [X. Q. Zhang et al., J. Appl. Phys. 108, 064113 (2010)]. To show the potential of the models, it is also applied to simulation of ferroelectrets with a lens shape. The results indicate that the electrical breakdown happens in a sequential manner, and the local piezoelectric coefficient varies with position. Thereby, the middle point on the surface exhibits the maximum d33. The simulation results obtained by the proposed models will provide insight for device optimization.

Film-thickness and composition dependence of epitaxial thin-film PZT-based mass-sensors

The transverse piezoelectric coefficient e31,f and mass-sensitivity were measured on piezoelectric cantilevers based on epitaxial PZT thin-films with film-thicknesses ranging from 100 to 2000nm. The highest values of e31,f and mass-sensitivity were observed at a film thickness of 500–750nm, while the observed remnant polarization Pr and longitudinal piezoelectric coefficient d33,f values become saturated with a film thickness of 750–1000nm. To obtain high performance by making use of its optimal film thickness, PZT thin films with various Zr/Ti ratios from 20/80 to 80/20 were studied. The experimental results indicated that the ferroelectric property reached a highest remnant polarization Pr at a Zr/Ti ratio of 20/80, while the longitudinal piezoelectric coefficient d33,f increased with increasing Zr content and reaches a maximum at a Zr/Ti ratio of 52/48. The findings suggest that the optimal composition for mass-sensitivity and transverse piezoelectric coefficient e31,f was shifted to the tetragonal part of the phase diagram with the Zr/Ti ratios of 45/55 and 40/60, respectively.

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.

Complete set of elastic, dielectric, and piezoelectric constants of [011]C poled rhombohedral Pb(In0.5Nb0.5)O3-Pb(Mg1/3Nb2/3)O3-PbTiO3:Mn single crystals.

Mn modified rhombohedral Pb(In0.5Nb0.5)O3-Pb(Mg1/3Nb2/3)O3-PbTiO3 (PIN-PMN-PT:Mn) single crystals poled along [011]C crystallographic direction exhibit a "2R" engineered domain configuration, with macroscopic mm2 symmetry. The complete sets of material constants were determined using combined resonance and ultrasonic methods, and compared to [001]C poled PIN-PMN-PT:Mn crystals. The thickness shear piezoelectric coefficient d15 and electromechanical coupling factor k15 were found to be on the order of ∼3000 pC/N and 0.92, respectively, with longitudinal piezoelectric coefficient d33 and coupling factor k33 being on the order of ∼1050 pC/N and 0.90. Of particular importance is that PIN-PMN-PT:Mn single crystals exhibited high mechanical quality factor Q33 ∼ 1000, comparable to "hard" PZT8 ceramics, which can also be confirmed by the low extrinsic contribution, being ≤2% from the Rayleigh analysis.

Effects of the Domain Size on Local d33 in Tetragonal (Na0.53K0.45Li0.02)(Nb0.8Ta0.2)O3 Ceramics

Lead‐free (Na0.53K0.45Li0.02)(Nb0.8Ta0.2)O3 (NKLNT) was prepared using a conventional cold‐pressing method. A commercial piezoresponse force microscope (PFM) was applied to observe the domain structures of NKLNT ceramics. The typical configuration of the ferroelectric domain was analyzed in abnormal grains with grain sizes that exceeded 40 μm, where tetragonal 90° domains are predominant. The local piezoresponse hysteresis loops were characterized and studied as a function of the domain width (dw) in the range 300–1000 nm. It was found that the amplitude signals increased and the coercive field reduced significantly with a decrease in the domain size. Finally, the local longitudinal piezoelectric coefficient (d33) increased as the domain size decreased.

THE HYDROSTATIC PIEZOELECTRICITY OF RELAXOR-PbTiO3 FERROELECTRIC CERAMICS AND CRYSTALS

The hydrostatic piezoelectricity of Pb ( Mg 1/3 Nb 2/3)–x PbTiO 3 (PMN–xPT) ceramics and PMN–0.32PT and Pb(Mg1/3Nb2/3)–Pb(In1/2Nb1/2)–PbTiO3 (PMN–PIN–PT) crystals were investigated through a quasi-static method. The results showed that pressure-induced depolarization occurred in PMN–xPT ceramics when pressure was above about 50 MPa, while there was no obvious pressure-induced depolarization for PMN–0.32PT and PMN–PIN–PT crystals in the whole pressure range (0~530 MPa). The hydrostatic piezoelectric coefficient d h of PMN–0.32PT and PMN–PIN–PT crystals was nearly independent of pressure. The d h of mono-domain orthorhombic and tetragonal phase crystals is slightly larger, on the order of 100 pC/N. In addition, the relationship between the hydrostatic piezoelectric coefficient d h and the longitudinal and transverse piezoelectric coefficients d33 and d31 for different crystal systems was summarized.

Influence of Platinum Bottom Electrodes on the Piezoelectric Performance of PZT Thin Films Hot Sputtered in a High Volume Production Tool

ABSTRACTIn this work high quality ferroelectric PZT films have been prepared in-situ by hot RF magnetron sputtering. 200 mm wafer were coated with PZT films of 1 μm and 2 μm thickness at sputter rates of 45 nm/min in a high volume production sputtering tool. The films were grown on oxidized Si substrates prepared either with sputtered Ti/TiO2/Pt, sputtered Ti/TiO2/Pt/TiO2 or evaporated Ti/Pt bottom electrodes at substrate holder temperatures in the range from 550 °C to 700 °C. At these temperatures, the material nucleates in the requisite piezoelectric perovskite phase without need of an additional post annealing treatment.The films were investigated with respect to their chemical composition and their crystallographic, piezoelectric and dielectric properties. At an intermediate chuck temperature of 600 °C the PZT thin films were characterized by a minimum volume fraction of secondary nonpiezoelectric phases. A Zr/(Zr+Ti) ratio of 0.53 has been achieved matching the morphotropic phase boundary. By improving the deposition process and poling procedure, a notable high e31,f coefficient of -17.3 C/m2 has been obtained. The corresponding longitudinal piezoelectric constant was determined to have an effective longitudinal piezoelectric coefficient d33,f of 160 pm/V.

The hydrostatic pressure dependence of the piezoelectric properties for the barium titanate and lead titanate crystals: Thermodynamic analysis

The influence of the hydrostatic pressure on the piezoelectric response for tetragonal BaTiO3 and PbTiO3 monodomain crystals is investigated using Landau–Ginzburg–Devonshire phenomenological approach. It is shown that hydrostatic pressure could enhance the piezoelectric properties in some directions of crystals. The piezoelectricy enhancement is attributed to the hydrostatic pressure-induced flattening of the elastic Gibbs free-energy profile and its corresponding dielectric softening. For BaTiO3 at 285 K, with increasing pressure, the free-energy profile tends to become flat along the polar [001]c direction, facilitating the dilatation and contraction of polarization. So the dielectric softens and the d33 obviously increases in the [001]c direction. But in the direction perpendicular to the polarization, the free-energy profile goes to steepen, which restrains the polarization rotation away from the [001]c polar axis and in turn makes the shear piezoelectric coefficient d15 decreased. As a result, the maximum longitudinal piezoelectric coefficient d33*(θ) initially going along [111]c axis finally turns to be along [001]c axis with pressure increasing. Whereas for PbTiO3 at room temperature, both along and perpendicular to the polar axis, the free-energy profile tends to flatten, but the flattening along the polar axis predominates all the time. That is to say, the hydrostatic pressure facilitates the polarization dilatation and contraction along the polar axis as well as the polarization rotation in (100)c plane, d33 and d15 both increase, but longitudinal piezoelectric coefficient d33*(θ) for PbTiO3 always displays its maximum value along the polar [001]c direction and increases continuously with pressure in the computational pressure range.

Self‐Bias Response of Lead‐Free (1−x)[0.948 K0.5Na0.5NbO3–0.052 LiSbO3]–xNi0.8Zn0.2Fe2O4–Nickel Magnetoelectric Laminate Composites

This study reports the magnetoelectric (ME) response of lead‐free particulate composites given as (1−x)[0.948 K0.5Na0.5NbO3–0.052 LiSbO3]–xNi0.8Zn0.2Fe2O4 (KNNLS–NZF) and bimorph laminates given as KNNLS–NZF/Ni/KNNLS–NZF. The particulate ME composites were found to exhibit island–matrix microstructure as confirmed by scanning electron microscopy and elemental mapping. Detailed investigations were conducted on optimization of the magnitude of magnetic and piezoelectric properties by varying the sintering condition and NZF mole fraction. It was found that longitudinal piezoelectric strain coefficient d33 and electromechanical coupling factor kp decreased with increasing NZF concentration. On the other hand, the magnitude of saturation magnetization Ms, remnant magnetization Mr, magnetic permeability μ, and magnetostriction λ was found to increase with increasing NZF fraction. The composition 0.7 KNNLS–0.3 NZF sintered at 1060°C was found to exhibit d33 of 73 pC/N, Ms of 19 emu/g, and maximum ME coefficient αE of 20.14 mV/cm·Oe under Hac=1 Oe at 1 kHz. The bimorph laminates were fabricated by embedding Ni plate between (1−x)KNNLS–xNZF disks with varying electrical connections to achieve radial and bending modes. The radial mode laminates were found to exhibit typical ME response without any self‐bias effect with maximum αE of 261.3 mV/cm·Oe and high DC magnetic field sensitivity of 1 μT at 1 kHz. The bending mode laminates were found to exhibit self‐biased ME response whose magnitude and shape was dependent upon the NZF concentration.

Piezoelectric anisotropy of a KNbO3 single crystal

Orientation dependence of the longitudinal piezoelectric coefficients (d33∗) of a KNbO3 single crystal has been investigated as a function of temperature by using the Landau–Ginzburg–Devonshire phenomenological theory. It is shown that the maximum of d33∗ is not always along the polarization direction of the ferroelectric phase. The enhancement of d33∗ along a nonpolar direction is attributed to a ferroelectric phase transition at which a polarization changes its direction. In the tetragonal phase, the maximum of d33t∗ at high temperatures is along the tetragonal polar direction and then changes its direction toward the polar direction of the orthorhombic phase when the temperature is close to the tetragonal-orthorhombic phase transition. The maximum of d33o∗ of the orthorhombic phase depends on both the high-temperature and low temperature ferroelectric phase transitions. In the rhombohedral phase, the maximum of d33r∗ is relatively insensitive to temperature due to the absence of any further phase transitions in the low temperature regime. These results can be generalized to the phase transitions induced by external electric field, pressure, and composition variations.

A generalized rule for large piezoelectric response in perovskite oxide ceramics and its application for design of lead-free compositions

We present a general rule for the perovskite oxide ceramics: “A large piezoelectric constant in ABO3 perovskite ceramics can be obtained by tuning the weight ratio of A and B sites, WA/WB or WB/WA, to 3. Piezoelectric constant decreases significantly when WA/WB or WB/WA is in the range of 0.5–2.0, termed as forbidden zone.” A comparative analysis was conducted for broad range of materials demonstrating the applicability of proposed rule. Further based on this rule optimized compositions in BaTiO3 and alkali niobate based systems were developed. Polycrystalline ceramics in modified BaTiO3 system were found to exhibit longitudinal piezoelectric coefficient (d33) of 330 pC/N, while alkali niobate ceramics showed d33 of 294 pC/N.

Prediction of relationships between hydrostatic coefficients and processing parameters of porous PZT ceramics by radial basis function

Abstract The high hydrostatic coefficients of porous piezoelectric materials provide the reduced acoustic impedance for the effective coupling with water medium as well as biological tissues. The hydrostatic strain coefficient (dh), voltage coefficients (gh) and longitudinal piezoelectric coefficient (d33) of porous piezoelectric materials has a strong dependence on processing parameters such as porosity parameter, polymer percentage, density and poling voltage. In this work, a nonparametric regression has been carried out to figure out the nonlinear relationships between the hydrostatic coefficients and its processing parameters. The nonparametric regression has been carried out by artificial neural network. The Network architecture utilized is radial basis function (RBF) which is combined with Fuzzy Clustering Method (FCM) to identify the hidden node numbers and widths. The porosity parameter was calculated from scanning electron micrographs of the porous piezoelectric materials using conventional image processing techniques. The results of the artificial neural network were evaluated against experimental data.

Homogenization of textured as well as randomly oriented ferroelectric polycrystals

Abstract Microstructural features such as spatial correlation of crystallographic orientations and morphological texture in piezoelectric polycrystals is modeled computationally. The mathematical homogenization of piezoelectric material is implemented using the finite element method (FEM) by solving the coupled equilibrium electrical and mechanical fields. A three-dimensional (3D) FEM model is adapted to polycrystalline medium. The dependence of macroscopic electromechanical properties on domain orientation and texture of single-crystalline as well as polycrystalline ferroelectric BaTiO3 and PbTiO3 are demonstrated based on this model. The homogenized piezoelectric moduli of the polycrystals and single-crystals of these materials exhibit remarkable but contrasting behaviors. The aggregate texture for polycrystalline ferroelectrics is assumed to have a Gaussian (normal) distribution. The longitudinal piezoelectric strain coefficient d33 assumes a higher value than the corresponding single-crystalline value of BaTiO3 at a distribution characterized by σ between 0.5 and 0.7 However, for PbTiO3 the maximum is shown at the perfect {0 0 1} texture. Therefore, polycrystalline materials are expected to be improved in their global piezoelectric performance by engineering the texture of the microstructure.

Effects of niobium doping on lead zirconate titanate films deposited by a sol–gel route

Niobium (Nb)-doped lead zirconate titanate (PZT) films have been prepared on platinized silicon substrates using a sol–gel method. The Zr/Ti ratios of the films are 53/47 and 40/60, and the Nb doping level ranges from 0 mol% to 3 mol%. Similar to the cases in bulk ceramics, after the doping with Nb, the remanent polarization Pr, effective transverse piezoelectric coefficients e31,c and pyroelectric coefficient p of the PZT films increase; but the longitudinal effective piezoelectric coefficient d33,c remains roughly unchanged. At the optimum Nb doping levels, the observed Pr, −e31,c and p reach a maximum value of 30 μC/cm2, 18 C/m2 and 350 μC/m2 K, respectively, for the PZT (53/47) films, and 37 μC/cm2, 7.9 c/m2 and 370 μC/m2 K for the PZT (40/60) films. Our results also reveal that there exist linear relations between p, e31,c/er and Pr.

PREPARATION AND PIEZOELECTRIC PROPERTIES OF SOL-GEL-DERIVED NB-DOPED PZT FILMS FOR MEMS APPLICATIONS

ABSTRACT Sol-gel-derived niobium (Nb)-doped lead zirconate titanate (PZT) films have been deposited on silicon substrates with a lead titanate seeding layer by the multiple-spin-coating technique. The doping level of Nb ranges from 0 to 2 mol%. With the seeding layer, the PZT films can crystallize well into the perovskite phase at a low temperature of 550°C for 2 h. The films are dense and have good dielectric and piezoelectric properties. Effective longitudinal and transverse piezoelectric coefficients (d33,c and e31,c) of the films have been measured. Our results reveal that the Nb dopant effects on the PZT films are very similar to the experimentally-known effects on the corresponding bulk ceramics, i.e. enhancing both the longitudinal and transverse piezoelectric properties. For the PZT film doped with 1 mol% Nb, the observed values of d33,c and e31,c are 74 pm/V and 12.8 C/m2, respectively.