Ferroelectric materials Research Papers - Academia.edu (original) (raw)

- by
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- Engineering, Chemistry, Quantum Chemistry, Optimization
- by el-sayed el-rabaie
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- Ferroelectric materials, Electromagnetic Fields, Notch Filters

We report the synthesis of polycrystalline barium titanate BaTiO3 thin films on silicon substrate prepared by sol- gel technique. The structure and composition of ferroelectric film ms have been analyzed by using x-ray photoelectron spectroscopy and Rutherford backscattering spectroscopy. These methods provide information on the core level electronic states and the film composition. The results indicate the films have no distinctive deviation from the stoichiometry within the accuracy of both spectroscopic methods. Thus, this study of surface structure and composition of ferroelectric films could lead to a better understanding of the observed change of electrical and optical properties and to the design of improved devices such as dynamic random access memories.

- by Daniel Hernandez Cruz
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- Spectroscopy, Proceedings, Thin Films, Ferroelectric materials

In this paper, we discuss the effect of non-homogeneity of the spontaneous polarization on electric susceptibility of ferroelectric films. Since the electric susceptibility represents response of the ferroelectrics to the given electric fields, hence determination of this parameter is very important. Using layer model, the spontaneous polarizations are calculated for each layer. Then these values are used in determining the electric susceptibility numerically. In this process, the effective medium theory is employed. It is found that the inhomogeneity of spontaneous polarization, especially near surface or bottom of the film, generates the small disturbance near resonance frequency of the ferroelectrics. The small dip appears in the susceptibility spectroscopy near the sharp dip which represents resonance. As the thickness of the film decreases, the small disturbance in susceptibility spectroscopy is increasingly visible. It means that the effect of inhomogeneity (surface effect) cannot be negligible in thin film. This result also shows the possibility to probe the surface effect by measuring reflectance while varying the frequency of incident wave.

- by K. Anjali and +2
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- Ferroelectrics, Ferroelectric materials, Lead-Free Piezoceramics, Dielectric and ferroelectric materials

El spray pirolisis es una técnica de deposición química en húmedo; se pueden generar aerosoles mediante distintos mecanismos fiscos, como lo son ondas ultrasónicas, gradientes de presión y fuerzas electrostáticas. Como tal, consiste en la atomización de un líquido en pequeñas gotas. Cuando al líquido en forma de películas delgadas se le permite fluir a través de una superficie vibrante, se rompe en finas gotas. Este fenómeno es conocido como atomización ultrasónica. Existen dos hipótesis formuladas para descripción de estos fenómenos, estas son: • Hipótesis de la onda capilar • Hipótesis de cavitación Se enfocara en la hipótesis de cavitación porque generalmente es aplicada a altas frecuencias. Vibrador ultrasónico y características de la niebla que produce Estas atomizaciones se logran por medio de nebulizadores ultrasónicos los cuales están basado en el principio de vibraciones de un cristal piezoeléctrico el cual es manejado por un campo eléctrico alternante. Los ultrasonidos son ondas sonoras generadas por frecuencias mayores 20,000 Hz. A estas frecuencias se ocasiona cavitación acústica en el líquido, que es la formación, crecimiento e implosión de micro-burbujas que contienen gases disueltos y vapor de agua. El rápido colapso de las burbujas de cavitación es cercanamente adiabática. Por lo que cada burbuja funciona como un micro reactor en el cual se alcanzan temperaturas del orden de 5000K y presiones de cientos de atmosferas. Existen un varios factores que influyen en la generación ultrasónica como lo son la frecuencia del ultrasonido, el gas disuelto, el poder acústico y la temperatura aparente del liquido. Precursores para la preparación de la solución.

In the present work we have synthesized the Er(3+)/Yb(3+) codoped barium titanate phosphor via co-precipitation method and studied its upconversion emission properties. The prepared BaTiO3 powder was found in cubic phase as a major component and having good crystallinity revealed by the XRD analysis. Optical band gap of the cubic barium titanate was calculated using the diffuse reflectance absorption spectrum. Good green upconversion emission is observed from the samples when excited by 980 nm diode laser. The variation in upconversion emission intensity is studied with the increase in excitation power as well as temperature of the sample. It is found that the emission bands centred at 524 and 548 nm are thermally coupled and can act as a temperature sensor in the 300-480 K temperature range.

- by Vineet Rai
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- Thermodynamics, Analytical Chemistry, Titanium, Crystallization
- by Bruno Crosignani
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- Crystals, Ferroelectric materials, Solitons, Temperature
- by Kenji Uchino
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- Acoustics, Strategy, Commerce, Actuators
- by Satyendra Kumar
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- Nonlinear Optics, Liquid Crystals, Thin Films, Ferroelectric materials
- by Mohamed Eltawil
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- Engineering, Power Electronics, Renewable Energy, Service Quality

Solid-state memory is an essential component of the digital age. With advancements in healthcare technology and the Internet of Things (IoT), the demand for ultra-dense, ultra-low-power memory is increasing. In this review, we present a comprehensive perspective on the most notable approaches to the fabrication of physically flexible memory devices. With the future goal of replacing traditional mechanical hard disks with solid-state storage devices, a fully flexible electronic system will need two basic devices: transistors and nonvolatile memory. Transistors are used for logic operations and gating memory arrays, while nonvolatile memory (NVM) devices are required for storing information in the main memory and cache storage. Since the highest density of transistors and storage structures is manifested in memories, the focus of this review is flexible NVM. Flexible NVM components are discussed in terms of their functionality, performance metrics, and reliability aspects, all of which are critical components for NVM technology to be part of mainstream consumer electronics, IoT, and advanced healthcare devices. Finally, flexible NVMs are benchmarked and future prospects are provided.

- by Munees Waran
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- Structural Analysis, Magnetism, Ferroelectric materials, Multiferroic Materials
- by Amr Al-Awamry
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- Ferroelectric materials, Microwave filters, Slotlines

Barium (Ba) doping at Bismuth (Bi) site is reported to enhance magnetic properties of Bismuth Ferrite (BiFeO 3) while Yttrium (Y) doping at the same is found to improve ferroelectric and dielectric properties. To investigate the combined effect of Ba and Y co-doping, Ba 0.1 Bi 0.9-x Y x FeO 3 (x ¼ 0.0, 0.1 and 0.2) are synthesized using chemical synthesis route and their magnetoelectric and dielectric properties are studied in detail. The X-Ray Diffraction study confirms the single phase nature of the synthesized samples. The ferroelectric property is enhanced for x ¼ 0.1 while the magnetic studies show enhanced magnetisation for both co-doped samples with highest enhancement in x ¼ 0.1. The doped samples exhibit a first order field induced metamagnetic transition. The dielectric constant also increases with reduced tangent loss and conductivity for x ¼ 0.1. Therefore, co-doping with Ba and Y improves the magnetoelectric and dielectric property of BiFeO 3 .

- by Swarnali Hait
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- Multiferroics, Magnetoelectrics, Ferroelectrics, Ferroelectric materials
- by Felix Lee
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- Engineering, Mechanical Engineering, Smart Materials, Energy Harvesting

Till date, fabrication of piezoelectric nanogenerator (PNG) with highly durable, high power density, and high energy conversion efficiency is of great concern. Here a flexible, sensitive, cost effective hybrid piezoelectric nanogenerator (HPNG) developed by integrating flexible steel woven fabric electrodes into poly(vinylidene fluoride) (PVDF)/aluminum oxides decorated reduced graphene oxide (AlO-rGO) nanocomposite film is reported where AlO-rGO acts as nucleating agent for electroactive β-phase formation. The HPNG exhibits reliable energy harvesting performance with high output, fast charging capability, and high durability compared with previously reported PVDF based PNGs. This HPNG is capable for harvesting energy from a variety and easy accessible biomechanical and mechanical energy sources such as, body movements (e.g., hand folding, jogging, heel pressing, and foot striking, etc.) and machine vibration. The HPNG exhibits high output power density and energy conversion efficiency, facilitating direct light on different color of several commercial light-emitting diodes instantly and powers up many portable electronic devices like wrist watch, calculator, speaker, and mobile liquid crystal display (LCD) screen through capacitor charging. More importantly, HPNG retains its performance after long compression cycles (≈158 400), demonstrating great promise as a piezoelectric energy harvester toward practical applications in harvesting biomechanical and mechanical energy for self-powered systems.

- by Sumanta Kumar Karan and +1
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- Supercapacitors, Nanogenerators, Ferroelectric materials, Piezoelectric Energy Harvesting

Transmittance measurements on various single crystal ferroelectric and dielectric materials, BaTiO3, SrTiO3, LiNbO3, LiTaO3, (PbMg1/3Nb2/3O3)0.73-(PbTiO3)0.27, LaAlO3, and Bi4Ge3O12,, over a broad millimeter-wave (MMW) frequency range have been performed. Frequency dependence of the complex dielectric permittivity has been measured in the MMW region using high-power sources for the first time, using a free-space, quasi-optical MMW spectrometer equipped with high-power backward wave oscillators (BWOs) as sources of coherent radiation, tunable in the range from 30 to 120 and 180 to 260 GHz. These results are compared with MMW permittivity of these materials obtained by other methods as well as to RF, microwave, and optical frequency permittivities for all the materials tested. The effects of both crystallographic orientation and quality of the surface polishing of the crystals have been examined. Uncertainties and possible sources of instrumentation and measurement errors related to the freespace MMW technique are discussed. This work demonstrates that precise MMW permittivity data can be obtained even on relatively small and thin crystals of different surface conditions and orientations using the high-power BWO-based quasioptical approach.

- by John McCloy
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- Engineering, Crystals, Ferroelectric materials, Physical sciences
- by Susan Trolier-McKinstry
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- Microelectromechanical systems, Thin Films, Actuators, Transducers

Ferroelectric materials exhibit piezoelectric natures. In this work,
PZT is selected as the prime component and the polymers which
exhibit few piezoelectric properties are selected. This paper
reviews for the different polymers like PVDF, PVC, PU, P(VDFTrFE) and Polyester resin. The composite obtained by the
individual polymer with PZT is used for transducer applications
and accelerometers. The various methods selected for the
composites have been reviewed as reported from literatures. The
thorough study on the composite revealed that volume fraction,
temperature, particle size of PZT affects the dielectric and
piezoelectric properties. There is an increase in the dielectric
properties and piezoelectric properties when the parameters like
volume fraction, temperature, particle size increase in their
respective dimensions.
Keywords: Ferroelectric, polymers, accelerometer, dielectric,
piezoelectric properties.

- by Gowdhaman P and +1
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- Polymers, Ferroelectrics, Piezoelectric ceramics, Ferroelectric materials
- by Amor Haddad
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- Crystal structure, Ferroelectric materials, XRD, Lattice Parameter

A study has been carried out to understand the different ceramics and different polymers to prepare
composite with 0-3 connectivity. This is purely a review study on ferroelectric materials. Dielectric and
piezoelectric properties for various composites have been discussed. It is clear that there is always an increase
in dielectric constant (ɛr) for an increase in volume fraction. The piezoelectric strain coefficient (d33) showed an
increase in values to the increase in volume fraction of the various ceramic-polymer composites. There is no
existence of steady pattern found in the voltage coefficient (g33) values. The values obtained for the above
confirms the usage of composites in various applications discussed in the introduction.
Keywords: Ceramic, polymer, ferroelectric, dielectric constant, piezoelectric strain coefficient, piezoelectric
voltage coefficient.

- by Gowdhaman P and +1
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- Ferroelectric materials, Dielectric and ferroelectric materials, Ferroeelctrics

Nano-crystalline Sr0.5Ba0.5Nb2O6 was synthesized by a one-pot method using PEG400 and citric acid. Calcination of the (Sr,Ba,Nb)-gel at 600 °C leads to Sr 0.5 Ba 0.5 Nb 2 O 6 with a crystallite size of 24(2) nm and a specific surface area of 38.5(10) m2 g-1. Sintering up to 1325 °C leads to ceramics with globular or irregular-shaped grains and average grain sizes between 1.3 and 2.4 µm, whereas higher temperatures lead to a rod-like microstructure. The indirect allowed optical band gap varies between 3.70(5) and 3.29(5) eV. Dielectric measurements show a diffuse phase transition and weak relaxor properties. The maximum of the permittivity occurs between 116 and 147 °C. The frequency dependence of the impedance can be well described by one or two RC-circuits depending on sintering temperature. The melting temperature is determined as 1506(7) °C with dH f = 140(20) kJ mol -1. The average linear thermal expansion coefficient is found to be 10.5(5)*10-6 K-1 .

- by Roberto Köferstein
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- Nanoparticles, Phase Transitions, Ferroelectrics, Ferroelectric materials

We have studied the diffuse scattering in the relaxor Pb(Mg1/3Nb2/3)O3 (PMN) using triple-axis neutron scattering techniques. The diffuse scattering first appears around the Burns temperature Td≈620K, indicating that its origin lies within the polar nanoregions (PNR’s). While the relative intensities of the diffuse scattering around (101), (200), and (300) are consistent with those previously reported by Vakhrushev et al., they are, surprisingly, entirely different from those of the lowest-energy transverse-optic (TO) phonon. This observation led Naberezhnov et al. to claim that this TO mode could not be the ferroelectric soft mode. However, a recent neutron study by Gehring et al. has unambiguously shown that the lowest-energy TO mode does soften on cooling and that the relative intensities are similar to those of PbTiO3. If the diffuse scattering in PMN originates from the condensation of a soft TO mode, then the atomic displacements of the PNR must satisfy the center-of-mass condition. But, the atomic displacements determined from diffuse scattering intensities do not fulfill this condition. To resolve this contradiction, we propose a simple model in which the total atomic displacement consists of two components δc.m. and δshift. Here δc.m. is created by the soft-mode condensation and thus satisfies the center-of-mass condition. On the other hand, δshift represents a uniform displacement of the PNR’s along their polar direction relative to the surrounding (unpolarized) cubic matrix. Within the framework of this model, we can successfully describe the neutron diffuse scattering intensities observed in PMN.

- by Peter Gehring
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- Neutron Diffraction, Dielectric Physics, Ferroelectrics, Perovskites
- by Harold Sabbagh
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- Fluorescence, Water Pollution, Finite Element, Integral Equations

A ﬂ exible version of traditional thin lead zirconium titanate ((Pb 1.1 Zr 0.48 Ti 0.52 O 3 )-(PZT)) based ferroelectric random access memory (FeRAM) on silicon shows record performance in ﬂ exible arena. The thin PZT layer requires lower operational voltages to achieve coercive electric ﬁ elds, reduces the sol-gel coating cycles required (i.e., more cost-effective), and, fabrication wise, is more suitable for further scaling of lateral dimensions to the nano-scale due to the larger feature size-to-depth aspect ratio (critical for ultra-high density non-volatile memory applications). Utilizing the inverse proportionality between substrate’s thickness and its ﬂ exibility, traditional PZT based FeRAM on silicon is transformed through a transfer-less manufac-turable process into a ﬂ exible form that matches organic electronics’ ﬂ exibility while preserving the superior performance of silicon CMOS electronics. Each memory cell in a FeRAM array consists of two main elements; a select/access transistor, and a storage ferroelectric capacitor. Flexible transistors on silicon have already been reported. In this work, we focus on the storage ferroelectric capacitors, and report, for the ﬁ rst time, its performance after transformation into a ﬂ exible version, and assess its key memory parameters while bent at 0.5 cm minimum bending radius.

- by Mohamed T Ghoneim and +2
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- Ferroelectric materials, Reliability, Flexible Electronics, Nonvolatile Memories
- by Ian Elder and +1
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- Resonators, Crystals, Ferroelectric materials

Raman spectra of КТа0.5Nb0.5O3 nanopowder solid solution were obtained at the temperatures from -1900С to 6000С and investigated for the first time. The compound was synthesized by a new technology. Temperature dependences of the intensity, width and frequency of the В1(TO2), А1(TO1), В1(TO3), А1(ТO3) and В2(TO3) modes are thoroughly analyzed. A significant expanding of the temperature ranges of all phase transitions, correlated with a spread of particle sizes is registered. It was found that an average temperature of each of the phase transitions is shifted in different way, in particular: a low-temperature transition at 30 degrees higher, the middle transition at 10 degrees higher, and the ferroelectric phase transition occurs at 20 degrees lower than the temperature of the corresponding transitions in single-crystal KТa0.5Nb0.5O3.

- by Iryna Golovina and +1
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- Raman Spectroscopy, Nanoparticles, Ferroelectric materials

The Army requires passive uncooled IR sensors for use in numerous vehicle and weapons platforms, including driver vision enhancement (DVE), rifle sights, seeker munitions, and unattended ground sensors (UGSs) and unattended aerial vehicles (UAVs). Recent advances in bio-inspired/biomimetic nanomaterials synthesis, laser material processing, and sensor design and performance testing, offer the opportunity to create uncooled IR detector focal-plane arrays with improved sensitivity, low thermal mass, and fast response times, along with amenability to low-cost, rapid prototype manufacture. We are exploring the use of genotype-inspired, digitally-scripted laser direct-write techniques, in conjunction with the kinetically controlled catalytic process for the growth of nanostructured multimetallic perovskites, to develop a novel approach to the fabrication of precision patterned 2-D focal-plane arrays of pyroelectric perovskite-based materials. The bio-inspired growth of nanostructured, multimetallic perovskite thin-films corresponds to the use of kinetically controlled vapor diffusion for the slow growth of pure, highly crystalline 6-nm barium titanate (BaTiO3) nanoparticles. This unique vapor-diffusion sol-gel route enables the formation of stoichiometric cubic-phase nanoparticles at room temperature and ambient pressure in the absence of a structure-directing template. Novel laser direct-write processing and synchronized electro-optic pulse modulation techniques have been utilized to induce site-selective, patterned phase transformation of microscale aggregates of the BaTiO3 nanoparticles from the non-pyroelectric cubic polymorph to the pyroelectric tetragonal polymorph. This paper reports on our initial collaborative investigations, including comprehensive structural characterization (XRD, TEM, and SEM) of the BaTiO3 nanoparticles and thin-films, along with preliminary laser-induced phase transformation results.

- by Krisztian Niesz
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- Manufacturing, Polymorphism, Kinetics, Biomimetics

Ferromagnetism is observed in LiNiO3 nanocrystals exposed to a reducing atmosphere intended to create oxygen vacancies. The existence of vacancies is confirmed by measuring the oxygen depletion across the selected nanoparticles by TEM. The magnetism shows no temperature dependence in the range of 4– 300 K. The density functional theory was used to perform spin polarized electronic structure calculations for LiNiO3 with and without oxygen vacancies. The calculated magnetic data qualitatively support the observed magnetic behavior.

- by F. Espinosa-Magaña and +4
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- Ferroelectric materials, Magnetic Properties, Oxygen Vacancies, Lithium Niobate

The bulk dense nanocrystalline BaTiO3 (BT) ceramics ranging from 20 to 100 nm have been successfully prepared by the spark plasma sintering (SPS) method. Raman spectra and X-ray diffraction were used in combination with electron microscopy to study the evolution of lattice structure and phase transformation behavior with grain growth from nanoscale to micrometer scale for BT ceramics. The results reveal that the SPS technique provides exceptional opportunity to compact ceramics to full density with nanograin size. It is also demonstrated that all structural modifications in nanocrystalline BT and low-symmetry structures still exist in 20 nm nanograin BT ceramics. The ferroelectric properties of crystalline structures were investigated by scanning force microscopy in piezoresponse mode. Piezoelectric hysteresis loop was recorded, demonstrating that 20 nm BT ceramics has a remanent polarization and is switchable by an electric field. Thus, if a critical grain size exists for ferroelectricity, it is less than 20 nm for polycrystalline BT ceramics.

- by hai wen
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- Materials Engineering, Mechanical Engineering, Microstructure, Manufacturing
- by Munees Waran
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- Ferroelectric materials
- by Takeshi Egami
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- Materials Science, Synchrotron Radiation, Ferroelectric materials, Diffraction
- by James Scott
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- Materials Engineering, Mechanical Engineering, Perovskites, Ferroelectric materials

The term big-data in the context of materials science not only stands for the volume, but also for the heterogeneous nature of the characterization data-sets. This is a common problem in combinatorial searches in materials science, as well as chemistry. However, these data-sets may well be 'small' in terms of limited step-size of the measurement variables. Due to this limitation, application of higher-order statistics is not effective, and the choice of a suitable unsupervised learning method is restricted to those utilizing lower-order statistics. As an interesting case study, we present here variable magnetic-field Piezoresponse Force Microscopy (PFM) study of composite multiferroics, where due to experimental limitations the magnetic field dependence of piezoresponse is registered with a coarse step-size. An efficient extraction of this dependence, which corresponds to the local magnetoelectric effect, forms the central problem of this work. We evaluate the performance of Principal Component Analysis (PCA) as a simple unsupervised learning technique, by pre-labeling possible patterns in the data using Density Based Clustering (DBSCAN). Based on this combinational analysis, we highlight how PCA using non-central second-moment can be useful in such cases for extracting information about the local material response and the corresponding spatial distribution.

- by Robert C Pullar
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- Machine Learning, Data Analysis, Principal Component Analysis, Magnetic Materials
- by Alexei Gruverman
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- Materials Engineering, Condensed Matter Physics, Mechanics, Microscopy
- by Satyanarayan Patel
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- Thermodynamics, Energy technology, Ferroelectric materials, Waste Heat
- by ayse merve aslan
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- Condensed Matter Physics, Magnetic Materials, Ferromagnetics, Magnetism
- by Matias Acosta
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- Engineering, Applied Physics, Ferroelectrics, Piezoelectric ceramics

In bulk ferroelectric ceramics, extrinsic contributions associated with motion of domain walls and phase boundaries are a significant component of the measured dielectric and piezoelectric response. In thin films, the small grain sizes, substantial residual stresses, and the high concentration of point and line defects change the relative mobility of these boundaries. One of the consequences of this is that thin films typically act as hard piezoelectrics. This paper reviews the literature in this field, emphasizing the difference between the nonlinearities observed in the dielectric and piezoelectric properties of films. The effect of ac field excitation levels, dc bias fields, temperature, and applied mechanical stress are discussed.

- by Susan Trolier-McKinstry
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- Materials Engineering, Applied Mechanics, Thin Films, Nonlinear Observer

In this work, computational molecular modeling and exploration was applied to study the nature of the negative piezoelectric effect in the ferroelectric polymer polyvinylidene fluoride (PVDF), and the results confirmed by actual nanoscale measurements. First principle calculations were employed, using various quantum-chemical methods (QM), including semi-empirical (PM3) and various density functional theory (DFT) approaches, and in addition combined with molecular mechanics (MM) methods in complex joint approaches (QM/MM). Both PVDF molecular chains and a unit cell of crystalline β-phase PVDF were modeled. This computational molecular exploration clearly shows that the nature of the so-called negative piezo-electric effect in the ferroelectric PVDF polymer has a self-consistent quantum nature, and is related to the redistribution of the electron molecular orbitals (wave functions), leading to the shifting of atomic nuclei and reorganization of all total charges to the new, energetically optimal positions, under an applied electrical field. Molecular modeling and first principles calculations show that the piezoelectric coefficient d 33 has a negative sign, and its average values lies in the range of d 33 ~−16.6 to −19.2 pC/N (or pm/V) (for dielectric permit-tivity ε=5) and in the range of d 33 ~−33.5 to −38.5 pC/N (or pm/V) (for ε=10), corresponding to known data, and allowing us to explain the reasons for the negative sign of the piezo-response. We found that when a field is applied perpendicular to the PVDF chain length, as polarization increases the chain also stretches, increasing its length and reducing its height. For computed value of ε~5 we obtained a value of d 31 ~+15.5 pC/N with a positive sign. This computational study is corroborated by measured nanoscale data obtained by atomic force and piezo-response force microscopy (AFM/PFM). This study could be useful as a basis for further insights into other organic and molecular ferroelectrics.

The synthesis of a periodically ordered, nanostructured composite consisting of CoFe2O4 and BaTiO3 is presented. In a first step, mesoporous CoFe2O4 is prepared by the structure replication method (nanocasting) using mesoporous KIT-6 silica as a structural mold. Subsequently, BaTiO3 is created inside the pores of CoFe2O4 by the citrate route, resulting in a well-ordered composite material of both phases. The two components are known for their distinct ferroic properties, namely ferrimagnetism (CoFe2O4) and ferroelectricity (BaTiO3), respectively. Therefore, this proof of synthesis concept offers new perspectives in the fabrication of composite materials with multiferroic properties.

- by Maxim Lebedev
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- Crystal Growth, Perovskites, Ferroelectric materials, Piezoelectric material

Dielectric data of new [Ba(NdxTi1−2xNbx )O3]0.30[Na0.5Bi0.5TiO3]0.70 (x = 0.075) relaxor ceramic was modelled using a new modified Lorentz equation (T and ω simultaneously) as proposed by us. The activation energy for thermally activated orientation of dipoles and relaxation times were estimated. Dielectric resonance and anti-resonance data as a function of temperature and angular frequency of other piezoelectric compound [Ba(Nd0.1Ti0.8Nb0.1)O3]0.35 [(Na0.5Bi0.5)TiO3]0.65 was also modelled using the modified Lorentz equation as proposed by us. It is shown that using this equation, it is possible to obtain the polarizability, piezoelectric charge constant, piezoelectric voltage constant and activation energy for resonance and anti-resonance.