The paper presents an overview of experimental evidence and present understanding of nonlinear dielectric, elastic and piezoelectric relationships in piezoelectric ceramics. This topic has gained an increasing recognition in recent years due to the use of such materials under extreme operating conditions, for example in electromechanical actuators and high power acoustic transducers. Linear behaviour is generally confined to relatively low levels of applied electric field and stress, under which the dielectric, elastic and piezoelectric relationships are described well by the standard piezoelectric constitutive equations. Nonlinear relationships are observed above certain ‘threshold’ values of electric field strength and mechanical stress, giving rise to field and stress-dependent dielectric (e), elastic (s) and piezoelectric (d) coefficients. Eventually, strong hysteresis and saturation become evident above the coercive field/stress due to ferroelectric/ferroelastic domain switching. The thermodynamic method provides one approach to describing nonlinear behaviour in the ‘intermediate’ field region, prior to large scale domain switching, by extending the piezoelectric constitutive equations to include nonlinear terms. However, this method seems to fail in its prediction of the amplitude and phase of high frequency harmonic components in the field-induced polarisation and strain waveforms, which arise directly from the nonlinear dielectric and piezoelectric relationships. A better fit to experimental data is given by the empirical Rayleigh relations, which were first developed to describe nonlinear behaviour in soft magnetic materials. This approach also provides an indication of the origins of nonlinearity in piezoelectric ceramics, in terms of ferroelectric domain wall translation (at intermediate field/stress levels) and domain switching (at high field/stress levels). The analogy with magnetic behaviour is also reflected in the use of Preisach-type models, which have been successfully employed to describe the hysteretic path-dependent strain-field relationships in piezoelectric actuators. The relative merits and limitations of the different modelling methods are compared and possible areas of application are identified.

Nonlinearity in piezoelectric ceramics

Shock compression of solids

Electrostriction plays an important role in the electromechanical behavior of ferroelectrics and describes a phenomenon in dielectrics where the strain varies proportional to the square of the electric field/polarization. Perovskite ferroelectrics demonstrating high piezoelectric performance, including BaTiO3, Pb(Zr1-xTix)O3, and relaxor-PbTiO3 materials, have been widely used in various electromechanical devices. To improve the piezoelectric activity of these materials, efforts have been focused on the ferroelectric phase transition regions, including shift the composition to the morphotropic phase boundary or shift polymorphic phase transition to room temperature. However, there is not much room left to further enhance the piezoelectric response in perovskite solid solutions using this approach. With the purpose of exploring alternative approaches, the electrostrictive effect is systematically surveyed in this paper. Initially, the techniques for measuring the electrostrictive effect are given and compa...

/pdf/electrostrictive-effect-in-ferroelectrics-an-alternative-3ay4udmtsa.pdf

Electrostrictive effect in ferroelectrics: An alternative approach to improve piezoelectricity

In the last 25 years, piezoelectric ceramic-polymer composites have been conceptualized, prototyped, fabricated, and implemented in an array of applications encompassing medical imaging and military missions, among others. A detailed snapshot of the materials used, and a detailed account of the major innovative methods developed in making various piezoelectric ceramic-polymer composites are presented. The salient aspects of processing of such composites are summarized, and structure-processing-property relations are described using connectivity as the unifying central concept. Computer-aided design (CAD)-based fabrication methods, which result in composites whose structural complexity surpass that of composites obtained with traditional methods, are described to introduce the reader to novel concepts in processing of piezocomposites. A brief survey of some recent advances made in modeling of (0-3), (1-3), and (2-2) composites also is provided.

Piezoelectric composites for sensor and actuator applications

Dielectric properties of model BaTiO3/polymer composites were measured over a broad frequency and temperature range. A series of BaTiO3/monomer suspensions were photocured into thin wafers. The wafers were equipped with aluminum electrodes, and the dielectric permittivity of the composites was investigated at frequencies from 100 Hz to 10 GHz and at temperatures from −140 to +150 °C. It has been found that for the same BaTiO3 loading dielectric characteristics of the composites strongly depend of the type of polymer. Polar polymers increase dielectric constant of the composites at low frequencies but have little effect at gigahertz frequencies. Dielectric losses of the composites show a maximum at some intermediate frequency within megahertz to gigahertz range that reflects the relaxation behavior of the polymer matrix. The magnitude of the losses increases with increasing polarity of the polymer component. At constant frequency and temperature, the composites follow a linear relationship between logarith...

https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=851772

Dielectric Properties of Polymer/Ferroelectric Ceramic Composites from 100 Hz to 10 GHz

Nonlinear behavior of an ultrasonic transducer

In this study, ac and dc conductivity measurements were performed under ambient atmosphere on doped lead zirconate titanate (PZT) ceramics in order to investigate the defect chemistry by identifying the predominant charge carriers. The considered compositions were acceptor (1% mol Mn or Mg) and donor (Nb or F) co-doped PZTs with [Donor] = 1 or 2% mol. The influence of donor concentration on the conductivity was determined. From the conduction activation energy values calculated in the temperature range 200–700 °C, the principal contributing charge carriers are doubly-ionized oxygen V O ¨ and lead vacancies VPb. For Mg doped PZTs, neither Nb nor F co-doping strongly reduce both conductivity levels and the dominant conducting species V O ¨ . For Mn doped materials, both donor co-dopants niobium and fluorine reduce the conductivity but do not have the same effect on the conduction mechanism at low temperature. With 2% Nb doping, the dominant conducting species are V O ¨ whereas electrical conduction is controlled by electrons from the second-ionization of oxygen vacancies with 2% F doping. The difference of oxygen vacancies content in (Mn, F) and (Mn, Nb) co-doped PZTs may be at the origin of the two distinct conducting species and of the different conductivity levels.

Influence of donor co-doping by niobium or fluorine on the conductivity of Mn doped and Mg doped PZT ceramics

Des changements importants de comportement sont observes sur des transducteurs de puissance utilisant des ceramiques de type PZT. Une meilleure caracterisation des materiaux piezoelectriques sous hauts niveaux s'avere alors necessaire. En effet, des phenomenes caracteristiques d'un comportement non lineaire tels que le decalage de la frequence de resonance avec hysteresis ou la generation d'harmoniques ont ete observes experimentalement. Ceci se traduit par des effets de saturation du niveau de deplacement de la face avant, une limitation des performances du systeme et un fonctionnement instable. Afin d'interpreter de tels comportements, une theorie non lineaire est proposee. Ce modele a ensuite ete applique a notre structure de transducteur. Une comparaison entre simulations et resultats experimentaux a permis de valider cette nouvelle approche. Les effets de saturation observes ont ete jusqu'a present toujours relies a la variation du coefficient d'amortissement, notre etude a permis de demontrer qu'une autre explication liee aux non linearites etait possible et permettait en meme temps d'expliquer d'autres phenomenes observes.

http://mastersonics.com/documents/mmm_basics/general_info/Publications/jp3v7p1197.pdf

Piezoelectric Ceramics Nonlinear Behavior. Application to Langevin Transducer

In the last two decades, Eyraud tried to interpret the soft characteristics in lead zirconate titanate ceramics (PZT) by an electron transfer between constitutive ions and/or dopants such as Ti3+/4+ or Fe2+/3+. These electron transfers are supposed to minimize the space charges (ρ p ) existing at the domain walls interface due to polarization divergences (ρ p = −div ), making the domain wall movement easier (soft PZTs). Recently, the Eyraud's model has been refined and the softening mechanism is now explained by electron exchange between oxygen and lead vacancies owing to the presence of these defects in every doped PZT. Based on the analogy with BaTiO3, the proposed correction of the model is justified using the energy levels of barium and oxygen vacancies given by Daniels and Hardtl. It is supposed that the material will exhibit soft properties if acceptor and donor sites are associated with neighbouring energy levels allowing direct electron tranfer between each other, without contributing to electron ...

Interpretation of the Softening Effect in PZT Ceramics Near the Morphotropic Phase Boundary

At frequencies close to resonance, Langevin transducers exhibit strong nonlinearities at low voltage levels. First, characteristic phenomena of a nonlinear behavior, such as the resonance frequency shift and the hysteresis effect, appear. Moreover, these nonlinearities result in an electrical and mechanical energy spreading over a discrete spectrum. Experimental results for current and tail mass displacement are given for power piezomaterial. They show a saturation of the fundamental amplitude due to the increase of the overtones amplitudes. To interpret these experimental results, a nonlinear oscillator model, based on nonlinear piezoelectric relationships, has been developed. A numerical solution of this nonlinear Langevin equation is given. Simulations and experimental results are in good agreement

Lucien Eyraud

Papers

Nonlinear behavior of an ultrasonic transducer

Influence of donor co-doping by niobium or fluorine on the conductivity of Mn doped and Mg doped PZT ceramics

Piezoelectric Ceramics Nonlinear Behavior. Application to Langevin Transducer

Interpretation of the Softening Effect in PZT Ceramics Near the Morphotropic Phase Boundary

Nonlinearities in Langevin transducers