Energy principle of ferroelectric ceramics and single domain mechanical model

Many physical experiments have shown that the domain switching in a ferroelectric material is a complicated evolution process of the domain wall with the variation of stress and electric field. According to this mechanism, the volume fraction of the domain switching is introduced in the constitutive law of ferroelectric ceramic and used to study the nonlinear constitutive behavior of ferroelectric body in this paper. The principle of stationary total energy is put forward in which the basic unknown quantities are the displacement ui, electric displacement Di and volume fraction pI of the domain switching for the variant I. Mechanical field equation and a new domain switching criterion are obtained from the principle of stationary total energy. The domain switching criterion proposed in this paper is an expansion and development of the energy criterion. On the basis of the domain switching criterion, a set of linear algebraic equations for the volume fraction PI of domain switching is obtained, in which the coefficients of the linear algebraic equations only contain the unknown strain and electric fields. Then a single domain mechanical model is proposed in this paper. The poled ferroelectric specimen is considered as a transversely isotropic single domain. By using the partial experimental results, the hardening relation between the driving force of domain switching and the volume fraction of domain switching can be calibrated. Then the electromechanical response can be calculated on the basis of the calibrated hardening relation. The results involve the electric butterfly shaped curves of axial strain versus axial electric field, the hysteresis loops of electric displacement versus electric filed and the evo- lution process of the domain switching in the ferroelectric specimens under uniaxial coupled stress and electric field loading. The present theoretic prediction agrees reasonably with the experimental results given by Lynch.

STUDY ON FRACTURE BEHAVIOR OF FERROELECTRIC CERAMICS UNDER COMBINED ELECTROMECHANICAL LOADING BY USING A MOIR(?) INTERFEROMETRY TECHNIQUE

This paper discusses an in situ observation of fracture behavior around a crack tip in ferroelectric ceramics under combined electromechanical loading by use of a moiré interferometry technique.The deformation field induced by the electric field and the stress concentration near the crack tip in three-points bending experiments was measured.By analysis of the moiré images it is found that under a constant mechanical load,the electric field almost has no effect on the crack extension in the case that the directions of the poling,electric field and crack extension are perpendicular to each other.When the poling direction is parallel to the crack extension direction and perpendicular to the electric field,the strain decreases faster than that calculated by FEM with and without electrical loading as one goes away from the crack tip.In addition,as the electric field intensity increases,the strain near the crack tip increases,and the strain concentration becomes more significant.

Dielectric Characteristics in BiFeO3-Modified SrTiO3 Incipient Ferroelectric Ceramics

We investigate the dielectric and ferroelectric properties of Sr1-xBixTi1-xFex03 solid solutions （x =0, 0.05, 0.1, 0.15 and 0.2） together with their structures. Through the analysis of Rietveld refinement of powder x-ray diffraction, a cubic structure in space group Pm3m is determined for all the compositions. An obvious dielectric relaxation peak differing from SrTiO3 is observed in the present ceramics. The peak temperature Tm increases with increasing x, and it approaches room temperature at x =0.2. The Vogel Fulcher law and Curie Weiss law fittings further confirm the relaxor ferroelectricity in the present ceramics.

Effect of electric boundary conditions on crack propagation in ferroelectric ceramics

In this paper, the effect of electric boundary conditions on Mode I crack propagation in ferroelectric ceramics is studied by using both linear and nonlinear piezoelectric fracture mechanics. In linear analysis, impermeable cracks under open circuit and short circuit are analyzed using the Stroh formalism and a rescaling method. It is shown that the energy release rate in short circuit is larger than that in open circuit. In nonlinear analysis, permeable crack conditions are used and the nonlinear effect of domain switching near a crack tip is considered using an energy-based switching criterion proposed by Hwang et al.（Acta Metal. Mater.,1995）. In open circuit, a large depolarization field induced by domain switching makes switching much more diffcult than that in short circuit. Analysis shows that the energy release rate in short circuit is still larger than that in open circuit, and is also larger than the linear result. Consequently,whether using linear or nonlinear fracture analysis, a crack is found easier to propagate in short circuit than in open circuit, which is consistent with the experimental observations of Kounga Njiwa et al.（Eng. Fract. Mech., 2006）.

Study of Dielectric and Mechanical Spectra on Point Defects and Phase Transition in Ferroelectric Ceramics

Ferroelectric materials have enormous potential applications in advanced techniques. However, there are still many problems in its practical application. Dielectric and mechanical (internal friction) measurements are very sensitive to phase transitions, relaxation process of point defects, domain walls and their mobility, which have severe effect on ferroelectric properties. These make them become very good means to investigate substantial information on structural features and to explore the fundamental principles in ferroelectric materials and their applications. In this paper, the dielectric and internal friction measurement were used to investigate the behaviors for point defects and phase transition in ferroelectric ceramics such as Bi_ 4-x La_ x Ti_ 3 O_ 12 , Bi_ 4 Ti_ 3-y Nb_ y O_ 12 , SrBi_ 2 Ti_ 2 O_ 9 , PbZr_ x Ti_ 1-x O_ 3 ,_ PMN-PT. They were used to clarify the mechanism for some ferroelectric behaviors.

Energy storage optimization of ferroelectric ceramics during phase-transition process of amorphous/nanocrystalline and polycrystalline by using a phaseffeld model for dielectric breakdown

Ferroelectric ceramics have the potential to be widely applied in the modern industry and military power systems due to their ultrafast charging/discharging speed and high energy density.Considering the structural design and electrical properties of ferroelectric capacitor,it is still a challenge to ffnd out the optimal energy storage of ferroelectric ceramics during the phase-transition process of amorphous/nanocrystalline and polycrystalline.In this work,a ffnite element model suitable for the multiphase ceramic system is constructed based on the phase ffeld breakdown theory.The nonlinear coupling relationship of multiple physical ffelds between multiphase ceramics was taken into account in this model.The basic structures of multiphase ceramics are generated by using the Voronoi diagram construction method.The speciffed structure of multiphase ceramics in the phase-transition process of amorphous/nanocrystalline and polycrystalline was further obtained through the grain boundary diffusion equation.The simulation results show that the multiphase ceramics have an optimal energy storage in the process of amorphous polycrystalline transformation,and the energy storage density reaches the maximum when the crystallinity is 13.96%and the volume fraction of grain is 2.08%.It provides a research plan and idea for revealing the correlation between microstructure and breakdown characteristics of multiphase ceramics.This simulation model realizes the nonlinear coupling of the multiphase ceramic mesoscopic structure and the phase ffeld breakdown.It provides a reference scheme for the structural design and performance optimization of ferroelectric ceramics.

Temperature/electric field induced photoluminescence-modulation effect in dysprosium-doped barium titanate ferroelectric ceramics

Lanthanide(Ln^(3+))based ferroelectric phosphors,with an integration of PL emission and ferroelectric effect,are unveiling an exciting realm of possibilities for multifunctional ferroelectric-optic materials.However,how the ferroelectric host enables the tuning on the PL emissions through modulating the local structure(e.g.,lattice site,symmetry,strains etc.)of the Ln^(3+)activator is not established yet.In this work,a luminescent-ferroelectric material,i.e.Dy^(3+)doped BaTiO_(3) ceramic(Ba_(1–x)Dy_(x)TiO_(3)(x=0–0.07),abbr:BTO:Dy^(3+)),was explored to address the aforementioned issues.The BTO:Dy^(3+)ceramics were synthesized by a solid-state reaction method.The crystal structure,photoluminescence(PL)and electric properties(dielectric constant,ferroelectric hysteresis and piezoelectric hysteresis loop)were systematically investigated.The BTO:Dy^(3+)ceramics show two predominant emission peaks,corresponding to the blue magnetic dipole transition(477 nm,^(4)F_(7/2)→^(6)H_(15/2))and yellow electric dipole transition(573 nm,^(4)F_(7/2)→^(6)H_(13/2)),the intensity ration of which can be modulated by the ferroelectric polarization that causes the slight lattice deformation.Such a polarization-emission modulation combining with the Dy^(3+) doping could accelerate the color change,from yellow to blue,which is characterized to detect the phase transition,with a method and mechanism were proposed,that is,the phase change is reflected by the PL characteristic peak intensity ratio.Therefore,the current results offer a convenient photoluminescence method for detecting the ferroelectric phase transition and a feasible approach to study the interaction between the photoluminescence and polarization in ferroelectric materials,for providing new insights for the development of multifunctional materials.

Multifunctional BNT-based ferroelectric ceramics with large electrostrain and strong photoluminescence properties

The development of multifunctional materials with optical and electrical properties has become a research hotspot in recent years.In this work,multifunctional 0.935(Bi_(0:5)Na_(0:5))TiO_(3)–0.065BaTiO_(3)(BNT–BT)-based ferroelectric ceramics doped with small amounts of CaMAlO_(4)(M=Dy,Ho)were prepared,and the effect of CaMAlO_(4)on the electrostrain and photoluminescence properties of the ceramics was studied.The results showed that the CaMAlO_(4)addition weakened the ferroelectric properties of the BNT–BT matrix,and promoted the improvement of the electrostrain performance.For samples doped with 1.5 mol%CaMAlO_(4),the unipolar strain Suni reached the largest values,which were 0.33%(M=Dy)and 0.38%(M=Ho)under an electric field of 70 kV/cm,corresponding to a large signal d^(*)_(33)(Smax=Emax)of 471 pm/V(M=Dy)and 543 pm/V(M=Ho),respectively.In addition,due to the existing Dy^(3+)and Ho^(3+)luminescent ions,the modified samples exhibited excellent photoluminescence performance,which exhibited bright yellow emission(M=Dy)and green emission eM=HoT under the blue excitation.Due to their multifunctional features,these materials have potential applications as“on-off”actuators,optical-electro integration and coupling devices.

Enhancing the dielectric and piezoelectric properties of Pb_(0.99)Gd_(0.01)Zr_(0.53)Ti_(0.47)O_(3) ferroelectric ceramics by Sr-doping

Recently,high-performance lead zirconate titanate(Pb(Zr_(1-x)Ti_(x))O_(3),PZT)ferroelectric ceramics have attracted intensive attention due to their wider operating temperature range,better temperature stability,as well as larger piezoelectric properties and higher energy conversion efficiency.In this study,the perovskite-type ferroelectric ceramics with a chemical formula of Pb_(0.99-x)Gd_(0.01)Sr_(x)Zr_(0.53)Ti_(0.47)O_(3)(x=0 and 0.02,abbr.PGZT and PGSZT,respectively)were prepared by the traditional solid-state reaction route.The influences of Sr-doping on the phase structure,dielectric properties,ferroelectric properties and piezoelectric properties of the PGZT ceramics were comprehensively investigated.The field-dependent P–E hysteresis loops of PGSZT were measured in the frequency range of 0.05–10 Hz and temperature range of 20–100℃.The results show that Sr-doping not only enhances the dielectric permittivity and piezoelectric coefficient of PGZT,but also decreases its dielectric loss tangent,with the d_(33) value of 473 pC/N,ε_(r) value of 1586 and tanδvalue of 0.016 found in PGSZT.Also,PGSZT shows a high Curie temperature(T_(C))of 350℃.The underlying mechanisms of the property enhancement were identified as that the introduced Sr^(2+) replaces the volatile Pb^(2+) located at the A-site of the perovskite structure,thereby reducing the concentration of lead vacancies and promoting the grain growth of the ceramics,consequently enhancing the dielectric and piezoelectric properties of PGZT.On the other hand,the frequency change in the low-frequency range(<1 Hz)played a significant impact on the remanent polarization(P_(r))and internal biased electric field(E_(i))of PGSZT,but the frequency dependence of coercive field(E_(c))tends to diminish in the high-frequency range(≥1 Hz).

Large scale domain switching around the tip of an impermeable stationary crack in ferroelectric ceramics driven by near-coercive electric field

It is widely accepted that the singular term plays a leading role in driving domain switching around the crack tip of ferroelectric ceramics.When an applied electric field approaches or even exceeds the coercive one,however,non-singular terms are no longer negligible and the switching of a large or global scale takes place.To analyze the large scale switching,one has to get a full asymptotic solution to the electric field in the vicinity of the crack tip.Take a double cantilever beam specimen as an example.The derivation of the full electric field is simplified as a mixed boundary value problem of an infinite strip containing a semi-infinite impermeable crack.The boundary value problem is solved by an analytic function and a conformal mapping to yield a full electric field solution in a closed form.Based on the full field solution,the large scale domain switching is examined.The switching zones predicted by the large and small scale switching models are illustrated and compared with each other near the tip of a stationary crack.

Composite Eshelby model and domain band geometries of ferroelectric ceramics

A method of composite Eshelby inclusion is proposed for aferroelectric grain with domain switching embedded in a polycrystalline ferroelectric matrix. The method quantifies the twinning structure due to spontaneous polarization, as well as the conventional and non-conventional domain structures after poling induced domain reorientation of 90 degree. The predicted parameters include the volume fraction, the thickness, and the surface inclination angle of switched domain plates. The domain wall energy for non-conventional domain structures is derived in terms of the arrays of misfit dislocations. The domain geometries predicted by the present work agree with the measured domain morphology near an indentation crack tip when subjected to lateral electric field.

Microscopic origin and relevant grain size effect of discontinuous grain growth in BaTiO_(3)-based ferroelectric ceramics

Barium titanate[BaTiO_(3)(BT)]-based ceramics are typical ferroelectric materials.Here,the discontinuous grain growth(DGG)and relevant grain size effect are deeply studied.An obvious DGG phenomenon is observed in a paradigmatic Zr^(4+)-doped BT-based ceramic,with grains growing from∼2.2–6.6 to∼121.8–198.4μm discontinuously near 1320℃.It is found that fine grains can get together and grow into large ones with liquid phase surrounding them above eutectic temperature.Then the grain boundary density(D g)is quantitatively studied and shows a first-order reciprocal relationship with grain size,and the grain size effect is dependent on D g.Fine grains lead to high D g,and then cause fine domains and pseudocubic-like phase structure because of the interrupted long-range ferroelectric orders by grain boundary.High D g also causes the diffusion phase transition and low Curie dielectric peak due to the distribution of phase transition temperature induced by internal stress.Local domain switching experiments reveal that the polarization orientation is more difficult near the grain boundary,implying that the grain boundary inhibition dominates the process of polarization orientation in fine-grain ceramics,which leads to low polarization but a high coercive field.However,large-grain ceramics exhibit easy domain switching and high&similar ferroelectricity.This work reveals that the grain boundary effect dominates the grain size effect in fine-grain ceramics,and expands current knowledge on DGG and grain size effect in polycrystalline materials.

Brittle-Ductile Transition of Ferroelectric Ceramics Induced by Thermally Activated Dislocation Emission

Thermally activated dislocation emission in high-temperature ferroelectric ceramics is investigated through an assumption of thermal stability and a novel analytical method. The stress intensity factor (SIF) arising from domain switching is evaluated by using a Green's function method, and the critical applied electric field intensity factor (CAEFIF) for brittle fracture at room temperature is obtained. Besides, the lowest temperature for single dislocation emission before brittle fracture is also obtained by constructing an energy balance. The multi-scale analysis of facture toughness of the ferroelectric ceramics at high temperature is carried out. Through the analysis, the CAEFIF for crack extension is recalculated. The results show that the competition and interaction effects between dislocation emission and brittle fracture are very obvious. Besides, the higher critical activation temperature, the more columns of obstacles will be overcome. Additionally, the shielding effect arising from thermally activated dislocations is remarkable, thus, the brittle-ductile transition can promote the fracture toughness of high-temperature ferroelectric ceramics.

DIELECTRIC RESPONSE AND IMPEDANCE SPECTROSCOPY OF(Na_(0.5)Bi_(0.5))_(0.95)Ba0:05Zr_(0.04)Ti_(0.96)O_(3)FERROELECTRIC CERAMIC

A new lead-free ferroelectric relaxor ceramic was prepared by conventional solid-state synthesis by modifying A-site and B-site in(Na_(0.5)Bi_(0.5))TiO_(3)system,i.e.,(Na_(0.5)Bi_(0.5))_(0.95)Ba_(0.05)Zr_(0.04)Ti_(0.96)O_(3)(0.05BNBZT).X-ray diiffraction studies reveal a single phase rhombohedral structure.Crystallite size and strain analysis has been done by Debye-Scherrer and Williamson-Hall technique.The tolerance factor is 0.81,indicating a stable Perovskite structure of the material.Scanning electron micrograph of the material shows a distribution of grains,average grain size is 1.41μm.Dielectric response of(Na_(0.5)Bi_(0.5))_(0.95)Ba_(0.05)Zr_(0.04)Ti_(0.96)O_(3),ferroelectric ceramic has been studied as a function of frequency over a wide range of temperatures.The studied ceramic exhibited maximum frequency dispersion in both real and imaginary part of dielectric susceptibility at and around the dielectric transition temperature(T_(m)).The frequency dependence of transition temperature,T_(m)(temperature of the maximum of dielectric constant)was studied in terms of Vogel-Fulcher relation.The dielectric relaxation of(Na_(0.5)Bi_(0.5))_(0.95)Ba_(0.05)Zr_(0.04)Ti_(0.96)O_(3)ceramic was studied at different temperatures using the complex impedance(Z*)and electrical modulus(M*)formalism.Impedance measurements were made on over a wide range of temperatures(300-600℃)and frequencies(45 Hz-5 MHz)which show the presence of both grain and grain boundary effects in the material.The Impedance spectroscopy is shown to be an effcient method capable of detecting the contributions of the resistances of grain boundaries(at higher temperature),in addition to granular contribution(at all temperatures),which influences the device properties of a material.The electric modulus(M*)formalism used in the analysis enabled us to distinguish and separate the relaxation processes.Conductivity studies in the material obey the Jonscher's power law in frequency(45 Hz-5 MHz)and temperature(30-600℃).These results give evidence that the lead-free ferroelectric ceramics is extensively may be used for device and electronic applications,when compared with lead-based materials.

Ultralow frequency dielectric dispersion in PZT+PFS ferroelectric ceramic

The depolarization decaying currents were measured for the PZT compound with morphotropic composition modified by the Fe 1=3 Sb 2=3 cations,i.e.,Pb[Fe_(1/3)Sb_(2/3)_(x)Ti_(y)Zr_(z)]o_(3) with x+y+z=1,x=0.1,y=0.44(morphotropic boundary)and y=0.47.The measurements were performed at room temperature and a few temperatures above(up to 473K),as well as at a few lower temperatures(down to 77K).The samples were poling at fields 0.02kV/cm and 0.2kV/cm at higher and lower temperatures,respectively.In the high temperature range,the time dependence depolarization current follows the fractional power law with two different exponents(n<1 and m>1),while in the low temperature range with a single exponent(n).The appropriate procedure has been used to transform the results obtained in the time domain into the frequency domain in order to calculate real and imaginary parts of the dielectric permittivity in the frequency range 5×10^(-5)-0.1Hz.The possible dielectric relaxation mechanisms have been discussed.

Distinct microstructure and property evolution of 0.76(Bi_(0.5)Na_(0.5))TiO_(3)-0.24SrTiO_(3) ferroelectric ceramics synthesized with different TiO_(2) reactants

Single phase 0.76(Bi_(0.5)Na_(0.5))TiO_(3)–0.24SrTiO_(3) ferroelectric ceramics have been synthesized with homogenous anatase and hierarchical rutile TiO_(2) raw reactants(BNST-A and BNST-R).Either calcined powder persists the microstructure characteristics of raw reactants.As the result,when the sintering temperature increases from 1000 to 1200℃,the average grain size and density of BNST-A increase from 0.49 to 1.48μm and 5.02 to 5.61 g/cm^(3),while those of BNST-R from 0.86 to 1.44μm and 5.37 to 5.61 g/cm^(3).BNST-A illustrates a predominant ergodic relaxor state,and BNST-R prefers a non-ergodic relaxor state,as evidenced by the distinct polarization-electric field loops and current-electric field curves.Especially,such a distinct ferroelectric state is independent of sintering temperature.It is believed that the special hierarchical microstructure of rutile TiO_(2) reactant is beneficial to form denser ceramics with larger grains,and thus suppresses the contributions of polar nanoregions and defect-induced built-in field to ferroelectric property,leading to non-ergodic relaxor state.This work clearly demonstrates the nonnegligible effects of TiO_(2) reactants on the microstructure and properties of BNST ferroelectric ceramics.

Preparation and Photostriction Properties of BiFeO_(3)-BaTiO_(3)Ceramics

Under illumination by 405,520 and 655 nm monochromatic visible light(light intensity of 30 kW/m^(2)),large photostriction(ΔL/L)of 0.19%,0.13%and 0.26%for 67BiFeO_(3)-33BaTiO_(3)(67BF-33BT)lead-free ferroelectric ceramics are obtained,respectively.By studying the ferroelectric and photoelectric properties in conjunction with in situ Raman spectroscopy,it is found that the photostrictive effect of 67BF-33BT is not caused by the electrical strain induced by abnormal photovoltaic voltage,but related to the optical induced oxygen octahedral distortion.The 67BF-33BT lead-free ferroelectric material with excellent photostrictive response in the visible light region is expected to play an important role in the field of optical drive electromechanical devices.

In-situ Raman observation on crack tips of Vickers indent in PLZT ceramics

Vickers indentation was introduced into the originally in-plane and out-of-plane poled PLZT ceramics.The Raman spectra were in-situ recorded at selected crack tips before and after the indentations,as well as after the applications of external electric field.The results show that the changes in Raman intensities of optical modes could be sensitively related to 90° domain switching around the crack tips which are strongly dependent on the directions of original polarization and geometric locations.When the direction of electric field was perpendicular to the direction of original polarization,the 90° domain switching at crack tips of the Vickers indentation on the originally in-plane poled PLZT ceramics caused most significant change in the Raman intensity,which inhibited the crack growth.However,when the direction of electric field was parallel to the direction of original polarization,the growth of crack tips became predominantly without the 90° domain switching,which led to the crack growth.

Structure, ferroelectric and dielectric properties of Bi_2 WO_6 with different bismuth content

This paper reports that the Bi2WO6 ferroelectric ceramics with excess Bi2O3 of 0.0, 2.0, 3.5 and 5.0wt.% of the stoichiometric composition are prepared by the conventional solid-state reaction method. Their microstructure, ferroelectric properties, the concentration and mobility of the defects have been analysed systematically. With increasing Bi content, the remnant polarization decreases, and the broken-down voltage increases. The optimum Bi excess, 3.5, lowers the oxygen vacancy concentration, while further Bi-addition brings about more defects. The activation energies fitted from cole-cole plots are 0.97 eV, 1.07 eV, 1.18 eV, and 1.33 eV, respectively. This suggests that the mobility of the defects is weakened by Bi-addition, which may be due to the increase of the ratio of the number of Bi2O2 layers to that of the oerovskite blocks.

Dielectric and Pyroelectric Characteristics of the Infrared Sensitive (Pb_(1-x)Sr_x)TiO_3 Ceramics

PST ferroelectric ceramics were fabricated successfully by a two-step method, i e first, PbTiO3 and SrTiO3 were sintered respectively, then mixed and sintered together. The process and characteristics of PST ferroelectric ceramics were introduced and researched. Their dielectric and pyroelectric characteristics are as follows dielectric constant 10^4 order, low dielectric loss （lower than 3.0% in the working frequency range of 1-1 000 kHz）, saturation polarization intensity 10^-1 C/m^2 order, and pyroelectric coefficient 10^-3 C/m^2·K order.