Effect Of Domain Switching Research Articles

A phase-field model for study of ferroelastic deformation behavior in yttria stabilized zirconia

A modified phase-field model coupled with linear elasticity is formulated to study the effect of ferroelastic domain switching on the deformation behavior of tetragonal-prime yttria-stabilized zirconia. Simulations are performed under uniaxial tension and compression using realistic domain microstructures. This work provides new insights into the mechanism of ferroelastic deformation by studying the evolution of domains under different loading directions and strain rates. The model predicts realistic stress-strain curves consisting of stress-plateaus with accurate domain switching behavior without setting a switching criterion based on a critical stress for nucleation of new domains. The results reveal that the origin of coercive stress lies in the balance between the energy absorbed by the domain switching process and the externally applied energy. Loading in different directions but parallel to the spontaneous strain results in different levels of coercive stress as domain switching absorbs different amounts of energy. For the same reason when the strain-rate increases, the coercive stress also increases. This work establishes the relation between the coercive stress and microstructural changes during ferroelastic domain switching.

Regulation of domain wall motion in PZT-based ceramics through the introduction of local stress fields

At present, a big challenge exists yet in the piezoelectric ceramic material that high piezoelectric performance and low losses (large Qm and low tanδ) are difficult to achieve concurrently due to the effects of domain switching and domain wall motion on electromechanical properties. In this work, by introducing secondary-phase particles (SnO2 particles) into the hard PZT matrix, we successfully build local stress fields in the ceramic. These local stress fields not only pin the domain and domain wall but also diminish the domain size and increase the domain wall density. The former is in favor of reducing the losses, while the latter is beneficial to promoting the piezoelectric properties. Thus, the optimized piezoelectric properties and losses in the ceramic can be obtained simultaneously. The results show that in the PZT/0.3 wt%SnO2 composite, the mechanical quality factor reaches 2800 and the dielectric loss is only 0.4 %, which are superior to the hard PZT matrix. Meanwhile, the composite ceramic has a high piezoelectric constant of 390 pC/N. These excellent properties will push the development of next-generation high-power electromechanical devices.

Large tunability properties of (Ba0.91Ca0.09)(Zr0.2Ti0.8)O3-x mol% CuO ceramics under bias of domain switching effect

Large tunability properties of (Ba0.91Ca0.09)(Zr0.2Ti0.8)O3-x mol% CuO ceramics under bias of domain switching effect

Deciphering the peculiar hysteresis loops of 0.05Pb(Mn1/3Sb2/3)O3–0.95Pb(Zr0.52Ti0.48)O3 piezoelectric ceramics

The majority of piezoelectric ceramics based on Pb(Zr, Ti)O3 (PZT) exhibit hysteretic behavior, which varies depending on various factors, including composition, microstructure and processing conditions. The ternary system 0.05Pb(Mn1/3Sb2/3)O3–0.95Pb(Zr0.52Ti0.48)O3 (5PMS-PZT) has shown attractive piezoelectric properties with superior thermal stability compared to pure Pb(Zr0.52Ti0.48)O3, but the underlying mechanisms of its complex hysteretic behavior have not been fully clarified yet. This work further delves into the hysteretic aspects of 5PMS-PZT ceramics and describes hysteresis features that have not been yet reported for any known piezoelectric system. Four current peaks in I-E loops and S-E loops with unconventional shapes, which have a significant dependence on applied field amplitude, frequency and electrical history have been observed here. This peculiar hysteretic behavior is influenced by convoluted effects of domain switching, electric field-induced structural transitions, point defects and aging/de-aging processes, whose combinations lead to unique hysteresis features.

The effect of domain switching on the lattice symmetry and dielectric properties of (Bi0.5Na0.3K0.2)TiO3–0.2SrTiO3-(Ba0.8Ca0.2)TiO3 piezo-ceramic by poling field

The present study illustrates the effect of domain switching on the structural, dielectric, and piezoelectric properties of [0.75(Bi0.5Na0.3K0.2)Ti O3-0.2SrTi O3-0.05(Ba0.8Ca0.2)Ti O3] (i.e., BNKT- ST-BCT) Pb-free ceramic caused by poling effect. The sample has been synthesized by the solid reaction technique. The poling conditions were changed from (10–50 kV/cm) for 30 min at 100 °C. The pristine ceramic sample showed pseudo-cubic crystal structure, while tetragonal structure was detected for all the poled samples. The pristine sample showed a normal ferroelectric loop with a low coercive field (Ec =12 kV/cm) owing to the domain grow caused by domain wall displacement. The effect of poling field into Raman spectra showed variation the volume fraction of orthorhombic and tetragonal phases. Increasing the intensity of the tetragonal phase is related to the increase in lattice symmetry of the poled samples at a high poling field. Relaxor to paraelectric phase transition was observed at Burn's temperature (TB) of the un-poled sample, while the poled rates undergo a ferroelectric to relaxor phase transition at depolarization temperature (Td). In the regime of the sub-switching domain, the maximum permittivity was found to increase by poling field due to Rayleigh effect, while at high poling field it was observed to decrease due to tunability effect. The maximum current peak of relaxor to ferroelectric phase transition was observed to mitigate by increasing the poling effect. The converse piezoelectric coefficient, (d33∗) was achieved to be higher in the un-poled sample due to the lowest crystal symmetry in the absence of a poling effect. The existence of poling process leads to shrink both current peak and (d33∗) values, indicating the dominated of the tetragonal phase rather than the orthorhombic phase. Such results offer distinct features of an un-poled ceramic sample that make it suitable for different technological applications such as energy storage devices, sensors, and actuators.

Bayesian 14C-rationality, Heisenberg Uncertainty, and Fourier Transform

Following some 30 years of radiocarbon research during which the mathematical principles of 14C-calibration have been on loan to Bayesian statistics, here they are returned to quantum physics. The return is based on recognition that 14C-calibration can be described as a Fourier transform. Following its introduction as such, there is need to reconceptualize the probabilistic 14C-analysis. The main change will be to replace the traditional (one-dimensional) concept of 14C-dating probability by a two-dimensional probability. This is entirely analogous to the definition of probability in quantum physics, where the squared amplitude of a wave function defined in Hilbert space provides a measurable probability of finding the corresponding particle at a certain point in time/space, the so-called Born rule. When adapted to the characteristics of 14C-calibration, as it turns out, the Fourier transform immediately accounts for practically all known so-called quantization properties of archaeological 14C-ages, such as clustering, age-shifting, and amplitude-distortion. This also applies to the frequently observed chronological lock-in properties of larger data sets, when analysed by Gaussian wiggle matching (on the 14C-scale) just as by Bayesian sequencing (on the calendar time-scale). Such domain-switching effects are typical for a Fourier transform. They can now be understood, and taken into account, by the application of concepts and interpretations that are central to quantum physics (e.g. wave diffraction, wave-particle duality, Heisenberg uncertainty, and the correspondence principle). What may sound complicated, at first glance, simplifies the construction of 14C-based chronologies. The new Fourier-based 14C-analysis supports chronological studies on previously unachievable geographic (continental) and temporal (Glacial-Holocene) scales; for example, by temporal sequencing of hundreds of archaeological sites, simultaneously, with minimal need for development of archaeological prior hypotheses, other than those based on the geo-archaeological law of stratigraphic superposition. As demonstrated in a variety of archaeological case studies, just one number, defined as a gauge-probability on a scale 0–100%, can be used to replace a stacked set of subjective Bayesian priors.

Ferroelastic toughening of single crystalline yttria-stabilized t' zirconia: A phase field study

Yttria stabilized zirconia with the tetragonal prime phase (t'-YSZ) is most widely used in thermal barrier coatings. In this paper, a concise 2D phase field (PF) model is proposed to simulate domain switching in single crystalline t'-YSZ, where the energy barrier for domain switching is explicitly considered. The coercive stress for domain switching can be easily tuned by adjusting the energy barrier for domain switching. After that, a coupled PF model is developed by combing the new PF model for domain switching and the existing PF model for fracture. The coupled PF model can simulate the domain switching and crack propagation simultaneously without any ad-hoc criteria. The propagation of an edge crack in single crystalline t'-YSZ under different types of loadings are then studied with PF simulations. The influences of crystalline orientation and loading types on crack propagation and domain switching are systematically discussed. The distribution of the domain switching zone is validated by analyzing the stress field around the crack tip. When the c-axis of the initial t' phase is in parallel with or perpendicular to the crack surface, the crack propagates in mode I due to the symmetry of the model. In order to assess the ferroelastic toughening quantitatively, the energy release rate (ERR) along with the crack growth is calculated, where a stepwise displacement load is applied to the numerical model. At each load step, the crack can reach the equilibrium state, where the energy release rate equals the crack growth resistance. By computing the energy release rate at each load step, the ferroelastic toughening effect of domain switching is revealed and quantitatively characterized. It is shown that the domain switching of the t' phase can produce obvious toughening effect on crack propagation. Besides crystal orientation, loading types can also have distinct influences on domain switching and the toughening effect. For crystal orientations asymmetric to the crack surface, the crack may deflect due to the asymmetric distribution of the domain switching zone. The coupled PF model developed in this paper can act as an effective numerical tool to characterize the fracture behavior and ferroelastic toughening effect of single crystalline t' zirconia.

90° ferroelectric domain switching effect on interfacial strain mediated magnetoelectric coupling

The phenomena associated with strain-mediated multiferroic behavior have been quantitatively studied by combining synchrotron x-ray diffraction (XRD), ferromagnetic resonance (FMR) and macroscopic strain measurements (digital image correlation) in a magnetoelectric composite (Ni film on PZT substrate). The ferroelectric and piezoelectric strains have been studied by analyzing the evolution of x-ray patterns (peak intensities and shifts), while the magnetic response is studied by FMR (energy shift of the resonance), during in situ application of electrical voltage. Being given the intrinsic selective phase nature of XRD, the lattice strains have also been measured in the Ni film and have been found to be comparable to the macroscopic one (full transmission from the PZT substrate). The PZT strain has been successfully separated into two contributions, i.e. ferroelectric and lattice strains, the first one being five times higher than the second one. Moreover the last is itself composed of two sub-contributions: pure piezoelectric effect and ferroelectric strain in surrounding grains (strain transfer at grain boundaries). Finally, through in situ FMR measurements, we showed that the ferroelectric contribution to the strain-mediated magnetoelectric response is ten times higher than the pure piezoelectric one.

Effect of domain switching contribution on polarization current, leakage current and switching charge density studied by PUND method in (Ba1−x,Cax)TiO3 ceramics

The present study illustrates the effect of domain switching on polarization current and leakage current in (Ba1−xCax)TiO3 (0 ≤ x ≤ 0.4) lead-free ceramics prepared by sol-gel method. The influence of Ca2+ concentration on the structural, microstructure and dielectric properties of BaTiO3 (BT) was investigated. The study shows that domain switching has a significant effect on polarization current and switching leakage current behavior. Un-switching leakage current was observed to be lower than the switching leakage current in whole range of electric field due to restrict the space charges contribution in the absent of domain switching effect. The highest polarization current and lowest leakage current were achieved in the composition x = 0.2. Effect of frequency into polarization current has been introduced, where the current peak increased and shifted to higher electric field by increasing the applied frequency due to the high rate change of electric field corresponding domain switching rate. The difference between remnant polarization estimated by P-E loop and Positive Up Negative Down (PUND) methods has been highlighted. The results show that the remnant polarization appraised by PUND method is lower than the value estimated by P-E loop due to absence of the leakage current contribution.

Electrical fatigue failure in (Na1/2Bi1/2)TiO3–BaTiO3 relaxor ceramics

AbstractMany devices containing ferroelectric ceramics are subjected to different loading conditions and cycles, and lack of adequate long‐term reliability studies is a major concern. Here, we explore a (Na1/2Bi1/2)TiO3–BaTiO3 solid solution and study electrical fatigue as a function of amplitude, temperature, frequency, and static offset voltage (dc bias). This is expected to act as a guide for other similar material systems. Empirical relationships to quantify the dependence of fatigue on these parameters are presented. With electric field amplitude (Emax), the number of cycles to fatigue failure (Nfail) varies as: Emax × = C, where a and C are constants whose values are different when the field amplitude is below and above the coercive field. With changes in temperature, Nfail exhibits an activated behavior and follows an Arrhenius relationship with an activation energy of 0.7 eV at an amplitude above the coercive field. In the absence of self‐heating, a power law relationship is observed between Nfail and frequency of fatigue cycles at an amplitude above the coercive field. On applying a dc bias, Nfail increases by an order of magnitude, an observation that is attributed to domain switching effects. A majority of the above‐mentioned effects have been explained in terms of the motion of domain walls under a given fatigue condition and their interaction with point defects.

In-situ XRD study of actuation mechanisms in BiFeO3-K0.5Bi0.5TiO3-PbTiO3 ceramics

In the present study, we report a nonergodic relaxor ferroelectric composition for high temperature piezoelectric applications, 0.57BiFeO3-0.21K0.5Bi0.5TiO3-0.22PbTiO3, which exhibits Tm around 420 °C. By combining the results of in-situ synchrotron XRD and strain measurements using digital image correlation, a pseudocubic nonergodic relaxor to rhombohedral ferroelectric transformation is identified, accompanied by a volume strain close to zero. A methodology is developed to determine the crystallographic parameters of the transformed rhombohedral ferroelectric phase in a strain-free state, using the invariant intersection for diffraction stress analysis. The phase transformation process was analyzed by methods combining peak profile fitting and full pattern refinement; the results obtained illustrate the strain arising from the phase transformation, together with intrinsic/extrinsic contributions and anisotropy in the field-induced strain. The study reveals unusual microscopic strain behavior, distinguished from that of normal rhombohedral ferroelectrics, showing the combined properties of ergodic and normal ferroelectric materials and leading to a dominant intrinsic lattice strain together with a weaker extrinsic domain switching effect. The elastic coupling between different grain families is also reflected in their similar strain orientation distribution (SOD) functions.

Effect of large-scale domain switching on intensity factors for a crack in 3D ferroelectric single crystals using the I-integral method

Due to their intrinsic brittleness, ferroelectric materials are prone to fracture under extreme electromechanical operational loads. The fracture of ferroelectric materials is usually accompanied by large-scale domain switching. This paper develops the interaction integral (I-integral) method for a crack in three-dimensional ferroelectrics through applying a virtual load increment to the current state. Unlike the widely-used switching-toughening model, the I-integral is not restricted to small scale switching. Due to designable choice of the virtual load increment, the I-integral allows to decouple the intensity factors of different fracture modes. The local intensity factors along the curved crack front can be directly extracted, since the I-integral is independent of integration volume. With these merits, the I-integral method is a very promising technique in fracture analysis of ferroelectrics under large-scale domain switching. Moreover, the I-integral method is used in combination with the phase field model to simulate a tensile test of nanoscale PbTiO3 ferroelectric single crystal with a semi-circular surface crack. Results show that various patterns of polarization pairs appear as soon as the applied load is increased beyond a critical value. The stable domain structures are divided into two layers by the plane where the crack is located and in each layers several polarization vortices formed eventually. Apart from the geometry and loading conditions, the position where the crack front is located with respect to the polarization vortex is a key factor affecting the switching-induced change of the stress intensity factor.

Mechanical switching of ferroelectric domains beyond flexoelectricity

The resurgence of interest in flexoelectricity has prompted discussions on the feasibility of switching ferroelectric domains ‘non-electrically’. In this work, we perform three-dimensional thermodynamic simulations in combination with ab initio calculations and effective Hamiltonian simulations to demonstrate the great effects of surface screening and surface bonding on ferroelectric domain switching triggered by local tip loading. A three-dimensional simulation scheme has been developed to capture the tip-induced domain switching behavior in ferroelectric thin films by adequately taking into account the surface screening effect and surface bonding effect of the ferroelectric film, as well as the finite elastic stiffness of the substrate and the electrode layers. The major findings are as follows. (i) Compared with flexoelectricity, surface effects can be overwhelming and lead to much more efficient mechanical switching caused by tip loading. (ii) The surface-assisted mechanical switching can be bi-directional without the necessity of reversing strain gradients. (iii) A mode transition from local to propagating domain switching occurs when the screening below a critical value. A ripple effect of domain switching appears with the formation of concentric loop domains. (iv) The ripple effect can lead to ‘domain interference’ and a deterministic writing of confined loop domain patterns by local excitations. Our study reveals the hidden switching mechanisms of ferroelectric domains and the possible roles of surface in mechanical switching. The ripple effect of domain switching, which is believed to be general in dipole systems, broadens our current knowledge of domain engineering.

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 difficult 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).

A mode III interfacial crack under nonuniform ferro-elastic domain switching

This paper deals with a mode III interfacial crack while considering the effect of domain switching. The analysis will focus on the variation of stress intensity factor caused by domain switching. Due to the mismatch of material properties, an asymmetric nonuniform domain switching zone around the interfacial crack is achieved under the nonuniform domain switching criterion. Employing the weight function method, we obtain analytic forms of mono-domain and multi-domain toughening effects about stationary and quasi-static steady-state growing cracks, respectively. Three coupling parameters are proposed to evaluate the influences of elastic and ferroelectric bimaterial properties. In conclusion, domain switching of mode III quasi-static steady-state growing interfacial crack can toughen the material. The research will give us ideas on material and initial poling orientation selection to maximize the ferro-elastic toughening effect.

Actuation characterization of the lightweight unimorph piezo-composite actuator for different loading cases

In this study, we focused on the actuation behavior of the lightweight piezo-composite unimorph actuator (LIPCA). Common loading configurations found in real applications of LIPCA have been studied including the center loading and tip loading cases. The domain switching effect that has strong influence on the performance of LIPCA was recorded. While a longitudinally compressed stress state within the PZT (lead zirconate titanate, Pb[Zr(x)Ti(1–x)]O3) layer in LIPCA is preferable to avoid failure during operation, experimental results showed that, for the transverse loading cases, the actuator should be arranged in a manner such that the stress state within the PZT is in as much tension as possible to encourage the non-180° domain switching. With investigated loading cases in this paper, suitable arrangements could help improve the actuation performance. The improvement can be up to almost 33% in simply-supported with center loading and 140% in clamped tip loading case.

Electrical conductivity of La0.58Sr0.4Co0.2Fe0.8O3 − δ during ferroelastic deformation under uniaxial compressive loading

In the present study, electrical conductivity of lanthanum strontium cobalt ferrite oxide and its relationship to ferroelastic deformation were examined under uniaxial compressive loading at elevated temperatures up to 1073K. The conductivity increases with increasing compressive stress at all temperatures. The increase in conductivity can be related to both geometrical and piezoelectric effects. From 293K to 873K, where the material exhibits ferroelastic behaviour, the variation in the total conductivity decreases with increasing temperature. The contribution of the piezoelectric effect to the total conductivity variation also decreases with increasing temperature and the maximum in piezoconductivity has a value of about 0.75% at 293K for a compressive stress of 100MPa. There is no effect of ferroelastic domain switching on the conductivity except for the geometric effect. At 1073K, where the ferroelastic characteristic almost disappears and the high-temperature creep behaviour appears, the conductivity is simply proportional to the compressive strain. The present results also indicate a possibility to use this material as strain sensor at elevated temperatures.

The effects of polarization dynamics and domain switching energies on field induced phase transformations of perovskite ferroelectrics

A time-dependent phase field model was utilized to investigate the electric field induced tetragonal-to-orthorhombic (T→O) planar phase transformations of perovskite materials, indicated by the simulated semi-discontinuous polarization-electric field hysteresis. Simulations show that transformations are sensitive to the crystallographic orientation of the applied electric field, the energy threshold for 90° domain switching and the rotation path between tetragonal variants. This indicates that the field induced phase transformation behavior has a significant influence on the evaluation and validation of the Landau coefficients.

A COD fracture model of ferroelectric ceramics with applications in electric field induced fatigue crack growth

In this paper, Crack Opening Displacement (COD) is introduced to study the fracture and fatigue of ferroelectrics. A fundamental solution for the COD of ferroelectrics is derived considering both the piezoelectric effect and ferroelectric effect. Bases on this solution, a nonlinear COD fracture model of ferroelectrics, which takes into account the effect of domain switching, is developed and accords well with the experimental results. Furthermore, fatigue crack growth in ferroelectrics is analytically investigated using this COD model. Comparison between the experimental results and the predicted electric-field-induced fatigue crack growth shows the applicability of the proposed COD model.

A ferroelectric and ferroelastic 3D hexahedral curvilinear finite element

An isoparametric 3D electromechanical hexahedral finite element integrating a 3D phenomenological ferroelectric and ferroelastic constitutive law for domain switching effects is proposed. The model presents two internal variables which are the ferroelectric polarization (related to the electric field) and the ferroelastic strain (related to the mechanical stress). An implicit integration technique of the constitutive equations based on the return-mapping algorithm is developed. The mechanical strain tensor and the electric field vector are expressed in a curvilinear coordinate system in order to handle the transverse isotropy behavior of ferroelectric ceramics. The hexahedral finite element is implemented into the commercial finite element code Abaqus® via the subroutine user element. Some linear (piezoelectric) and non linear (ferroelectric and ferroelastic) benchmarks are considered as validation tests.