Remanent Strain Research Articles

Time-dependent relaxation dynamics of remanent strain in textured PMN–PZ–PT and PMN–PIN–PT piezoceramics

Crystallographically textured lead-based piezoceramics, particularly Pb(Mg1/3Nb2/3)O3–PbZrO3–PbTiO3 (PMN–PZ–PT) and Pb(Mg1/3Nb2/3)O3–Pb(In1/2Nb1/2)O3–PbTiO3 (PMN–PIN–PT), play a pivotal role in electromechanical applications due to their enhanced field-induced strain responses. However, challenges in precision positioning arise from heightened remanent strain (Sr) caused by embedded templates in the textured grains, impacting strain cycle consistency due to increased time delay for Sr relaxation. This study investigates the time-dependent relaxation dynamics of Sr in textured PMN–PZ–PT and PMN–PIN–PT piezoceramics, focusing on experimentally determining relaxation time between cycles required for complete Sr relaxation. Our findings reveal that the relaxation time in textured piezoceramics is notably longer than that in their non-textured counterparts, primarily due to pinning of domain walls by embedded templates. This work provides insights into the strain relaxation characteristics of piezoceramics and underscores the importance of time delay in designing precision positioning systems for improved reliability.

Impact of transient liquid phase on the cold sintering of multiferroic BiFeO3

Cold sintering of perovskite materials is still, despite years of research, challenging. The key objective when cold-sintering oxide materials is finding an appropriate liquid phase that triggers pressure-dissolution process and mechano-chemical compaction and densification of ceramics. In this study, cold sintering of the multiferroic BiFeO3 perovskite is reported for the first time. When organic additives or solvents are used, these effectively sinter the compound, but cause precipitation of secondary phases that impede grain-to-grain contacts and the polarization coupling, and result in electrically conductive samples. We found that it is critical to carefully select the sintering additives based on their reactivity, decomposition temperature and products, while ensuring a significant level of wettability and matrix solubility. NaOH/KOH mixture was found to be the best sintering aid, resulting in remanent polarization and strain responses of cold-sintered BFO comparable to those reported for conventionally sintered ceramics.

Voltage modulated magnetic anisotropy of rare earth iron garnet thin films on a piezoelectric substrate

Voltage-tuning of magnetic anisotropy is demonstrated in ferrimagnetic insulating rare earth iron garnets on a piezoelectric substrate, (011)-oriented PMN-PT. A 42 nm thick yttrium-substituted dysprosium iron garnet (YDyIG) film is grown via pulsed laser deposition followed by a rapid thermal anneal to crystallize the garnet into ≈5 μm diameter grains. The annealed polycrystalline film is magnetically isotropic in the film plane with total anisotropy dominated by shape and magnetoelastic contributions. Application of an electric field perpendicular to the substrate breaks the in-plane easy axis along [01[Formula: see text]] and an intermediate axis along [100]. The results are explained in terms of the piezoelectric remanent strain caused by poling the substrate, which is transferred to the YDyIG and modulates the magnetoelastic anisotropy.

Tailoring hardness behaviors of BIT-based piezoceramics via doping and annealing strategies

Bismuth titanate (BIT) piezoelectric ceramics are perceived as a strong competitor in high temperature applications. Currently, a mass of work has been done to optimize the electrical performance of the ceramic utilizing different strategies. However, little attention has been paid to the mechanical behaviors of BIT ceramics, especially the research on mechanical hardness behaviors under doping and annealing, limiting the deep understanding for ceramics and its further development of practical applications. In this work, the mechanical hardness behaviors of a type of bismuth titanate-based ceramics [Bi3.96Ce0.04Ti3-xWxNbxO12 (BCTWN)] at different doping contents and selectively annealing temperatures were investigated using nanoindentation and Vickers indentation techniques. The results show that the hardness is strongly dependent doping contents, wherein the samples with smaller grain size and higher density exhibit bigger hardness. For the poled samples, a higher annealing temperature could restore more domain walls and induce more oxygen vacancies in the samples, along with higher elastic recovery and less remanent strain, shedding extra deformation resistance to make sample harder. Moreover, a schematic of defect assistant domain wall pinning mechanism is proposed to further rationalize the enhanced deformation resistance by annealing strategy. This work helps us deep understand the deformation mechanism of BIT ceramics beneath indentation, and provides insight into tailoring mechanical hardness behaviors via doping and annealing strategies.

Microstructure and mechanical properties evolution during thermomechanical processing of a Ti–Nb–Zr–Ta–Sn–Fe alloy

During the last decades, Titanium-based alloys have shown a suitable combination of strength, ductility, corrosion and biocompatibility properties, that marks them as suitable implant materials for biomedical applications. In this study, a Ti–30Nb–12Zr–5Ta–2Sn-1.25Fe (wt%) alloy was produced by melting in a cold crucible induction in levitation furnace, deformed by cold rolling, with a total deformation degree (thickness reduction) of 50%, in five equal steps, and solution treated at 850 °C, with progressive treatment durations, from 5min to 20min, in 5min increments. The initial microstructure is homogenous, consisting of equiaxed β-Ti phase grains showing an average grain size close to 135 μm. The applied cold deformation induces changes in the microstructure, which shows the presence of deformation bands, twins, dislocation bands and of an increased crystal defects density and residual strain–stress fields. Also, an increase in strength and decrease in ductility properties are noticed due to the strain hardening. The applied solution treatment leads to the regeneration of the microstructure, the obtained microstructure showing homogeneous equiaxed β-Ti phase grains, with an average grain size between 60 μm and 80 μm, depending on the solution treatment duration. Also, a decrease in strength and increase in ductility properties are noticed due to the lowering of the crystal defects density, remanent strain–stress fields and an increase of the average grain size.

Strain transfer in porous multiferroic composites of CoFe2O4 and PbZrxTi1−xO3

This manuscript examines the mechanism of strain-coupling in a multiferroic composite of mesoporous cobalt ferrite (CFO), conformally filled with lead zirconate titanate (PZT). We find that when the composites are electrically poled, remanent strain from the piezoelectric PZT layer can be transferred to the magnetostrictive CFO layer. X-ray diffraction shows that this strain transfer is greatest in the most porous samples, in agreement with magnetometry measurements, which show the greatest change in sample saturation magnetization in the most porous samples. Strain analysis shows that porosity both accommodates greater lattice strain and mitigates the effects of substrate clamping in thin film strain-coupled composites.

Local monoclinic polarization rotation promoting a different domain alignment in rhombohedral Pb(Zr,Ti)O3 ferroelectrics

Domain switching takes a substantial role in the macroscopic electrical properties of perovskite-type ferroelectric materials. However, the attainable domain alignment in polycrystalline states is often far away from the saturation due to the constraint of long-range crystallographic symmetry. Herein, we report a field-induced saturated polarization alignment, facilitated by local monoclinic polarization rotation in conventional rhombohedral $\mathrm{Pb}({\mathrm{Zr}}_{0.54}{\mathrm{Ti}}_{0.46}){\mathrm{O}}_{3}$ via advanced electrical basing in situ synchrotron x-ray diffraction and pair distribution function measurements. It is found that the polarization alignment can reach the upper limit of theoretically calculated value in rhombohedral ceramic during high electric-field poling, and such a state can be maintained upon removal of electric field. In situ pair distribution function analysis demonstrates the occurrence of monoclinic distortion at local length $(<10\phantom{\rule{0.16em}{0ex}}\AA{})$, where the electric-field driven polarization rotation emerges, and promoting the alignment of polarization variations. Concurrently, large local piezoelectric strain $(1000\phantom{\rule{0.16em}{0ex}}\mathrm{pm}/\mathrm{V})$ and intrinsic lattice piezoelectric response $(1400\phantom{\rule{0.16em}{0ex}}\mathrm{pm}/\mathrm{V})$ during poling are found to be generated, while large remanent strains are also observed. These results offer fresh insight into the role of local structure in domain switching behavior and have potential for the theoretical investigation of domain alignment in ferroelectrics.

Revealing intrinsic and extrinsic piezoelectric contributions in phase coexistence system of PbTiO3-BiScO3

PbTiO3-BiScO3 ceramics possess high piezoelectricity and high Curie temperature simultaneously, presenting a very promising candidate for high-temperature actuators and transducers. Figuring out the underlying piezoelectric mechanisms is of great importance for its application. Herein, we reveal the quantified intrinsic and extrinsic contributions to the high electrostrain of the morphotropic composition with phase coexistence by employing the advanced in situ electrical biasing high-energy synchrotron X-ray diffraction combined with the STRAP (strain, texture, and Rietveld analysis for piezoceramics from diffraction) methodology. An electric field-induced phase transformation is observed between the coexisting tetragonal and rhombohedral phases. It is found that the tetragonal phase contributes most of the domain switching strain, while the predominant lattice strain is from the rhombohedral phase. With phase fraction changes, the quantitative results demonstrate that the field-induced electrostrain is mainly contributed by the intrinsic lattice strain. In contrast, the high irreversible domain switching strain dominates the large remanent strain. It implies that transforming the large remanent strain into reversible strain would be a strategic direction to improve the piezoelectric response. The present results provide a further understanding of the high piezoelectricity and could help to advance the application of PbTiO3-BiScO3.

A new class of ion substitution to achieve high electrostrain under low electric field in BNT‐based ceramics

AbstractFor Bi0.5Na0.5TiO3 (BNT)‐based materials, the effective way of composition modification to solve the drawback of considerable remanent strain (Srem) and achieve high electrostrain appeals intensive research interest, which often accompanies by a high electric field threshold to trigger the transition from ergodic relaxor (ER) state to ferroelectric (FE) state. Here, a unipolar electrostrain of 0.40% with the high normalized strain d33*(=Smax/Emax) of 793 pm/V under a low electric field of 5 kV/mm is firstly reported in rare‐earth Ce‐modified 0.935Bi0.5Na0.5TiO3–0.065BaTiO3 ceramics. Through the A‐ and B‐sites substitution with donor characteristic of multivalent Ce ion, two modification effects (i.e., compositional disorder and A‐site vacancy) are induced to weaken the A–O bonds and break the long‐range order. Microscopically, the proportion among three coexisted space groups (R3c, P4mm, and P4bm) changes in an opposite law when Ce concentration or poling electric field is served as variable, respectively. The domain size degrades after doping, but there still coexist small‐sized polar regions and labyrinth‐type domains in the optimal compound, wherein better reversibility is proved compared with undoped specimen from writing domain mode. As a result, the good reversibility and low electric field threshold (i.e., low‐energy barrier) to integrate relaxor state into FE state are ascribed to the coexistence of three phases and the coexistence of small‐sized polar regions and labyrinth‐type domains. This work not only enlarges the class of ion substitution other than the familiar substitution ions to achieve high electrostrain but also supplies a simple and propagable way to improve the relatively high electric field threshold through understanding the intrinsic mechanism of Ce ion.

Direct Observations of Changes in Ferroelectric Domain Configurations Around the Indentation and Ahead of the Crack Front

The indentation response of polycrystalline lead zirconate titanate (PZT) with varying ferroelastic domain configurations is investigated using nano and micro indentation. In the fully depoled state (with completely random domain configurations), PZT exhibit higher hardness, H as compared to poled PZT. Severe cracking is observed at the imprint corners at high indentation loads and the ferro-elastic domain configurations are visualized in the vicinity and ahead of the crack using piezoresponse force microscopy. The domains remain fully plastic in the regions from where the crack has propagated and just ahead of the crack while farther from the crack their remain elastic. The results are rationalized using remanent strain, e r results highlight the toughening mechanisms in the as poled PZTs. and converse piezocharge coefficient, d *33 measured around microcrack. The results highlight the toughening mechanisms in the as poled PZTs.

Stress- and frequency-dependent properties of relaxor-like sodium bismuth titanate

Despite the importance of $({\mathrm{Na}}_{1/2}{\mathrm{Bi}}_{1/2})\mathrm{Ti}{\mathrm{O}}_{3}$ as an end member in lead-free ferroelectrics and as an oxide ion conductor, the relaxor/ferroelectric nature remains unclear. In order to understand the relaxor-like behavior, frequency-dependent macroscopic mechanical measurements of polycrystalline $({\mathrm{Na}}_{1/2}{\mathrm{Bi}}_{1/2})\mathrm{Ti}{\mathrm{O}}_{3}$ were performed as a function of poling state, revealing the role of a potential field-induced long-range ferroelectric order on the nonlinear hysteretic stress-strain behavior. The mechanical measurements showed an increase in remanent strain and decrease in coercive stress with electrical poling, consistent with previous studies of relaxors. Electrical poling and mechanical texturing were found to influence the frequency dispersion of the relative permittivity, highlighting the potentially relaxor-like response. Further, the relative permittivity showed a directional dependence with respect to the previously applied electrical and mechanical fields. These data are discussed in conjunction with ex situ stress- and electric-field-dependent piezoresponse force microscopy measurements that revealed a clear ferroelectric domain switching through the application of a sufficiently high electric field, but no change of the domain configuration for uniaxial compressive stresses up to \ensuremath{-}750 MPa. The in situ stress-dependent crystal structure, which was characterized using synchrotron x-ray diffraction, however, indicates stress-induced ferroelastic domain switching as the primary hysteretic process.

Quenching‐circumvented ergodicity in relaxor Na1/2Bi1/2TiO3‐BaTiO3‐K0.5Na0.5NbO3

AbstractQuenching alkaline bismuth titanates from sintering temperatures results in increased lattice distortion and consequently higher depolarization temperature. This work investigates the influence of quenching on the ergodicity of relaxor Na1/2Bi1/2TiO3‐BaTiO3‐K0.5Na0.5NbO3. A distinct departure from ergodicity is evidenced from the increase in remanent polarization and the absence of frequency dispersion in the permittivity response of poled samples. Further, the samples exhibit enhanced negative strain upon application of electric field, indicating proclivity towards correlated polar nanoregions, corroborated by the enhanced tetragonal distortion. As a result, ergodic relaxor Na1/2Bi1/2TiO3‐6BaTiO3‐3K0.5Na0.5NbO3 exhibits a depolarization temperature of 85°C with a 60% increase in remanent polarization and approximately a threefold increase in remanent strain upon quenching. Quenching‐induced changes in the local environment of Na+ and Bi3+ cations hinder the development of ergodicity promoted by the A‐site disorder. These results provide new insight into tailoring ergodicity of relaxor ferroelectrics.

Fabrication of (Bi0.5K0.5)TiO3 modified BaTiO3-Bi(Mg0.5Ti0.5)O3-BiFeO3 piezoelectric ceramics

The lead-free x(Bi0.5K0.5)TiO3-0.23BaTiO3-0.02Bi(Mg0.5Ti0.5)O3-(0.75-x)BiFeO3 piezoelectric ceramics (x = 0.05, 0.07, 0.09, and 0.11) were prepared by solid-state reaction method. The increase of (Bi0.5K0.5)TiO3 concentration revealed a decrease of dielectric maximum temperature (Tm), however, the values were higher than 420 °C. The Rietveld structure refinement for each composition showed pseudo-cubic symmetry and the rhombohedral distortion (90 - αF) was gradually decreased from 0.27° to 0.09° for x = 0.05 and 0.11, respectively. The saturation and remanent polarization were increased and a coercive field was decreased, while the critical exponent (γ) was increased from 1.407 (x = 0.07) to 1.821 (x = 0.11) revealing more relaxor-like behavior with higher (Bi0.5K0.5)TiO3 content. The remanent polarization, coercive field, and piezoelectric strain constant of 31.9 μC/cm2, 23.6 kV/cm, and 315 pm/V, respectively, obtained in the composition with x = 0.11 are significantly higher than those reported previously for other Bi-based piezoelectric ceramics with Tm>250 °C.

Fracture behavior in electrically poled alkaline bismuth- and potassium- based lead-free piezoceramics using Vickers indentation

The fracture behavior of unpoled and electrically poled Ka0.5Na0.5NbO3 (KNN)- and Na1/2Bi1/2TiO3 (NBT)- based lead-free piezoceramics were characterized using the Vicker's indentation technique and compared with soft Pb(Zr,Ti)O3 piezoceramics. In the unpoled state, NBT-based piezoceramics demonstrate the largest fracture toughness in comparison with KNN-based and soft PZT piezoceramics due to its large intrinsic fracture toughness, which is in accordance with the previous reports. In the electrically poled state, KNN- and NBT- based piezoceramics exhibit large fracture toughness along the poling direction as opposed to perpendicular to the poling direction, with aspect ratios of 1.2 and 1.1, significantly smaller than that for PZT (1.8). The variations of the remanent strain and the process zone, which are related to the texture and the material properties during crack propagation were used to rationalize the results.

The polarization process of ferroelectric materials in the framework of variational inequalities

AbstractWe are concerned with the mathematical modeling of the polarization process in ferroelectric media. We assume that this dissipative process is governed by two constitutive functions, which are the free energy function and the dissipation function. The dissipation function, which is closely connected to the dissipated energy, is usually non‐differentiable. Thus, a minimization condition for the overall energy includes the subdifferential of the dissipation function. This condition can also be formulated by way of a variational inequality in the unknown fields strain, dielectric displacement, remanent polarization and remanent strain. We analyze the mathematical well‐posedness of this problem. We provide an existence and uniqueness result for the time‐discrete update equation. Under stronger assumptions, we can prove existence of a solution to the time‐dependent variational inequality. To solve the discretized variational inequality, we use mixed finite elements, where mechanical displacement and dielectric displacement are unknowns, as well as polarization (and, if included in the model, remanent strain). It is then possible to satisfy Gauss' law of zero free charges exactly. We propose to regularize the dissipation function and solve for all unknowns at once in a single Newton iteration. We present numerical examples gained in the open source software package Netgen/NGSolve.

Finite-element modeling of ferroelectric material behavior at morphotropic phase boundaries between tetragonal, rhombohedric and orthorhombic phases

The nonlinear response of ferroelectric/ferroelastic material below the Curie temperature is analyzed at morphotropic phase boundaries with account of tetragonal, rhombohedric and orthorombic phases. The results are obtained by means of finite-element homogenization with using the micromechanical model taking into account the dissipative nature of the domain wall motion. The results of simulation have revealed the extremal values of spontaneous polarization and remanent strain at morphotropic phase boundaries for the tetragonal/rhombohedral and tetragonal/orthorhombic compositions.

Mechanical versus electromechanical hardening in relaxor ferroelectric Na1/2Bi1/2TiO3-BaTiO3 with ZnO inclusions

The stress-strain response of composites constituting relaxor 0.94Na1/2Bi1/2TiO3–0.06BaTiO3 matrix phase with ZnO inclusions is investigated. The ZnO inclusions are found to increase the transformation stress (unpoled) for the relaxor-ferroelectric transformation and the coercive stress (poled) for domain switching. The plastic and remanent strain decreases with increasing volume fraction of the hard ZnO inclusions. This mechanical hardening mechanism is contrasted quantitatively to electromechanical hardening by comparing the transformation stress and coercive stress to the poling field and coercive field respectively, as well as the corresponding plastic strain from mechanical loading to the total strain quantified by electric field loading.

Influence of the annealing conditions on temperature-dependent ferroelastic behavior of LSCF

The macroscopic ferroelastic behavior of polycrystalline (La0.6Sr0.4)0.95Co0.2Fe0.8O3−δ and its dependence on annealing conditions was investigated over a temperature range from −150 °C to 150 °C. A temperature- and defect concentration-dependent variation of the ferroelastic behavior was attributed to internal stresses, oxygen deficiency, and a corresponding change of the crystal structure. In particular, there was an observed decrease in remanent strain and the formation of a closed ferroelastic hysteresis loop at temperatures below approximately 0 °C for samples annealed in air, which was suppressed through the reduction in oxygen vacancies by annealing the samples in oxygen. The macroscopic mechanical behavior as a function of annealing conditions is discussed with respect to the crystal structure and oxygen deficiency determined by means of x-ray and neutron diffraction.

Mechanically induced ferroelectric domain evolution during crack propagation

Ferroelectric switching near the crack tip in lead zirconate titanate ceramics leads to a change of both polarization and remanent strain, which affects substantially the stress field and fracture behavior. In particular, for tetragonal crystals the 90° domain reorientation is believed to enhance fracture toughness of the damaged piezoelectric ceramics. Current research models evolution of the domain reorientation processes during crack propagation by a micromechanical model using finite element analysis. The crack growth is numerically simulated by means of electromechanical cohesive elements along the prospective crack path. The study of these irreversible dissipative mechanisms makes the main subject of our numerical investigations. The computed 3D scattering of domain orientations in a mechanically loaded PZT-PIC151 CT-specimen is compared with in situ x-ray diffraction experiments in synchrotron (Jones et al 2007 Acta Mater. 55, 5538–5548). It is found that the preferred orientation and intensity of domain distribution in the mechanically loaded specimen depend on the in-plane position and are related to the projected deviatoric stresses/strains. In contrast to simulations with a fixed crack tip (Kozinov and Kuna 2018 Arch. Appl. Mech.), during crack propagation the maximal tensile stresses and region of highest intensity of domain reorientation are moved with the crack tip and smeared over a process zone. While the crack length increases, the domain switching belt causes a shielding effect leading to an apparent materials toughening. Such fully coupled, three-dimensional simulation of crack growth resistance curves is the first one in ferroelectrics.

Phase‐Field Study of Electromechanical Coupling in Lead‐Free Relaxor/Ferroelectric‐Layered Composites

The interface coupling effect of multilayer lead‐free ceramic/ceramic relaxor/ferroelectric composites is studied by finite element–based phase‐field simulations. The macroscopic electromechanical behavior of such composite systems is influenced by both polarization and strain coupling through the electrical and mechanical interaction of connected layers. Separating such interconnected phenomena is difficult experimentally. Here, we direct investigate different coupling effect by introducing soft and charge interphase layers in the serial‐type layer composite model. The large strain response of the composite results from the electric field–induced nonpolar–polar phase transition of the relaxor constituent. A new relaxor phase‐field model is first developed to reproduce this phase transition and parameterized by fitting the measured hysteresis loops. It is then directly compared to the experimental results of the serial‐type composite composed of 0.91Bi1/2Na1/2TiO3–0.06BaTiO3–0.03AgNbO3 and 0.93Bi1/2Na1/2TiO3–0.07BaTiO3. Results show that the lateral strain coupling in the serial layer contributes considerably to the large signal piezoelectric coefficient . The primary enhancement in is due a reduction in the remanent strain of the ferroelectric layer caused by the lateral mismatch. Moreover, charge interphase layers in the composite can introduce an internal electric field, leading to a weaker large‐signal response compared with the composite with coherent interfaces.