Flexoelectric Effect Research Articles

Enhanced flexoelectricity of liquid with hydrated ions

Flexoelectricity, denoted as an electromechanical coupling effect from strain gradient introduced polarization, is prevalent in dielectric materials. However, its application in low-viscosity liquids has been limited by the scale of the flexoelectric coefficient. This study explores the flexoelectric coefficient of various hydrated ion solutions through a series of experiments. Additionally, the interplay between ion adsorption and the flexoelectric effect is investigated by using interfacial voltage detection. By introducing hydrated structures into liquids, a significant enlargement of the flexoelectric coefficient up to 2.3 × 10−9 C m−1 is obtained in Fe2(SO4)3 solution by four times than DI water. These findings highlight the remarkable electromechanical properties of liquid materials with hydrated ions and suggest promising avenues for the application of liquid dielectrics in hydrovoltaic technology, ionotronic devices, and energy harvesters.

Exploring the Possibility of Thermally Assisted Creation and Annihilation of Anti‐Frenkel Defects in a Multiferroic Oxide for Tuning Interfacial Ferroelectricity

AbstractLattice defects such as oxygen vacancies, interstitials, and their complexes are present in crystalline oxide materials. In particular, anti‐Frenkel defects, which refer to charge‐neutral anion vacancy‐interstitial pairs, are strongly coupled with ferroelectric and dielectric properties as electric dipoles. However, in order to observe their macroscopic manifestation, delicate defect controls are required to the extent that electronic and ionic charges are almost completely suppressed. Here, the thermal cycle dependence of dielectric and piezoelectric properties is scrutinized in the strain‐driven morphotropic phase boundaries of multiferroic La‐substituted BiFeO3 thin films. Electrochemical impedance spectroscopy provides the Warburg feature that is considered evidence of the ionic origin. The observations are discussed based on anti‐Frenkel defects that are created or annihilated reversibly by thermal cycles through high‐temperature structural phase transition temperature or magnetic Néel temperature. The defect dipoles are spontaneously aligned by the flexoelectric effect in the phase boundaries inducing a metastable interfacial ferroelectric phase. The findings offer useful insight into defect dipoles.

Flexoelectric and surface effects on bending deformation and vibration of piezoelectric nanolaminates: Analytical solutions

In this paper, a model of double-layer rectangular piezoelectric nanolaminates with different upper and lower surface properties is established. The bending and vibration behavior of the piezoelectric nanolaminates are evaluated and analyzed, taking into consideration the flexoelectric and surface effects. Utilizing the surface piezoelectric model, flexoelectric theory, and Kirchhoff plate theory, this study provides analytical solutions for the bending deflection and natural frequency of rectangular piezoelectric nanolamination materials under various boundary conditions. The results indicate that the effects of flexoelectric and surface influences on piezoelectric nanolaminates are associated with residual surface stress and flexoelectric coefficients. These effects can enhance the bending stiffness and decrease the natural frequency of the piezoelectric nanolaminates. Furthermore, altering the residual stress on the upper and lower surfaces of the laminates separately will result in different trends in bending deflection, while causing a consistent trend in natural frequency change. When the electric potential direction of piezoelectric nanolaminates is different, the bending deflection of piezoelectric nanolaminates will change accordingly. The natural frequency of piezoelectric nanolaminates is determined by the absolute value of the flexoelectric coefficients, and is independent of their positive or negative values. Both the surface effect and the flexoelectric effect are influenced by size-dependent behaviors. When the thickness of the laminates is sufficiently large, both the surface effect and flexoelectric effect can be disregarded. This paper's research methods and results provide theoretical models and analytical methods for the microstructure design, multi-physical field characterization, and bending deformation behavior of intelligent components containing rectangular piezoelectric nanolaminates.

Fracture analysis of spatially graded piezoelectric-flexoelectric materials using XIGA

Dielectric Functionally Graded Materials (FGMs) exhibit superior flexoelectric properties. Gradual changes in material properties lead to large strain gradients and excellent flexoelectric responses. Cracks behave in a complex manner inside piezoelectric-flexoelectric FGMs subjected to electromechanical loading. An extended isogeometric analysis (XIGA)-based formulation is developed for flexoelectric FGMs with crack discontinuities. Ceramic-polymer FGMs of barium titanate (BTO) and polyvinylidene fluoride (PVDF) are selected for analysis since this material combination has shown better flexoelectric response solely due to gradation. A higher-order electromechanical J-integral is used to study the behavior of cracks. The fracture behavior of different crack geometries at various grading indices and levels of flexoelectricity is investigated. A crack interaction study is conducted with varying crack parameters. The length-scale effect on the energy release rate is also shown. A significant reduction in the energy release rate is observed in FGMs due to the flexoelectric effect.

Flexoelectricity Modulated Electron Transport of 2D Indium Oxide.

The phenomenon of flexoelectricity, wherein mechanical deformation induces alterations in the electron configuration of metal oxides, has emerged as a promising avenue for regulating electron transport. Leveraging this mechanism, stress sensing can be optimized through precise modulation of electron transport. In this study, the electron transport in 2D ultra-smooth In2O3 crystals is modulated via flexoelectricity. By subjecting cubic In2O3 (c-In2O3) crystals to significant strain gradients using an atomic force microscope (AFM) tip, the crystal symmetry is broken, resulting in the separation of positive and negative charge centers. Upon applying nano-scale stress up to 100nN, the output voltage and power values reach their maximum, e.g. 2.2mV and 0.2pW, respectively. The flexoelectric coefficient and flexocoupling coefficient of c-In2O3 are determined as ≈0.49nCm-1 and 0.4V, respectively. More importantly, the sensitivity of the nano-stress sensor upon c-In2O3 flexoelectric effect reaches 20nN, which is four to six orders smaller than that fabricated with other low dimensional materials based on the piezoresistive, capacitive, and piezoelectric effect. Such a deformation-induced polarization modulates the band structure of c-In2O3, significantly reducing the Schottky barrier height (SBH), thereby regulating its electron transport. This finding highlights the potential of flexoelectricity in enabling high-performance nano-stress sensing through precise control of electron transport.

Flexoelectric and transverse shear effects on band gaps in periodic microbeams

This paper applies wave equations and boundary conditions to a periodic electro-elastic microbeam, which incorporates transverse shear, microstructure and flexoelectric effects to anticipate the occurrence of band gaps in elastic waves. The new model has been simplified as the flexoelectric model and classical elastic model, as special cases. Meanwhile, compared to Bernoulli-Euler beam model, it is found that transverse shear effect has a significant effect on the band gap predictions of thick beams, but this effect is negligible for slender beams, indicating that this new model can be used to predict band gaps of both thick and slender beams in the high-frequency range. Furthermore, the impacts of microstructure and flexoelectric effects as well as material and microstructural parameters on band gaps are studied. The numerical results show that the influence of flexoelectricity on band gaps is the primary in the submicron beams, while the microstructure effect is the main in the micron beams. Additionally, the band gap frequencies and sizes (bandwidth) are significantly affected by the beam thickness, unit cell length and volume fraction. Thus, these discoveries demonstrate the feasibility of tailoring the band gap frequencies and sizes through the adjustment of material and microstructural parameters.

Piezoelectric layer guided in-plane surface waves with flexoelectricity and gradient effects

With the rapid advancement of 5 G technology, the demand for surface acoustic wave (SAW) devices is experiencing exponential growth. Precisely forecasting the speed at which Rayleigh waves propagate, taking into account size effects and flexoelectric properties, is vital for enhancing SAW device design. To address this need, the study explores Rayleigh wave propagation in a stratified system consisting of a nanoscale piezoelectric guiding layer atop an isotropic elastic substrate. The governing equations, boundary conditions, and interface continuity conditions between the guiding layer and substrate are established through the Hamiltonian principle. Following this, the dispersion equations for Rayleigh waves under electric open-circuit and electric short-circuit conditions are derived and solved numerically. Additionally, the effects of flexoelectricity, inertial gradients, strain gradients, electric field gradients, and the piezoelectric guiding layer thickness on the phase velocity of Rayleigh waves are extensively explored. Our findings indicate that flexoelectricity and strain gradients elevate the phase velocity, while inertial gradients and electric field gradients result in a decrease in the phase velocity. As the frequency of Rayleigh waves increases, the impact of these factors becomes more prominent. In addition, it is observed that electric field gradients play a less significant role compared to inertial gradients and strain gradients. The findings of this study could offer valuable insights for the advancement of miniaturized SAW devices designed for high-frequency service.

Layer-Dependent Electromechanical Response in Twisted Graphene Moiré Superlattices.

The coupling of mechanical deformation and electrical stimuli at the nanoscale has been the subject of intense investigation in the realm of materials science. Recently, twisted van der Waals (vdW) materials have emerged as a platform for exploring exotic quantum states. These states are intimately tied to the formation of moiré superlattices, which can be visualized by directly exploiting the electromechanical response. However, the origin of the response, even in twisted bilayer graphene (tBLG), remains unsettled. Here, employing lateral piezoresponse force microscopy (LPFM), we investigate the electromechanical responses of marginally twisted graphene moiré superlattices with different layer thicknesses. We observe distinct LPFM amplitudes and spatial profiles in tBLG and twisted monolayer-bilayer graphene (tMBG), exhibiting effective in-plane piezoelectric coefficients of 0.05 and 0.35 pm/V, respectively. Force tuning experiments further underscored a marked divergence in their responses. The contrasting behaviors suggest different electromechanical couplings in tBLG and tMBG. In tBLG, the response near the domain walls is attributed to the flexoelectric effect, while in tMBG, the behaviors can be comprehended within the context of the piezoelectric effect. Our results not only provide insights into electromechanical and corporative effects in twisted vdW materials with different stacking symmetries but may also offer a way to engineer them at the nanoscale.

Reversible Mechanical Switching of Ferroelastic Stripe Domains in Multiferroic Thin Films.

The application potential of ferroelectric thin films largely relies on the controllability of their domain structure. Among the various proposed strategies, mechanical switching is being considered as a potential alternative to replace electrical switching for control of the domain structure of ferroelectric thin films via, e.g., the flexoelectric effect. So far, studies on mechanical switching are confined to out-of-plane polarization switching in ferroelectric thin films, which are in pristine or prepoled single-domain states. In this work, we report reversible in-plane mechanical switching of the monoclinic phase (MC phase) stripe domains in BiFeO3 thin films can be realized by scanning tip force. Via controlling the fast scan direction of the scanning probe microscopy tip and the magnitude of the tip force, the effective trailing field induced by the local tip force can be rotated to consequently switch the net in-plane polarization of the two-variant stripe domain patterns by either 90° or 180°. Moreover, the monoclinic to rhombohedral (MC-R) phase transition occurs during mechanical switching with the distribution of R-phase domains dependent on the switching paths. These results extend our current understanding of the mechanical switching behavior in ferroelectric thin films and should be instructive for their future applications.

Modeling of size dependent buckling behavior of piezoelectric sandwich perforated nanobeams rested on elastic foundation with flexoelectricity

This article presents a size dependent mathematical model and an analytical solution methodology to accurately simulate and analyze the size dependent buckling behavior of piezoelectrically layered sandwich nanobeams with perforated core embedded in an elastic medium with flexoelectricity. The electric enthalpy energy function is expressed in terms of the electric and the flexoelectric effects. Regular squared cutouts perforation pattern is adopted for the perforated core. Closed forms for the equivalent geometrical parameters of perforated core are developed. The shear deformation effect is incroporated using the Timoshenko beam theory (TBT). To capture the nonlocality and the microstructure length scale effects, the nonlocal strain gradient elasticity theory is modified and adopted to include the electromechanical nonclassical effects. The Hamiltonian principle is utilized to derive the equilibrium equations. An analytical solution methodology is developed to derive closed forms for critical buckling loads. The developed solution procedure is implemented into a MATLAB software code. The accuracy of the developed procedure is verified by comparing obtained results with corresponding cases reported in the literature. Influences of different design variables on the electromechanical buckling behavior are explored through intensive parametric studies. Results obtained showed the significant effects of the flexoelectricity and the piezoelectric parameters on the size dependent buckling behavior of piezoelectric sandwich nanobeams with perforated core. Size dependent electromechanical as well as mechanical buckling behaviors could be controlled by adjusting these parameters. The developed procedure and the obtained numerical results are helpful in many technological and industrial applications as MEMS and NEMS.

A size-dependent electro-mechanical buckling analysis of flexoelectric cylindrical nanoshells

In this paper, a buckling analysis for flexoelectric cylindrical nanoshells under axial compression is performed by considering the higher-order shear deformation theory and non-uniform pre-buckling deformation. Size-dependent critical buckling stresses and buckling mode shapes are obtained by the Galerkin's method with newly proposed displacement functions. Numerical results are compared with existing solutions and excellent agreements are observed. Furthermore, a comprehensive parametric study of boundary conditions, geometrical parameters and applied electric voltage is carried out to reveal the influence of flexoelectric effect on the size-dependent buckling characteristics of flexoelectric cylindrical nanoshells.

P‐246: Late‐News Poster: Effective flicker reduction through luminance compensation between pixels in the fringe field switching mode using positive dielectric liquid crystals

We develop the positive dielectric liquid crystals for flicker free that saves the power consumption and improves the image quality. The dielectric constant was optimized for a low flexoelectric effect and flicker is advanced by adding the LC component which reduces the luminance difference between frames. We confirmed that the a‐Si TFT LCD Panel incorporating the developed LC operates without flicker at the driving frequency of 40Hz.

Bending induced polarization charges in non-polar porous polymer for stroke rehabilitation

Owing to the flexibility, lightweight, long-life and low cost, polymers are promising candidates to realize electromechanical conversion in wearable electronics. The flexoelectric effect enables non-piezoelectric materials to achieve electromechanical coupling, thereby broadening application ranges of nonpolar polymers. In this work, the porous samples of polydimethylsiloxane (PDMS) with various pore sizes and porosities are fabricated by the sacrificial salt template method and the chemical gas foaming method. The flexoelectric polarization response can be tuned directly by the structural characters of the porous PDMS. The transverse flexoelectric coefficient of porous PDMS can reach approximately 2.9 times the counterpart of the bulk one. The competitive mechanism between strain gradient and permittivity is proposed on flexoelectricity of random porous media by dielectric impedance spectrums and finite element analyses. The present regulation of flexoelectricity provides an alternative to electromechanical conversion. With the deep learning technique based on one-dimensional convolution neural networks, actions of both sick and normal legs of various stroke patients can be well recognized by the designed device of rehabilitation. The present rehabilitation monitoring system, which is an innovative application of the flexoelectricity in the porous polymers, offers a new approach to support physical therapy for post-stroke patients.

Reversible flexoelectric domain engineering at the nanoscale in van der Waals ferroelectrics

The universal flexoelectric effect in solids provides a mechanical pathway for controlling electric polarization in ultrathin ferroelectrics, eliminating potential material breakdown from a giant electric field at the nanoscale. One challenge of this approach is arbitrary implementation, which is strongly hindered by one-way switching capability. Here, utilizing the innate flexibility of van der Waals materials, we demonstrate that ferroelectric polarization and domain structures can be mechanically, reversibly, and arbitrarily switched in two-dimensional CuInP2S6 via the nano-tip imprinting technique. The bidirectional flexoelectric control is attributed to the extended tip-induced deformation in two-dimensional systems with innate flexibility at the atomic scale. By employing an elastic substrate, artificial ferroelectric nanodomains with lateral sizes as small as ~80 nm are noninvasively generated in an area of 1 μm2, equal to a density of 31.4 Gbit/in2. Our results highlight the potential applications of van der Waals ferroelectrics in data storage and flexoelectronics.

Synergetic Improvement of Flexoelectric Coefficient in Liquid Crystal Embedded Flexible PVDF Polymer Composite for Energy Harvesting Applications.

Flexoelectricity is the universal electric polarization of dielectrics upon exertion of a non-uniform strain gradient. With the advancement of nano-technology and miniaturization of electronic devices, flexoelectricity holds the promise to address the power requirements for such device operation. The direct flexoelectric effect in liquid crystal (LC) embedded poly(vinylidene fluoride) (PVDF) polymer films is examined for the first time by the application of external strain on the films. Physical characterizations such as Differential Scanning Calorimetry (DSC), dielectric spectroscopy, X-ray diffraction, and field emission scanning electron microscopy (FESEM) are carried out to study the composite films' intrinsic and extrinsic properties like dielectric, crystallinity, and morphologies. The value of the flexoelectric coefficient (μ12) increases with the concentration of LC incorporation. At 3wt%, μ12 attains a maximum value of 68nCm-1, which is more than a threefold increase compared to that of the pure PVDF film. The role of Maxwell-Wagner-Sillars (MWS) polarization in determining flexoelectric polarization in polymer composites is also discussed. Moreover, the influence of the microstructure and domain size formation in determining the flexoelectric response are discussed in detail to infer the behavior of the flexoelectric coefficients of the films. Potential device applications based on this phenomenon have been proposed for future research in sensing and actuation.

Nonlinear Energy Harvesting From a Base Excited Size-Dependent Flexoelectric Nanostructure with Off-Center Rigid Tip Mass Subjected to Axial Pulsating Excitation

This study explores the incorporation of flexoelectricity and size-dependence effects in electricity harvesting from a novel nanostructure. This nanostructure, featuring a cylindrical-shaped rigid tip mass, is stimulated at the base with axial pulsating excitation. Designed with a nanobeam material, the energy harvester accounts for structural nonlinearity, flexoelectricity, and the presence of an off-center rigid mass, operating under multiple excitations. The eigenanalysis is employed to delve into the dynamic characteristics of the system, providing engineers with insights to identify safe operating regions and operational constraints. Additionally, perturbation techniques are utilized to estimate steady-state voltage and power characteristics, with a focus on maximizing voltage and power generation. The study underscores the impact of size dependence on nanoscale design, flexoelectricity, asymmetric tip mass, and various excitation parameters within a constrained operating range. Analysis reveals how saddle-node and pitchfork bifurcations can disrupt energy harvesting performance and suggests strategies for mitigating these issues by adjusting operational parameters. Moreover, the study emphasizes the significant role of the off-center rigid tip mass in energy estimation compared to conventional microstructure-based energy harvesters. Analytical findings are rigorously validated against numerical results under different resonant scenarios, showcasing the accuracy of the analytical approach in capturing nonlinear sources and optimizing energy harvesting from nanostructures.

Merits and Demerits of Machine Learning of Ferroelectric, Flexoelectric, and Electrolytic Properties of Ceramic Materials.

In the present review, the merits and demerits of machine learning (ML) in materials science are discussed, compared with first principles calculations (PDE (partial differential equations) model) and physical or phenomenological ODE (ordinary differential equations) model calculations. ML is basically a fitting procedure of pre-existing (experimental) data as a function of various factors called descriptors. If excellent descriptors can be selected and the training data contain negligible error, the predictive power of a ML model is relatively high. However, it is currently very difficult for a ML model to predict experimental results beyond the parameter space of the training experimental data. For example, it is pointed out that all-dislocation-ceramics, which could be a new type of solid electrolyte filled with appropriate dislocations for high ionic conductivity without dendrite formation, could not be predicted by ML. The merits and demerits of first principles calculations and physical or phenomenological ODE model calculations are also discussed with some examples of the flexoelectric effect, dielectric constant, and ionic conductivity in solid electrolytes.

Integration of hydrogen evolution and dye removal in flexocatalysis by centrosymmetric semiconductor nanorods

In this work, coupling of the hydrogen (H2) production and dye degradation was first realized in a single flexocatalytic process using cerium oxide nanorods (CeO2 NRs). The flexoelectric polarization in a bending nanorod created an internal electric field, which promoted the separation of the thermal-excited electrons and holes. As a consequence, the H2 evolution rate of the flexocatalysis in dark was twice higher than that of the photocatalysis by the same CeO2 NRs. Moreover, simultaneous dye degradation was realized without reducing the H2 evolution rate, with the degradation constant rate of 0.065 min−1, dye removal efficiency of 89.3%, and H2 generation at 486.4 μmol g−1 h−1. The dual-functional catalytic performance of the CeO2 NRs was benefited from the unique periodic flexoelectric field induced by the ultrasound vibration, which could not be achieved by photocatalysis. This work revealed the important role of flexoelectric effect in overcoming the limitation in photocatalysis, which could be extended to a wide range of semiconductor nanomaterials for designing novel kinds of advanced flexocatalysts.

Enhancement of electromechanical response in curved antiferroelectric AgNbO3 ceramics by flexoelectric effect

AgNbO3 is a typical antiferroelectric ceramic with weak ferroelectricity at room temperature. Due to this feature, AgNbO3 has received a lot of attention in electromechanical applications, but most of these studies have focused on the doping of other elements in AgNbO3. In this study, curved AgNbO3 ceramics were fabricated using a gravity-driven annealing process, and the field-induced strains were investigated. The curved ceramic exhibited a significantly higher field-induced nominal strain compared to a flat ceramic. Experimental results revealed that the curved AgNbO3 sample exhibited a maximum nominal strain of 1.22%, significantly surpassing the theoretical value of 0.13%. Analysis of various characterizations confirmed the presence of flexoelectricity, and flexoelectricity played an important role in the ultrahigh electromechanical response of curved AgNbO3 ceramics. Additionally, we demonstrated that curved AgNbO3 ceramics can enhance the flexoelectric coefficient. These findings suggest that curved antiferroelectric ceramics can enhance their displacement output, meeting the requirements for applications in large-strain actuators.

Novel strategies for low-voltage NAND flash memory with negative capacitance effect

Here, we present a novel approach to employing a negative capacitance (NC) phenomenon in the blocking oxide of charge trap flash (CTF) memory. To achieve this, we developed an inversible mono-domain like ferroelectric (IMFE) film through high-pressure post-deposition annealing in a forming gas at 200 atm (FG-HPPDA). The FG-HPPDA process enables to form a uniform alignment of domains and facilitates invertible domain switching behavior in ferroelectrics, generating an internal field by the flexo-electric effect as well as interface-pinned polarization by chemical reaction. Subsequently, to stabilize the NC effect, we fabricated the IMFE/Al2O3 heterostructure, which exhibits an outstanding capacitance-boosting feature. Finally, we successfully demonstrate unprecedented CTF memory with the NC effect in a blocking oxide. Our unique CTF device shows the improved performance (maximum incremental-step-pulse-programming (ISPP) slope ∼1.05) and a large MW (>8 V), attributed to the capacitance boosting by NC phenomenon.