Flexoelectric Polarization Research Articles

Flexoelectric Polarization in a Nematic Liquid Crystal Enhanced by Dopants with Different Molecular Shape Polarities.

Flexoelectricity may have an important impact on the switching properties of nematic and cholesteric liquid crystals due to the linear coupling between the flexoelectric polarization of the liquid crystal and the applied electric field. This coupling is the origin of the extraordinary electro-optic effect in cholesterics aligned in the uniform lying helix texture, resulting in fast switching and field control of both rise and fall times. Therefore, the flexoelectric properties of the liquid crystals have become an important issue when designing and synthesizing liquid crystal materials and/or preparing their mixtures with appropriate flexoelectric compounds (dopants). Here, we report on the flexoelectric polarization of a highly polar nematic liquid crystal host enhanced by doping it with two newly synthesized dopants SK 1–6 and SK 1–8, possessing a hockey stick molecular shape, and comparing their doping effect with the one of the dimeric dopants CB7CB possessing a symmetric bend molecular shape. All dopants were dissolved in small concentration (5 wt %) in the nematic host so that the linear approximation of the dependence of the difference between splay es and bend eb flexoelectric constants, that is, (es – eb), on the concentration of the dopant in the host material can be applied. In this way, (es – eb) was estimated for the hockey stick dopants SK 1–6 and SK 1–8 to be 0.182 and 0.204 nC/m, respectively. The obtained flexoelectric polarization of these dopants is among the highest reported in the literature so far.

Giant room temperature compression and bending in ferroelectric oxide pillars

Plastic deformation in ceramic materials is normally only observed in nanometre-sized samples. However, we have observed high levels of plasticity (>50% plastic strain) and excellent elasticity (6% elastic strain) in perovskite oxide Pb(In1/2Nb1/2)O3-Pb(Mg1/3Nb2/3)O3-PbTiO3, under compression along <100>pc pillars up to 2.1 μm in diameter. The extent of this deformation is much higher than has previously been reported for ceramic materials, and the sample size at which plasticity is observed is almost an order of magnitude larger. Bending tests also revealed over 8% flexural strain. Plastic deformation occurred by slip along {110} <1bar{1}0 > . Calculations indicate that the resulting strain gradients will give rise to giant flexoelectric polarization. First principles models predict that a high concentration of oxygen vacancies weaken the covalent/ionic bonds, giving rise to the unexpected plasticity. Mechanical testing on oxygen vacancies-rich Mn-doped Pb(In1/2Nb1/2)O3-Pb(Mg1/3Nb2/3)O3-PbTiO3 confirmed this prediction. These findings will facilitate the design of plastic ceramic materials and the development of flexoelectric-based nano-electromechanical systems.

Engineering of atomic-scale flexoelectricity at grain boundaries

Flexoelectricity is a type of ubiquitous and prominent electromechanical coupling, pertaining to the electrical polarization response to mechanical strain gradients that is not restricted by the symmetry of materials. However, large elastic deformation is usually difficult to achieve in most solids, and the strain gradient at minuscule is challenging to control. Here, we exploit the exotic structural inhomogeneity of grain boundary to achieve a huge strain gradient (~1.2 nm−1) within 3–4-unit cells, and thus obtain atomic-scale flexoelectric polarization of up to ~38 μC cm−2 at a 24° LaAlO3 grain boundary. Accompanied by the generation of the nanoscale flexoelectricity, the electronic structures of grain boundaries also become different. Hence, the flexoelectric effect at grain boundaries is essential to understand the electrical activities of oxide ceramics. We further demonstrate that for different materials, altering the misorientation angles of grain boundaries enables tunable strain gradients at the atomic scale. The engineering of grain boundaries thus provides a general and feasible pathway to achieve tunable flexoelectricity.

Coexistence of Flexo- and Ferro-Electric Effects in an Ordered Assembly of BaTiO3 Nanocubes.

It has been reported that the flexoelectric effect could be dominant in the nanoscale. The discrepancy between theory and experiments on the frequency dependence of the dielectric constant of an ordered assembly of BaTiO3 nanocubes is nearly resolved by assuming the coexistence of flexo- and ferro-electric effects. Although flexoelectric polarizations perpendicular to the applied alternating electric field contribute to the dielectric constant, those parallel to the electric field do not contribute because the magnitude of the flexoelectric polarization does not change due to the mismatch of strain at the interface of the nanocubes. On the other hand, some dielectric response is possible for the ferroelectric component of the polarization parallel to the electric field.

Flexoelectric-induced photovoltaic effects and tunable photocurrents in flexible LaFeO3 epitaxial heterostructures

By engineering strain gradients in dielectrics, the flexoelectric effect can be created, which yields interesting physical properties via electromechanical coupling. Here, we report flexoelectric-induced photovoltaic effects in centrosymmetric LaFeO3 thin-film heterostructures grown on flexible mica substrates, in which partial relaxation of lattice-mismatch strain against LaAlO3 stretching layers results in giant strain gradients and pronounced electrical polarizations. The flexoelectric polarization modulates band alignment and leads to significant photovoltaic effects with a short-circuit current density of ∼0.4 mA/cm2 and an open circuit voltage of ∼ -0.45 V in Pt/LaFeO3/LaNiO3 devices. In addition, by concavely/convexly bending the mica substrate, mechanical strain gradients give rise to bi-directionally tunable photocurrents, in which continuously change of short-circuit current density with a magnitude of ∼100% and good reproducibility in repetitive bending operations are observed in the Pt/LaFeO3/LaNiO3 devices. The present work demonstrates an approach to design self-powered photoelectric devices with an electromechanical degree of freedom based on the flexoelectric effect in flexible thin-film heterostructures.

Nanofluidics of nematic liquid crystals in hollow capillaries.

The aim of this paper is to investigate the response of a homogeneously aligned nematic nanosized hollow cavity (HANNHC) confined between two charged horizontal coaxial cylinders and subjected to both a radially applied electrostatic field E, arising from the surface charge density κ and the temperature gradient ∇T set between these cylinders. This was done within the framework of an extension of the classical Ericksen-Leslie theory, supplemented by thermomechanical correction of the shear stress and Rayleigh dissipation function, as well as taking into account the entropy balance equation. The physical mechanism responsible for the excitation of the hydrodynamic flow in the HANNHC is based on the interaction of the director and temperature gradients and the static electric field. Calculations show that under the influence of both the ∇T and E, a stationary flow u^{st} is excited in the HANNHC in the horizontal direction. It is shown that the electric force enforced by the flexoelectric polarization plays a crucial role in the excitation of u^{st} between these cylinders.

Fast liquid crystal light shutter with polymer stabilisation

We present a fast-switching liquid crystal device comprising fringe field switching (FFS) electrode structure deposited onto one of the device substrates. Initially, the liquid crystal in the device has a homeotropic alignment. The generated periodic electric field by the FFS electrode results in a periodic splay/bend elastic deformation, thus giving rise to flexoelectric polarization along the substrate normal. At low applied voltages, this periodic elastic deformation, is substantially localized in a very thin portion of the liquid crystal layer adjacent to the substrate surface bearing the electrode and it is stabilized by a polymer network. Thus, the flexoelectric polarization becomes permanently present in the device and has non-zero value at field-off state. The polymer network with splay/bend configuration occupies very small part of the liquid crystal layer (∼0.5 μm), which is thinner than the light wavelength and therefore is optically invisible. Simultaneously with the formation of the polymer network, possessing splay/bend configuration, a polymer network with polymeric bundles oriented preferably along the substrates’ normal is formed. As we will show, the presence of the polymer network, consisting of surface and bulk parts, reduces substantially the switching times of the liquid crystal device more than one order bringing them to μs range.

Magnetically-Induced Flexoelectric Effects in the Second-order Extension of a Composite Fiber with Piezomagnetic and Flexoelectric Layers

In this paper, we studied a magnetically-induced axial flexoelectric polarization field in a second-order extension of a composite fiber with both piezomagnetic and flexoelectric dielectric component phases. Based on the macroscopic flexoelectric and piezomagnetic theories, a one-dimensional (1D) model was derived by a variational formulation based on Hamilton’s principle, in which one zero-order electric potential and three relevant deformation modes such as extension, thickness-stretch, and symmetric thickness-shear were considered. A cantilevered fiber under a static magnetic field was analytically solved, in which an axial electric polarization was induced by the curved cross section through flexoelectric coupling. The mechanical and electrical behaviors that occurred in response to the magnetic effects under different thickness ratios of the composite fiber were discussed. It was found that symmetric shear deformations and polarizations were significant at certain thickness ratios. Lastly, this paper provided a potential idea for designing flexoelectric devices when magnetic fields are involved.

Atomic-scale imaging of flexoelectric polarization around engineered crack tips

Atomic-scale imaging of flexoelectric polarization around engineered crack tips

Atomic coordinates and polarization map around a pair of 12a[011¯] dislocation cores produced by plastic deformation in relaxor ferroelectric PIN–PMN–PT

The core structures of dislocations are crucial for understanding the plastic deformation mechanisms and the functional properties of materials. Here, we use the scanning transmission electron microscopy imaging techniques of high-resolution high angle annular dark field and integrated differential phase contrast to investigate the atomic structure of a pair of climb-dissociated 12a[011¯] dislocations in a bending-deformed relaxor ferroelectric Pb(In1/2Nb1/2)O3–Pb(Mg1/3Nb1/3)O3–PbTiO3 single crystal. Cations at one dislocation core are found to arrange in the same way as the climb-dissociated 12a[011¯] dislocation core in SrTiO3, while the other one is different. Oxygen depletion was observed at both dislocation cores. Geometric phase analysis of the lattice rotation shows opposite signs at both sides of the dislocations, demonstrating the strain gradient, which is known to give rise to flexoelectric polarization. Using the peak finding method, the polarization (a combination of ferroelectric and flexoelectric) around dislocations was mapped at the unit-cell scale. The polarization direction obtained is consistent with that predicted based on the flexoelectric effect in a perovskite oxide with [011] geometry. Head-to-head positively charged and tail-to-tail negatively charged domain walls were revealed based on the polarization map, suggesting a new way to stabilize charged domain walls via dislocations. A distinct dislocation core configuration has been observed, and a unit-cell scale polarization map helps understand the flexoelectric effects (coupling between strain gradient and polarization) around dislocations in a relaxor ferroelectric.

Flexocaloric effect in ferroelectric materials: methods of indirect evaluation

Ferroelectric materials have great potential use for solid-state refrigeration. However, their working temperature is restricted to Curie temperature; the working temperature can be increased by the new component of strain gradient-driven caloric effect or flexocaloric effect (FCE). The FCE relies on the inhomogeneous strain of the crystal lattice to induce polarization in centrosymmetric crystals (flexoelectricity). The strain gradient-induced polarization is defined by flexoelectric polarization coefficient and is utilized to estimate the FCE. As the FCE is a relatively new phenomenon, several ways can be used to calculate it. Different methods of flexocaloric quantification in ferroelectric materials (Pb(Mg1/3Nb2/3)O3 and Ba0.67Sr0.33TiO3) are discussed in the present work. The FCE can be obtained based on the measured properties and combination between the polarization and strain. This allows one to study the actual or net flexocaloric behavior in the material. It was found that the quantification of temperature change varies according to the method used for estimation. The experimental confirmation is required for validation of the proposed methods of estimation. Further, this work also discusses the possibility of other ways that are untouched by the research community. The analysis indicates a substantial untapped potential for solid-state refrigeration and warrants further research.

Correlation Between Corrugation-Induced Flexoelectric Polarization and Conductivity of Low-Dimensional Transition Metal Dichalcogenides

Tunability of polar and semiconducting properties of low-dimensional transition metal dichalcogenides (TMDs) have propelled them to the forefront of fundamental and applied physical research. These materials can vary from non-polar to ferroelectric, and from direct-band semiconductor to metallic. However, in addition to classical controls such as composition, doping, and field effect in TMDs the additional degrees of freedom emerge due to the curvature-induced electron redistribution and associated changes in electronic properties. Here we numerically explore the elastic and electric fields, flexoelectric polarization and free charge density for a TMD nanoflake placed on a rough substrate with a sinusoidal profile of the corrugation using finite element modelling. Numerical results for different flake thickness and corrugation depth yield insight into the flexoelectric nature of the out-of-plane electric polarization and establish the unambiguous correlation between the polarization and static conductivity modulation caused by inhomogeneous elastic strains coupled with deformation potential and strain gradients, which evolve in TMD nanoflake due to the adhesion between the flake surface and corrugated substrate. We revealed a pronounced maximum at the thickness dependences of the electron and hole conductivity of MoS2 and MoTe2 nanoflakes placed on a metallic substrate, which opens the way for their geometry optimization towards significant improvement their polar and electronic properties, necessary for their advanced applications in nanoelectronics and memory devices.Specifically, obtained results can be useful for elaboration of nanoscale straintronic devices based on the bended MoS2, MoTe2 and MoSTe nanoflakes, such as diodes and bipolar transistors with a bending-controllable sharpness of p-n junctions.

Flexoelectric Thin-Film Photodetectors.

The flexoelectric effect, which manifests itself as a strain-gradient-induced electrical polarization, has triggered great interest due to its ubiquitous existence in crystalline materials without the limitation of lattice symmetry. Here, we propose a flexoelectric photodetector based on a thin-film heterostructure. This prototypical device is demonstrated by epitaxial LaFeO3 thin films grown on LaAlO3 substrates. A giant strain gradient of the order of 106/m is achieved in LaFeO3 thin films, giving rise to an obvious flexoelectric polarization and generating a significant photovoltaic effect in the LaFeO3-based heterostructures with nanosecond response under light illumination. This work not only demonstrates a novel self-powered photodetector different from the traditional interface-type structures, such as the p-n and Schottky junctions but also opens an avenue to design practical flexoelectric devices for nanoelectronics applications.

Mechanical Manipulation of Silicon-based Schottky Diodes via Flexoelectricity

Silicon-based Schottky barrier diodes (SBDs), as a two-terminal circuit element, are widely used in modern industries due to its low cost and better compatibility with the complementary metal oxide semiconductor (CMOS) technology. Flexoelectricity resulting from strain gradient is a distinctive electromechanical coupling phenomenon compared to piezoelectricity resulting from strain. Flexoelectricity can exist in any dielectric due to the non-uniform strain breaking symmetry of materials. In this paper, we utilize the induced flexoelectric polarization to tune the behavior of a SBD made of metal and p-type Silicon. Making use of conductive atomic force microscopy (C-AFM), we measured current-voltage of the fabricated Si-based SBD under different tip forces. In order to conduct a quantitative study on the tuning effect of flexoelectricity on the performance of the fabricated Si-based SBD, we introduce an effective barrier height and provide a modified current equation according to the classical thermionic emission theory. The results show that flexoelectricity plays a significant role in dictating the Schottky barrier height, maximum rectified current (density), reverse saturation current (density), rectification ratio, and open voltage of the fabricated SBD. In addition, based on the Hertzian contact model and the measured data, the nonzero flexoelectric coefficients of the used p-type silicon are obtained.

High-Performance Phototransistors Based on MnPSe3 and Its Hybrid Structures with Au Nanoparticles.

Layered metal thiophosphates with a general formula MPX3 (M is a group VIIB or VIII element and X is a chalcogen) have emerged as a novel member in a two-dimensional (2D) family with fascinating physical and chemical properties. Herein, the photoelectric performance of the few-layer MnPSe3 was studied for the first time. The multilayer MnPSe3 shows p-type conductivity and its field-effect transistor delivers an ultralow dark current of about 0.1 pA. The photoswitching ratio reaches ∼103 at a wavelength of 375 nm, superior to that of other thiophosphates. A responsivity and detectivity of 392.78 mA/W and 2.19 × 109 Jones, respectively, have been demonstrated under irradiation of 375 nm laser with a power intensity of 0.1 mW/cm2. In particular, the photocurrent can be remarkably increased up to 30 times by integrating a layer of Au nanoparticle array at the bottom of the MnPSe3 layer. The metal-semiconductor interfacial electric field and the strain-induced flexoelectric polarization field caused by the underlying nanorugged Au nanoparticles are proposed to contribute together to the significant current improvement.

Сравнение характеристик тонких пленок PZT на подложках из сапфира и кремния

The properties of ferroelectric sol-gel PZT films deposited on a silicon-on-sapphire (SOS) substrate are compared with those of PZT films formed on a Si substrate. The crystalline structure, asymmetry of the hysteresis loops, polarization dependences of the transient current, short-circuit photocurrent, and open-circuit photovoltage, as well as the substrate bending have been studied. The PZT on SOS films are textured in a single (111) direction and exhibit symmetric hysteresis loops with a strong remanent polarization. The PZT films on Si are textured in the main (111) and weaker (100) directions, have weaker polarization, and exhibit an asymmetry of the hysteresis loops, which is reflected in the magnitude of the transient current and photocurrent. It is shown that the sapphire substrate has a convex bending that causes a compressive stress in the film plane, which weakens the effect of the lattice mismatch between PZT and Pt. By contrast, the Si substrate has a concave curvature, which causes the film to stretch. The deformations and mechanical stresses within the films were estimated. For PZT on Si, an estimate of the strain gradient along the (111) axis was obtained, which makes it possible to relate the asymmetry of the hysteresis loops to the flexoelectric polarization, with the flexoelectric coefficient for sol-gel PZT films found to be 0.0154 µC/cm. The results obtained show that the sapphire substrate provides a better quality of thin PZT films.

Modeling flexoelectricity in soft dielectrics at finite deformation

This paper develops the equilibrium equations describing the flexoelectric effect in soft dielectrics under large deformations. Previous works have developed related theories using a flexoelectric coupling tensor of mixed material–spatial character. Here, we formulate the model in terms of a flexoelectric tensor completely defined in the material frame, with the same symmetries of the small-strain flexocoupling tensor and leading naturally to objective flexoelectric polarization fields. The energy potential and equilibrium equations are first expressed in terms of deformation and polarization, and then rewritten in terms of deformation and electric potential, yielding an unconstrained system of fourth order partial differential equations (PDE). We further develop a theory of geometrically nonlinear extensible flexoelectric rods under open and closed circuit conditions, with which we examine analytically cantilever bending and buckling under mechanical and electrical actuation. Besides being a simple and explicit model pertinent to slender structures, this rod theory also allows us to test our general theory and its numerical implementation using B-splines. This numerical implementation is robust as it handles the electromechanical instabilities in soft flexoelectric materials.

Dynamic dielectric-response model of flexoelectric polarization from kHz to MHz range in an ordered assembly of BaTiO3 nanocubes

Due to the strain gradient near each surface of a BaTiO3 nanocube in their ordered assembly, electric polarization appears due to flexoelectric effect. The magnitude of the flexoelectric polarization could be one order of magnitude larger than that of ferroelectric spontaneous polarization of BaTiO3. Thus, dielectric response of an assembly could be dominated by that of the flexoelectric polarization if there is no ferroelectric domain-wall motion. Numerical simulations of the dielectric response of a BaTiO3 nanocube in an ordered assembly are performed from kHz to MHz range based on a dynamic model of flexoelectric polarization assuming anharmonic potential. The calculated temperature dependence of the dielectric constant is consistent with the experimental data of high dielectric constant with nearly-flat temperature dependence. It is suggested that high dielectric constant with nearly-flat temperature dependence is not originated in ferroelectric nature of BaTiO3 nanocubes but originated in flexoelectric polarization in nanocubes which is also seen in non-ferroelectric materials.

Factors influencing flexoelectric polarization in liquid crystals

The work experimentally investigated the factors affecting the formation and physical parameters of flexoelectric polarization in liquid crystals (LC) with nematic as well as smectic A- and C-phases. Factors such as the heating temperature of the sample, orientation effects near the nematic – isotropic state (N-I) phase transition, and the initial orientation of LC molecules were studied. The thickness of the studied layers is from 10 to 100 μm, the frequency of exposure is 1000 Hz. It was found that the flexosignal takes maximum value in homeotropically oriented samples in the nematic phase. When approaching the N-I phase transition, the magnitude of the flex signal increases, which is associated with an increase in the deviation angle of the director of the LC. As the dipole moment grows, the quadrupole moment also increases. This is due to the tendency of LC molecules to form dipole pairs with antiparallel orientation of electric moments. The estimate of the flexural value U1ω yielded (for example, for MBBA) with a planar orientation 3 times less than with a homeotropic one. The presence of the second harmonic U2ω is a consequence of the orientational instability of surface polarization. The rapid growth of U2ω is associated with an increase in the square of the director deviation angle .

Exploration of mechanical, thermal conductivity and electromechanical properties of graphene nanoribbon springs.

Recent experimental advances [Liu et al., npj 2D Mater. Appl., 2019, 3, 23] propose the design of graphene nanoribbon springs (GNRSs) to substantially enhance the stretchability of pristine graphene. A GNRS is a periodic undulating graphene nanoribbon, where undulations are of sinus or half-circle or horseshoe shapes. Besides this, the GNRS geometry depends on design parameters, like the pitch's length and amplitude, thickness and joining angle. Because of the fact that parametric influence on the resulting physical properties is expensive and complicated to examine experimentally, we explore the mechanical, thermal and electromechanical properties of GNRSs using molecular dynamics simulations. Our results demonstrate that the horseshoe shape design GNRS (GNRH) can distinctly outperform the graphene kirigami design concerning the stretchability. The thermal conductivity of GNRSs was also examined by developing a multiscale modeling, which suggests that the thermal transport along these nanostructures can be effectively tuned. We found that however, the tensile stretching of the GNRS and GNRH does not yield any piezoelectric polarization. The bending induced hybridization change results in a flexoelectric polarization, where the corresponding flexoelectric coefficient is 25% higher than that of graphene. Our results provide a comprehensive vision of the critical physical properties of GNRSs and may help to employ the outstanding physics of graphene to design novel stretchable nanodevices.