Multiple Flexoelectric Actuation and Control of Plates

Surface effects in Mode III fracture of flexoelectric bodies

An ultra-high strain gradient field usually exists near dislocations, which breaks the inversion symmetry in dielectrics and induces electric polarization in the material through the flexoelectric effect. Flexoelectricity is an electromechanical coupling phenomenon commonly found in dielectric material, and this flexoelectric effect in anisotropic materials also exhibits complex and significant directional dependencies. In this article, anisotropic strain gradient theory and mathematical methods are used to establish precise constitutive and governing equations for cubic flexoelectric materials. The framework incorporates four constitutive tensors: the second-order reciprocal dielectric susceptibility, the fourth-order elastic tensor, the fourth-order flexoelectric tensor, and the sixth-order elastic tensor. Both open-circuit and short-circuit conditions are considered to define the bounds of the governing equations. By applying Green's function, we address the fundamental nonsingular dislocation problem and derive the displacement and elastic distortion tensors for screw and edge dislocations in cubic flexoelectric materials. Our results not only provide solutions to straight dislocation problems in flexoelectric cubic materials but also can serve as a basis for tuning flexoelectricity in materials by dislocation engineering.

Piezoelectric materials have been widely used for structural sensing due to the linear electromechanical coupling effect. Flexoelectricity, generally existing in all dielectrics, describes the linear inhomogeneous electromechanical coupling phenomena. Previous studies have shown that the direct flexoelectric effect is sensitive to the bending deformation. This study focuses on comparison and differences between two sensing mechanisms, that is, the flexoelectric and the piezoelectric effects, and explores their distinctive characteristics and potential applications. Based on the direct flexoelectric/piezoelectric effects, flexoelectric/piezoelectric materials treated as flexoelectric/piezoelectric sensors are applied to two ring models with identical dimensions. The mathematical models of thin elastic rings laminated with flexoelectric/piezoelectric sensors are established. Open-circuit sensing signals are derived for further evaluation and comparison. Sensing capabilities of these two materials and mechanisms are compared with respect to ring thickness, sensor thickness, and ring radius in case studies. Results show that the piezoelectric sensing signal appears to be sensitive for both bending-dominant and membrane-dominant vibrations, while the flexoelectric signal is much more prominent than the piezoelectric one for sensing of bending-dominant vibrations. For a flexible structure performing transverse vibration, the bending behavior is usually dominant. Thus, the flexoelectric effect could provide an effective alternative for structural sensing.

ABSTRACTThe flexoelectric effect refers to the electromechanical coupling between electric polarization and mechanical strain gradient. It universally exists in a variety of materials in any space group, such as liquid crystals, dielectrics, biological materials, and semiconductors. Because of its unique size effect, nanoscale flexoelectricity has shown novel phenomena and promising applications in electronics, optronics, mechatronics, and photovoltaics. In this review, we provide a succinct report on the discovery and development of the flexoelectric effect, focusing on flexoelectric materials and related applications. Finally, we discuss recent flexoelectric research progress and still‐unsolved problems.

A description of the guiding field line (GFL) model is presented for spherical torus geometry. The model is extended to cover small banana orbits that are trapped either above or below the midplane. Comparison of the model with the fluid and neoclassical theories demonstrates correctness of the model, though it shows that the model is not exactly equivalent to them. The GFL model provides a more general description for the orbit-squeezing effect resulting from the large gradient of the radial electric field. It shows that not only does the deformation of banana orbits, but also the change of the passing particles' orbits, affect the current in plasma. Besides, it appears that the change of the orbits' shape, as projected on the magnetic surface, contributes to modification of the current along with the radial squeezing/expanding. Distortion of the current by the gradient of the electric field is found to be predominantly in the direction parallel to the magnetic field, while almost no effect is seen for the perpendicular component.

In this paper, we investigate the photoionization microscopy of the Rydberg hydrogen atom in a gradient electric field for the first time. The observed oscillatory patterns in the photoionization microscopy are explained within the framework of the semiclassical theory, which can be considered as a manifestation of interference between various electron trajectories arriving at a given point on the detector plane. In contrast with the photoionization microscopy in the uniform electric field, the trajectories of the ionized electron in the gradient electric field will become chaotic. An infinite set of different electron trajectories can arrive at a given point on the detector plane, which makes the interference pattern of the electron probability density distribution extremely complicated. Our calculation results suggest that the oscillatory pattern in the electron probability density distribution depends sensitively on the electric field gradient, the scaled energy and the position of the detector plane. Through our research, we predict that the interference pattern in the electron probability density distribution can be observed in an actual photoionization microscopy experiment once the external electric field strength and the position of the electron detector plane are reasonable. This study provides some references for the future experimental research on the photoionization microscopy of the Rydberg atom in the non-uniform external fields.

While electric field induced ferroelectric switching has been extensively studied and broadly utilized, pure mechanical switching via flexoelectric effect has recently opened up an alternative method for domain writing due to their highly localized, electrically erasable and electric damage free characteristics. Thus far, few studies have been made on the coupling effect of electro-mechanical switching in ferroelectric materials, likely due to the experimental difficulty in the accurate definition of the tip-surface contact area and in the identification of mechanical contribution from electrical effect. Here, we employed self-consistent phase-field modeling to investigate the bi-polar switching behavior of (001) oriented Pb(Zr0.2Ti0.8)O3 thin film under concurrent electric and strain field created via a piezoresponse force microscope probe. By separating the effects from electric field, homogeneous strain and strain gradient, we revealed that the homogeneous strain suppresses the spontaneous polarization and accordingly increases the coercive field, and the strain gradient favors unipolar switching and inhibit it in the reverse direction, thus causing lateral offset of the hysteresis loop. The uncertainty of flexoelectric coefficients and the influence of flexocoupling coefficients on switching have also been discussed. Our study could necessitate further understanding of the electric, piezoelectric, and flexoelectric contribution to the switching behavior in nanoscale ferroelectric oxides.

Additional comments on “A proposed method for measuring the electric dipole moment of the neutron using acceleration in an electric field gradient and ultracold neutron interferometry”

According to ourhypothesis that ortho (O) to para (P) hydrogenconversion is promoted by an inhomogeneous electric field on the surfaceof the insulating oxide with high ionicity, we searched for OP conversioncatalysts using lattice energy as an indicator of high ionicity. Asa result, we found new oxide catalysts, including SiO2,γ-Al2O3, and CeO2 combinedwith 3d late transition metal cocatalysts. The fraction of para-H2 on 5%Fe-loaded SiO2 powder reached 50% (equilibriumvalue at 77 K) within 20 min. The activities of these catalysts aresignificantly superior to those of benchmark catalysts, such as Mn3O4. The cocatalyst nanoparticles of 1–12nm size dispersed on the oxide catalysts adsorb hydrogen well withoutdissociating it. The nuclear spin state of ortho-H2 adsorbedat the asymmetric site (nonzero electric field gradient) of the oxidesurface is thermally excited by nuclear quadrupole interaction, andthe OP conversion rate is increased by nuclear spin relaxation.

In ferroelectric ultrathin films, built-in electric fields are often present due to the flexoelectric effect and the difference of work functions at asymmetric electrodes, which may change the properties of the materials. In this paper, the influence of build-in electric fields induced by flexoelectric effect and/or work function difference on the misfit strain-temperature phase diagrams, and the electrocaloric properties of epitaxial BaTiO3 ultrathin films are investigated by using an extended nonlinear thermodynamic theory. It is found that the flexoelectric effect, i.e., the coupling of polarization and strain gradient, changes the misfit strain-temperature phase diagrams notably, in which the phases with out-of-plane polarizations increase due to the presence of a built-in field. The electrocaloric properties are remarkably enhanced when the built-in fields induced by both the flexoelectric effect and work function difference are considered. In particular, a giant adiabatic temperature change of 7.89 K in ultrathin Pt/BaTiO3/SrRuO3 capacitors at 460 K is predicted. Moreover, it is demonstrated that the peak of adiabatic temperature change versus working temperature is shifted from a high temperature to room temperature, suggesting that ferroelectric ultrathin films with asymmetric electrodes and strain gradient are promising candidates for room temperature refrigeration.

Internal Length Gradient (ILG) Material Mechanics Across Scales and Disciplines

Theory required for estimating the electric field gradients (EFGs) in ionic solids incorporating the effects of the ligand distortions due to the internal crystalline electric fields has been described. The EFGs have been derived from the distorted electronic charge distributions surrounding the nucleus under consideration in addition to the appropriate contributions from the multipole distributions in the lattice. Application of the theory has been made to study extensively the nuclear quadrupole interactions of the excited states of $^{111}\mathrm{Cd}$ and $^{117}\mathrm{In}$ in ${\mathrm{CdCl}}_{2}$. The results have been compared with those obtained under the cases: (i) "without ligand distortion"---which neglects the distortions of the ligands but considers the electronic as well as the "monopole and dipole" distributions in the crystal in a manner described previously, (ii) "monopoles and dipoles only" on the entire lattice, and (iii) "monopoles only" on the entire lattice. The ligand-distortion effects have been found to be very significant and the net EFGs change sign because of the ligand distortions. The need for obtaining the experimental sign of the quadrupole interaction frequencies in ${\mathrm{CdCl}}_{2}$ has been emphasized to understand the ligand-distortion effects on the EFG. Analysis of the EFGs from the cases considered reveals that the electronic contributions are dominant. This requires reanalysis of the experimental quadrupole interaction frequencies observed by the time-differential perturbed-angular-correlation technique in some Cd salts. The reanalysis yields the quadrupole moment $|Q(^{111}\mathrm{Cd})|$ very close to that obtained by Behrend and Budnick from the study of the circular polarization of the 247-keV $\ensuremath{\gamma}$ ray of $^{111}\mathrm{Cd}$.

The equations of motion are solved for ions moving in a model electric field that corresponds to the nightside equatorial region of the magnetosphere. The model represents the poleward region of the Harang discontinuity mapped to the magnetosphere. Within this region the model electric field has a constant earthward gradient superimposed on a constant dawn‐to‐dusk electric field. In combination with the earthward drift motion due to the dawn‐to‐dusk field, the electric field gradient introduces an earthward inertia drift, which is proportional to the ion mass and therefore faster for O+ ions than for H+ ions or electrons. It is also found that the entry of the ions into the gradient region causes phase bunching and as a result ion density striations form. The striations are enhanced for more abrupt changes in the electric field gradient, a weaker magnetic field, a stronger cross‐tail electric field and colder O+ ions. The first two conditions apply during the growth phase of a substorm. Using the Tsyganenko (1987) model a minimum electric field gradient value of 1 × 10−9 V/m2 ((1 mV/m)/1000 km) at L = 6‐7 is found. Charge neutrality requires coupling with the ionosphere through electrons moving along magnetic field lines, and such electrons may be the cause of multiple auroral arcs.

In a piezoelectric material, an applied uniform strain can induce an electric polarization (or vice versa). Crystallographic considerations restrict this technologically important property to noncentrosymmetric systems. It has been shown both mathematically and physically that a nonuniform strain can potentially break the inversion symmetry and induce polarization in nonpiezoelectric materials. The coupling between strain gradients and polarization, and conversely between strain and polarization gradients, is investigated in this work. While the conventional piezoelectric property is nonzero only for certain select materials, the nonlocal coupling of strain and electric field gradients is (in principle) nonzero for all dielectrics, albeit manifesting noticeably only at the nanoscale, around interfaces or in general in the vicinity of high field gradients. Based on a field theoretic framework accounting for this phenomena, we (i) develop the fundamental solutions (Green's functions) for the governing equations, and (ii) motivated by eventual applications for quantum dots, solve the general embedded mismatched inclusion problem with explicit results for the spherical and cylindrical shape. Expectedly, our results for the aforementioned problems are size dependent and indicate generation of high electric fields reaching values of approximately hundreds of kV/m in selected sizes and locations---even in isotropic centrosymmetric nonpiezoelectric materials.

In order to obtain any relation between an electric field gradient (E.F.G.) at the site of 23 Na nucleus in Sodium Nitrite crystals and spontaneous polarization, the observed E.F.G. along the b -axis in the ferroelectric phase is formally expanded with the long range order parameter S . The E.F.G. in a fictitious perfectly ordered state and in a disordered one are calculated as a function of temperature. The E.F.G. of both fictitious states are calculated in a point charge approximation on the basis of a simplified model. The calculated S from the first order expansion series in terms of the observed E.F.G. and the calculated E.F.G. shows a good agreement with the S obtained from the observed spontaneous polarization except in the vicinity of the transition temperature. An effect of the order-disorder rearrangement of NO 2 - ion is concluded to reflect the temperature dependence of the E.F.G. observed in the ferroelectric phase.