Linear Piezoelectricity Research Articles

Nanoscale Insights into Photovoltaic Hysteresis in Triple-Cation Mixed-Halide Perovskite: Resolving the Role of Polarization and Ionic Migration.

Triple-cation mixed-halide perovskites of composition Csx (FAy MA1- y )1 -x Pb(Iz Br1 -z )3 (CsFAMA) have been reported to possess excellent photovoltaic efficiency with minimal hysteresis; in this work, nanoscale insight is shed into the roles of illumination-induced polarization and ionic migration in photovoltaic hysteresis. By examining the concurrent evolution of ionic distribution and spontaneous polarization of CsFAMA under light illumination using dynamic-strain-based scanning probe microscopy, strong linear piezoelectricity arising from photoenhanced polarization is observed, while ionic migration is found to be not significantly increased by lightening. Nanoscale photocurrents are mapped under a series of biases using conductive atomic force microscopy, revealing negligible difference between forward and backward scans, and local IV curves reconstructed from principal component analysis show minimal hysteresis of just 1%. These observations at the nanoscale are confirmed in a macroscopic perovskite solar cell made of CsFAMA, exhibiting a high efficiency of 20.11% and with hysteresis index as small as 3%. Ionic migration, polarization, and photocurrent hysteresis are thus directly correlated at the nanoscale, and photoenhanced polarization in triple-cation mixed-halide perovskites is established, which does not contribute to the photovoltaic hysteresis.

An immersed boundary hierarchical B-spline method for flexoelectricity

This paper develops a computational framework with unfitted meshes to solve linear piezoelectricity and flexoelectricity electromechanical boundary value problems including strain gradient elasticity at infinitesimal strains. The high-order nature of the coupled PDE system is addressed by a sufficiently smooth hierarchical B-spline approximation on a background Cartesian mesh. The domain of interest is embedded into the background mesh and discretized in an unfitted fashion. The immersed boundary approach allows us to use B-splines on arbitrary domain shapes, regardless of their geometrical complexity, and could be directly extended, for instance, to shape and topology optimization. The domain boundary is represented by NURBS, and exactly integrated by means of the NEFEM mapping. Local adaptivity is achieved by hierarchical refinement of B-spline basis, which are efficiently evaluated and integrated thanks to their piecewise polynomial definition. Nitsche’s formulation is derived to weakly enforce essential boundary conditions, accounting also for the non-local conditions on the non-smooth portions of the domain boundary (i.e. edges in 3D or corners in 2D) arising from Mindlin’s strain gradient elasticity theory. Boundary conditions modeling sensing electrodes are formulated and enforced following the same approach. Optimal error convergence rates are reported using high-order B-spline approximations. The method is verified against available analytical solutions and well-known benchmarks from the literature.

Static and dynamic response of graphene nanocomposite plates with flexoelectric effect

In this work, the electromechanical behaviors of graphene reinforced nanocomposite (GRNC) plates with flexoelectric effect were studied by using Kirchhoff's plate theory, Navier's solution and extended linear piezoelectricity theory in conjunction with the mechanics of materials (MOM) and finite element models. The static and dynamic responses of simply supported flexoelectric GRNC nanoplates under different loadings such as uniformly distributed, varying distributed, inline and point loads were investigated. The developed MOM and FE models envisage that the effective piezoelectric constants of a GRNC account for the actuating capability in its transverse direction due to the applied electric field in the plane. The elastic properties of pristine and defective graphene sheets were also estimated via molecular dynamics (MD) simulations and the obtained results are found in good agreement with the existing experimental and numerical results. Our results reveal that the flexoelectric effect on the static and dynamic responses of GRNC nanoplate is substantial and cannot be neglected. The electromechanical response of GRNC plates can be engineered to attain the desired deflection characteristics and resonant frequencies for a range of nanoelectromechanical systems using different boundary conditions as well as geometrical parameters such as aspect ratio/thickness of nanoplate and volume fraction of graphene.

Research on elastic modes of circular deformable mirror for adaptive optics and active optics corrections.

In this paper, an elastic mode method of deformable mirror is proposed to decompose arbitrary wave-front errors of adaptive optics system. The elastic modes are derived with an analytical method of linear piezoelectricity based on a bimorph piezoelectric deformable mirror (BPDM), and the three-dimensional formulas of elastic modes are presented. Here a BPDM with an aperture of 165 mm as an example is numerically studied. Two different kinds of dynamic boundary conditions are considered, and the dependence of the elastic modes aberrations upon the orders and rotational symmetries is evaluated. Besides, a comparative study for elastic mode and Zernike polynomials is presented in the numerical analysis. The results have demonstrated that the elastic mode method can be not only used instead of Zernike polynomials, but also more effective to decompose arbitrary wave-front errors of a deformable mirror. Furthermore, finite element analysis method is used to validate the analytic method. The conclusions have shown reasonably consistent results between the two methods.

Atomic-Scale Insight into the Reversibility of Polar Order in Ultrathin Epitaxial Nb:SrTiO <sub>3</sub>/BaTiO <sub>3</sub> Heterostructure and Its Implication to Resistive Switching

Ferroelectric heterostructures with bi-stable state of polarization are appealing for data storage as well as tunable functionalities such as memristor behavior. While an increasing number of experimental and theoretical studies suggest that polarization persists in ultrathin epitaxial heterostructures approaching just a couple of unit cells, the switching of such polar order is much less well understood, and whether polarization can be reversed in ultrathin ferroelectric heterostructures remains to be answered. Here we fabricate high-quality 7-unit cell thick BaTiO3 (BTO) films on Nb-doped single crystalline SrTiO3 (NSTO) substrate, and demonstrate their apparent yet unambiguously false polarization reversal due to charge injection using comprehensive piezoresponse force microscopy (PFM) studies. The presence of weak polar order consistent with linear piezoelectricity is confirmed at the atomic scale by high resolution integrated differential phase contrast (IDPC) of transmission electron microscopy (TEM) as well as macroscopic second harmonic generation (SHG), while the lack of polarization reversal under the voltage applied is supported by density functional theory calculation showing the persistence of dead layer on the surface. Nevertheless, poling-induced electric conduction differing by two orders of magnitude is observed, demonstrating resistive switching in ferroelectric heterostructure in the absence of polarization reversal, even with weak polar order. Our finding has technological implications on emerging memristor applications with potentially more accessible states than bi-stable polarization modulated mechanism, and raises technical challenges to unambiguously demonstrate polarization switching in ultrathin films at their critical size limit.

Bending of piezoelectric beams with the flexoelectric effect under applied load at any position

Flexoelectricity describes the coupling between polarization and strain gradients and presents a strong size dependence at nanoscale. In the current work, based on the extended linear piezoelectricity theory with flexoelectricity, we study bending of piezoelectric beams with consideration of flexoelectric effect. When a concentrated force at any position and electric voltage is exerted, the expression for bending deflection of simply-supported and clamped beams is derived. The obtained results show that flexoelectric effect can cause a softer elastic behavior of simply-supported and clamped beams. Sensitivity analysis of the transverse deflection and bending moment is made for two typical boundary conditions. Flexoelectric effect has a more significant effect on the bending response of a piezoelectric beam with smaller thickness.

On sliding interface contact in layered smart structures

• A dynamic, rough contact model is developed for smart structures. • Partial contact conditions and limiting cases are concerned. • The electric field and magnetic field are given explicitly. • The critical loading to achieve the full contact is determined. • Influences of the velocity and the gap are demonstrated. Based on the linear piezoelectricity and magnetoelectroelasticity theories, this study presents an exact solution for a frictionless, dynamic periodic contact problem of smart structures. Anisotropic piezoelectric materials and anisotropic magneto-electro-elastic materials both with wavy surfaces moves smoothly. The Galilean transformation and the dual series equation methods are used to derive exact solutions for dynamic wavy surface contact problem. The stresses, displacements, electric field and magnetic field are given explicitly for partial contact conditions. The influences of the velocity and the gap at the crests of the wavy surfaces on various physical quantities are detailed for the selected material coefficients of piezoelectric materials PVDF and magneto-electro-elastic materials BaTiO 3 − CoFe 2 O 4 . The illustrative examples imply that a higher critical loading leads to a full contact under two conditions: (1) at a higher velocity or (2) with an increased gap at the crests of the wavy surfaces. The largest magnitude of the surface normal stresses can be relieved by either lowering the velocity or reducing the gap at the crests of the wavy surfaces. The largest magnitudes of the surface electrical displacements and magnetic inductions occur at the edges of the contact region with spikes occurring, which suggests that the edges of the contact region are the likely locations of potential crack initiation and propagation.

Improving piezoelectric and pyroelectric properties of electrospun PVDF nanofibers using nanofillers for energy harvesting application

In this study, it was aimed to increase the piezoelectric and pyroelectric properties of electrospun polyvinylidene fluoride (PVDF) nanofibers simultaneously by using specific nanofillers. Graphene oxide (GO), graphene, and halloysite nanotubes with different concentrations (0, 0.05, 0.4, and 1.6% wt/wt) were combined with PVDF solution and were fabricated in the form of nanofibers through electrospinning. Pyroelectric properties of samples were measured by submerging sealed samples in hot water (360°K) and ice (270°K). The piezoelectric properties of the samples were evaluated through bending tests. The microstructural, mechanical, and thermal properties of the electrospun PVDF nanocomposite were investigated using scanning electron microscope, Instron instrument, and thermogravimetric analysis, respectively. To further support the experimental observations for generating electric voltage in the bended nanogenerator, the PVDF nanogenerator (PNG) was also modeled by a finite element analysis based on the theory of linear piezoelectricity using COMSOL Multiphysics simulation software. Experimental results showed that adding nanofillers could improve the piezoelectric and pyroelectric properties of all samples, associated with the increment of β‐phase in the nanofibers. It was concluded that adding nanofillers could increase pyroelectricity about 50% more than piezoelectricity in pristine PVDF nanofiber web. The PNG containing 1.6 wt% GO showed the highest efficiency in terms of piezoelectricity and pyroelectricity. In addition, the results showed that the ratio of piezoelectric to pyroelectric coefficients was constant (~1.5) and it was independent of the nanofiller type and content. The effect of external force and vibration frequency on the output voltage was also investigated. Increasing the compressive force and vibration frequency caused a greater output voltage. Finally, the fabricated nanogenerator was integrated on insole and elbow to investigate its energy harvesting capabilities from body movement.

Effect of flexoelectricity on the electromechanical response of graphene nanocomposite beam

Owing to its unique multifunctional and scale-dependent physical properties, graphene is emerged as promising reinforcement to enhance the overall response of nanotailored composite materials. Most recently, the piezoelectricity phenomena in graphene sheets was found through interplay between different non-centrosymmetric pores, curvature and flexoelectricity phenomena. This has added new multifunctionality to existing graphene and it seems the use of piezoelectric graphene in composites has yet to be fully explored. In this article, the mechanics of materials and finite element models were developed to predict the effective piezoelectric and elastic (piezoelastic) properties of the graphene reinforced nanocomposite material (GRNC). An analytical model based on the linear piezoelectricity and Euler beam theories was also developed to investigate the electromechanical response of GRNC cantilever beam under both electrical and mechanical loads accounting the flexoelectric effect. Furthermore, molecular dynamics simulations were carried out to determine the elastic properties of graphene which were used to develop the analytical and numerical models herein. The current results reveal that the flexoelectric effect on the elastic behavior of bending of nanocomposite beams is significant. The electromechanical behavior of GRNC cantilever beam can be tailored to achieve the desired response via a number of ways such as by varying the volume fraction of graphene layer and the application of electrical load. Our fundamental study highlights the possibility of developing lightweight and high performance piezoelectric graphene based nanoelectromechanical systems such as sensors, actuators, switches and smart electronics as compared with the existing heavy, brittle and toxic piezoelectric materials.

Nonlinear vibrations of elastic beam with piezoelectric actuators

This paper presents theoretical and experimental investigations into nonlinear flexural vibrations of a structure composed of a host beam with piezoelectric ceramic actuators symmetrically bonded to its top and bottom surfaces. The composite beam is supported at its ends to completely restrain axial displacements or to impose the displacement of one or both ends. Applying voltage to piezoelectric actuators one creates prestress which can stabilize the structure when the external compressive force appears. The analytical model for describing flexural vibration of a beam under both the external load and piezoelectric actuation is based on the Euler–Bernoulli beam. The piezo material exhibits linear piezoelectricity with constitutive equations including electromechanical coupling. Due to geometrical nonlinearity, the solution to the problem has been obtained by using the Lindstedt-Poincare perturbation method. The main results concern the effect of the residual piezo force on the non-linear vibration frequency of the structure. In the experimental part of the study two laboratory stands have been designed and built for three and five segmented beams to find out and prove the effect of the electric field on the residual force and the natural frequency of both systems. Very good agreement between theoretical and experimental results has been observed.

Piezoelectricity of atomically thin WSe2 via laterally excited scanning probe microscopy

Lattices of odd-layered two-dimensional (2D) transition metal dichalcogenides (TMDs) such as WSe2 are non-centrosymmetric, and thus could possess linear piezoelectricity that is attractive for applications such as nanoelectromechanical systems (NEMS) and nanogenerators. Measuring the electromechanical coupling of 2D TMDs, however, is rather challenging, since its D3h point group symmetry makes conventional piezoresponse force microscopy (PFM) inapplicable. Here we develop a lateral excitation scanning probe microscopy (SPM) technique that enables mapping of the piezoelectric response of atomically thin WSe2 directly on a substrate with high spatial resolution. Planar electrodes are used to excite piezoelectric vibrations while imposing anisotropic in-plane mechanical constraint to the WSe2, resulting in an out-of-plane deformation due to Poisson's effect that can be measured by an SPM probe. Using this technique, we show that WSe2 monolayer and trilayers exhibit strong electromechanical response linear to the applied excitation biases that is distinct from the substrate, while WSe2 bilayers show negligible electromechanical response as expected. The effective piezoelectric coefficient is estimated to be 5.2 pm/V from the measurement, consistent with theoretical predictions. This method can be conveniently applied to a wide range of 2D materials with similar symmetry.

Piezoelectricity and valley chern number in inhomogeneous hexagonal 2D crystals

Conversion of mechanical forces to electric signal is possible in non-centrosymmetric materials due to linear piezoelectricity. The extraordinary mechanical properties of two-dimensional materials and their high crystallinity make them exceptional platforms to study and exploit the piezoelectric effect. Here, the piezoelectric response of non-centrosymmetric hexagonal two-dimensional crystals is studied using the modern theory of polarization and k·p model Hamiltonians. An analytical expression for the piezoelectric constant is obtained in terms of topological quantities, such as the valley Chern number. The theory is applied to semiconducting transition metal dichalcogenides and hexagonal Boron Nitride. We find good agreement with available experimental measurements for MoS2. We further generalize the theory to study the polarization of samples subjected to inhomogeneous strain (e.g., nanobubbles). We obtain a simple expression in terms of the strain tensor, and show that charge densities ≳1011cm−2 can be induced by realistic inhomogeneous strains, ϵ ≈ 0.01–0.03.

An analysis of PN junctions in piezoelectric semiconductors

We present a theoretical study on the equilibrium state of a PN junction, which is created by two piezoelectric semiconductor half spaces doped oppositely, based on the equations of linear piezoelectricity and the conservation of charge for holes and electrons. The nonlinearity associated with the drift currents of electrons and holes, which appears as products of the unknown carrier concentrations and the unknown electric field, is linearized for small carrier concentration perturbations. An analytical solution is rigorously derived, which is able to show the shaping of the PN junction near the interface. The electromechanical fields and concentrations of electrons and holes near the interface of the PN junction, and the forward-bias current-voltage characteristics of the PN junction under different applied stresses, are calculated and discussed. The effects of a few physical parameters on the properties of the PN junction are investigated as well.

Optimal shape control of piezolaminated beams with different boundary condition and loading using genetic algorithm

Piezoelectric actuators are effectively used to control the response of light weight structures in shape, vibration and buckling. Optimization for the shape control of piezoelectric beam is the recent challenge which requires proper numerical technique to perform. The shape control of a composite beam using surface-bounded piezoelectric actuators has been investigated in the present work. The mathematical model is developed using two-node Timoshenko beam element coupling with the theory of linear piezoelectricity. First-order shear deformation theory is employed in the formulation to consider the effect of shear. In the analysis, the effect of the actuators position for different set of boundary conditions is investigated. For different boundary conditions which include clamped-free-, clamped–clamped- and simply supported beam, optimisation of piezoelectric patch location is investigated. Moreover, a genetic algorithm is adopted and implemented to optimize the required voltage to maintain the desired shape of the beam. This optimization technique is applied to different cases of composite beams with varying the boundary condition.

Theoretical model of homogenized piezoelectric materials with small non-collinear periodic cracks

An analytical model for the homogenization of a piezoelectric material with small periodic fissures is proposed on the basis of the method of asymptotic expansions for the elastic displacement, the electric scalar potential and the test functions. Starting from the variational formulation of the three-dimensional problem of linear piezoelectricity, we have at first obtained that concerning a cracked piezoelectric structure, before the implementation of homogenized equations for a piezoelectric structure with a periodic distribution of cracks. It then follows, the characterization of the homogenized law between the mechanical strain and the electric potential, on one hand, and the mechanical stress and the electric displacement, on the other hand. Contrary to the previous investigations, the focus of this paper is the development of a mathematical model taking the non-parallelism of cracks into account.

Optical performance of piezoelectrically actuated MEMS tunable lenses with various pupil geometries

A square geometry for the diaphragm of microelectromechanical systems (MEMS) tunable lenses with circular pupils is often used. This square diaphragm introduces aberrations that would not be present for a circular diaphragm and the question arises of whether it could be advantageous to also consider other than circular geometries for the pupil. To investigate this question, we have extended a previously established modeling framework for piezoelectrically actuated MEMS tunable lenses to devices with general polygonal-shaped pupils. It models the static optoelectromechanical coupling for symmetric configurations based on laminated-plate theory, linear piezoelectricity, and ray tracing. The framework helps to find geometrical parameters that give a diffraction-limited tunable lens with a minimum F-number. The tunable lens’ optical performance and its focusing capability, alone and in combination with a fixed lens, were calculated in terms of object distances and actuation voltages. Using the modeling framework, we show that the modulation transfer function of the tunable lens and the fixed lens combination remains the same up to a ±10-deg field of view after voltage adjustment to refocus on near objects. In addition, we found that pupil masking of the tunable lens can provide a beneficial tradeoff between the lens dioptric power and its RMS wavefront error.

Dynamic electromechanical behavior of single-crystal α-quartz

Electrical response from dynamic compression tests on x-cut single crystal α-quartz specimens at strain rates of 103 s−1 reveal nonsimilar stress-charge behavior during damage evolution. Specifically, when quartz is undergoing extensive and irreversible dynamic brittle fracture under a compressive stress impulse of up to 1.8 GPa, the effective piezoelectric stress coefficient (d) exhibits approximately a 24% increase from loading to unloading. The experimental results are examined in the framework of the theory of linear piezoelectricity in order to understand the role of increasing crack density and crystal orientation on electroelastic properties.

Photo-induced ferroelectric switching in perovskite CH3NH3PbI3 films.

The photovoltaic conversion efficiency of perovskite solar cells based on organic-inorganic CH3NH3PbI3 has risen spectacularly from 3.8% to over 20% in just seven years, yet quite a few important fundamental issues have not been settled, and the role of spontaneous polarization remains poorly understood. While piezoresponse force microscopy (PFM) has been adopted to probe possible ferroelectricity in CH3NH3PbI3, the reported data are often conflicting and inconclusive, due to the complexity in the apparent piezoresponse and its switching that may arise from ionic motions, electrostatic interactions, and other electromechanical mechanisms. Here, using a combination of microscopic and macroscopic measurements, we unambiguously establish the linear piezoelectricity of CH3NH3PbI3 arising from its spontaneous polarization, which can be switched by an electric field, though other electromechanical contributions such as ionic motions are also shown to exist. More importantly, we demonstrate strong interactions between polarization and light in technologically relevant CH3NH3PbI3 films with good conversion efficiencies, observing that the spontaneous polarization can also be switched by light illumination in the absence of an electric field. The light is shown to reduce the coercive voltage of CH3NH3PbI3 and shifts its nucleation bias, suggesting that the photo-induced switching is caused by ionic motions in combination with a photovoltaic field. This set of studies offer strong evidence on the interactions among photo-induced charges, polarization, and ions in perovskite CH3NH3PbI3, and these fundamental observations lay the ground for answering the technologically important question regarding the effects of ferroelectricity on its photovoltaic conversion.

Modeling framework for piezoelectrically actuated MEMS tunable lenses.

WWe report a modeling framework for evaluating the performance of piezoelectrically actuated MEMS tunable lenses. It models the static opto-electromechanical coupling for symmetric configurations of piezoelectric actuators based on the laminated-plate theory, linear piezoelectricity, and ray tracing. With these assumptions, it helps to find geometrical parameters for actuators on clamped square or circular diaphragms that give a diffraction-limited tunable lens with minimum F-number. The tunable lens' optical performance and its focusing capability, alone and in combination with a paraxial fixed lens, were calculated in terms of object distance and actuation voltage. Using the modeling framework, we confirmed that the modulation transfer function for objects located at different distances remains the same after voltage adjustment.

Theoretical analysis of a piezoelectric ceramic tube polarized tangentially for hydraulic vibration energy harvesting

A piezoelectric energy harvester, consisting of a long and thin lead zirconate titanate ceramic tube with tangential polarization, is proposed in this paper for scavenging vibration energy. This harvester operates in 3–3 mode while subjected to radial dynamic hydraulic pressure acting at the inner surface of the tube. Based on the linear piezoelectricity theory, the analytical solutions for the output power density of the device and their dependence upon the vibration frequency, the geometrical parameters of the tube, and the impedance of the load circuit are derived. The numerical results indicate the considerably enhanced performances by adjusting the thickness and radius of the ceramic tube. The stress in the ceramic is calculated to ensure that the applied force is within the operational range. The load impedance has a great effect on the performance of the harvester. A wideband energy harvester, which usually consisted of complex architectures in previous research works, is obtained in this pare by just adjusting the value of the load impedance. This opens up a new approach for us to design wideband energy harvesters with simple structures and thus small size, light weight and low cost.