Open-circuit Electrical Boundary Conditions Research Articles

Active vibration control of piezoelectric smart beams with radial basis function generated finite difference collocation method

A local collocation method based on finite difference generated radial basis functions considering supplementary polynomials is used to solve the governing equations of cantilever piezoelectric smart beams. The natural modes of vibration of a bimorph and a three-layered smart beam with an interior aluminium core are analysed for both open-circuit and closed-circuit electrical boundary conditions. Very accurate results are obtained at a low computational cost. Subsequently, a constant gain velocity feedback active vibration control system is implemented, and the time and frequency response functions of both beams subjected to initial impulse and displacement conditions are investigated. Different values of the applied gain and varying thickness of the piezoelectric layers are analysed. The governing equations are established using equivalent-single-layer first-order-shear-deformation theory with through-the-thickness quadratic layerwise electric potential for improved accuracy.

Large amplitude vibration of FG-CNT reinforced composite annular plates with integrated piezoelectric layers on elastic foundation

The aim of the present study is to investigate the applications of piezoelectric layers and carbon nanotubes (CNTs) in enhancing nonlinear vibration behaviors of functionally graded carbon nanotube reinforced composite (FG-CNTRC) annular plates. A nonlinear formulation is developed with regard to the first-order shear deformation theory, von Karman geometrical nonlinearity in conjunction with the Hamilton principle. A Pasternak elastic foundation is assumed to be in contact with the annular plate during deformation. The distribution of electric potential across the thickness of piezoelectric layers is simulated via a combination of sinusoidal and linear functions. Both closed and open circuit electrical boundary conditions are taken into account for the bottom and top surfaces of piezoelectric layers. Generalized differential quadrature method is utilized to discretize the nonlinear equations of motion, Maxwell equation and boundary conditions, and then direct iterative method is used to solve the nonlinear system of equations. An extensive parametric study is directed to provide an insight into effects of the thickness of piezoelectric layers, piezoelectric materials, volume fraction and distribution of CNTs, geometrical parameters, elastic foundation coefficient, and mechanical/electrical boundary conditions on the nonlinear dynamic responses of the annular plate. It is found that both distribution and volume fraction of CNTs have a remarkable effect on nonlinear natural frequencies of FG-CNTRC annular plates. It is also revealed that the type of piezoelectric materials, thickness of piezoelectric layers and electrical boundary condition play a pivotal role in improving dynamic responses of FG-CNTRC annular plates. It is also found that presence of elastic foundation increases hardening responses of FG-CNTRC annular plates.

Electromechanical coupling in piezoelectric nanobeams due to the flexoelectric effect

The flexoelectric effect is a coupling of polarization and strain gradient, which exists in a wide variety of materials and may lead to strong size-dependent properties at the nanoscale. Based on an extension to the classical beam model, this paper investigates the electromechanical coupling response of piezoelectric nanobeams with different electrical boundary conditions including the effect of flexoelectricity. The electric Gibbs free energy and the variational principle are used to derive the governing equations with three types of electrical boundary conditions. Closed-form solutions are obtained for static bending of cantilever beams. The results show that the normalized effective stiffness increases with decreasing beam thickness in the open circuit electrical boundary conditions with or without surface electrodes. The induced electric potential due to the flexoelectric effect is obtained under the open circuit conditions, which may be important for sensing or energy harvesting applications. An intrinsic thickness depending on the material properties is identified for the maximum induced electric potential. The present results also show that flexoelectricity has a more significant effect on the electroelastic responses than piezoelectricity at the nanoscale. Our analysis in the present study can be useful for understanding of the electromechanical coupling in nanobeams with flexoelectricity.

The effect of the surface electrode distributions on domain structures of ferroelectric thin films

Various domain structures in ferroelectric thin films with four different surface interdigital electrodes are simulated based on the time-dependent Ginzburg-Landau method. The four different electrode distributions are that (a) both surfaces are symmetrically arranged interdigital electrodes, (b) top surface is covered with interdigital electrode while bottom surface is covered with full electrode, (c) both surfaces are alternately arranged interdigital electrodes and (d) top surface is covered with interdigital electrodes while bottom is not covered with electrode. These electrode distributions could be converted to corresponding electrical boundary conditions of the phase field equations. Compared with ideal short circuit and open circuit electrical boundary conditions, there are some special domain structures (vortices, flux-closure structures and a/c domains) due to the change of depolarization electric energy and Landau energy with different surface electrodes. The domain structures in ferroelectric thin films have an obvious size effect with the surface interdigital electrodes. These results indicate we can obtain the various domain structures of ferroelectric thin films by turning different surface electrode distributions.

Phase-transition character in (Ba0.50,Sr0.50)TiO3 nanodots from first principles

A first-principles-derived scheme combined with an efficient Monte Carlo technique is performed to investigate the character of phase transitions in (Ba0.50,Sr0.50)TiO3 (BST50) nanodots under ideal short-circuit (SC) and open-circuit (OC) electrical boundary conditions, and the corresponding properties are subsequently compared to the properties of bulk BST50. Our calculations indicate that the ferroelectric properties change dramatically when transitioning from 3D (bulk) to 0D (nanodot) systems under short-circuit conditions. While BST bulk exhibits three first-order ferroelectric phase transitions, BST dot shows a single second-order ferroelectric phase transition. On the other hand, new insight into the character and signature of the phase transition associated with a toroid moment of polarization, which occurs in nanodots under open-circuit conditions, is provided.

Domain structures of ferroelectric films under different electrical boundary conditions

A two-dimensional phase field simulation of ferroelectric films is used that incorporates Landau-Devonshire energy, gradient energy and depolarization electrical energy. A new intermediate electrical boundary condition is firstly presented to study the effects on domain structures of ferroelectric films. Two-dimensional simulations of domain structures are carried out under the open circuit (OC), short circuit (SC) and intermediate (IM) electrical boundary conditions. The simulation results show that there are multi-vortices domains and 180° multi-stripes domains under OC and SC electrical boundary condition, respectively. And there is a transition from multi-vortices domains to 180° multi-stripes domains under the IM electrical boundary condition due to competition between the elastic energy and depolarization electrical energy in the films. The present IM electrical boundary condition can completely characterize different degrees of compensation for surface charges by the electrodes and further describe the effect on the depolarization electrical energy. It can also be reduced to OC and SC electrical boundary conditions. Hence, for nano-thin ferroelectric films, the IM electrical boundary condition plays an important role in the formation of domain structures.

Finite size effects in ferroelectric-semiconductor thin films under open-circuit electric boundary conditions

General features of finite size effects in the ferroelectric-semiconductor film under open-circuit electric boundary conditions are analyzed using Landau-Ginzburg-Devonshire theory and continuum media electrostatics. The temperature dependence of the film critical thickness, spontaneous polarization, and depolarization field profiles of the open-circuited films are found to be significantly different from the characteristics of short-circuited ones. In particular, we predict the re-entrant type transition boundary between the mono-domain and poly-domain ferroelectric states due to reduced internal screening efficiency and analyzed possible experimental scenarios created by this mechanism. Performed analysis is relevant for the quantitative description of free-standing ferroelectric films phase diagrams and polar properties. Also our results can be useful for the explanation of the scanning-probe microscopy experiments on free ferroelectric surfaces.

Strain-induced control of domain wall morphology in ultrathinPbTiO3films

Ab initio effective Hamiltonian simulations reveal a strain-induced control of domain morphology in epitaxial ${\mathrm{PbTiO}}_{3}$ ultrathin films being under open-circuit electrical boundary conditions. More precisely, rather different out-of-plane domain structures are found to be the ground state, depending on the value of the misfit strain. Examples include domain walls lying in different crystallographic planes or even being wandering. Analysis of the computations allows us to reveal the precise interactions responsible for such strain-driven domain reorganization.

Effects of a rotating electric field on the properties of epitaxial (001) Pb(Zr,Ti)O3 ultrathin film: a first-principles-based study

Pb(Zr,Ti)O3 ultrathin films under open-circuit electrical boundary conditions and subjected to an electric field rotating in the () plane are investigated via the use of an effective Hamiltonian, for different magnitudes of this field. Varying the direction and magnitude of the electric field leads to specific reorganization of dipoles into original configuration states, whose microstructures and macroscopic properties are revealed. In particular, a novel (direction of the electric field—versus—magnitude of the electric field) phase diagram is reported here. The field-induced correlation between the polar distortions and the oxygen octahedral tilting is also discussed.

Controllable acoustic rectification in one-dimensional piezoelectric composite plates

Theoretical studies are presented for the band structures and power transmission spectra for both symmetric and asymmetric Lamb wave modes in a one-dimensional piezoelectric composite plate consisting of piezoelectric ceramics placed periodically in epoxy by the plane wave expansion method and the harmonic response analysis method, respectively. The one-way transmission, two-way transmission, and two-way forbidden models of acoustic rectification for Lamb waves can be established in specific frequency ranges by introducing corresponding modes conversion and selection mechanisms, and the steady-state displacement fields of these models are also calculated for the proposed plate. The numerical results show that the power extinction ratio for one-way transmission model is up to 104. The piezoelectric composite plate can be switched between these models rapidly and efficiently only by applying the open-circuit and short-circuit electric boundary conditions antisymmetrically or symmetrically on the piezoelectric ceramic unit's boundaries instead of changing any geometrical structure, and the composite plate's architecture structure is also simple enough for the on-chip integration in the engineering field.

Thickness-Dependent Polarization of StrainedBiFeO3Films with Constant Tetragonality

We measure the ferroelectric polarization of BiFeO3 films down to 3.6 nm using low energy electron and photoelectron emission microscopy. The measured polarization decays strongly below a critical thickness of 5-7 nm predicted by continuous medium theory whereas the tetragonal distortion does not change. We resolve this apparent contradiction using first-principles-based effective Hamiltonian calculations. In ultrathin films, the energetics of near open circuit electrical boundary conditions, i.e., an unscreened depolarizing field, drive the system through a phase transition from single out-of-plane polarization to nanoscale stripe domains. It gives rise to an average polarization close to zero as measured by the electron microscopy while maintaining the relatively large tetragonal distortion imposed by the nonzero polarization state of each individual domain.

Prediction of the Magnetotoroidic Effect from Atomistic Simulations

An effective Hamiltonian technique is used to investigate the effect of applying curled electric fields on physical properties of stress-free BiFeO(3) dots being under open-circuit electrical boundary conditions. It is discovered that such fields can lead to a control of not only the magnitude but also the direction of the magnetization. Such control originates from the field-induced transformation or switching of electrical vortices and their couplings with oxygen octahedral tilts and magnetic dipoles. This control involves striking intermediate states and constitutes a novel phenomenon that can be termed a "magnetotoroidic" effect.

EpitaxialPb(Zr,Ti)O3Ultrathin Films under Open-Circuit Electrical Boundary Conditions

The temperature-versus-misfit-strain phase diagram of Pb(Zr,Ti)O3 ultrathin films under open-circuit electrical boundary conditions is simulated via the use of an effective Hamiltonian. Two novel phases, both exhibiting dipolar nanodomains and oxygen octahedral tilting, are discovered. The interplay between dipolar, antiferrodistortive, alloying, and strain degrees of freedom induces several striking features in these two phases, such as the chemical pinning of domain walls, the enhancement of oxygen octahedral tilting near the domain walls, and the existence of dipolar waves and cylindrical dipolar chiral bubbles.

Optimization of Smart Beams for Maximum Modal Electromechanical Coupling Using Genetic Algorithms

In this article, the piezoelectric coverage area of a shear deformable cantilever beam is optimized for maximum modal electromechanical coupling coefficient. A discrete layer finite element model with piezoelectric capability is implemented to solve the free vibration problem under open-circuit and short-circuit electric boundary conditions. A binary-coded genetic algorithm was used to carry out the optimization. The piezoelectric coverage locations are found to be dependent upon the mode of vibration, which is primarily due to charge cancelation at higher modes. Optimal distribution tends to cover part of the beam experiencing maximum bending. It is shown that the type of base beam material has negligible effect on the optimum locations of the piezoelectric material. Furthermore, an optimum ratio of piezoelectric-to-beam thickness exists for the first three modes.

Discovery of Incipient Ferrotoroidics from Atomistic Simulations

An effective Hamiltonian technique is used to investigate the effect of quantum vibrations on properties of stress-free KTaO3 nanodots under open-circuit electrical boundary conditions. We discover that these vibrations suppress the paraelectric-to-ferrotoroidic transition, or, equivalently, wash out the formation of vortex states. Such suppression leads to the saturation of the so-called ferrotoroidic susceptibility at low temperature, and to a peculiar local structure that exhibits short-range, needlelike correlations of the individual toroidal moments.

Electric displacement as the fundamental variable in electronic-structure calculations

Finite-field calculations in periodic insulators are technically and conceptually challenging, due to fundamental problems in defining polarization in extended solids. While significant progress has been made recently with the establishment of techniques to fix the electric field E or the macroscopic polarization P in first-principles calculations, both methods lack the ease of use and conceptual clarity of standard zero-field calculations. Here we develop a new formalism in which the electric displacement D, rather than E or P, is the fundamental electrical variable. Fixing D has the intuitive interpretation of imposing open-circuit electrical boundary conditions, which is particularly useful in studying ferroelectric systems. Furthermore, the analogy to open-circuit capacitors suggests an appealing reformulation in terms of free charges and potentials, which dramatically simplifies the treatment of stresses and strains. Using PbTiO3 as an example, we show that our technique allows full control over the electrical variables within the density functional formalism.

Coupling of surface relaxation and polarization inPbTiO3 from atomistic simulation

Molecular dynamics simulations are used to characterize ferroelectricity on the (001) surfaces ofPbTiO3 (PT), one of the most widely studied ferroelectric materials. Two differentempirical interatomic shell model potentials are used. Both PbO andTiO2 surface terminations in PT under open circuit electrical boundary conditions arecharacterized. The results are found to be in good agreement with the results of densityfunctional theory calculations. The atomic relaxations, interlayer spacings and surfacerumplings of each of the four possible surface terminations are analyzed. The deviation ofthe polarization from the bulk value is observed to be larger when the polarizationpoints out of the surface than when it points into the surface. Analysis of thesurface energies for free-standing films shows that polarization parallel to thesurface is energetically more favorable than the polarization normal to the surfaces.

Surface and Substrate Effects on the Ferroelectric Properties of PbTiO3 Ultrathin Films

The effects of the antiferrodistortive surface reconstruction and the interface with a SrTiO 3 substrate on the ferroelectric properties of PbTiO 3 ultrathin films are investigated using an interatomic potential approach with parameters determined from first-principles results. First we show that a shell model developed for the bulk describes properly the surface properties of PbTiO 3 , in particular the antiferrodistortive surface reconstruction recently observed from x-ray scattering. We investigate also the effects of the surface reconstruction on the polarization behavior of ultrathin films under open-circuit electrical boundary conditions, showing that the surface layer participates in the ferroelectricity. Finally, film-substrate interface effects on the ferroelectric properties are investigated simulating PbTiO 3 ultrathin films on a SrTiO 3 substrate.

Surface reconstruction and ferroelectricity inPbTiO3thin films

Surface and ferroelectric properties of PbTiO$_3$ thin films are investigated using an interatomic potential approach with parameters computed from first-principles calculations. We show that a model developed for the bulk describes properly the surface properties of PbTiO$_3$. In particular, the antiferrodistortive surface reconstruction, recently observed from X-ray scattering, is correctly reproduced as a result of the change in the balance of long-range Coulombic and short-range interactions at the surface. The effects of the surface reconstruction on the ferroelectric properties of ultrathin films are investigated. Under the imposed open-circuit electrical boundary conditions, the model gives a critical thickness for ferroelectricity of 4 unit cells. The surface layer, which forms the antiferrodistortive reconstruction, participates in the ferroelectricity. A decrease in the tetragonality of the films leads to the stabilization of a phase with non-vanishing in-plane polarization. A peculiar effect of the surface reconstruction on the in-plane polarization profile is found.