Enhanced size-dependent piezoelectricity and elasticity in nanostructures due to the flexoelectric effect

Majdoub, M. S.; Sharma, Pradeep; Çağın, Tahir

doi:10.1103/physrevb.77.125424

Cited by 540 publications

(268 citation statements)

References 41 publications

(37 reference statements)

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“…For example, in nanostructures such as nanowires and nanorods, strain relaxation is facile, possibly causing a large flexoelectric effect. Sharma and co-workers [50] have already studied the flexoelectric effect in such nanostructures. In particular, they have predicted that flexoelectricity might be used to enhance pieozoelectric responses above bulk values.…”

Section: Future Perspectivesmentioning

confidence: 99%

Giant flexoelectric effect through interfacial strain relaxation

Lee

Noh

2012

Phil. Trans. R. Soc. A.

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Interfacial strain gradients in oxide epitaxial thin films provide an interesting opportunity to study flexoelectric effects and their potential applications. Oxide epitaxial thin films can exhibit giant and tunable flexoelectric effects, which are six or seven orders of magnitude larger than those in conventional bulk solids. The strain gradient in an oxide epitaxial thin film can generate an electric field above 1 MV m −1 by flexoelectricity, large enough to affect the physical properties of the film. Giant flexoelectric effects on ferroelectric properties are discussed in this overview of recent experimental observations.

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Section: Future Perspectivesmentioning

confidence: 99%

Giant flexoelectric effect through interfacial strain relaxation

Lee

Noh

2012

Phil. Trans. R. Soc. A.

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“…Our use of linear interpolation restricts us from capturing potentially important effects based on strain gradients, in particular the phenomenon of flexoelectricity that can be relevant at small scales [MSC08]. However, this phenomenon is relevant at large strain gradients that typically can only occur in localized regions of the sample.…”

Section: Discussionmentioning

confidence: 99%

Atomistic-to-continuum multiscale modeling with long-range electrostatic interactions in ionic solids

Marshall

Dayal

2014

Journal of the Mechanics and Physics of Solids

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We present a multiscale atomistic-to-continuum method for ionic crystals with defects. Defects often play a central role in ionic and electronic solids, not only to limit reliability, but more importantly to enable the functionalities that make these materials of critical importance. Examples include solid electrolytes that conduct current through the motion of charged point defects, and complex oxide ferroelectrics that display multifunctionality through the motion of domain wall defects. Therefore, it is important to understand the structure of defects and their response to electrical and mechanical fields. A central hurdle, however, is that interactions in ionic solids include both short-range atomic interactions as well as long-range electrostatic interactions. Existing atomistic-to-continuum multiscale methods, such as the Quasicontinuum method, are applicable only when the atomic interactions are short-range. In addition, empirical reductions of quantum mechanics to density functional models are unable to capture key phenomena of interest in these materials.To address this open problem, we develop a multiscale atomistic method to coarse-grain the longrange electrical interactions in ionic crystals with defects. In these settings, the charge density is rapidly varying, but in an almost-periodic manner. The key idea is to use the polarization density field as a multiscale mediator that enables efficient coarse-graining by exploiting the almost-periodic nature of the variation. In regions far from the defect, where the crystal is close-to-perfect, the polarization field serves as a proxy that enables us to avoid accounting for the details of the charge variation. We combine this approach for long-range electrostatics with the standard Quasicontinuum method for short-range interactions to achieve an efficient multiscale atomistic-to-continuum method. As a side note, we examine an important issue that is critical to our method: namely, the dependence of the computed polarization field on the choice of unit cell. Potentially, this is fatal to our coarse-graining scheme; however, we show that consistently accounting for boundary charges leaves the continuum electrostatic fields invariant to choice of unit cell.

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“…It is worth remarking that theories of electroelastic media which include strain gradients in the constitutive equations have been recently investigated to account for the so called "flexoelectric effect" which consists in the converse effect, where polarization arises due to a strain gradient (Maranganti et al 2006, Majdoub et al 2008. The interest into both direct and converse effects is motivated by their suitability to account for a noticeable electromechanical coupling in thin structures and at interfaces or surfaces.…”

Section: Introductionmentioning

confidence: 99%

Dynamic eigenvector problem in thermoelectroelasticity of dissipative ionic crystals

Romeo

2010

European Journal of Mechanics - A/Solids

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A two dimensional problem in the Stroh formalism is derived for the continuum theory of thermoelectroelasticity with polarization gradients. Dissipative effects are accounted for, according to a constitutive model outlined in previous works. The eigenvector problem is studied in the frequency domain to obtain a representation of the solution in terms of two classes of modes corresponding to opposite signs of imaginary part of the eigenvalues. Impedance and admittance tensors are exploited to express the energy flux of the thermoelectroelastic transformed field across an interface S. The compatibility conditions at S are also derived. The eigenvector equations are then rewritten in the time domain to obtain two convolution-type integral equations for the Hilbert transforms of the real fields corresponding to each mode.

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Enhanced size-dependent piezoelectricity and elasticity in nanostructures due to the flexoelectric effect

Cited by 540 publications

References 41 publications

Giant flexoelectric effect through interfacial strain relaxation

Giant flexoelectric effect through interfacial strain relaxation

Atomistic-to-continuum multiscale modeling with long-range electrostatic interactions in ionic solids

Dynamic eigenvector problem in thermoelectroelasticity of dissipative ionic crystals

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