Erratum: “Symmetry of flexoelectric coefficients in crystalline medium” [J. Appl. Phys. <b>110</b>, 104106 (2011)]

Shu, Longlong; Wei, Xiaoyong; Ting, Pang; Yao, Xi; Wang, Chunlei

doi:10.1063/1.4896397

Cited by 16 publications

(10 citation statements)

References 1 publication

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“…13 In principle, it is one of the fundamental properties of crystalline dielectric materials and should be present universally in all 32 point groups and 7 Curie groups due to its tensor nature as an even rank tensor, just like the electrostriction coefficients. 14,15 In principle, such tensor symmetry renders highly symmetrical materials, e.g., cubic and isotropic materials, to yield electric polarization under inhomogeneous mechanical field through the direct flexoelectric effect. This greatly enhances the feasibility of flexoelectric material as new and attractive sensing/actuating solid materials.…”

Section: Introductionmentioning

confidence: 99%

Relationship between direct and converse flexoelectric coefficients

Shu

Huang

et al. 2014

Journal of Applied Physics

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Flexoelectric effect, as a universal electromechanical coupling, has drawn lots of interests in dielectric materials. However, due to the restrictions of present measurement techniques, only part of coefficients has been experimentally examined. In this study, we derived the coordinatedependent Gibbs free energy density function in the inhomogeneous spatial field to investigate the relationship between the direct and converse flexoelectric coefficients. In crystalline mediums and systems, the direct and converse flexoelectric coefficients are proved to equivalent according to the Maxwell relation. These results will broaden the application of the Maxwell relation into nonlinear spatial field, and provide the guideline for experimental measurement and prediction of flexoelectric coefficients. V C 2014 AIP Publishing LLC. [http://dx.

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Section: Introductionmentioning

confidence: 99%

Relationship between direct and converse flexoelectric coefficients

Shu

Huang

et al. 2014

Journal of Applied Physics

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“…However, in nanoscale material systems, the strain gradient could be enhanced to 10 8 m À1 , and consequently, the flexoelectric effect becomes significant. Since then, there have been extensive studies 5,6 on the symmetry [7][8][9] and magnitude [10][11][12] of flexoelectric coefficient, the effect of flexoelectricity on domain walls, [13][14][15][16] domain pattern, 17,18 and polarization rotations, 19 and the flexoelectricity-driven domain switching. [20][21][22][23] Gruverman et al introduced large strain gradient in Pb(Zr 0.2 Ti 0.8 )O 3 (PZT) thin films by bending the substrates and thereby switched the polarization.…”

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confidence: 99%

“…For cubic symmetry, the flexoelectric tensor has three independent components F 1111 , F 1122 , and F 1221 . [7][8][9] By using the Voigt notation F 11 ¼ F 1111 , F 12 ¼ F 1122 , and F 44 ¼ 2F 1221 , Eq. (5) can be expanded as…”

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confidence: 99%

Coupling of electrical and mechanical switching in nanoscale ferroelectrics

Cao

Chen

et al. 2015

Applied Physics Letters

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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(Zr 0.2 Ti 0.8)O 3 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.

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“…In this theory, flexoelectricity is represented by a fourth-order flexoelectric coupling tensor, whose symmetry is well understood [24][25][26] .…”

Section: Introductionmentioning

confidence: 99%

Revisiting pyramid compression to quantify flexoelectricity: A three-dimensional simulation study

et al. 2015

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Flexoelectricity is a universal property of all dielectrics, by which they generate a voltage in response to an inhomogeneous deformation. One of the controversial issues in this field concerns the magnitude of flexoelectric coefficients measured experimentally, which greatly exceed theoretical estimates. Furthermore, there is a broad scatter amongst experimental measurements. The truncated pyramid compression method is one of the common setups to quantify flexoelectricity, the interpretation of which relies on simplified analytical equations to estimate strain gradients. However, the deformation fields in 3D pyramid configurations are highly complex, particularly around its edges. In the present work, using three-dimensional self-consistent simulations of flexoelectricity, we show that the simplified analytical estimations of strain gradients in compressed pyramids significantly overestimate flexoelectric coefficients, thus providing a possible explanation to reconcile different estimates. In fact, the interpretation of pyramid compression experiments is highly nontrivial. We systematically characterize the magnitude of this overestimation, of over one order of magnitude, as a function of the truncated pyramid configuration. These results are important to properly characterize flexoelectricity, and provide design guidelines for effective electromechanical transducers exploiting flexoelectricity.

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Erratum: “Symmetry of flexoelectric coefficients in crystalline medium” [J. Appl. Phys. 110, 104106 (2011)]

Cited by 16 publications

References 1 publication

Relationship between direct and converse flexoelectric coefficients

Relationship between direct and converse flexoelectric coefficients

Coupling of electrical and mechanical switching in nanoscale ferroelectrics

Revisiting pyramid compression to quantify flexoelectricity: A three-dimensional simulation study

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