Electric field gradients and spontaneous quadrupoles in elastic ferroelectrics

Arvanitakis, Antonios I.; Kalpakides, V.K.; Hadjigeorgiou, E.P.

doi:10.1007/s00707-010-0422-6

Cited by 10 publications

(6 citation statements)

References 38 publications

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“…Using these conditions (13) and also accounting for the hexagonal symmetry of considered crystals, we can state that the micro-inertia tensor has a similar structure to the classical elasticity tensor, i.e., in Voigt notation, it can be represented as follows:…”

Section: Second Gradient Electro-elasticity Theorymentioning

confidence: 99%

“…In the present paper, we extend the lattice-dynamics-based calibration method for the piezoelectric materials and structures, which are described within the second gradient electro-elasticity theory [13, 14]. To the best of the author’s knowledge, this was not done previously and only elastic materials have been considered in such approaches [1, 4, 5].…”

Section: Introductionmentioning

confidence: 99%

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Second gradient continuum model for anisotropic elastic and piezoelectric structures calibrated based on phonon dispersion relations

Solyaev

2023

Mathematics and Mechanics of Solids

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In this paper, we present a variant of the second gradient continuum model that allows description of the spatial dispersion effects of high-frequency waves in anisotropic crystals. The considered model takes into account the strain and inertia gradient effects and the classical electro-mechanical coupling. The simplified constitutive equations of the model contain seven and four length scale parameters for piezoelectric hexagonal crystals and elastic cubic crystals, respectively. It is shown that all except one length scale parameter can be identified based on the fitting of the continuum model to the lattice dynamics calculations for the dispersion relations of the bulk acoustic phonons. Examples of the identification are presented for hexagonal piezoelectric ZnO and AlN and for cubic diamond and Si crystals. Using a calibrated model, we then obtain the dispersion relations for the high-frequency Bleustein–Gulyaev wave in piezoelectric crystals and for the shear horizontal surface wave in elastic crystals. The last one is predicted by the gradient models only for the high frequencies, while at low frequencies this wave degenerates to the bulk shear wave. Examples of calculations are also provided for the Rayleigh wave propagating through the homogeneous piezoelectric half-space and layered ZnO(AlN)/diamond/Si structures. It is shown that this kind of surface wave can be used to identify the last unknown length scale parameter of the model.

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Section: Second Gradient Electro-elasticity Theorymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Second gradient continuum model for anisotropic elastic and piezoelectric structures calibrated based on phonon dispersion relations

Solyaev

2023

Mathematics and Mechanics of Solids

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“…Mindlin [26] applied the polarization gradient theory to explain the size effect in a thin dielectric film. In 1993, Kalpakidis and Massalas [27] proposed an electric gradient by extending the work of Tiersten [25], then Arvanitakis et al [28] explored the role of the electric gradient and quadrupole polarization in the size effect of thin ferroelectric film. Yang et al [29] analyzed the electric field gradient effects in an antiplane problem of piezoelectric materials.…”

Section: Introductionmentioning

confidence: 99%

“…where Π α and Π n are the surface and normal components, respectively [28]. The symbol  s is the surface gradient operator.…”

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confidence: 99%

Microscale size effects on the electromechanical coupling in piezoelectric material for anti-plane problem

Yue

Aifantis

2014

Smart Mater. Struct.

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A continuum model of piezoelectric material with strain and electric gradient effects is proposed in this work. An energy variational principle with strain, strain gradient, electric field and electric field gradient as independent variables is presented to develop the equilibrium equations and all boundary conditions. Moreover, two internal length characteristics of the underlying microstructure are introduced in the constitutive equations. This model is employed to an anti-plane problem of the piezoelectric material, and a general solution is obtained in polar coordinates. Special attention is paid to an infinite piezoelectric medium with a microvoid. It is found that electromechanical fields predicted by the gradient model not only depend on the material parameters, but also on the relative size of the microvoid with respect to the scale of microstructure. More importantly, some new interesting phenomena are observed due to the gradient effects of strain and electric fields.

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“…Notice that in the above equations we have discarded the second terms in Eqs. (2.62) and the terms q s ij,ji in Gauss equation so as to simplify the set of equations obtaining Continuum phase field approaches exact analytical solutions (5). Also, the reversible part of quadrupole polarization is neglected.…”

Section: Analytical Solutionsmentioning

confidence: 99%

Theoretical and computational aspects οf phase transitions in elastic ferroelectric materials

Αρβανιτάκης¹

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This work would not have been completed without the support and guidance of several people over the course of completing my Ph.D.First, I would like to sincerely thank my supervisor Professor Vassilios Kalpakides for his immense help in shaping this work. Professor Kalpakides was always near for any kind of problem that has arisen during the preparation of this thesis. He is the kind of teacher that inspires trust and close to him i have learned that research requires patience and dedication. I would also like to thank Pr. Evangelos Hadjigeorgiou for his guidance and valuable discussions through the preparation of my thesis. I also thank Professor Cristian Dascalu, who accepted to be an advisor and even though he was far away, he kept watching my progress with great interest. I sincerely thank my many colleagues in our mechanics of materials research group for their support and encouragement during my course of study. Most importantly, I would like to thank my family and all my good friends. I could not have achieved this goal without their love and support. I especially thank my brother Alexandros and my sister Peny for their encouragement and love.Finally, I would like to thank the Department of Materials Science and Engineering for its warm hospitality and the State Scholarships Foundation (I. K.Y.) of Greece for providing a scholarship which supported financially this research.

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Electric field gradients and spontaneous quadrupoles in elastic ferroelectrics

Cited by 10 publications

References 38 publications

Second gradient continuum model for anisotropic elastic and piezoelectric structures calibrated based on phonon dispersion relations

Second gradient continuum model for anisotropic elastic and piezoelectric structures calibrated based on phonon dispersion relations

Microscale size effects on the electromechanical coupling in piezoelectric material for anti-plane problem

Theoretical and computational aspects οf phase transitions in elastic ferroelectric materials

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