2015
DOI: 10.1103/physrevb.91.104103
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Revisiting pyramid compression to quantify flexoelectricity: A three-dimensional simulation study

Abstract: 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 o… Show more

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Cited by 82 publications
(80 citation statements)
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“…This is also the case for the flexoelectric theory. However, in practice, the numerical methods mentioned above neglect these nonlocal conditions or consider smooth enough domains so that they do not appear [22][23][24][25][28][29][30]. In this work, we show that non-local boundary conditions are mathematically required and we consider them in the formulation and implementation.…”
Section: Introductionmentioning
confidence: 94%
See 1 more Smart Citation
“…This is also the case for the flexoelectric theory. However, in practice, the numerical methods mentioned above neglect these nonlocal conditions or consider smooth enough domains so that they do not appear [22][23][24][25][28][29][30]. In this work, we show that non-local boundary conditions are mathematically required and we consider them in the formulation and implementation.…”
Section: Introductionmentioning
confidence: 94%
“…For the first time to our knowledge, the complete set of boundary conditions is explicitly considered in a numerical solution of the flexoelectric boundary value problem. In the seminal Mindlin's theory of strain gradient elasticity [42][43][44], which is the basis for deriving a stable flexoelectric theory [22][23][24]45], additional non-local boundary conditions are required along non-smooth regions of the domain boundary (i.e. corners in 2D and edges in 3D).…”
Section: Introductionmentioning
confidence: 99%
“…For example, Mao & Purohit [39] have presented analytical solutions to several one-and two-dimensional problems and later extended their analysis to determine singular fields around point defects, dislocations and cracks [40]. Finite-element studies have also been conducted by Abdollahi et al [41][42][43][44]. They studied several non-trivial geometries, e.g.…”
Section: Introductionmentioning
confidence: 99%
“…Therefore, we ascribe the flexoelectric response of the columnar BTO nanostructured films to their truncated pyramid geometry, which leads to substantial strain gradients under moderate loads. Indeed, compressing materials of truncated square pyramid geometries has become a standard approach to generate strong strain gradients and study the flexoelectric effect,[11b,13] even though the quantitative analysis of the experiments is nontrivial due to the complexity of the stress fields developed in such geometries . We can, though, estimate the strain gradient produced by applying a force of 1000 nN to a truncated pyramid with the dimensions of that displayed in Figure c to be ≈10 5 m −1 (see details in Figure S10 in the Supporting Information).…”
Section: Characterization Of Ferroelectricity and Transport Propertiementioning
confidence: 99%