Flexoelectric effect in finite samples

TL;DR

This paper uses phenomenological theory to analyze the static flexoelectric effect in finite samples, revealing that the electromechanical response is symmetric under certain conditions and highlighting the importance of surface effects and boundary conditions.

Contribution

It demonstrates that the symmetry of the flexoelectric response in finite samples holds under standard boundary conditions and clarifies the role of surface piezoelectricity and boundary conditions in flexoelectric behavior.

Findings

Electromechanical response is symmetric in finite samples with standard boundary conditions.

Surface piezoelectricity contribution is comparable to bulk contribution.

Flexoelectric coefficient scaling with dielectric constant does not imply bulk control.

Abstract

Static flexoelectric effect in a finite sample of a solid is addressed in terms of phenomenological theory for the case of a thin plate subjected to bending. It has been shown that despite an explicit asymmetry inherent to the bulk constitutive electromechanical equations which take into account the flexoelectric coupling, the electromechanical response for a finite sample is "symmetric". "Symmetric" means that if a sensor and an actuator are made of a flexoelectric element, performance of such devices can be characterized by the same effective piezoelectric coefficient. This behavior is consistent with the thermodynamic arguments offered earlier, being in conflict with the current point of view on the matter in literature. This result was obtained using standard mechanical boundary conditions valid for the case where the polarization vanishes at the surface. It was shown that, for the case where there is the polarization is nonzero at the surface, the aforementioned symmetry of electromechanical response may be violated if standard mechanical boundary conditions are used, leading to a conflict with the thermodynamic arguments. It was argued that this conflict may be resolved when using modified mechanical boundary conditions. It was also shown that the contribution of surface piezoelectricity to the flexoelectric response of a finite sample is expected to be comparable to that of the static bulk contribution (including the material with high values of the dielectric constant) and to scale as the bulk value of the dielectric constant (similar to the bulk contribution). This finding implies that if the experimentally measured flexoelectric coefficient scales as the dielectric constant of the material, this does not imply that the measured flexoelectric response is controlled by the static bulk contribution to the flexoelectric effect.