Flexoelectric effect in finite samples

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, there exists a situation where 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 the polarization at the surface is not zero, 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 is suggested that this conflict may be resolved when using modified mechanical boundary conditions. It is 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 materials 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. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4745037]