Compact explicit matrix representations of the flexoelectric tensor and a graphic method for identifying all of its rotation and reflection symmetries

Abstract

Flexoelectricity is an electromechanical phenomenon produced in a dielectric material, with or without centrosymmetric microstructure, undergoing a non-uniform strain. It is characterized by the fourth-order flexoelectric tensor which links the electric polarization vector with the gradient of the second-order strain tensor. Our previous work [Le Quang and He, Roy. Soc. London, Ser. A 467, 2369-2386 solved the fundamental theoretical problem of determining the number and types of all rotational symmetries that the flexoelectric tensor can exhibit. In the present one, compact explicit matrix representations of the flexoelectric tensor are provided so as to facilitate the use of it with any possible rotational symmetry. The number and types of all reflection symmetries that the flexoelectric tensor can have are also determined. To identify the rotational symmetry and reflection symmetry of a given flexoelectric tensor, a simple and efficient graphic method based on the concept of pole figures is presented and illustrated.

The emancipation of flexoelectricity

“…47 We also see the prospects of using flexoelectricity for mechanical reading of memory devices 3 and topics underpinning the theory of flexoelectricity. 48,49 An extensive and detailed overview of the mathematical and computational modeling of flexoelectricity is presented in Ref. 50.…”