Closed-form expressions for computing flexoelectric coefficients in textured polycrystalline dielectrics

The volume average of the constituting properties of a textured polycrystalline aggregate (the Voigt average) provides a simple way to estimate the effective properties of such an aggregate in terms of its crystallographic symmetry, texture symmetry, and the properties of the constituting crystallites. Despite the interest in estimate or characterizing flexoelectric properties, few studies have addressed the problem of finding effective flexoelectric properties from the continuum phases of the constituents. Instead, most of them focus on single-crystals at the atomic level. This study provides, for the first time, closed-form expressions that allow the direct flexoelectric coefficients to be computed for textured polycrystalline dielectrics. Crystallites can belong to any class of cubic symmetry or to the tetragonal TI Laue group, while no restriction is imposed on texture symmetry. These expressions are reduced to very simple ones when cubic crystallites with fiber texture are considered. The proposed formulation provides information on the matrix structure of the homogenized material related to the crystallographic symmetry and texture. We close with some illustrative examples.