  Upon application of a uniform strain, internal sub-lattice shifts within the
unit cell of a non-centrosymmetric dielectric crystal result in the appearance
of a net dipole moment: a phenomenon well known as piezoelectricity. A
macroscopic strain gradient on the other hand can induce polarization in
dielectrics of any crystal structure, even those which possess a
centrosymmetric lattice. This phenomenon, called flexoelectricity, has both
bulk and surface contributions: the strength of the bulk contribution can be
characterized by means of a material property tensor called the bulk
flexoelectric tensor. Several recent studies suggest that strain-gradient
induced polarization may be responsible for a variety of interesting and
anomalous electromechanical phenomena in materials including electromechanical
coupling effects in non-uniformly strained nanostructures, dead layer effects
in nanocapacitor systems, and giant piezoelectricity in perovskite
nanostructures among others. In this work, adopting a lattice dynamics based
microscopic approach we provide estimates of the flexoelectric tensor for
certain cubic ionic crystals, perovskite dielectrics, III-V and II-VI
semiconductors. We compare our estimates with experimental and theoretical
values wherever available, address the discrepancy that exists between
different experimental estimates and also re-visit the validity of an existing
empirical scaling relationship for the magnitude of flexoelectric coefficients
in terms of material parameters.
