  Abstract: In this paper we show that experimentally realizable apparently
piezoelectric thin-film super-lattices can be created from non-piezoelectric
materials provided an odd-order (e.g. trilayer) stacking sequence is used. The
size-dependent mechanism of flexoelectricity, which couples gradients of strain
to polarization, allows such a possibility. We present closed-form analytical
expressions for the response of various thin-film and super-lattice
configurations. We also clarify some of the subtleties that arise in
considering interface boundary conditions in the theory of flexoelectricity as
well as the relationship of flexoelectricity to the frequently used
polarization gradient terms used in modeling ferroelectrics. We find that for
certain (optimum) material combinations and length scales, thin film
superlattices yielding apparent piezoelectricity close to 75 % of ferroelectric
Barium Titanate may be achievable.
