Nikhil Sharma

In this paper we show that experimentally realizable apparently piezoelectric thin-film superlattices can be created from nonpiezoelectric 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 superlattice configurations. We also clarify some of the subtleties… Show more

In this paper we show that experimentally realizable apparently piezoelectric thin-film superlattices can be created from nonpiezoelectric 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 superlattice 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. Show less

Our atomistic calculations of a prototype nanostructure reveal emergence of size-dependent "giant" piezoelectricity in both non-piezoelectric and piezoelectric dielectrics under inhomogeneous conditions e.g. an enhancement in the effective piezoelectric constant of nearly 500 % is found for tetragonal BaTiO3 around 5 nm (and a corresponding 80 % increase for the paraelectric cubic phase at the same size). We argue that flexoelectricity (strain gradient induced polarization) is responsible for… Show more

Our atomistic calculations of a prototype nanostructure reveal emergence of size-dependent "giant" piezoelectricity in both non-piezoelectric and piezoelectric dielectrics under inhomogeneous conditions e.g. an enhancement in the effective piezoelectric constant of nearly 500 % is found for tetragonal BaTiO3 around 5 nm (and a corresponding 80 % increase for the paraelectric cubic phase at the same size). We argue that flexoelectricity (strain gradient induced polarization) is responsible for the increased electromechanical coupling. We develop a theoretical model for a cantilever nanobeam under bending (using material parameters obtained independently from experiments) to reconcile our atomistic predictions. We find that flexoelectricity also renders the elastic modulus size-dependent, exhibiting an asymptotic scaling of 1/h2. The agreement is excellent and based on the obtained insights we argue on the universality of piezoelectricity enhancement for all dielectrics. Show less

In this work, predicated on nanoscale size-effects, we explore the tantalizing possibility of creating apparently piezoelectric composites without using piezoelectric constituent materials. In a piezoelectric material an applied uniform strain can induce an electric polarization (or vice-versa). Crystallographic considerations restrict this technologically important property to non-centrosymmetric systems. Non-uniform strain can break the inversion symmetry and induce polarization even in… Show more

In this work, predicated on nanoscale size-effects, we explore the tantalizing possibility of creating apparently piezoelectric composites without using piezoelectric constituent materials. In a piezoelectric material an applied uniform strain can induce an electric polarization (or vice-versa). Crystallographic considerations restrict this technologically important property to non-centrosymmetric systems. Non-uniform strain can break the inversion symmetry and induce polarization even in non-piezoelectric dielectrics. The key concept is that all dielectrics (including non-piezoelectric ones) exhibit the aforementioned coupling between strain gradient and polarization—an experimentally verified phenomenon known in some circles as the flexoelectric effect. This flexoelectric coupling, however, is generally very small and evades experimental detection unless very large strain gradients (or conversely polarization gradients) are present. Based on a field theoretic framework and the associated Greens function solutions developed in prior work, we quantitatively demonstrate the possibility of “designing piezoelectricity,” i.e. we exploit the large strain gradients present in the interior of composites containing nanoscale inhomogeneities to achieve an overall non-zero polarization even under an uniformly applied stress. We prove that the aforementioned effect may be realized only if both the shapes and distributions of the inhomogeneities are non-centrosymmetric. Our un-optimized quantitative results, based on limited material data and restrictive assumptions on inhomogeneity shape and distribution, indicate that apparent piezoelectric behavior close to 10% of Quartz may be achievable for inhomogeneity sizes in the 4 nm range. In future works, it is not unreasonable to expect enhanced performance based on optimization of shape, topology and appropriate material selection. Show less

In a piezoelectric material, an applied uniform strain can induce an electric polarization (or vice versa). Crystallographic considerations restrict this technologically important property to noncentrosymmetric systems. It has been shown both mathematically and physically that a nonuniform strain can potentially break the inversion symmetry and induce polarization in nonpiezoelectric materials. The coupling between strain gradients and polarization, and conversely between strain and… Show more

In a piezoelectric material, an applied uniform strain can induce an electric polarization (or vice versa). Crystallographic considerations restrict this technologically important property to noncentrosymmetric systems. It has been shown both mathematically and physically that a nonuniform strain can potentially break the inversion symmetry and induce polarization in nonpiezoelectric materials. The coupling between strain gradients and polarization, and conversely between strain and polarization gradients, is investigated in this work. While the conventional piezoelectric property is nonzero only for certain select materials, the nonlocal coupling of strain and electric field gradients is (in principle) nonzero for all dielectrics, albeit manifesting noticeably only at the nanoscale, around interfaces or in general in the vicinity of high field gradients. Based on a field theoretic framework accounting for this phenomena, we (i) develop the fundamental solutions (Green’s functions) for the governing equations, and (ii) motivated by eventual applications for quantum dots, solve the general embedded mismatched inclusion problem with explicit results for the spherical and cylindrical shape. Expectedly, our results for the aforementioned problems are size dependent and indicate generation of high electric fields reaching values of approximately hundreds of kV/m in selected sizes and locations—even in isotropic centrosymmetric nonpiezoelectric materials. Show less