Size-dependent super-piezoelectricity and elasticity in nanostructures due to the flexoelectric effect

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. 

Please refer to the attached paper (accepted for publication in Physical Review B) for details.