Enhanced size-dependent piezoelectricity and elasticity in nanostructures due to the flexoelectric effect
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Crystalline piezoelectric dielectrics electrically polarize upon application of uniform mechanical strain. Inhomogeneous strain, however, locally breaks inversion symmetry and can potentially polarize even nonpiezoelectric (centrosymmetric) dielectrics. Flexoelectricity-the coupling of strain gradient to polarization-is expected to show a strong size dependency due to the scaling of strain gradients with structural feature size. In this study, using a combination of atomistic and theoretical approaches, we investigate the "effective" size-dependent piezoelectric and elastic behavior of inhomogeneously strained nonpiezoelectric and piezoelectric nanostructures. In particular, to obtain analytical results and tease out physical insights, we analyze a paradigmatic nanoscale cantilever beam. We find that in materials that are intrinsically piezoelectric, the flexoelectricity and piezoelectricity effects do not add linearly and exhibit a nonlinear interaction. The latter leads to a strong size-dependent enhancement of the apparent piezoelectric coefficient resulting in, for example, a "giant" 500% enhancement over bulk properties in BaTi O3 for a beam thickness of 5 nm. Correspondingly, for nonpiezoelectric materials also, the enhancement is nontrivial (e.g., 80% for 5 nm size in paraelectric BaTi O3 phase). Flexoelectricity also modifies the apparent elastic modulus of nanostructures, exhibiting an asymptotic scaling of 1/h2, where h is the characteristic feature size. Our major predictions are verified by quantum mechanically derived force-field-based molecular dynamics for two phases (cubic and tetragonal) of BaTi O3. 2008 The American Physical Society.