Enhanced size-dependent piezoelectricity and elasticity in nanostructures due to the flexoelectric effect

M. S. Majdoub, P. Sharma, and T. Cagin
Phys. Rev. B 77, 125424 – Published 25 March 2008; Erratum Phys. Rev. B 79, 119904 (2009)

Abstract

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 BaTiO3 for a beam thickness of 5nm. Correspondingly, for nonpiezoelectric materials also, the enhancement is nontrivial (e.g., 80% for 5nm size in paraelectric BaTiO3 phase). Flexoelectricity also modifies the apparent elastic modulus of nanostructures, exhibiting an asymptotic scaling of 1h2, 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 BaTiO3.

  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
2 More
  • Received 5 November 2007

DOI:https://doi.org/10.1103/PhysRevB.77.125424

©2008 American Physical Society

Erratum

Authors & Affiliations

M. S. Majdoub1, P. Sharma1,2,*, and T. Cagin3

  • 1Department of Mechanical Engineering, University of Houston, Houston, Texas 77204, USA
  • 2Department of Physics, University of Houston, Houston, Texas 77204, USA
  • 3Department of Chemical Engineering, Texas A&M University, College Station, Texas 77845, USA

  • *Corresponding author; psharma@uh.edu

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand
Issue

Vol. 77, Iss. 12 — 15 March 2008

Reuse & Permissions
Access Options
Author publication services for translation and copyediting assistance advertisement

Authorization Required


×
×

Images

×

Sign up to receive regular email alerts from Physical Review B

Log In

Cancel
×

Search


Article Lookup

Paste a citation or DOI

Enter a citation
×