Surface Piezoelectricity, Size-effects in Nanostructures and the Emergence of Piezoelectricity in Non-piezoelectric Materials
S. Dai, M. Gharbi, P. Sharma and H.S. Park
Journal of Applied Physics 2011; 110:104305
Abstract
In this work, using a combination of a theoretical framework and atomistic calculations, we highlight the concept of surface
piezoelectricity that can be used to interpret the piezoelectricity of nanostructures. Focusing on three specific material systems
(ZnO, SrTiO3 and BaTiO3), we discuss the renormalization of apparent piezoelectric behavior at small scales. In a rather interesting
interplay of symmetry and surface effects, we show that nanostructures of certain non-piezoelectric materials may also exhibit
piezoelectric behavior. Finally, for the case of ZnO, using a comparison with first principles calculations, we also comment on the
fidelity of the widely-used core-shell interatomic potentials to capture non-bulk electro-mechanical response.
This paper is available in PDF form
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A New Multiscale Formulation for the Electromechanical Behavior of Nanomaterials
H.S. Park, M. Devel and Z. Wang
Computer Methods in Applied Mechanics and Engineering 2011; 200:2447-2457
Abstract
We present a new multiscale, finite deformation, electromechanical formulation to capture the response of surface-dominated nanomaterials
to externally applied electric fields. To do so, we develop and discretize a total energy that combines both mechanical and electrostatic
terms, where the mechanical potential energy is derived from any standard interatomic atomistic potential, and where the electrostatic
potential energy is derived using a Gaussian-dipole approach. By utilizing Cauchy-Born kinematics, we derive both the bulk and surface
electrostatic Piola-Kirchoff stresses that are required to evaluate the resulting electromechanical finite element equilibrium equations,
where the surface Piola-Kirchoff stress enables us to capture the non-bulk electric field-driven polarization of atoms near the surfaces
of nanomaterials. Because we minimize a total energy, the present formulation has distinct advantages as compared to previous approaches,
where in particular, only one governing equation is required to be solved. This is in contrast to previous approaches which require
either the staggered or monolithic solution of both the mechanical and electrostatic equations, along with coupling terms that link
the two domains. The present approach thus leads to a significant reduction in computational expense both in terms of fewer equations
to solve and also in eliminating the need to remesh either the mechanical or electrostatic domains due to being based on a total Lagrangian
formulation. Though the approach can apply to three-dimensional cases, we concentrate in this paper on the one-dimensional case. We first
derive the necessary formulas, then give numerical examples to validate the proposed approach in comparison to fully atomistic
electromechanical calculations.
This paper is available in PDF form
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Piezoelectric Constants for ZnO Calculated Using Classical Polarizable Core-Shell Potentials
S. Dai, M.L. Dunn and H.S. Park
Nanotechnology 2010; 21:445707
Abstract
We demonstrate the feasibility of using classical atomistic simulations, i.e. molecular dynamics and molecular statics, to study the
piezoelectric properties of ZnO using core-shell interatomic potentials. We accomplish this by reporting piezoelectric constants for
ZnO as calculated using two different classical interatomic core-shell potentials, that originally proposed by
Binks et al., and that proposed by Nyberg et al. We demonstrate that the
classical core-shell potentials are able to qualitatively reproduce the piezoelectric constants as compared to benchmark \emph{ab initio}
calculations. We further demonstrate that while the presence of the shell is required to capture the electron polarization effects that
control the clamped ion part of the piezoelectric constant, the major shortcoming of the classical potentials is a significant
underprediction of the clamped ion term as compared to previous ab initio results. However, the present results suggest
that overall, these classical core-shell potentials are sufficiently accurate to be utilized for large scale atomistic
simulations of the piezoelectric response of ZnO nanostructures.
This paper is available in PDF form
.