Elsevier

Computational Materials Science

Volume 68, February 2013, Pages 320-324
Computational Materials Science

A first principles investigation of the mechanical properties of g-ZnO: The graphene-like hexagonal zinc oxide monolayer

https://doi.org/10.1016/j.commatsci.2012.10.019Get rights and content

Abstract

We investigate the mechanical properties, including high order elastic constants, of the graphene-like hexagonal zinc oxide monolayer (g-ZnO) using first-principles calculations based on density-functional theory. Compared to the graphene-like hexagonal boron nitride monolayer (g-BN), g-ZnO is much softer, with 17% in-plane stiffness and 36%, 33%, and 33% ultimate strengths in armchair, zigzag, and biaxial strains respectively. However, g-ZnO has a larger Poisson’s ratio, 0.667, about three times that of g-BN. It was found that the g-ZnO also sustains much smaller strains before the rupture. We obtained the second, third, fourth, and fifth order elastic constants for a rigorous continuum description of the elastic response of g-ZnO. The second order elastic constants, including in-plane stiffness, are predicted to monotonically increase with pressure while the Poisson’s ratio monotonically decreases with increasing pressure.

Highlights

► First time to predict the nonlinear elastic properties of g-ZnO. ► Up to fifth order elastic constants for a rigorous continuum description. ► Prediction of the pressure-dependent second order elastic constants.

Introduction

With a wide bandgap (3.37 eV), a large exciton biding energy (60 meV), piezoelectricity, chemical stability, and biocompatibility, zinc oxide (ZnO) is a verstile functional material and is widely used in optics, photonics, and electronics. The applications includes light-emitting diodes, solar cells, field effect transistors, mechanical actuators, piezoelectric sensors, surface acoustic wave devices, waveguides, photocatalysts, and nanogenerators [1], [2], [3]. A hexagonal zinc oxide monolayer (g-ZnO) is a graphene-like 2D material, which is only monoatomically thick (Fig. 1) and chemically stable from both ab initio DFT calculations [4], [5], [6], [7] and experiment [8]. The electronic and magnetic properties were extensively studied [9], [10], [11], [12], [13], [14], [15], [16], as well as the elasticity and piezoelectricity [5], [7]. The bandgap of g-ZnO is predicted to be 3.57–5.64 eV [7], [9], larger than that in bulk. The in-plane Young’s modulus was reported to be 24% of graphene [7]. The Poisson ratio is 0.71.

Two-dimentional (2D) nanomaterials are the basic “building blocks” for all other structures: buckyballs (0D) by wrapping, nanotubes (1D) by rolling, bulk (3D) by stacking [17]. However, due to the quantum confinement resulting from the reduction of the third dimention, 2D nanomaterials present very different properties from bulk. For example, the mechanical strengths are an order of magnitude larger than those in bulk. Mechanical properties are critical in designing parts or structures with g-ZnO regarding the practical applications. Strain engineering is a common and important approach tailoring the functional and structural properties of nanomaterials [18], [9]. One can expect that the properties of g-ZnO will be affected by applied strain too. In addition, g-ZnO is vulnerable to be strained with or without intent because of its monatomic thickness. For example, there are strains because of the mismatch of lattices constants or surface corrugation with substrates [19], [20]. Therefore, the knowledge of the mechanical properties of g-ZnO is highly desired.

Depending on the loading, the mechanical properties are divided into four strain domains: linear elastic, nonlinear elastic, plastic, and fracture. Materials in the first two strain domains are reversible, i.e., they can restore to equilibrium status after the release of the loads. On the contrary, the last two domains are nonreversible. Defects are nucleated and accumulated with the increase of the strain, until rupture. As in graphene, the nonlinear mechanical properties are prominent since it remained elastic until the intrinsic strength was reached [21], [22]. Thus it is of great interest to examine the nonlinear elastic properties of g-ZnO, which is necessary to understand the strength and reliability of structures and devices made of g-ZnO.

Several previous studies have shown that 2D monolayers present a large nonlinear elastic deformation during the tensile strain up to the ultimate strength of the material, followed by a strain softening until fracture [23], [24], [25], [26], [22]. We expect that the g-ZnO behaves in a similar manner. Under large deformation, the strain energy density needs to be expanded as a function of strain in a Taylor series to include quadratic and higher order terms. The higher order terms account for both nonlinearity and strain softening of the elastic deformation. They can also express other anharmonic properties of 2D nanostructures including phenomena such as thermal expansion and phonon–phonon interaction [21].

Due to a large bandgap, ZnO is an alternative material to the nitride semiconductors. Thus it is interesting to compare the mechanical properties of g-ZnO with g-BN, the graphene analogue of BN [27]. The goal of this paper is to study the mechanical behaviors of g-ZnO at large strains and find an accurate continuum description of the elastic properties from ab initio density functional theory calculations. The total energies of the system, forces on each atom, and stresses on the simulation boxes are directly obtained from DFT calculations. The response of g-ZnO under the nonlinear deformation and fracture is studied, including ultimate strength and ultimate strain. The high order elastic constants are obtained by fitting the stress–strain curves to analytical stress–strain relationships that belong to the continuum formulation [24]. We compared g-ZnO with the well known 2D materials such as g-BN, graphene, and graphyne [28]. Based on our result of the high order elastic constants, the pressure dependence properties, such as sound velocities and the second order elastic constants, including the in-plane stiffness, are predicted. Our results for the continuum formulation could also be useful in finite element modeling of the multiscale calculations for mechanical properties of g-ZnO at the continuum level. The remainder of the paper is organized as follows. Section 2 presents the computational details of DFT calculations. The results and analysis are in Section 3, followed by conclusions in Section 4.

Section snippets

Density functional theory calculations

We consider a conventional unit cell containing six atoms (3 Zinc atoms and 3 oxygen atoms) with periodic boundary conditions (Fig. 2). The 6-atom conventional unit cell is chosen to capture the “soft mode”, which is a particular normal mode exhibiting an anomalous reduction in its characteristic frequency and leading to mechanical instability. This soft mode is a key factor in limiting the strength of monolayer materials and can only be captured in unit cells with hexagonal rings [29].

The

Atomic structure

We first optimize the equilibrium lattice constant for g-ZnO. The total energy as a function of lattice spacing is obtained by specifying nine lattice constants varying from 3.0 Å to 3.6 Å, with full relaxations of all the atoms. A least-square fit of the energies versus lattice constants with a fourth-order polynomial function yields the equilibrium lattice constant as a = 3.291 Å. The most energetically favorable structure is set as the strain-free structure in this study and the atomic structure,

Conclusions

In summary, we studied the mechanical response of g-ZnO under various strains using DFT based first-principles calculations. It is observed that g-ZnO exhibits a nonlinear elastic deformation up to an ultimate strain, which is 0.17, 0.24, and 0.20 for armchair, zigzag, and biaxial directions, respectively. The deformation and failure behavior and the ultimate strength are anisotropic. It has a low in-plane stiffness (47.8 N/m) and a large Poisson ratio compared to g-BN and graphene. Compared to g

Acknowledgements

The authors would like to acknowledge the generous financial support from the Defense Threat Reduction Agency (DTRA) Grant # BRBAA08-C-2-0130, the U.S. Nuclear Regulatory Commission Faculty Development Program under contract # NRC-38-08-950, and U.S. Department of Energy (DOE) Nuclear Energy University Program (NEUP) Grant # DE-NE0000325.

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