Mechanical properties of graphyne and its analogous decorated with Na and Pt

Accepted Manuscript Mechanical properties of graphyne and its analogous decorated with Na and Pt Aidin Ahmadi, Mahdi Faghihnasiri, Hamid Ghorbani Shiraz, Moones Sabeti

PII:

S0749-6036(16)30902-8

DOI:

10.1016/j.spmi.2016.09.041

Reference:

YSPMI 4531

To appear in:

Superlattices and Microstructures

Received Date: 8 September 2016 Accepted Date: 27 September 2016

Please cite this article as: A. Ahmadi, M. Faghihnasiri, H.G. Shiraz, M. Sabeti, Mechanical properties of graphyne and its analogous decorated with Na and Pt, Superlattices and Microstructures (2016), doi: 10.1016/j.spmi.2016.09.041. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

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Mechanical properties of graphyne and its analogous decorated with Na and Pt Aidin Ahmadia, Mahdi Faghihnasirib∗, Hamid Ghorbani Shirazc, Moones Sabetid a

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Young Researchers and Elite Club, South Tehran Branch, Islamic Azad University, Tehran, Iran Young Researchers and Elite Club, Central Tehran Branch, Islamic Azad University, Tehran, Iran c Young Researchers and Elite Club, Mashhad Branch, Islamic Azad University, Mashhad, Iran d Department of Physics, NRTC, Iran b

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Abstract

In this paper, the mechanical properties of Na and Pt decorated arrays of 2D graphyne sheet is investigated. The proposed structures are consisted of Na and Pt decorated graphyne sheet (CC),

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analogous system of Boron nitride sheet (BN-yne), and graphyne-like BN sheet (CC-BN-yne). The properties such as In-plane stiffness and Bulk module are studied using Energy-Strain correlation. The calculations were carried out based on Density functional theory (DFT) using the generalized gradient approximation (GGA) framework. The results offered very competitive values of stiffness and Bulk module for Pt decorated CC and BN-yne. However, the Pt decorated CC-BN-yne structure demonstrated around 80% of stiffness and 77% of Bulk module, compared to those of pure structure. Na decorated

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system showed the same trend for all three mentioned structures.

Keywords: Graphyne; Density functional theory; Young and Bulk modulus; Elastic-Plastic regions.

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Introduction

Porous media have demonstrated several interesting properties [1, 2]. Amongst these porous materials, carbonaceous materials have received high attentions based on abundance in the earth’s crust. Due to

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wide range of properties, carbon nanomaterials (CNs) have been defined as high usable materials in several fields such as solid state physics and materials science [2, 3].CNs are divided into four distinct categories of 0D (Fullerene), 1D (Carbon nanotube), 2D (Graphene) and 3D (Diamond, Graphite) [3]. Recently, 2D CNs such as graphene has attracted considerable attentions. Several properties such as high charge mobility, desirable mechanical flexibility, and high surface area [4] have made graphene a potential material for the numerous applications such as high-sensitive mechanical sensors [5, 6], robots *

Corresponding Author’s emails: [email protected], [email protected]

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[7, 8], motion sensors [9, 10], and seismographic systems [11] could be mentioned. Elastic characteristics of nanostructures could be estimated through calculation of distributed force and correlation of the sheer stresses and relative length. Young's module is one of the most important properties which can be used to describe the elasticity properties. In case of 2D allotrope such as graphene, Young's module is measured

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using experimental methods and Atomic Force Microscopy. Recently, Graphyne, as a new member of carbonaceous nanosheet family, has been fabricated by chemical vapor deposition method and has simulated hot researches [12, 13]. Graphene organizes by sp2 hybridized carbon atoms; while graphyne includes both sp and sp2 hybridized carbon atoms. These

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approaches have made high degrees of similarity such as mobility, stability, and mechanical properties. However, several acetylenic bonds, in the graphyne, propose numerous considerable physical properties

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[14-19].

Puigdollers et al. studied wide range of structural, mechanical, and electronic properties of graphyne using Density functional theory (DFT), and compared the results with those of graphene. It was proved that graphene offers superior value for in-plane stiffness. The inclusion of acetylenic linkages in graphyne structure reduces the number of bonds and the planar density, and consequently, decreases the rigidity of the material. Also, the Fermi velocities are found to be higher in the case of graphene. In fact, graphyne is a semiconductor with the measured band gap of 0.46 eV in the M point. This fact, as well as the

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anisotropy of the carrier has made graphyne a very interesting material due to its electronic properties. However, the graphyne presented high Poisson’s ratio of 0.87, compared to graphene. This phenomenon was attributed to the sparsity of in-plane atoms in graphyne that provided high value contractions[20]. Also, Asadpour et al. studied the mechanical properties of simple graphyne, graphyne-like BN, and

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analogous system of BN, using DFT calculations. They calculated in-plane stiffness through variation of strain energy and demonstrated that graphyne reveals highest in-plane stiffness with the value of 190.69 N/m. In addition, the highest Poisson’s ratio and largest module (both sheer and bulk) obtained through

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analogous system of BN and graphyne, respectively [21]. Recently, decorated systems have been investigated in experiment [22] and computational studies. In fact, the variation of intrinsic properties has prepared several desirable features and this is attributed to the decorated species. Recently, it has been proved that Na- decorated graphyne can be employed as a carbonaceous electronic conductor. This capability was attributed to the charge donation from sodium to carbon [23]. Also, the adsorption of hydrosulfuric over graphene system has been studied using DFT calculations. The scientists proved that orbital hybridization could be performed between H2S and Ptdecorated graphene, while such stable hybridization could not be established between H2S and non-

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decorated graphene [24]. As far as we know, there is no report for consideration of mechanical properties of Na- and Pt-decorated graphyne and analogous systems. In this study, we present computational results of electronic and mechanical properties of metal decorated 2D-graphyne and its analogous structures, BN-yne. Also, the third structure was considered as BN

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hexagonal configurations jointed by C-chains, CC-BN-yne. We supposed that BN sheet and its hybrid sheet with graphene has been successfully synthesized [25-27].

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Calculation Details and Results

The DFT calculations were carried out through Local Combination of Atomic Orbital (LCAO) using the Ab-initio simulation code, Spanish Initiative Electronic Structure for Thousands of Atoms (SIESTA)

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[28]. The calculations were performed within the generalized gradient approximation (GGA) as detailed by Perdew–Burke–Ernzerh of (PBE) [29,30] to study the effects of electronic exchange and correlation. The split-valence double-ζ basis set of atomic orbitals was introduced, including polarization functions with an energy shift of 50 meV and a split norm of 0.25 [31]. A 25×25×1 Monkhorst–Pack grid for kpoint mesh of the Brillouin zone was proposed, and the local relaxations of atoms were delayed until the residual forces over individual atom reached lower than 0.005 eV/Å. Also, the cut-off energy of 325 Ry

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for the grid integration was examined in the calculations to represent the charge density. The interlayer vacuum of about 15 Å was introduced to minimize the interactions. The examined structures (figure 1) were trade off and the optimum values for lattice vectors were obtained which show good agreement with the literature data [32]. The calculations demonstrated that obtained bond lengths offer a stable configuration for the systems consisted of Carbon, Nitrogen, and

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Boron. The results for computed lattice vectors and bond lengths are presented in Table 1. Liu et al. examined different adsorption sites of Na over graphyne, including hexagonal hollow site,

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triangle hollow site, and the site above acetylenic bond [33]. They demonstrated that favorable site for the spontaneous adsorption of Na is the site above the hollow site of triangle formed with acetylenic bonds, like other alkali metal adsorption on graphyne; since, it contributed to the lowest adsorption energy of 2.37 eV [34-37].

Thus, we employed this approach in the computation with2 decorated sites, below and above nanosheets. With these details, we investigated the mechanical properties for Na and Pt decorated systems of CC, BNyne, and CC-BN-yne.

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Mechanical Properties: Mechanical properties of proposed structures were investigated under strain range of [-2% ~ 2%]; socalled harmonic elastic deformation range. Configuration of the structures was kept in this range and

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consequently, the mechanical properties were stable.

Young's module (Y)and Bulk module (B) Young's module

Elastic properties of homogeneous structures can be demonstrated by Young's module (Y) and Bulk module (B). Young's module denotes the stiffness of the system. Since the thickness of mono-layer

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structures such as graphyne may be trivial, the stiffness could be stated as in-plane stiffness. Young’s module can be expressed as [21]:

Where V0, ES, and ε (=

∆ ) 

1 ∂  E V ∂ε

(1)

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Y=

represent optimized unit cell volume, total strain energy, and axial strain,

respectively. According to the literature [21], ES is described as the difference between strain energy of axial and that ofε = 0:

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E = E (ε) − E (ε = 0)

(2)

According to Equation 1, the calculations should be carried out under the condition of uniaxial strain of unit cell structure.

of -0.02 <ε< 0.02.

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We found the second-order derivative of the energy by input strain, at the region of homogeneity, range

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The calculations at the regions which were inconsistence with the energy equation, may lead to high-order terms that are not trivial. Thereby, Young’s module was calculated at the region of -0.02 ~ 0.02. Under tensile and compressive strains, the unit cells at the uniaxial direction emerged between -2% and 2% with the step of 0.5%. Also, total strain energies for given strains were obtained. Under uniaxial strain, the ∆

variation of strain energy with respect to axial strain (  ) was applied to unit cells of CC, BN-yne, and CC-BN-yne. The minimum points with the lowest energy level can be translated as the optimum configuration for structures. The neighbor points can introduce the modes under tensile and compressive strains, which possess higher energy levels.

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Bulk module Bulk module could be found as the second derivative of the total strain energy with respect to the volume of the unite cell [21]:

Where V0 and

   

∂ E ∂V 

(3)

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B = V

are defined as equilibrium volume of unit cell and the second derivative of strain with

respect to volume of unit cell.

According to the Equation 3, unit cell should be considered under biaxial strains. The calculated results of

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these approaches were gathered for tensile and compressive strains. Since we focused on planar structures, biaxial tensile could be applied in the calculation of B.

Similar to equation 1, we calculated the second-order derivative of the energy by input strain, at the

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region of homogeneity, range of -0.02 <ε< 0.02 .

As mentioned, calculation at the regions inconsistence with the energy equation may lead to high-order terms that are not trivial; thereby, B was considered at this region. The unit cells at the biaxial strains were considered between -2% and 2% with the step of 1%. Also, total strain energies for given strains were obtained. Trend of strain energy by biaxial strains for unit cells of CC, BN-yne, and CC-BN-yne were investigated. The minimums with the lowest energy level can be translated as the optimum

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configuration for mentioned structures.

The calculations were performed with the aforementioned characteristics. Table 2 demonstrates the results of In-plane stiffness and Bulk module for examined structures. Regardless the decorated metal atoms, the results confirmed that the BN-yne and CC offers analogous values for both In-plane stiffness and Bulk module. It could be related to the structural integrity that is

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found in these structures; especially in the case of CC. In fact, the variation of components in case of CCBN-yne, caused several bond lengths; it caused several breakage points and emerged as the lowest In-

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plane stiffness as well as B, compared to the other nanosheets. Among decorated arrays, Na decorated ones obtained higher values of B. Na decorated structures demonstrated the Bulk module of 109.61, 68.95, and 68.83 N/m for CC, CC-BN-yne, and BN-yne, respectively; while they were calculated to be 79.36, 61.65, and 80.16 N/m for Pt decorated systems, in the same order.

Two major items may play key role in this regard: i) the physical size and ii) the electronegativity. Considering the physical size, since Na is in good consistency with the C, B, and N, the decorated systems are more stable, compared to Pt decorated ones. Moreover, Pt has higher electronegativity than Na; hence, the instability, which comes from attraction of free electrons, may be considerable.

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Elastic-Plastic regions As illustrated, linear mechanical properties such as Young’s and Bulk modulus are correlated with biaxial strain in the harmonic elastic deformation ranging from -2% to 2%. Here, the proposed nanostructures were characterized under more strains to demonstrate more mechanical behaviors. To do so, they were

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examined with biaxial tensions up to 36. In figure 2, the variation in strain energy ET (ε) is displayed in terms of applied strain. Here, we labeled the critical points in the elastic range;εc1 and εc2 [21]. The irreversible deformations, which occur in the plastic region, are observed at higher tensions; i.e. the nanostructure is passed the yielding point and has reached to the non-harmonic region. The εc1 and εc2 are the maximum point of derivative curve and yielding point, respectively.

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As the applied strain increases, the strain energy increases till the yielding point. Once the tension is released, the system may offer the initial array configuration and size, at ε=0. For ε < εc1, the variation of

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ET(ε) by tension may define as a parabolic curve, consequently, the value of

  () 

is independent of

tension. However, for ε > εc1 the harmonic schematic is not detected.

Values for first and second critical points are presented in table 3. The biaxial points of εc1 obtained larger for graphyne, compared to other structures. This value achieved equivalent for both Na/ and Pt/CC; also, the plastic region for these nanostructures has been started from similar tension value. There is a difference between figure2 (e) and others. There is a sharp change on the elastic region for the

local maximum.

Conclusion

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Na/CC-BN-yne. The reason might be that the shear stress enhances linearly with the strain up to small

In this paper, mechanical properties of Na and Pt decorated structures of CC, BN-yne, and CC-BN-yne

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were investigated based on DFT. Variation of strain energy with uniaxial strain resulted in the values of in-plane stiffness. The values for Na and Pt decorated CC, BN-yne, and CC-BN-yne were presented. The achieved results showed that the largest value was presented by CC; which were higher than that of

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obtained from non-decorated systems. While the Na decorated systems were considered, the value of Bulk module of graphyne was obtained to be larger than other structures. Whereas the trend of Bulk modulus function for Pt decorated systems was not consistent with Na decorated ones. The observed discrepancy may bold the effects of size of decorative material as well as its electron resonance properties.

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Acknowledgements This work was supported by the Nano Research and Training Center of Iran (NRTC.ir) (Grant no.

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3.1395.07.03).

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Figures

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Figure 1- Unit cells for examined nanostructures; a) Na/CC, b) Pt/CC, c) Na/BN, d) Pt/BN, e) Na/CC-BN-yne, and f) Pt/CC-BN-yne (In the unite cell structures: Brown, Green, Gray, Yellow, and dark Gray are defined as C, B, N, Na, and Pt)

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Figure 2- The variation in strain energy with biaxial strains. Strains corresponding to two critical points in the elastic range are labeled asεc1 andεc2; (a) Na/CC, (b) Pt/CC, (c) Na/BN-yne, (d) Pt/BN-yne, (e) Na/CC-BN-yne, and (f) Pt/CC-BN-yne.

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Table 1-Bond length and Lattice vectors for three proposed structure CC Bond length (Å) Lattice Vectors (Å) C-C 1.4 A 6.8710 C-C 1.4 B 6.8710 C-C 1.4 C 15

BN-yne

C-C C-B B-N

Bond length (Å) 1.24 1.49 1.4

A B C

A B C

CC-BN-yne 148.09 68.95

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Table 2-In-plane stiffness and Bulk modulus Na CC BN-yne In-plane stiffness 198.42 122.28 Bulk module 109.61 68.83

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CC-BN-yne

Lattice Vectors (Å) 7.0045 7.0045 15

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B-N N-N B-B

Bond length (Å) 1.4 2.67 2.67

Lattice Vectors (Å) 6.9790 6.9790 15

Pt BN-yne 159.20 80.16

CC 160.39 79.36

Table 3-First and second critical points

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CC BN-yne CC-BN-yne

εc1 10 8 8

Pt (%) εc2 12 14 10

εc1 10 4 6

Na (%) εc2 12 6 26

CC-BN-yne 128.54 61.65

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The research highlight are as follow:

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1. DFT calculations carried out using Local Combination of Atomic Orbital (LCAO) by the ab initio simulation code, (SIESTA). 2. The achieved results showed that the largest values of In-plane stiffness, either in Na and Pt decorated arrays, were recognized by pristine graphyne. 3. The results demonstrated that the pristine graphyne and BN-yne have the highest Bulk module when decorated with Na and Pt, respectively.