Abstract
This study presents the elastic properties and nonlinear elasticity of the two-dimensional noncarbon nanomaterials of hexagonal lattice structures having molecular structure XY. Four nitride-based and two phosphide-based two-dimensional nanomaterials, having graphene-like hexagonal lattice structure, are considered in the present study. The four empirical parameters associated with the attractive and repulsive terms of the Tersoff–Brenner potential are calibrated for noncarbon nanomaterials and tested for elastic properties, nonlinear constitutive behavior, bending modulus, bending and torsional energy. The mathematical identities for the tangent constitutive matrix in terms of the interatomic potential function are derived through an atomistic–continuum coupled multiscale framework of the extended version of Cauchy–Born rule. The results obtained using newly calibrated empirical parameters for cohesive energy, bond length, elastic properties, and bending rigidity are compared with those reported in the literature through experimental investigations and quantum mechanical calculations. The continuum approximation is attained through the finite element method. Multiscale evaluations for elastic properties and nonlinear stretching of the nanosheets under in-plane loads are also compared with those obtained from atomistic simulations.
References
1.
Iijima
, S.
, 1991
, “Helical Microtubules of Graphitic Carbon
,” Nature
, 354
(6348
), pp. 56
–58
. 10.1038/354056a02.
Gaffney
, A. M.
, Santos-Martinez
, M. J.
, Satti
, A.
, Major
, T. C.
, Wynne
, K. J.
, Gun'ko
, Y. K.
, Annich
, G. M.
, Elia
, G.
, and Radomski
, M. W.
, 2015
, “Blood Biocompatibility of Surface-Bound Multiwalled Carbon Nanotubes
,” Nanomed. Nanotechnol. Biol. Med.
, 11
(1
), pp. 39
–46
. 10.1016/j.nano.2014.07.0053.
Lahiri
, D.
, Singh
, V.
, Li
, L. H.
, Xing
, T.
, Seal
, S.
, Chen
, Y.
, and Agarwal
, A.
, 2012
, “Insight Into Reactions and Interface Between Boron Nitride Nanotube and Aluminium
,” J. Mater. Res.
, 27
(21
), pp. 2760
–2770
. 10.1557/jmr.2012.2944.
Özçelik
, V. O.
, Durgun
, E.
, and Ciraci
, S.
, 2015
, “Modulation of Electronic Properties in Laterally and Commensurately Repeating Graphene and Boron Nitride Composite Nanostructures
,” J. Phys. Chem. C
, 119
(23
), pp. 13248
–13256
. 10.1021/acs.jpcc.5b015985.
Wechwithayakhlung
, C.
, Packwood
, D. M.
, Chaopaknam
, J.
, Worakajit
, P.
, Ittisanronnachai
, S.
, Chanlek
, N.
, Promarak
, V.
, Kongpatpanich
, K.
, Harding
, D. J.
, and Pattanasattayavong
, P.
, 2019
, “Tin (ii) Thiocyanate Sn (NCS) 2–A Wide Bandgap Coordination Polymer Semiconductor with a 2D Structure
,” J. Mater. Chem. C
, 12
(12
), pp. 3452
–3462
. 10.1039/C8TC06150E6.
Shur
, M.
, 2019
, “Wide Bandgap Semiconductor Technology: State-of-the-Art
,” Solid-State Electron.
, 155
, pp. 65
–75
. 10.1016/j.sse.2019.03.0207.
Yu
, D. P.
, Sun
, X. S.
, Lee
, C. S.
, Bello
, I.
, Lee
, S. T.
, Gu
, H. D.
, Leung
, K. M.
, Zhou
, G. W.
, Dong
, Z. F.
, and Zhang
, Z.
, 1998
, “Synthesis of Boron Nitride Nanotubes by Means of Excimer Laser Ablation at High Temperature
,” Appl. Phys. Lett.
, 72
(16
), pp. 1966
–1968
. 10.1063/1.1212368.
Chen
, Y.
, Zou
, J.
, Campbell
, S. J.
, and Le Caer
, G.
, 2004
, “Boron Nitride Nanotubes: Pronounced Resistance to Oxidation
,” Appl. Phys. Lett.
, 84
(13
), pp. 2430
–2432
. 10.1063/1.16672789.
Hernandez
, E.
, Goze
, C.
, Bernier
, P.
, and Rubio
, A.
, 1998
, “Elastic Properties of C and BxCyNz Composite Nanotubes
,” Phys. Rev. Lett.
, 80
(20
), pp. 4502
–4505
. 10.1103/PhysRevLett.80.450210.
Kudin
, K. N.
, Scuseria
, G. E.
, and Yakobson
, B. I.
, 2001
, “C2F, BN, and C Nanoshell Elasticity From ab Initio Computations
,” Phys. Rev. B
, 64
(23
), p. 235406
. 10.1103/PhysRevB.64.23540611.
Akdim
, B.
, Pachter
, R.
, Duan
, X.
, and Adams
, W. W.
, 2003
, “Comparative Theoretical Study of Single-Wall Carbon and Boron-Nitride Nanotubes
,” Phys. Rev. B
, 67
(24
), p. 245404
. 10.1103/PhysRevB.67.24540412.
Peng
, Q.
, Ji
, W.
, and De
, S.
, 2012
, “Mechanical Properties of the Hexagonal Boron Nitride Monolayer: Ab Initio Study
,” Comput. Mater. Sci.
, 56
, pp. 11
–17
. 10.1016/j.commatsci.2011.12.02913.
Şahin
, H.
, Cahangirov
, S.
, Topsakal
, M.
, Bekaroglu
, E.
, Akturk
, E.
, Senger
, R. T.
, and Ciraci
, S.
, 2009
, “Monolayer Honeycomb Structures of Group-IV Elements and III-V Binary Compounds: First-Principles Calculations
,” Phys. Rev. B
, 80
(15
), p. 155453
. 10.1103/PhysRevB.80.15545314.
Singh
, A. K.
, Zhuang
, H. L.
, and Hennig
, R. G.
, 2014
, “Ab Initio Synthesis of Single-Layer III-V Materials
,” Phys. Rev. B
, 89
(24
), p. 245431
. 10.1103/PhysRevB.89.24543115.
Kochaev
, A.
, 2017
, “Elastic Properties of Noncarbon Nanotubes as Compared to Carbon Nanotubes
,” Phys. Rev. B
, 96
(15
), p. 155428
. 10.1103/PhysRevB.96.15542816.
Ghasemzadeh
, F.
, and Kanjouri
, F.
, 2018
, “Strain Effect on the Electronic Properties of III-Nitride Nanosheets: Ab-initio Study
,” Sci. China Technol. Sci.
, 61
(4
), pp. 535
–541
. 10.1007/s11431-017-9177-117.
Peng
, Q.
, Chen
, X. J.
, Liu
, S.
, and De
, S.
, 2013
, “Mechanical Stabilities and Properties of Graphene-Like Aluminum Nitride Predicted From First-Principles Calculations
,” RSC Adv.
, 3
(19
), pp. 7083
–7092
. 10.1039/c3ra40841h18.
Jafari
, H.
, Ravan
, B. A.
, and Faghihnasiri
, M.
, 2018
, “Mechanical and Electronic Properties of Single-Layer TiN and AlN Under Strain
,” Solid State Commun.
, 282
, pp. 21
–27
. 10.1016/j.ssc.2018.07.01019.
Hao
, J. H.
, Wang
, Y. F.
, Yin
, Y. H.
, Jiang
, R.
, Wang
, Y. F.
, and Jin
, Q. H.
, 2015
, “An Ab initio Study of the Size-Dependent Mechanical Behavior of Single-Walled AlN Nanotubes
,” Solid State Sci.
, 45
, pp. 30
–34
. 10.1016/j.solidstatesciences.2015.05.00120.
Zhou
, Z.
, Zhao
, J.
, Chen
, Y.
, von Ragué Schleyer
, P.
, and Chen
, Z.
, 2007
, “Energetics and Electronic Structures of AlN Nanotubes/Wires and Their Potential Application as Ammonia Sensors
,” Nanotechnology
, 18
(42
), p. 424023
. 10.1088/0957-4484/18/42/42402321.
Zhang
, D.
, and Zhang
, R. Q.
, 2003
, “Theoretical Prediction on Aluminium Nitride Nanotubes
,” Chem. Phys. Lett.
, 371
(3–4
), pp. 426
–432
. 10.1016/S0009-2614(03)00289-622.
Peng
, Q.
, Liang
, C.
, Ji
, W.
, and De
, S.
, 2013
, “Mechanical Properties of g-GaN: A First-Principles Study
,” Appl. Phys. A
, 113
(2
), pp. 483
–490
. 10.1007/s00339-013-7551-423.
Qian
, Z.
, Hou
, S.
, Zhang
, J.
, Li
, R.
, Shen
, Z.
, Zhao
, X.
, and Xue
, Z.
, 2005
, “Stability and Electronic Structure of Single-Walled InN Nanotubes
,” Physica E Low Dimens. Syst. Nanostruct.
, 30
(1–2
), pp. 81
–85
. 10.1016/j.physe.2005.07.00224.
Peng
, Q.
, Sun
, X.
, Wang
, H.
, Yang
, Y.
, Wen
, X.
, Huang
, C.
, Liu
, S.
, and De
, S.
, 2017
, “Theoretical Prediction of a Graphene-Like Structure of Indium Nitride: A Promising Excellent Material for Optoelectronics
,” Appl. Mater. Today
, 7
, pp. 169
–178
. 10.1016/j.apmt.2017.03.00125.
Ren
, M.
, Li
, M.
, Zhang
, C.
, Yuan
, M.
, Li
, P.
, Li
, F.
, Ji
, W.
, and Liu
, X.
, 2015
, “First-Principles Study on the Electronic and Magnetic Properties of InN Nanosheets Doped With 2p Elements
,” Physica E Low Dimens. Syst. Nanostruct.
, 67
, pp. 1
–6
. 10.1016/j.physe.2014.10.03626.
Zhuang
, H. L.
, and Hennig
, R. G.
, 2012
, “Electronic Structures of Single-Layer Boron Pnictides
,” Appl. Phys. Lett.
, 101
(15
), p. 153109
. 10.1063/1.475846527.
Zhu
, Z.
, Cai
, X.
, Niu
, C.
, Wang
, C.
, and Jia
, Y.
, 2016
, “Computational Prediction of the Diversity of Monolayer Boron Phosphide Allotropes
,” Appl. Phys. Lett.
, 109
(15
), p. 153107
. 10.1063/1.496476328.
Wang
, Y.
, Huang
, C.
, Li
, D.
, Li
, P.
, Yu
, J.
, Zhang
, Y.
, and Xu
, J.
, 2019
, “Tight-Binding Model for the Electronic Structure of Hexagonal Boron Phosphide Monolayer and Bilayer
,” J. Phys.: Condens. Matter
, 31
(28
), p. 285501
. 10.1088/1361-648X/ab152829.
Lisenkov
, S. V.
, Vinogradov
, G. A.
, and Lebedev
, N. G.
, 2005
, “A new Class of Noncarbon AlP Nanotubes: Structure and Electronic Properties
,” J. Exp. Theor. Phys. Lett.
, 81
(4
), pp. 185
–189
. 10.1134/1.191487830.
Albe
, K.
, and Möller
, W.
, 1998
, “Modelling of Boron Nitride: Atomic-Scale Simulations on Thin-Film Growth
,” Comput. Mater. Sci.
, 10
(1–4
), pp. 111
–115
. 10.1016/S0927-0256(97)00172-931.
Benkabou
, F.
, Certier
, M.
, and Aourag
, H.
, 2003
, “Elastic Properties of Zinc-Blende GaN, AlN and InN From Molecular Dynamics
,” Mol. Simul.
, 29
(3
), pp. 201
–209
. 10.1080/089270202100004967332.
Tungare
, M.
, Shi
, Y.
, Tripathi
, N.
, Suvarna
, P.
, and Shahedipour-Sandvik
, F.
, 2011
, “A Tersoff-Based Interatomic Potential for Wurtzite AlN
,” Physica Status Solidi
, 208
(7
), pp. 1569
–1572
. 10.1002/pssa.20100108633.
Kang
, J. W.
, and Hwang
, H. J.
, 2004
, “Molecular Dynamics Simulations of Single-Wall GaN Nanotubes
,” Mol. Simul.
, 30
(1
), pp. 29
–35
. 10.1080/0892-702031000159622334.
Jeng
, Y. R.
, Tsai
, P. C.
, and Fang
, T. H.
, 2004
, “Molecular Dynamics Investigation of the Mechanical Properties of Gallium Nitride Nanotubes Under Tension and Fatigue
,” Nanotechnology
, 15
(12
), pp. 1737
–1744
. 10.1088/0957-4484/15/12/00635.
Kang
, J. W.
, and Hwang
, H. J.
, 2004
, “Atomistic Study of III-Nitride Nanotubes
,” Comput. Mater. Sci.
, 31
(3–4
), pp. 237
–246
. 10.1016/j.commatsci.2004.03.00436.
Moon
, W. H.
, and Hwang
, H. J.
, 2004
, “Molecular-Dynamics Simulation of Structure and Thermal Behaviour of Boron Nitride Nanotubes
,” Nanotechnology
, 15
(5
), pp. 431
–434
. 10.1088/0957-4484/15/5/00537.
Sekkal
, W.
, Bouhafs
, B.
, Aourag
, H.
, and Certier
, M.
, 1998
, “Molecular-Dynamics Simulation of Structural and Thermodynamic Properties of Boron Nitride
,” J. Phys.: Condens. Matter
, 10
(23
), pp. 4975
–4984
. 10.1088/0953-8984/10/23/00638.
Verma
, V.
, Jindal
, V. K.
, and Dharamvir
, K.
, 2007
, “Elastic Moduli of a Boron Nitride Nanotube
,” Nanotechnology
, 18
(43
), p. 435711
. 10.1088/0957-4484/18/43/43571139.
Powell
, D.
, 2006
, “Elasticity, Lattice Dynamics and Parametrisation Techniques for the Tersoff Potential Applied to Elemental III-V Semiconductors
,” PhD thesis
, University of Sheffield, UK.40.
Liao
, M. L.
, Wang
, Y. C.
, Ju
, S. P.
, Lien
, T. W.
, and Huang
, L. F.
, 2011
, “Deformation Behaviours of an Armchair Boron-Nitride Nanotube Under Axial Tensile Strains
,” J. Appl. Phys.
, 110
(5
), p. 054310
. 10.1063/1.362606541.
Sevik
, C.
, Kinaci
, A.
, Haskins
, J. B.
, and Çağın
, T.
, 2011
, “Characterization of Thermal Transport in Low-Dimensional Boron Nitride Nanostructures
,” Phys. Rev. B
, 84
(8
), p. 085409
. 10.1103/PhysRevB.84.08540942.
Los
, J. H.
, Kroes
, J. M. H.
, Albe
, K.
, Gordillo
, R. M.
, Katsnelson
, M. I.
, and Fasolino
, A.
, 2017
, “Extended Tersoff Potential for Boron Nitride: Energetics and Elastic Properties of Pristine and Defective h-BN
,” Phys. Rev. B
, 96
(18
), p. 184108
. 10.1103/PhysRevB.96.18410843.
Kumar
, R.
, Rajasekaran
, G.
, and Parashar
, A.
, 2016
, “Optimised Cut-off Function for Tersoff-Like Potentials for a BN Nanosheet: A Molecular Dynamics Study
,” Nanotechnology
, 27
(8
), p. 085706
. 10.1088/0957-4484/27/8/08570644.
Boldrin
, L.
, Scarpa
, F.
, Chowdhury
, R.
, and Adhikari
, S.
, 2011
, “Effective Mechanical Properties of Hexagonal Boron Nitride Nanosheets
,” Nanotechnology
, 22
(50
), p. 505702
. 10.1088/0957-4484/22/50/50570245.
Jiang
, L.
, and Guo
, W.
, 2016
, “Analytical Solutions for Elastic Binary Nanotubes of Arbitrary Chirality
,” Acta Mech. Sin.
, 32
(6
), pp. 1046
–1057
. 10.1007/s10409-016-0581-346.
Oh
, E. S.
, 2010
, “Elastic Properties of Boron-Nitride Nanotubes Through the Continuum Lattice Approach
,” Mater. Lett.
, 64
(7
), pp. 859
–862
. 10.1016/j.matlet.2010.01.04147.
Singh
, S.
, 2020
, “Critical Assessment of the Interatomic Potentials for the Elastic Properties of the Noncarbon Monolayer Nanomaterials
,” Comput. Mater. Sci.
, 177
, p. 109550
. 10.1016/j.commatsci.2020.10955048.
Tersoff
, J.
, 1988
, “A New Empirical Approach for the Structure and Energy of Covalent Systems
,” Phys. Rev. B
, 37
(12
), pp. 6991
–7000
. 10.1103/PhysRevB.37.699149.
Zhuang
, H. L.
, Singh
, A. K.
, and Hennig
, R. G.
, 2013
, “Computational Discovery of Single-Layer III-V Materials
,” Phys. Rev. B
, 87
(16
), p. 165415
. 10.1103/PhysRevB.87.16541550.
Brenner
, D. W.
, 1990
, “Empirical Potential for Hydrocarbons for Use in Simulating the Chemical Vapour Deposition of Diamond Films
,” Phys. Rev. B
, 42
(15
), pp. 9458
–9471
. 10.1103/PhysRevB.42.945851.
Huang
, Y.
, Wu
, J.
, and Hwang
, K. C.
, 2006
, “Thickness of Graphene and Single-Wall Carbon Nanotubes
,” Phys. Rev. B
, 74
(24
), p. 245413
. 10.1103/PhysRevB.74.24541352.
Singh
, S.
, and Patel
, B. P.
, 2018
, “Effect of Initial Strain and Material Nonlinearity on the Nonlinear Static and Dynamic Response of Graphene Sheets
,” J. Sound Vib.
, 423
, pp. 373
–400
. 10.1016/j.jsv.2018.02.05953.
Singh
, S.
, and Patel
, B. P.
, 2018
, “Large Deformation Static and Dynamic Response of Carbon Nanotubes by Mixed Atomistic and Continuum Models
,” Int. J. Mech. Sci.
, 135
, pp. 565
–581
. 10.1016/j.ijmecsci.2017.11.04154.
Singh
, S.
, and Patel
, B. P.
, 2015
, “Atomistic–Continuum Coupled Model for Nonlinear Analysis of Single-Layer Graphene Sheets
,” Int. J. Non-Linear Mech.
, 76
, pp. 112
–119
. 10.1016/j.ijnonlinmec.2015.06.00855.
Singh
, S.
, 2019
, “Refined Multiscale Model Based on the Second Generation Interatomic Potential for the Mechanics of Graphene Sheets
,” Mech. Mater.
, 133
, pp. 26
–36
. 10.1016/j.mechmat.2019.03.00456.
Singh
, S.
, 2019
, “Exploring the Effect of Dihedral Energy on the Nonlinear Mechanics of the Carbon Nanotubes Using Multiscale Modelling
,” ASME J. Vib. Acoust.
, 141
(4
), p. 041018
. 10.1115/1.404324257.
Neumann
, H.
, 1995
, “Properties of Group III-Nitrides
,” Cryst. Res. Technol.
, 30
(7
), p. 910
. 10.1002/crat.217030070458.
Camacho-Mojica
, D. C.
, and López-Urías
, F.
, 2015
, GaN Haeckelite Single-Layered Nanostructures: Monolayer and Nanotubes. Scientific Reports 5, 17902.59.
Mokhalingam
, A.
, Ghaffari
, R.
, Sauer
, R. A.
, and Gupta
, S. S.
, 2020
, “Comparing Quantum, Molecular and Continuum Models for Graphene at Large Deformations
,” Carbon
, 159
, pp. 478
–494
. 10.1016/j.carbon.2019.12.01460.
Blevins
, R. D.
, 1979
, Formulas for Natural Frequency and Mode Shapes
, Van Nostrand Reinhold Company
.Copyright © 2020 by ASME
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