Abstract
Hybrid graphene/h-BN model is studied via molecular dynamics simulation to observe the evolution of graphene layer upon heating. Model containing 20,064 atoms is heated up from 50 to 8000 K via Tersoff and Lennard–Jones potentials. Various thermodynamic quantities, structural characteristics, and the occurrence of liquid-like atoms are studied. The Lindemann criterion for 2D case is calculated and used to observe the appearance of liquid-like atoms. The atomic mechanism of structural evolution upon heating is analyzed on the basis of the occurrence/growth of liquid-like atoms, the formation of clusters, the coordination number, and the ring statistics. The liquid-like atoms tend to form clusters and the largest cluster increases slightly in order to form a single largest cluster of liquid-like atoms. The other models such as free-standing graphene, zigzag GNR, and armchair GNR are also presented to have an entire picture about the evolution of graphene upon heating in different models. Note that the largest clusters of free-standing graphene as well as zigzag GNR, and armchair GNR tend to decrease to form a ring-like 2D liquid carbon.
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Novoselov K, Geim AK, Morozov S, Jiang D, Katsnelson M, Grigorieva I, Dubonos S, Firsov A (2005) Two-dimensional gas of massless Dirac fermions in graphene. Nature 438:197–200. https://doi.org/10.1038/nature04233
Zhang Y, Jiang Z, Small J, Purewal M, Tan Y-W, Fazlollahi M, Chudow J, Jaszczak J, Stormer H, Kim P (2006) Landau-level splitting in graphene in high magnetic fields. Phys Rev Lett 96:136806. https://doi.org/10.1103/PhysRevLett.96.136806
Geim AK, Novoselov KS (2007) The rise of graphene. Nat Mater 6:183. https://doi.org/10.1038/nmat1849
Meric I, Han MY, Young AF, Ozyilmaz B, Kim P, Shepard KL (2008) Current saturation in zero-bandgap, top-gated graphene field-effect transistors. Nat Nanotechnol 3:654. https://doi.org/10.1038/nnano.2008.268
Wang WL, Meng S, Kaxiras E (2008) Graphene nanoflakes with large spin. Nano Lett 8:241. https://doi.org/10.1021/nl072548a
Nakada K, Fujita M, Dresselhaus G, Dresselhaus MS (1996) Edge state in graphene ribbons: nanometer size effect and edge shape dependence. Phys Rev B 54:17954. https://doi.org/10.1103/PhysRevB.54.17954
Novoselov KS, Geim AK, Morozov S, Jiang D, Katsnelson M, Grigorieva I, Dubonos S, Firsov A (2005) Two-dimensional gas of massless Dirac fermions in graphene. Nature 438:197. https://doi.org/10.1038/nature04233
Son Y-W, Cohen ML, Louie SG (2006) Energy gaps in graphene nanoribbons. Phys Rev Lett 97:216803. https://doi.org/10.1103/PhysRevLett.97.216803
Han MY, Özyilmaz B, Zhang Y, Kim P (2007) Energy band-gap engineering of graphene nanoribbons. Phys Rev Lett 98:206805. https://doi.org/10.1103/PhysRevLett.98.206805
Jin-Xiang D, Xiao-Kang Z, Qian Y, Xu-Yang W, Guang-Hua C, De-Yan H (2009) Optical properties of hexagonal boron nitride thin films deposited by radio frequency bias magnetron sputtering. Chin Phys B 18:4013. https://doi.org/10.1088/1674-1056/18/9/066
Li C, Bando Y, Zhi C, Huang Y, Golberg D (2009) Thickness-dependent bending modulus of hexagonal boron nitride nanosheets. Nanotechnology 20:385707. https://doi.org/10.1088/0957-4484/20/38/385707
Suenaga K, Colliex C, Demoncy N, Loiseau A, Pascard H, Willaime F (1997) Synthesis of nanoparticles and nanotubes with well-separated layers of boron nitride and carbon. Science 278:653–655. https://doi.org/10.1126/science.278.5338.653
Han W-Q, Mickelson W, Cumings J, Zettl A (2002) Transformation of BxCyNz nanotubes to pure BN nanotubes. Appl Phys Lett 81:1110–1112. https://doi.org/10.1002/adma.200700179
Kawasaki T, Ichimura T, Kishimoto H, Akbar AA, Ogawa T, Oshima C (2002) Double atomic layers of graphene/monolayer h-BN on Ni (111) studied by scanning tunneling microscopy and scanning tunneling spectroscopy. Surf Rev Lett 9:1459–1464. https://doi.org/10.1142/S0218625X02003883
Novoselov K, Mishchenko A, Carvalho A, Neto AC (2016) 2D materials and van der Waals heterostructures. Science 353:aac9439. https://doi.org/10.1126/science.aac9439
Giovannetti G, Khomyakov PA, Brocks G, Kelly PJ, Van Den Brink J (2007) Substrate-induced band gap in graphene on hexagonal boron nitride: ab initio density functional calculations. Phys Rev B 76:073103. https://doi.org/10.1126/science.aac9439
Dean CR, Young AF, Meric I, Lee C, Wang L, Sorgenfrei S, Watanabe K, Taniguchi T, Kim P, Shepard KL (2010) Boron nitride substrates for high-quality graphene electronics. Nat Nanotechnol 5:722. https://doi.org/10.1038/nnano.2010.172
Decker R, Wang Y, Brar VW, Regan W, Tsai H-Z, Wu Q, Gannett W, Zettl A, Crommie MF (2011) Local electronic properties of graphene on a BN substrate via scanning tunneling microscopy. Nano Lett 11:2291–2295. https://doi.org/10.1021/nl2005115
Yankowitz M, Xue J, Cormode D, Sanchez-Yamagishi JD, Watanabe K, Taniguchi T, Jarillo-Herrero P, Jacquod P, LeRoy BJ (2012) Emergence of superlattice Dirac points in graphene on hexagonal boron nitride. Nat Phys 8:382. https://doi.org/10.1038/nphys2272
Bokdam M, Khomyakov PA, Brocks G, Zhong Z, Kelly PJ (2011) Electrostatic doping of graphene through ultrathin hexagonal boron nitride films. Nano Lett 11:4631–4635. https://doi.org/10.1021/nl202131q
Martins T, Miwa RD, Da Silva AJ, Fazzio A (2007) Electronic and transport properties of boron-doped graphene nanoribbons. Phys Rev Lett 98:196803. https://doi.org/10.1007/s13204-013-0220-2
Lherbier A, Blase X, Niquet Y-M, Triozon F, Roche S (2008) Charge transport in chemically doped 2D graphene. Phys Rev Lett 101:036808. https://doi.org/10.1103/PhysRevLett.101.036808
Wang X, Li X, Zhang L, Yoon Y, Weber PK, Wang H, Guo J, Dai H (2009) N-doping of graphene through electrothermal reactions with ammonia. Science 324:768–771. https://doi.org/10.1126/science.1170335
Kaner R, Kouvetakis J, Warble C, Sattler M, Bartlett N (1987) Boron-carbon-nitrogen materials of graphite-like structure. Mater Res Bull 22:399–404. https://doi.org/10.1016/0025-5408(87)90058-4
Liu AY, Wentzcovitch RM, Cohen ML (1989) Atomic arrangement and electronic structure of BC2N. Phys Rev B 39:1760. https://doi.org/10.1103/PhysRevB.39.1760
Miyamoto Y, Rubio A, Cohen ML, Louie SG (1994) Chiral tubules of hexagonal BC2N. Phys Rev B 50:4976. https://doi.org/10.1103/PhysRevB.50.4976
Weng-Sieh Z, Cherrey K, Chopra NG, Blase X, Miyamoto Y, Rubio A, Cohen ML, Louie SG, Zettl A, Gronsky R (1995) Synthesis of BxCyNz nanotubules. Phys Rev B 51:11229. https://doi.org/10.1016/S0009-2614(01)00993-9
Hernandez E, Goze C, Bernier P, Rubio A (1998) Elastic properties of C and BxCyNz composite nanotubes. Phys Rev Lett 80:4502. https://doi.org/10.1103/PhysRevLett.80.4502
Golberg D, Bando Y, Bourgeois L, Kurashima K, Sato T (2000) Large-scale synthesis and HRTEM analysis of single-walled B-and N-doped carbon nanotube bundles. Carbon 38:2017–2027. https://doi.org/10.1016/S0008-6223(00)00058-0
Golberg D, Bando Y, Dorozhkin P, Dong Z-C (2004) Synthesis, analysis, and electrical property measurements of compound nanotubes in the BCN ceramic system. MRS Bull 29:38–42. https://doi.org/10.1557/mrs2004.15
Jung J, Qiao Z, Niu Q, MacDonald AH (2012) Transport properties of graphene nanoroads in boron nitride sheets. Nano Lett 12:2936–2940. https://doi.org/10.1021/nl300610w
Son M, Lim H, Hong M, Choi HC (2011) Direct growth of graphene pad on exfoliated hexagonal boron nitride surface. Nanoscale 3:3089–3093. https://doi.org/10.1039/C1NR10504C
Tang S, Ding G, Xie X, Chen J, Wang C, Ding X, Huang F, Lu W, Jiang M (2012) Nucleation and growth of single crystal graphene on hexagonal boron nitride. Carbon 50:329–331. https://doi.org/10.1016/j.carbon.2011.07.062
Tang S, Wang H, Zhang Y, Li A, Xie H, Liu X, Liu L, Li T, Huang F, Xie X (2013) Precisely aligned graphene grown on hexagonal boron nitride by catalyst free chemical vapor deposition. Sci Rep 3:2666. https://doi.org/10.1038/srep02666
Yang W, Chen G, Shi Z, Liu C-C, Zhang L, Xie G, Cheng M, Wang D, Yang R, Shi D (2013) Epitaxial growth of single-domain graphene on hexagonal boron nitride. Nat Mater 12:792. https://doi.org/10.1021/nn5058968
Tang S, Wang H, Wang HS, Sun Q, Zhang X, Cong C, Xie H, Liu X, Zhou X, Huang F (2015) Silane-catalysed fast growth of large single-crystalline graphene on hexagonal boron nitride. Nat Commun 6:6499. https://doi.org/10.1038/ncomms7499
Kim KK, Hsu A, Jia X, Kim SM, Shi Y, Hofmann M, Nezich D, Rodriguez-Nieva JF, Dresselhaus M, Palacios T (2011) Synthesis of monolayer hexagonal boron nitride on Cu foil using chemical vapor deposition. Nano Lett 12:161–166. https://doi.org/10.1021/nl203249a
Gao L, Ren W, Xu H, Jin L, Wang Z, Ma T, Ma L-P, Zhang Z, Fu Q, Peng L-M (2012) Repeated growth and bubbling transfer of graphene with millimetre-size single-crystal grains using platinum. Nat Commun 3:699
Kim G, Jang A-R, Jeong HY, Lee Z, Kang DJ, Shin HS (2013) Growth of high-crystalline, single-layer hexagonal boron nitride on recyclable platinum foil. Nano Lett 13:1834–1839. https://doi.org/10.1021/nl400559s
Arjmandi-Tash H, Kalita D, Han Z, Othmen R, Nayak G, Berne C, Landers J, Watanabe K, Taniguchi T, Marty L (2018) Large scale graphene/h-BN heterostructures obtained by direct CVD growth of graphene using high-yield proximity-catalytic process. J Phys Mater 1:015003
Kawaguchi M, Kawashima T, Nakajima T (1996) Syntheses and structures of new graphite-like materials of composition BCN (H) and BC3N (H). Chem Mater 8:1197–1201. https://doi.org/10.1021/cm950471y
Ci L, Song L, Jin C, Jariwala D, Wu D, Li Y, Srivastava A, Wang Z, Storr K, Balicas L (2010) Atomic layers of hybridized boron nitride and graphene domains. Nat Mater 9:430. https://doi.org/10.1038/nmat2711
Stillinger FH, Weber TA (1985) Computer simulation of local order in condensed phases of silicon. Phys Rev B 31:5262. https://doi.org/10.1103/PhysRevB.33.1451
Bazant MZ, Kaxiras E, Justo JF (1997) Environment-dependent interatomic potential for bulk silicon. Phys Rev B 56:8542. https://doi.org/10.1088/0953-8984/22/3/035802
Justo JF, Bazant MZ, Kaxiras E, Bulatov VV, Yip S (1998) Interatomic potential for silicon defects and disordered phases. Phys Rev B 58:2539. https://doi.org/10.1103/PhysRevB.58.2539
Marks N (2000) Generalizing the environment-dependent interaction potential for carbon. Phys Rev B 63:035401. https://doi.org/10.1103/PhysRevB.63.035401
Finnis M, Sinclair J (1984) A simple empirical N-body potential for transition metals. Philos Mag A 50:45. https://doi.org/10.1080/01418618408244210
Baskes M (1987) Application of the embedded-atom method to covalent materials: a semiempirical potential for silicon. Phys Rev Lett 59:2666. https://doi.org/10.1103/PhysRevLett.59.2666
Pettifor D (1989) New many-body potential for the bond order. Phys Rev Lett 63:2480. https://doi.org/10.1103/PhysRevLett.63.2480
Pettifor D, Oleinik I (1999) Analytic bond-order potentials beyond Tersoff-Brenner. I. Theory. Phys Rev B 59:8487. https://doi.org/10.1103/PhysRevB.59.8500
Brenner DW, Shenderova OA, Harrison JA, Stuart SJ, Ni B, Sinnott SB (2002) A second-generation reactive empirical bond order (REBO) potential energy expression for hydrocarbons. J Phys Condens Matter 14:783. https://doi.org/10.1088/0953-8984/14/4/312
Van Duin AC, Dasgupta S, Lorant F, Goddard WA (2001) ReaxFF: a reactive force field for hydrocarbons. J Phys Chem A 105:9396–9409. https://doi.org/10.1021/jp004368u
Van Duin AC, Strachan A, Stewman S, Zhang Q, Xu X, Goddard WA (2003) ReaxFFSiO reactive force field for silicon and silicon oxide systems. J Phys Chem A 107:3803–3811. https://doi.org/10.1021/jp0276303
Chenoweth K, Van Duin AC, Goddard WA (2008) ReaxFF reactive force field for molecular dynamics simulations of hydrocarbon oxidation. J Phys Chem A 112:1040–1053. https://doi.org/10.1021/jp709896w
Tersoff J (1988) New empirical approach for the structure and energy of covalent systems. Phys Rev B 37:6991. https://doi.org/10.1103/PhysRevB.37.6991
Tersoff J (1989) Modeling solid-state chemistry: interatomic potentials for multicomponent systems. Phys Rev B 39:5566. https://doi.org/10.1103/PhysRevB.41.3248.2
Nord J, Albe K, Erhart P, Nordlund K (2003) Modelling of compound semiconductors: analytical bond-order potential for gallium, nitrogen and gallium nitride. J Phys Condens Matter 15:569. https://doi.org/10.1088/0953-8984/15/32/324
Brenner DW (1990) Empirical potential for hydrocarbons for use in simulating the chemical vapor deposition of diamond films. Phys Rev B 42:9458
Yu N, Polycarpou AA (2004) Adhesive contact based on the Lennard–Jones potential: a correction to the value of the equilibrium distance as used in the potential. J Colloid Interface Sci 278:428–435. https://doi.org/10.1016/j.jcis.2004.06.029
Kang JW, Hwang HJ (2004) Comparison of C60 encapsulations into carbon and boron nitride nanotubes. J Phys Condens Matter 16:3901. https://doi.org/10.1088/0953-8984/16/23/010
Plimpton S (1995) Fast parallel algorithms for short-range molecular dynamics. J Comput Phys 117:1. https://doi.org/10.1006/jcph.1995.1039
Hoang VV, Cam Tuyen LT, Dong TQ (2016) Stages of melting of graphene model in two-dimensional space. Philos Mag 96:1993–2008. https://doi.org/10.1080/14786435.2016.1185183
Gleiman S, Chen C-K, Datye A, Phillips J (2002) Melting and spheroidization of hexagonal boron nitride in a microwave-powered, atmospheric pressure nitrogen plasma. J Mater Sci 37:3429. https://doi.org/10.1023/A:1016502804363
Le Roux S, Petkov V (2010) ISAACS–interactive structure analysis of amorphous and crystalline systems. J Appl Crystallogr 43:181. https://doi.org/10.1107/S0021889809051929
Humphrey W, Dalke A, Schulten K (1996) VMD: visual molecular dynamics. J Mol Graph 14:33
Bak P (1982) Commensurate phases, incommensurate phases and the devil’s staircase. Rep Prog Phys 45:587. https://doi.org/10.1088/0034-4885/45/6/001
Savvatimskiy A (2005) Measurements of the melting point of graphite and the properties of liquid carbon (a review for 1963–2003). Carbon 43:1115–1142. https://doi.org/10.1016/j.carbon.2004.12.027
March NH, Tosi MP (2002) Introduction to liquid state physics. World Scientific, Singapore. https://doi.org/10.1063/1.3024519
Mermin ND, Wagner H (1966) Absence of ferromagnetism or antiferromagnetism in one-or two-dimensional isotropic Heisenberg models. Phys Rev Lett 17:1133. https://doi.org/10.1103/PhysRevLett.17.1133
Mermin ND (1968) Crystalline order in two dimensions. Phys Rev 176:250. https://doi.org/10.1103/PhysRevB.20.4762
Landau LD, Lifshitz EM (2013) Course of theoretical physics, vol 5. Elsevier, Amsterdam
Bedanov V, Gadiyak G, Lozovik YE (1985) On a modified Lindemann-like criterion for 2D melting. Phys Lett A 109:289. https://doi.org/10.1209/epl/i1998-00205-7
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Authors thank for financial support from the National Foundation for Science and Technology Development (NAFOSTED) under Grant 103.01.2015.101.
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Nguyen, H.T.T. Graphene layer of hybrid graphene/hexagonal boron nitride model upon heating. Carbon Lett. 29, 521–528 (2019). https://doi.org/10.1007/s42823-019-00056-6
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DOI: https://doi.org/10.1007/s42823-019-00056-6