MNSMS  Vol.2 No.4 , October 2012
A First Principles Investigation of the Mechanical Properties of g-TlN
Abstract: We investigate the structure and mechanical properties of proposed graphene-like hexagonal thallium nitride monolayer (g-TlN) using first-principles calculations based on density-functional theory. Compared to graphene-like hexagonal boron nitride monolayer (g-BN), g-TlN is much softer, with 12% in-plane stiffness, 25%, 22%, and 20% ultimate strengths in armchair, zigzag, and biaxial strains respectively. However, g-TlN has a larger Poisson’s ratio, 0.69, about 3.1 times that of g-BN. It was found that the g-TlN also sustains much smaller strains before rupture. We obtained the second, third, fourth, and fifth order elastic constants for a rigorous continuum description of the elastic response of g-TlN. 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.
Cite this paper: Q. Peng, C. Liang, W. Ji and S. De, "A First Principles Investigation of the Mechanical Properties of g-TlN," Modeling and Numerical Simulation of Material Science, Vol. 2 No. 4, 2012, pp. 76-84. doi: 10.4236/mnsms.2012.24009.

[1]   K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva and A. A. Firsov, “Electric Field Effect in Atomically Thin Carbon Films,” Science Magazine, Vol. 306, No. 5696, 2004, pp. 666-669. doi:10.1126/science.1102896

[2]   K. S. Novoselov, D. Jiang, F. Schedin, T. J. Booth, V. V. Khotkevich, S. V. Morozov and A. K. Geim, “Two-Dimensional Atomic Crystals,” Proceedings of the National Academy of Sciences, USA, Vol. 102, No. 30, 2005, pp. 10451-10453. doi:10.1073/pnas.0502848102

[3]   K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos and A. A. Firsov, “Two-Dimensional Gas of Massless Dirac Fermions in Graphene,” Nature, Vol. 438, No. 7065, 2005, pp. 197-200. doi:10.1038/nature04233

[4]   Y.-M. Lin, K. A. Jenkins, A. Valdes-Garcia, J. P. Small, D. B. Farmer and P. Avouris, “Operation of Graphene Transistors at Gigahertz Frequencies,” Nano Letters, Vol. 9, No. 1, 2009, pp. 422-426. doi:10.1021/nl803316h

[5]   Y.-M. Lin, C. Dimitrakopoulos, K. A. Jenkins, D. B. Farmer, H.-Y. Chiu, A. Grill and P. Avouris, “100-Ghz Transistors from Wafer-Scale Epitaxial Graphene,” Science Magazine, Vol. 327, No. 5966, 2010, p. 662. doi:10.1126/science.1184289

[6]   L. Liao, Y.-C. Lin, M. Bao, R. Cheng, J. Bai, Y. Liu, Y. Qu, K. L. Wang, Y. Huang and X. Duan, “High-Speed Graphene Transistors with a Self-Aligned Nanowire Gate,” Nature, Vol. 467, No. 7313, 2010, pp. 305-308. doi:10.1038/nature09405

[7]   Y. Ma, Y. Dai, M. Guo and B. Huang, “Graphene-Diamond Interface: Gap Opening and Electronic Spin Injection,” Physics Review B, Vol. 85, No. 23, 2012, pp. 235448-223452. doi:10.1103/PhysRevB.85.235448

[8]   G. Brumfiel, “Graphene Gets Ready for the Big Time,” Nature, Vol. 458, No. 7237, 2009, pp. 390-391. doi:10.1038/458390a

[9]   R. Mas-Balleste, C. Gomez-Herrero, J. Gómez-Herrero and F. Zamora, “2D Materials: To Graphene and Beyond,” Nanoscale, Vol. 3, No. 1, 2011, pp. 20-30.

[10]   T. P. Kaloni, Y. C. Cheng and U. Schwingenschloegl, “Electronic Structure of Superlattices of Graphene and Hexagonal Boron Nitride,” Journal of Material Chemistry, Vol. 22, No. 3, 2012, pp. 919-922. doi:10.1039/c1jm14895h

[11]   J. N. Coleman, M. Lotya, A. O’neill, S. D. Bergin, P. J. King, U. Khan, K. Young, A. Gaucher, S. De, R. J. Smith, I. V. Shvets, S. K. Arora, G. Stanton, H.-Y. Kim, K. Lee, G. T. Kim, G. S. Duesberg, T. Hallam, J. J. Boland, J. J. Wang, J. F. Donegan, J. C. Grunlan, G. Moriarty, A. Shmeliov, R. J. Nicholls, J. M. Perkins, E. M. Grieveson, K. Theuwissen, D. W. Mccomb, P. D. Nellist and V. Nicolosi, “Two-Dimensional Nanosheets Produced by Liquid Exfoliation of Layered Materials,” Science Magazine, Vol. 331, No

[12]   A. Nag, K. Raidongia, K. P. Hembram, R. Datta, U. V. Waghmare and C. N. Rao, “Graphene Analogues of Bn: Novel Synthesis and Properties,” ACS Nano, Vol. 4, No. 3, 2010, pp. 1539-1544. doi:10.1021/nn9018762

[13]   C. Li, Y. Bando, C. Zhi, Y. Huang and D. Golberg, “Thickness-Dependent Bending Modulus of Hexagonal Boron Nitride Nanosheets,” Nanotechnology, Vol. 20, No. 38, 2009, pp. 385707-385712. doi:10.1088/0957-4484/20/38/385707

[14]   L. Song, L. Ci, H. Lu, P. B. Sorokin, C. Jin, J. Ni, A. G. Kvashnin, D. G. Kvashnin, J. Lou, B. I. Yakobson and P. M. Ajayan, “Large Scale Growth and Characterization of Atomic Hexagonal Boron Nitride Layers,” Nano Letters, Vol. 10, No. 8, 2010, pp. 3209-3215. doi:10.1021/nl1022139

[15]   M. Topsakal, E. Aktürk and S. Ciraci, “First-Principles Study of Twoand One-Dimensional Honeycomb Structures of Boron Nitride,” Physics Review B, Vol. 79, No. 11, 2009, pp. 115442-115452. doi:10.1103/PhysRevB.79.115442

[16]   K. Watanabe, T. Taniguchi and H. Kanda, “Direct-Bandgap Properties and Evidence for Ultraviolet Lasing of Hexagonal Boron Nitride Single Crystal,” Nature Material, Vol. 3, No. 6, 2004, pp. 404-409. doi:10.1038/nmat1134

[17]   C. Zhi, Y. Bando, C. Tang, H. Kuwahara and D. Golberg, “Large-Scale Fabrication of Boron Nitride Nanosheets and Their Utilization in Polymeric Composites with Improved Thermal and Mechanical Properties,” Advanced Material, Vol. 21, No. 28-32, 2009, pp. 2889-2893.

[18]   G. Y. Guo and J. C. Lin, “Systematic ab Initio Study of the Optical Properties of Bn Nanotubes,” Physics Review B, Vol. 71, No. 16, 2005, pp. 165402-165413. doi:10.1103/PhysRevB.71.165402

[19]   W. Han, W. Mickelson, J. Cumings and A. Zettl, “Transformation of Bxcynz Nanotubes to Pure Bn Nanotubes,” Applied Physics Letters, Vol. 81, No. 6, 2002, pp. 11101112. doi:10.1063/1.1498494

[20]   K. Suenaga, C. Colliex, N. Demoncy, A. Loiseau, H. Pascard and F. Willaime, “Synthesis of Nanoparticles and Nanotubes with Well-Separated Layers of Boron Nitride and Carbon,” Science Magazine, Vol. 278, No. 5338, 1997, pp. 653-655. doi:10.1126/science.278.5338.653

[21]   A. P. Suryavanshi, M. F. Yu, J. G. Wen, C. C. Tang and Y. Bando, “Elastic Modulus and Resonance Behavior of Boron Nitride Nanotubes,” Applied Physics Letters, Vol. 84, No. 14, 2004, pp. 2527-2529. doi:10.1063/1.1691189

[22]   X. Blase, A. Rubio, S. G. Louie and M. L. Cohen, “Stability and Band-Gap Constancy of Boron-Nitride Nanotubes,” Europhyics Letter, Vol. 28, No. 5, 1994, pp. 335341. doi:10.1209/0295-5075/28/5/007

[23]   D. Golberg, Y. Bando, Y. Huang, T. Terao, M. Mitome, C. Tang and C. Zhi, “Boron Nitride Nanotubes and Nanosheets,” ACS Nano, Vol. 4, No. 6, 2010, pp. 29792993. doi:10.1021/nn1006495

[24]   L. Liu, Y. P. Feng and Z. X. Shen, “Structural and Electronic Properties of H-Bn,” Physics Review B, Vol. 68, No. 10, 2003, pp. 104102-104109. doi:10.1103/PhysRevB.68.104102

[25]   K. N. Kudin, G. E. Scuseria and B. I. Yakobson, “C2f, Bn and C Nanoshell Elasticity from ab Initio Computations,” Physics Review B, Vol. 64, No. 23, 2001, pp. 235406235415. doi:10.1103/PhysRevB.64.235406

[26]   A. Zhang, H. F. Teoh, Z. Dai, Y. P. Feng and C. Zhang, “Band Gap Engineering in Graphene and Hexagonal Bn Antidot Lattices: A First Principles Study,” Applied Physics Letters, Vol. 98, No. 2, 2011, pp. 023105-023107. doi:10.1063/1.3536517

[27]   T. Kawasaki, T. Ichimura, H. Kishimoto, A. A. Akbar, T. Ogawa and C. Oshima, “Double Atomic Layers of Graphene/Monolayer H-Bn on Ni(111) Studied by Scanning Tunneling Microscopy and Scanning Tunneling Spectroscopy,” Surface Review and Letters, Vol. 9, No. 3-4, 2002, pp. 1459-1464. doi:10.1142/S0218625X02003883

[28]   J. Slawinska, I. Zasada, P. Kosinski and Z. Klusek, “Reversible Modifications of Linear Dispersion: Graphene between Boron Nitride Monolayers,” Physics Review B, Vol. 82, No. 8, 2010, pp. 085431-085435. doi:10.1103/PhysRevB.82.085431

[29]   G. Giovannetti, P. A. Khomyakov, G. Brocks, P. J. Kelly and J. Van Den Brink, “Substrate Induced Band Gap in Graphene on Hexagonal Boron Nitride: Ab Initio Density Functional Calculations,” Physics Review B, Vol. 76, No. 7, 2007, pp. 073103-073106. doi:10.1103/PhysRevB.76.073103

[30]   S. Bhowrnick, A. K. Singh and B. I. Yakobson, “Quantum Dots and Nanoroads of Graphene Embedded in Hexagonal Boron Nitride,” The Journal of Physical Chemistry C, Vol. 115, No. 20, 2011, pp. 9889-9893. doi:10.1021/jp200671p

[31]   L. Ci, L. Song, C. Jin, D. Jariwala, D. Wu, Y. Li, A. Srivastava, Z. F. Wang, K. Storr, L. Balicas, F. Liu and P. M. Ajayan, “Atomic Layers of Hybridized Boron Nitride and Graphene Domains,” Nature Material, Vol. 9, No. 5, 2010, pp. 430-435. doi:10.1038/nmat2711

[32]   Q. Peng and S. De, “Tunable Band Gaps of Mono-Layer Hexagonal BNC Heterostructures,” Physical E, Vol. 44, No. 7-8, 2012, pp. 1662-1666. doi:10.1016/j.physe.2012.04.011

[33]   Q. Peng, A. R. Zamiri, W. Ji and S. De, “Elastic Properties of Hybrid Graphene/Boron Nitride Monolayer,” Acta Mechanica, in press, 2012. doi:10.1007/s00707-012-0714-0

[34]   J. Zhou, K. Lv, Q. Wang, X. S. Chen, Q. Sun and P. Jena, “Electronic Structures and Bonding of Graphyne Sheet and Its Bn Analog,” Journal of Chemical Physics, Vol. 134, No. 17, 2011, pp. 174701-174706. doi:10.1063/1.3583476

[35]   A. Schleife, F. Fuchs, C. Roedl, J. Furthmueller and F. Bechstedt, “Branch-Point Energies and Band Discontinuities of Iii-Nitrides and Iii-/Ii-Oxides from Quasiparticle Band-Structure Calculations,” Applied Physics Letter, Vol. 94, No. 1, 2009, pp. 012104-012106. doi:10.1063/1.3059569

[36]   F. Bernardini, V. Fiorentini and D. Vanderbilt, “Spontaneous Polarization and Piezoelectric Constants of Iii-V Nitrides,” Physics Review B, Vol. 56, No. 16, 1997, pp. R10024-R10027. doi:10.1103/PhysRevB.56.R10024

[37]   O. Ambacher, “Growth and Applications of Group Iii Nitrides,” Journal of Physics D, Vol. 31, No. 20, 1998, pp. 2653-2710. doi:10.1088/0022-3727/31/20/001

[38]   M. Ferhat and A. Zaoui, “Do All Iii-V Compounds Have the Zinc-Blende or Wurtzite Ground State Structure,” Applied Physics Letter, Vol. 88, No. 16, 2006, pp. 161902161904. doi:10.1063/1.2196050

[39]   Y. Wang and S. Shi, “Structural and Electronic Properties of Monolayer Hydrogenated Honeycomb Iii-V Sheets from First-Principles,” Solid State Communications, Vol. 150, No. 31, 2010, pp. 1473-1478. doi:10.1016/j.ssc.2010.05.031

[40]   N. S. Dantas, J. S. De Almeida, R. Ahuja, C. Persson and A. F. Da Silva, “Novel Semiconducting Materials for Optoelectronic Applications: Al1-Xtlxn Alloys,” Applied Physics Letter, Vol. 92, No. 12, 2008, pp. 121914-121916. doi:10.1063/1.2901146

[41]   H. M. A. Mazouz, A. Belabbes, A. Zaoui and M. Ferhat, “First-Principles Study of Lattice Dynamics in ThalliumV Compounds,” Superlattices Microstructures, Vol. 48, No. 6, 2010, pp. 560-568. doi:10.1016/j.spmi.2010.09.012

[42]   M. Vanschilfgaarde, A. Sher and A. B. Chen, “Intlsb—An Infrared Detector Material,” Applied Physics Letter, Vol. 62, No. 16, 1993, pp. 1857-1859. doi:10.1063/1.109523

[43]   M. Vanschilfgaarde, A. B. Chen, S. Krishnamurthy and A. Sher, “Intip—A Proposed Infrared Detector Material,” Applied Physics Letter, Vol. 65, No. 21, 1994, pp. 27142716. doi:10.1063/1.112567

[44]   K. Yamamoto, H. Asahi, M. Fushida, K. Iwata and S. Gonda, “Gas Source Molecular Beam Epitaxy Growth of Tlinp for New Infrared Optical Devices,” Journal of Applied Physics, Vol. 81, No. 4, 1997, pp. 1704-1707. doi:10.1063/1.364013

[45]   R. Beneyton, G. Grenet, P. Regreny, M. Gendry, G. Hollinger, B. Canut and C. Priester, “Experimental and Theoretical Investigation into the Difficulties of Thallium Incorporation into Iii-V Semiconductors,” Physics Review B, Vol. 72, No. 12, 2005, pp. 125209. doi:10.1103/PhysRevB.72.125209

[46]   L. Shi, Y. Duan, X. Yang, G. Tang, L. Qin and L. Qiu, “Structural, Electronic and Elastic Properties of WurtziteStructured Tlxal1-Xn Alloys from First Principles,” Materials Science in Semiconductor Processing, Vol. 15, No. 5, 2012, pp. 499-504. doi:10.1016/j.mssp.2012.03.013

[47]   N. Saidi-Houat, A. Zaoui, A. Belabbes and M. Ferhat, “Ab Initio Study of the Fundamental Properties of Novel Iii-V Nitride Alloys Ga1-Xtlxn,” Materials Science and Engineering: B, Vol. 162, No. 1, 2009, pp. 26-31. doi:10.1016/j.mseb.2009.01.031

[48]   N. Saidi-Houat, A. Zaoui and M. Ferhat, “Structural Stability of Thallium-V Compounds,” Journal of Physics: Condensed Matter, Vol. 19, No. 10, 2007, pp. 106221106239. doi:10.1088/0953-8984/19/10/106221

[49]   L. Shi, Y. Duan and L. Qin, “Structural Phase Transition, Electronic and Elastic Properties in Tlx (X = N, P, as) Compounds: Pressure-Induced Effects,” Computational Materials Science, Vol. 50, No. 1, 2010, pp. 203-210. doi:10.1016/j.commatsci.2010.07.027

[50]   S. Li-Wei, D. Yi-Feng, Y. Xian-Qing and T. Gang, “Phonon and Elastic Instabilities in Zincblende Tln under Hydrostatic Pressure from First Principles Calculations,” Chinese Physics Letter, Vol. 28, No. 10, 2011, pp. 100503100507. doi:10.1088/0256-307X/28/10/100503

[51]   E. Chigo Anota, M. Salazar Villanueva and H. Hernandez Cocoletzi, “Electronic Properties of Group Iii-a Nitride Sheets by Molecular Simulation,” Physica Status Solidi (c), Vol. 7, No. 7-8, 2010, pp. 2252-2254. doi:10.1002/pssc.200983499

[52]   F. Guinea, M. I. Katsnelson and A. K. Geim, “Energy Gaps and a Zero-Field Quantum Hall Effect in Graphene by Strain Engineering,” Nature Physics, Vol. 6, No. 1, 2010, pp. 30-33. doi:10.1038/nphys1420

[53]   Y. Ma, Y. Dai, W. Wei, C. Niu, L. Yu and B. Huang, “First-Principles Study of the Graphene@Mose2 Heterobilayers,” The Journal of Physical Chemistry C, Vol. 115, No. 41, 2011, pp. 20237-20241. doi:10.1021/jp205799y

[54]   Z. H. Aitken and R. Huang, “Effects of Mismatch Strain and Substrate Surface Corrugation on Morphology of Supported Monolayer Graphene,” Journal of Applied Physics, Vol. 107, No. 12, 2010, pp. 123531-123540. doi:10.1063/1.3437642

[55]   C. Lee, X. Wei, J. W. Kysar and J. Hone, “Measurement of the Elastic Properties and Intrinsic Strength of Monolayer Graphene,” Science Magazine, Vol. 321, No. 5887, 2008, pp. 385-388. doi:10.1126/science.1157996

[56]   X. Wei, B. Fragneaud, C. A. Marianetti and J. W. Kysar, “Nonlinear Elastic Behavior of Graphene: Ab Initio Calculations to Continuum Description,” Physics Review B, Vol. 80, No. 20, 2009, pp. 205407-205414. doi:10.1103/PhysRevB.80.205407

[57]   Q. Peng, W. Ji and S. De, “Domain Size Effect on Mechanical Properties of the Hybrid Graphene/Boron Nitride Monolayer,” under review.

[58]   Q. Peng, W. Ji and S. De, “Mechanical Properties of the Hexagonal Boron Nitride Monolayer: Ab Initio Study,” Computational Materials Science, Vol. 10, No. 8, 2012, pp. 11-17. doi:10.1016/j.commatsci.2011.12.029

[59]   Q. Peng, W. Ji and S. De, “Mechanical Properties of Graphyne Monolayer: A First-Principles Study,” Physical Chemistry Chemical Physics, Vol. 14, 2012, pp. 1338513391. doi:10.1039/c2cp42387a

[60]   C. A. Marianetti and H. G. Yevick, “Failure Mechanisms of Graphene under Tension,” Physics Review Letter, Vol. 105, No. 24, 2010, pp. 245502-245505. doi:10.1103/PhysRevLett.105.245502

[61]   G. Kresse and J. Hafner, “Ab Initio Molecular Dynamics for Liquid Metals,” Physics Review B, Vol. 47, No. 1, 1993, pp. 558-561. doi:10.1103/PhysRevB.47.558

[62]   G. Kresse and J. Hafner, “Ab Initio Molecular-Dynamics Simulation of the Liquid-Metal-Amorphous-Semicon Ductor Transition in Germanium,” Physics Review B, Vol. 49, No. 20, 1994, pp. 14251-14269. doi:10.1103/PhysRevB.49.14251

[63]   G. Kresse and J. Furthuller, “Efficiency of Ab-Initio Total Energy Calculations for Metals and Semiconductors Using a Plane-Wave Basis Set,” Computational Materials Science, Vol. 6, No. 1, 1996, pp. 15-50. doi:10.1016/0927-0256(96)00008-0

[64]   G. Kresse and J. Furthuller, “Efficient Iterative Schemes for ab Initio Total-Energy Calculations Using a PlaneWave Basis Set,” Physics Review B, Vol. 54, No. 16, 1996, pp. 11169-11186. doi:10.1103/PhysRevB.54.11169

[65]   P. Hohenberg and W. Kohn, “Inhomogeneous Electron Gas,” Physical Review B, Vol. 136, No. 3B, 1964, pp. B864-B871. doi:10.1103/PhysRev.136.B864

[66]   W. Kohn and L. J. Sham, “Self-Consistent Equations Including Exchange and Correlation Effects,” Physics Review, Vol. 140, No. 4A, 1965, pp. A1133-A1138. doi:10.1103/PhysRev.140.A1133

[67]   J. Perdew, K. Burke and M. Ernzerhof, “Generalized Gradient Approximation Made Simple,” Physics Review Letter, Vol. 77, No. 18, 1996, pp. 3865-3868. doi:10.1103/PhysRevLett.77.3865

[68]   P. E. Blochl, “Projector Augmented-Wave Method,” Physics Review B, Vol. 50, No. 24, 1994, pp. 17953-17979. doi:10.1103/PhysRevB.50.17953

[69]   R. O. Jones and O. Gunnarsson, “The Density Functional Formalism, Its Applications and Prospects,” Reviews of Modern Physics, Vol. 61, No. 3, 1989, pp. 689-746. doi:10.1103/RevModPhys.61.689

[70]   M. Topsakal, S. Cahangirov and S. Ciraci, “The Response of Mechanical and Electronic Properties of Graphane to the Elastic Strain,” Applied Physics Letter, Vol. 96, No. 9, 2010, pp. 091912-091914. doi:10.1063/1.3353968

[71]   Q. Peng, C. Liang, W. Ji and S. De, “Change of Nonlinear Mechanical Properties by Hydrogenation: Graphane vs Graphene,” under review.

[72]   J. F. Nye, “Physical Properties of Crystals,” Oxford Science Publications, Oxford, 1995.

[73]   S. Y. Davydov, “Third Order Elastic Moduli of Single Layer Graphene,” Physics of the Solid State, Vol. 53, No. 3, 2011, pp. 665-668. doi:10.1134/S1063783411030073