Elastic properties of a macroscopic graphene sample from phonon dispersion measurements

Carbon

Volumn 50, Issue 13, 2012, Pages 4903-4910

  Politano, Antonio ^a   Marino, Antonio Raimondo ^a   Campi, Davide ^b   Farías, Daniel ^c,d   Miranda, Rodolfo ^c,d,e   Chiarello, Gennaro ^a,f  

^a UNIVERSITY OF CALABRIA   (Italy)

^b UNIVERSITY OF MILANO BICOCCA   (Italy)

^c UNIVERSIDAD AUTÓNOMA DE MADRID   (Spain)

^d INSTITUTO NICOLÁS CABRERA   (Spain)

^e INSTITUTO MADRILEÑO DE ESTUDIOS AVANZADOS EN NANOCIENCIA IMDEA NANOCIENCIA   (Spain)

^f Consorzio Nazionale Interuniversitario di Scienze Fisiche della Materia ^*  (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

ELASTIC PROPERTIES; ENERGY-LOSS SPECTROSCOPY; HIGH-CRYSTALLINE QUALITY; HIGH-TENSILE STRENGTH; INTERATOMIC FORCES; MACROSCOPIC SAMPLE; METAL SUBSTRATE; PHONON DISPERSIONS; POISSON'S RATIO; TECHNOLOGICAL APPLICATIONS; YOUNG'S MODULUS;

ACOUSTIC DISPERSION; BENDING STRENGTH; CARBON FIBERS; ELASTICITY; ELECTROMECHANICAL DEVICES; STRAIN MEASUREMENT;

GRAPHENE;

EID: 84864473432     PISSN: 00086223     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.carbon.2012.06.019     Document Type: Article

References (70)

1. A.H. Castro Neto Graphene: Phonons behaving badly Nat Mater 6 3 2007 176 177
2. A. Politano, A.R. Marino, V. Formoso, and G. Chiarello Evidence of Kohn anomalies in quasi-freestanding graphene on Pt(1 1 1) Carbon 50 2 2012 734 736
3. 3 bonding Carbon 49 13 2011 4511 4517
4. S. Park, J. An, J.W. Suk, and R.S. Ruoff Graphene-based actuators Small 6 2 2010 210 212
5. Y. Wang, R. Yang, Z. Shi, L. Zhang, D. Shi, and E. Wang Super-elastic graphene ripples for flexible strain sensors ACS Nano 5 5 2011 3645 3650
6. S. Scharfenberg, D.Z. Rocklin, C. Chialvo, R.L. Weaver, P.M. Goldbart, and N. Mason Probing the mechanical properties of graphene using a corrugated elastic substrate Appl Phys Lett 98 9 2011 091908
7. V. Alzari, D. Nuvoli, R. Sanna, S. Scognamillo, M. Piccinini, and J.M. Kenny In situ production of high filler content graphene-based polymer nanocomposites by reactive processing J Mater Chem 21 41 2011 16544 16549
8. E. Tomasetti, R. Legras, and B. Nysten Quantitative approach towards the measurement of polypropylene/(ethylene-propylene) copolymer blends surface elastic properties by AFM Nanotechnology 9 4 1998 305
9. C. Reynaud, F. Sommer, C. Quet, N. El Bounia, and T.M. Duc Quantitative determination of Young's modulus on a biphase polymer system using atomic force microscopy Surf Interf Anal 30 1 2000 185 189
10. C. Lee, X. Wei, J.W. Kysar, and J. Hone Measurement of the elastic properties and intrinsic strength of monolayer graphene Science 321 5887 2008 385 388
11. Y. Pan, H. Zhang, D. Shi, J. Sun, S. Du, and F. Liu Highly ordered, millimeter-scale, continuous, single-crystalline graphene monolayer formed on Ru (0 0 0 1) Adv Mater 21 27 2009 2777 2780
12. J. Coraux, A.T. N'Diaye, C. Busse, and T. Michely Structural coherency of graphene on Ir(1 1 1) Nano Lett 8 2 2008 565 570
13. P. Sutter, J.T. Sadowski, and E. Sutter Graphene on Pt(1 1 1): growth and substrate interaction Phys. Rev. B 80 24 2009 245411
14. M. Gao, Y. Pan, C. Zhang, H. Hu, R. Yang, and H. Lu Tunable interfacial properties of epitaxial graphene on metal substrates Appl Phys Lett 96 5 2010 053109
15. M. Gao, Y. Pan, L. Huang, H. Hu, L.Z. Zhang, and H.M. Guo Epitaxial growth and structural property of graphene on Pt(1 1 1) Appl Phys Lett 98 3 2011 033101
16. A. Politano, A.R. Marino, V. Formoso, and G. Chiarello Hydrogen bonding at the water/quasi-freestanding graphene interface Carbon 49 15 2011 5180 5184
17. Politano A, Marino AR, Formoso V, Farías D, Miranda R, Chiarello G. Quadratic dispersion and damping processes of π plasmon in monolayer graphene on Pt(1 1 1). Plasmonics; 2012. http://dx.doi.org/10.1007/s11468-11011- 19317-11461.
18. A.B. Preobrajenski, M.L. Ng, A.S. Vinogradov, and N. Mårtensson Controlling graphene corrugation on lattice-mismatched substrates Phys Rev B 78 7 2008 073401
19. B. Borca, S. Barja, M. Garnica, M. Minniti, A. Politano, and J.M. Rodriguez-García Electronic and geometric corrugation of periodically rippled, self-nanostructured graphene epitaxially grown on Ru(0 0 0 1) New J Phys 12 9 2010 093018
20. A. Politano, B. Borca, M. Minniti, J.J. Hinarejos, A.L. Vázquez de Parga, and D. Farías Helium reflectivity and Debye temperature of graphene grown epitaxially on Ru(0 0 0 1) Phys Rev B 84 3 2011 035450
21. A. Politano, A.R. Marino, and G. Chiarello Phonon dispersion of quasi-freestanding graphene on Pt(1 1 1) J. Phys: Condens Matter 24 10 2012 104025
22. A. Politano, and G. Chiarello Vibrational investigation of catalyst surfaces: change of the adsorption site of CO molecules upon coadsorption J Phys Chem C 115 28 2011 13541 13553
23. A. Politano, V. Formoso, E. Colavita, and G. Chiarello Probing collective electronic excitations in as-deposited and modified Ag thin films grown on Cu(1 1 1) Phys Rev B 79 4 2009 045426
24. Cazzanelli E, Caruso T, Castriota M, Marino AR, Politano A, Chiarello G, et al.; in preparation.
25. A. Politano, A.R. Marino, V. Formoso, D. Farías, R. Miranda, and G. Chiarello Evidence for acoustic-like plasmons on epitaxial graphene on Pt(1 1 1) Phys Rev B 84 3 2011 033401
26. M. Rocca Low-energy EELS investigation of surface electronic excitations on metals Surf Sci Rep 22 1-2 1995 1 71
27. D. Farías, K.H. Rieder, A.M. Shikin, V.K. Adamchuk, T. Tanaka, and C. Oshima Modification of the surface phonon dispersion of a graphite monolayer adsorbed on Ni(1 1 1) caused by intercalation of Yb, Cu and Ag Surf Sci 454 1-2 2000 437 441
28. A.M. Shikin, D. Farías, V.K. Adamchuk, and K.H. Rieder Surface phonon dispersion of a graphite monolayer adsorbed on Ni(1 1 1) and its modification caused by intercalation of Yb, La and Cu layers Surf Sci 424 1 1999 155 167
29. J. Wintterlin, and M.L. Bocquet Graphene on metal surfaces Surf Sci 603 10-12 2009 1841 1852
30. J.H. Seol, I. Jo, A.L. Moore, L. Lindsay, Z.H. Aitken, and M.T. Pettes Two-dimensional phonon transport in supported graphene Science 328 5975 2010 213 216
31. Z. Hartmut Phonons in layered compounds J Phys: Condens Matter 13 34 2001 7679
32. V. Perebeinos, and J. Tersoff Valence force model for phonons in graphene and carbon nanotubes Phys Rev B 79 24 2009 241409
33. Lindahl N, Midtvedt D, Svensson J, Nerushev OA, Lindvall N, Isacsson A, et al. Determination of the bending rigidity of graphene via electrostatic actuation of buckled. Membranes; 2012. doi:arXiv:1203.4397v1201.
34. 2F, BN, and C nanoshell elasticity from ab initio computations Phys Rev B 64 23 2001 235406
35. D.B. Zhang, E. Akatyeva, and T. Dumitrica Bending ultrathin graphene at the margins of continuum mechanics Phys Rev Lett 106 25 2011 255503
36. D. Garcia-Sanchez, A.M. van der Zande, A.S. Paulo, B. Lassagne, P.L. McEuen, and A. Bachtold Imaging mechanical vibrations in suspended graphene sheets Nano Lett 8 5 2008 1399 1403
37. P. Merino, M. Svec, A.L. Pinardi, G. Otero, and J.A. Martín-Gago Strain-driven moiré superstructures of epitaxial graphene on transition metal surfaces ACS Nano 5 7 2011 5627 5634
38. A. Fasolino, J.H. Los, and M.I. Katsnelson Intrinsic ripples in graphene Nat Mater 6 11 2007 858 861
39. S. Viola Kusminskiy, D.K. Campbell, and A.H. Castro Neto Lenosky's energy and the phonon dispersion of graphene Phys Rev B 80 3 2009 035401
40. L.J. Karssemeijer, and A. Fasolino Phonons of graphene and graphitic materials derived from the empirical potential LCBOPII Surf Sci 605 17-18 2011 1611 1615
41. T. Aizawa, R. Souda, S. Otani, Y. Ishizawa, and C. Oshima Bond softening in monolayer graphite formed on transition-metal carbide surfaces Phys Rev B 42 18 1990 11469
42. A. Bosak, M. Krisch, M. Mohr, J. Maultzsch, and C. Thomsen Elasticity of single-crystalline graphite: inelastic x-ray scattering study Phys Rev B 75 15 2007 153408
43. C. Oshima, T. Aizawa, R. Souda, Y. Ishizawa, and Y. Sumiyoshi Surface phonon dispersion curves of graphite (0 0 0 1) over the entire energy region Solid State Commun 65 12 1988 1601 1604
44. D. Sánchez-Portal, E. Artacho, J.M. Soler, A. Rubio, and P. Ordejón Ab initio structural, elastic, and vibrational properties of carbon nanotubes Phys Rev B 59 19 1999 12678
45. O.L. Blakslee, D.G. Proctor, E.J. Seldin, G.B. Spence, and T. Weng Elastic constants of compression-annealed pyrolytic graphite J Appl Phys 41 8 1970 3373 3382
46. E.J. Seldin, and C.W. Nezbeda Elastic constants and electron-microscope observations of neutron-irradiated compression-annealed pyrolytic and single-crystal graphite J Appl Phys 41 8 1970 3389 3400
47. J.P. Lu Elastic properties of carbon nanotubes and nanoropes Phys Rev Lett 79 7 1997 1297
48. J.-W. Jiang, J.-S. Wang, and B. Li Young's modulus of graphene: a molecular dynamics study Phys Rev B 80 11 2009 113405
49. K.V. Zakharchenko, M.I. Katsnelson, and A. Fasolino Finite temperature lattice properties of graphene beyond the quasiharmonic approximation Phys Rev Lett 102 4 2009 046808
50. S. Arghavan, and A.V. Singh Free vibration of single layer graphene sheets: lattice structure versus continuum plate theories J Nanotechnol Eng Med 2 3 2011 031005 031006
51. S. Bera, A. Arnold, F. Evers, R. Narayanan, and P. Wölfle Elastic properties of graphene flakes: boundary effects and lattice vibrations Phys Rev B 82 19 2010 195445
52. E. Cadelano, P.L. Palla, S. Giordano, and L. Colombo Elastic properties of hydrogenated graphene Phys Rev B 82 23 2010 235414
53. G. Gui, J. Li, and J. Zhong Band structure engineering of graphene by strain: first-principles calculations Phys Rev B 78 7 2008 075435
54. F. Liu, P. Ming, and J. Li Ab initio calculation of ideal strength and phonon instability of graphene under tension Phys Rev B 76 6 2007 064120
55. K.H. Michel, and B. Verberck Theory of the elastic constants of graphite and graphene Phys Status Solidi B 245 10 2008 2177 2180
56. E. Cadelano, P.L. Palla, S. Giordano, and L. Colombo Nonlinear elasticity of monolayer graphene Phys Rev Lett 102 23 2009 235502
57. G. Zhou, W. Duan, and B. Gu First-principles study on morphology and mechanical properties of single-walled carbon nanotube Chem Phys Lett 333 5 2001 344 349
58. M. Arroyo, and T. Belytschko Finite crystal elasticity of carbon nanotubes based on the exponential Cauchy-Born rule Phys Rev B 69 11 2004 115415
59. Adamyan V, Zavalniuk V. Phonons in graphene with point defects. J. Phys.: Condens. Matt. 2011;23(1):015402.
60. J. Zhou, and R. Huang Internal lattice relaxation of single-layer graphene under in-plane deformation J Mech Phys Solids 56 4 2008 1609 1623
61. G. Otero, C. Gonzalez, A.L. Pinardi, P. Merino, S. Gardonio, and S. Lizzit Ordered vacancy network induced by the growth of epitaxial graphene on Pt(1 1 1) Phys Rev Lett 105 21 2010 216102
62. M.-F. Yu, B.S. Files, S. Arepalli, and R.S. Ruoff Tensile loading of ropes of single wall carbon nanotubes and their mechanical properties Phys Rev Lett 84 24 2000 5552
63. M.-F. Yu, O. Lourie, M.J. Dyer, K. Moloni, T.F. Kelly, and R.S. Ruoff Strength and breaking mechanism of multiwalled carbon nanotubes under tensile load Science 287 5453 2000 637 640
64. C.D. Reddy, A. Ramasubramaniam, V.B. Shenoy, and Y.-W. Zhang Edge elastic properties of defect-free single-layer graphene sheets Appl Phys Lett 94 10 2009 101904
65. C.S. Ruiz-Vargas, H.L. Zhuang, P.Y. Huang, A.M. van der Zande, S. Garg, and P.L. McEuen Softened elastic response and unzipping in chemical vapor deposition graphene membranes Nano Lett 11 6 2011 2259 2263
66. M. Klintenberg, S. Lebègue, C. Ortiz, B. Sanyal, J. Fransson, and O. Eriksson Evolving properties of two-dimensional materials: from graphene to graphite J Phys: Condens Matter 21 33 2009 335502
67. T. Aizawa, Y. Hwang, W. Hayami, R. Souda, S. Otani, and Y. Ishizawa Phonon dispersion of monolayer graphite on Pt(1 1 1) and NbC surfaces: bond softening and interface structures Surf Sci 260 1-3 1992 311 318
68. T. Aizawa, R. Souda, Y. Ishizawa, H. Hirano, T. Yamada, and K.-I. Tanaka Phonon dispersion in monolayer graphite formed on Ni(1 1 1) and Ni(001) Surf Sci 237 1-3 1990 194 202
69. G. Bertoni, L. Calmels, A. Altibelli, and V. Serin First-principles calculation of the electronic structure and EELS spectra at the graphene/Ni(1 1 1) interface Phys Rev B 71 7 2005 075402
70. G. Benedek, and G. Onida Bulk and surface dynamics of graphite with the bond charge model Phys Rev B 47 24 1993 16471 16476