Abstract
High-resolution electron energy loss spectroscopy is a suitable tool for investigating phonons in graphene, due to its exceptional energy resolution in both the energy and momentum domains. In this chapter, we show that the experimental phonon dispersion of graphene can be used to estimate elastic properties and electron–phonon coupling. Novel coupling mechanisms of Dirac cone electrons in graphene with out-of-plane optical phonons of the graphene lattice, activated only whenever the graphene sheet is supported by a solid substrate, are also discussed.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Aizawa, T., Souda, R., Ishizawa, Y., Hirano, H., Yamada, T., Tanaka, K.-I., Oshima, C.: Phonon dispersion in monolayer graphite formed on Ni(111) and Ni(001). Surf. Sci. 237, 194–202 (1990)
AL Taleb, A., Yu, H.K., Anemone, G., Farías, D., Wodtke, A.M.: Helium diffraction and acoustic phonons of graphene grown on copper foil. Carbon 95, 731–737 (2015)
Allard, A., Wirtz, L.: Graphene on metallic substrates: suppression of the Kohn anomalies in the phonon dispersion. Nano Lett. 10, 4335–4340 (2010)
Alzari, V., Nuvoli, D., Sanna, R., Scognamillo, S., Piccinini, M., Kenny, J.M., Malucelli, G., Mariani, A.: In situ production of high filler content graphene-based polymer nanocomposites by reactive processing. J. Mater. Chem. 21, 16544–16549 (2011)
Arghavan, S., Singh, A.V.: Free vibration of single layer graphene sheets: lattice structure versus continuum plate theories. J. Nanotechnol. Eng. Med. 2, 031005–031006 (2011)
Arroyo, M., Belytschko, T.: Finite crystal elasticity of carbon nanotubes based on the exponential Cauchy-Born rule. Phys. Rev. B 69, 115415 (2004)
Aynajian, P., Keller, T., Boeri, L., Shapiro, S.M., Habicht, K., Keimer, B.: Energy gaps and kohn anomalies in elemental superconductors. Science 319, 1509–1512 (2008)
Basko, D.M., Piscanec, S., Ferrari, A.C.: Electron-electron interactions and doping dependence of the two-phonon Raman intensity in graphene. Phys. Rev. B 80, 165413 (2009)
Batzill, M.: The surface science of graphene: Metal interfaces, CVD synthesis, nanoribbons, chemical modifications, and defects. Surf. Sci. Rep. 67, 83–115 (2012)
Benedek, G., Hulpke, E., Steinhogl, W.: Probing the magnetic forces in fcc-Fe(001) films by means of surface phonon spectroscopy. Phys. Rev. Lett. 87, 027201 (2001)
Bera, S., Arnold, A., Evers, F., Narayanan, R., Wölfle, P.: Elastic properties of graphene flakes: boundary effects and lattice vibrations. Phys. Rev. B 82, 195445 (2010)
Blakslee, O.L., Proctor, D.G., Seldin, E.J., Spence, G.B., Weng, T.: Elastic constants of compression-annealed pyrolytic graphite. J. Appl. Phys. 41, 3373–3382 (1970)
Bosak, A., Krisch, M., Mohr, M., Maultzsch, J., Thomsen, C.: Elasticity of single-crystalline graphite: inelastic x-ray scattering study. Phys. Rev. B 75, 153408 (2007)
Cadelano, E., Palla, P.L., Giordano, S., Colombo, L.: Nonlinear elasticity of monolayer graphene. Phys. Rev. Lett. 102, 235502 (2009)
Cadelano, E., Palla, P.L., Giordano, S., Colombo, L.: Elastic properties of hydrogenated graphene. Phys. Rev. B 82, 235414 (2010)
Cao, A., Yuan, Y.: Atomistic study on the strength of symmetric tilt grain boundaries in graphene. Appl. Phys. Lett. 100, 211912 (2012)
Castro Neto, A.H., Guinea, F., Peres, N.M.R., Novoselov, K.S., GEIM, A.K.: The electronic properties of graphene. Rev. Mod. Phys. 81, 109–162 (2009)
Caudal, N., Saitta, A.M., Lazzeri, M., Mauri, F.: Kohn anomalies and nonadiabaticity in doped carbon nanotubes. Phys. Rev. B 75, 115423 (2007)
Chis, V., Benedek, G.: Phonon-Induced surface charge density oscillations in quantum wells: a first-principles study of the (2 × 2)-K overlayer on Be(0001). J. Phys. Chem. A 115, 7242–7248 (2011)
Clark, N., Oikonomou, A., Vijayaraghavan, A.: Ultrafast quantitative nanomechanical mapping of suspended graphene. Physica Status Solidi (b) 250, 2672–2677 (2013)
de Juan, F., Fertig, H.A.: Power-law Kohn anomaly in undoped graphene induced by Coulomb interactions. Phys. Rev. B 85, 085441 (2012)
de Juan, F., Fertig, H.A.: Power law kohn anomalies and the excitonic transition in graphene. Solid State Commun. 152, 1460–1468 (2012)
de Juan, F., Politano, A., Chiarello, G., Fertig, H.A.: Symmetries and selection rules in the measurement of the phonon spectrum of graphene and related materials. Carbon 85, 225–232 (2015)
Dedkov, Y.S., Fonin, M., Laubschat, C.: A possible source of spin-polarized electrons: the inert graphene/Ni(111) system. Appl. Phys. Lett. 92, 052506 (2008)
Elias, D.C., Gorbachev, R.V., Mayorov, A.S., Morozov, S.V., Zhukov, A.A., Blake, P., Ponomarenko, L.A., Grigorieva, I.V., Novoselov, K.S., Guinea, F., Geim, A.K.: Dirac cones reshaped by interaction effects in suspended graphene. Nat. Phys. 7, 701–704 (2011)
Endlich, M., Molina-Sánchez, A., Wirtz, L., Kröger, J.: Screening of electron-phonon coupling in graphene on Ir(111). Phys. Rev. B 88, 205403 (2013)
Eom, D., Prezzi, D., Rim, K.T., Zhou, H., Lefenfeld, M., Xiao, S., Nuckolls, C., Hybertsen, M.S., Heinz, T.F., Flynn, G.W.: Structure and electronic properties of graphene nanoislands on Co(0001). Nano Lett. 9, 2844–2848 (2009)
Fair, K.M., Arnold, M.D., Ford, M.J.: Determination of the elastic properties of graphene by indentation and the validity of classical models of indentation. J. Phys.: Condens. Matter 26, 015307 (2014)
Gamo, Y., Nagashima, A., Wakabayashi, M., Terai, M., Oshima, C.: Atomic structure of monolayer graphite formed on Ni(111). Surf. Sci. 374, 61–64 (1997)
Giovannetti, G., Khomyakov, P.A., Brocks, G., Karpan, V.M., van den Brink, J., Kelly, P.J.: Doping graphene with metal contacts. Phys. Rev. Lett. 101, 026803 (2008)
Gui, G., Li, J., Zhong, J.: Band structure engineering of graphene by strain: first-principles calculations. Phys. Rev. B 78, 075435 (2008)
Hwang, E.H., Das Sarma, S.: Screening, Kohn Anomaly, Friedel Oscillation, and RKKY interaction in bilayer graphene. Phys. Rev. Lett. 101, 156802 (2008)
Jhon, Y.I., Zhu, S.-E., Ahn, J.-H., Jhon, M.S.: The mechanical responses of tilted and non-tilted grain boundaries in graphene. Carbon 50, 3708–3716 (2012)
Jiang, J.-W., Wang, J.-S., Li, B.: Young’s modulus of graphene: a molecular dynamics study. Phys. Rev. B 80, 113405 (2009)
Kalosakas, G., Lathiotakis, N.N., Galiotis, C., Papagelis, K.: In-plane force fields and elastic properties of graphene. J. Appl. Phys. 113, 134307 (2013)
Kam, K., Scarpa, F., Adhikari, S. & Chowdhury, R.: Graphene nanofilm as pressure and force sensor: a mechanical analysis. Physica Status Solidi (b) 250, 2085–2089 (2013)
Kilian, O., Allan, G., Wirtz, L.: Near Kohn anomalies in the phonon dispersion relations of lead chalcogenides. Phys. Rev. B 80, 245208 (2009)
Kohn, W.: Image of the Fermi surface in the vibration spectrum of a metal. Phys. Rev. Lett. 2, 393–394 (1959)
Kudin, K.N., Scuseria, G.E., Yakobson, B.I.: C2F, BN, and C nanoshell elasticity from ab initio computations. Phys. Rev. B 64, 235406 (2001)
Kwon, S.Y., Ciobanu, C.V., Petrova, V., Shenoy, V.B., Bareño, J., Gambin, V., Petrov, I., Kodambaka, S.: Growth of semiconducting graphene on palladium. Nano Lett. 9, 3985–3990 (2009)
Lazzeri, M., Mauri, F.: Nonadiabatic Kohn anomaly in a doped graphene monolayer. Phys. Rev. Lett. 97, 266407 (2006)
Lazzeri, M., Piscanec, S., Mauri, F., Ferrari, A.C., Robertson, J.: Electron transport and hot phonons in Carbon nanotubes. Phys. Rev. Lett. 95, 236802 (2005)
Lee, C., Wei, X., Kysar, J.W., Hone, J.: Measurement of the elastic properties and intrinsic strength of monolayer graphene. Science 321, 385–388 (2008)
Lee, G.-H., Cooper, R.C., An, S.J., Lee, S., van der Zande, A., Petrone, N., Hammerberg, A.G., Lee, C., Crawford, B., Oliver, W., Kysar, J.W., Hone, J.: High-Strength chemical-vapor–deposited graphene and grain boundaries. Science 340, 1073–1076 (2013)
Lin, Z., Zhigilei, L.V., Celli, V.: Electron-phonon coupling and electron heat capacity of metals under conditions of strong electron-phonon nonequilibrium. Phys. Rev. B 77, 075133 (2008)
Liu, F., Ming, P., Li, J.: Ab initio calculation of ideal strength and phonon instability of graphene under tension. Phys. Rev. B 76, 064120 (2007)
Lu, J.P.: Elastic properties of Carbon nanotubes and nanoropes. Phys. Rev. Lett. 79, 1297 (1997)
Michel, K.H., Verberck, B:. Theory of the elastic constants of graphite and graphene. Physica Status Solidi (b) 245, 2177–2180 (2008)
Milošević, I., Kepčija, N., Dobardžić, E., Damnjanović, M., Mohr, M., Maultzsch, J., Thomsen, C.: Kohn anomaly in graphene. Mater. Sci. Eng B-Adv. Funct. Solid-State Mater. 176, 510–511 (2011)
Milošević, I., Kepčija, N., Dobardžić, E., Mohr, M., Maultzsch, J., Thomsen, C., Damnjanović, M.: Symmetry based analysis of the Kohn anomaly and electron-phonon interaction in graphene and carbon nanotubes. Phys. Rev. B 81, 233410 (2010)
Miniussi, E., Pozzo, M., Baraldi, A., Vesselli, E., Zhan, R.R., Comelli, G., Menteş, T.O., Niño, M.A., Locatelli, A., Lizzit, S., Alfè, D.: Thermal stability of corrugated epitaxial graphene grown on Re(0001). Phys. Rev. Lett. 106, 216101 (2011)
Novoselov, K.S., Geim, A.K., Morozov, S.V., Jiang, D., Katsnelson, M.I., Grigorieva, I.V., Dubonos, S.V., Firsov, A.A.: Two-dimensional gas of massless Dirac fermions in graphene. Nature 438, 197–200 (2005)
Oshima, C., Aizawa, T., Souda, R., Ishizawa, Y., Sumiyoshi, Y.: Surface phonon dispersion curves of graphite (0001) over the entire energy region. Solid State Commun. 65, 1601–1604 (1988)
Pan, Y., Zhang, H., Shi, D., Sun, J., Du, S., Liu, F., Gao, H.-J.: Highly ordered, millimeter-scale, continuous, single-crystalline graphene monolayer formed on Ru (0001). Adv. Mater. 21, 2777–2780 (2009)
Park, S., An, J., Suk, J.W., Ruoff, R.S.: Graphene-based actuators. Small 6, 210–212 (2010)
Peng, Q., Liang, C., Ji, W., De, S.: A theoretical analysis of the effect of the hydrogenation of graphene to graphane on its mechanical properties. Phys. Chem. Chem. Phys. 15, 2003–2011 (2013)
Perebeinos, V., Tersoff, J.: Valence force model for phonons in graphene and carbon nanotubes. Phys. Rev. B 79, 241409 (2009)
Piscanec, S., Lazzeri, M., Mauri, F., Ferrari, A.C., Robertson, J.: Kohn Anomalies and electron-phonon interactions in graphite. Phys. Rev. Lett. 93, 185503 (2004)
Piscanec, S., Lazzeri, M., Robertson, J., Ferrari, A.C., Mauri, F.: Optical phonons in carbon nanotubes: Kohn anomalies, Peierls distortions, and dynamic effects. Phys. Rev. B 75, 035427 (2007)
Pletikosić, I., Kralj, M., Pervan, P., Brako, R., Coraux, J., N’Diaye, A.T., Busse, C., Michely, T.: Dirac cones and minigaps for graphene on Ir(111). Phys. Rev. Lett. 102, 056808 (2009)
Politano, A., Borca, B., Minniti, M., Hinarejos, J.J., Vázquez De Parga, A.L., Farías, D., Miranda, R.: Helium reflectivity and Debye temperature of graphene grown epitaxially on Ru(0001). Phys. Rev. B 84, 035450 (2011a)
Politano, A., Chiarello, G.: Probing Young’s modulus and Poisson’s ratio in graphene/metal interfaces and graphite: a comparative study. Nano Res. 8, 1847–1856 (2015)
Politano, A., de Juan, F., Chiarello, G., Fertig, H.A.: Emergence of an out-of-plane optical phonon (ZO) Kohn anomaly in quasifreestanding epitaxial graphene. Phys. Rev. Lett. 115, 075504 (2015)
Politano, A., Marino, A.R., Campi, D., Farías, D., Miranda, R., Chiarello, G.: Elastic properties of a macroscopic graphene sample from phonon dispersion measurements. Carbon 50, 4903–4910 (2012)
Politano, A., Marino, A.R., Formoso, V., Chiarello, G.: Evidence of Kohn anomalies in quasi-freestanding graphene on Pt(111). Carbon 50, 734–736 (2012)
Politano, A., Marino, A.R., Formoso, V., Farías, D., Miranda, R., Chiarello, G.: Evidence for acoustic-like plasmons on epitaxial graphene on Pt(111). Phys. Rev. B 84, 033401 (2011)
Reddy, C.D., Ramasubramaniam, A., Shenoy, V.B., Zhang, Y.-W.: Edge elastic properties of defect-free single-layer graphene sheets. Appl. Phys. Lett. 94, 101904 (2009)
Reddy, K.M., Gledhill, A.D., Chen, C.-H., Drexler, J.M., Padture, N.P.: High quality, transferrable graphene grown on single crystal Cu(111) thin films on basal-plane sapphire. Appl. Phys. Lett. 98, 113117 (2011)
Reynaud, C., Sommer, F., Quet, C., el Bounia, N., Duc, T.M.: Quantitative determination of Young’s modulus on a biphase polymer system using atomic force microscopy. Surf. Interface Anal. 30, 185–189 (2000)
Ruiz-Vargas, C.S., Zhuang, H.L., Huang, P.Y., van der Zande, A.M., Garg, S., McEuen, P.L., Muller, D.A., Hennig, R.G., Park, J.: Softened elastic response and unzipping in chemical vapor deposition graphene membranes. Nano Lett. 11, 2259–2263 (2011)
Sánchez-Portal, D., Artacho, E., Soler, J.M., Rubio, A., Ordejón, P.: Ab initio structural, elastic, and vibrational properties of carbon nanotubes. Phys. Rev. B 59, 12678 (1999)
Sasaki, K., Yamamoto, M., Murakami, S., Saito, R., Dresselhaus, M.S., Takai, K., Mori, T., Enoki, T., Wakabayashi, K.: Kohn anomalies in graphene nanoribbons. Phys. Rev. B 80, 155450 (2009)
Scarpa, F., Adhikari, S., Srikantha Phani, A.: Effective elastic mechanical properties of single layer graphene sheets. Nanotechnology 20, 065709 (2009)
Scharfenberg, S., Rocklin, D.Z., Chialvo, C., Weaver, R.L., Goldbart, P.M., Mason, N.: Probing the mechanical properties of graphene using a corrugated elastic substrate. Appl. Phys. Lett. 98, 091908 (2011)
Seldin, E.J., Nezbeda, C.W.: Elastic constants and electron-microscope observations of neutron-irradiated compression-annealed pyrolytic and single-crystal graphite. J. Appl. Phys. 41, 3389–3400 (1970)
Shikin, A.M., Farías, D., Adamchuk, V.K., Rieder, K.H.: Surface phonon dispersion of a graphite monolayer adsorbed on Ni(111) and its modification caused by intercalation of Yb, La and Cu layers. Surf. Sci. 424, 155–167 (1999)
Sicot, M., Bouvron, S., Zander, O., Rudiger, U., Dedkov, Y.S., Fonin, M.: Nucleation and growth of nickel nanoclusters on graphene Moiré on Rh(111). Appl. Phys. Lett. 96, 3–093115 (2010)
Sutter, P., Sadowski, J.T., Sutter, E.: Graphene on Pt(111): growth and substrate interaction. Phys. Rev. B 80, 245411 (2009)
Talwar, D.N., Vandevyver, M., Kunc, K., Zigone, M.: Lattice dynamics of zinc chalcogenides under compression: phonon dispersion, mode Grüneisen, and thermal expansion. Phys. Rev. B 24, 741–753 (1981)
Tomasetti, E., Legras, R., Nysten, B.: Quantitative approach towards the measurement of polypropylene/(ethylene-propylene) copolymer blends surface elastic properties by AFM. Nanotechnology 9, 305 (1998)
TSE, W.K., Hu, B.Y.K., Das Sarma, S.: Chirality-induced dynamic Kohn anomalies in graphene. Phys. Rev. Lett. 101, 066401 (2008)
Wagner, P., Ivanovskaya, V.V., Rayson, M.J., Briddon, P.R., Ewels, C.P.: Mechanical properties of nanosheets and nanotubes investigated using a new geometry independent volume definition. J. Phys.: Condens. Matter 25, 155302 (2013)
Wang, B., Günther, S., Wintterlin, J., Bocquet, M.-L.: Periodicity, work function and reactivity of graphene on Ru(0001) from first principles. New J. Phys. 12, 043041 (2010)
Wang, C.G., Lan, L., Liu, Y.P., Tan, H.F.: Multiple component correlation model for elastic modulus of single layer graphene sheets. Physica E 56, 372–376 (2014)
Wang, R., Wang, S., Wu, X., Liang, X.: First-principles calculations on third-order elastic constants and internal relaxation for monolayer graphene. Physica B 405, 3501–3506 (2010)
Wang, Y., Yang, R., Shi, Z., Zhang, L., Shi, D., Wang, E., Zhang, G.: Super-elastic graphene ripples for flexible strain sensors. ACS Nano 5, 3645–3650 (2011)
Wintterlin, J., Bocquet, M.L.: Graphene on metal surfaces. Surf. Sci. 603, 1841–1852 (2009)
XIAO, J.R., Staniszewski, J., Gillespie Jr, J.W.: Fracture and progressive failure of defective graphene sheets and carbon nanotubes. Compos. Struct. 88, 602–609 (2009)
Zakharchenko, K.V., Katsnelson, M.I., Fasolino, A.: Finite temperature lattice properties of graphene beyond the quasiharmonic approximation. Phys. Rev. Lett. 102, 046808 (2009)
Zhang, Y.Y., Wang, C.M., Cheng, Y., Xiang, Y.: Mechanical properties of bilayer graphene sheets coupled by sp3 bonding. Carbon 49, 4511–4517 (2011)
Zhou, G., Duan, W., Gu, B.: First-principles study on morphology and mechanical properties of single-walled carbon nanotube. Chem. Phys. Lett. 333, 344–349 (2001)
Zhou, J., Huang, R.: Internal lattice relaxation of single-layer graphene under in-plane deformation. J. Mech. Phys. Solids 56, 1609–1623 (2008)
Zhou, L., Wang, Y., Cao, G.: Elastic properties of monolayer graphene with different chiralities. J. Phys.: Condens. Matter 25, 125302 (2013)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2017 Springer International Publishing AG
About this chapter
Cite this chapter
Alfano, M., Lamuta, C., Chiarello, G., Politano, A. (2017). Elastic Properties and Electron–Phonon Coupling of Graphene/Metal Interfaces Probed by Phonon Dispersion. In: Morandi, V., Ottaviano, L. (eds) GraphITA . Carbon Nanostructures. Springer, Cham. https://doi.org/10.1007/978-3-319-58134-7_4
Download citation
DOI: https://doi.org/10.1007/978-3-319-58134-7_4
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-58132-3
Online ISBN: 978-3-319-58134-7
eBook Packages: Chemistry and Materials ScienceChemistry and Material Science (R0)