Eur. Phys. J. Special Topics 213, 77–102 (2012) © EDP Sciences, Springer-Verlag 2012 DOI: 10.1140/epjst/e2012-01665-4 T HE EUROPEAN P HYSICAL JOURNAL SPECIAL TOPICS Review Unravelling low lying phonons and vibrations of carbon nanostructures: The contribution of inelastic and quasi-elastic neutron scattering S. Rols 1, a , C. Bousige 1,2 , J. Cambedouzou 2, b , P. Launois 2 , J.-L. Sauvajol 3 , H. Schober 1 , V.N. Agafonov 4 , V.A. Davydov 5 , and J. Ollivier 1 1 Institut Laue Langevin, 38042 Grenoble Cedex 9, France 2 Laboratoire de Physique des Solides, UMR CNRS 8502, Universit´ e Paris-Sud, 91405 Orsay, France 3 Laboratoire Charles Coulomb, UMR 5221, Universit´ e Montpellier 2, 34095 Montpellier, France 4 Laboratoire d’ ´ Electrodynamique des Mat´ eriaux Avanc´ es, UMR CNRS-CEA 6157, Universit´ e Fran¸cois Rabelais, 37200 Tours, France 5 L. F. Vereshchagin Institute for High Pressure Physics of the RAS, Troitsk, Moscow region, 142190, Russia Received 27 June 2012 / Received in final form 27 September 2012 Published online 3 December 2012 Abstract. We illustrate the contribution of inelastic neutron scattering to the understanding of the vibrations and lattice excitations of fullerenes and carbon nanotubes, through some significant experimen- tal results. Particular emphasis is placed on the study of intra and inter-molecular modes of fullerene C 60, as well as on the order/disorder transition characteristic of these molecules. In addition, a significant part of this article is dedicated to various intercalation compounds of fullerenes and carbon nanotubes, such as the co-crystal “fullerene- cubane” consisting of an arrangement of molecules of spherical and cubic shapes, or the compound called “peapods”, in which fullerene C 60 are inserted inside carbon nanotubes. 1 Introduction 1.1 Some historical facts Until 1985, carbon was essentially known under two distinct allotropes: graphite and diamond (see Fig. 1). These materials, although both constituted exclusively of car- bon atoms, show significantly different physical properties. For example, graphite is black and crumbly (it is used for pencils), while diamond is transparent and stands as a reference material for its hardness. These different physical properties reflect a e-mail: rols@ill.eu b Present address: Institut de Chimie S´ eparative de Marcoule, UMR 5257, 30207 Bagnols-sur-Ceze, France.