1063-7834/02/4401- $21.00 © 2002 MAIK “Nauka/Interperiodica” 0186 Physics of the Solid State, Vol. 44, No. 1, 2002, pp. 186–194. Translated from Fizika Tverdogo Tela, Vol. 44, No. 1, 2002, pp. 180–187. Original Russian Text Copyright © 2002 by Lozovik, Popov. 1. INTRODUCTION Over the last decade, after the discovery of fullerenes [1] and the development of the method of their preparation in macroscopic amounts [2], consider- able interest has been expressed by researchers in other carbon nanostructures, specifically in nanoparticles that have a shell structure and can be produced in an arc dis- charge [3, 4]. The structure and energetics of these nanoparticles have been investigated in a number of works [5–13]. However, to date, the thermodynamic properties of these objects have not been adequately studied. The melting of a cluster can differ essentially from phase transitions in macroscopic systems [14–20]. In particular, the melting of a cluster with a shell structure can be represented as a hierarchy of transitions with several stages of the destruction of the order of particle arrangement. For example, for two-dimensional clus- ters in an external confining potential with Coulomb [14–16], screened Coulomb [18], logarithmic [19], and dipole [20] interactions between particles, the distur- bance of the order in the mutual arrangement of neigh- boring shells precedes the breakdown of the order in the particle arrangement inside the shell. This phenome- non, which involves relative reorientations of shells and, at an increasing temperature, their relative rota- tion, is referred to as the orientational melting of a clus- ter. Investigation into the relative rotation of shells in nanoparticles is of great interest in nanomechanics. In particular, Porto et al. [21] proposed a technique for transferring energy to a shell consisting only of three particles in such a way as to induce directed shell rotation. The van der Waals interaction between atoms of neighboring shells in a carbon nanoparticle is consider- ably weaker than the chemical interaction between atoms inside the shell. It is quite probable that these objects undergo orientational melting [5]. Possible ori- entational melting was also considered for a long two- shell nanotube [22] and single-shell nanotube ropes [23]. In the present work, we investigated the orienta- tional melting in a C 60 @C 240 carbon nanoparticle com- posed of two shells, namely, C 60 and C 240 fullerenes with I h symmetry. The energy characteristics of the studied nanoparticle (such as the interaction and strain energies for shells and the barriers to their relative rota- tion) were determined at zero temperature. The thermo- dynamic properties of the nanoparticle in the course of orientational rotation were investigated using the molecular dynamics technique. A definition was pro- posed for the temperature of complete orientational melting of a nanoparticle. This temperature was calcu- lated. 2. NUMERICAL CALCULATION AND SIMULATION TECHNIQUES Our choice of the nanoparticle shells (C 60 and C 240 fullerenes with I h symmetry) as the subject of investiga- tion was made for the following reasons. First, the examination of transmission electron microscope images of nanoparticles revealed that the diameter of the inner shell can be close to the diameter of the C 60 fullerene [24, 25]. Second, fullerenes whose size is smaller than that of C 60 are absent among the fullerenes extracted from a fullerene-containing soot with ben- zene, toluene, and other solvents (see, for example, [26, 27]). This fact was explained under the assumption that fullerene atoms shared by two adjacent pentagons can Molecular Dynamics Study of Orientational Melting and Thermodynamic Properties of C 60 @C 240 Nanoparticles Yu. E. Lozovik and A. M. Popov Institute of Spectroscopy, Russian Academy of Sciences, Troitsk, Moscow oblast, 142092 Russia e-mail: lozovik@isan.troitsk.ru Received February 26, 2001 Abstract—The barriers to relative shell rotation and other energy characteristics of C 60 @C 240 two-shell carbon nanoparticles (“onions”) with outer shells of different shapes are calculated. The disturbance of the orienta- tional order in the mutual arrangement of shells with an increase in temperature (orientational melting) is stud- ied using the molecular dynamics method. The intershell orientational diffusion is represented by an Arrhenius relationship, and the Arrhenius parameters are calculated numerically. A definition is proposed for the temper- ature of short-range order disturbance in systems that undergo melting without structural change. The calcu- lated temperature of orientational melting of the C 60 @C 240 nanoparticle is approximately equal to 60 K. © 2002 MAIK “Nauka/Interperiodica”. FULLERENES AND ATOMIC CLUSTERS