JOURNAL OF SOLID STATE CHEMISTRY 141, 164 — 167 (1998) ARTICLE NO. SC987938 Packing Models for High-Pressure Polymeric Phases of C 60 V. A. Davydov,* V. Agafonov,- A. V. Dzyabchenko,‡ R. Ce´olin,- and H. Szwarc *Institute of High Pressure Physics of the Russian Academy of Sciences, 142092 Troitsk, Moscow Region, Russian Federation; -Laboratoire de Chimie Physique, J.E. 1990, Faculte ´ de Pharmacie, Universite ´ de Tours, 31 avenue Monge, 37200 Tours, France; ‡Karpov Institute of Physical Chemistry, ul. Obukha 10, 107120 Moscow, Russian Federation; and Laboratoire de Chimie Physique des Mate ´ riaux Amorphes, URA 1104, CNRS, Universite ´ Paris Sud, Ba L timent 490, 91405 Orsay, France Received October 14, 1997; in revised form May 18, 1998; accepted June 24, 1998 Packing models of three polymeric phases of C 60 obtained through pressure–temperature treatments have been recon- sidered through a lattice energy minimization method using atom–atom potentials. Orthorhombic phase O, previously as- signed Immm symmetry, is best described by space group Pmnn. Whereas the Immm model contains one orientation of the poly- meric chains, the Pmnn model presents two orientations related by a glide plane. For the tetragonal phase, two packing patterns of polymeric tetragonal layers are possible: one with Immm symmetry represents a pseudotetragonal packing of translation- ally identical adjacent layers; the second packing pattern, actual- ly tetragonal (P4 2 /mmc), consists of two layers related by a4 2 screw axis and is &4 kJ mol 1 more stable. Concerning phase R, three packing modes of hexagonal layers are possible; the previously published structure of phase R corresponds to the least stable packing. Thus, the previous structural descriptions should be reexamined.  1998 Academic Press INTRODUCTION The solid-state polymerization of C  at high pressure leads to a new class of fulleride compounds. By varying the pressure—temperature treatment, one may obtain crystalline polymers containing chains (1D) or layers (2D) (1—6). At very high pressure, in the 10-GPa range, an amorphous 3D polycondensed compound of C  is formed (7,8). High-pres- sure p—¹ phase diagrams of C  have been proposed (5, 6, 8). It appears that there are two 2D polymeric phases of C  : the tetragonal (T) and the rhombohedral (R) ones (3). Both phases are stable at high pressure up to approximately 1073 K and at higher temperatures they transform into hard amorphous carbon (5, 9). A mechanism of the T and R phase formation from the high-pressure orthorhombic phase (hereafter called phase O) is described in (5). However, there is some disagreement about the structure of phase O, To whom correspondence should be addressed. E-mail: szwarc@ cpma.u-psud.fr. which may be indexed either as orthorhombic or as rhom- bohedral (10). Concerning the low-pressure region, it was shown that an orthorhombic phase (O) that may be viewed as different from O is formed at 1.5 GPa and 723 K (10, 11). It was suggested that O may be an intermediary for the formation of the tetragonal modification. The main weakness of these studies lies in the poor resolution of the experimental X-ray profiles, which is likely the origin of the remaining discrepancies. In this work new structural models of the orthorhombic, tetragonal, and rhombohedral phases are proposed using energy packing calculations to supplement the X-ray data. CALCULATION METHOD Intermolecular potentials involving both Lennard-Jones potentials and electrostatic parts due to the interactions of bond-centered partial charges (12) were used. This scheme was chosen because it was found (13) that it gives better results than those proposed by Cheng and Klein (14) and Burgos et al. (15) as to what concerns the secondary min- imum corresponding to the double bond to the hexagon orientation inside the C  crystal. In particular, it repro- duces the two orientations (double bond to pentagon and double bond to hexagon) as two separate energy minima, the hexagon-oriented packing energy being 2.5 kJ mol higher than the pentagon-oriented one (to be compared with 18 kJ mol as calculated using (15), whereas the ex- periment-derived value is 1 kJ mol). Furthermore, the de- viations of molecular orientations (1 and 8°, respectively) with respect to those that David et al. derived from experi- ments (16) are quite satisfactory. Program PMC (17) was used for crystal lattice energy calculations. The geometry of the C  unit of the polymeric chain was taken as identical to that of the free molecule with ideal I  symmetry assuming that geometrical changes due to polymerization are not significant for calculation purposes. The shorter bonding distance between adjacent C  units 164 0022-4596/98 $25.00 Copyright  1998 by Academic Press All rights of reproduction in any form reserved.