Abstract A unified approach to the analysis of the mechanisms that lead to the edge reconstruction of graphite and growth of a variety of non-planar graphitic structures, such as nanotubes, is suggested. Transmission electron microscopy (TEM) shows that nano-arches are formed on the edge planes of natural and synthetic graphite, as well as graphite polyhedral crystals, which are built of graphene sheets; this makes the edge recon- struction of graphite different from the surface recon- struction of other crystals. A theoretical study of edge zipping in graphite and formation of tubular carbon structures has been performed using an integrated ap- proach combining molecular dynamics simulation and analytical continual energetics modeling. The suggested theoretical framework describes the formation of curved surfaces in a wide range of dimensions, which is a gener- al feature of the growth of layered materials. Layered materials isostructural to graphite, such as hexagonal BN, demonstrate similar edge structures and also form nanotubes. Thus, the ability of materials to form arches as a result of edge reconstruction points out to their abili- ty to form nanotubes and vice versa. TEM studies of graphite and hexagonal boron nitride provide experimen- tal verification of our analytical model. Keywords Graphite · Continual energetics · Molecular dynamics · Nanotube · Transmission electron microscopy · Edge reconstruction Introduction Every field of engineering seems to have a favorite ma- terial. Steel is the most important material for mechani- cal engineers. Silicon dominates in electronics. Nano- technologists selected carbon from the beginning be- cause of the fullerenes [1] and nanotubes [2], which have been considered objects on the size scale compatible with nanodevices. Carbon and carbon-based materials attract the attention of researchers not only because of their morphology and mechanical properties but also due to their unique electronic properties including high tem- perature superconductivity [3], rectifying behavior [4], and field effect transistors [5–7]. Conventional graphite forms hexagonal plate-like crystals (kish graphite) [8], with weak bonding between graphite layers. Most of the carbon materials produced at temperatures 1000–2000 °C have a disordered structure (carbon black, soot, glassy carbon and carbon fibers). Graphitization of solid carbon occurs at temperatures close to 3000 °C. Partial graphitization and the formation of polygons was observed after heat treatment of carbon black at 2800 °C [9]. However, making large crystals of graphite is extremely difficult and both natural and man- made crystals do not exceed several millimeters in size. Thus, large and perfect graphite crystals occur probably less frequently than large diamonds. Graphite whiskers [10] and carbon nanotubes (NT) [11] represent unusual forms of sp 2 carbon due to the distortion of their graphite sheets. In graphite whiskers, a graphite sheet (graphene) simply rolls into a scroll [10] and the layers have short and medium range order, but not the long-range periodicity of crystalline graphite. The discovery of single-wall nanotubes (SWNT), SWNT ropes, self-assembled SWNT single crystals [12], and multiwall carbon nanotubes (MWNT), consisting of co- axial closed or open tubes, demonstrated the existence of a variety of non-planar structures built of graphene sheets. Great interest in novel nanostructures, such as nanotubes, fullerenes and other nonplanar carbon allo- tropes, resulted in a decreasing interest in bulk planar graphite. In spite the fact that SWNTs, MWNTs, whis- kers, and graphite polyhedral crystals (GPC) [13] are built from the same graphene sheets as bulk graphite (Fig. 1), they are often considered separately from graphite [14]. S. Rotkin Beckman Institute, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA Y. Gogotsi ( ✉ ) Drexel University, Department of Materials Engineering, 3141 Chestnut St., Philadelphia, PA 19104, USA e-mail: gogotsi@drexel.edu Tel.: 215-895-6446, Fax: 215-895-6760 Mat Res Innovat (2002) 5:191–200 © Springer-Verlag 2002 ORIGINAL ARTICLE Slava V. Rotkin · Yury Gogotsi Analysis of non-planar graphitic structures: from arched edge planes of graphite crystals to nanotubes Received: 29 October 2001 / Accepted: 5 November 2001