Page 377 - Fiber Fracture

ATOMIC TRANSFORMATIONS 359

INTRODUCTION

Carbon is unique among the elements in its ability to assume a wide variety of
different structures and forms. It is now a little more than ten years ago since a new
family of carbon cage structures, all based on a three-fold coordinated sp2 network,
was discovered, thereby inaugurating the science of fullerenes. Of these, c60 is the
best known member. However, perhaps the most exciting among the recent additions
to the fullerene family are carbon nanotubes, discovered soon after the c60 was made
in quantity. Carbon nanotubes are hollow cylinders consisting of single or multiple
sheets of graphite (graphene) wrapped into a cylinder, as illustrated in Fig. 1. They
are believed to have extraordinary structural, mechanical and electrical properties,
which derive from the special properties of carbon bonds, their unique quasi-one-
dimensional nature, and their cylindrical symmetry. For instance, the graphitic network
upon which the nanotube structure is based is well known for its strength and elasticity,
thereby providing for unmatched mechanical strength. Nanotubes can also be metallic
or semiconducting, depending on their indices (see Fig. 1). This opens up the very
interesting prospects of junctions and devices made entirely out of carbon. Because
of these very unusual characteristics and the potential compatibility of nanotubes
with organic matter, their discovery has been greeted with a considerable amount
of excitement within the scientific community. However, since they were originally
synthesized in minute quantities only, relatively few experimental techniques were
initially available for their study. Indeed, the original experimental work was only able
to address nanotube structure through high-resolution transmission electron microscopy
(HRTEM). Their discovery, however, has stimulated much theoretical work. In turn,
these investigations have benefited significantly from the substantial progress achieved
in the past 2-3 decades in the development of theoretical methods, some of which now
have a truly predictive power. Astonishing properties have been predicted, which has
stimulated further experiments, so that the progress has been very rapid, with hundreds

Fig. 1. Nanotube structures are obtained by rolling a graphene sheet into a cylinder, so that the lattice
points 0 and 0 fold onto each other. Mathematically, their structures are uniquely defined by specifying the
coordinates of the smallest folding vector (n,rn) in the basis of graphene lattice vectors a and b. The (n,O)
zigzag and (n,n) armchair tubes are mirror-symmetric; all other tubes are chiral.