Page 82 - Carbon Nanotubes

TOPOLOGICAL AND SP3 DEFECT STRUCTURES
IN NANOTUBES

T. W. EBBESEN' and T. TAKADA~
'NEC Research Institute, 4 Independence Way, Princeton, NJ 08540, U.S.A.
2Fundamental Research Laboratories, NEC Corporation, 34 Miyukigaoka, Tsukuba 305, Japan
(Received 25 November 1994; accepted 10 February 1995)

Abstract-Evidence is accumulating that carbon nanotubes are rarely as perfect as they were once thought
to be. Possible defect structures can be classified into three groups: topological, rehybridization, and in-
complete bonding defects. The presence and significance of these defects in carbon nanotubes are discussed.
It is clear that some nanotube properties, such as their conductivity and band gap, will be strongly affected
by such defects and that the interpretation of experimental data must be done with great caution.
Key Words-Defects, topology, nanotubes, rehybridization.

1. INTRODUCTION 2. CLASSES OF DEFECTS
Carbon nanotubes were first thought of as perfect Figure 1 show examples of nanotubes that are far
seamless cylindrical graphene sheets - a defect-free from perfect upon close inspection. They reveal some
structure. However, with time and as more studies of the types of defects that can occur, and will be dis-
have been undertaken, it is clear that nanotubes are cussed below. Having defined a perfect nanotube as
not necessarily that perfect; this issue is not simple be- a cylindrical sheet of graphene with the minimum
cause of a variety of seemingly contradictory observa- number of pentagons at each tip to form a seamless
tions. The issue is further complicated by the fact that structure, we can classify the defects into three groups:
the quality of a nanotube sample depends very much 1) topological defects, 2) rehybridization defects and
on the type of machine used to prepare it[l]. Although 3) incomplete bonding and other defects. Some defects
nanotubes have been available in large quantities since will belong to more than one of these groups, as will
1992[2], it is only recently that a purification method be indicated.
was found[3]. So, it is now possible to undertakevarious
accurate property measurements of nanotubes. How- 2.1 Topological defects
ever, for those measurements to be meaningful, the The introduction of ring sizes other than hexagons,
presence and role of defects must be clearly understood. such as pentagons and heptagons, in the graphene
The question which then arises is: What do we call sheet creates topological changes that can be treated
a defect in a nanotube? To answer this question, we as local defects. Examples of the effect of pentagons
need to define what would be a perfect nanotube. and heptagons on the nanotube structure is shown in
Nanotubes are microcrystals whose properties are Fig. 1 (a). The resulting three dimensional topology
mainly defined by the hexagonal network that forms follows Euler's theorem[8] in the approximation that
the central cylindrical part of the tube. After all, with we assume that all the individual rings in the sheet are
an aspect rat.io (length over diameter) of 100 to 1000, flat. In other words, it is assumed that all the atoms
the tip structure will be a small perturbation except of a given cycle form a plane, although there might
near the ends. This is clear from Raman studies[4] and be angles between the planes formed in each cycle. In
is also the basis for calculations on nanotube proper- reality, the strain induced by the three-dimensional ge-
ties[5-71. So, a perfect nanotube would be a cylindrical ometry on the graphitic sheet can lead to deformation
graphene sheet composed only of hexagons having a of the rings, complicating the ideal picture, as we shall
minimum of defects at the tips to form a closed seam- see below.
less structure. From Euler's theorem, one can derive the follow-
Needless to say, the issue of defects in nanotubes ing simple relation between the number and type of
is strongly related to the issue of defects in graphene. cycles nj (where the subscript i stands for the number
Akhough earlier studies of graphite help us under- of sides to the ring) necessary to close the hexagonal
stand nanotubes, the concepts derived from fullerenes network of a graphene sheet:
has given us a new insight into traditional carbon ma-
terials. So, the discussion that follows, although aimed 3n, + 2n, + n5 - n7 - 2n8 - 372, = 12
at nanotubes, is relevant to all graphitic materials.
First, different types of possible defects are described. where 12 corresponds to a total disclination of 4n (i.e.,
Then, recent evidences for defects in nanotubes and a sphere). For example, in the absence of other cycles
their implications are discussed. one needs 12 pentagons (ns) in the hexagonal net-
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