Electronic and magnetic properties of deformed and defective single wall carbon nanotubes
ABSTRACT The combined effect of radial deformation and defects on the properties of semiconducting single wall carbon nanotubes are studied using density functional theory. A Stone–Thrower–Wales defect, a substitutional nitrogen impurity, and a mono-vacancy at the highest curvature side of a radially strained nanotube are considered. The energies characterizing the deformation and defect formation, the band gap energies, and various bond lengths are calculated. We find that there is magneto-mechanical coupling behavior in the nanotube properties which can be tailored by the degree of radial deformation and the type of defect. The carbon nanotube energetics and magnetism are also explained in terms of electronic structure changes as a function of deformation and types of defects present in the structure.
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Article: Mechanics of carbon nanotubes[show abstract] [hide abstract]
ABSTRACT: Soon after the discovery of carbon nanotubes, it was realized that the theoretically predicted mechanical properties of these interesting structures–including high strength, high stiffness, low density and structural perfection–could make them ideal for a wealth of technological applications. The experimental verification, and in some cases refutation, of these predictions, along with a number of computer simulation methods applied to their modeling, has led over the past decade to an improved but by no means complete understanding of the mechanics of carbon nanotubes. We review the theoretical predictions and discuss the experimental tech-niques that are most often used for the challenging tasks of visualizing and manipulating these tiny structures. We also outline the computational approaches that have been taken, including ab initio quantum mechanical simulations, classical molecular dynamics, and continuum mod-els. The development of multiscale and multiphysics models and simulation tools naturally arises as a result of the link between basic scientific research and engineering application; while this issue is still under intensive study, we present here some of the approaches to this topic. Our concentration throughout is on the exploration of mechanical properties such as Young's modulus, bending stiffness, buckling criteria, and tensile and compressive strengths. Finally, we discuss several examples of exciting applications that take advantage of these properties, including nanoropes, filled nanotubes, nanoelectromechanical systems, nanosensors, and nanotube-reinforced polymers. This review article cites 349 references.
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ABSTRACT: Recent experimental studies and atomistic simulations have shown that carbon nanotubes (CNTs) display strong interplay between the mechanical deformation and electrical properties. We have developed a simple and accurate method to determine atom positions in a uniformly deformed CNT via a continuum analysis based on the interatomic potential. A shift vector is introduced to ensure the equilibrium of atoms. Such an approach, involving only three variables for the entire CNT, agrees very well with the molecular mechanics calculations. We then study the effect of mechanical deformation on the band gap change of single wall CNTs under tension, torsion, and combined tension/torsion via the k-space tight-binding method. Prior studies without this shift vector lead to significant overestimation of the band gap change. It is established that the conducting CNTs may easily become semi-conducting ones subject to mechanical deformation, but the semi-conducting CNTs never become conducting ones upon deformation.Journal of the Mechanics and Physics of Solids 01/2004; · 3.41 Impact Factor
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ABSTRACT: We report the direct experimental observation of the semiconductor-metal transition in single-wall carbon nanotubes (SWNTs) induced by compression with the tip of an atomic force microscope. This transition is probed via electric force microscopy by monitoring SWNT charge storage. Experimental data show that such charge storage is different for metallic and semiconducting SWNTs, with the latter presenting a strong dependence on the tip-SWNT force during injection. Ab initio calculations corroborate experimental observations and their interpretation.Physical Review Letters 06/2008; 100(25):256804. · 7.94 Impact Factor
Electronic and magnetic properties of deformed and defective
single wall carbon nanotubes
Yaroslav V. Shtogun*, Lilia M. Woods
Department of Physics, University of South Florida, 4202 East Fowler Ave., Tampa, FL 33620-5700, USA
A R T I C L E I N F O
Received 8 May 2009
Accepted 11 July 2009
Available online 23 July 2009
A B S T R A C T
The combined effect of radial deformation and defects on the properties of semiconducting
single wall carbon nanotubes are studied using density functional theory. A Stone–
Thrower–Wales defect, a substitutional nitrogen impurity, and a mono-vacancy at the high-
est curvature side of a radially strained nanotube are considered. The energies characteriz-
ing the deformation and defect formation, the band gap energies, and various bond lengths
are calculated. We find that there is magneto-mechanical coupling behavior in the nano-
tube properties which can be tailored by the degree of radial deformation and the type of
defect. The carbon nanotube energetics and magnetism are also explained in terms of elec-
tronic structure changes as a function of deformation and types of defects present in the
? 2009 Elsevier Ltd. All rights reserved.
Single wall carbon nanotubes (CNTs) are cylindrically rolled
infinite graphene sheets characterized by a chiral index
(n,m), which determines many of their characteristics .
Their unique electronic and mechanical properties make
them potential building blocks for nanoelectronic devices.
At different stages of the CNT growth, purification or device
production processes, however, mechanical deformations or
defects may occur in their structure. Thus the development
of such devices requires fundamental knowledge of structural
and electronic properties of not only perfect, but also
mechanically altered CNTs. In addition, exploring the modifi-
cations of CNT properties by creating defects or deforming
the CNT structure intentionally has been viewed as an addi-
tional route to control the CNT charge transport [2–5].
Tuning various properties of CNTs through mechanical
deformations has drawn substantial interest from research-
ers. Radial squashing is of particular interest. It has been
shown that using an atomic force microscope (AFM)  or
scanning tunneling microscopy techniques  metal–semi-
conductor transitions take place upon radial deformation of
the CNT cross-section. Also, the CNT conductance is reduced
by two orders of magnitude due to local sp3bonds formation
induced by an AFM tip squashing . Similar changes can be
achieved if CNTs are placed under sufficiently high external
hydrostatic pressure [9–11]. Radially deformed CNTs have also
been studied theoretically. First principle calculations have
revealed that important factors, such as the mirror-symmetry
breaking, r?p hybridization due to higher curvature regions
and the interaction between the low curvature regions are
responsible for the metal–insulator transitions and electronic
structure modulations in CNTs with different chiralities [12–
In addition to radial deformations, CNT properties can be
modified by the presence of topological defects in their struc-
ture [18–21]. The Stone–Thrower–Wales defect (STW), which
is one C–C bond rotated by 90? in the CNT network , is
one of the most common defects in the CNT structure. Such
C–C bond rotations appear during the CNT growth process
or during high temperature treatments [23,24]. The effect of
the STW defect on the CNT properties has been intensively
0008-6223/$ - see front matter ? 2009 Elsevier Ltd. All rights reserved.
* Corresponding author: Fax: +1 813 9745813.
E-mail address: firstname.lastname@example.org (Y.V. Shtogun).
C A R B O N 4 7 (2 0 09 ) 3 25 2 –3 2 62
available at www.sciencedirect.com
journal homepage: www.elsevier.com/locate/carbon
investigated in previous works [25–27], which have shown
that metal–semiconductor transitions in the CNT electronic
structure are induced depending on the STW concentration
. On the other hand, the presence of STW defects also in-
creases reactivity of CNT surface upon adsorption of various
molecules or atoms [29,30].
Other factors, such as, the interaction with atoms, mole-
cules, or nanoparticles, also cause changes in the CNT elec-
tronic properties [31–33]. Studies of even synthesizing new
nanotubes (BC4N) from CNT with substitutional atoms have
also been reported . In addition, atoms such as boron
and nitrogen are common dopants, which can appear in the
CNTs during laser-ablation and arc-discharge synthesize pro-
cesses or during substitutional reaction methods [35–37]. The-
oretical studies have shown that the presence of such
impurities leads to breaking of the CNT mirror symmetry
and shifting of the Fermi level, creating additional impurity
states in the energy band structure, improving the carrier
conductivity, and increasing CNT reactivity to other com-
Furthermore, vacancies produce significant changes in the
CNT transport, mechanical, and optical properties as well.
Vacancies can be present as a native defect during synthesis
of CNTor can be created intentionally by ion or electron irra-
diation methods [41,42]. Electronic structure calculations
have shown that a single vacancy is characterized by remov-
ing a C atom from the carbon network, which leads to the for-
mation of a pentagon and a nonagon with one dangling bond
. Also, depending on the vacancy concentration and CNT
chirality, the conductance of such defective CNT decreases
and new states appear in the energy band structure [44,45].
In addition, the electronic properties of CNT with vacancies
can be tuned by external electric field or radial deformation
Recently, it has been shown that the application of two
external stimuli leads to even richer changes in the CNT prop-
erties. For example, the presence of an external electric field
in defective  or radially deformed CNTs , as well as Si
doped in radially deformed CNTs  have been shown to
provide additional ways of tuning their properties.
In this work, we investigate another way of tailoring CNT
properties by considering the combined effects of radial
deformation and a defect located at the highest curvature re-
gion of the CNT structure. Two types of radial squashing are
studied – narrower than the tube’s cross-section and wider
than the tube’s cross-section. The first type corresponds to
deformations achieved by narrow hard surfaces, while the
second one corresponds to deformations achieved by infinite
hard surfaces. Also, three types of defects at the highest cur-
vature of the deformed CNTare investigated here. These are a
STW defect, a substitutional N impurity, and a single vacancy.
We present first principle calculations and analyze the
electronic structure in terms of the type and degree of radial
deformation and type of the defect in the CNT structure. Our
results show that CNT metal–semiconductor transitions can
occur for various combinations of mechanical alterations,
and reveal what the important electronic and magnetic struc-
ture changes for each case are. In particular, we investigate
the evolution of the energy band gap and the various defect
formation energies as a function of radial deformation. We
also explore the possibilities of mechanically induced mag-
netic properties of the radially deformed and defective CNT.
Thus by considering CNTs under two external mechanical
stimuli, we show additional ways to tune their properties.
Our results are of interest to experimentalists interpreting
their data of applying stress to realistic CNTs. Furthermore,
this study reveals greater capabilities for CNT applications
in new devices.
2.Computational method and model
The results presented here are obtained using self-consistent
density functional theory (DFT) within the local density
approximation (LDA) for the exchange-correlation functional
implemented in the Vienna Ab Initio Simulation Package
(VASP) . This code uses a plane-wave basis set and a peri-
odic supercell method. The core electrons are accounted for
either by utilizing ultrasoft Vanderbilt pseudopotentials or
by the projector-augmented wave method . Here we use
the ultrasoft pseudopotentials. The Brillouin zone is sampled
by (1 · 1 · 7) Monkhorst–Pack k-grid with an energy cutoff of
420 eV for all systems. Also, the relaxation criteria for all sys-
tems are 10?5eV for the total energy and 0.005 eV/A˚ for the
total force. Spin-polarization effects are included in the calcu-
lations of the defective CNT.
To illustrate our results, we consider a single wall semi-
conducting zigzag (8, 0) CNT. The supercell consists of four
unit cells along the z-axis of the CNT and for a defect-free
CNT it has dimensions (22.12 · 22.12 · 17.03) A˚3after relaxa-
tion. Such a supercell helps to avoid interactions between
neighboring defects and simulates isolated defects in the
First, we investigate a radially deformed defect-free (8,0)
CNT. The radial deformation is obtained by applying stress
to the opposite sides of the CNT cross-section along the y-
direction, which causes squeezing in the y-direction and
elongation in the x-direction (Fig. 1a–c, e and f). It is character-
ized by a dimensionless parameter g = (R ? Ry)/R (in%), where
R is the radius of the perfect CNT and Ryis the semi-minor
axis connecting the CNT lowest curvature regions (Fig. 1c).
We consider two types of squashing. One is radial defor-
mation between two hard surfaces with a cross-section smal-
ler than the CNT cross-section. In this case, we assume that
the extension of the wall along the x-axis is equal to one C–
C bond (?1.44 A˚). Thus the y-coordinates of the top and bot-
tom rows on the lowest curvature are fixed, and all other coor-
dinates are taken to be free (Fig. 1e). The other one
corresponds to radial deformation between two hard surfaces
with a cross-section larger than the CNT cross-section. In this
case, the y-coordinates of the atoms from the top and bottom
flat regions are kept fixed, while all other coordinates are al-
lowed to relax (Fig. 1g).
Depending on the degree of deformation, the radial cross-
section of the CNT takes different forms. When g < 35%, the
CNT has an elliptical-like cross-section after relaxation,
regardless of the type of squashing. For g P 35%, the CNT
has a ‘‘Peanut’’-like form after deforming between narrow
walls (Fig. 1e), and a ‘‘Flat’’-like form after deforming between
wide walls (Fig. 1g) after relaxation. We studied radial defor-
C A R B O N 4 7 ( 20 0 9 ) 3 2 5 2–32 6 2
mation of (8,0) CNT up to g = 75% for the Peanut and up to
g = 65% for the Flat configurations. In all cases, allowing all
coordinates to relax restores the original circular cross-sec-
tion indicating that these types of deformation are elastic.
After the (8,0) CNTwas deformed and relaxed, a single de-
fect is created at the highest curvature region. The structure
is relaxed again by keeping the appropriate constraints for ra-
dial squashing described earlier. We investigate a STW defect
by rotating one C–C bond (Fig. 1d), a single N impurity by
substituting one C atom (Fig. 1f), and a mono-vacancy (MV)
by removing one C atom (Fig. 1h). Releasing all coordinates re-
stores the circular form of the CNTwith a defect in its surface,
thus the CNT is elastic regardless of the defects present.
3. Results and discussion
3.1. Changes in the deformed and defective CNT structure
Here we present the results from the calculations related to
the changes of various bonds in the CNT structure upon defor-
mation and defect introduction. We areparticularly interested
in the CNT bonds located at the highest curvature sides and
the bonds comprising the defects (Fig. 1b, d, f and h). The evo-
lution of the C–C1 and C–C2 distances for the defect-free (8,0)
CNT as a function of deformation are shown in Fig. 2a) (C–
C2 = C–C3dueto symmetry). Thefigure indicates thatthebond
along the CNT axis decreases, while the C–C2 bond increases
when g increases. Also, the C–C2 distance changes the most
for the Flat configuration, for which the bond is stretched by
?0.08 A˚ (g ? 0 ? 65%), while there is little difference in C–C1
distance between the Peanut and Flat structure.
We find that the most stable configuration for the STW de-
fect is when the rotated bond is perpendicular to the CNTaxis
(Fig. 1d). Fig. 2b) shows the various bond changes as a func-
tion of g. It is evident, that there is no significant difference
between the corresponding distances for the Peanut and Flat
configurations with the exception of the C1–C2 bond. In fact,
for larger g the C1–C2 in the Flat CNT is changed the most
as compared to the other bonds. Also, the C1–C2 functional
behavior is very similar to the one for the C–C2 in the de-
fect-free CNT. Surprisingly the bond located at the highest
curvature site and perpendicular to the CNT axis, C6–C7,
shows little variation as a function of g.
The substitutional N impurity is created at the highest cur-
vature side of the perfect and deformed CNT. Fig. 2c) shows
that the N–C1 and N–C2 bonds exhibit similar dependence
Fig. 1 – (a) Cross-sectional and (b) side view of an undeformed defect-free (8,0) CNT, (c) radially deformed (8,0) CNTwith
g = 20%, (d) side view of a STW defect, (e) Peanut structure with g = 65%, (f) side view of N impurity, (g) Flat structure with
g = 65%, and (h) side view of a MV. Only the symmetry equivalent atoms in the STW and MV defects are shown.
C A R B O N 4 7 (2 0 0 9) 3 2 52 –3 2 62
on g as the corresponding C–C bonds in the defect-free CNT
(Fig. 2a). Thus not much disturbance in the CNT structure is
caused by the N atom. However, due to the larger size of N,
the N–C1 and N–C2 are smaller by 0.01 A˚and 0.03 A˚than the
C–C1 and C–C2, respectively, for all g. Our calculations also
show that the N–C1 bond decreases slightly as a function of
g and it is similar for both types of deformations. Conse-
quently, N–C2 = N–C3 has increased by 0.08 A˚ for the Flat
CNT and by 0.04 A˚for the Peanut one.
It has been shown, that removing one C atom from CNT
network leads to the formation of several metastable MV con-
figurations in CNT [52,53]. The most stable MV configuration is
characterized bya pentagon and a nonagonalong theCNTaxis
for zigzag CNTs and is shown in Fig. 1h. Fig. 2d and e shows
how the bonds involved in the MV change as a function of g.
It is interesting to see that while for the other studied cases
(defect-free, STW and N impurity) all C–C distances change
in a relatively continuous manner, the C–C bonds comprising
the MV for larger g do not. In particular, when the distance be-
tween thetwoflatportionsbecomeslessthan 3.4 A˚for theFlat
CNT, some bonds are found to experience relatively ‘‘sudden’’
jumps and dips. The biggest changes are found in the bonds
lying at the highest curvature regions. For example, C1–C2 is
increased by 0.06 A˚, C6–C7 by 0.08 A˚, while the C5–C8 is de-
creased by 0.11 A˚for the Flat CNT. Thus the MV causes larger
local disturbance in the deformed CNT structure as compared
to the other isolated defects.
3.2.Energetics of the deformed and defective CNT
We also calculate different energies characterizing the defor-
mation and defect formation. The deformation energy of a
defect-free CNT is defined as:
g¼ Eg? E;
where Eg is the total energy for the deformed CNTand E is the
total energy for the undeformed perfect CNT.
The formation energy for the STW defect, N impurity, and
MV at the highest curvature of the radially deformed CNT is
calculated, respectively, as:
g=STW¼ Eg=STW? Eg;
g=N¼ Eg=N? Eg? lNþ lC;
g=MV¼ Eg=MV? Egþ l;
where Eg/STW,N,MVare the total energies for the deformed CNT
with the appropriate defect, lN,Care the chemical potentials
for a free nitrogen and carbon atom, respectively, and l is
the chemical potential of a carbon atom from the CNT (energy
per C atom in the supercell).
Fig. 3a shows the deformation energy as a function of the
degree of radial deformation for the two types of squashing.
per for the Flat structure as compared to the Peanut one. It is
realized that for higher deformations, we press up to five
(35% < g < 65%) rows of carbon atoms on the top and bottom
gincreases non-linearly, however this increase is much stee-
Fig. 2 – Bond lengths as a function of deformation for (a) a defect-free (8,0) CNT, (b) (8,0) CNTwith a STW defect, (c) (8,0) CNT
with a N impurity, (d) and (e) (8,0) CNTwith a MV.
Fig. 3 – (a) The deformation energy as a function of g for Peanut and Flat CNT structures. (b) The formation energy for the
single defects as a function of g for the Peanut and Flat CNT structures. Cross-sectional view of the deformed and defective
(8,0) CNT after relaxation for various cases are also shown.
C A R B O N 4 7 ( 20 0 9 ) 3 2 5 2–32 6 2
of the flat regions for the Flat structure, as compared to one
row on the top and bottom of the flatter regions for the Peanut
structure. Consequently, large distortions at the highest cur-
vature regions and elongations along the x-axis are created
for the Flat configurations – Fig. 1 g). However, for the Peanut
configurations, mainly the distance between the top and bot-
tom C rows is decreased, while very little elongation along the
x-axis and practically no change in the highest curvature re-
gions for g > 35% are found – Fig. 1e). Therefore more energy
is needed to account for the larger distortions in the curved
regions for the Flat structure as compared to the Peanut
one. In addition to the distortion effects, there is a repulsion
contribution to the deformation energy from the flat graph-
ene-like regions in the Flat structure for very large deforma-
tions. At g P 50% the distance between the flat regions
becomes 2Ry6 3.13 A˚, which is smaller than the equilibrium
distance ?3.4 A˚in graphite . For the Peanut structure, this
repulsion is smaller since only two rows from the top and bot-
tom of the CNT network are brought closer than 3.4 A˚.
The formation energies for the different defects as a func-
tion of g are also shown (Fig. 3b). The energies Eg/STW,N,MVde-
crease for all types of defects as g increases. Thus less energy
is needed to make a defect on a deformed CNTas compared to
a circular one. Our calculations show that Ef
for the STW defect, and it is very close in value for the Peanut
and Flat structures. Also, Ef
rity is practically the same for both Peanut and Flat configura-
significantly for the two types of deformation for larger g.
For example, Ef
teau as a function of g, while Ef
decreases non-linearly. We relate this to the fact that the C–
C bonds exhibit more dramatic changes in the Flat CNT
(Fig. 2d and e). Thus it is easier to break the three bonds to
create a MV after deforming between two wide walls as com-
pared to the case between two narrow walls. Fig. 3b) suggests
that it is easier to create a defect on CNT under larger radial
strain as compared to a circular or lightly deformed CNT.
The least amount of energy is needed to make a STW defect
as compared to the greatest amount of energy to make a
MV. This is understood by realizing that the STW defect in-
volves the least disturbance in the CNT structure (just one
C–C bond is rotated), followed by introducing an impurity
(one C is substituted by N) and by creating a MV (one C atom
is removed by breaking three bonds, two of them become
connected and the third one is a dangling one).
The degree of radial deformation and the presence of each
isolated defect also affect the band gap energy of the CNT. The
perfect defect-free (8,0) CNT is a semiconductor with a rela-
tively large band gap (Eg= 0.55 eV). Squashing the CNT radi-
ally leads to decreasing of Eg until the gap is closed at
g = 23% (Fig. 4). Thus the CNT becomes a metal . Note that
the semiconductor–metal transition corresponds to a rather
discontinuous change in the C–C1 and C–C2 bonds (Fig. 2a).
One also sees that this transition occurs before the deformed
CNTacquires a Flat or a Peanut shape. Further deformation of
the defect-free CNT does not result in opening of a band gap.
The band gap energy Egfor defective CNTas a function of g
is also shown (Fig. 4). Initially (g = 0%) the gap is larger for the
CNT with a STW defect and smaller for the CNT with a N
g=STWis the lowest
g=Nfor the substitutional N impu-
g=MVis the largest for MV defect and it differs
g=MVfor the Peanut configuration stays at a pla-
g=MVfor the Flat configuration
impurity and a MV as compared to Eg of the defect-free
CNT. The squeezing closes Egat g = 23% for the CNT with an
N impurity or a MV, and at g = 25% with a STW defect. How-
ever, further deformation of the (8,0) CNTwith the MV results
in opening of a band gap with its highest value Eg= 0.2 eV at
g = 55% for the Peanut structure. Egbecomes non-zero again
following another gap closure at g = 65%. Fig. 4 also shows
that Eg= 0 for all g P 25% for the CNT with the N impurity,
and that there is a very small gap Eg= 0.01 eV at g = 55% and
g = 65% for the STW defect in the Peanut CNT structure.
3.3.Electronic structure modulations
To further study the combined effect of the radial deforma-
tion and isolated defects in the CNT structure, we carry out
detailed analysis of the electronic structure changes for vari-
ous cases. In Fig. 5, we show the band structures for several
values of g of a defect-free (8,0) CNT and an (8,0) CNT with a
STW defect at its highest curvature side. The applied radial
squashing lifts the degeneracy of the energy bands for the de-
fect-free CNT (Fig. 5a). As g increases, the lowest conduction
band starts to move towards the Fermi level. At g = 23%, the
highest valence band reaches the Fermi level and crosses with
the lowest conduction band at a point different than C. The
electronic structure analysis shows that r?p orbital hybrid-
ization due to atoms residing on the higher curvature sides
is the main reason for the semiconductor–metal transition
here. These results confirm the findings in previous studies
reporting electronic structure calculations of CNTunder rela-
tively small radial deformation [12–14]. Further increase in g
amplifies the effect of r–p admixture and leads to the move-
ment of the point of energy band crossing with EFtowards the
X point. For sufficiently large radial strain (g > 50%), multiple
crossings at the Fermi level from higher conduction and lower
valence bands occur, indicating that the squashed CNT has
became a better metal.
The electronic structure calculations show that for a per-
fect defect-free CNT, all atoms from the CNT network contrib-
ute to the energy bands. As g > 0%, the energy bands around
the EFlevel are mainly composed of orbitals from the atoms
Fig. 4 – The energy band gap Egof the perfect and defective
(8,0) CNT as a function of radial deformation g.
C A R B O N 4 7 (2 0 0 9) 3 2 52 –3 2 62
located at the highest curvature regions. When g P 55% for
the case of Peanut deformation, contribution from the orbi-
tals of the atoms from the top and bottom rows separated
by 2Ry(Fig. 1c) is also found in the energy bands around EF.
The effect of radial deformation can also be traced in the
Fig. 6a–c show that for radial strain g = 25% in the Peanut con-
figuration, the charge redistribution is mainly around the
higher curvature CNT sides, while for the Flat configuration
charge is redistributed over the flat CNT portions as well.
The energy band structure for the deformed (8,0) CNTwith
a STW defect is similar to the one for the defect-free radially
deformed CNT (Fig. 5b). The main differences at g = 0% are the
larger band gap and the presence of a relatively flat level asso-
onthe carbon network.
ciated with the defect at E ? ?2.9 eV in the conduction region
for the CNT with STW (in red). As g increases, this flat level
starts to move away from EF, while the highest valence band
and the lowest conduction band start to move towards EFin
a similar manner as in the case of the defect-free CNT. A very
small energy gap Eg? 0.01 eV is found at g = 55% and g = 65%
for the Peanut CNTwith a STW defect, while Eg= 0 eV for all
other g. Our analysis shows that again the r–p hybridization
due to the orbitals from the atoms at the highest curvature re-
gions contributes mainly to the energy band structure around
EF. We find that the lowest conduction band is mainly com-
posed from the orbitals from the defect, while the highest va-
lence band is composed mainly from orbitals from the rest of
Fig. 5 – Energy band structure of (a) defect-free (8,0) CNT, (b) (8,0) CNTwith a STW defect on its highest curvature site for
different degrees of radial deformation g.
C A R B O N 4 7 ( 20 0 9 ) 3 2 5 2–32 6 2
The local disturbance by the STW defect also affects the
charge accumulation on the CNT. Fig. 6d–f) shows that even
though the defect is at the highest curvature side, little charge
accumulation is found on the defect itself except on the C6–
C7 bond. Most of the total charge is found on the atoms sur-
rounding the STW defect regardless of the applied radial
The electronic structure of the deformed (8,0) CNTwith a N
impurity and a MV is also analyzed. In Fig. 7, we present our
results for the total Density of States (DOS) for the various
cases. Spin-polarization effects are also included in the calcu-
lations in order to study the possibility of magnetic properties
of CNT. Such possibility has been suggested by other authors
who have considered doped CNTand CNTwith vacancies [55–
It has been shown that the DOS and energy band structure
of the N-doped CNT depends on the concentration of impuri-
ties [57,58,19]. For concentrations more than 1%, a flat level in
the energy band gap is found in the 0.2 ? 0.27 eV region below
the bottom of the conduction band. Here, the N concentration
is 0.78%, and no such flat level between the highest valence
and lowest conduction bands is found (Fig. 7a). As g is in-
creased, the lowest conduction and the highest valence bands
move towards the EF, thus Egdecreases. The total DOS for the
Peanut and Flat structures increase significantly for g > 45%
suggesting that the CNT characteristics becomes more metal-
lic-like. The electronic structure analysis reveals that the en-
ergy bands in the vicinity of the Fermi level are mainly
composed of the pxand pyorbitals of the atoms from the
highest curvature CNT regions. The orbitals from the N atom
contribute to the lowest conduction band, which is also par-
tially occupied. For 0 < g < 25% the r–p hybridization increases
leading to closing of the energy gap and the extra e?is rela-
tively localized in the lowest conduction band. For g > 25%,
the EFis located above the crossing point of the conduction
and valence bands, which causes multiple crossing of the EF
due to the continuing increase in the r–p admixture and the
presence of the extra e?.
It is evident from Fig. 7a) that the extra N e?can induce
spin-polarization effects in the CNT electronic structure at
g = 0%. Around ? ?2.8 eV sharper features in the DOS for spin
‘‘up’’ are found. However, the radial deformation has a pro-
found effect on the spin-polarization effects of the CNTwith
the N impurity. For g < 25% spin ‘‘up’’ and spin ‘‘down’’ states
show differences in the valence region, but for g P 25%, the
total DOS are practically the same, except for the Flat CNT
at g = 65%. Fig. 7b) depicts the evolution of the CNT local mag-
netic moments m as a function of deformation. m experiences
a maximum at g = 5%, and it becomes m = 0 (g = 25%) almost
when the CNT becomes a metal (g = 23%). However, when
g = 65% the Flat CNT has its largest value for m = 0.92 lB(not
shown in Fig. 7b) suggesting that the deformation and the N
impurity have a complicated inter-relationship.
Further insight into the N defective (8,0) CNT can be gained
by examining the spin density for various deformations g
(Fig. 8a–c). The spin density is maximal on the N atom and
the surrounding C atoms. The localization of the e?spin
shows striking differences for the different g. For the g = 20%
case, the unpaired e?is much more delocalized as compared
to the g = 10% case, where the e?spin density localized
around the impurity site is much more intense. This behavior
is similar to the one found in semiconducting (zigzag) CNT,
where the N e?is localized around the N impurity. However,
for metallic (armchair) CNTs, N e?is completely delocalized
. At the same time, for g = 65% the Flat CNT is a metal,
but the m has its highest value – m = 0.92 lB. Consequently,
the e?spin is localized around the impurity and neighboring
The results from the spin-polarized calculations for the
radially deformed (8,0) CNT with MV are also shown in
Fig. 7c). At g = 0%, there is a sharp localized peak at ?
?3.41 eV in the conduction region of the spin ‘‘up’’ and
‘‘down’’ total DOS. The main contribution to this peak comes
from the pxand pyorbitals of the C atoms comprising the MV.
As the CNTis deformed, this peak starts to broaden and move
closer to EF. This is due to the increased r–p admixture from
the CNT atoms located in the highest curvature locations to-
gether with the C atoms forming the MV as g increases. For
g = 45%, two such peaks appear for the Peanut and Flat struc-
tures, which also become broadened for larger g. The major
contribution to this peak comes from the pxorbitals of C1,
C5 and C8 atoms as well as pyorbitals of the C atoms of the
pentagon of MV (Fig. 1 h). For g = 65% this broadening contin-
ues but with additional sharp features from the MV at higher
energy in the conduction region.
Comparing the total DOS for spin ‘‘up’’ and ‘‘down’’ states
shows that for almost all g there is little difference between
them. The exception is the conduction and valence regions
Fig. 6 – Total charge density plots for (8,0) CNT (a) defect-free structure with g = 25%, (b) Peanut structure with g = 65%, (c) Flat
structure with g = 65%, (d) STW defect with g = 25%, (e) Peanut structure with STWand g = 65%, and (f) Flat structure with STW
and g = 65%. The isosurface value is 0.0185 e/A ˚3.
C A R B O N 4 7 (2 0 0 9) 3 2 52 –3 2 62
around EFof the g = 65% deformation for the Peanut CNT. For
this case, we find that there is a small magnetic moment
m = 0.04 lB. These findings lead us to conclude that there is
an intricate connection between the electronic structure of
the deformed CNT with a mono-vacancy and the CNT mag-
netic properties. The origin of magnetism in CNTwith vacan-
cies is an issue which is still under debate. Several reasons
have been shown to be responsible for their spin-polarization
effects: under-coordinated C atom with a localized unpaired
spin, concentration of vacancies, CNT chirality, sp3pyramidi-
zation and related bond length changes, and vacancy location
with respect to the CNT structure [57,59].
Other researchers have found that for the MV orientation
investigated here (Fig. 1h), semiconducting (n,0) CNT do not
show magnetic properties . We also confirm this for
g = 0%.Ourcalculationsshowthatthisbehaviourpersistseven
for radially squeezed defective CNT until very large g. Even
though the sp3mixture of the carbon atoms changes signifi-
Fig. 7 – (a) Total Density of States for spin ‘‘up’’ and ‘‘down’’ carriers of (8,0) CNTwith a substitutional N impurity on its highest
curvature site at different g for Peanut and Flat structures. (b) The magnetic moment as a function of g for the (8,0) CNTwith
the N impurity. (c) Total Density of States for spin ‘‘up’’ and ‘‘down’’ carriers of (8,0) CNTwith a MV defect on its highest
curvature site at different g for Peanut and Flat structures.
Fig. 8 – Spin density isosurface plots for (a) (8,0) CNTwith a N
impurity for g = 10% (isosurface value = 0.004 lB/A ˚3), (b) (8,0)
CNTwith a N impurity for g = 20% (isosurface value = 0.004
lB/A ˚3), (c) flat (8,0) CNTwith a N impurity for g = 65%
(isosurfacevalue = 0.0122 lB/A ˚3),and(d)Peanut(8,0)CNTwith
a MV for g = 65% (isosurface value = 0.018 lB/A ˚3).
C A R B O N 4 7 ( 20 0 9 ) 3 2 5 2–32 6 2
cantly as the deformation increases, this effect alone does not
seemto beenough to induce magnetismin the CNT, suggested
in other studies [59,60]. However, for g = 65% for the Peanut
CNT the spin density plot in Fig. 8d) shows that the e–spin is
rather localized around the dangling bond of the MV suggest-
paired spin is important for the magnetic properties of the
localization is found in the cases for other values of g.
It has been predicted that localized zigzag states associ-
ated with edges of H-terminated graphitic ribbons produce a
flat band at the Fermi level [61,62]. The presence of such a flat
band leads to electron–electron interactions, and conse-
quently to magnetic polarization with moments localized at
the zigzag states. The mono-vacancy is such a zigzag edge.
However, the characteristic zigzag edge flat band may not
be evident here due to the combined role of the chirality of
the CNT, the r–p admixture, and the concentration and orien-
tation of the MV. Applying radial deformation can change the
r–p hybridization and bond lengths in such a way that the
zigzag edge flat bands are evident again. Examining the en-
ergy band structure shows that for the Peanut configuration
with g = 65% dispersionless portions of the lowest conduction
and highest valence bands composed mainly of the r and p
electrons are found at the Fermi level. No such flat bands
are obtained for the other values of radial deformation. These
observations suggest that the magnetic flat-band theory to-
gether with r–p orbital admixture may explain the origin of
magnetic polarization of radially deformed zigzag CNT with
isolated vacancies [61,62].
In conclusion, we have presented ab initio calculations based
on density functional theory revealing the electronic struc-
ture modifications of single walled radially deformed and
defective CNT. The particular way of mechanically altering
the CNT structure investigated here corresponds to first radi-
ally deforming the CNT, after which a single defect is created
at its highest curvature region. Experimentally this can be
done by squashing the CNT between two narrow or between
two wide hard walls, and then introducing a rotated C–C
bond, a N impurity or a single vacancy, by another experimen-
tal technique such as ion or electron irradiation.
Our calculations show that in general it is easier to create a
defect in the carbon network for CNTwith larger degree of ap-
plied radial strain. In addition, the amount of energy needed
to create a defect in the carbon network involving less distur-
bance (such as STW defect) is less compared to creating a de-
fect with larger disturbance (such as a mono-vacancy). We
also found that for all types of defects, the (8,0) CNT experi-
ences a semiconductor–metal transition at approximately
the same value of radial strain regardless of the defects. How-
ever, further deformation leads to opening of a smaller energy
gap in the CNT electronic structure when a mono-vacancy is
present, while for all other defects, no such gap is found.
The detailed electronic structure analysis reveals that the
main reason for the semiconductor–metal transition is the
balance between the r–p hybridization from the radial defor-
mation and from the atoms forming the defect. Furthermore,
this study demonstrates that there is dependence between
the mechanical and magnetic properties of defective and
radially strained CNT. We find that the simultaneous applica-
tion of radial strain and a defect, such as impurity or vacancy,
can induce magnetism in the CNT for certain combinations of
g and types of defects. The origin of the magneto-mechanical
behavior of the CNT is explained in terms of the interplay be-
tween the r–p orbitals admixture, energy band structure, and
types of defects in the structure.
Acknowledgement is made to the donors of the American
Chemical Society Petroleum Research Fund for support of this
research. L.M.W. was also supported by the US Army Medical
Research and Material Command under Award No. W81XWH-
07-1-0708 during part of this work. Useful conversations with
Dr. Thomas Reinecke from the Naval Research Laboratory are
also gratefully acknowledged. Finally, we would like to
acknowledge the use of the services provided by the Research
Computing Core at the University of South Florida, the Tera-
Grid Advanced Support Program at the University of Illinois,
and the High Performance Computing facilities of DoD.
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