Comparative theoretical study of single-wall carbon and boron-nitride nanotubes
Brahim Akdim and Ruth Pachter
Air Force Research Laboratory, Materials and Manufacturing Directorate, AFRL/MLPJ, WPAFB, Ohio 45433
Xiaofeng Duan
Major Shared Resource Center for High Performance Computing, ASC/HP, WPAFB, Ohio 45433
W. Wade Adams
Rice University, Center for Nanoscale Science and Technology, Houston, Texas 77005
Received 13 January 2003; published 6 June 2003
We present a comprehensive comparative study of properties of BN and C nanotubes using a full potential
linear combination of atomic orbitals approach, as well as a planewave pseudopotential method. This paper
covers our results on the structural, mechanical, vibrational, and electronic properties, examining in detail the
effects of intertube coupling. Structural aspects and mechanical properties are discussed and compared in BN
and C nanotubes, and to experiment. Upshifts in the values of the radial breathing modes, due to intertube
coupling, are found to be small and systematic, about 2% in zigzag nanotubes, and varying from 2 to 7 % in
armchair tubes, for both materials. Finally, the effects of intertube interactions on the van Hove singularities are
discussed.
DOI: 10.1103/PhysRevB.67.245404 PACS numbers: 61.46.+w, 62.25.+g, 73.22.Gk, 78.30.Na
I. INTRODUCTION
From the time of their discovery, carbon C
1
and boron-
nitride BN
2
nanotubes BN-NT’s and CNT’s have been
receiving ever-increasing interest due to their novel proper-
ties and potential application in nanodevices. It is well estab-
lished that CNT’s can be either metallic or semiconducting,
depending on the tube chirality and diameter, suggesting a
variety of nanoelectronics applications.
3–6
Furthermore, the
high stiffness demonstrated experimentally by Young’s
moduli and tensile strength
7,8
measurements, and by theoret-
ical predictions
9–11
are notable, extending their potential ap-
plications, for example, to composite reinforced materials;
12
other application areas are being explored as well, such as
hydrogen storage,
13
or field emission;
14–16
all of which have
been recently summarized.
17
BN-NT’s are also interesting
materials, due to their constant wide band gap 5.5 eV,
18
independent of chirality and diameter, and in their ability to
sustain heat. It has been shown recently that BN-coated
CNT’s demonstrate better field emission
19
than as-produced
CNT’s.
Resonant Raman spectroscopy has become a promising
technique in probing and characterizing the structure of
nanotubes,
20,21
which can be explained in terms of models
that take into account the valence and conduction * en-
ergy bands. The strong resonance Raman effect in nanotubes
permits the study of their optical and electronic properties,
which occurs between the singularities of the conduction and
valence bands, and previous studies established a relation-
ship with tube diameter.
21–24
However, relatively simplistic
models may not be appropriate to predict RBM’s, especially
for small diameter tubes, and to provide insight into the ef-
fects of intertube interactions. Indeed, recently a study of
single-wall carbon nanotube properties C( n , n ) and C( n ,0),
n =(4,6,8,10)], was carried out,
25
where CNT’s were mod-
eled as isolated tubes or crystalline ropes, using a full-
potential linear combination of atomic orbitals FP-LCAO
density functional theory approach. Although the full poten-
tial all-electron scheme is computationally intensive, the ac-
curacy in modeling single-wall CNT’s was evident in com-
parison to other theoretical work and experiment. Moreover,
previous high-level theoretical calculations
10,11
have been
rather limited, and a comprehensive study using highly ac-
curate methods, to validate an approach for a reliable predic-
tion of RBM’s in CNT’s and BN-NT’s, has not been carried
out thus far. In this paper, we report an extensive and rigor-
ous investigation using the all-electron LCAO and plane-
wave pseudopotential methods PW-PP. Calculated Young’s
moduli of CNT’s are found to be in excellent agreement with
recent experimental measurements
7
and in light of these
newly reported results, it is suggested that our calculated
values for BN-NT’s are also appropriately estimated. For the
RBM’s of CNT’s, we validated our fitting constants by cal-
culating the value of the RBM of an isolated large diameter
C20,20 nanotube, and compared it with the extrapolated
value; we also fitted our RBM results to the suggested model
by Bachilo et al.
24
Although we obtained excellent agree-
ment with the fitted constant,
24
the proposed model does not
hold for a large radius tube. Finally, we studied the effects of
intertube interactions on the van Hove singularities vHS of
CNT’s, and calculated the ratio ( E
22
/ E
11
) to be in good
agreement with recent experimental data.
26
II. COMPUTATIONAL DETAILS
FP-LCAO and PW-PP schemes, using DMOL3 and
CASTEP,
27
were applied, adopting the generalized gradient
approximation GGA, with the Perdew and Wang
28
exchange-correlation functional and a double-numeric basis
set. A hexagonal symmetry of order 8 with inversion was
PHYSICAL REVIEW B 67, 245404 2003
0163-1829/2003/6724/2454048/$20.00 ©2003 The American Physical Society 67 245404-1