PHYSICAL REVIEW B 76, 014108 共2007兲
Axial buckling and compressive behavior of nickel-encapsulated multiwalled carbon nanotubes
Abha Misra,1 Pawan K. Tyagi,1 Padmnabh Rai,1 Dipti Ranjan Mahopatra,1 Jay Ghatak,2 P. V. Satyam,2
D. K. Avasthi,3 and D. S. Misra1,*
1Physics
Department, IIT Bombay, Powai, Mumbai 400 076, India
Institute of Physics, Sachivalaya Marg, Bhubaneswar 751005, India
3Inter-University Accelerator Center, Aruna Asaf Ali Marg, New Delhi 110067, India
共Received 25 January 2007; revised manuscript received 14 May 2007; published 16 July 2007兲
2
In a recent report 关Sun et al., Science 312, 1119 共2006兲兴, the partially filled material inside multiwalled
carbon nanotubes 共MWNTs兲 was shown to have shrunk and deformed in the axial direction under 300 kV
electron irradiation. In this experiment, 100 MeV Au7+ ion irradiation was performed to study the deformation
and defects in uniformly nickel filled MWNTs with high-resolution transmission electron microscopy and
Raman spectroscopy. We propose that high-pressure induced torsion in confined nickel could possibly result in
successive compressions and expansions of the tubes, leading to axial buckling of MWNTs. The tangential
Raman G band systematically upshifts as the ion fluence increases, attributed to the torsional strain. In contrast
to a square root dependence of the buckling wavelength 共␭兲 on the radius 共r兲 and thickness 共t兲 of the tubes
关␭ = 3.5共rt兲1/2兴, as predicted by theoretical models, the exponential fit of the data that assumes ␭ ⬀ e冑共r/t兲 also
produces an excellent fit.
DOI: 10.1103/PhysRevB.76.014108
PACS number共s兲: 62.25.⫹g, 65.80.⫹n, 61.46.Hk
I. INTRODUCTION
The buckling of the single walled carbon nanotubes
共SWNTs兲 and multiwalled carbon nanotubes 共MWNTs兲 has
been a topic of intense research, as is evident from a number
of papers published recently.1–12 Initial interest in buckling
goes back to Euler13 who discovered the elastic instability
and found that a rod, when compressed longitudinally, would
buckle sideway if the strain exceeds a certain critical value.
The sp2 carbon bond in the basal plane of the graphite is the
stiffest in nature. This provides the SWNTs and MWNTs
exceptional hardness and the tubular structure allows the material to be flexible and can undergo large elastic deformation
without breaking. Theoretical models2–12 have been used to
understand the buckling of the SWNTs and MWNTs, most
have applied the beam theory and the continuous cell models
to generate the buckling in the tube walls by clamping the
tube ends. However, the models do not impose the structural
constraints of nested nanotube structure and use the value of
0.34 nm for the thickness of the wall of the SWNTs. The
models predict a square root dependence of the buckling
wavelength 共␭兲 on the radius 共r兲 and thickness 共t兲 of the
tubes 关␭ = 3.5共rt兲1/2兴. The situation is further compounded by
the fact that the experimental data and the actual experiments
producing buckled structures of nanotubes are almost nonexistent. Most of the experiments have depended on the bending of the tubes that really does not satisfy the conditions of
the models that both ends of the tubes be constrained. A
recent study by Ni et al.14 showed axially compressed buckling of SWNTs filled with C60, CH4, or Ne molecules. Wang
et al.15 assumed the effect of critical radial pressure to explain the compressive stress to understand the axial strain.
Recently, we synthesized the nickel filled MWNTs in our
laboratory and reported the excellent crystalline orientation
of the nickel nanorods.16,17 These nanorods are confined inside the MWNTs of length of 0.29– 0.90 ␮m and would be
ideally clamped under the stiff sp2 carbon bonds in the basal
1098-0121/2007/76共1兲/014108共5兲
plane of graphite structure. The irradiation of these exciting
structures with Au7+ ions of 100 MeV would generate highpressure induced stress between the two lattices, as the electronic energy loss of the ions are different for graphene and
nickel lattices and also the losses occur over an extremely
short period 共10−12 s兲. We report on this innovative method
of generating highly stressed buckling patterns in the nickel
filled MWNTs along a length of about 0.90 ␮m. The irradiated tubes with strained walls are studied in detail by highresolution transmission electron microscopy 共HRTEM兲 and
Raman spectroscopy. We have measured the wavelength of
the buckled structure and fitted it with the existing theoretical
models.
II. EXPERIMENT
Nickel-encapsulated MWNTs used in this study were synthesized by microwave plasma chemical vapor deposition
apparatus, the details of which are reported elsewhere.17 The
MWNTs were treated with isopropyl alcohol in an ultrasonic
bath and were transferred by replica technique onto a carbon
coated copper grid for transmission electron microscopy
共TEM兲. The lattice imaging of the MWNTs, as well as of the
nickel filling, along with electron diffraction patterns before
and after irradiation, is recorded using HRTEM in a JEOL
TEM 2010 共UHR model兲 operated at 200 kV. The microgrids were irradiated perpendicularly by Au7+ ion beam with
energies of 100 MeV at room temperature using 15UD pelletron at IUAC, New Delhi with the fluences of 1012, 5
⫻ 1012, and 3 ⫻ 1013 ions/ cm2, respectively. Raman spectra
of the pristine and irradiated tubes are recorded in a confocal
Jobin-Yvon Raman spectrometer with a 514.5 nm, Ar+ laser
共20 mW power兲 and 100⫻ objective lens.
III. RESULTS
Figure 1共a兲 shows the TEM image of the nickelencapsulated nanorods and Figs. 1共b兲 and 1共c兲 are the HR-
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©2007 The American Physical Society
PHYSICAL REVIEW B 76, 014108 共2007兲
MISRA et al.
FIG. 1. 共a兲 The TEM image of the nickel-encapsulated nanorods. 关共b兲 and 共c兲兴 HRTEM images of nickel filling inside the core
of the tubes and the pristine nanotube walls. The 共111兲 oriented
planes of nickel are clearly visible across the tube in image 共b兲
making an angle at 39.6° with the tube axis. The graphite walls with
interplanar separation of 0.322± 0.002 nm evident in image 共c兲 are
of perfect shape with no evidence of planar defects. 关共d兲–共f兲兴 Low
magnification images of the buckled MWNTs after the irradiation
with Au7+ ions of 100 MeV at a fluence of 3 ⫻ 1013 ions/ cm2; the
inset of 共f兲 shows the electron diffraction pattern after the buckling.
The diffraction pattern shows the presence of the diffused rings and
a few diffraction spots, indicating the polycrystalline nature of the
filling and the tube walls. 关共g兲 and 共h兲兴 High-resolution images
showing the curvature of the tube walls near the carbon-nickel
interface.
TEM images showing the lattice fringes of the pristine nickel
and tube walls before the ion irradiation. The mean outer
diameter of the MWNTs, as determined from TEM images in
Fig. 1共a兲, varies in the range 30– 50 nm and that of nickel
nanorods is 13– 17 nm. The length of the filled tubes varies
between 0.29 and 0.90 ␮m and the nanotubes appear straight
before irradiation without any evidence of axial disorder, as
is evident from the lattice images in Figs. 1共b兲 and 1共c兲; the
encapsulated nickel, as well as the tube walls, has a nearly
perfect structure without any crystalline defects within the
resolution of our HRTEM. The lattice spacing of the crystal-
line planes of nickel, estimated to be 0.196± 0.004 nm,
matches closely to the d spacing of 共111兲 Miller planes
共0.203 nm兲. These planes are inclined at an angle of 39.6°
with respect to the tube axis, as already reported in our earlier work.16 The fringes observed on the walls of the
MWNTs correspond to 共002兲 graphitic basal planes having
separation of 0.322± 0.002 nm.
Figures 1共d兲–1共h兲 are the TEM images of the nickelencapsulated tubes after the irradiation with Au7+ ions of
100 MeV at fluence of 3 ⫻ 1013 ions/ cm2. Figures 1共d兲–1共f兲
are low magnification images of the buckled MWNTs while
Figs. 1共g兲 and 1共h兲 show the curvature of the tube walls in
intimate contact with the nickel and that of the outer walls,
respectively. As is evident from Figs. 1共d兲–1共h兲, an axial
compression and expansion of the nanorods, as well as of the
tube walls, have taken place after the irradiation, clearly
showing a wavelike pattern along the length of the tube, the
wavelength of which can be easily measured. Figures 1共g兲
and 1共h兲 depict the progressive curvature produced in the
graphite walls as one moves away from the nickel carbon
interface. The curvature of the graphite walls produced due
to the heavy ion irradiation is lower in the immediate vicinity
of the nickel filling and it increases away from the interface,
with the steepest curvature being produced in the walls at
some intermediate location. It is clear from the figure that
defects on tube walls start propagating from the outer tube
walls with sharp curvature while graphite walls near the interface have large curvature. The lattice spacing of the graphite walls in the immediate vicinity of the nickel filling, as
shown in Fig. 1共g兲, is altered to 0.333± 0.002 nm, as compared to 0.322± 0.002 nm before irradiation. Similarly, the
angle between the nickel 共111兲 planes and the tube axis
changes to 81.6°, as opposed to 39.6° before irradiation, as
shown in Fig. 1共g兲. It is interesting to note that the buckling
of the nickel-encapsulated MWNTs is not observed at fluence lower than 3 ⫻ 1013 ions/ cm2. To further confirm these
results, the samples prepared under the same conditions were
irradiated with Au+ ions of 1.5 MeV and fluence of 5
⫻ 1015 ions/ cm2. No buckling was, however, observed.
Figure 2 shows Raman spectra of the nanotubes irradiated
with Au7+ ions of energy of 100 MeV at three fluences, 1012,
5 ⫻ 1012, and 3 ⫻ 1013 ions/ cm2, respectively. Our pristine
tubes show three major bands in Raman spectra: 共i兲 at
1347 cm−1, D band, which originates from the finite size
effects in sp2 carbons generally associated with the presence
of disordered graphite, 共ii兲 at 1573 cm−1, G band 共E2g symmetry兲, due to the tangential breathing mode in MWNTs; and
共iii兲 at 1609 cm−1, D⬘ band 共A1g symmetry兲, associated with
the maximum in the two-dimensional phonon density of
states of graphene.18 In our samples, the Raman band at
1573 cm−1 downshifts from its original position19 of
1580 cm−1, perhaps due to the coupling of the phonons in the
graphene and nickel lattices. Although there is no buckling
observed in tubes irradiated with the fluences of 1012 and 5
⫻ 1012 ions/ cm2, the Raman G band associated with the E2g
mode shifts to 1578 cm−1 关Fig. 2共b兲兴 in the tubes irradiated
with 5 ⫻ 1012 ions/ cm2. We do not observe any significant
change in Raman spectra for the tubes irradiated with
1012 ions/ cm2. The position of the G band shifts to
1586 cm−1 in the tubes irradiated with the fluence of 3
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PHYSICAL REVIEW B 76, 014108 共2007兲
AXIAL BUCKLING AND COMPRESSIVE BEHAVIOR OF…
FIG. 2. Raman spectra of the
nanotubes irradiated with Au7+
ions of energy of 100 MeV at
three fluences, 1012, 5 ⫻ 1012, and
3 ⫻ 1013 ions/ cm2, respectively.
The inset of the figure shows the
shift in the position of the G band
as a function of the ion fluence.
⫻ 1013 ions/ cm2, as shown in Fig. 2共c兲. A small shoulder at
the left of the D band can be also seen in Fig. 2共c兲. A probable reason for the origin of this shoulder could be the phonon confinement in disordered graphite. Another interesting
observation is the significant broadening of the G band with
the irradiation. The details of the Raman analysis are shown
in Table I.
IV. DISCUSSION
7+
High energy Au ions used in the present case dominantly lose their energy in any lattice via the electronic energy loss 共dE / dx兲e, the value of which for the case of nickel
lattice is 32.5 keV/ nm. In contrast, the theoretical simulations have shown that the threshold energy for the creation of
defects in the nickel lattice is 艌67 keV/ nm.20 In a recent
publication, we have proposed that the value of 共dE / dx兲e in
nickel nanorods can increase significantly due to the confinement of the nanorods.21 As the energy value crosses the
threshold value, according to the thermal spike model, a cylindrical region of nanometer size of highly excited electrons
is created in nickel nanorods which transfers energy to the
lattice in picoseconds. This may lead to the melting of the
nickel nanorods confined inside the MWNTs. As the molten
nickel solidifies, the difference in thermal expansion coefficients 共␣兲 of nickel and carbon generate the required stress to
produce buckling. It may be noted that there is a huge difference in the values of ␣; the ratio of ␣Ni / ␣C as reported in
the literature is 16, where ␣C is the radial thermal expansion
coefficient of the nanotubes. Our preliminary calculations
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PHYSICAL REVIEW B 76, 014108 共2007兲
MISRA et al.
TABLE I. The peak position, FWHM, and relative intensities of
the D and D⬘ bands with respect to the G band in the MWNTs after
irradiation with Au7+ ions of energy of 100 MeV at three fluences,
1012, 5 ⫻ 1012, and 3 ⫻ 1013 ions/ cm2, respectively.
Peak
position
共cm−1兲
Peak width
共cm−1兲
1 ⫻ 1012
1347.3
1573.0
1609.0
5 ⫻ 1012
Fluence
共ions/ cm2兲
3 ⫻ 1013
I共D兲 / I共G兲
I共D⬘兲 / I共G兲
64.4
39.7
22.8
0.74
0.19
1275.3
1345.1
1578.1
1609.9
45.5
66.2
50.2
19.9
1.58
0.31
1161.9
1344.9
1586.3
116.5
148.4
95.1
1.13
FIG. 3. 共Color online兲 The plot of ␭ vs 冑r for the various tubes
of different diameters used in the present experiments.
1
show that the stress generated at the interface of graphite and
nickel is of the order 100 GPa and compares favorably to the
recently reported value of 40 GPa by Sun et al.22 Thus, the
high pressure onto the nickel core resulted from different
thermal expansion coefficients between the tube walls and
the core and/or interface melting. The resultant shear stress at
the interface causes the twisting of the nanorod inside the
carbon nanotube and generates torsional buckling along the
length of the tube.23
A possible outcome of the shear stress generated during
the melting and subsequent cooling can be the formation of
the Stone-Wales-type defects23 on the tube walls which is
accompanied by elongation of the tube structure along the
axis connecting the pentagons and shrinking along the perpendicular direction and results in multiple buckling along
the axial direction. Earlier experiments by Ajayan et al.24 on
single walled nanotubes had shown that after electron irradiation, the tube develops several necks along the body due
to the generation of such defects. The large blueshift and
FWHM noted in the Raman G band in the samples irradiated
with the fluence of 3 ⫻ 1013 ions/ cm2 are strong evidence for
the defects generated due to the irradiation. Wu et al.23 have
shown that the torsional strain may lead to a significant blueshift in the Raman G band at 1573 cm−1 in single wall carbon nanotubes.
The values of ␭ and r in our case can be easily calculated
and we can fit the equation ␭ = 3.5共rt兲1/2; however, in our
case, t = n ⫻ 0.34 nm. Since the number of walls is particularly large in our experiments, the value of 冑n will be nearly
constant for large values of n. Figure 3 shows the plots of ␭
vs 冑r for the various tubes of various diameters used in the
present experiments. We have fitted the data by assuming a
linear behavior of ␭ vs 冑r and, contrary to the theoretical
calculations as done by Bower et al.25 and Pantano et al.,26
the linear fit does not appear to be very satisfactory. On the
other hand, the exponential fit of the data that assumes ␭
⬀ e冑共r/t兲 produces an excellent fit, as shown in Fig. 3. We
should, however, point out that the exponential fit does not
really follow from any physical argument, and thus there
must be a simpler explanation for the linear fit. An alternate
possibility could be that ␭ ⬀ r and the t could be used as a
parameter dependent upon r, leading to a square root law, as
described above. This interesting result would then indicate
that the thickness of the walls of the tubes should not be
taken as 0.34 nm, which is definitely justified for the multiwalled nanotubes. The discussion signifies that the understanding of the elastic properties of the nanotubes on the
basis of continuum shell theory may be incomplete and one
has to include the other constraints of the structure such as
nested lattice and the atomicity of the tubes.
As mentioned earlier, the buckling is observed only in the
samples irradiated with 100 MeV Au7+ ions and with the
fluence of 3 ⫻ 1013 ions/ cm2, although Raman results show
the presence of defects even in the samples irradiated with
the fluence of 5 ⫻ 1012 ions/ cm2. The Raman G band in the
samples irradiated with 5 ⫻ 1012 ions/ cm2 shifts by 5.1 cm−1
and FWHM is 50.2 cm−1. One possible explanation could be
that at lower fluence, i.e., at 5 ⫻ 1012 ions/ cm2, the critical
value of the strain required to buckle the tubes has still not
been attained. The critical imposed strain of nickel nanorods
can be calculated using a formula approximated to a simple
rod, ␧c = 1 / 2共␲d / L兲2, where d and L are the diameter and
length, respectively, of the nickel nanorod. For the nickel
nanorods in our case having diameter d = 13 nm and length
L ⬃ 450 nm, the value of ␧c is calculated to be 0.004, while
for MWNTs having outer diameter of 40 nm, it is 0.039, an
order of magnitude higher than that for the nanotubes. A
lower critical value of strain for nickel nanorods indicate that
the onset of the described structural changes takes place in
nickel first followed by graphite walls. The value of critical
strain for MWNTs calculated in our case is comparatively
lower than the simulated values obtained for SWNTs for L
= 6 nm and d = 1 nm by Yakobson et al.7 which clearly signifies a low strain structure for MWNTs.
014108-4
V. CONCLUSION
In conclusion, an axial buckling behavior in nickel filled
PHYSICAL REVIEW B 76, 014108 共2007兲
AXIAL BUCKLING AND COMPRESSIVE BEHAVIOR OF…
thick walled MWNTs has been observed after 100 MeV
Au7+ ion irradiation. We have explained the results by irradiation induced melting of the confined nickel nanorods. The
torsional stress generated at the time of the melting may
result in the buckling behavior of the tubes. We find that the
buckling wavelength can be fitted with the exponential function ␭ ⬀ e冑共r/t兲 instead of a square root dependence of the
*Corresponding author. [email protected]
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