Ultimate strength of carbon nanotubes: A theoretical study Page: 4
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ZHAO, NARDELLI, AND BERNHOLC
6
4
4) -2
W -4
-6
6
4
2
0
4) -2
C
w -4
-6a)
rte
C
a,
wStrain (%)
FIG. 3. Comparison between ab initio and tight-binding results
for a (5,5) nanotube and a graphene sheet. (a), (c) Formation ener-
gies; (b), (d) activation energies. The ab initio results are connected
by a solid line, while a dashed line connects the tight-binding
results.
those from ab initio calculations. However, the differences
between tight-binding and ab initio results increase with
strain. For example, the formation energies of the Stone-
Wales defect in the (5,5) tube differ by 0.1 eV at 0% strain
and by 0.7 eV at 15% strain. This increase can be attributed
to the fact that the tight-binding parameters were fitted to
data for unstrained carbon systems. Therefore, their accuracy
and reliability decrease with increasing strain. Moreover, the
agreement between the tight-binding and ab initio results is
much better for graphene than for the (5,5) tube. This is6
S4
4) -2
C
w -4
-6
6
4
V-4
-6-2
-4
10
a4
0)
w4Strain (%)
10
15
FIG. 5. Curvature effects on the formation and activation ener-
gies of the (5-7-7-5) defect in strained armchair nanotubes and
graphene under transverse strain. Circles correspond to a (5,5) tube,
squares to a (10,10) tube, and diamonds to a graphene sheet. See
text.
because graphite data were used in fitting the original tight-
binding parameters, while carbon nanotube data were not. In
general, however, the tight-binding method is a good alter-
native to the computationally costly ab initio method. Turn-
ing to the classical potential results, while they are able to
give a qualitative and semiquantitative description of the me-
chanical behavior of nanotubes, they tend to underestimate
the ultimate limit of the elastic response. This is shown ina)
)
LM
d)
a
wStrain (%)
FIG. 4. Comparison between ab initio and classical potential
results for a (5,5) nanotube and a graphene sheet. (a), (c) Formation
energies; (b), (d) activation energies. The ab initio results are con-
nected by a solid line, while a dashed line connects the classical
potential results.-2
10C)
0
wStrain (%)
10
15
FIG. 6. Curvature effects on the formation and activation ener-
gies of the (5-7-7-5) defect in strained zigzag nanotubes and
graphene under longitudinal strain. Circles correspond to a (9,0)
tube, squares to a (17,0) tube, and diamonds to a graphene sheet.144105-4
Formation Energy
S5 10 15
' -. Activation Energy
b) 'S-..i.. Formation Energy
a)
0 5 10 15
-..--- Activation Energy
b)
' IPHYSICAL REVIEW B 65 144105
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Zhao, Qingzhong; Buongiorno Nardelli, Marco & Bernholc, Jerry. Ultimate strength of carbon nanotubes: A theoretical study, article, March 27, 2002; [College Park, Maryland]. (https://digital.library.unt.edu/ark:/67531/metadc234919/m1/4/: accessed April 23, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT College of Arts and Sciences.