Modified embedded atom method study of the mechanical properties of carbon nanotube reinforced nickel composites Page: 4
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PHYSICAL REVIEW B 81, 104103 (2010)
TABLE II. Young's modulus (Ell) (in GPa) for single-walled (SWCNTs) and a multiwalled (MWCNT) carbon nanotubes obtained from
our MEAM Ni-C potential are tabulated and compared with the literature values.
This work Previous calculations Experiments
820 (Xiao et al., MD)a
900 (Agrawal et al., MD)b 270-900 (Yu et al.)c
5500 (Yakobson, MD)d 790 (Li et al.)e
552 [SWCNT(5,0)] 974 (Lu, MD)' 900 (Demcyzek et al.)g
832 [SWCNT(10,0)] 1325 (Cheng and Gao, MD)h 816+ 410 (Salvetat et al.)i
892 [SWCNT(15,0)] 1238 (Jin and Yuan, Force-Field)J 1200 (Tombler et al.)k
740 (MWCNT) 1220 (Hernaindez et al., TB-MD)' 1250 (Krishnan et al.)m
4700 (Tu, LDA)n
764 (Zhou et al., LCAO-MO cluster)
965, 972 (Ogata and Shibutani, TB, DFT)P
1470 (Pullen, GGA)q
1060 (Li and Chou, MM)r
899(5,0), 916(10,0), 923(15,0) (Meo and
E of 832 GPa for SWCNT(10,0) agrees with the value cal-
culated by Xiao et al. (820 GPa), Agrawal et al.27 (900 GPa),
and Lu (975 GPa).24 Our results from the same CNT is also
in reasonable agreement with the values of 965 and 972 GPa
calculated using tight-binding and density-functional theory,
respectively, by Ogata and Shibutani.40 On the contrary,
Hernandez and coworkers36 reported a much greater value of
1220 GPa for this nanotube using tight-binding MD. These
large differences may be attributed to differences in the CNT
volume estimation due to variations in effective CNT wall
thickness. In spite of extensive studies, the variations in wall
thickness of CNTs remain an unresolved question.46
B. Ni/CNT composites:
1. Single-crystal elastic constants
A necessary condition for mechanical stability of a struc-
ture is that its strain energy must be positive against arbitrary
but small homogeneous elastic deformations. For an ortho-
rhombic crystal, this imposes the following constraints:47
Cl1+C22>2C12, C22+C33>2C23, C11+C33>2C31, Cii>0 (i
= 1-6), and c11+c22+c33+2c12+2c23+2c31 >0. These crite-
ria simplify to c11>0, c44>0 c11+2c12>0, and c11-c12
> 0 for cubic crystals such as fcc Ni. Hence, we examined
the mechanical stability of the Ni/CNT composites using ap-
propriate single-crystal elastic constants for composites with
both low and high CNT volume fractions. The calculated
values for elastic constants cij are summarized in Table III.
For single-crystal Ni, the MEAM calculated values for
cll, cl2, and c44 agree well with experiments.48,49 The shear
elastic constants c11 - c12 and c11 +2c12 determine stability.
Physically, c44 plays a subtle role and represents the resis-
tance of the system to a shear deformation such as in the
(100) plane in the  direction. Similarly, (c11-c12)/2
represents the resistance to shear deformation across, for ex-
ample, a (110) plane in the  direction. Similar observa-
tions hold for an orthorhombic crystal. From the Table III
data, it is observed that for Ni/CNT composites, the cii (i
= 1-6), c11+c22-2c12, C22+C33-2c23, C11+C33-2c13, and
c11+C22+C33+2c12+2c23+2c13 are all positive, and thus it
can be reasonably concluded that Ni/CNTs composites are
mechanically stable. This is an encouraging result for the
fabrication of nanocomposite materials by embedding the
CNTs in metal matrices.
For Ni/CNTs, c11 show moderate increase in composites
with low CNT volume fractions and significantly large in-
crease in composites with high CNT volume fractions com-
pared to that of pure Ni. These increases depend on the type
and diameter size of the embedded nanotubes. For example,
composites Ni/SWCNT(5,0), Ni/SWCNT(10,0), and Ni/
SWCNT(15,0) show an increase of 5, 10, and 12 GPa, re-
spectively, for low CNT volume fraction and 19, 39, and 42
GPa, respectively, for high CNT volume fraction. Ni/
MWCNT shows the largest increase in c1 than for any of the
Ni/SWCNTs. In this case, c11 shows an increase of 30 GPa
and 109 GPa, respectively, for low and high CNT volume
fractions compared to that of Ni. In the transverse directions,
c22 or c33 show gradual decrease for Ni/SWCNTs compared
to pure Ni. However, in these cases, composites with higher
CNT volume fractions show a larger decrease compared to
composites with low CNT volume fractions. Interestingly,
the Ni/MWCNT nanocomposite shows very small or no
changes for c22 or c33.
UDDIN et al.
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Uddin, Jamal; Baskes, Michael I.; Srivilliputhur, Srinivasan; Cundari, Thomas R., 1964- & Wilson, Angela K. Modified embedded atom method study of the mechanical properties of carbon nanotube reinforced nickel composites, article, March 11, 2010; [College Park, Maryland]. (digital.library.unt.edu/ark:/67531/metadc107769/m1/4/: accessed June 26, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT College of Arts and Sciences.