Modified embedded atom method study of the mechanical properties of carbon nanotube reinforced nickel composites Page: 3
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MODIFIED EMBEDDED ATOM METHOD STUDY OF THE...
SWCNT(5,0) SWCNT(10,0) SWCNT(15,0) MWCNT
(a) (b) (c) (d)
FIG. 1. (Color online) Space filling unit cells of (n,0) CNTs.
SWCNT and MWCNT refer to single-walled and multiwalled CNT.
(a) SWCNT(5,0), (b) SWCNT(10,0), and (c) SWCNT(15,0).
MWCNT in (d) is built by assembling SWCNT(5,0),
SWCNT(10,0), and SWCNT(15,0) nanotubes coaxially. The ap-
proximate tubular height for the unit cell is 4.26 A for all
(10,0), and (15,0) chiral indices and tubular diameters of
3.97 A, 7.86 A, and 11.77 A, respectively, were studied.
These CNTs were embedded in a supercell containing 37 044
nickel atoms. The atomic structure and the crystallographic
orientation of the SWCNTs and supercells are shown in Figs.
1 and 2. This supercell has 21 X 21 X 21 unit cells and is
approximately 7.4 nm X 7.4 nm X 7.4 nm in three perpen-
As the CNT volume fraction is an important variable in
determining the composite mechanical properties, we used
two different concentrations of each CNTs for Ni/CNT com-
posites. The three supercells had a CNT volume fraction of
0.83%, 1.85%, and 3.37% when single CNTs were used.
When four CNTs are embedded in each supercell, the CNT
 1010 '
FIG. 2. (Color online) Atomistic structures and the crystallo-
graphic orientations of the supercells. (a) Fully minimized pure
nickel (face-centered-cubic lattice), (b) nickel matrix with an em-
bedded MWCNT, (c) nickel matrix with four embedded MWCNT,
(d) full extent of a MWCNT embedded in the nickel supercell.
Periodic boundary conditions are applied for pure nickel and Ni/
CNT matrix along the three dimensions.
PHYSICAL REVIEW B 81, 104103 (2010)
volume fractions were increased to 3.33%, 7.40%, and
13.46% for (5,0), (10,0), and (15,0) SWCNTs, respectively.
Since the Ni matrix does not penetrate the hollow inside of
CNT, we treated the CNTs as solid beams for volume frac-
The MWCNTs were built by inserting SWCNTs into each
other coaxially while maintaining their individual periodic-
ity. For composites made with MWCNTs, the CNT volume
fractions were similar to the volume fractions of
SWCNT(15,0). For example, Fig. 2(d) shows MWCNT that
fits the periodicity of fcc Ni matrix. The wall thickness of
SWCNTs were assumed to be 0.32 nm based on electron-
density distribution calculations23 and similar methods.24,25
To simulate the Ni/CNTs nanocomposites with low CNT
volume fractions, four different single-crystal Ni supercells
containing a hollow cylindrical void at the center were built.
For studying nanocomposites with high CNT volume frac-
tions, four different single-crystal Ni supercells were built
with four cylindrical voids approximately equidistant to each
other. The cylindrical void runs from one face to the opposite
face of the supercell with the cylinder axis aligned parallel to
the supercell  direction (a axis). The radii of these voids
were chosen to fit SWCNT(5,0), SWCNT(10,0),
SWCNT(15,0), and the MWCNT, leaving an appropriate
amount of space for Ni-C interatomic bonding. The nano-
composites were formed by embedding the CNTs into the
voided Ni supercells. The resulting composites contain a ho-
mogeneous distribution of aligned CNTs. Two simulation
cells with embedded CNTs are shown in Figs. 2(b) and 2(c).
Mechanical properties and stress-strain relationships were
determined from the relaxed configurations. Elastic constants
for Ni and Ni/CNTs were calculated from strain-energy-
applied strain relationships by fitting the strain energy per
volume to a parabola. Strains of 0.1% deformation around
the fully minimized structures were chosen to maintain de-
formations within the linear elastic regime. For each defor-
mation step (0.0002 step size), we minimized system energy
by relaxing positions of all atoms. Nine-independent elastic
constants (c11, c22, C33, C12, C23, C31, C44, C55, and C66) and
three independent constants (c11, c12, and c44) of Ni/CNTs
and pure fcc Ni were determined in this study. The direction-
dependent Young's modulus (E),26 which measures the stiff-
ness of a material, was calculated from the slope of the
strain-stress curves for pristine CNTs. Young's modulus for
CNTs with only longitudinal response were calculated with
0.0002 increments in the applied strain. For Ni matrix and
Ni/CNT systems, E was calculated from the appropriate
single-crystal elastic constants.
III. RESULTS AND DISCUSSION
A. Pristine CNTs
Table II shows that the Young's moduli of individual
CNTs obtained in our work agree well with numerous pub-
lished experimental28'30'3133 and theoretical values.22,24,2743
Most of the experimental measurements of E were carried
out for MWCNTs. Also, Young's moduli of SWCNTs show a
large variation from 0.78 to 3.6 TPa and that only a few
experimental results are available.33,35,37,44,45 Our calculated
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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/m1/3/: accessed July 21, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT College of Arts and Sciences.