PHYSICAL REVIEW B 81, 104103 (2010)
TABLE I. Parameters for the MEAM potentials of Ni, C, and Ni-C. The parameters are the cohesive
energy Ec (eV), the equilibrium nearest-neighbor distance re (A), the exponential decay factor for the uni-
versal energy function a, the scaling factor for the embedding energy A, the four exponential decay factors
for the atomic densities /3(i), the four weighting factors for the atomic densities t(i), and the density scaling
factor po. Angular screening parameters for the MEAM potentials for binary systems.
MEAM potentials Angular screening parameters
Ni C Ni-C Cmax Cmin
Ec 4.45 7.37 4.82 Ni-Ni-Ni 2.8 0.8
re 2.49 1.54 2.01 Ni-C-Ni 2.8 2.0
a 4.99 4.38 4.82 C-Ni-C 2.8 2.0
A 1.10 1.49 Ni-Ni-C 2.8 2.0
p3(0) 2.45 4.26 Ni-C-C 2.8 2.0
/(1) 1.50 5.00 C-C-C 2.8 2.0
/3(2) 6.00 3.20
/(3) 1.50 3.98
t(o) 1.00 1.00
t() 5.79 7.50
t(2) 1.60 1.04
t(3) 3.70 -1.01
pO 1.00 1.00
II. COMPUTATIONAL DETAILS
A. Theoretical formalism
In MEAM, the total energy of a system is
following form:
given in the
E = 1 Fi(Pi) +- - Sq 7(Ri),
L 2j( i)
where Fi is the embedding function for an atom i embedded
in a background electron density pi, Sij is the screening func-
tion, and Pij(Rij) is the pair interaction between atoms i and
j separated by a distance Rii. For the calculations of energy,
the functional forms of Fi and cpi should be given. The back-
ground electron density at each atomic site is computed by
combining several partial electron-density terms for various
angular contributions with weight factors t(h)(h=0-3) (direc-
tionality of bonding). Each partial electron density is a func-
tion of atomic configuration and atomic electron density. The
atomic electron densities pa(h)(h= 0-3) are given as
pa(h)(R) -= Po exp[- P(h)(R/re - 1)],
where po, the atomic electron-density scaling factor, and /(h),
the decay lengths, are adjustable parameters, and re is the
nearest-neighbor (NN) distance in the equilibrium reference
structure. A specific form is given to the embedding function
Fi but not to the pair interaction Pij. Instead, a reference
structure where individual atoms occupy perfect-crystal atom
sites is defined and the potential energy per atom of the ref-
erence structure is estimated from the zero-temperature uni-
versal equation of state by Rose et al.18 The value of the pair
interaction is evaluated from the known values of the poten-
tial energy per atom and the embedding energy, which is a
function of the nearest-neighbor distance.
In the original MEAM,17 only the first nearest-neighbor
interactions were considered. The second (2NN) and more
distant neighbor interactions were neglected by using strong
many-body screening function. The second-nearest-neighbor
interactions have been included in the modified formalism by
adjusting screening parameters Cmin to decrease the many-
body screening effect. In addition, a radial cutoff function is
also applied to reduce calculation time. The MEAM for an
alloy system is based on the MEAM potentials for the com-
ponent elements. The 2NN MEAM formalism19 gives 14 in-
dependent model parameters for pure elements: four
(Ec, re, B, d) for the universal equation of state, seven
(/(0), "(1), ,(2), /(3), t(1), t(2), t(3)) for the electron density, one
(A) for the embedding function, and two (Cmin, Cmax) for the
many-body screening. The details of the MEAM formalism
have been published in the literature.17,20,2'
B. Simulation methods
The MEAM potential parameters that describe the inter-
atomic interactions for Ni, C, and Ni-C composites are listed
in the Table I. It treats nickel, carbon, and the Ni-C interac-
tions, and allows the formation of chemical bonds with ap-
propriate atomic hybridization. Similar MEAM potential pa-
rameters have been shown to model the catalytic growth of
CNTs on nickel nanocatalysts well.22 We performed molecu-
lar static calculations at T= 0 K. Periodic boundary condi-
tions were applied along all three directions of the supercells.
The Ni matrices and Ni/CNT composites were relaxed to
minimize their energies.
The Ni/CNT composites were simulated using three
single-walled nanotubes (SWCNTs) with varying diameters
and a multiwalled (MWCNT) nanotube. We chose CNTs
with zigzag structures for this study. SWCNTs with (5,0),
104103-2
UDDIN et al.
