# Modified embedded atom method study of the mechanical properties of carbon nanotube reinforced nickel composites Page: 2

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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 1.00II. 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.

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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/m1/2/: accessed March 23, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT College of Arts and Sciences.