Simulation of Surface Morphology and Defect Structure in Copper Nanoparticles
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Simulation of Surface Morphology and Defect Structure in Copper Nanoparticles Yoshiaki Kogure and Masao Doyama Teikyo University of Science & Technology Uenohara, Yamanashi 409-0193, Japan ABSTRACT Molecular dynamics simulation for the morphology and the defect structure in nanoparticles has been performed. The nanoparticles are consisted of 1300 – 5000 atoms and the EAM potential developed by the present authors is adopted to calculate the interactions between atoms. The atom consisting the surfaces or defects are selected thorough the potential energy of individual atoms and structure is investigated by calculating the local crystalline order. A relation between the cooling rate and the particle morphology is also investigated. INTRODUCTION The nanoparticles or fine particles are known to have peculiar properties due to confined volume and large surface effects. The quantum mechanical energy level intervals in electronic and phonon states are larger than bulk materials due to strongly confined spaces, then the thermal, the mechanical, the electric, and the magnetic properties are different from the bulk materials. These characteristic properties of nanoparticles have large potentiality for the industrial materials. On the other hand, the confined system is suitable to the molecular dynamics simulation studies, because the number of atoms are manageable by a computer and the results can be compared with experiment. Structure and atomistic processes during the nanoparticle formation is simulated in this paper. . METHOD OF SIMULATION The embedded atom method (EAM) potential can express the many body interaction of atoms in metals and the potential is suitable for the simulation of the surface and the defects [1,2]. The EAM potential functions developed by the present authors are used in the present study [3]. The potential function was characterized on the point of anharmonicity and defect energy [4]. The potential has been adopted in the molecular dynamics simulations [5].
B8.4.1
Figure 1. Formation of nanoparticles. Shape of outer surface and the radial distribution function at 0, 20000 and 39000 MD step are shown.
. The potential energy of i-th atom is expressed as E i = F ( ρ ) + ∑ φ (rij ) ,
(1)
j
where, F ( ρ ) is the embedding energy, ρ the electron density, and rij the distance between
i-th and j-th atoms and the function F ( ρ ) is expressed as
F ( ρ ) = Dρ log ρ , ρ = ∑ f (rij )
(2)
j
Functions f (rij ) and φ (rij ) are
f (rij ) = A(rc − r ) exp(− crij ) ,
(3)
φ (rij ) = B(rc − r ) exp(− c 2 rij ) .
(4)
2
2
The potential functions contains five parameters ( A, B, C1 , C 2 , D ) and these are determined by fitting the potential functions to the experimental values of the cohesive energy, the elastic constants and the vacancy formation energy in copper crystal As an initial condition 1000 – 5000 atoms are arranged in fcc structure. Then the particle velocity of individual atom is gradually increased until the corresponding temperature becomes 1800 K, where the
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