Computer Simulation of Surface Diffusion of Copper on Copper (111) and (100) Surfaces
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(2) (3)
F(p)= a(,O/pe)n+b(p/pe)
(4)
(5) Pi= X f(rij) Here Etotal is the total internal energy. Ei is the internal energy associated with atom i. p is the electron density at atom i due to all other atoms. F( p i) is the embedding energy of atom i into electron density p i - P e is the electron density at an atom at equilibrium. (D (r ij) is the two body central potential between atoms i and j separated by rij" f (r i) is the contribution to the electron density at atom i due to atom j at the distance r ij from atom i. f (r) = f old (t) - f c (r)
(6)
643 Mat. Res. Soc. Symp. Proc. Vol. 355 01 99 5 Materials Research Society
surface
Table 1. Binding energy of atom clusters to copper (11)
Energy Number of Energy Number Config- Total per bond per binding nearest of atoms ration in cluster energy neighbor bond in cluster, (eV) (eV) atoms (eV) E2 3N+m BN/(3N+m) BN N 0.87 3 2.60 * 1 0.40 0.80 3x2+1= 7 5.62 *• 2 0.38 0.76 3x3+3=12 8.97 :, 3 0.37 0.72 3x4+5=17 12.28 * 4 " 0.38 0.75 3x4+4=16 11.94 • 0.36 0.71 3x5+7=22 15.57 5 *.. 0.35 0.70 3x6+9=27 o °*• 18.82 6 3x6+8=26 0.71 0.35 "" 18.47 0.35 0.70 "*o. 18.85 3x6+9=27 0.34 0.68 3x7+12=33 22.37 7 *', 0.32 0.68 3x7+ 11=32 ° . 21.76 fold = feexp{ -
3
(7)
(r/re)- 1)
e (r) = f old( r c) + g(r)f'ol(r c)/g(r c)
(8)
D(r) = CDold(r) - Dc(r) Dold(r) = (Pc(r) =( g(r)
=
CDeexp{-
(9) (10)
y(r/re -1)}
old (rc) + g(r) q)' old (r c) / g'(r c) 1-exp
{ 0'(r/re)-rc/r e)
1
(11)
(12)
For copper, Oh and Johnson [I] give ,3=5, y =8.5,
c5=20, rc =1.9 re, 0 e=0. 36 952 eV, a
= -4.0956, b = -1.6979, n = 0.44217, and P e= 12.793. BINDING ENERGIES OF ATOM CLUSTERS TO COPPER (11)
PLANE
The binding energies of atom clusters to the copper (111) surface have been calculated . The crystal used has a (I 11) surface containing 2310 atoms, with 11 atoms in direction, 14 atoms in the direction and 15 atoms in the direction. 420 atoms near the center of the (111) plane were relaxed. Let the binding energy of an N adatom clusters be BN. Each adatom has three nearest neighbor bonds to the (111) plane, 3E1 . Let the binding energy per bond in the adatom cluster be E2 and the number of bonds m. BN can be represented as BN = 3NE 1 + mE 2 , where 3E 1 is the binding energy of a single adatom to the (111) plane and m is the number of bonds within the cluster and E2 is the binding energy of the bond within the cluster. It was found that El = 0.87 eV and E2 = 0.4 - 0.32 eV. The results are shown in Table 1. The binding energy (2.60 eV) of the first atom to the (11l) plane is lower than that of the atom stick to the next nearest neighbor to the atom adsorbed (see Table 1). The binding energy (2.9 eV) of
644
Fig. 1. The configurations of the tri-adatoms
(a) 600 tri-adatoms (b) 1200 tri-adatoms (c) 1800 tri-adatoms the last atom to complete a hexagon with one atom at the center (7 atom cluster) is higher than other cases. The difference between the binding energy of an atom at a normal site (form fcc structure, N-site) and that of an atom at a hexagonal site (H-site) which forms a stacking
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