Chemistry Reference
In-Depth Information
exp
r
ij
r
0
αβ
1
E
i
=
A
−
p
−
(6.5)
αβ
αβ
j
,
r
αβ
<
r
c
and
E
i
is the band energy term obtained by the second-moment approximation of
the electron density of states, expressed as
exp
r
ij
r
0
αβ
1
E
i
2
αβ
=−
r
c
ξ
−
2
q
αβ
−
(6.6)
j
,
r
ij
<
indicate the chemical nature of atoms,
r
αα
is the first-
neighbor atomic distance of the pure substance,
r
0
The indexes
α
and
β
αβ
=
r
αα
+
r
ββ
/
,
r
ij
is the distance between atoms
i
and
j
,
r
c
is the cutoff distance for the interaction.
The quantity
2if
α
=
β
is an effective hopping integral and
q
describes its dependence on
the relative interatomic distance. In the most general case, the band energy term in
(
6.6
) is a functional expression representing a sum over the local electronic charge
density induced at site
i
from atoms at site
j
. The hopping integral
ξ
ξ
originates
from quantum mechanical TB models and its value directly relates to the overlap-
ping of electron tight-binding wave functions of neighboring atoms [
11
,
12
]. This
is the reason for
to be strongly influenced by the local atomic environment and
therefore to be coverage dependent. This refinement is essential for simulation of
epitaxial interfaces, since the local atomic arrangement is entirely different at low
concentration of adatoms and at complete monolayer [
13
,
15
]. It has been shown
that accounting for the coverage dependence of
ξ
, the atomistic simulations gen-
erate system behavior in complete accordance with the real physical experiment:
(i) formation of lattice gas; (ii) surface intermixing; (iii) formation of c(2
ξ
×
2),
p(4
1) 2D superstructures; (iv) critical behavior and Ising-type order-
disorder transition of the c(2
×
1), and p(5
×
×
2) phase, etc. [
4
,
10
]. The values of the hopping inte-
gral
and all related parameters
A
,
p
, and
q
in the interacting potential, (
6.5
) and
(
6.6
), are taken from [
11
]. These values are consistent with the overall thermody-
namic properties of the real system since they reproduce basic physical characteris-
tics as melting point, evaporation energy, elastic constants, etc.
The physical model is designed to allow description of wide-ranging surface
morphology including atomic terraces, steps, kinks, large flat domains, vacancies.
The system, constructed as a 3D continuum space, is limited to sizes
L
x
ξ
=
38,
5 lattice units in the corresponding space directions. The
initial configuration is Cu(111) stepped crystal surface with random adsorption of
Pb atoms. The coverage is kept constant throughout the simulation experiment. The
large atomic terraces allow random migration of single atoms and compact clusters
on top surface layer as well as diffusion into the substrate by way of direct incor-
poration. In contrast to smooth domains, the presence of steps tolerates diffusion
through the periphery of atomic terraces. Hence, all possible mass transfer processes
are feasible in the model. The interface energy, pair distribution function (PDF)
analysis, and series successive snapshots of system configurations reveal the time
L
y
=
22, and
L
z
=
