Environmental Engineering Reference
In-Depth Information
radius
r
0
r
0
r
W
3
r
n
3
m
a
D
π
4
n
D
,
(2.16)
where
m
a
is the mass of an individual cluster atom and
r
W
is the Wigner-Seitz
radius [24, 25], which is given by
3
m
a
4
1/3
r
W
D
.
(2.17)
π
The Wigner-Seitz radius is the fundamental cluster parameter, and Table 2.2 con-
tains its values for some elements [26-28].
If we assume the size of the region where there is strong interaction between the
colliding atom and cluster to be small in comparison with the cluster size, we can
use the hard-sphere model for atom-cluster collision with the radius of the hard
sphere equal to the cluster radius
r
0
. If an incident atom is reflected elastically from
the cluster surface, the diffusion cross section of atom-cluster collision is
σ
D
π
r
0
. (2.18)
We have same expression for the atom-cluster diffusion cross section if an atom
is captured by the cluster surface and then leaves this surface isotropically. Corre-
spondingly, the rate constant for atom-cluster collision is
r
8
T
m
σ
D
k
0
n
2/3
,
r
2
W
,
k
D
v
T
k
0
D
(2.19)
Ta b l e 2 . 2
Parameters of some metals and semiconductors:
is the liquid density at the melting
point or at room temperature, and
r
W
is the Wigner-Seitz radius.
,g/cm
3
,g/cm
3
,g/cm
3
Element
r
W
, Å
Element
r
W
, Å
Element
r
W
,Å
Li
0.512
1.71
Zn
6.57
1.58
La
5.94
2.10
Be
1.69
1.28
Ga
6.08
1.66
Hf
12
1.81
Na
0.927
2.14
Rb
1.46
2.85
Ta
15
1.68
Mg
1.584
1.82
Sr
6.98
1.71
W
17.6
1.61
Al
2.375
1.65
Zr
5.8
1.84
Re
18.9
1.58
K
0.828
2.65
Mo
9.33
1.60
Os
20
1.56
Ca
1.378
2.26
Rh
10.7
1.56
Ir
19
1.59
Sc
2.80
1.85
Pd
10.4
1.60
Pt
19.8
1.57
Ti
4.11
1.66
Ag
9.32
1.66
Au
17.3
1.65
V
5.5
1.54
Cd
8.00
1.77
Hg
13.6
1.80
Cr
6.3
1.48
In
7.02
1.86
Tl
11.2
1.93
Fe
6.98
1.47
Sn
6.99
1.89
Pb
10.7
1.97
Co
7.75
1.44
Sb
6.53
1.95
Bi
10.0
2.02
Ni
7.81
1.44
Cs
1.843
3.06
U
17.3
1.77
Cu
8.02
1.47
Ba
3.34
2.54
Pu
16.7
1.70
