Environmental Engineering Reference
In-Depth Information
where
M
and
A
are a metal atom and an atom of the buffer gas, respectively, and
n
is
the number of cluster atoms. Assuming each contact of a metal atom with a cluster
leads to their sticking together, we have according to formula (2.18)
r
0
for the
cross section of this process, where
r
0
is the cluster radius within the framework of
the liquid drop model. Correspondingly, the rate constant for atom attachment to a
cluster of
n
atoms is
σ
D
π
s
8
T
π
s
8
T
m
a
π
r
0
D
k
0
n
2/3
r
2
W
.
k
n
D
m
a
π
,
k
0
D
(6.67)
Here
m
a
is the mass of the metal atom. The rate of the pairwise process in
scheme (6.66) exceeds significantly the rate of three body process for a number
density of buffer gas atoms that is governed by the parameter
k
0
N
a
K
G
D
1 ,
(6.68)
where
N
a
is the number density of buffer gas atoms,
K
is the rate constant for
formation of a diatomic molecule in three body collisions, and its typical value in
Ta b l e 6 . 2
Parameters of charged metal clus-
ters.
and
is the average cluster charge at a tem-
perature of 1000 K for argon as a buffer gas
if the cluster charging is determined by pro-
cesses of attachment of electrons and pos-
itive ions to the cluster. The rate constant
k
e
for electron-cluster collision is given at
T
D
1000 K [41].
Z
is
the metal work function, EA is the atom elec-
tron affinity,
Δ
D
I
C
EA
2
I
is the atomic ionization potential,
W
T
is the tem-
perature where the average cluster charge is
zero for a the mean cluster size
W
,
n
D
1000 and
D
10
13
cm
3
,
electron number density
N
e
Δ
,eV
T
,10
3
K
Z
/
n
1/3
k
e
,10
8
cm
3
/s
Element
I
,eV
W
,eV EA,eV
Ti
6.82
3.92
0.08
-0.96
2.51
0.084
1.7
V
6.74
4.12
0.52
-0.98
2.63
0.078
1.5
Fe
7.90
4.31
0.15
-0.57
2.75
0.074
1.3
Co
7.86
4.41
0.66
-0.30
2.82
0.073
1.3
Ni
7.64
4.50
1.16
-0.20
2.87
0.072
1.3
Zr
6.84
3.9
0.43
-0.53
2.51
0.093
2.1
Nb
6.88
3.99
0.89
-0.21
2.57
0.085
1.7
Mo
7.10
4.3
0.75
-0.75
2.74
0.081
1.6
Rh
7.46
4.75
1.14
-0.90
3.00
0.078
1.5
Pd
8.34
4.8
0.56
-0.70
3.04
0.080
1.5
Ta
7.89
4.12
0.32
-0.03
2.65
0.085
1.7
W
7.98
4.54
0.82
-0.28
2.90
0.081
1.6
Re
7.88
5.0
0.2
-1.92
3.12
0.080
1.5
Os
8.73
4.7
1.1
0.43
3.01
0.078
1.5
Ir
9.05
4.7
1.56
1.21
3.03
0.080
1.5
Pt
8.96
5.32
2.13
0.45
3.38
0.081
1.6
Au
9.23
4.30
2.31
2.94
2.85
0.083
1.9
