Environmental Engineering Reference
In-Depth Information
6.3
Cluster Plasma
6.3.1
Ionization Equilibrium for Metal Clusters in a Cluster Plasma
A cluster plasma is an ionized gas containing clusters [40, 41, 111], and the num-
ber density of clusters is small compared with the number density of atoms and
molecules. Clusters in a cluster plasma may grow and evaporate during evolution
of the cluster plasma. We will be guided by a cluster plasma consisting of a buffer
gas and metal clusters. Hence, this cluster plasma includes both metal clusters and
metal atoms, and the total number density of metal atoms is small compared with
that of gas atoms. Under these conditions, metal clusters and metal atoms are of
importance for cluster processes, and a buffer gas has the role of a stabilization
component. Below we analyze several such systems which may be used for gener-
ation of metal clusters.
There are various methods to generate metal clusters in a cluster plasma. In
all cases, metal atoms are injected in a gas or gas flow, and then metal clusters
are formed from these atoms. Metal atoms may be injected in a gas as a result of
evaporation of metal atoms from a metal surface and erosion of a metal surface by
laser radiation or the ion (electron) beam of a gas discharge. The effective method
of creation of a cluster plasma is based on injection of some metal compounds in a
flow of a dense plasma, where these compounds are destroyed, andmetal atoms are
joined in metal clusters under appropriate conditions. This scenario uses a large
binding energy of atoms in clusters as it takes place for most metals.
If we deal with a cluster plasma including metal clusters, a positive charge of
this plasma is connected with metal clusters since their ionization potential is low-
er than that for buffer gas atoms. We consider below the ionization equilibrium
involving metal clusters that is realized according to the scheme
M
C
Z
C
1
n
M
C
Z
n
C
e
$
.
(6.58)
Here
M
is a metal atom and
M
n
is a metal cluster consisting of
n
atoms and having
charge
Z
.ByanalogywiththeSahaformula,wehavefortheprobability
P
Z
(
n
)for
a cluster consisting of
n
atoms to have charge
Z
2
m
e
T
e
2
3/2
exp
,
P
Z
(
n
)
N
e
P
Z
C
1
(
n
)
D
I
Z
(
n
)
T
e
(6.59)
π
„
2
where
T
e
is the electron temperature,
m
e
is the electron mass,
N
e
is the electron
number density, and
I
Z
(
n
) is the ionization potential of the cluster consisting of
n
atoms and having charge
Z
.
Note that the ionization equilibrium (6.58) in an ionized gas results from step-
wise ionization of charged clusters in collisions with electrons and three body re-
combination of charged clusters and electrons. But because the number density of
the internal electrons of a metal cluster greatly exceeds that of the plasma electrons,
