Environmental Engineering Reference
In-Depth Information
sition of metal-containing molecules is
6
6
N
a
k
gas
exp
ε
T
τ
D
d
(
T
)
D
.
(6.93)
chem
ν
We compare this time with the time for conversion of free metal atoms into metal
clusters in the case of prompt decomposition of metal-containing molecules that
is given by (6.74). Since this time is short compared with the time for flow drift in
an aggregation tube, the coagulation mechanism may determine the subsequent
cluster growth, and the average cluster size is given by (6.80) or by (6.82).
Table 6.4 contains some results for this regime of cluster generation to represent
the real character of the cluster generation process. We assume metal-containing
molecules to be injected into a cylinder of radius
1mmin theflowcenter,
and this radius is small compared with the tube radius; the argon pressure is
p
D
0
D
1 atm, and the concentration of metal-containing molecules is
c
M
1% in the
central part with respect to argon atoms. For definiteness we take the flow velocity
w
D
D
300 cm/s and the tube length
l
D
30cm,thatis,thetimefortheflowbeing
located inside the tube is 0.1 s.
Let us give some comments regarding the data in Table 6.4. Here
is the density
of metal-containing compounds at room temperature,
T
m
and
T
b
are their melting
and boiling temperatures, respectively,
ε
X
is the binding energy per halogen atom
in this compound,
M
is the binding energy per metal atom in the bulk metal, the
temperatures
T
1
and
T
2
are given by (6.88) and (6.89),
c
M
ε
T
is the temperature
increase resulting from process (6.87) if the extracted energy is consumed on heat-
ing of the buffer gas,
T
is the temperature at the tube center, which is chosen as
indicated above, and
N
a
is the number density of argon atoms at a pressure of 1
atm, so the total number density of metal atoms (free and bound) is
N
m
δ
0.01
N
a
.
To estimate the character of consumption of metal-containing compound, we
give in Table 6.4 the rate
dM
/
dt
of the compound flux, that is, the compound mass
inserted in the argon flux, and the rate of deposition
dl
/
dt
,thatis,therateof
film growth
dl
/
dt
if the flux of metal clusters is deposited on a substratum. These
values are given by formulas
D
4
r
3
W
3
m
dM
dt
D
π
dl
dt
D
dM
dt
2
wN
m
m
c
,
,
2
where
M
c
and
m
are the masses of a metal-contained molecule and a metal atom,
respectively.
We now determine the kinetic parameters of this system under the above con-
ditions. The time
chem
for destruction of a metal-containing molecule follows
from (6.93), and a typical time for heat transport is given by
τ
2
0
D
τ
,
heat
4
where
is the thermal diffusivity coefficient of argon. As is seen, usually heat
transport proceeds faster than release of free metal atoms, and heating of argon due
