Environmental Engineering Reference
In-Depth Information
where
permittivity of the layer, in coulomb V
1
m
1
D
v
diffusion coefficient of vacancies, in m
2
s
1
a
cation-cation distance, in meters
V
potential across the layer, in volts
Q
summation of activation energy values for the formation of defects and
their diffusion through the film, in joules.
Bose and Sircar observed the obeyance of a similar cubic law for Ag-Br
2
[39] and Ag-Cl
2
[40] systems during halide film growth in the thin film range
at and around room temperature. They used the above Eq. 5.102 in the following
modified form considering positive holes instead of ions or cation vacancies:
d
d
t
3
D
˙
Ω
V
2
Q
RT
1
ξ
exp
(5.103)
4
π
akT
2
where
D
˙
diffusion coefficient of positive holes in m
2
s
1
.
This type of cubic law is generally to be observed only at a lower thickness
level and at such a temperature range so that the field-creating electrons are avail-
able. However, it is difficult to define the exact temperature necessary for electron
availability because the energetics of thermionic emission for metal in contact
with the film will vary from system to system. In conclusion, the mechanism of
cubic rate law is still a controversial issue.
5.6 SCALE GROWTH BY LATTICE AND GRAIN
BOUNDARY DIFFUSION
In Wagner's theory of oxidation for thick, compact, nonporous, adherent oxide
scale or other reaction product layer (sulfide, halide, etc.) formation, it is assumed
that the transport of the reactants through the scale takes place by lattice diffusion
or volume diffusion due to the presence of point defects in the growing scale.
This theory has been very successful in explaining the reaction mechanism for
a number of metal-oxidant systems at high temperatures. As a general rule, lattice
diffusion tends to predominate at high temperatures for product scales with a
relatively large concentration of point imperfections. But one has to appreciate
that solid state diffusional transport also takes place along grain boundaries and
through dislocations, especially at low and intermediate temperatures. Thus in the
overall treatment of oxidation process, the effects and contributions of nonlattice
transport in the growing product scale must also be considered.
The principal difference between the diffusional properties of mono- and poly-
crystalline substances results from the fact that polycrystalline substances contain
additional linear and planer defects along which diffusion of different migrating
