Environmental Engineering Reference
In-Depth Information
(o)
X
µ
1
Z
2
|
k
r
(
t
1
t
2
)
t
3
σ
d
µ
X
(5.64)
F
2
|
(i)
X
µ
Regarding temperature of exposure, Wagner's equation (5.63) provides no clue
as to what should be the minimum temperature for its validity. Experimental
results on the oxidation of copper show that activation energy for the oxide
growth rate is identical to that for diffusion rate of Cu
ions in Cu
2
O. Consider-
ation of experimental data on Cu-Cu
2
O-O
2
(g) and a few other systems roughly
indicates that the minimum temperature for validity of Wagner's parabolic rate
law will be around 0.4
T
m
, where
T
m
is the melting point of scale compound.
Further investigations relating to halogenation kinetics of silver and copper (ha-
lide growth process) have shown the obeyance to Wagner's rate law mechanism
even at a temperature as low as 303 K. Of course, this is true beyond a certain
halide thickness range depending on the individuality of the system.
The electrochemical steps in diffusional growth of oxide scales involving two
kinds of mass and charge transport are schematically presented in Fig. 5.15. These
clearly depict that the diffusional growth of a corrosion product formed on a
metal substrate at elevated temperature is essentially an electrochemical process
in which the oxidation and reduction reactions are taking place at the two reaction
interfaces, i.e., metal-oxide and oxide-oxygen, respectively. The scales are both
ionic and electronic conductors and the galvanic cell formed remains active by
internal short circuiting.
One can now examine the application and verification of Wagner's theoretical
expression for different metal-oxidant systems as reported by a large number of
investigators. As illustrations, three metal-oxidant systems are being chosen in
which oxidation product layers are (1) predominantly ionic, (2) predominantly
p-type oxide (metal-deficient or oxygen excess), and (3) predominantly n-type
oxide (metal excess or oxygen-deficient).
(1) If one considers an iodide film growth on silver, it is to be remembered
that an isolated crystal of AgI is an ionic conductor exhibiting predominance of
Frenkel type of disorder. That is, the concentration of vacancies on silver sublat-
tice and an equal number of silver ions at interstitial sites is of very high order
compared to intrinsic electronic defects like positive holes in the valence band
and excess electrons in the conduction band of AgI film.
However, when AgI film initially grown on Ag is further exposed to iodine
vapor, it exhibits electronic conductivity due to injection of positive holes in the
valence band. Subsequent iodine incorporation into the growing AgI lattice can
be represented by the following defect formation reaction:
1
2
I
2
(v)
I
I
V
′
Ag
h
•
(5.65)
