Environmental Engineering Reference
In-Depth Information
It is also known from thermodynamics that
1
2
d
RT
2
d
µ
I
µ
I
2
dln
P
I
2
d
µ
x
(5.69)
Now utilizing this expression (5.69) in the rational rate constant (
k
r
) given by
Eq. 5.64, one obtains
P
(o)
I
2
P
(i)
1
F
2
RT
2
P
1/2
I
2
k
r
⋅
I
2
σ
h
•
(
P
I
2
1 atm)
⋅
dln
P
I
2
(5.70)
P
(o)
I
2
P
(i)
I
2
d
P
I
2
P
I
2
RT
σ
h
•
2F
2
P
1/2
I
2
(5.71)
Therefore,
RT
F
2
⋅σ
h
•
[
P
1/2
(o)
k
r
P
1/2
(i)
I
2
]
(5.72)
I
2
Since
P
(o)
I
2
at the AgI/I
2
(v) interface at any temperature is much greater than the
equilibrium
P
(i)
I
2
at the Ag/AgI, i.e.,
P
(o)
I
2
P
(i)
I
2
, the expression for rational rate
constant (
k
r
) simplifies to the form:
RT
F
2
σ
h
•
P
1/2
k
r
(kg equivalent m
1
s
1
)
(5.73)
I
2
Parabolic rate constant values for the growth of thick films of AgCl, AgBr, and
AgI in corresponding halogen atmospheres conform to the theoretically predicted
pressure dependence [20] and thus confirm the defect model as has been proposed
by Wagner [19] for such types of ionic halide lattice.
(2) When oxidation product layers are predominantly p-type conductors,
e.g., FeO, NiO, CoO, MnO, Cu
2
O, Cu
2
S, FeS, CuI, UO
2
, etc., the compounds are
nonstoichiometric in nature, exhibiting either metal deficiency or oxidant excess.
Oxidation of copper at high temperatures can be cited as an example.
During oxidation of copper, incorporation of oxygen into Cu
2
O lattice leads
to the following defect formation equilibrium:
1
2
O
2
(g)
O
O
2V
Cu
2h
•
(5.74)
In p-type oxides, virtual electronic current equilibrium condition is fulfilled
across the oxide layer. Since concentration of defects are small compared to the
total number of lattice sites, application of ideal mass action law to Eq. 5.74
