Environmental Engineering Reference
In-Depth Information
valid for ionic conductivity, i.e.,
O
2
(as per Wagner [28]). Further-
more, one can write the following relation from a thermodynamic standpoint:
σ
Cu
σ
Cu
P
1/7
1
2
d
RT
2
d
µ
O
µ
O
2
dln
P
O
2
(5.78)
Now, utilizing the above expressions, the rational rate constant for copper oxida-
tion simplifies to the form:
P
(o)
O
2
P
(i)
O
2
RT
4F
2
σ
k
r
Cu
P
1/7
O
2
dln
P
O
2
(5.79)
7
4
RT
F
2
σ
0
Cu
[
P
1/7
(o)
O
2
P
1/7
(i)
O
2
]
(5.80)
7
4
RT
F
2
σ
Cu
P
1/7
(o)
O
2
(5.81)
[since
P
1/7
(o)
O
2
P
1/7
(i)
O
2
]
The close agreement of theoretically estimated rate constant values to those
experimentally obtained further confirms the defect model of Cu
2
O as proposed
by Wagner [18].
(3) When the oxidation products are predominantly n-type conductors, e.g.,
ZnO, CdO, BeO, SiO
2
, ZrO
2
, TiO
2
, etc., the compounds formed on the corre-
sponding metals are nonstoichiometric, exhibiting either excess metal ions at in-
terstitial sites or vacancies at oxidant ion sites. Oxidation behavior of zinc in the
temperature range of 573-673 K [18] can be considered as an example to illus-
trate such systems.
The following defect formation equilibrium occurs when oxidation of zinc
takes place in an oxygen atmosphere at elevated temperatures:
1
2
O
2
(g)
ZnO
Zn
••
i
2e
′
(5.82)
Here conductivity is mainly due to the transport of excess electrons in the conduc-
tion band of ZnO lattice, i.e., virtual electronic current equilibrium exists across
the growing ZnO on the Zn substrate. Therefore, the thickening process of ZnO
film will be controlled by the transport of interstitial Zn ions through the ZnO
lattice.
One can write the following expression for equilibrium constant of the above
defect equilibrium (5.82) at any temperature (
T
), assuming the validity of the
mass action law:
n
2
P
1/2
O
2
K
e
(
T
)
[Zn
•
i
]
⋅
(5.83)
