Environmental Engineering Reference
In-Depth Information
Figure 5.16
Concentration of zinc ions in interstitial lattice positions through the ZnO
layer, according to Wagner. Lines 1 and 2 show the concentration decrease of the zinc
ions in the interstitial lattice positions at low and high oxygen pressures. As can be seen,
(
dc
ZnO
•
/
d
ξ)
1
(
dc
ZnO
•
/
d
ξ)
2
[Ref. 15].
etc. Al
2
O
3
,Cr
2
O
3
, or SiO
2
layer growth rates on corresponding substrate are
much slower in comparison to the majority of base metal oxides. This is because
these compounds are nearly stoichiometric in nature. In other words, their inher-
ent defect concentrations are quite small. On the other hand, FeO, NiO, or Cu
2
O
growth rates on the corresponding metal are much faster, and this is attributable
to the presence of appreciable concentrations of point defects in such oxides. It
has been reported (29) that under similar experimental conditions, the concentra-
tion of defects in FeO is
10 at. %, that in NiO
0.1 at. %, and that in Cr
2
O
3
negligibly small (
0.001 at. %). Figure 5.17 represents the comparative oxidation
rates of Fe, Ni, and Cr at 973 K in one atmosphere oxygen pressure. This figure
shows that the chromium oxidation rate is only 1/1000th the value of that for
iron. Moreover, it is known that the rate constants are related to electrical conduc-
tivity of the compounds being formed (2). Some of the conductivity values for
various oxides are presented in Table 5.3.
Actually, the rate constant values are controlled by the transport coefficient
factor, which is nothing but the product of diffusivity (
D
i
) and concentration (
C
i
)
of the species i, the value of which will decide the rate-limiting step for thickening
of the oxide layer.
Subsequently, Wagner [30] derived another expression of rational rate con-
stant similar to the original one (5.64). In the latter expression, the rate constant
