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Page 30 of 57
Accepted Manuscript
30
Figure 9.
Comparison between the experimental and calculated steady-state data for (a) pH=8.15
(b) pH=10.
4.3. Determination of Iron Interstitials Diffusion Coefficient
Based upon the PDM, the metal interstitials generated at the m/bl interface move toward
the bl/s interface and the driving force for this transport phenomenon is primarily the electric
field (
ε
) (i.e., migration). The diffusivity of iron interstitials through the passive layers was
calculated according to Equation (47) [22] as a function of potential and is plotted in Figure 10.
Figure 10.
Calculated diffusivity of iron interstitials as a function of potential,
T
= 22
o
C
The diffusivity of iron interstitials (the presumed dominant point defect) is calculated to
be in the range of 10
-14
to 10
-16
cm
2
/s and to be essentially independent of the applied potential,
as predicted by PDM. The calculated diffusion coefficients for iron interstitials are in close
agreement with those reported in the literature [44,57,58]. However, a small dependence on pH
is found (Figure 10), where none should probably exist. The origin of this dependence is
currently unknown, but it probably arises because of uncertainties in the values of fundamental
parameters determined by the optimization. We note that the interstitial diffusivity is a “deeply
buried” parameter, whose value is sensitive to the optimization at very low frequencies (down to
10
-2
Hz), where the measured impedance data are the least accurate, but at which the impedance
is not particularly sensitive to the value of
D
i
. We will address this problem in future work by
measuring the impedance down to a lower frequency of 10
-3
Hz, where defect transport plays a
more significant role in determining the impedance of the system than it does at the higher,
minimum frequency of 10
-2
Hz employed in the present work.
5. Summary and Conclusions
Page 31 of 57
Accepted Manuscript
31
The findings of this work on the nature of the passive state on iron can be summarized as
follows:
Optimization of the impedance model derived from the PDM on the experimental EIS
data has resulted in determination of sets of parameters that can be used to predict the
accumulation of general corrosion damage on iron in pH-neutral solutions.
Extension of the PDM to include a parallel electronic resistance and a Randles circuit
representing a redox impedance for the redox reaction that accepts the electronic charge
generated within the barrier layer by ionization of the defects, shows that, provided any
redox species are at sufficiently low concentrations, the parallel impedance is sufficiently
high (order of 3 × 10
9
Ω.cm
2
) that values for the PDM parameters can still be extracted
by optimization of the impedance model on experimental EIS data. The parallel
electronic impedance was calculated theoretically using the defect concentrations in the
barrier layer, which were derived from the parameter values (rate constants, transfer
coefficients, etc.) obtained from optimization of the PDM on the experimental EIS data.
The thickness of the barrier oxide layer of the passive films that form anodically on iron
within the passive range, as measured experimentally using spectroscopic ellipsometry is
found to be in reasonable agreement with that calculated employing the PDM using
values for various model parameters determined by optimizing the PDM on experimental
EIS data. The passive current density for iron within the passive range, as measured
experimentally, is found to be in good agreement with that calculated from the PDM
using values for various model parameters determined by optimization. The thickness of
the barrier layer was observed to increase linearly with applied voltage and the passive
Page 32 of 57
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32
current density was found to be independent of voltage, as predicted by the PDM, for the
case where no change in cation oxidation state occurs upon barrier layer dissolution or
cation ejection. This represents powerful confirmation of the validity of the PDM, at
least in the case of iron.
6. Acknowledgments
The authors gratefully acknowledge the support of this work by the ONDRAF/NIRAS of
Belgium.
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