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Page 35 of 57
Accepted Manuscript
35
[29] D. D. Macdonald and M. Urquidi-Macdonald, Application of Kramers
‐
Kronig Transforms
in the Analysis of Electrochemical Systems: I . Polarization Resistance,
J. Electrochem. Soc
.
132
(1985) 2316.
[30] M. Urquidi-Macdonald, S Real and D. D. Macdonald, Application of Kramers
‐
Kronig
Transforms in the Analysis of Electrochemical Impedance Data: II . Transformations in the
Complex Plane,
J. Electrochem. Soc
.
133
(1986) 2018.
[31] J. Ai, Y-Z. Chen, M. Urquidi-Macdonald, and D.D. Macdonald, Electrochemical Impedance
Spectroscopic Study of Passive Zirconium: I. High-Temperature, Deaerated Aqueous Solutions ,
J. Electrochem. Soc
.
154
(2007) C43.
[32] J. Ai, Y-Z. Chen, M. Urquidi-Macdonald, and D.D. Macdonald, Electrochemical Impedance
Spectroscopic Study of Passive Zirconium: II. High-Temperature, Hydrogenated Aqueous
Solutions,
J. Electrochem. Soc
.
154
(2007) C52.
[33] D. D. Macdonald and A. Sun, An electrochemical impedance spectroscopic study of the
passive state on Alloy-22,
Electrochim. Acta
,
51
(2006) 1767.
[34] J. Geringer, M.L. Taylor, D.D Macdonald, Predicting the steady state thickness of passive
films with the Point Defect model in fretting corrosion experiments,
Electrochemical and Solid-
State Science
, in progress.
[35] DataFit, Oakdale Engineering, www.oakdaleengr.com
[36] K. Levenberg, A Method for the Solution of Certain Problems in Least Squares,
Quart.
Appl. Math
.
2
(1944) 164.
[37] “Ellis 2: Complex curve fitting for one independent variable | IgorExchange.” [Online].
Available: http://www.igorexchange.com/project/Ellis2. [Accessed: 07-Aug-2012].
[38]
T. Bäck and H.-P. Schwefel, An Overview of Evolutionary Algorithms for Parameter Optimization,
Evolutionary Computation
1
(1993) 1.
[39] O. Rosas-Camacho, M. Urquidi-Macdonald, and D. D. Macdonald, Deterministic Modeling
of the Corrosion of Low-Carbon Steel by Dissolved Carbon Dioxide and the Effect of Acetic
Acid. I-Effect of Carbon Dioxide,
ECS Transactions
19
(29) (2009) 143.
Page 36 of 57
Accepted Manuscript
36
[40] J. Ai, Y. Chen, M. Urquidi-Macdonald and D. D. Macdonald, Electrochemical impedance
spectroscopic study of passive zirconium,
Journal of Nuclear Materials
379
(2008) 162.
[41] D. D. Macdonald , J. Ai, Y. Chen, and M. Urquidi-Macdonald , Electrochemical Impedance
Spectroscopic Study of Passive Zirconium in High Temperature De-aerated Aqueous Solutions,
ECS Transactions
2
(17)(2007) 29.
[42] M. Bojinov, G. Fabricius, T. Laitinen, K. Makela, T.Saario and G. Sundholm, Coupling
between ionic defect structure and electronic conduction in passive films on iron, chromium and
iron–chromium alloys,
Electrochim Acta
45
(2000) 2029.
[43] M. Bojinov, G. Fabricius, P. Kinnunen, T. Laitinen, K. Makela, T.Saario and G. Sundholm,
Electrochemical study of the passive behaviour of Ni–Cr alloys in a borate solution—a mixed-
conduction model approach,
J. Electroanal.Chem
.
504
(2001) 29.
[44] M. Bojinov, G. T. Laitinen, K. Makela and T.Saario. and G. Sundholm, Conduction
Mechanism of the Passive Film on Iron Based on Contact Electric Impedance and Resistance
Measurements,
J. Electrochem. Soc
.
148
(2001) B243.
[45] A. T. Fromhold and E.L. Cook, Diffusion currents in large electric fields for discrete
lattices,
J. Appl. Phys
.
38
(1967) 1546.
[46] www.olisystems.com
[47] R. D. L. Kronig, On the theory of dispersion of x-rays,
J. Opt. Soc. Am.
12
(1926) 547.
[48] H. A. Kramers, Zur Struktur der Multiplett-S-Zustände in zweiatomigen Molekülen. I,
Z.
Phys.
30
(1929) 521.
[49] D. D. Macdonald , M. Urquidi-Macdonald, Kramers
‐
Kronig Transformation of Constant
Phase Impedances,
J. Electrochem. Soc
.
137
(1990) 515.
[50] M. Urquidi-Macdonald, S. Real, and D. D. Macdonald, Applications of Kramers—Kronig
transforms in the analysis of electrochemical impedance data—III. Stability and linearity,
Electrochim. Acta
35
(1990) 1559.
[51] S.N. Sivanandam and S.N. Deepa, Introduction to Genetic Algorithms,
Springer Verlag
,
(2007).
[52] M. Gulsen, A. Smith and D. Tate, A genetic algorithm approach to curve fitting,
Int. J Prod.
Res
.
33
(1995) 1911.
Page 37 of 57
Accepted Manuscript
37
[53] T.VanderNoot and I. Abrahams, The use of genetic algorithms in the non-linear regression
of immittance data,
Journal of Electroanalytical Chemistry
448
(1) (1998) 17.
[54] “GenCurvefit | IgorExchange.” [Online]. Available:
http://www.igorexchange.com/project/gencurvefit. [Accessed: 07-Aug-2012].
[55] B. M. Marx, Exploring the Mechanisms of Passivity on Iron: Experimental Methods for
Characterizing and Developing Models to Describe Nano-Oxide Growth,
The Pennsylvania State
University, University Park, USA
(2006).
[56] M. Büchler, P. Schmuki and H. Böhni, Formation and Dissolution of the Passive Film on
Iron Studied by a Light Reflectance Technique,
J. Electrochem. Soc.
144
(1997) 2307.
[57] Y.F. Cheng, C. Yang, J.L. Luo, Determination of the diffusivity of point defects in passive
films on carbon steel,
Thin Solid films
416
(2002) 169.
[58] X. Zhang, J.C. Wren, I. Betova, M. Bojinov, Estimation of kinetic parameters of the passive
state of carbon steel in mildly alkaline solutions from electrochemical impedance spectroscopic
and X-ray photoelectron spectroscopic data,
Electrochim. Acta
56
(2011) 5910.
Tables
Page 38 of 57
Accepted Manuscript
38
Table 1:
Coefficients for the rate constants for the reactions that generate and annihilate point
defects at the m/bl interface [Reactions (1) – (3)] and at the bl/s interface [Reactions (4) – (6)],
Figure 1, and for dissolution of the film [19-21].
pH
c
L
b
V
a
i
i
i
i
i
e
e
e
k
k
0
Reaction
)
(
1
V
a
i
)
(
1
cm
b
i
c
i
Units of
0
i
k
(1)
'
1
'
e
v
M
V
m
m
M
k
M
)
1
(
1
K
1
-
1
β
s
1
(2)
'
2
e
v
M
m
m
i
k
)
1
(
2
K
2
-
2
β
s
cm
mol
2
(3)
'
2
..
3
e
V
M
m
O
M
k
)
1
(
3
K
3
-
3
β
s
cm
mol
2
(4)
'
)
(
4
e
M
M
k
M
4
4
βδ
s
cm
mol
2
(5)
'
)
(
5
e
M
M
k
i
5
5
βδ
s
cm
(6)
H
O
O
H
V
O
k
O
2
6
2
..
6
2
6
βδ
s
cm
(7)
)
(
2
2
2
7
O
H
M
H
MO
k
)
(
7
7
(
δ
-
)
β
s
cm
mol
2
Page 39 of 57
Accepted Manuscript
39
Table 2:
Parameter values used to calculate the electronic impedance in parallel with the barrier
layer.
Parameter
Value/units
Source
D
e
10
-11
/ cm
2
s
-1
[44]
ˆ
30
[18]
C
25×10
-6
/ F cm
-2
Estimated as a typical value
O
H
2
0.5
Estimated by using OLI software [46]
B
3.92×10
-11
/ A cm
-2
Estimated by using OLI software [46]
D
i
1.4×10
-14
/ cm
2
s
-1
Preliminary optimization
D
o
1.4×10
-14
/ cm
2
s
-1
Preliminary optimization