j.electacta.2013.03.143

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Table 3: Parameter values after optimization of the point defect model on the experimental impedance data for iron in borate buffer solution [0.3 M H3BO3 + 0.075 M Na2B4O7] + 0.001 M EDTA [Ethylenediaminetetraacetic acid, EDTA, disodium salt], at T=21oC.

pH=8.15

Eapp vs SHE/V		0.044		0.244			0.544		0.844		Average
	-2		-7		Manuscript-7 -7 -7
Current density (A cm-2)		1.28×10-6		1.81×10-6			5.20×10-7		4.75×10-7		------------
Thickness of barrier layer (nm)		0.86		1.00			1.57		1.73		------------
CPE-Y (S sα cm-2)		1.94×10-5		1.25×10-5			4.67×10-6		5.30×10-6		------------
CPE-α		0.94		0.95			0.94		0.96		------------
Electric field (ε)		3×106		3×106			3×106		3×106		assumed
Warburg coefficient (σ)		1.97×105		7.38×105			1.61×106		6.09×105		------------
Di (cm2 s-1)		1.08×10-15		3.03×10-14			1.18×10-14		1.42×10-14		------------
Polarizability of the BOI (α)		0.724		0.724			0.724		0.724		0.724
Transfer coeff. reaction 1 (α2)		0.01		0.003			0.02		0.01		0.01
Transfer coeff. reaction 2 (α3)		0.19		0.17			0.18		0.17		0.17
k02 (mol cm-2 s-1)		3.88×10-12		5.95×10-12			1.68×10-12		1.54×10-12		3.2×10-12
k03 (mol cm-2 s-1)		4.98×10-16		4.47×10-16			8.85×10-16		5.03×10-16		5.8×10-16
k07 (mol cm-2 s-1)		5.52×10-12		6.68×10-12			1.99×10-12		2.49×10-12		5.5×10-12
Rs (ohm cm2)		36		34.6			34.6		34.7		------------
Φ0f/s		-0.1		-0.1			-0.1		-0.1		assumed
β		-0.03		-0.03			-0.03		-0.03		assumed
Cdl (F cm-2)		1.16×10-6		1.63×10-6			4.25×10-6		1.26×10-6		------------
Rct (ohm cm2)		3.46×109		2.96×109			3.86×109		2.97×109		------------
				pH=10
Cdl (F cm ) Accepted2.19×10 8.04×10							4.89×10		2.35×10		-----------
Eapp vs SHE/V		0.044		0.244			0.544		0.844		Average
Current density (A cm )		3.42×10		5.15×10			7.62×10		4.55×10		-----------
Thickness of barrier layer (nm)		1.47		1.56			2.15		2.28		-----------
CPE-Y (S sα cm-2)		1.79×10-5		1.21×10-5			7.60×10-6		6.15×10-6		-----------
CPE-α		0.94		0.96			0.96		0.94		-----------
Electric field (ε)		3×106		3×106			3×106		3×106		assumed
Warburg coefficient (σ)		1.32×105		7.54×104			1.40×105		1.35×105		-----------
Di (cm2 s-1)		3.47×10-17		2.55×10-17			1.94×10-16		6.42×10-17		-----------
Polarizability of the BOI (α)		0.724		0.724			0.724		0.724		0.724
Transfer coeff. reaction 1 (α2)		0.02		0.01			0.005		0.01		0.01
Transfer coeff. reaction 2 (α3)		0.11		0.14			0.11		0.19		0.13
k02 (mol cm-2 s-1)		1.30×10-12		1.78×10-12			2.80×10-12		1.68×10-12		1.89×10-12
k03 (mol cm-2 s-1)		2.03×10-16		2.69×10-16			1.78×10-16		7.16×10-16		3.41×10-16
k07 (mol cm-2 s-1)		3.35×10-12		4.64×10-12			1.27×10-12		2.12×10-12		2.84×10-12
Rs (ohm cm2)		31.5		31.5			34.6		32		-----------
Φ0f/s		-0.1		-0.1			-0.1		-0.1		assumed
β		-0.03		-0.03			-0.03		-0.03		assumed
-2			-7			-7		-7		-7
Rct (ohm cm2)		3.54×109		3.22×109			3.68×109		3.76×109		-----------

Page 40 of 57

Figure Captions

Figure 1. Interfacial defect generation/annihilation reactions that are postulated to occur in the growth of anodic barrier oxide films according to the Point Defect Model. m metal atom, VM cation vacancy on the metal sublattice of the barrier layer, Mi interstitial cation, M M metal cation on the metal sublattice of the barrier layer, VO oxygen vacancy on the oxygen sublattice of the barrier layer, OO oxygen anion on the oxygen sublattice of the barrier layer,

M metal cation in solution.

Figure 2. Equivalent electrical circuit describing the total impedance of the system

Figure 3. Randles equivalent electrical circuit describing the impedance of the redox reaction that accepts the electronic charge from the barrier layer. Here Wz – is the solution-based Warburg impedance, Rct is the charge transfer resistance of electrochemical cathodic reaction (e.g., hydrogen evolution) and Cdl is the capacity of the double layer.

Figure 4. Nyquist plot for parallel impedance for the case for iron in borate buffer solution [0.3 M H3BO3 + 0.075 M Na2B4O7] + 0.001 M EDTA [Ethylenediaminetetraacetic acid, EDTA, disodium salt], pH=8.15, T = 21 oC and E = 0.044 V (SHE).

Figure 5. Bode plot (magnitude of the impedance) for the case for iron in borate buffer solution

[0.3 M H3BO3		+ 0.075 M Na2B4O7] + 0.001 M EDTA, pH=8.15, T = 21 oC, and E = 0.044 V
(SHE).		Manuscript
(SHE).	Accepted
	Accepted

Figure 6. Bode plot (phase angle) for the case for iron in borate buffer solution [0.3 M H3BO3 + 0.075 M Na2B4O7] + 0.001 M EDTA, pH=8.15, T = 21 oC and E = 0.044 V (SHE).

Figure 7. Experimental and simulated impedance spectra for iron in borate buffer solution [0.3 M H3BO3 + 0.075 M Na2B4O7 , as appropriate] + 0.001 M EDTA [Ethylenediaminetetraacetic acid, disodium salt], (a) pH = 8.15 and (b)10, T=21 oC as a function of applied potential, solid lines show the best fit calculation according to PDM.

Figure 8. Comparison of obtained kinetic parameters from PDM optimization as a function of applied potential (a) standard rate constants (pH=8.15), (b) transfer coefficients (pH=8.15), (c) standard rate constants (pH=10.0) and (d) transfer coefficients (pH=10.0) (Lines are showing the linear regressions).

Figure 9. Comparison between the experimental and calculated steady-state data (a) current density (pH=8.15), (b) barrier layer thickness (pH=8.15), (c) current density (pH=10.0) and (d) barrier layer thickness (pH=10.0) (Lines are showing the linear regressions).

Figure 10. Calculated diffusivity of iron interstitials as a function of potential, T = 22 oC(Lines are showing the linear regressions).

Page 41 of 57