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Electrochimica Acta 56 (2011) 8727– 8733

Contents lists available at ScienceDirect

Electrochimica Acta

jou rn al hom epa ge: www.elsev ier .com/ locate /e lec tac ta

IS study of potentiostatically formed passive film on 304 stainless steel

arzad Mohammadia,∗, Tirdad Nickchia, M.M. Attara,b, Akram Alfantazia

Department of Materials Engineering, The University of British Columbia, Vancouver, BC, CanadaDepartment of Polymer Engineering and Color Technology, Amirkabir University of Technology, P.O. Box 15875-4413, Tehran, Iran

r t i c l e i n f o

rticle history:eceived 26 May 2011eceived in revised form 19 July 2011ccepted 19 July 2011vailable online 27 July 2011

a b s t r a c t

Passive film was potentiostatically grown on Type 304 stainless steel at potentials between −0.4 and 0.3 Vvs. Hg/HgSO4 in 50 mV intervals. Electrochemical impedance spectroscopy was used to study properties ofthe grown passive films. Relevant circuit analogs were selected to fit the electrochemical impedance dataobtained at each potential. The resultant parameters were used to calculate film thickness through bothfilm capacitance and resistance. The calculated thicknesses were compared with ellipsometry thickness

eywords:ISassive filmllipsometryircuit analog

measurement results. An overestimation occurred when the film resistance was used to calculate the filmthickness. On the other hand, when the CPE parameter Q was used, the film thickness was underestimated.Available approaches were employed to calculate the effective capacitance of the film. A comparisonbetween the film thickness calculated from the effective capacitance and ellipsometry measurementssuggested a surface distribution of time constants on the surface.

ime constant

. Introduction

Although stainless steels make up for only a few percent of thelobal steel production, their importance is far greater than theirroduction rate. Corrosion resistance offered by stainless steels

s a key feature of many engineering and industrial devices andpplications. Stainless steels owe their corrosion resistance to theormation of a thin protective layer on the surface with limitedonic and electronic conductivity. Formation of this layer is sponta-eous in most cases and significantly reduces the electrochemicaleaction rates on the surface.

The nature and properties of this layer has been the subject ofany research studies [1–3]. Surface analysis techniques have been

tilized to study the composition and structure of the passive film.ome of these include X-ray photo electron spectroscopy (XPS)4–7], ellipsometry [8] and atomic force microscopy (AFM) [9]. Aowerful technique widely used for indirect characterization ofassive film properties is electrochemical impedance spectroscopyEIS). Using EIS, the response of physico-chemical systems to thexcitation frequency is measured. This has been widely used toharacterize the passive film formed on stainless steels, for exam-le [10–12], aluminum [13], silicon [14], etc. One approach for

nterpreting the EIS results is using equivalent electrical circuits

o simulate the EIS spectra. Different electrical circuit analogs areroposed to simulate the behavior of passive layers on stainlessteels. Each of the circuits is a combination of electrical circuits

∗ Corresponding author. Tel.: +1 7788553026.E-mail address: fmohamma@interchange.ubc.ca (F. Mohammadi).

013-4686/$ – see front matter © 2011 Elsevier Ltd. All rights reserved.oi:10.1016/j.electacta.2011.07.072

© 2011 Elsevier Ltd. All rights reserved.

based on the hypothesized physico-chemical model describing thebehavior of passive film. These finally are used to extract informa-tion on semiconducting properties [15], structure and thickness ofthe passive film [16–19].

The aim of this study is to evaluate the existing models andexplore the possibilities in applying them to a specific passivealloy/solution system. This will show how the existing models pre-dict the thickness and structure of the passive film. Due to itsubiquity, the Type 304 SS/sulfate solution is used in this study.

2. Experimental

A Princeton Applied Research (PAR) Versastat 4 potetio-stat/galvanostat was used for all the electrochemical measure-ments. In order to furnish clean and oxide free surfaces prior toexperiments, potentiostatic conditioning tests were performed at−1.5 V vs. Hg/HgSO4 for 3200 s. The potentiodynamic tests wereperformed from −1.5 to 1.5 V vs. Hg/HgSO4 with a scan rate of0.167 mV s−1. The potentiostatic tests at the passive region was per-formed from −0.4 to 0.3 V vs. Hg/HgSO4 at each 50 mV intervals for1 h. Following the potentiostatic step for growth of passive film, EIStests on type 304 SS were performed with RMS applied potentialamplitude of 10 mV at the specific potential in the frequency rangeof 0.01–10,000 Hz with sampling rate of 10 points per decade.

A conventional water-jacketed three-electrode cell consisting

of graphite as counter electrode (CE), mercury/mercurous sulfate(0.658 vs. SHE/V) as reference electrode (RE), and Type 304 SS asthe working electrode was used. All the potentials in this work arereported vs. the Hg/HgSO4 reference electrode.

8728 F. Mohammadi et al. / Electrochimica Acta 56 (2011) 8727– 8733

04 st

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temperature. As observed in Fig. 5, the potential range of −0.4 to0.3 V vs. Hg/HgSO4 lies in the passive region. According to Fig. 5the current density starts to increase at 0.25 V vs. Hg/HgSO4 from2.01E − 7 �A cm−2 to 2.53E − 7 �A cm−2 at 0.30 V vs. Hg/HgSO4.

Fig. 1. SEM Image of the microstructure of 3

304 Stainless steel with actual composition of C 0.08 (wt%), Mn.02 (wt%), Fe 45.57 (wt%), S 0.001 (wt%), Si 0.31 (wt%), Cu 0.16wt%), Ni 32.16 (wt%), Cr 19.59 (wt%), Al 0.46 (wt%) and Ti 0.08wt%) was used in this study. Fig. 1 shows an SEM image of the

icrostructure of the 304 stainless steel along with elemental X-rayaps for nickel, carbon and chromium. As can be seen, the alloying

lements are distributed uniformly and thus it can be concludedhat the stainless steel was not sensitized.

Since the main purpose of the present work was to study theassive film and not its interactions with the environment, theriteria for solution selection were (a) simplicity (b) not beingggressive to the passive film. Therefore, the test solution contained.1 mol dm−3 sodium sulfate and all the tests were performed atoom temperature and the air saturation conditions. All the chemi-al agents were procured from Fisher Scientific and solutions wererepared with deionized water.

The in situ grinding apparatus consists of a disk with a diameterf 1.5 cm and height of 1 cm, on which 1200 SiC emery paper wasdhered (Fig. 2). The disk was connected to a rotor using a shaftnd rotates at 500 rpm. The grinding disk was positioned on the

mm × 2 mm sample to grind the surface while the electrode wasotentiostatically conditioned at −1.5 V vs. Hg/HgSO4. The thick-ess calculations using EIS were compared with thickness databtained by ellipsometry. The passive films formed at −0.25, −0.05,.15 and 0.30 V vs. Hg/HgSO4 were studied and the passive filmshicknesses were measured using a 300–1700 nm spectral rangellipsometer.

. Results and discussion

To maintain consistent conditions under which passive films formed, the surface should be free of any previously formedxides. Therefore, samples were cathodically polarized at −1.5 V

s. Hg/HgSO4 prior to anodic polarization. However, the resultsndicated that some products remained on the surface even afterathodic polarization was carried out for 2 h. Fig. 3 shows the cur-ent density (j) vs. time (t) and Fig. 4 shows the Nyquist diagram at

ainless steel and X-ray map for Cr, Ni and C.

−1.5 V vs. Hg/HgSO4, respectively. As apparent from Fig. 3, a highercurrent was measured for the polished sample in comparison withthe unpolished one in the cathodic region. As depicted in Fig. 4 theresponse of the polished sample forms a smaller loop compared tothe response of the unpolished one suggesting a higher polarizationresistance for the unpolished electrode. Therefore, it can be con-cluded from Figs. 2 and 3 that in the case of passive materials suchas 304 stainless steel, application of cathodic polarization alone willnot eliminate the entire passive film from the surface. To com-pletely remove the remaining products, in situ grinding methodwas utilized. The sample was ground for 30 s at 500 rpm while itwas potentiostatically held at −1.5 V vs. Hg/HgSO4.

Fig. 5 shows the potentiodynamic polarization diagram for 304stainless steel in 0.1 mol dm−3 sodium sulfate solution at ambient

Fig. 2. Schematic representation of the in situ grinding apparatus.

F. Mohammadi et al. / Electrochimica Acta 56 (2011) 8727– 8733 8729

Fig. 3. Current density vs. time for 304 stainless steel cathodically polarized at−1.5 V vs. Hg/HgSO4 in 0.1 mol dm−3 sodium sulfate solution.

Fig. 4. Nyquist plot for for 304 stainless steel cathodically polarized at −1.5 V vs.Hg/HgSO4 in 0.1 mol dm−3 sodium sulfate solution.

Fig. 5. Potentiodynamic polarization curve for 304 stainless steel immersed in0.1 mol dm−3 sodium sulfate solution.

Fig. 6. Select Nyquist diagrams of EIS experiments performed on 304 stainless steelimmersed in 0.1 mol dm−3 sodium sulfate solution at 50 mV intervals.

0.25 V vs. Hg/HgSO4 can be considered as the onset of passivefilm breakdown where the passive film behavior starts to change.Although the current density increases from 0.25 V vs. Hg/HgSO4 to0.30 V vs. Hg/HgSO4, it is still less that 0.3 �A cm−2 indicating thatthe film is still reasonably protective. Therefore, to study the passivefilm, EIS experiments were performed in this potential range.

Fig. 6 shows the results of the EIS experiments carried out inthe potential range described in Fig. 5. As apparent in Fig. 6 theimpedance of the system increases by raising the potential from−0.4 V vs. Hg/HgSO4 up to 0 V vs. Hg/HgSO4 and then decreases upto 0.3 V vs. Hg/HgSO4. The behavior observed in Fig. 6 is consis-tent with the potentiodynamic results presented in Fig. 5 where aminimum occurs in the current density close to 0 V vs. Hg/HgSO4.

Equivalent electrical circuit models were employed to analyzepassive layer characteristics [19–21]. Different parameters wereobtained by fitting circuit analogs to the experimental EIS data.These parameters include film and double layer capacitances andresistances as well as the solution resistance. Some of the modelsassumed a non-ideal capacitive behavior and considered that con-stant phase elements (CPE) were present in the system. A constantphase element is an equivalent electrical circuit component imitat-ing behavior of an imperfect capacitor. The electrical impedance ofa CPE can be calculated according to Eq. (1).

ZCPE = 1Q (ωi)n (1)

where Q is a constant with the units of F cm−2 s(n−1) and n is avalue representing the deviation from purely capacitive behavior.When the value of n approaches unity, pure capacitive behavior isobserved and Q is equivalent to the film capacitance (C). Param-eters extracted from fitting electrical models to the experimentalresults were used to calculate the passive layer thickness. In orderto obtain the passive layer thickness, the simulated resistance andcapacitance of the film were used.

Using the film simulated capacitance through each model; thefilm thickness (dfilm) at different potentials was calculated accord-ing to the formula (2):

dFilm = εε0A

C(2)

where ε0 is the permittivity of the vacuum and has a value of8.85 × 10−12 F m−1, ε is the relative permittivity and it was set to30 [22], A is the effective surface area of the sample (m2) and C isthe capacitance of the film (F).

8730 F. Mohammadi et al. / Electrochimica Acta 56 (2011) 8727– 8733

Table 1Parameters n and �2 obtained by fitting models A–C to the EIS spectra of 304 stainless steel immersed in 0.1 mol dm−3 sodium sulfate solution.

Model A Model B Model C

n = 1 0.87 < n < 0.93 0.89 < n < 0.911.86 × 10−4 < �2 < 1.37 × 10−3 3.53 × 10−4 < �2 <6.68 × 10−3 1.49 × 10−4 < �2 < 7.49 × 10−4

Fs

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with potential up to about 0 V vs. Hg/HgSO4. The curve of modelB reaches a maximum around 0 V vs. Hg/HgSO4 where the currentdensity is the lowest and a further increase in the potential beyond

Table 2

ig. 7. Relevant electrical circuit analogs used to simulate EIS spectra of 304 stainlessteel immersed in 0.1 mol dm−3 sodium sulfate solution.

The second approach for determination of film thickness wasased on the values predicted for passive film resistance (R) by eachodel and the following formula was used to calculate the film

hickness:

Film = RA

�(3)

here � is the specific resistivity of the passive layer.The literature relevant to EIS simulation of passive films was sur-

eyed and three most commonly used electrical equivalent modelsere selected to interpret the EIS spectra (Fig. 7). A brief description

f the models will be presented here.Model A: in this model, R1 and C1 represent the capacitive and

esistive behavior of the interface between the metal and barrierayer (passive film), Cb and Rb are representatives of the barrierayer, C2 and R2 represent the interface between the electrolytend the barrier layer and Rs is the electrolyte resistance [19,23]. Asnderstood, in this model a purely capacitive behavior is assumedor the passive film.

Model B: the passive film and electrical double layer aressumed to show non-ideal capacitive behavior. R1 and Q1 areepresentatives of the electrical double layer whereas R2 and Q2epresent the resistive and capacitive behavior of the passive film.ccording to this model, the two RQ elements are connected ineries with the solution resistance (RS) [20,24].

Model C: In this model, the passive film is considered to have aorous structure and to show non-ideal capacitive behavior. R1 ishe electrolyte resistance inside the pores and Q1 is associated withhe oxide film. R2 is the charge transfer resistance of electrochemi-al processes taking place inside the pore and Q2 is associated withlectrical double layer [21,25,26].

Fig. 8 shows typical results of fitting models A, B and C to thexperimental results obtained at 0.1 V vs. Hg/HgSO4. As apparentrom Fig. 8, there is a good agreement between the model predic-ions and the experimental data. Chi square and n values extractedrom fitting different models to the experimental data are given in

able 1 for the entire range of passive potential. From Table 1 it isvident that the values predicted by each model for n are not veryar from unity. Therefore, it was assumed that the deviation from

Fig. 8. Models A–C fitted to experimental EIS spectrum of 304 stainless steel at 0.1 Vvs. Hg/HgSO4 in 0.1 mol dm−3 sodium sulfate solution.

ideal capacitive behavior was small and the CPE parameter (Q) wasused to calculate the film thickness according to Eq. (2) (Fig. 9).

Also included in Fig. 9 are the potentiostatic current densities ateach passive potential. Film thickness measurements using ellip-sometry method are represented in Table 2.

As can be seen in Fig. 9, a sharp decrease and increase in themagnitude of current densities occurs at the beginning and end-ing of the passive potential region indicating the start of passivepotential region and transpassive potential, respectively. A ratherstable current density can be observed in the passive region witha minimum occurring around 0 V vs. Hg/HgSO4. This behavior maybe attributed to the change in passive film thickness. The trendobserved for current density in Fig. 9 is similar to that presented inFig. 5. However, since Fig. 5 is plotted on a logarithmic scale the dif-ferences are more difficult to discern than Fig. 9. Moreover, in Fig. 5the potential was swept at 0.16 mV s−1 and the previously formedpassive layers could be still in some effect at higher potentials whilein Fig. 9 the current was measured after an hour of potentiostaticpolarization representing the film formed and stabilized only ateach particular potential.

Different behaviors can be seen in the thickness diagrams shownin Fig. 9. Significant fluctuations are observed in the film thick-ness predictions provided by model A. These fluctuations are notconsistent with current density behavior over the passive poten-tial region. Prediction of film thickness by models B is consistentwith the curve of current density vs. potential. Models B predictsthat the film thickness increases as the current density decreases

Film thickness measurements through ellipsometry as a function of potential.

E vs. (Hg/HgSO4)/V −0.250 −0.050 0.150 0.300Thickness/nm 2.0 2.2 2.6 2.1

F. Mohammadi et al. / Electrochimica Acta 56 (2011) 8727– 8733 8731

el A b

tmHtic

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F

Fig. 9. Passive film thickness predictions by mod

his point results in lower thickness predictions. On the other hand,odel C shows a good trend in thickness predictions up to 0 V vs.g/HgSO4, but a sharp reduction in thickness is observed in poten-

ials higher than 0 V vs. Hg/HgSO4 followed by another rise and falln the curve. This trend in thickness change is not consistent withurrent density.

It can be concluded that the assumption of pure capacitiveehavior for passive film, as presented in model A, does not renderccurate predictions. Another conclusion that can be made fromig. 9 is that the film thicknesses calculated using the values of Qredicted by all models are less than the values of film thicknesseasured by ellipsometry shown in Table 1. Therefore, it can be

oncluded that comparing to the ellipsometry results, an underes-imation of film thickness occurs if capacitance is substituted by

in Eq. (2). Thus, although the measures of n are not significantlyower than unity, it is not appropriate to replace capacitance by Q.

A similar diagram was produced using Eq. (3) and is shown inig. 10. The value of 109 � cm that was used for specific resistivity

Fig. 10. Passive film thickness predictions by

ased on capacitance and models B&C based on Q.

in Eq. (3) was extracted from previous studies [27,28]. Fig. 10 alsoincludes the thickness values obtained by ellipsometry and the cur-rent measurements at each passive potential. It is apparent fromFig. 10 that passive film resistance values predicted by models Band C overestimate the passive film thickness significantly. ModelA, on the other hand, makes predictions with similar magnitudesas those of ellipsometry film thickness measurements. However,the regime of the change of predicted thickness with potential iserratic and is not consistent with the current density variation inthe passive potential region. This observation may be attributed tothe specific resistivity not being a constant and being a function ofthe applied potential. Therefore, using specific resistivity for calcu-lation of film thickness is not an accurate approach unless specificvalues are given for each particular condition.

As it was shown, using Q and R values in calculation of pas-sive film thickness leads to erroneous measures so that Q resultsin underestimation and R values cause overestimation of the filmthickness. It was shown that although the n values are close to

models A–C based on film resistance.

8732 F. Mohammadi et al. / Electrochimica Acta 56 (2011) 8727– 8733

on ef

uncafaeBt

seb

R

Fig. 11. Passive film thickness predictions by models B and C based

nity, using Q is not an effective way of estimating the film thick-ess. There are, however, two approaches to obtaining the effectiveapacitance of a system from the predicted CPE parameters. Thesepproaches were presented by Brug et al. [29] and Hsu and Mans-eld [30]. Two different surface distributions of time constants aressumed in determining the effective capacitance from CPE param-ter Q [12]. A surface distribution of time constants is assumed byrug whereas Hsu and Mansfeld assume a normal distribution ofime constants on the surface.

Hsu and Mansfeld assumed a normal distribution of time con-tants on the surface in which case the global impedance of thelectrode includes contributions from each part of the film and cane represented according to Eq. (4).

f = Z − Re =∑

i

Zi (4)

Fig. 12. Passive film thickness predictions by model C based on

fective capacitance calculated through Hsu and Mansfeld formula.

where Rf is the film impedance, Z is the global impedance, Re is thesolution resistance and Zi represent the local impedance of film lay-ers. As presented in Eq. (4), in the case of normal distribution of timeconstants Re does not contribute to their dispersion and thereforeis deducted from the global impedance to give film impedance. Theeffective capacitance of the film (Ceff) in this case can be calculatedaccording to Eq. (5).

Ceff = Q 1/nRf(1−n)/n (5)

O Chasing et al. [31] and Bidoia et al. [32] described the crucial roleplayed by the ohmic resistance of the solution in the appearance ofCPE behavior for a surface distribution of time constants. While anohmic resistance is inescapable in practical situations, Brug showed

that for a proper surface distribution of time constants the effectivecapacitance can be calculated through Eq. (6) [29].

Ceff = Q 1/nRe(1−n)/n (6)

effective capacitance calculated through Brug formula.

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Hsu and Mansfeld’s approach was applied to predictions madey both models B and C. Using formula (5), the effective capac-

tances were calculated from which the film thicknesses wereerived. These results along the ellipsometry measurements andhe current density are plotted in Fig. 11. As apparent from Fig. 11he predicted thicknesses by both models are neither in agreementith current density nor in the thickness range measured by ellip-

ometry. Therefore, it may be concluded that the time constantistribution is not in the normal direction to the surface.

Brug’s formula has not been applied to model B to obtainffective capacitance. As described earlier, electrolyte resistance isecessary for observation of CPE behavior in a surface distributionf time constants. Brug’s approach requires electrolyte resistancen series with the CPE representing the passive film, which is nothe case in model B. Further investigation is necessary on thepplication of Brug’s formula to more complicated circuit analogs.owever, Brug’s formula was applied to model C and effectivelm capacitances were calculated and the results are presented inig. 12. As can be seen in Fig. 12, predictions of model C accordingo Brug’s formula are in good agreement with current density andllipsometry thickness measurements. Model C predicts 1.71 nmnd 2.45 nm for film thickness at −0.4 and 0.3 V vs. Hg/HgSO4,espectively. These results along with those presented in Fig. 12uggests a surface distribution for time constants on the substrate.

. Conclusions

Application of in situ grinding method revealed that cathodicpolarization does not completely remove the effect of passivelayer previously formed on 304 stainless steel.Ellipsometry measurements indicated that the thickness of thepassive film formed on 304 stainless steel in 0.1 mol dm−3

sodium sulfate solution was between 2 nm and 2.6 nm. Thick-ness measurements by ellipsometry were consistent with currentdensities over the passive potential region.Values of CPE parameter Q predicted by all models resulted inan underestimation of the film thickness whereas film resistancemeasures overestimated the film thickness.Application of Hsu and Mansfeld formula to the experimentaldata did not improve the film thickness predictions by models.

However, using Brug’s approach, model C (porous model) showedbetter consistency with ellipsometry measurements and currentdensity suggesting a surface distribution of time constants on 304stainless steel in 0.1 mol dm−3 sodium sulfate solution.

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a Acta 56 (2011) 8727– 8733 8733

Acknowledgment

The authors would like to thank the Natural Sciences and Engi-neering Research Council of Canada (NSERC) for providing financialsupport.

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