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A Practical Anodic and Cathodic Curve Intersection Model to Understand Multiple Corrosion Potentials of Fe-Based Glassy Alloys in OH- Contained Solutions

  • Y. J. Li,

    Affiliation Key Laboratory for Liquid-Solid Structural Evolution and Processing of Materials, Ministry of Education, Shandong University, Jinan 250061, China

  • Y. G. Wang,

    Affiliation Key Laboratory for Liquid-Solid Structural Evolution and Processing of Materials, Ministry of Education, Shandong University, Jinan 250061, China

  • B. An,

    Affiliation Key Laboratory for Liquid-Solid Structural Evolution and Processing of Materials, Ministry of Education, Shandong University, Jinan 250061, China

  • H. Xu,

    Affiliation Key Laboratory for Liquid-Solid Structural Evolution and Processing of Materials, Ministry of Education, Shandong University, Jinan 250061, China

  • Y. Liu,

    Affiliation Key Laboratory for Liquid-Solid Structural Evolution and Processing of Materials, Ministry of Education, Shandong University, Jinan 250061, China

  • L. C. Zhang,

    Affiliation School of Engineering, Edith Cowan University, 270 Joondalup Drive, Joondalup, Perth, WA6027, Australia

  • H. Y. Ma,

    Affiliation School of Chemistry and Chemical Engineering, Shandong University, Jinan, Shandong 250100, China

  • W. M. Wang

    weiminw@sdu.edu.cn

    Affiliation Key Laboratory for Liquid-Solid Structural Evolution and Processing of Materials, Ministry of Education, Shandong University, Jinan 250061, China

A Practical Anodic and Cathodic Curve Intersection Model to Understand Multiple Corrosion Potentials of Fe-Based Glassy Alloys in OH- Contained Solutions

  • Y. J. Li, 
  • Y. G. Wang, 
  • B. An, 
  • H. Xu, 
  • Y. Liu, 
  • L. C. Zhang, 
  • H. Y. Ma, 
  • W. M. Wang
PLOS
x

Abstract

A practical anodic and cathodic curve intersection model, which consisted of an apparent anodic curve and an imaginary cathodic line, was proposed to explain multiple corrosion potentials occurred in potentiodynamic polarization curves of Fe-based glassy alloys in alkaline solution. The apparent anodic curve was selected from the measured anodic curves. The imaginary cathodic line was obtained by linearly fitting the differences of anodic curves and can be moved evenly or rotated to predict the number and value of corrosion potentials.

Introduction

Fe-based glassy alloys have been widely used in industry because of their high glass-forming ability, soft magnetic properties, good corrosion and wear resistance and ultrahigh strength properties [15]. Recently, the Fe78Si9B13 metallic glass is the leading product in Chinese Fe-based amorphous ribbons market [6]. In 1988 year, Yoshizawa and co-workers [1] invent the alloy labeled as Finemet with the composition of Fe73.5Si13.5B9Cu1Nb3, which has a super soft magnetic property and is used widely in electronic devices. For Fe-based glassy alloys, there exhibits a clear passive zone in the polarization curve in OH- contained solutions, while the passive zone is very short in the solution without OH- [5]. Meanwhile, the corrosion resistance becomes an important factor to consider in using Fe-based glasses [7,8]. Hence, it is valuable to study the electrochemical behavior of Fe78Si9B13 and Fe73.5Si13.5B9Cu1Nb3 glasses in different environments.

Measuring potentiodynamic polarization curve is one of the traditional methods to evaluate electrochemical properties [9,10]. And many works on multiple corrosion potentials in polarization curve for stainless steels in acidic solution have been reported in the literature [1115]. Regarding the influencing factors on the corrosion potentials, Escrivà-Cerdán et al. [16] have found that high-alloyed austenitic stainless steel UNS N08031 (Alloy 31) has three corrosion potentials in phosphoric acid at 60 and 80°C since the temperature can favor the cathodic reaction. Qiao et al. [17] have reported that a certain sulfuric acid and oxygen concentration can induce three corrosion potentials during the polarization of a nitrogen bearing stainless steel. It has been found that the corrosion behavior of pure titanium shows three corrosion potentials when corroded in the H2SO4 solution containing 0.001 M and 0.002 M fluride ions [18]. In addition, the speed jet of phosphoric acid solution to the stainless steel can also induce three corrosion potentials [19]. However, to the authors’ knowledge, three corrosion potentials occurring in the alkaline solution for Fe-based glassy alloys have not been reported so far.

The occurrence of multiple corrosion potentials was reported to be attributed to the instability of passive film. Kelly et al. [20] have reported that the formation mechanism of three corrosion potentials is that the anodic and cathodic Evans lines intersect at three points and there exist one anodic loop and one cathodic loop between the three corrosion potentials. It was also pointed that the origin of the cathodic loop is related to the greater rate of the cathodic reaction than that of the passive current density and the former can conceal the latter at these potentials near the active-passive transition. Qiao et al. [17] have constructed ideal polarization curve models based on the aforementioned mechanism to understand the appearance of three corrosion potentials under certain sulfuric acid concentration and oxygen content. However, the authors have not given the direct relation between the ideal polarization curve and experimental data, which is valuable to discover.

In addition, many works have pointed out that the scanning rate and solution concentration have a significant impact on electrochemical behavior. Zhang et al. [21] have found that the scanning rate can directly affect the Tafel slope. It have been confirmed by Manning et al. that the pitting potential and scanning rate have a functional relationship [22]. In addition, Nakagawa et al. [23] have pointed that the fluoride concentration and pH can affect the polarization test of titanium in NaF solution with various concentrations and pH values.

In this study, our major aim is to build a practical accurate model to explain the occurrence of multiple corrosion potentials of Fe-based glassy ribbons when scanning rate (ν) or NaOH concentration (cNaOH) reaches a specific value. In our model, we process a new method to construct the imaginary cathodic line from the measured anodic polarization curves.

Materials and Methods

The commercial Fe78Si9B13 glassy ribbons and master alloys were supplied by Qingdao Yunlu Energy Technology Company Ltd. The original size of the commercial ribbons was 40 mm in width, 35 μm in thickness and about 20000 mm in length, from which the ribbon samples with size of 3×40 mm were cut for electrochemical tests. Fe78Si9B13 master alloy was prepared by melting iron, pure silicon and Fe-B alloy in medium induction furnace, and Fe73.5Si13.5B9Cu1Nb3 master alloy was obtained by melting of pure iron, silicon, copper, niobium and ferroboron alloy. The Fe73.5Si13.5B9Cu1Nb3 glassy ribbons were obtained using a single copper roller in the lab. X-ray diffraction analysis (as shown in Refs [24] and [25]) proves that the as–spun ribbon samples are in fully amorphous state. Since the most of metallic materials in the industrial application are in crystalline state. In this paper, we focus on the metallic glasses, which are sparser than the metallic crystalline materials; by the way, we are also interested in the electrochemical behavior of their crystalline counterpart, i.e. master alloys. Hence, we choose the master alloys as the comparison.

All electrochemical measurements were carried out using a standard three–electrode system: working electrode, platinum counter electrode and Hg/HgO reference electrode. All the measurements were only conducted on the wheel sides of the ribbons and their free sides were covered by silicone rubber. CHI 660E electrochemical workstation was used for measuring the polarization curves. All experiments were performed at room temperature (298 K). In the measurement of potentiodynamic polarization curves with a series of scanning rates (ν), the electrolyte was 0.6 M NaCl + 0.12 M NaOH. In the measurement of polarization curves with different NaOH concentrations (cNaOH), ν was fixed at 1 mV/s and the electrolyte was 0.6 M NaCl + x M NaOH (0.04 ≤ x ≤ 0.7). All measurements were repeated at least three times to ensure good reproducibility.

To understand the anodic process of Fe78Si9B13 glassy ribbon in 0.6 M NaCl + 0.12 M NaOH, the ribbons were polarized to three different potentials which were located after the first anodic peak, 2ad anodic peak and three corrosion potentials, respectively. The sample surface morphology was examined using scanning electron microscopy (SEM, SU-70). The surface was also analyzed by X-ray photoelectron spectroscopy (XPS, ESCALAB 250Xi) performed on a photoelectron spectrometer with Al-Kα excitation.

Results

Polarization with different scanning rates

Fig 1A shows the electrochemical polarization curves of Fe78Si9B13 glassy ribbons in 0.6 M NaCl + 0.12 M NaOH solution with the scanning rates ν = 0.5–5 mV/s. As ν is reduced from 5 to 1.5 mV/s, the polarization curves have the similar shapes with two current density peaks P1 and P2 in A-B-C and C-D-E zones, respectively. As ν was further reduced to 1 mV/s, three corrosion potentials appear with the sacrifice of P1, and the polarization curve is divided into I, II, I’ and II’ zones. The current density in both I and I’ zones is negative, and that in II and II’ is positive. Hence, II is called anodic loop and I’ is called cathodic loop. The curve with ν = 0.5 mV/s has only one corrosion potential, and there exist one and two small troughs before and after it respectively. It should be noted that, the measured polarization curve of Fe78Si9B13 master alloy with ν = 1 mV/s has one corrosion potential, and no distinct current density peak P1 or P2 (Fig 1A). This indicates that the occurrence of three corrosion potentials is not only related to ν, but also to microstructure.

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Fig 1. Electrochemical tests of samples.

(a) Potentiodynamic polarization curves of Fe78Si9B13 glassy ribbons and the corresponding master alloy with different scanning rates ν in 0.6 M NaCl + 0.12 M NaOH solution. For clarity, the curves of Fe78Si9B13 glassy ribbons with ν = ν0, 2 ν0, 3 ν0, 4 ν0, 6 ν0 and 10 ν0 are shifted upward by multiplying the raw data with 102, 104, 106, 108, 1010 and 1012 respectively. (b) Variation of the current densities iP1 and peak potentials EP1 with the square root of ν. (c) Variation of the current densities iP2 and peak potentials EP2 with ν. P1 and P2 indicate the two current density peaks such as A-B-C and C-D-E zones in the polarization curve with ν = 10 ν0 (ν0 = 0.5 mV/s), respectively.

http://dx.doi.org/10.1371/journal.pone.0146421.g001

Moreover, in Fig 1A, as the scanning rate v is decreased from 5 to 2 mV/s, the pitting potential Epit decreases, whereas Epit increases with further decreasing v from 1.5 to 0.05 mV/s. In the first changing range of v, the positive relationship between Epit and v can be explained by the point defect medol (PDM) [26,27]. However, in the second range, it is found that the passive current density ipass is apparently lower than that in the first range, and according to the argument that cumulative anodic change density, Qc, is constant, which is presented as [28]: (1) where Eocp is the open circuit potential, Δtp is the anodic polarization time duration until the stable pitting. Now we get: (2)

When ipass has a larger decreasing rate than the decreasing rate of v, Epit might increase. Hence, it is understood that Epit increases when v varies from 1.5–0.05 mV/s. This phenomenon is similar to the fact that Qc and Epit sometimes increase abnormally with decreasing v in the experimental data of Zhang and co-workers’ work [26].

As seen from Fig 1B, the values of current density ip and the corresponding potential Ep of P1 vary linearly with the square root of the scanning rate ν. According to Müller and Calandra’s model [29,30], P1 can be explained by ohmic resistance caused by the insoluble reaction products on the sample surface and the ip1 and Ep1 can be expressed as (3) (4) where k is the specific conductivity of the solution within the pores of the film, ρ the film density, δ the film thickness, M the molar mass of the film formed by the flow of Coulombs, R0 the external resistance, θP the surface fractional coverage and A0 the electrode area.

Fig 1C shows that the ip of P2 decreases linearly but the corresponding Ep decreases slightly with the decrease of the scanning rate. According to Srinivasan and Gileadi’s model [31], P2 is related to an adsorption process and the ip2 and Ep2 can be defined by (5) (6) where K is the velocity constant ratio of adsorption to desorption, γ is the charge required to form a monolayer of adsorbed species and other symbols have their usual meaning in electrochemistry.

In addition, the polarization curves of Fe73.5Si13.5B9Cu1Nb3 glassy ribbons in 0.6 M NaCl + 0.12 M NaOH solution with ν = 6–10 mV/s are shown in Fig 2. The polarization curves with ν = 8–10 mV/s have a similar shape with one current density peak. With decreasing ν, the current density of the peak decreases, but its potential approximately remains constant. As ν decreases to 7 mV/s, three corrosion potentials present like Fe78Si9B13 glassy ribbon with 1 mV/s and they divide the polarization curve into I, II, I’ and II’ zones with the current density symbol of negative, positive, negative and positive, respectively. The polarization curve with ν = 6 mV/s has only one corrosion potential with a small trough before it. Similarly, the polarization curve of Fe73.5Si13.5B9Cu1Nb3 master alloy with 7 mV/s does not have three corrosion potentials or a distinct current density peak in anodic part. In addition, the Epit of samples creases with decreasing v, which is similar to the phenomenon in the second changing range of v in Fe78Si9B13 (Fig 1A).

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Fig 2. Potentiodynamic polarization curves of Fe73.5Si13.5B9Cu1Nb3 glassy ribbons and the corresponding master alloy with different scanning rates ν in 0.6 M NaCl + 0.12 M NaOH solution.

For clarity, the curves of Fe73.5Si13.5B9Cu1Nb3 glassy ribbons with ν = 6 ν0, 7 ν0, 8 ν0, 9 ν0 and 10 ν0 are shifted upward by multiplying the raw data with 102, 104, 106, 108 and 1010 respectively.

http://dx.doi.org/10.1371/journal.pone.0146421.g002

Polarization with different NaOH concentrations

Fig 3 displays the polarization curves of Fe78Si9B13 glassy alloys in 0.6 M NaCl + x M NaOH solutions with the scanning rate ν = 1 mV/s. The characteristic of the polarization curve in Fig 3 as well as those in Figs 1A and 2 are listed in Table 1. The curves with cNaOH = 0.2–0.7 M have two current density peaks as the same as those obtained in 0.6 M NaCl + 0.12 M NaOH solution with ν = 5 to 1.5 mV/s. With decreasing cNaOH, the corrosion potential and both two peaks’ potentials shift to right, and the passive range shortens. When cNaOH decreases to 0.2 M, hydrolysis reaction near 0.6 V transforms into pitting corrosion reaction. Three corrosion potentials Ec1, Ec2 and Ec3 occur and divide the polarization curve into I, II, I’ and II’ zones looped with negative and positive symbols when cNaOH decreases to 0.12 and 0.08 M. Apparently, the values of Ec1, Ec2 or Ec3 with cNaOH = 0.08 M respectively are higher than the corresponding one with cNaOH = 0.12 M. When cNaOH decreases to 0.04 M, the number of potentials decreases to one and the pitting potential Epit becomes further negative. The OH- dependent Epit obeys the following relation between the pitting potential and the PH of the electrolyte [32]: (7) where the value of a is 690 mV and b is 21 mV for Sn66Ni34 alloy in NaCl solution with various pH values. We use Eq (7) to give only a qualitative explanation on the cNaOH dependent Epit is present paper.

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Fig 3. Potentiodynamic polarization curves of Fe78Si9B13 glassy ribbons in 0.6 M NaCl + x M NaOH (x = 0.04–0.7) solution with ν = 1mV/s.

For clarity, the curves with c = 0.8 c0, 1.2 c0, 2 c0, 4 c0, 5 c0 and 7 c0 are shifted upward by multiplying the raw data with 102, 104, 106, 108, 1010 and 1012 respectively.

http://dx.doi.org/10.1371/journal.pone.0146421.g003

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Table 1. Variation of polarization parameters of Fe78Si9B13 and Fe73.5Si13.5B9Cu1Nb3 glassy ribbons.

http://dx.doi.org/10.1371/journal.pone.0146421.t001

For clarity, the characteric parameters of the measured polarization curves of Fe78Si9B13 and Fe73.5Si13.5B9Cu1Nb3 glassy samples with various scanning rates and cNaOH as well as their standard deviation are listed in Table 1.

SEM and XPS measurement after various polarizations

In order to investigate the nature of the anodic current density peaks of Fe78Si9B13 glassy alloys in 0.6 M NaCl + 0.12 M NaOH, the scanning rate ν = 1 mV/s and 2 mV/s were chosen to polarize the glassy ribbons until three different points S1, S2 and S3, which are indicated in Fig 1A. Samples S1 and S2 were polarized with ν = 2 mV/s until the end of the first and second anodic peaks, respectively; while sample S3 was polarized to a similar potential to S2 with ν = 1 mV/s after experiencing three corrosion potentials. The surface morphologies of these samples are shown in Fig 4. A lot of white flake-like products in size of about 0.1–1 μm present on all the samples and their size, i.e. the surface roughness of samples, increases in order of S1 < S2 < S3. Meanwhile, the surface morphology of S3 is similar to that of S2 rather than S1.

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Fig 4. SEM micrographs for the surfaces of (a) and (b) S1, (c) and (d) S2, and (e) and (f) S3 samples.

S1 and S2 were polarized with ν = 2 mV/s until the end of the first and second anodic peaks, respectively, while S3 was polarized to a similar potential to S2 with ν = 1 mV/s after experiencing three corrosion potentials. S1, S2 and S3 are indicated in Fig 1A.

http://dx.doi.org/10.1371/journal.pone.0146421.g004

Fig 5 shows the X-ray photoelectron spectroscopy (XPS) spectra of Fe 2p and Si 2p recorded from the surfaces of S1, S2 and S3. For the spectra of Fe 2p, the total peak intensity of S1 is greater than that of S2 or S3, possibly due to the higher surface roughness of S2 and S3. The Fe 2p spectrum can be decomposed into two peaks belonging to FeO and Fe2O3 [33]. According to earlier work [34], the XPS spectrum of Si 2p of S1 can be decomposed into three peaks: SiO2, SiOx/Si and Si. But for S2 and S3, it can only be decomposed into two peaks corresponding to SiO2 and SiOx/Si. The decomposed peak fractions for Fe 2p and Si 2p spectra are listed in Table 2. Apparently the FeO and SiO2 fractions of samples change in the order S1 > S2 > S3, but the Fe2O3 and SiOx/Si fractions change oppositely. Overall, the decomposited XPS result of S3 is similar to that of S2, but different from S1.

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Fig 5. XPS spectra of (a) Fe 2p and (b) Si 2p recorded from the surfaces of S1, S2 and S3.

S1 and S2 were polarized with ν = 2 mV/s until the end of the first and second anodic peaks, respectively, while S3 was polarized to a similar potential to S2 with ν = 1 mV/s after experiencing three corrosion potentials. S1, S2 and S3 are indicated in Fig 1A.

http://dx.doi.org/10.1371/journal.pone.0146421.g005

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Table 2. The fraction of decomposed peaks from XPS spectra for Fe 2p and Si 2p of the surfaces of S1, S2 and S3.

http://dx.doi.org/10.1371/journal.pone.0146421.t002

Discussion

Practical model to explain the occurrence of multiple corrosion potentials of Fe-based glassy ribbons

From Fig 1A, the polarization curves of Fe78Si9B13 glassy ribbons with the scanning rate ν ≥ 1.5 mV/s have two current density peaks P1 and P2 in the anodic part. As ν = 1 mV/s, there are three corrosion potentials in the polarization curve. Kelly et al. [20] have pointed that three corrosion potentials Ec1, Ec2, and Ec3 are the intersecting points of anodic and cathodic Evans lines based on the following equation (8) where ia is anodic current density, ic is cathodic current density. Similarly, Qiao et al. [17] have supposed a schematic mechanism of corrosion with three Ec by intersecting an ideal anodic polarization curve with an ideal cathodic reaction line, there are different intersection numbers by changing the former’s or latter’s position.

It’s known that the cathodic reaction in alkaline solution is the oxygen reduction reaction [35] (9) and /or the water reduction reaction (10)

The cathodic part does not show the limiting value representing the oxygen reduction reaction, but shows a relatively higher current density (Fig 1A). In addition, a lot of gas bubbles can be observed on the sample corroding surface in the experiment. Both phenomena show that the cathodic reaction in alkaline solution is dominated by water reduction (reaction (10)) [35]. Hence, decreasing cNaOH can enhance the cathodic reaction and increase the corrosion potential (Fig 3). According to Lee [36], there are three possible determining steps in reaction (10).

(11a)(11b)(11c)

The reaction rate U can be written as the following formula based on reaction (11a) by neglecting the back reaction (12) where n is the total number of electrons involved in the reaction, α the transfer coefficient, ψ the potential between the sample and the solution and Kf the rate constant for the forward reaction. Then the current density i can be written as (13) where aH2O denotes the activity of H2O. Combining Eqs (12) with (13), we will get (14)

So the cathodic reaction can be represented by a line in the half logarithmic coordinates. Such linear relation in logi-ψ can be obtained in a straightforward way according to Ref. [36]. Hence, it is understood that Kelly and Qiao used the cathodic line to explain the variation of polarization curves [17,20].

However, there are several unknown parameters like Kf, α and aH2O in present polarization process. In the following sections, we propose a simple method to deduce an imaginary cathodic line, evenly move it or rotate it, and try to discuss the evolution of the polarization curves, especially the formation of three corrosion potentials (Figs 1A, 2 and 3).

Evenly moving the imaginary cathodic line.

As shown in Fig 1A, the active anodic peaks P1 and P2 with the scanning rate ν = 5 mV/s can be divided into four potential ranges, i.e., AB, BC, CD and DE. According to Lu et al. [37], the measured current density i(E) of anodic polarization curve except the steady passive ranges can be expressed by (15) where i0-m, E0 and B are exchange current density, equilibrium potential and symmetry like coefficient, respectively. Generally, B is also denoted by (15a) here β is symmetry coefficient, R is gas constant, T is temperature, F is Faraday’s constant [37]. In this paper, R, T and F are constants, which can be move before the exponent function.

From Figs 1A and 3 and Table 1, the second current density peak varies much smaller than the first peak with the variation of ν and cNaOH. So P2 could be omitted in following analysis for simplification like omitting the higher terms in series expansion. Hence, the anodic polarization curves with ν = 5 and 3 mV/s could be described as following: (16) (17)

Since the curve shape with ν = 5 mV/s is similar to that with ν = 3 mV/s, a further simplification and assumption could be made as (18) and (19) hence, the current density difference Δi can be expressed as (20)

Herein, we set (21) where a0 is constant and a0>β1. Now, by expansing the right item in Eq (21) with Talor`s series and omitting the higher order terms, the difference Δi can be expressed as (22) (23)

Eq (23) shows a liner relation between logΔi and ψ. Its intercept and slope can be obtained by linearly fitting the difference i-i′ of the measured curves which is shown in Fig 6A. When ν changes, the exchange current density i0–1 should change according to Eq (17), and then log(-Δi0), i.e. the intercept of the Eq (23), changes; while the slope of Eq (23) does not change. In other words, the line of logΔi-ψ moves evenly with changing ν.

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Fig 6. The schematic of practical cathodic and anodic curve intersection model.

(a) Deducing of imaginary cathodic line from the difference of measured anodic curves; (b) deducing the corrosion potentials of Fe78Si9B13 glassy ribbon with 1 mV/s from that with ν = 5 mV/s in 0.6 M NaCl + 0.12 M NaOH solution by imposing an extrapolated imaginary cathodic line, i.e. moving evenly the imaginary cathodic line; (c) deducing the polarization curve of Fe73.5Si13.5B9Cu1Nb3 glassy ribbon with ν = 7 mV/s from that with ν = 10 mV/s in 0.6 M NaCl + 0.12 M NaOH solution by rotating the imaginary cathodic line; and (d) deducing the polarization curve of Fe78Si9B13 glassy ribbons with cNaOH = 0.12 and 0.08 M from that with 0.7 M by rotating the imaginary cathodic line.

http://dx.doi.org/10.1371/journal.pone.0146421.g006

Apparently, Eq (23) is similar to Eq (14). If Eq (20) is approximately regarded as Butler-Volmer formula, the current density difference i and current density i with ν = 5 mV/s can be regarded as imaginary cathodic and anodic current densities, respectively, i.e. i′ can be deduced if Δi and i are known. In other words, we can predict the characteristic of a new current density i′ by subtracting an imaginary cathodic line i from the apparent cathodic curve i with v = 5 mV/s. In present work, the construction of an imaginary cathodic line is explained in the following and illustrated in Fig 6 and Table 3.

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Table 3. The values of slope and intercept for imaginary cathodic line (ICL) for the anodic and cathodic curve intersection model of of the two samples; solution: 0.6 M NaCl+0.12 M NaOH solution.

http://dx.doi.org/10.1371/journal.pone.0146421.t003

Firstly, we subtract the curves with ν = 3 mV/s from that with ν = 5 mV/s, and fitting the difference into a line in logΔi-E graph with a intercept and a slope as shown in Fig 6A and denoted in Table 3 with the v change of 5 mV/s → 3 mV/s; we also subtract the curves with v = 2 mV/s and 1.5 mV/s from that with v = 5 mV/s and obtain the groups of slopes and intercepts, which are listed in Table 3 and denoted by the ν changes of 5 mV/s → 2 mV/s and 5 mV/s → 1.5 mV/s, respectively. Here, the slopes fluctuate with an average value; while the intercepts decrease with decreasing ν, which is consistent with Eq (23). Secondly, we choose the average value of above slopes and the linearly extrapolated value from the known intercepts in Table 3 to make the imaginary cathodic line for v = 1 mV/s i.e. moving the known imaginary cathodic line upward evenly, which is denoted by the ν change of 5 mV/s → 1 mV/s.

After constructing the imaginary cathodic line for ν = 1 mV/s, we impose it on the apparent anodic curve with ν = 5 mV/s, and intersecting the apparent anodic curve at three points, and indicating that the deduced polarization curve with 1 mV/s has three corrosion potentials (Fig 6B). In addition, according to Eq (20), the current density symbol of I and I’ zones, in which the anodic curve is lower than the imaginary cathodic line, is negative, being consistent with the measured polarization curve (Fig 1A). As ν = 0.5 mV/s, the imaginary cathodic line, whose slope and intercept are determinded with the ν change of 5 mV/s → 0.5 mV/s in Table 3, intersects the apparent anodic curve at about -0.6 VHg/HgO and is nearly tangent to P1 of the apparent anodic curve at about -0.8 VHg/HgO. Thus, a trough rather thanEc1 or Ec2 appears in the measured polarization curves with ν = 0.5 mV/s. In short words, the imaginary cathodic line and apparent anodic curve intersection model can be used to deduce the multiple corrosion potentials in polarization curves.

Rotating the imaginary cathodic line.

For the polarization curves of Fe73.5Si13B9Cu1Nb3 glassy ribbons with various ν (Fig 2), the anodic and cathodic curve intersection model is also applied based on Eq (20). Here, because the curve with ν = 10 mV/s is similar to that with ν = 9 mV/s, Eqs (16) and (17) are used to describe the former and latter curves, respectively. Assuming (24a) (24b)

We will get (25)

Here, we set (26) where a′ varies with ν and a′ >β2. Combining Eqs (25) with (26), expansing the right item of Eq (26) with Talor`s series and omitting the higher order terms, we will have (27)

Eq (27) is also similar to Eq (14), so it can be considered as an imaginary cathodic line. With changing ν, its intercept is constant, but its slope changes, i.e. the line rotates around the intersection with vertical axis (ψ = 0), which is different from Eq (23). For predicating the corrosion potential with a given ν (Fig 2), we use the active anodic region of the curve with 10 mV/s as the apparent anodic curve. After subtracting the measured curves with 9 and 8 mV/s and linearly fitting the differences, the intercepts and slopes of the lines in logΔi-E can be obtained, which are listed in Table 3 and denoted by changing ν with 10 mV/s → 9 mV/s and 10 mV/s → 8 mV/s, respectively. Here, the variation of intercept is smaller than that of slope, which is consistent with Eq (27). So the average value of intercepts is chosen for constructing an imaginary cathodic line for ν = 7 mV/s, and its slope is linearly extrapolated from the first two slopes i.e. rotating the known imaginary cathodic line around its intersection with vertical axis (as shown by the line in Fig 6C and denoted by the ν change of 10 mV/s → 7 mV/s in Table 3). After constructing the imaginary cathodic line with ν = 7 mV/s, we impose it on the apparent anodic curve and get three interceptions at different potentials, which is consistent with the measured curve (Fig 2). In addition, according to Eq (25), the current density symbol of I and I’ zones is negative, being consistent with the measured polarization curve (Fig 2). As ν = 6 mV/s, the imaginary cathodic line, corresponding to the ν change of 10 mV/s → 6 mV/s in Table 3, intersects the apparent anodic curve at about -0.3 VHg/HgO and simultaneously tends to be tangent to the current density peak of the apparent anodic curve. Thus, the measured polarization curve with ν = 6 mV/s contains a trough before the corrosion potential.

Meanwhile, the measured corrosion potentials , and and the deduced ones and for Fe78Si9B13 and Fe73.5Si13.5B9Cu1Nb3 glassy ribbons in 0.6 M NaCl + 0.12 M NaOH solution with ν = 1 and 7 mV/s are summarized in Table 4, respectively. For Fe78Si9B13 glassy ribbons, the deduced or respectively is slightly higher than the corresponding measured or , but is lower than . It is explained by the fact that the first peak of measured curves moves to left side with decreasing ν and their second peak moves to right (Fig 1A). For Fe73.5Si13.5B9Cu1Nb3 glassy ribbons, each measured corrosion potential is very close to the deduced counterpart, which is consistent with the fact that the current density peaks of the polarization curves approximately have no lateral displacement (Fig 2).

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Table 4. The measured and deduced value and for the two samples; solution: 0.6 M NaCl + 0.12 M NaOH solution.

http://dx.doi.org/10.1371/journal.pone.0146421.t004

In addition, using the anodic and cathodic curve intersection model, the evolution of polarization curves with various hydroxyl concentrations can also be analyzed by the imaginary cathodic line with Eqs (23) or (27). The active anodic region of the curve obtained in the solution with cNaOH = 0.7 M is chosen as the apparent anodic curve. After subtracting the curves obtained in solutions with cNaOH = 0.5, 0.4 and 0.2 M and linearly fitting the difference, various intercepts and slopes could be obtained, which are summarized in Table 5 and denoted by the cNaOH changes of 0.7 M → 0.5 M, 0.7 M → 0.4 M and 0.7 M → 0.2 M, respectively. The intercept decreases slightly with the decrease of NaOH concentration, which is opposite to the desired varying tendency of an imaginary cathodic line in our intersection model. Hence, to deduce the corrosion potentials with cNaOH = 0.12, 0.08 and 0.04 M, we select Eq (27) as the starting point, set the intercept as a constant equal to the average value of the first three intercepts, and linearly extrapolate the slope by the first three slopes i.e. rotating the known imaginary cathodic line around its intersection with vertical axis (ψ = 0 (as shown by the lines in Fig 6D and denoted by the cNaOH changes of 0.7 M → 0.12 M and 0.7 M → 0.08 M in Table 5)).

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Table 5. The values of slope and intercept for imaginary cathodic line (ICL) for the anodic and cathodic curve intersection model of Fe78Si9B13 glassy ribbon; solution: 0.6 M NaCl + x M NaOH.

http://dx.doi.org/10.1371/journal.pone.0146421.t005

After getting the imaginary cathodic line, the anodic and cathodic curve intersection model can be used to deduce the corrosion potentials with 0.12 and 0.08 M NaOH solutions (Fig 6D). As cNaOH = 0.12 and 0.08 M, both the imaginary cathodic lines whose slope and intercept are determinded with the cNaOH changes of 0.7 M → 0.12 M and 0.7 M → 0.08 M, respectively in Table 5, intersect the apparent anodic curve at three corrosion potentials (Fig 6D). According to Eq (25), the deduced current density symbol of I and I’ zones is negative and consistent with the measured polarization curve (Fig 3). As cNaOH = 0.04 M, the imaginary cathodic line, whose slope and intercept are determinded with the cNaOH change of 0.7 M → 0.04 M in Table 5, intersects the apparent anodic curve at about -0.6 VHg/HgO and is nearly to be tangent to P1 of the apparent anodic curve, being consistent with the emergence of the trough in the measured polarization curve with cNaOH = 0.04 M. The measured and deduced corrosion potentials of 0.12 and 0.08 M are summarized in Table 6. Apparently, three corrosion potentials Ec1, Ec2 and Ec3 in the polarization curves are successfully predicted. The deduced corrosion potential , or is slightly lower than the corresponding measured , or respectively, which is consistent with the fact that two current density peaks move to right with decreasing cNaOH (Fig 3).

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Table 6. The measured and deduced value and for Fe78Si9B13 glassy ribbons; solution: 0.6 M NaCl + 0.12 and 0.08 M NaOH.

http://dx.doi.org/10.1371/journal.pone.0146421.t006

It should be noted that choosing the starting polarization curve is very important in our anodic and cathodic curve intersection model. If the ν or cNaOH of the starting polarization curves is far beyond the ν or cNaOH for multiple potentials phenomenon, our model will become invalid. Moreover, if the ν or cNaOH of the starting polarization curves is far below the ν or cNaOH for the multiple potentials phenomenon, our model will fail to predict it. It should be noted that the applicable v range of our intersection model for Fe78Si9B13 ribbon is different from that for Fe73.5Si13.5B9Cu1Nb3 ribbon, due to the occurrence of their multiple corrosion potentials at different v.

Nature of the first and second peaks in the anodic polarization curves of Fe-Si-B glassy ribbons

According to the previous explanation about the anodic dissolution of Fe-based alloys in alkaline solution [38], the first current density peak (P1) can be expressed (28) (29) (30) (31)

Kelsall et al. [39] have reported that the oxidation of silicon in steel is in preference to iron at low potentials. In present case, Eq (32) should be included in the first current peak P1.

(32)

Since SiO2 bears a high chemical stability and a dielectric character [40,41], it is understood that the first peak is an ohmic resistance controlled reaction (Fig 1B).

For the second peak (P2), it is a process of the formation of stable Fe2O3 [42], and can be expressed (33) (34)

Kelsall et al. [39,43] have pointed out that Fe2SiO4 can be formed from iron oxide and SiO2/Si (IV) species at higher potentials. So the second current peak P2 should also contain the following reaction (35)

According to the previous paper [44], both Eqs (33) and (34) are controlled by the adsorption step of OH-, and it is expected that the second peak is characterized as the adsorption controlled reaction (Fig 1C).

As shown in Fig 1A, sample S1 has only experienced the first peak (P1) with the scanning rate ν = 2 mV/s in 0.6 M NaCl + 0.12 M NaOH solution, S2 has experienced the first and second peaks (P1 and P2) with ν = 2 mV/s. As indicated by reactions (28)–(32), the first current peak P1 is the formation process of FeO, Fe2O3 and SiO2. And the second current peak P2 is the conversion process from FeO to Fe2O3 (Eqs (33) and (34)). In addition, the formation of P2 consumes some SiO2 according to Eq (35). These reactions are confirmed by the higher SiO2 and FeO fractions of S1 in XPS results compared with S2 (Fig 5 and Table 2).

Sample S3 has experienced three corrosion potentials (Ec1, Ec2 and Ec3) and P2, ending the polarization at a similar potential to S2 with ν = 1 mV/s. The XPS decomposition similarity between S2 and S3 (Fig 5 and Table 2) indicates that, although the polarization curves of S3 contains three corrosion potentials Ec1, Ec2 and Ec3 at the expense of the formation of P1, the anodic reaction of P1 still happened, which is hidden by the enhanced cathodic reaction. In other words, it is reasonable to obtain the measured anodic curves with ν = 5 mV/s as the apparent anodic curve in our practical model.

According to the above analysis, the distinct peak P1 with formation of FeO, Fe2O3 and SiO2 is necessary condition for the appearance of three corrosion potentials according to the practical model; while the second peak is not the necessary condition for their appearance in polarization curves. It should be noted that the formation of the anodic peak P1 or P2 is closely associated with the composition and microstructure of Fe-based alloys.

Conclusions

Two anodic peaks (P1 and P2) present in the polarization curve of Fe78Si9B13 glassy ribbon in NaCl + NaOH solution when the scanning rate ν or NaOH concentration cNaOH is high enough. The former peak formation is ohmic resistance controlled, which is associated with the formation of SiO2, and the latter is adsorption controlled, accompanying the damage of the SiO2 film. The formation of P1 or P2 is closely associated with the composition and microstructure of Fe-based alloys. Three corrosion potentials (Ec1, Ec2 and Ec3) are observed in the polarization curve for Fe-based glassy ribbons in OH- contained solutions when ν or cNaOH reaches a specific value.

The occurrence of multiple corrosion potentials is explained by a practical anodic and cathodic curve intersection model. In this model, we choose the measured anodic curve as the apparent anodic curve, from it subtract the measured anodic curves with various ν or cNaOH and linearly fit the difference as the imaginary cathodic line. By moving the cathodic line evenly or rotating it and imposing it with the apparent anodic curve, the number of intersections can be obtained and the number of corrosion potentials can be predicted. The practical model shows that the distinct P1 is the necessary condition for the occurrence of three corrosion potentials.

Acknowledgments

The work is supported by the National Natural Science Foundation of China (No. 51171091 and No.51471099), the National Basic Research Program of China (973 Program) (No. 2012CB825702), the Excellent Youth Project of Shandong Natural Science Foundation (No. JQ201012) and the Australian Research Council (ARC) Discovery Projects (DP130103592).

Author Contributions

Conceived and designed the experiments: WMW. Performed the experiments: YJL YGW BA YL. Analyzed the data: WMW. Contributed reagents/materials/analysis tools: WMW. Wrote the paper: WMW LCZ HYM. Modified the revised manuscript: HX.

References

  1. 1. Yoshizawa Y, Oguma S, Yamauchi K (1988) New Fe-based soft magnetic alloys composed of ultrafine grain structure. Journal of Applied Physics 64: 6044–6046. doi: 10.1063/1.342149
  2. 2. Pang SJ, Zhang T, Asami K, Inoue A (2002) Synthesis of Fe-Cr-Mo-C-B-P bulk metallic glasses with high corrosion resistance. Acta Materialia 50: 489–497. doi: 10.1016/s1359-6454(01)00366-4
  3. 3. Inoue A, Shen BL, Chang CT (2006) Fe- and Co-based bulk glassy alloys with ultrahigh strength of over 4000MPa. Intermetallics 14: 936–944. doi: 10.1016/j.intermet.2006.01.038
  4. 4. Li YJ, An B, Wang YG, Liu Y, Zhang HD, Yang XG, et al. (2014) Severe corrosion behavior of Fe78Si9B13 glassy alloy under magnetic field. Journal of Non-Crystalline Solids 392–393: 51–58. doi: 10.1016/j.jnoncrysol.2014.03.030
  5. 5. An B, Li YJ, Liu Y, Wang YG, Zhang LC, Wang WM (2014) Unique corrosion behavior of Fe78Si9B13 glassy alloy with different circumferential speeds under various chloride ion levels. Journal of Alloys and Compounds 593: 16–23. doi: 10.1016/j.jallcom.2014.01.086
  6. 6. Gui Q. Composition, technology and properties of 1K101 amorphous ribbons: Central institute of iron and steel; 2012.
  7. 7. Han Y, Kong FL, Chang CT, Zhu SL, Inoue A, Shalaan E, et al. (2015) Syntheses and corrosion behaviors of Fe-based amorphous soft magnetic alloys with high-saturation magnetization near 1.7 T. Journal of Materials Research 30: 547–555 doi: 10.1557/jmr.2014.389
  8. 8. Shi MJ, Pang SJ, Zhang T (2015) Towards improved integrated properties in FeCrPCB bulk metallic glasses by Cr addition. Intermetallics 61: 16–20 doi: 10.1016/j.intermet.2015.02.010
  9. 9. Yim CD, Yang J, Woo SK, Ha HY, You BS (2015) The effects of microstructural factors on the corrosion behaviour of Mg-5Sn-xZn (x = 1, 3wt%) extrusions. Corrosion Science 90: 597–605. doi: 10.1016/j.corsci.2014.11.003
  10. 10. Zarrouk A, Hammouti B, Lakhlifi T, Traisnel M, Vezin H, Bentiss F (2015) New 1H-pyrrole-2, 5-dione derivatives as efficient organic inhibitors of carbon steel corrosion in hydrochloric acid medium: Electrochemical, XPS and DFT studies. Corrosion Science 90: 572–584. doi: 10.1016/j.corsci.2014.10.052
  11. 11. Qiao YX, Zheng YG, Ke W, Okafor PC (2009) Electrochemical behaviour of high nitrogen stainless steel in acidic solutions. Corrosion Science 51: 979–986. doi: 10.1016/j.corsci.2009.02.026
  12. 12. Ye W, Li Y, Wang FH (2006) Effects of nanocrystallization on the corrosion behavior of 309 stainless steel. Electrochimica acta 51: 4426–4432. doi: 10.1016/j.electacta.2005.12.034
  13. 13. Pan C, Liu L, Li Y, Wang SG, Wang FH (2011) Passive film growth mechanism of nanocrystalline 304 stainless steel prepared by magnetron sputtering and deep rolling techniques. Electrochimica Acta 56: 7740–7748. doi: 10.1016/j.electacta.2011.05.106
  14. 14. Pan C, Liu L, Li Y, Zhang B, Wang FH (2012) The electrochemical corrosion behavior of nanocrystalline 304 stainless steel prepared by magnetron sputtering. Journal of the Electrochemical Society 159: C453–C460. doi: 10.1149/2.034211jes
  15. 15. Meng GZ, Li Y, Shao YW, Zhang T, Wang YQ, Wang FH (2014) Effect of Cl- on the Properties of the Passive Films Formed on 316L Stainless Steel in Acidic Solution. Journal of Materials Science & Technology 30: 253–258. doi: 10.1016/j.jmst.2013.07.010
  16. 16. Escrivà-Cerdán C, Blasco-Tamarit E, García-García DM, García-Antón J, Guenbour A (2012) Passivation behaviour of Alloy 31 (UNS N08031) in polluted phosphoric acid at different temperatures. Corrosion Science 56: 114–122. doi: 10.1016/j.corsci.2011.11.014
  17. 17. Qiao YX, Zheng YG, Okafor PC, Ke W (2009) Electrochemical behaviour of high nitrogen bearing stainless steel in acidic chloride solution: Effects of oxygen, acid concentration and surface roughness. Electrochimica Acta 54: 2298–2304. doi: 10.1016/j.electacta.2008.10.038
  18. 18. Wang ZB, Hu HX, Liu CB, Zheng YG (2014) The effect of fluoride ions on the corrosion behavior of pure titanium in 0.05 M sulfuric acid. Electrochimica Acta 135: 526–535. doi: 10.1016/j.electacta.2014.05.055
  19. 19. Guenbour A, Hajji MA, Jallouli EM, Bachir AB (2006) Study of corrosion–erosion behaviour of stainless alloys in industrial phosphoric acid medium. Applied Surface Science 253: 2362–2366. doi: 10.1016/j.apsusc.2006.05.005
  20. 20. Kelly RG, Scully JR, Shoesmith DW, Buchheit RG (2002) Electrochemical techniques in corrosion science and engineering, 270 Madison Avenue, New York: Marcel Dekker, Inc. doi: 10.1201/9780203909133
  21. 21. Zhang XL, Jiang ZH, Yao ZP, Song Y, Wu ZD (2009) Effects of scan rate on the potentiodynamic polarization curve obtained to determine the Tafel slopes and corrosion current density. Corrosion Science 51: 581–587. doi: 10.1016/j.corsci.2008.12.005
  22. 22. Manning PE (1980) The effect of scan rate on pitting potentials of high performance alloys in acidic chloride solution. Corrosion 36: 468–474. doi: 10.5006/0010-9312-36.9.468
  23. 23. Nakagawa M, Matsuya S, Shiraishi T, Ohta M (1999) Effect of fluoride concentration and pH on corrosion behavior of titanium for dental use. Journal of Dental Research 78: 1568–1572. pmid:10512392 doi: 10.1177/00220345990780091201
  24. 24. Ye SL, Li XY, Bian XF, Wang WM, Yin LJ, An B (2013) Remelting treatment and heredity phenomenon in the formation of Fe78Si9B13 amorphous alloy. Journal of Alloys and Compounds 562: 143–149. doi: 10.1016/j.jallcom.2013.02.006
  25. 25. An B. Effects of cooling rate and solution concentration on corrosion resistance of Fe-based amorphous alloys: Shandong University; 2014.
  26. 26. Zhang YZ, Urquidi-Macdonald M, Engelhardt GR, Macdonald DD (2012), Development of localized corrosion damage on low pressure turbine disks and blades: II. Passivity breakdown. Electrochimica Acta 69: 12–18 doi: 10.1016/j.electacta.2012.01.023
  27. 27. Urquidi‐Macdonald M, Macdonald DD (1987) Theoretical Distribution Functions for the Breakdown of Passive Films. Journal of the Electrochemical Society 134: 41–46 doi: 10.1149/1.2100433
  28. 28. Yi Y, Cho P, Zaabi AA, Addad Y, Jang C (2014) Potentiodynamic polarization behaviour of AISI type 316 stainless steel in NaCl solution. Corrosion Science 74: 92–97 doi: 10.1016/j.corsci.2013.04.028
  29. 29. Almeida CMVB, Giannetti BF (2001) Protective film growth on tin in perchlorate and citric acid electrolytes. Materials Chemistry and Physics 69: 261–266. doi: 10.1016/s0254-0584(00)00458-2
  30. 30. Calandra AJ, De Tacconi NR, Pereiro R, Arvia AJ (1974) Potentiodynamic current/potential relations for film formation under OHMIC resistance control. Electrochimica Acta 19: 901–905. doi: 10.1016/0013-4686(74)85041-3
  31. 31. Srinivasan S, Gileadi E (1966) The potential-sweep method: A theoretical analysis. Electrochimica Acta 11: 321–335. doi: 10.1016/0013-4686(66)87043-3
  32. 32. Refaey SAM, Taha F, Hasanin THA (2006) Passivation and pitting corrosion of nanostructured Sn-Ni alloy in NaCl solutions. Electrochimica Acta 51: 2942–2948. doi: 10.1016/j.electacta.2005.09.033
  33. 33. Naumkin AV, Kraut-Vass A, Gaarenstroom SW (2012) Powell CJ NIST Standard Reference Database 20, Version 41 (Web Version) (http://srdatanistgov/xps/).
  34. 34. Sato K, Izumi T, Iwase M, Show Y, Morisaki H, Yaguchi T, et al. (2003) Nucleation and growth of nanocrystalline silicon studied by TEM, XPS and ESR. Applied Surface Science 216: 376–381. doi: 10.1016/s0169-4332(03)00445-8
  35. 35. Pyun SI, Moon SM (2000) Corrosion mechanism of pure aluminium in aqueous alkaline solution. Journal of Solid State Electrochemistry 4: 267–272. doi: 10.1007/s100080050203
  36. 36. Lee TS (1971) Hydrogen over potential on pure metals in alkaline solution. Journal of The Electrochemical Society 118: 1278–1282. doi: 10.1149/1.2408305
  37. 37. Lu ZP, Huang CB, Huang DL, Yang W (2006) Effects of a magnetic field on the anodic dissolution, passivation and transpassivation behaviour of iron in weakly alkaline solutions with or without halides. Corrosion Science 48: 3049–3077. doi: 10.1016/j.corsci.2005.11.014
  38. 38. Čekerevac M, Simičić M, Bujanović LN, Popović N (2012) The influence of silicate and sulphate anions on the anodic corrosion and the transpassivity of iron and silicon-rich steel in concentrated KOH solution. Corrosion Science 64: 204–212. doi: 10.1016/j.corsci.2012.07.019
  39. 39. Kelsall GH, Williams RA (1991) Electrochemical Behavior of Ferrosilicides (FexSi) in Neutral and Alkaline Aqueous Electrolytes I. Thermodynamics of Systems at 298 K. Journal of the Electrochemical Society 138: 931–940. doi: 10.1002/chin.199123018
  40. 40. Green ML, Gusev EP, Degraeve R, Garfunkel EL (2001) Ultrathin (< 4 nm) SiO2 and Si-O-N gate dielectric layers for silicon microelectronics: Understanding the processing, structure, and physical and electrical limits. Journal of Applied Physics 90: 2057–2121. doi: 10.1063/1.1385803
  41. 41. Xu Y, Cheng XL, Liu Z, Shi HR, Jian JM (2011) Influence of Magnetron Sputtering and Annealing Treatment on the Organizational Properties of ZnO/SiO2 Composite Films. Applied Mechanics and Materials 66: 1094–1099. doi: 10.4028/www.scientific.net/amm.66-68.1094
  42. 42. Amaral ST, Müller IL (1999) A RRDE study of the electrochemical behavior of iron in solutions containing silicate and sulphate at pH 10–13. Corrosion Science 41: 759–771. doi: 10.1016/s0010-938x(98)00149-8
  43. 43. Kelsall GH, Williams RA (1991) Electrochemical Behavior of Ferrosilicides (FexSi) in Neutral and Alkaline Aqueous Electrolytes II. Electrochemical Kinetics and Corrosion Behavior. Journal of the Electrochemical Society 138: 941–951. doi: 10.1002/chin.199123019
  44. 44. Casella IG, Gatta M (2002) Study of the electrochemical deposition and properties of cobalt oxide species in citrate alkaline solutions. Journal of Electroanalytical Chemistry 534: 31–38. doi: 10.1016/s0022-0728(02)01100-2