- Email: [email protected]
Impedance of metastable pitting corrosion
Journal of
Electroanalytical Chemistry Journal of Electroanalytical Chemistry 575 (2005) 33–38 www.elsevier.com/locate/jelechem
Impedance of metastable pitting corrosion S. Krakowiak *, K. Darowicki, P. S´lepski Department of Electrochemistry, Corrosion and Materials Engineering, Gdansk University of Technology, 11/12 Narutowicza Str., 80-952 Gdan´sk, Poland Received 25 June 2004; received in revised form 31 August 2004; accepted 1 September 2004 Available online 18 October 2004
Abstract A metastable pitting corrosion impedance investigation has been performed. The shape of the dc current is connected with the shape of the impedance diagram. The corrosion rate inside an active pit is charge transfer controlled. The active surface area expansion is proportional to the double layer capacity changes. Changes of the electrolyte resistance inside the pit have been detected. 2004 Elsevier B.V. All rights reserved. Keywords: Pitting corrosion; Stainless steels; Dynamic electrochemical impedance spectroscopy; Metastable pitting corrosion
1. Introduction The fluctuations of anodic current under potentiostatic control have been recognized for a long time [1] as resulting from the occurrence of metastable pits. Many authors correlate the current fluctuations of anodic current with the generation of pits. The recorded current fluctuations are termed current electrochemical noise. Recently, this has been promoted as a tool for pitting corrosion analysis [2–4]. Changes in the noise signal are often taken as an indication that conditions are favorable for pit initiation to occur. Bertocci and YangXiang [5] observed the current electrochemical noise at a potential chosen close to the pitting corrosion potential. Before pit stabilization, the current fluctuations were probably due to the occurrence of unstable pits, which then repassivate. A typical event on the current time curve consisted of an anodic increase, followed by a sharp decrease. After initiation of stable pits, the average anodic current increased but fluctuations were also recorded. Keddam et al. [6] correlated the fluctuations of passive current with the high frequency dielec*
Corresponding author. Tel.: +48 58 3471217; fax: +48 58 3471092. E-mail address: [email protected] (S. Krakowiak).
0022-0728/$ - see front matter 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.jelechem.2004.09.001
tric behavior of a passive film. Tsuru and Saikiri [7] worked on 304 stainless steel and found that the elementary event consists of a progressive current increase followed by a sharp decrease. Moreover, the frequency of fluctuations tends to decrease with polarization time. Therefore, Darowicki et al. [8–10] proposed the application of joint time–frequency methods for electrochemical noise analysis such as the wavelets transformation and the short time Fourier transformation. These mathematical tools showed some usefulness in the noise analysis. Many authors claim that the shape of an individual current fluctuation depends on the processes occurring in the passive layer. We agree with this opinion, but there is no direct evidence as to how the observed current depends on the structure and changes of the passive layer. Recently, Darowicki et al. [8–10] described a new impedance technique termed dynamic electrochemical impedance spectroscopy (DEIS), which can be used under non-stationary conditions. This method allows the dynamics of the creation and repassivation of metastable pits to be investigated. So, there is a possibility of correlating the shape of metastable current noise events with the changes of impedance versus time. That is why we decided to perform an investigation of metastable
34
S. Krakowiak et al. / Journal of Electroanalytical Chemistry 575 (2005) 33–38
pitting corrosion by means of the DEIS method and to analyze the instantaneous impedance spectra obtained in detail. The technique of impedance investigations of pit growth presented here is original.
60.0
2. Experimental Solutions for tests were prepared from thrice distilled water and weighed amounts of sodium chloride. The concentration of sodium chloride solution was 0.5 mol/dm3. Steel electrodes of 3.14 · 104 cm2 area were prepared by grinding with abrasive paper of 180–1200 gradation and then polished using Al2O3. Next, they were rinsed with distilled water and degreased with acetone. Before measurements the electrodes were conditioned for an hour in the laboratory. The measurements were carried out in a three-electrode measurement vessel. Working electrodes were made of the 304 stainless steel to be investigated. An AgjAgCl (0.5 mol dm3 NaCl) electrode was used as the reference electrode. A platinum mesh (Fischer electrode) was the auxiliary electrode. The dynamic impedance measurements were performed on a set-up assembled in the Department of Electrochemistry, Corrosion and Materials Engineering. Generation of the ac signal was performed with a National Instruments Ltd. PCI-6111E digital–analog card. Two National Instruments PCI6052E digital–analog cards were used for measurement of the current and voltage signals. The operation of the measurement cards was synchronized. A KGLstat v. 2.1 potentiostat was used as a current–voltage converter. The perturbation signal was a package composed of voltage sinusoids of the frequency range 10.9 kHz to 70 Hz. The low limit of measurement frequency depended on the length of the analyzing window. In other words, the low frequency limit depended on the time scale of the analysis performed. The sampling frequency was fS = 25 kHz. The amplitudes of all sinusoids were equal to 6 mV. The dc potential was equal to 650 mV vs. the reference electrode.
I/µA
40.0
20.0
0.0 0.0
15.0
30.0 t/s
45.0
60.0
Fig. 1. Metastable current electrochemical noise of a stainless steel electrode in 0.5 M NaCl, E = 650 mV vs. AgjAgCl reference electrode.
relation of the impedance spectrum with the shape of an elementary event, this experiment was performed under special conditions. The stabilized potential was the sum of the dc component Edc = 650 mV and twelve elementary sinusoidal voltage perturbations with deterministic frequencies. The amplitudes of all elementary sinusoidal signals were identical and equal to 6 mV. The decomposition of the global current response signal allows determination of the dc current shape of the current peaks. Additionally, the application of ac components to short time Fourier analysis allows instantaneous impedance spectra to be obtained. Such a method of experiment realization gives an impedance–time diagram and the electrochemical current simultaneously. For a more accurate analysis only one metastable peak was selected from the full time record. This selected peak is presented in Fig. 2. 25.0
20.0
Changes of the noise signal are often taken as an indication that conditions are favorable for pit initiation to occur. Under special conditions, the initiated corrosion pits undergo a complete repassivation process. In this case, the current electrochemical noise recorded has a characteristic shape as presented in Fig. 1. Current electrochemical noise is composed of a few, very well resolved peaks. Each peak represents the elementary process, which consists of a pit initiation step, a pit growth step and a repassivation step. For the cor-
I/µA
15.0
3. Results and discussion
10.0
5.0
0.0 16.0
20.0
24.0
28.0
t/s Fig. 2. Selected metastable current peak of stainless steel in 0.5 M NaCl.
S. Krakowiak et al. / Journal of Electroanalytical Chemistry 575 (2005) 33–38
This shape may be correlated with Fig. 3, which depicts the pit created on the electrode surface. The electrode surface was extremely low [11]. In such a situation, the surface of the pit was of the same order as the electrode surface. The shape of the current peak has a characteristic form; a relatively slow increase in anodic current, followed by a sharp decrease. Theoretically, this peak is equivalent to one elementary stochastic event. The increase in the dc current is observed after the time t = 17.5 s. However, the pit repassivation process proceeds in time t 24.5 s. Hence, the duration time of a metastable pit is equal to 7 s. The pit growth process is relatively slow but the repassivation is fast and it is carried out in a very narrow time frame. For the same period of time, the impedance–time diagram has been computed and this is presented in Fig. 4. The impedance diagram presented in Fig. 4 consists of a set of elementary impedance spectra. Each elementary spectrum was evaluated for a time range equal to the length of the analyzing window. In this case, the length of the Hanning window was equal to 10 ms. In other words, for the time period equal to 100 ms, we assumed that the stationarity conditions were fulfilled and for this period of time, one impedance spectrum was computed. The global impedance–time diagram is a composition of the elementary impedance spectra and shows regular changes. For the passive time range the impedance spectra have the form of straight lines. In the time range from t = 17.5–22.5 s the impedance spectra correspond to a pit growth process. Therefore, their shapes vary with time. This is obvious, because the growth of the pit is accompanied by an increase in the rate of the corrosion process inside the pit. However, after the time t = 22.5 s we observe significant changes of the impedance caused by the repassivation process inside the pit. After the repassivation process, the shapes of the impedance spectra are identical with that in the pre-initiation stage.
35
Fig. 4. Impedance–time diagram corresponding to a metastable pit.
In order to perform an analysis of the impedance– time diagram in greater depth, an electrical equivalent circuit was applied in the form presented in Fig. 5. The electrical equivalent circuit consists of two branches. The first branch represents the surface area without active pits (passive layer) and only inactive pits are present. The second branch of the electrical equivalent circuit corresponds to the impedance of active pits. RX simulates the electrolyte resistance. It is well known that the passive layer includes many micro- and nanocracks. Strehblow [12], Vetter and Strehblow [13] and Sato et al. [14] claim that this property of the passive layer is natural but on the other hand, the presence of cracks promotes the pit creation process. According to de Levie [15], the impedance inside the inactive pits can be represented by a transmission line. Recently, this problem has been widely discussed by Bisquert et al. [16]. The introduction of the parameter K is connected to the geometry of inactive micro- and nanocracks. Such elements can be modeled by a ‘‘transmission line’’ consisting of identical RC cells. The impedance of such a circuit for relatively high measurement frequencies may be represented by Eq. (1).
Fig. 3. Images of the electrode surface before (a) and after (b) an impedance/time measurement experiment.
36
S. Krakowiak et al. / Journal of Electroanalytical Chemistry 575 (2005) 33–38 25.0
3.0
CPL
Active pit CDL
15.0
I/µA
RΩ
CPL / nF
ZIP
20.0
2.8
Passive layer
2.6 10.0
REP 2.4
RCT
5.0
Fig. 5. Electrical equivalent circuit.
ð1Þ
1 ; jxC PL
0.0 28.0
10.0
25.0
20.0
8.0
I/µA
15.0
6.0 10.0
4.0 5.0
2.0 16.0
0.0
20.0
24.0
28.0
t/s Fig. 7. The dependence of the impedance parameter, K, versus time.
200.0
25.0
160.0
20.0
120.0
15.0
80.0
10.0
40.0
5.0
ð3Þ
where ZPL(jx) is the impedance of the passive layer and CPL is the capacity of the passive layer. The experimental impedance results were analyzed by means of the derived electrical equivalent circuit. The correlation analysis performed gives the dependences of each element of the equivalent circuit versus time. These dependences are shown in Figs. 6–10. Apart from the changes of the passive layer capacity versus time, the changes of the dc current are also included in Fig. 6. This method of graphical presentation of the experimental results facilitates discussion. During active pit initiation and growth, the passive layer capacity decreases. For the instant of the repassivation process, the passive layer capacity is strongly depressed and after this moment, it exhibits a value similar to that in the pre-initiation stage.
I/µA
Z PL ðjxÞ ¼
24.0
Fig. 6. The dependence of the passive layer capacity, CPL, versus time.
ð2Þ
where ZAP(jx) is the impedance inside the active pits, RCT is the charge transfer resistance inside the active pits or cracks, CDL is the double layer capacity inside the active pits and REP is the electrolyte resistance inside the active pits or cracks. The part of the surface area without active or inactive pits is represented by the passive layer capacity CPL:
20.0
t/s
K / MΩ Hz1/2
where ZIP(jx) is the impedance inside the inactive pits and K = (RIP/CIP)1/2 is the impedance parameter inside the inactive pits. RIP is the electrolyte resistance per unit length of inactive pit. CIP is the electrical capacity per unit length of inactive pit. Due to the dynamic mode of the experiment, the impedance measurements had to be realized in a limited range of frequencies. The low limit of the measurement frequency depends on the dynamics of the process investigated. The parts of the surface area including the active pits are represented by the impedance: RCT Z AP ðjxÞ ¼ REP þ ; 1 þ jxC DL RCT
2.2 16.0
CDL / nF
K Z IP ðjxÞ ¼ pffiffiffiffiffi ; jx
0.0 16.0
20.0
24.0
0.0 28.0
t/s
Fig. 8. The dependence of the double layer capacity, CDL, versus time.
As mentioned above, the parameter K describes the impedance inside the inactive pits or cracks. In the pre-initiation stage this parameter is equal to 7.6 · 106 X Hz1/2. The growth process of the pits or cracks causes depression of this parameter. For the repassivation time,
S. Krakowiak et al. / Journal of Electroanalytical Chemistry 575 (2005) 33–38 4.0
25.0
20.0
15.0
I/µA
RCT / M
3.0
2.0 10.0 1.0
0.0 16.0
5.0
20.0
24.0
0.0 28.0
t/s
2.0
25.0
1.6
20.0
1.2
15.0
0.8
10.0
The shape of the impedance spectra indicates charge transfer control of pitting corrosion. In this case, the rate of pitting corrosion is proportional to the reciprocal of charge transfer resistance. On the other hand, the charge transfer resistance depends also on the expansion of the active surface area. Therefore, the charge transfer resistance versus time dependence should be correlated with the changes of the dc current. The charge transfer resistance decreases during pit growth and a simultaneous increase in the dc current is observed. The changes of these two parameters versus time are strictly correlated. The charge transfer resistance value decreases monotonically from infinity to the minimum value. However, the dc current increases monotonically from the minimum value representing the passive state to the maximum value characterizing the maximum geometry of the active pits. For the repassivation time, both a sharp decrease in the dc current and a sharp increase in the charge transfer resistance are detected. The electrolyte resistance inside the active pits during expansion of the pit geometry should be changing. The electrolyte resistance inside the pit is a sensitive measure of the geometric changes of the active pits.
I/µA
REP/M
Fig. 9. The dependence of the charge transfer resistance, RCT, versus time.
37
4. Conclusion 0.4
0.0 16.0
5.0
0.0
20.0
24.0
28.0
t/s Fig. 10. The dependence of the electrolyte resistance inside the active pits, REP, versus time.
the value of K is a minimum. In this moment of time, the value of the impedance parameter changes rapidly. This change is a result of the repassivation process. Once the repassivation is complete, the parameter K attains a value identical with that in the pre-initiation stage. The changes in the double layer capacity with respect to time are a very good measure of the pit growth process. This dependence is presented in Fig. 8. The double layer capacity is connected strictly with the active part of the surface area inside the active pits or cracks. Therefore, the changes in this parameter are equivalent to the changes of the active surface area. During the expansion of active pits, the active area increases as does the double layer capacity. The shape of the double layer capacity versus time plot is similar to the shape of the current change versus time plot. In the moment of repassivation, a sharp depression of the double layer capacity is observed.
DEIS is a powerful tool for investigation of pitting corrosion. For the first time, the impedance of metastable pits was evaluated and each stage of the pitting process could be investigated. The double layer capacity is simply correlated with the active surface area inside the pit, therefore, measurements of this parameter versus time gives information about the growth of pits. The corrosion process inside the active pits is controlled by a charge transfer process. The possibility of evaluating the charge transfer resistance allows determination of the corrosion rate inside the pits. The electrolyte resistance inside active pits also depends on time. Assuming that the depth of the active pits is constant, the changes of electrolyte resistance are due to expansion of the active surface area. Finally, an analysis in greater depth of the values obtained allows determination of the pitting corrosion rate and changes of the active surface area inside the pit.
References [1] J.M. Defranoux, Corros. Sci. 3 (1963) 75. [2] B. Baroux, Pitting corrosion of stainless steels, in: P. Marcus, J. Oudar (Eds.), Corrosion Mechanisms in Theory and Practice, Marcel Dekker Inc, New York, 1995, pp. 265–310. [3] R.G. Kelly, Passivity and localized corrosion, in: R.G. Kelly, J.R. Scully, D.W. Shoesmith, R.G. Buchheit (Eds.), Electrochemical
38
[4]
[5] [6] [7] [8] [9] [10]
S. Krakowiak et al. / Journal of Electroanalytical Chemistry 575 (2005) 33–38 Techniques in Corrosion Science and Engineering, Marcel Dekker Inc, New York, 1967, pp. 55–124. G.S. Frankel, M. Rohwerder, Electrochemical techniques for corrosion, in: M.S. Stratmann, G.S. Frankel (Eds.), Encyclopedia of Electrochemistry, Corrosion and Oxide Films, vol. 4, WileyVCH, Weinheim, 2003, pp. 689–720. U. Bertocci, Y. Yang-Xiang, J. Electrochem. Soc. 136 (1963) 1011. M. Keddam, M. Krarti, C. Pallotta, Corrosion 43 (1987) 454. T. Tsuru, M. Saikiri, Corros. Eng. 39 (1990) 401. K. Darowicki, J. Electroanal. Chem. 486 (2000) 101. K. Darowicki, J. Orlikowski, G. Lentka, J. Electroanal. Chem. 486 (2000) 106. K. Darowicki, J. Orlikowski, A. Arutunow, Electrochim. Acta 48 (2003) 4189.
[11] G.T. Burstein, G.O. Ilevbare, Corros. Sci. 38 (1996) 2257. [12] H.-H. Strehblow, Mechanism of pitting corrosion, in: P. Marcus, J. Oudar (Eds.), Corrosion Mechanism in Theory and Practice, Marcel Dekker, Inc, New York, 1995, pp. 201–237. [13] K.J. Vetter, H.-H. Strehblow, Ber. Bunsenges Phys. Chem. 74 (1970) 1024. [14] N. Sato, K.D.J. Kudo, T. Noda, Electrochim. Acta 16 (1971) 1909. [15] R. de Levie, in: P. Delahay (Ed.), Advances in Electrochemistry and Electrochemical Engineering, vol. VI, Interscience, New York, 1967, p. 329. [16] J. Bisquert, G. Garcia-Belmonte, F. Fabregat-Santiago, N.S. Farriols, P. Bogdanoff, E.C. Pereira, J. Phys. Chem. B 104 (2000) 2287.
Electroanalytical Chemistry Journal of Electroanalytical Chemistry 575 (2005) 33–38 www.elsevier.com/locate/jelechem
Impedance of metastable pitting corrosion S. Krakowiak *, K. Darowicki, P. S´lepski Department of Electrochemistry, Corrosion and Materials Engineering, Gdansk University of Technology, 11/12 Narutowicza Str., 80-952 Gdan´sk, Poland Received 25 June 2004; received in revised form 31 August 2004; accepted 1 September 2004 Available online 18 October 2004
Abstract A metastable pitting corrosion impedance investigation has been performed. The shape of the dc current is connected with the shape of the impedance diagram. The corrosion rate inside an active pit is charge transfer controlled. The active surface area expansion is proportional to the double layer capacity changes. Changes of the electrolyte resistance inside the pit have been detected. 2004 Elsevier B.V. All rights reserved. Keywords: Pitting corrosion; Stainless steels; Dynamic electrochemical impedance spectroscopy; Metastable pitting corrosion
1. Introduction The fluctuations of anodic current under potentiostatic control have been recognized for a long time [1] as resulting from the occurrence of metastable pits. Many authors correlate the current fluctuations of anodic current with the generation of pits. The recorded current fluctuations are termed current electrochemical noise. Recently, this has been promoted as a tool for pitting corrosion analysis [2–4]. Changes in the noise signal are often taken as an indication that conditions are favorable for pit initiation to occur. Bertocci and YangXiang [5] observed the current electrochemical noise at a potential chosen close to the pitting corrosion potential. Before pit stabilization, the current fluctuations were probably due to the occurrence of unstable pits, which then repassivate. A typical event on the current time curve consisted of an anodic increase, followed by a sharp decrease. After initiation of stable pits, the average anodic current increased but fluctuations were also recorded. Keddam et al. [6] correlated the fluctuations of passive current with the high frequency dielec*
Corresponding author. Tel.: +48 58 3471217; fax: +48 58 3471092. E-mail address: [email protected] (S. Krakowiak).
0022-0728/$ - see front matter 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.jelechem.2004.09.001
tric behavior of a passive film. Tsuru and Saikiri [7] worked on 304 stainless steel and found that the elementary event consists of a progressive current increase followed by a sharp decrease. Moreover, the frequency of fluctuations tends to decrease with polarization time. Therefore, Darowicki et al. [8–10] proposed the application of joint time–frequency methods for electrochemical noise analysis such as the wavelets transformation and the short time Fourier transformation. These mathematical tools showed some usefulness in the noise analysis. Many authors claim that the shape of an individual current fluctuation depends on the processes occurring in the passive layer. We agree with this opinion, but there is no direct evidence as to how the observed current depends on the structure and changes of the passive layer. Recently, Darowicki et al. [8–10] described a new impedance technique termed dynamic electrochemical impedance spectroscopy (DEIS), which can be used under non-stationary conditions. This method allows the dynamics of the creation and repassivation of metastable pits to be investigated. So, there is a possibility of correlating the shape of metastable current noise events with the changes of impedance versus time. That is why we decided to perform an investigation of metastable
34
S. Krakowiak et al. / Journal of Electroanalytical Chemistry 575 (2005) 33–38
pitting corrosion by means of the DEIS method and to analyze the instantaneous impedance spectra obtained in detail. The technique of impedance investigations of pit growth presented here is original.
60.0
2. Experimental Solutions for tests were prepared from thrice distilled water and weighed amounts of sodium chloride. The concentration of sodium chloride solution was 0.5 mol/dm3. Steel electrodes of 3.14 · 104 cm2 area were prepared by grinding with abrasive paper of 180–1200 gradation and then polished using Al2O3. Next, they were rinsed with distilled water and degreased with acetone. Before measurements the electrodes were conditioned for an hour in the laboratory. The measurements were carried out in a three-electrode measurement vessel. Working electrodes were made of the 304 stainless steel to be investigated. An AgjAgCl (0.5 mol dm3 NaCl) electrode was used as the reference electrode. A platinum mesh (Fischer electrode) was the auxiliary electrode. The dynamic impedance measurements were performed on a set-up assembled in the Department of Electrochemistry, Corrosion and Materials Engineering. Generation of the ac signal was performed with a National Instruments Ltd. PCI-6111E digital–analog card. Two National Instruments PCI6052E digital–analog cards were used for measurement of the current and voltage signals. The operation of the measurement cards was synchronized. A KGLstat v. 2.1 potentiostat was used as a current–voltage converter. The perturbation signal was a package composed of voltage sinusoids of the frequency range 10.9 kHz to 70 Hz. The low limit of measurement frequency depended on the length of the analyzing window. In other words, the low frequency limit depended on the time scale of the analysis performed. The sampling frequency was fS = 25 kHz. The amplitudes of all sinusoids were equal to 6 mV. The dc potential was equal to 650 mV vs. the reference electrode.
I/µA
40.0
20.0
0.0 0.0
15.0
30.0 t/s
45.0
60.0
Fig. 1. Metastable current electrochemical noise of a stainless steel electrode in 0.5 M NaCl, E = 650 mV vs. AgjAgCl reference electrode.
relation of the impedance spectrum with the shape of an elementary event, this experiment was performed under special conditions. The stabilized potential was the sum of the dc component Edc = 650 mV and twelve elementary sinusoidal voltage perturbations with deterministic frequencies. The amplitudes of all elementary sinusoidal signals were identical and equal to 6 mV. The decomposition of the global current response signal allows determination of the dc current shape of the current peaks. Additionally, the application of ac components to short time Fourier analysis allows instantaneous impedance spectra to be obtained. Such a method of experiment realization gives an impedance–time diagram and the electrochemical current simultaneously. For a more accurate analysis only one metastable peak was selected from the full time record. This selected peak is presented in Fig. 2. 25.0
20.0
Changes of the noise signal are often taken as an indication that conditions are favorable for pit initiation to occur. Under special conditions, the initiated corrosion pits undergo a complete repassivation process. In this case, the current electrochemical noise recorded has a characteristic shape as presented in Fig. 1. Current electrochemical noise is composed of a few, very well resolved peaks. Each peak represents the elementary process, which consists of a pit initiation step, a pit growth step and a repassivation step. For the cor-
I/µA
15.0
3. Results and discussion
10.0
5.0
0.0 16.0
20.0
24.0
28.0
t/s Fig. 2. Selected metastable current peak of stainless steel in 0.5 M NaCl.
S. Krakowiak et al. / Journal of Electroanalytical Chemistry 575 (2005) 33–38
This shape may be correlated with Fig. 3, which depicts the pit created on the electrode surface. The electrode surface was extremely low [11]. In such a situation, the surface of the pit was of the same order as the electrode surface. The shape of the current peak has a characteristic form; a relatively slow increase in anodic current, followed by a sharp decrease. Theoretically, this peak is equivalent to one elementary stochastic event. The increase in the dc current is observed after the time t = 17.5 s. However, the pit repassivation process proceeds in time t 24.5 s. Hence, the duration time of a metastable pit is equal to 7 s. The pit growth process is relatively slow but the repassivation is fast and it is carried out in a very narrow time frame. For the same period of time, the impedance–time diagram has been computed and this is presented in Fig. 4. The impedance diagram presented in Fig. 4 consists of a set of elementary impedance spectra. Each elementary spectrum was evaluated for a time range equal to the length of the analyzing window. In this case, the length of the Hanning window was equal to 10 ms. In other words, for the time period equal to 100 ms, we assumed that the stationarity conditions were fulfilled and for this period of time, one impedance spectrum was computed. The global impedance–time diagram is a composition of the elementary impedance spectra and shows regular changes. For the passive time range the impedance spectra have the form of straight lines. In the time range from t = 17.5–22.5 s the impedance spectra correspond to a pit growth process. Therefore, their shapes vary with time. This is obvious, because the growth of the pit is accompanied by an increase in the rate of the corrosion process inside the pit. However, after the time t = 22.5 s we observe significant changes of the impedance caused by the repassivation process inside the pit. After the repassivation process, the shapes of the impedance spectra are identical with that in the pre-initiation stage.
35
Fig. 4. Impedance–time diagram corresponding to a metastable pit.
In order to perform an analysis of the impedance– time diagram in greater depth, an electrical equivalent circuit was applied in the form presented in Fig. 5. The electrical equivalent circuit consists of two branches. The first branch represents the surface area without active pits (passive layer) and only inactive pits are present. The second branch of the electrical equivalent circuit corresponds to the impedance of active pits. RX simulates the electrolyte resistance. It is well known that the passive layer includes many micro- and nanocracks. Strehblow [12], Vetter and Strehblow [13] and Sato et al. [14] claim that this property of the passive layer is natural but on the other hand, the presence of cracks promotes the pit creation process. According to de Levie [15], the impedance inside the inactive pits can be represented by a transmission line. Recently, this problem has been widely discussed by Bisquert et al. [16]. The introduction of the parameter K is connected to the geometry of inactive micro- and nanocracks. Such elements can be modeled by a ‘‘transmission line’’ consisting of identical RC cells. The impedance of such a circuit for relatively high measurement frequencies may be represented by Eq. (1).
Fig. 3. Images of the electrode surface before (a) and after (b) an impedance/time measurement experiment.
36
S. Krakowiak et al. / Journal of Electroanalytical Chemistry 575 (2005) 33–38 25.0
3.0
CPL
Active pit CDL
15.0
I/µA
RΩ
CPL / nF
ZIP
20.0
2.8
Passive layer
2.6 10.0
REP 2.4
RCT
5.0
Fig. 5. Electrical equivalent circuit.
ð1Þ
1 ; jxC PL
0.0 28.0
10.0
25.0
20.0
8.0
I/µA
15.0
6.0 10.0
4.0 5.0
2.0 16.0
0.0
20.0
24.0
28.0
t/s Fig. 7. The dependence of the impedance parameter, K, versus time.
200.0
25.0
160.0
20.0
120.0
15.0
80.0
10.0
40.0
5.0
ð3Þ
where ZPL(jx) is the impedance of the passive layer and CPL is the capacity of the passive layer. The experimental impedance results were analyzed by means of the derived electrical equivalent circuit. The correlation analysis performed gives the dependences of each element of the equivalent circuit versus time. These dependences are shown in Figs. 6–10. Apart from the changes of the passive layer capacity versus time, the changes of the dc current are also included in Fig. 6. This method of graphical presentation of the experimental results facilitates discussion. During active pit initiation and growth, the passive layer capacity decreases. For the instant of the repassivation process, the passive layer capacity is strongly depressed and after this moment, it exhibits a value similar to that in the pre-initiation stage.
I/µA
Z PL ðjxÞ ¼
24.0
Fig. 6. The dependence of the passive layer capacity, CPL, versus time.
ð2Þ
where ZAP(jx) is the impedance inside the active pits, RCT is the charge transfer resistance inside the active pits or cracks, CDL is the double layer capacity inside the active pits and REP is the electrolyte resistance inside the active pits or cracks. The part of the surface area without active or inactive pits is represented by the passive layer capacity CPL:
20.0
t/s
K / MΩ Hz1/2
where ZIP(jx) is the impedance inside the inactive pits and K = (RIP/CIP)1/2 is the impedance parameter inside the inactive pits. RIP is the electrolyte resistance per unit length of inactive pit. CIP is the electrical capacity per unit length of inactive pit. Due to the dynamic mode of the experiment, the impedance measurements had to be realized in a limited range of frequencies. The low limit of the measurement frequency depends on the dynamics of the process investigated. The parts of the surface area including the active pits are represented by the impedance: RCT Z AP ðjxÞ ¼ REP þ ; 1 þ jxC DL RCT
2.2 16.0
CDL / nF
K Z IP ðjxÞ ¼ pffiffiffiffiffi ; jx
0.0 16.0
20.0
24.0
0.0 28.0
t/s
Fig. 8. The dependence of the double layer capacity, CDL, versus time.
As mentioned above, the parameter K describes the impedance inside the inactive pits or cracks. In the pre-initiation stage this parameter is equal to 7.6 · 106 X Hz1/2. The growth process of the pits or cracks causes depression of this parameter. For the repassivation time,
S. Krakowiak et al. / Journal of Electroanalytical Chemistry 575 (2005) 33–38 4.0
25.0
20.0
15.0
I/µA
RCT / M
3.0
2.0 10.0 1.0
0.0 16.0
5.0
20.0
24.0
0.0 28.0
t/s
2.0
25.0
1.6
20.0
1.2
15.0
0.8
10.0
The shape of the impedance spectra indicates charge transfer control of pitting corrosion. In this case, the rate of pitting corrosion is proportional to the reciprocal of charge transfer resistance. On the other hand, the charge transfer resistance depends also on the expansion of the active surface area. Therefore, the charge transfer resistance versus time dependence should be correlated with the changes of the dc current. The charge transfer resistance decreases during pit growth and a simultaneous increase in the dc current is observed. The changes of these two parameters versus time are strictly correlated. The charge transfer resistance value decreases monotonically from infinity to the minimum value. However, the dc current increases monotonically from the minimum value representing the passive state to the maximum value characterizing the maximum geometry of the active pits. For the repassivation time, both a sharp decrease in the dc current and a sharp increase in the charge transfer resistance are detected. The electrolyte resistance inside the active pits during expansion of the pit geometry should be changing. The electrolyte resistance inside the pit is a sensitive measure of the geometric changes of the active pits.
I/µA
REP/M
Fig. 9. The dependence of the charge transfer resistance, RCT, versus time.
37
4. Conclusion 0.4
0.0 16.0
5.0
0.0
20.0
24.0
28.0
t/s Fig. 10. The dependence of the electrolyte resistance inside the active pits, REP, versus time.
the value of K is a minimum. In this moment of time, the value of the impedance parameter changes rapidly. This change is a result of the repassivation process. Once the repassivation is complete, the parameter K attains a value identical with that in the pre-initiation stage. The changes in the double layer capacity with respect to time are a very good measure of the pit growth process. This dependence is presented in Fig. 8. The double layer capacity is connected strictly with the active part of the surface area inside the active pits or cracks. Therefore, the changes in this parameter are equivalent to the changes of the active surface area. During the expansion of active pits, the active area increases as does the double layer capacity. The shape of the double layer capacity versus time plot is similar to the shape of the current change versus time plot. In the moment of repassivation, a sharp depression of the double layer capacity is observed.
DEIS is a powerful tool for investigation of pitting corrosion. For the first time, the impedance of metastable pits was evaluated and each stage of the pitting process could be investigated. The double layer capacity is simply correlated with the active surface area inside the pit, therefore, measurements of this parameter versus time gives information about the growth of pits. The corrosion process inside the active pits is controlled by a charge transfer process. The possibility of evaluating the charge transfer resistance allows determination of the corrosion rate inside the pits. The electrolyte resistance inside active pits also depends on time. Assuming that the depth of the active pits is constant, the changes of electrolyte resistance are due to expansion of the active surface area. Finally, an analysis in greater depth of the values obtained allows determination of the pitting corrosion rate and changes of the active surface area inside the pit.
References [1] J.M. Defranoux, Corros. Sci. 3 (1963) 75. [2] B. Baroux, Pitting corrosion of stainless steels, in: P. Marcus, J. Oudar (Eds.), Corrosion Mechanisms in Theory and Practice, Marcel Dekker Inc, New York, 1995, pp. 265–310. [3] R.G. Kelly, Passivity and localized corrosion, in: R.G. Kelly, J.R. Scully, D.W. Shoesmith, R.G. Buchheit (Eds.), Electrochemical
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