Zhiheng Zhang

Benoît Ter-Ovanessian
email: benoit.ter-ovanessian@insa-lyon.fr

Sabrina Marcelin

Bernard Normand

Investigation of the passive behavior of a Ni-Cr binary alloy using successive electrochemical impedance measurements

Keywords: Ni-base alloy, Passive behavior, Electrochemical impedance spectroscopy, Passive film properties. * From graphical method ** From calculation equations (4, 8, 9, 10)

de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

As stated by D.D. Macdonald in 1999 [START_REF] Macdonald | Passivity -The key to our metals-based civilization[END_REF], passivity should be considered "the key to our metals-based civilization". Today, research and development on passive materials continues to lead to scientific and technological improvements and improved material design in many industrial fields, including the energy, transport, and health sectors. Because passivity plays a crucial role in material applications, investigations of passive behavior remain topical issues in corrosion science.

The long-term stability of passive materials, even sometimes in harsh environments, is mainly attributed to the growth of an extremely thin passive film (a few nanometers in thickness) protecting the metal. Observation of this passive film using conventional equipment is challenging, even using transmission electron microscopy (TEM). Moreover, this passive film is commonly considered a complex multilayer structure closely related to the material underneath as well as the physicochemistry of the environment. This complexity makes it difficult to attain a complete understanding of the passivity. Nevertheless, over the past decades, several analytical methods and techniques have been developed to study passive films. Among surface analytical techniques, X-ray photoelectron spectroscopy (XPS), which provides semiquantitative information on the chemical composition of passive films, is one of the most frequently used [START_REF] Stypula | The characterization of passive films on chromium electrodes by XPS[END_REF][START_REF] Abreu | Comparative study of passive films of different stainless steels developed on alkaline medium[END_REF][START_REF] Olsson | Passive films on stainless steels -Chemistry, structure and growth[END_REF]. Several other analytical techniques are also often employed such as scanning tunneling microscopy (STM) [START_REF] Maurice | XPS, LEED and STM study of thin oxide films formed on Cr(110)[END_REF][START_REF] Maurice | Passive films at the nanoscale[END_REF][START_REF] Marcus | On some fundamental factors in the effect of alloying elements on passivation of alloys[END_REF] and ellipsometry [START_REF] Chin | An Ellipsometric Spectroscopic Study of the Passive Film on Iron-Potential and Chloride Ion Dependence[END_REF][START_REF] Cahan | The Nature of the Passive Film on Iron I. Automatic Ellipsometric Impedance Studies[END_REF][START_REF] Iida | Ellipsometry of passive oxide films on nickel in acidic sulfate solution[END_REF].

In addition to these methods, different sets of electrochemical techniques are used to determine the kinetic parameters related to the growth, steady state, and breakdown of the passive film and permit a ranking to be established and materials to be selected based on their passive behavior.

The potentiodynamic polarization technique (potential sweep) -cyclic or not -is one of the most frequently used techniques for studying the electrochemical behavior of a passive material. From the resulting polarization curves, the ability to achieve passivity, the passive potential region, the passive current density, the potential of breakdown, and the relative stability of the passive film can all be determined. Even though this data is necessary to study passive materials, this information remains insufficient to fully describe the passive film behavior and its resistance. The rate-determining step hinders the overall passivation analysis. Moreover, for a specific corrosion mode, the results are dependent on the scan rate. For example, it is commonly known that the determination of the pitting potential is very sensitive to the sweep rate [START_REF] Yi | Potentiodynamic polarization behaviour of AISI type 316 stainless steel in NaCl solution[END_REF].

Another point of vigilance is the evolution of the passive film with the sequence of experiments that are performed. Indeed, for certain materials, several days are required to attain stability or reach the steady state of the passive material/solution interface; consequently, the results obtained after only a few minutes of immersion in an electrolyte are not representative of the long-term passive system.

To complete the analysis of a passive material/solution interface, electrochemical impedance spectroscopy (EIS) is a suitable complementary electrochemical technique that generally contributes to the description of the interface in terms of mechanisms and kinetics. Although EIS is mainly performed at the open-circuit potential (OCP), it is not rare to use EIS at different applied potentials (selected from the polarization curves) to investigate the evolution of the passive film and determine physical parameters, kinetic constants, and migration/diffusion coefficients based on descriptive or predictive models of the evolution of the passive state. For example, the Point Defect Model (PDM) [START_REF] Macdonald | The Point Defect Model for the Passive State[END_REF][START_REF] Macdonald | The history of the Point Defect Model for the passive state : A brief review of film growth aspects[END_REF][START_REF] Sharifi-Asl | Modeling of the electrochemical impedance spectroscopic behavior of passive iron using a genetic algorithm approach[END_REF] was developed to predict the growth and breakdown of passive films. In this model, EIS is used to explore the properties of passive films as a function of applied potential and pH [START_REF] Macdonald | Characterization of vacancy transport in passive films using low frequency electrochemical impedance spectroscopy[END_REF][START_REF] Macdonald | An electrochemical impedance analysis of passive films on nickel(111) in phosphate buffer solutions[END_REF] using various parameters, such as interfacial rate constants and the electrical field strength, as variables [START_REF] Macdonald | The Point Defect Model for the Passive State[END_REF]. The Mixed Conduction Model (MCM) [START_REF] Bojinov | Estimation of the parameters of oxide film growth on nickel-based alloys in hightemperature water electrolytes[END_REF][START_REF] Vorotyntsev | Multi-component diffusion approach to transport across electroactive-polymer films with two mobile charge carriers[END_REF][START_REF] Beverskog | A mixed-conduction model for oxide films on Fe, Cr and Fe-Cr alloys in high-temperature aqueous electrolytes -I. Comparison of the electrochemical behaviour at room temperature and at 200 °C[END_REF] also uses EIS to emphasize the coupling between ionic and electronic defect structures in steady-state passive films and to predict the local conductivity within the film. In this model, the point-defect formation and transport are caused by the exponential evolution of the conductivity between the metal/film and film/solution interfaces. By considering a passive film to be a highly disordered semiconductor, the complementary Mott-Schottky approach, the determination of the semiconductive properties of a semiconductor in the presence of an electrolyte, can be transposed to the study of passive films. The obtained properties, including the semiconductive type, flat band potential, and charge carrier densities, can provide information about the relation between the electronic properties and passive film growth, steady state, and susceptibility to breakdown. In the PDM, the point defects are the semiconductor charge carriers. Their evolution with the applied potential is a required input in the calculation. However, the main deviation of the results obtained using the Mott-Schottky approach results from the differential capacitance measurement during a scan of potential, generally at a single frequency. Recently, the use of multi-frequency measurements, which avoids the issue of frequency selection and dependency, has generated interest [START_REF] Ter-Ovanessian | Passive films growth on different Ni-Cr alloys from the migration of cation vacancies[END_REF][START_REF] Marcelin | Electronic properties of passive films from the multi-frequency Mott-Schottky and power-law coupled approach[END_REF].

On the basis of these preliminary remarks and considering that EIS can provide more information about passivation phenomena, successive EIS measurements were used in the current work on a nickel-based alloy, known to be a passive material, from the cathodic to anodic domain. This procedure was applied in an attempt to provide continuous information on the passive material/electrolyte interface during potential-step polarizations. In addition, the evolution of each physical parameter extracted from the impedance diagrams, for example the thickness and resistivity within the passive film, could be discussed [START_REF] Orazem | Enhanced Graphical Representation of Electrochemical Impedance Data[END_REF][START_REF] Benoit | Comparison of different methods for measuring the passive film thickness on metals[END_REF][START_REF] Hirschorn | Constant-Phase-Element Behavior Caused by Resistivity Distributions in Films: I . Theory[END_REF][START_REF] Hirschorn | Constant-phase-element behavior caused by resistivity distributions in films: II. Applications[END_REF]. The study consisted of two parts. The first part was devoted to validation of the methodology. In this part, the effects of experimental parameters on potentiostatic polarization curves, namely the dwell time at each potential step and the potential step size, were studied. The aims were to minimize the experiment duration, to find the best compromise between time and accuracy, and to ensure that the measurements were performed under steady-state conditions. The second part of the study focused on the use of this technique, termed successive EIS (SEIS), to characterize the passive behavior of a binary model Ni-Cr alloy containing 20 wt.% Cr (Ni-20Cr) in different electrolytic solutions using the optimized experimental parameters. The impedance diagrams were interpreted using the recent impedance interpretation approach to highlight the behavior of the passive film during the overall polarization process. Using enhanced graphical representation, the thickness of the passive film as well as the parameters of the constant phase element (CPE) behavior generally observed for passive material, could be estimated [START_REF] Orazem | Enhanced Graphical Representation of Electrochemical Impedance Data[END_REF][START_REF] Benoit | Comparison of different methods for measuring the passive film thickness on metals[END_REF]. Additionally, the CPE behavior of a passive film was described Hirschorn et al. using the power-law equation (power law model, PLM) [START_REF] Hirschorn | Constant-Phase-Element Behavior Caused by Resistivity Distributions in Films: I . Theory[END_REF][START_REF] Hirschorn | Constant-phase-element behavior caused by resistivity distributions in films: II. Applications[END_REF]. They showed that the CPE behavior of a passive film could be attributed to a power-law distribution of the resistivity of oxides throughout the passive film. On the one hand, graphical methods can help to establish a preliminary description of the measured EIS data, with the advantage being that the relevant CPE parameters are not linked to a specific model. This approach can also provide guidance for the development of an appropriate physical model for a passive film. On the other hand, the normal distribution of the CPE behavior of a passive film can be described by the PLM. Furthermore, the potentiostatic information obtained using SEIS was compared with potentiodynamic polarization results. Finally, XPS was employed to verify the chemical composition and structure of the passive film in the different solutions to complement the PLM results.

Experimental

Material and surface preparation

The Ni-20Cr alloy was provided by Sumitomo Metal Industries, Ltd. (Japan). The chemical composition (wt.%) of the alloy was as follows: Cr 19.79%, Fe 0.018%, Mn 0.045%, Mg 0.005%, C 0.001%, Si <0.001%, balance Ni. Metallographical examination revealed an austenitic structure and no carbide.

Before the electrochemical measurements, the specimens were ground with SiC papers up to grit P4000, followed by successive mirror polishing to 3 μm and 1 μm with diamond paste. The specimens were cleaned with deionized water in an ultrasonic bath for 5 min before each grinding and polishing step. Finally, they were cleaned in ethanol and dried with argon flow.

Electrochemical measurements

A conventional three-electrode cell was used for the electrochemical measurements. The Ni-20Cr binary alloy (exposure area = 0.56 cm 2 ) was used as the working electrode. A graphite rod was used as the counter electrode, and a saturated mercury sulfate electrode (MSE, E= +658 mV vs. SHE) was used as the reference electrode. All the electrochemical measurements were performed using a Gamry Reference 600 electrochemical potentiostat. Three aerated solutions of different pH were used for the electrochemical tests: 10 g/L Na 2 SO 4 with H 2 SO 4 (pH=2), 0.01 M Na 2 SO 4 (pH=5.8), and 0.05 M H 3 BO 3 + 0.075 M Na 2 B 4 O 7 10H 2 O (pH=9.2), referred to as pH=2, pH=5.8, and pH=9.2, respectively, in the remainder of the manuscript. These solutions were selected to study the passive behavior in acidic, neutral, and basic solution. The last solution was specifically selected because the solubility of the Cr-rich oxide or hydroxide is generally low for pH superior to 8. Moreover, the solubility of oxygen is remarkably high in the borate solution that enhance the stability of the oxides [START_REF] Rai | Chromium(III) Hydrolysis Constants and Solubility of Chromium(III) Hydroxide[END_REF][START_REF] Jovancicevic | The transport properties of oxygen in aqueous borate solutions[END_REF][START_REF] El Euch | Temperature dependence of the electrochemical behavior of the 690 Ni-base alloy between 25 and 325 °C[END_REF]. All the electrochemical measurements were performed at room temperature (22 ± 3°C).

The procedure for successive electrochemical impedance measurement is described below. The selected film forming condition was 24 h at OCP. To characterize the as-formed passive film, impedance measurement in the frequency range from 10 kHz to 5 mHz with 8 points per decade and a sine wave with 10-mV amplitude was performed at the last reached value of the open-circuit potential (E OCP ). Then, the first potential step of SEIS was performed at -0.1 V vs. E OCP for a selected dwell time directly followed by EIS in the frequency range of 10 kHz to 0.1 Hz with 8 points per decade and a sine wave with 10-mV amplitude. Other potential steps with a potential step size in the anodic direction were sequentially performed with the associated impedance measurements. This process was continuous and ended at +1.2 V vs. E OCP . To determine the optimal measurement conditions, the effects of the dwell time (30, 120, and 600 s) and the potential step size (25 and 50 mV) were studied in the borate buffer solution 0.05 M H 3 BO 3 + 0.075 M Na 2 B 4 O 7 10H 2 O (pH=9.2). The borate buffer solution was selected because of the low solubility of Cr 2 O 3 in this medium [START_REF] El Euch | Temperature dependence of the electrochemical behavior of the 690 Ni-base alloy between 25 and 325 °C[END_REF].

Surface analysis

The chemical compositions of the passive films were characterized using XPS on a PHI Quantera SXM with monochromatic Al Kα (1486.6 eV). A take-off angle of 90° was used and was not changed during the experiments. Charge compensation was performed throughout the experiments using a dual-beam neutralizer, and the remaining charge was adjusted using the aliphatic carbon peak at 284.8 eV of adventitious carbon in the C1s region. For high-resolution spectra, a pass energy of 23 eV was used. The studied passive films were formed at OCP for 24 h for each electrolyte (acidic, neutral, and basic).

Theoretical approach

The high-frequency part of an electrochemical impedance diagram obtained in the presence of a passive film is generally concerned by a CPE [START_REF] Orazem | Dielectric Properties of Materials Showing Constant-Phase-Element (CPE) Impedance Response[END_REF]. The CPE parameters (α and Q eff ) were determined using an enhanced graphical method [START_REF] Orazem | Enhanced Graphical Representation of Electrochemical Impedance Data[END_REF]. The effective CPE exponent α was estimated from a modified phase anglefrequency Bode representation after estimation of the electrolyte resistance (R e,est ):

φ = , (1)
where φ adj is the phase angle corrected by the electrolyte resistance and Z ' and Z '' are the real and imaginary part of the impedance, respectively. For α≠1, the CPE parameter α can be assessed using the following equation: φ = -90° .

(

) 2
The effective coefficient of the CPE (Q eff ) can be determined from Z '' [START_REF] Orazem | Electrochemical Impedance Spectroscopy[END_REF], with ω = 2πf:

= sin # $% & ' ( ) . (3)
As the capacitance governs the impedance at very high frequency, the resistance behavior can be neglected. Thus, the complex capacitance representation emphasizes values at high frequency, enabling determination of the highfrequency limit of the real part of the complex capacitance [START_REF] Orazem | Electrochemical Impedance Spectroscopy[END_REF]. The highfrequency-limit capacitance here is related to the dielectric field within the passive film [START_REF] Chakri | Improved EIS Analysis of the Electrochemical Behaviour of Carbon Steel in Alkaline Solution[END_REF]. Hence, the thickness of the passive film (*) can be estimated from the capacitance from the complex representation (+ , ). C ∞ is the estimated limiting capacitance at high frequency from the complex capacitance representation. Thus, * can be determined using the formula

* = --. / 0 , ( 4
)
where δ is the calculated thickness of the passive film, ε is the dielectric constant of the oxide (ε=12 for Cr 2 O 3 ) [START_REF] Lovreček | Semiconducting aspects of the passive layer on chromium[END_REF], and ε 0 is the vacuum permittivity (8.85×10 -14 F cm -1 ). The calculated thickness of a passive film has shown good agreement with that determined using other techniques [START_REF] Benoit | Comparison of different methods for measuring the passive film thickness on metals[END_REF]. In addition, the enhanced graphical representation was beneficial in determining four parameters used for fitting with the PLM (by reducing the number of unknown parameters).

As introduced before, the CPE behavior of a passive film can be considered to have a physical meaning instead of being a corrected mathematical formula. The variation of the passive film properties can be described using the PLM by the distribution of the resistivity ( 1 ) throughout the passive film thickness (* ) [START_REF] Hirschorn | Constant-Phase-Element Behavior Caused by Resistivity Distributions in Films: I . Theory[END_REF][START_REF] Hirschorn | Constant-Phase-Element Behavior Caused by Resistivity Distributions in Films II. Applications[END_REF]:

2 2 3 = 2 3 2 . + 1 - 2 3 2 . ξ 7 . (5)
Here, 1 8 is the resistivity at the interface between the electrolyte and passive film; 1 : is the resistivity at the interface between the metal and its oxide; and ξ is the dimensionless position ξ = y/δ, where y corresponds to the depth position within the passive film. γ is calculated from the CPE parameter α (γ=1/(1-α)) and indicates how sharply the resistivity varies. According to the postulate of the PLM, the dielectric constant of the film does not change throughout the thickness of the passive film. The integrated expression of the film impedance can thus be written as follows [START_REF] Hirschorn | Constant-Phase-Element Behavior Caused by Resistivity Distributions in Films: I . Theory[END_REF]:

; = < 82 3 =>) ?2 . >= @ (--. A ) , (6)
where

< = 1 + 2.88 # $ ' &.DEF . ( 7
)
From the PLM, the CPE parameters α and Q eff can be estimated as follows:

GHH = --. ) I82 3 =>) . (8)
And, the corresponding capacitance of a passive film can be calculated as follows:

+ JKL = GHH 1 : MM : $ < . (9)
This last equation allows the capacitance of the passive film to be determined in another way.

The theoretical approach and methodology are summarized in Fig. 1.

The Electrical Equivalent Circuit (EEC) of the overall model used to describe the oxidized metal/electrolyte interface is presented in Fig. 2. R e represents the resistance of the electrolyte. PLM is the element corresponding to Eq. ( 6) used to describe the passive film response to the anodic non-faradaic branch. The passive film is considered a dielectric layer. The CPE behavior can be attributed to the normal distribution of resistivity throughout the passive film, adjusted by the PLM [START_REF] Chakri | Improved EIS Analysis of the Electrochemical Behaviour of Carbon Steel in Alkaline Solution[END_REF]. C dl is the capacitance of the electrochemical double layer. As the order of magnitude of the C dl is generally ten times higher than the one of the passive film, it is assumed that the determination of the passive film capacitance by complex capacitance plane representation is not significantly affected. Generally, C dl is approximately on the order of 50 µF/cm 2 , causing an error of 5%-10% in the estimated value of the oxide capacitance [START_REF] Chakri | Improved EIS Analysis of the Electrochemical Behaviour of Carbon Steel in Alkaline Solution[END_REF]. Moreover, the value of the C dl is supposed to vary slightly on a passive electrode in the passive potential range but remains a parameter difficult to determine accurately. Consequently, as C dl have a minor influence on the passive film properties, it was preferred to neglect it during the entire fitting process. R ct is the chargetransfer resistance, which is attributed to the faradaic branch. For the impedance data acquired from the cathodic domain to the beginning of the anodic domain (-0.1 to 0.1 V vs. E OCP ), the contribution of the cathodic reaction has been considered within the charge-transfer resistance. For more anodic potentials, this resistance R ct can be considered infinite because the cathodic reaction becomes negligible. In the more anodic potential domain, the contribution of the faradaic branch can also be neglected for transport phenomena in the passive film. Within the impedance data obtained in this potential range, the charge-transfer resistance was removed from the equivalent circuit. Each impedance diagram was fitted using the non-commercial software SIMAD developed at the LISE UMR 8235 CNRS, Sorbonne University, Paris.

Results and discussion

Validation of the methodology

A preliminary investigation was performed to optimize the experimental parameters (step size and dwell time) in accordance with a conventional polarization curve, ensuring that the conditions of stationarity of the interface phenomena were respected. First, the effect of dwell time at each step of potential was studied. The potential step size was fixed at 50 mV, and different polarization dwell times (30, 120, and 600 s) were tested. After that, two different step sizes (25 and 50 mV) were tested, with the dwell time fixed at 120 s.

In Fig. 3, the solid line corresponds to the potentiodynamic polarization curve, whereas each point of the dotted curves is the last value of the current density reached during potentiostatic polarization. A current density variation lower than 1×10 -5 mA s -1 was considered criterion as the steady-state condition for the impedance measurements and for the different sets of experimental conditions. For all the curves, the corrosion potentials fell in the small range between -0.62 and -0.50 V vs. MSE. Characteristics of a passive material in a basic solution after 24 h of passive film growth are observed in all the curves: a cathodic branch, a slight increase in current density, a plateau, and a dissolutionrepassivation-redissolution process in the potential range more positive than 0.0 V vs. MSE [START_REF] Mishra | The activation/depassivation of nickel-chromium-molybdenum alloys in bicarbonate solution: Part I[END_REF][START_REF] Mishra | The activation/depassivation of nickelchromium-molybdenum alloys: An oxyanion or a pH effect -Part II[END_REF]. This finding indicates that all the curves characterized the same electrochemical reactions for substantially identical current densities.

Comparison of the potentiodynamic and potentiostatic polarization curves revealed that the testing dwell time and step size did not result in any significant deviation. To confirm this conclusion, impedance diagrams obtained during the successive impedance measurements at four potential steps corresponding approximately to potentials of -0.50, -0.25, 0, and 0.25 V vs. MSE are presented, interpreted, and compared in Figure 4(a, b, c, d).

Fig. 4 presents Nyquist plots obtained at different selected potential steps from successive EIS tests with different dwell times and step sizes. As observed in Fig. 4(a)-(c), the Nyquist diagrams were very similar for each tested condition.

A conventional truncated and depressed semicircle classically seen for a passive film/electrolyte interface was observed. There was more discrepancy between the Nyquist diagrams in Fig. 4(d) as a function of the tested parameters, most likely because of the significant increase of the current density near this potential. The dissolution-repassivation-redissolution process occurring within this potential range is sensitive to small differences in potential. In any case, the impedance values remained of the same order of magnitude. The parameters for interpreting the EIS diagrams are reported as a function of the experimental conditions in Table 1: C ∞ is the capacitance obtained from the complex capacitance representation, δ is the calculated thickness of the passive film according to Eq. 4, the values of α and Q eff were determined from enhanced graphical representation, ρ δ,c is the calculated resistivity according to Eq. 8, which was used to calculate the characteristic frequency using the following equation:

N 8 = &%2 3,O --. . (10)
Here, f δ is the characteristic frequency, indicating the limit of the frequency domain of validity of the PLM ([f 0 ; fδ]). The fitted value of resistivity at the interface between the passive film and electrolyte, ρ δ , is also reported and compared with the calculated value. R ct and C PLM are the charge-transfer resistance and calculated capacitance, respectively, and are also reported in Table 1. R ct was only considered at the potential of -0.50 V vs. MSE.

Consistent with previous observations, even though the values of the EIS parameters were not identical, they were still of the same order of magnitude. First, because the experiments were conducted using an overpotential relative to E OCP , it is possible that the potentials for each specimen were not exactly -0.50, -0.25, 0.0, and 0.25 V vs. MSE. In addition, the differences in the values is mainly included in the standard deviation of such tests. It is also worth mentioning that for some cases, the values of the fitted resistivity and the calculated one are different for the same experimental conditions. This difference is most likely linked to the sensitivity of ρ δ , which is closely related to the determination of δ, α, and Q eff . Except for ρ δ and ρ δ,c , the experimental conditions did not appear to significantly affect the values of the EIS parameters. For all the presented potentials, the deviations for α and Q eff were very narrow. At -0.50 and -0.25 V vs. MSE, the capacitance estimated from the complex capacitance representation and the calculated thickness of the passive films were quite close for the different experimental conditions. The capacitance was approximately 3 μFcm 2 , and the thickness of the passive film was approximately 3 nm. At the potential of 0.0 V vs. MSE, the estimated capacitance increased and the thickness of the passive film was reduced to less than 3 nm. Finally, at the potential of 0.25 V vs. MSE, the capacitances increased to higher than 5 μFcm 2 and the calculated thicknesses of the passive film were below 2 nm. According to the polarization curves in Fig. 3, the potential of 0.0 V vs. MSE is the starting potential of the second oxidation process, which is consistent with an increasing capacitance and a decreasing thickness. For the last potential, no clear tendency could be extracted from the comparison of the capacitance and thickness under the different experimental conditions.

In conclusion, the validity of the SEIS method was confirmed in this preliminary work: the reconstructed potentiostatic polarization curves and potentiodynamic polarization curves shown in Fig. 3 exhibit the same tendency, the same potential of transition, and similar current densities and the impedance data do not show any significant dependence on the experimental conditions (dwell time and step size). The current densities measured using the potentiostatic method were close for each dwell time and lower than those measured using the potentiodynamic method, suggesting that steady state was reached. Furthermore, during successive electrochemical impedance measurements, the high frequencies were principally investigated (100 kHz-0.1 Hz) because the capacitive behavior of a passive film mainly contributes at high frequencies.

These results indicate that the basic prerequisites of compliance of linearity, stability, and causality necessary to perform EIS analysis were satisfied [START_REF] Hamadou | Electrochemical impedance spectroscopy study of thermally grown oxides exhibiting constant phase element behaviour[END_REF].

The overall testing time for each impedance measurement (100 kHz-0.1 Hz) was ~2 min. As the dwell times and step sizes used in this study had no significant effect on the EIS results, a dwell time of 120 s and a step size of 50 mV were selected to minimize the duration of the experiment while maintaining the accuracy of the analysis.

Investigation of passive behavior at different pH

The previously validated method was used to study the electrochemical behavior of the Ni-20Cr alloy in three different solutions: Initially, the samples were immerged for 24 h in the different solutions to allow the growth of the passive film and steady state to be reached. The Nyquist plots are presented in Fig. 5, and the results obtained using the enhanced graphical method and fitting are presented in Table 2. The electrochemical impedance diagrams for the three solutions were characterized by truncated and depressed semicircles. The values of the impedance at low frequencies were high, consistent with the presence of a passive film. With increasing pH of the electrolyte, C ∞ decreased and the thickness increased. For both the acidic and near-neutral solution, the calculated capacitance from the complex representation was approximately 5 μFcm -2 and the estimated passive film thickness was approximately 2 nm. Notably, the passive film grown in the borate buffer solution had a smaller capacitance and higher thickness. For the CPE parameters (α and Q eff ) estimated from the graphical representation, there was no significant differences among the values. The α values were higher than 0.9. These results indicate the high homogeneity and capacitive behavior of the passive film formed at OCP in the three different solutions. The fitted value of ρ δ decreased with increasing pH, suggesting modification of the outer layer of the passive film in terms of charge carrier density or hydroxide/oxide ratio. Except for the passive film grown in borate buffer solution, no obvious deviation between the fitted and calculated values of ρ δ was observed. However, for the three experimental conditions, the calculated capacitance from the PLM was comparable to the value estimated from the graphical representation, validating the consistency of this approach. For the charge-transfer resistance (R ct ), the values were of the same order of magnitude (10 6 Ωcm 2 ), which is consistent with the existence of a protective passive layer [START_REF] Chen | Application of Impedance Spectroscopy and Surface Analysis to Obtain Oxide Film Thickness[END_REF].

XPS was employed to determine the compositions of the passive films. Fig. 6 presents high-resolution spectra of the Cr 2p 3/2 , Ni 2p 3/2 , and O 1s regions of the Ni-20Cr alloy passive film after 24 h of immersion in the different solutions. A summary of the binding energies corresponding to the different forms of the studied chemical elements is presented in Table 3 [START_REF] Biesinger | Resolving surface chemical states in XPS analysis of first row transition metals, oxides and hydroxides: Cr, Mn, Fe, Co and Ni[END_REF][START_REF] Feng | Passivity of 316L stainless steel in borate buffer solution studied by Mott -Schottky analysis , atomic absorption spectrometry and X-ray photoelectron spectroscopy[END_REF][START_REF] Biesinger | X-ray photoelectron spectroscopic chemical state Quantification of mixed nickel metal, oxide and hydroxide systems[END_REF][START_REF] Kunihiko Chiba | H2O trapping on various materials studied by AFM and XPS[END_REF][START_REF] Luo | Effect of cold deformation on the electrochemical behaviour of 304L stainless steel in contaminated sulfuric acid environment[END_REF]. The Cr 2p 3/2 spectra were fitted using the method presented by Biesinger et al. [START_REF] Biesinger | Resolving surface chemical states in XPS analysis of first row transition metals, oxides and hydroxides: Cr, Mn, Fe, Co and Ni[END_REF]. The Cr 2p 3/2 spectra were fitted with seven peaks, shown in Fig. 6 (a). The peaks at low binding energy at approximately 574.2 eV correspond to metallic Cr(0), and those at the higher binding energy of 577.4 eV can be assigned to chromium hydroxide Cr(OH) 3 . The remaining five peaks at binding energies of 575.7, 576.7, 577.5, 578.5, and 578.9 eV are attributed to chromium oxide Cr 2 O 3 .

The 2p 3/2 region of Ni was fitted according to data found in the literature [START_REF] Chen | Application of Impedance Spectroscopy and Surface Analysis to Obtain Oxide Film Thickness[END_REF][START_REF] Biesinger | Resolving surface chemical states in XPS analysis of first row transition metals, oxides and hydroxides: Cr, Mn, Fe, Co and Ni[END_REF]. From this deconvolution, three different chemical environments were extracted.

That at the low binding energy of 852.7 eV can be attributed to Ni(0) in the metallic state. At higher binding energy, two different contributions were fitted to account for nickel oxide and hydroxide. The two peaks appeared at 853.8 and 855.6 eV, respectively. Their positions were constrained to Ni(0) to enable an estimate of the different oxide and hydroxide ratios in the film. Conversely to the presented results, Ni metal is usually fitted with an asymmetric line shape because Ni metal conducts electrons [START_REF] Biesinger | X-ray photoelectron spectroscopic chemical state Quantification of mixed nickel metal, oxide and hydroxide systems[END_REF]. However, the results deviation is not significant in our case.

The O 1s spectra were fitted with three components of oxide O 2-, hydroxide OH -, and water H 2 O. The peak at 530.2 eV corresponds to O 2-, which can be attributed to the metallic oxides in the passive film. However, the peaks at 531.8 and 533 eV correspond to OH -of metallic hydroxides and bonded water/adsorbed water or impurities on the surface of the sample [START_REF] Kunihiko Chiba | H2O trapping on various materials studied by AFM and XPS[END_REF][START_REF] Luo | Effect of cold deformation on the electrochemical behaviour of 304L stainless steel in contaminated sulfuric acid environment[END_REF].

The Cr 2 O 3 /Cr(OH) 3 ratio in the acidic, neutral, and basic solutions was 2.5, 2.1, and 1.7, respectively, and the NiO/Ni(OH) 2 ratio was 0.5, 0.6, and 0.2, respectively. Notably, the ratios of the metal oxides formed in acidic and neutral solution were close; however, the ratio decreased in basic solution. This result indicates that the compositions of passive films formed in acidic and neutral solutions are closer, consisting of many more metallic oxides than metallic hydroxides. This finding could be confirmed by the ratio of O 2-/OH -from the spectra. The O 2-/OH -ratio of the passive film formed in acidic, neutral, and basic solutions was 0.34, 0.3, and 0.24, respectively. The evolution of the passive film with the pH of the solution observed in this study is consistent with that reported in other works using XPS or other analytical surface techniques [START_REF] Freire | The passive behaviour of AISI 316 in alkaline media and the effect of pH : A combined electrochemical and analytical study[END_REF][START_REF] Liu | Influence of pH on the passivation behavior of 254SMO stainless steel in 3.5% NaCl solution[END_REF].

For comparison with impedance data, the thickness of passive film may be estimated from XPS measurements as followed [START_REF] Benoit | Comparison of different methods for measuring the passive film thickness on metals[END_REF]: [START_REF] Tanuma | Electron Inelastic Mean Free Paths. V. Data for 14 Organic Compounds over the 50-2000 eV Range[END_REF], the estimated thickness of passive film formed in solutions of pH =2, pH =5.8 and pH =9.2 are 2.9 nm, 2.8 nm and 2.5 nm, respectively. The estimated deviation of the thickness measurement obtained with this method is commonly 15-20%. Consequently, the thickness obtained by XPS analysis was consistent with the thickness determined by impedance diagrams investigations. However, it worth mentioning that the trend of the evolution of the thickness of passive film with the solution pH was different for both techniques. For impedance study, the thickness increased with the pH, while the contrary was observed by XPS. One possible explanation remains on the contribution of the hydroxide form which is not taken into account in Eq.11, whereas the presence of hydroxide was more pronounced into passive films grown in basic solution.

P QR = S QR /T cos W X #1 + Y Z[ \] Y \] • `\] `Z[ \] • a \] a Z[ \] ' (11

Analysis of passive film properties from successive impedance diagrams

The measured potentiostatic polarization curves in the three solutions are presented in Fig. 7; the potentiodynamic curves are shown for comparison. As described in part 4.1, the shape of the polarization curves obtained using the SEIS method were similar to those of the dynamic polarization curves, and the current densities were of the same order of magnitude.

In the three solutions, passive behavior was observed for both the potentiodynamic and potentiostatic polarization curves. The corrosion potentials increased in the positive direction with decreasing pH. In acidic solution, the corrosion potential was approximately -0.37 V vs. MSE, and the transpassive region began at 0.3 V vs. MSE. Similarly, for the neutral solution, the corrosion potential shifted to -0.52 V vs. MSE, and the passive-transpassive transition region was smoother and detected at 0.22 V vs. MSE. The curve obtained in basic solution had secondary oxidation peaks, as discussed before. The corrosion potential was approximately -0.65 V vs. MSE, and the secondary oxidation started at 0 V vs. MSE.

According to the polarization curves, the analysis of the impedance diagrams using the PLM model was only applied in the potential domain of existence of the passive film. Thus, for the basic solution, the evolution of the resistivity in the potential range corresponding to secondary oxidation and the transpassive phenomenon are not discussed. Another EEC must be developed for this potential range.

In the passive domain, each impedance diagram was analyzed using the enhanced graphical method and fitted with SIMAD according to the EEC presented in Fig. 1. The charge-transfer resistance was used to fit the first four potentials when the cathodic reaction was considered. However, as the chargetransfer resistance tended to an infinite value, it is not taken into account. The evolution with applied potential of all the other parameters obtained by the analysis is reported in Fig. 8.

Fig. 8(a) shows the evolution of the thickness of the passive film with the applied potential. The passive film formed in borate buffer solution was the thickest, with those formed in the acidic and neutral solutions having similar thicknesses. This result can be attributed to the presence of a large amount of hydroxide in the passive film at high pH [START_REF] Sato | Thickness and structure on iron in acidic and basic solution[END_REF]. The thickness of the passive film formed in acidic solution (pH=2) was stable and close to 1.7 nm up to the potential of 0.1 V vs. MSE. When the applied potential was over 0.1 V vs. MSE, the thickness decreased sharply to less than 1 nm. The thickness of the passive film formed in the neutral solution of 0.01 M Na 2 SO 4 (pH=5.8) changed less when the potential reached more anodic values, maintaining a value between 1.5 and 2.0 nm in the potential range from -0.5 to 0 V vs. MSE. Beyond that range, for more anodic applied potentials, the thickness decreased. The calculated thickness of the passive film in borate buffer solution decreased from 3.2 nm at a potential near -0.6 V vs. MSE to 1.5 nm at a potential of 0.5 V vs. MSE. In all the cases, a decrease of the passive film thickness occurred before the sharp increase in current density related to the secondary oxidation of Cr. This finding indicates that the thickness of the passive film evolves even if the measured current density remains constant. The decrease of the thickness with increasing potential may be related to the semiconductor properties of Cr oxide grown on Ni-Cr alloys [START_REF] Ter-Ovanessian | Passive films growth on different Ni-Cr alloys from the migration of cation vacancies[END_REF]. Effectively, as Cr oxide acts as a p-type semiconductor, the generation of cation vacancies promoted by the increase of potential results in a thinning effect of the passive layer.

The evolution of the CPE parameters (α and Q eff ) with potential is shown in Fig. 8 (b) and (c). Similar trends were observed for the evolution of α in acidic and neutral solution. In the range of potentials lower than -0.1 V vs. MSE , a plateau was observed. The value of α remained approximately 0.95 in the plateau region, indicating that the distribution within the passive film did not change with applied potential in this range. When the applied potential was more anodic than -0.1 V vs. MSE, α significantly decreased from 0.95 to 0.8 for potentials between -0.1 V vs. MSE and 0.50 V vs. MSE. This result indicates that continuous evolution of the passive film occurred during the polarization and occurred before the transpassive potential. In addition, the potential applied in the anodic direction over -0.1 V vs. MSE, Q eff , continuously increased with imposed anodic potential and exceeded 10 -4 μFcm -2 s 1-α at 0.50 V vs. MSE. . A similar result was observed for the borate buffer solution. The value of α remained stable at approximately 0.92 in the potential range [-0.6 V vs. MSE; -0.25 V vs. MSE], followed by a decrease to 0.85 at 0.05 V vs. MSE. In the potential range of secondary oxidation, the value of α increased again, reaching approximately 0.89 at 0.3 V vs. MSE, suggesting the formation of a new oxide layer at the surface. When the potential was nobler than 0.3 V vs. MSE, α decreased continuously. The variation of α indicates a change of the structure of the passive film with applied potential. The decrease of α generally indicates an increase of the dispersion of time constants related to surface heterogeneity or chemical composition distribution within the passive film [START_REF] Hirschorn | Determination of effective capacitance and film thickness from constantphase-element parameters[END_REF]. It may also suggest the transition from a protective passive layer to a reactive surface at transpassive potentials.

The evolution of the resistivity ρ 0 at the interface between the Ni-Cr alloy and passive film with potential in the three electrolytes is shown in Fig. 8 (d). In the potential range from -0.1 to 0.1 V vs. OCP, the impedances were fitted with the equivalent circuit considering the contribution of the charge-transfer resistance (Fig. 2). There was no obvious change of resistivity ρ 0 (interface between the Ni-Cr alloy and passive film) resulting from the cathodic reaction. With further increase of the applied potential, ρ 0 decreased, reached a plateau, and finally decreased again. The evolution of ρ 0 is closely related to the evolution of the current density (Fig. 7), and the transition potentials are similar. The evolution of ρ 0 suggests modification of the Ni-Cr/passive film interface by the presence of more point defects locally decreases the resistivity. This finding indicates that ρ 0 and the measured current density are closely related to the transport of point defects and the electrochemical kinetic constants at this inner interface.

The evolution of the resistivity ρ δ at the interface between the passive film and electrolyte with potential is shown in Fig. 8 (e). The value of ρ δ was fitted using the PLM and was drastically lower than ρ 0 . The ρ δ value in the acidic solution was 10 6 Ω cm at approximately -0.49 V vs. MSE and remained steady until the applied potential reached 0.0 V vs. MSE. Then, ρ δ increased to 10 7 Ω cm at a potential of 0.35 V vs. MSE. The evolution of ρ δ in the neutral solution followed a similar trend to that in the acidic solution. The first fitted value of ρ δ at -0.50 V vs. MSE was approximately 10 6 Ω cm, and the value remained almost stable up to -0.1 V vs. MSE. After that, ρ δ increased with increasing potential. Conversely, a different trend was observed for the evolution of ρ δ in the boric buffer solution. The first fitted value for ρ δ at -0.60 V vs. MSE was approximately 10 5 Ω cm, which is smaller than that in the other two media. Then, upon further increase in the applied potential, ρ δ continued increasing to approximately 10 6 Ω cm at a potential of 0.0 V vs. MSE. The value of ρ δ in boric acid solution was lower than that in the acidic and neutral solutions. This difference was caused by the different chemical compositions of the passive film in solutions of different pH, as confirmed by the XPS results. The evolution of ρ δ indicates continuous modification of the outer oxide layer with the applied potential, suggesting variation of the oxide/hydroxide ratio or densification of this outer layer.

Evolution of resistivity profiles as a function of polarization and pH

Using the values of α, ρ 0 , and ρ δ , resistivity profiles throughout the passive film were constructed for each tested potential using Eq. 5. The calculated distributions of resistivity within the passive films grown in the different solutions are shown in Fig. 9. Adimensional thickness and normalized resistivity were selected to highlight the common tendency of passive film variation with applied potential for all the tested solutions.

For all the cases, the resistivity distribution profile consisted of two separate parts. From the alloy/passive film interface, the first part consisted of a plateau with ρ equal to ρ 0 . The second part reflects power-law decay of the resistivity, reaching the passive film/solution interface resistivity ρ δ . This dual distribution of the resistivity can be understood from the dual structure of the passive film with an inner dense oxide layer and an outer hydrated and hydroxide layer. As the value of ρ 0 is high and close to the resistivity of the bulk oxide, the length of the plateau may be related to the size of the inner chromium oxide layer and the decay may be related to the modified oxide being affected by the vicinity of electrolyte. It is also interesting that the resistivity distribution profile is similar to the transition layer model proposed by Sato [START_REF] Sato | Thickness and structure on iron in acidic and basic solution[END_REF]. In the transition layer model, the passivating film consists of an inner anhydrous oxide layer and an outer hydrous oxide layer. There is a critical extent of hydration that depends on the solution pH and decreases with decreasing concentration of OH -in the solution.

In the acidic and neutral solutions (Fig. 9 (a) and (b)), the lengths of the plateau were quite similar, almost 50% of the total thickness of the passive layer. The distributions of the resistivity were also close, indicating that the passive films that formed in the acidic and neutral solutions were similar. This finding is consistent with the XPS results showing that the compositions of the passive films formed in the acidic and neutral solutions were similar. The length of the plateau was shorter (approximately 25% of the total thickness) in Fig. 9 (c), indicating that the dense chromium oxide in the passive film formed in basic solution was thinner. This last result is consistent with the presence of more hydroxide in the passive film grown in the borate buffer solution.

The evolution of the resistivity profiles was similar for the three tested solutions.

The length of the plateau decreased with increasing applied potential. As ρ δ increased with the applied potential, the resistivity decay was smoother at higher potential. These results suggest that during the anodic polarization, the passive film is modified all along its thickness: the defectiveness of the inner oxide increases (ρ 0 decreases) as the thickness decreases; while ρ δ of the outer layer of the passive film increases, suggesting chemical modification of this layer in terms of the density of point defects or the chemistry. This last tendency is more noticeable for the passive film grown in the acidic and neutral solutions. Hence, increasing the applied potential appears to affect the charge-carrier transport and distribution throughout the passive film. This evolution is consistent with the following transpassive phenomenon that relies on a charge-transfer reaction that the passive film is no longer blocking as well as a potential dissolution of the film.

In-situ analysis of passive film behavior during polarization

One of the most important findings of this work is that the passive film continuously evolves during the polarization test even if the polarization curves show a current density plateau. Another result is that regardless of the pH, the evolution of the passive film properties shows similar trends in the potential range of "passive behavior". Fig. 10 presents a schematic representation of the evolution of the different parameters measured and determined from the analysis of the impedance diagram for the passive film grown in borate buffer solution. It is worth mentioning that the transitions indicated below (related to modification of the trend in the evolution of the parameters) were also observed for the other tested cases but shifted to less cathodic potentials as the solution pH decreased, which is consistent with the OCP shift.

The potential-step polarization curve reveals three potential domains: one corresponding to the increase of the current density from low current density at E OCP to the current density of the passive plateau, one corresponding to the passive plateau, and one corresponding to the transpassive phenomenon. As previously mentioned, the evolution of ρ 0 is related to the evolution of the current density during polarization. This relation indicates that the metal/passive film interface evolves via the generation and transport of cation vacancies from the electrolyte/passive film interface. The electrochemical kinetic constants are linked to the annihilation of those vacancies. For the passive plateau, although the current density remains constant, α and ρ δ change after remaining constant with the applied potential. This result indicates that the modifications of the structure of the passive film (thinning of the inner oxide layer) related to its chemical composition (change in oxide/hydroxide ratio) or its reactivity (increase of the point defect densities or mobilities or the balance of the electrochemical reaction kinetics) are promoted before the transpassive phenomenon but also before the thinning. Indeed, the thickness of the passive film decreases while the transpassive potential is not reached. This work demonstrates the evolving character of the passive film. Even if polarization curves indicate the steady-state character of the passive film in a potential range (passive plateau), its structure, chemistry, or properties differ significantly as a function of the potential. Such behavior is generally hidden in conventional potentiodynamic studies.

It is also important to notice that by applying SEIS and the proposed analysis methodology to adjust the electrochemical impedance diagrams, the evolutions of the parameters α, ρ 0 , and ρ δ clearly demonstrate that the PLM impedance is related to the anodic contribution of the current density and ionic species distribution and transport through the passive film.

Conclusion

In this work, an electrochemical analysis method combining potentiostatic polarization with electrochemical impedance measurement at each potential step was used to successfully study the passive behavior of Ni-20Cr binary alloy. This method, termed successive electrochemical impedance spectroscopy (SEIS), was tested under various experimental conditions (dwell times and step sizes). The effects of the duration between each potential step and potential step size on the potentiostatic polarization curves were investigated, and the results were validated by comparison with more conventional potentiodynamic polarization curves. Our findings confirmed that the potentiostatic polarization curves were comparable to the potentiodynamic polarization curves (scan rate of 0.5 mV/s) and that the electrochemical impedance measurements were not significantly affected by those parameters.

In the second part of this study, the optimized method was applied for the study of passive films grown on a binary Ni-20Cr alloy in three solutions with different pH values. This method shows great potential for the study of passivity phenomenon owing to the interpretation of the impedance data through enhanced graphical representation and the power-law model allowing more parameters related to the passive film properties to be determined. Indeed, the application of SEIS provides a lot of information on the passive film properties and their evolution with the applied potential. Using this proposed methodology, it is possible to explore the evolutionary nature of a passive film. Hence, as a complement to monitoring the evolution of the current density (measured at each potential step), the modification of the thickness, chemical composition, and reactivity can be assessed in situ using this original method.

  ) where P QR (nm) is the thickness of the chromium oxide, b QR /T and b c /T are the intensities of the chromium in the oxide and metallic forms, respectively. d c /T and d QR /T are atom densities of the chromium in the metallic and oxide forms (d c /T = 83 atom/nm 3 and d QR /T = 41 atom/nm 3 ) and S c /T and S QR /T are attenuation lengths of the chromium in the metallic and oxide forms. While S c /T and S QR /T are calculated considering this work

Figure captions:Fig. 1 .

 1 Figure captions:

Fig. 2 .

 2 Fig. 2. Electrical equivalent circuit (EEC) used to fit impedance diagrams.

Fig. 3 .

 3 Fig. 3. Comparison of potentiodynamic polarization curve (straight line, 0.5 mV/s) and potentiostatic curves for Ni-20Cr alloy in solution pH=9.2 for a) different dwell times and b) different step sizes.

Fig. 4 .

 4 Fig. 4. Nyquist diagrams for Ni-20Cr alloy obtained at different potentials for different dwell times and step sizes in aerated 0.05 M H 3 BO 3 + 0.075 M Na 2 B 4 O 7 10H 2 O borate buffer solution (pH=9.2): a) near -0.50 V vs. MSE, b) near -0.25 V vs. MSE, c) near 0.0 V vs. MSE, and d) near 0.25 V vs. MSE.

Fig. 5 .

 5 Fig. 5. Nyquist diagrams obtained at the OCP for Ni-20Cr alloy in the three aerated solutions at pH=2, pH=5.8, and pH=9.2.

Fig. 6 .

 6 Fig. 6. XPS spectra of (a) Cr 2p 3/2 , (b) Ni2p 3/2 , and (c) O 1s of the passive film formed on Ni-20Cr in solution with (1) pH=2, (2) pH=5.8, and (3) pH=9.2.

Fig. 7 .

 7 Fig. 7. Potentiodynamic polarization curves obtained at a scan rate of 0.5 mV/s (line) and from potentiostatic measurements (symbol) for Ni-20Cr alloy in the three aerated solutions with pH=2, pH=5.8, and pH=9.2.

Fig. 8 .

 8 Fig. 8. Evolution of physical parameters: (a) calculated thickness of passive film, (b) CPE exponent α, (c) CPE parameter Q eff , (d) resistivity ρ 0 (alloy/passive film interface), and (e) resistivity ρ δ (passive film/electrolyte interface) for the Ni-20Cr alloy in the three aerated solutions with pH=2, pH=5.8, and pH=9.2.

Fig. 9 .

 9 Fig. 9. Normalized resistivity of passive film of Ni-20Cr alloy in solution of (a) pH=2, (b) pH=5.8, and (c) pH=9.2 from Eq. (4) as a function of dimensionless position with ξ as a parameter.

Fig. 10 .

 10 Fig. 10. Schematic representation of the evolution of the different impedance parameters related to the film passive properties.

Table 1

 1 Interpreted impedance parameters using the enhanced graphical method, calculation and fitting from the impedances performed at different potentials .

	Potential	Step	Dwell	C∞	α*	Qeff (μF/cm 2 s 1-α )	δ (nm) **	fδ (MHz)	ρδ,c	CPLM	Rct (kΩcm 2 )	ρδ (kΩcm) ***
	applied	size	time	(μF/cm 2 ) *		*		**	(kΩcm) **	(μF/cm 2 )	***
	(V vs.	(mV)	(s)							**
	MSE)
	-0.50	50	30	2.81	0.93	10.36	3.7	11.77	12.73	2.95	3.68×10 3	25.15
				3.25	0.92	11.75	3.2	11.93	12.56	3.20	2.30×10 3	26.08
				3.52	0.94	10.07	3.0	0.92	162.1	3.48	1.82×10 3	27.86
		25		3.91	0.93	11.29	2.7	1.40	106.8	3.86	2.85×10 3	88.95
	-0.25	50	30	2.96	0.89	15.51	3.1	0.11	363.38	2.94	-	410.18
				3.36	0.89	15.14	3.1	3.19	940.25	3.34	-	380.12
				2.95	0.90	12.93	3.6	0.47	320.29	2.94	-	316.63
		25		3.97	0.91	14.02	2.6	1.56	710.01	3.94	-	336.49
	0.0	50	30	4.12	0.83	45.69	2.5	0.29	523.40	4.11	-	826.43
				3.90	0.84	42.16	2.4	0.37	276.13	3.87	-	974.43
				3.73	0.83	42.66	2.8	0.34	436.38	3.62	-	718.29
		25		4.54	0.84	36.44	2.3	0.14	1667.00	4.51	-	1637.12
	0.25	50	30	10.46	0.86	79.00	1.7	0.16	14.00	7.48	-	26.68
				5.85	0.86	74.31	1.8	0.20	10.0	5.82	-	9.97
				6.24	0.87	78.74	1.7	55.08	2.72	5.94	-	5.94
		25		8.09	0.85	108.68	1.3	5.36	23.39	8.22	-	15.75

Table 2

 2 Interpreted impedance parameters using the enhanced graphical method, calculation and fitting from the impedances performed at OCP in the different

	10 g/L Na 2 SO 4 acidified with

Table 3

 3 XPS binding energies E b

	Cr2p 3/2	peak	Cr(0) Cr 2 O 3	Cr 2 O 3	Cr 2 O 3	Cr 2 O 3	Cr 2 O 3	Cr(OH) 3
	[38]			(1)	(2)	(3)	(4)	(5)
		E b /eV 574.2 575.7	576.7	577.5 578.5 578.9 577.4
	Ni 2p 3/2	peak	Ni(0) NiO	Ni(OH) 2
	[39,40]
		E b /eV 852.7 853.8	855.6
	O 1s	peak	O 2-	OH -	H 2 O
	[41,42]			metallic	bonded
				hydroxides	water
		E b /eV 530.2 531.8	533

Acknowledgments

The authors acknowledge funding received from the region of Auvergne-Rhône-Alpes in France (SCUSI 2018/18 006577 01-22464), Brigitte Georges (Science et Surface) for the XPS measurements, Jules Galipaud for assistance with the XPS analysis, and the China Scholarship Council (CSC) for the Ph.D. grant for Zhiheng Zhang.

Data availability

The raw/processed data required to reproduce these findings cannot be shared at this time as the data also forms part of an ongoing study.

Table captions:

Table Interpreted impedance parameters using the enhanced graphical method, calculation and fitting from the impedances performed at different potentials.

Table Interpreted impedance parameters using the enhanced graphical method, calculation and fitting from the impedances performed at OCP in the different electrolytes.