# Generation of pits on CoCrFeMnNi high entropy alloy: an electrochemical impedance study of a single event

Yaojun Hou, Oumaïma Gharbi, Kevin Ogle, Fan Sun, Mireille Turmine, Vincent Vivier

► To cite this version:

Yaojun Hou, Oumaïma Gharbi, Kevin Ogle, Fan Sun, Mireille Turmine, et al. Generation of pits on CoCrFeMnNi high entropy alloy: an electrochemical impedance study of a single event. Electrochimica Acta, 2025, 526, pp.146193. 10.1016/j.electacta.2025.146193. hal-05041648

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Submitted on 21 Apr 2025

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Distributed under a Creative Commons Attribution 4.0 International License
Generation of pits on CoCrFeMnNi high entropy alloy: an electrochemical
impedance study of a single event

Yaojun HOU,¹ Oumaïma GHARBI,¹ Kevin OGLE,² Fan SUN,² Mireille TURMINE,¹

Vincent VIVIER¹, *

¹ Sorbonne Université, CNRS, Laboratoire de Réactivité de Surface (LRS), Paris, France

² Chimie Paristech, PSL University, CNRS, Institut de Recherche Chimie Paris, Paris, France

*vincent.vivier@sorbonne-universite.fr

**Abstract**

In this study, a single pit was successfully generated on the surface of a CoCrFeMnNi
alloy using a home-made device consisting of an electrochemical work station coupled with
a microflow-cell. The three-dimensional morphology of the single pit was observed by
optical microscopy, revealing that the pit radius increased with the polarization of the
material, while at the same time the pit depth remained constant. Additionally, the various
stages of pit evolution, including pit initiation, pit propagation, and pit repassivation were
investigated as a function of the alloy polarization using electrochemical methods, in
particular, electrochemical impedance spectroscopy (EIS). The incubation and initiation rates
of a single pit increased with the anodic polarization of the electrode, which was attributed to
an increase in the dissolution kinetics. The mechanism during the propagation phase was
shown to be independent of the polarization potential. Interestingly, it was also shown that
the repassivation step occurred in distinct stages, potentially due to a limited ion diffusion,
which warrants further investigation.

**Key words:** Model pit, Electrochemical impedance spectroscopy, High entropy alloys, Single event
Graphical abstract

<figure><img src="image_2.png" /></figure>

<figure><img src="image_3.png" /></figure>
# 1. Introduction

With a multitude of uses, alloys are essential materials that underpin our modern world [1]. However, one of the most detrimental factors affecting alloys is corrosion [2], which can vary depending on the specific composition of the alloy [3], environmental conditions [4], and other factors. Several common types of corrosion are observed in alloys, including uniform corrosion [5]; galvanic corrosion [6]; or pitting corrosion [7] which is characterized by the localized formation of small pits or craters on the alloy surface. Among these different types of corrosion, pitting corrosion is particularly damaging because pits are usually too small to be detected early at the surface of the material, thus progressing rapidly in depth, leading to a reduced equipment lifespan and significant safety risks [2].

Over several decades of pitting corrosion research, many researchers have focused on the influence of the thickness, composition [8], and structure [9] of the passive film on the initiation of pitting corrosion. Frankel et al. [10] proposed in 2017, a unified perspective on the passive film breakdown and pit growth. They suggested that the protective performance of the passive film plays a decisive role in less extreme environments or for alloys less susceptible to pitting corrosion. However, the kinetics and stability of pitting should be considered for more aggressive conditions. Pitting growth kinetics are influenced by the concentration of aggressive anions such as $Cl^-$ and the electrochemical potential of the material. In fact, in some cases, differences in pitting potential can be entirely explained by differences in pitting growth kinetics, indicating that variations in passive film characteristics are not relevant [11], especially when the pit has started to spread.

A significant yet often overlooked scientific issue is the incubation time before pitting initiation, which depends on factors such as the concentration of corrosive species, the polarization of the material, the passive film thickness, and the temperature [12]. Pou et al. [13] investigated the mechanism of iron passive film breakdown by chloride ions in borate buffer solution (pH = 8.4). They showed that the rate of passive film breakdown is proportional to the concentration of $Cl^-$ and hydrogen ions, and is exponentially related to the breakdown potential and potential drop across the oxide film, and were expressed as:

$$ \frac{1}{t_i} = k[Cl^-]^n \qquad (1) $$

$$ \frac{1}{t_i} = ke^{BV} \qquad (2) $$
where $t_i$ is incubation time, $k$ and $n$ are constants, $B$ represents a factor associated with the potential dependence of the reaction rate, and $V$ the applied potential. Additionally, other research groups have reported a relationship between the incubation time and the polarization of the alloy [14,15], concluding that the incubation time decreases as the potential increases.

Natural pits can form randomly across the surface of the material [16], without any specific pattern, making it difficult to study the growth behavior in situ. As a result, artificial pitting is often used for controlled experiments. Ernst and Newman [17] were among the first to study pit growth kinetics in stainless steel foils, showing that pit depth follows a parabolic law with time and is independent of the applied potential, while lateral pit growth is linear with time and dependent on the electrode polarization. However, this 2D single-pit approach can only investigate the evolution of either the lateral or vertical development of pits, failing to fully capture the precise kinetic information of real pits. Later, a new method was developed for creating single pit on stainless steel by masking specimens with photoresist, leaving a 100 µm in diameter unmasked region [18]. However, this method often resulted in small crevice formation at the edges of the masking material before pits could form. To address this issue, several techniques have been developed to prevent crevice corrosion through the local injection of an aggressive solution.

Based on the work developed by Fushimi et al. [19,20], single pit generation and propagation on iron was studied in acidic, neutral and basic solutions [21,22]. This method, which involves the production of a limited quantity of chloride ions by means of an Ag/AgCl microelectrode, does not, however, allow measurements to be made for long propagation times. Then, Aouina et al. and Heurtault et al. [23–25] devised an alternative technique that made use of a glass microcapillary, positioned near the electrode surface. The microcapillary was attached to a syringe, loaded with chloride ion solution, and a syringe pump to regulate the injection rate. This device has proven to be an efficient tool for studying localized corrosion.

Aouina et al. [26] successfully prepared single-pit corrosion on the surface of 316L stainless steel using a glass capillary technique and investigated the influence of $SO_4^{2-}$ and $ClO_4^-$ anions on the single-pit propagation mechanism. Heurtault et al. [24] conducted experiments on the initiation and propagation of single pit on 316L stainless steel using the same technique. They examined the radial and depth evolution of disk-shaped single pits, revealing a critical pitting depth and determining a minimum bulk chloride ion concentration
required to sustain single-pit propagation. Tian et. al [27,28] employed this method to investigate metastable pitting corrosion and the effect of the applied potential on the initiation of single pits on stainless steel. Their results showed that the average lifetime of metastable pits decayed with applied potential. Moreover, they observed that pit mouth morphologies and three-dimensional structures, including pit volume, depth, and width, increased with the alloy polarization. However, their research focused primarily on the initiation of single pits, with less attention given to the propagation and repassivation steps.

To date, no study has explored the effect of the polarization of the material on the initiation, propagation, and repassivation mechanisms of high-entropy alloys for generating a single pit. Therefore, this work is focused on the study of these mechanisms during the different stages of the formation of a single pit on CoCrFeMnNi (Cantor alloy) using electrochemical methods, and particularly electrochemical impedance spectroscopy (EIS).

## 2. Experimental

### 2.1 Sample preparation

The cantor alloy was fabricated using PIM-25 pressurized induction furnace as described elsewhere [29]. The chemical composition for the cantor alloy used was Ni=19.1, Cr=20.2, Fe=20.6, Mn=20.8, and Co=19.3 (at.%). Samples were cut into sheets with a dimension of 5×5×15 mm³. Before experiments, sample surface was ground with a series of P240 to P4000 grit SiC papers, rinsed with deionized water and ethanol, and dried under a stream of high-purity N₂ gas.

### 2.2 Electrochemical measurement

All the electrochemical experiments were performed using a three-electrode cell and a Gamry Ref 600+ potentiostat. The working, reference and counter electrodes were the Cantor alloy, a saturated calomel electrode (SCE), and a platinum grid, respectively. The experiments were performed in a 0.5 M H₂SO₄ solution. EIS was carried out with a sinewave potential amplitude of 10 mV, in a frequency domain ranging from 100 kHz to 10 mHz. This amplitude was selected so as to fulfill the linearity and stationarity of the measurement.

### 2.3 Generation of a single pit

In order to investigate the susceptibility of the Cantor alloy to pitting corrosion, an electrochemical workstation dedicated to single pit investigation was developed (Fig. 1). This device, already described elsewhere in more detail [24–26], consisted of an
electrochemical cell, a syringe pump, a micropositioning system to handle the microcapillary, and a low-noise and wide current range potentiostat. The position of the microcapillary above the surface sample can be controlled by measuring the electrolyte resistance [29,30].

The Cantor alloy was immersed in a 0.5 M H₂SO₄ electrolyte solution, keeping the surface of the sample facing up. The micro capillary (outer diameter is 1.6 mm, inner diameter is 2 µm) was set on the top of Cantor alloy, the distance of the capillary to the sample was about 10 to 15 µm. The capillary was connected to a syringe, which was filled with concentrated Cl⁻ solution diluted in a sulfuric acid electrolyte (1 M NaCl + 0.5 M H₂SO₄), in order to inject, at will, Cl⁻ ions using a KD Scientific syringe infusion pump. The flow rate of the injection was controlled by the syringe pump, and in this work, the injection rate was 0.1 µL/min. The experimental procedure for preparing the metallic substrate consisted of a one-minute polarization at -0.5 VₛCE (to always have the same condition for the surface sample), followed by a potentiodynamic polarization from -0.5 to a selected potential between 0.3 and 0.7 VₛCE to control the passive film formation. Then, the sample was left at the corrosion potential for 30 minutes. The last step was to inject Cl⁻ at a given potential to study the effect of the polarization on the single pit. During the single pit propagation step, EIS measurements can be performed (see below).

<figure><img src="image_4.png" /><figcaption>**Fig. 1.** Sketch of electrochemical device developed for generating a single pit.</figcaption></figure>

## 2.3 3D observation

The pits generated were observed using an OLYMPUS DSX1000 optical microscope and a Genetic Pro microscope, Delta Optical, allowing a 3D observation of the sample.
### 3. Results and discussion

#### 3.1 Electrochemical behavior of passive film

The main goal of this study is to focus on the passive films formed after 30 min by a potentiostatic polarization at different potentials on the passive domain, namely 0.3, 0.4, 0.5, 0.6, and 0.7 V~SCE~. These potentials are shown on the polarization curve of the Cantor alloy obtained in 0.5 M H~2~SO~4~ solution (Fig. 2).

<figure><img src="image_5.png" /><figcaption>**Fig. 2.** Potentiodynamic polarization curve for the Cantor alloy in 0.5 M H~2~SO~4~ at a scan rate of 0.1 mVs~1~. The impedance measurements were performed at the five potentials depicted in the curve.</figcaption></figure>

After 30 minutes of potentiostatic polarization at different potentials on the passive domain to control the passive film formation on the Cantor alloy surface, EIS measurements were performed, as shown in Fig. 3. The Nyquist plots show a capacitive behavior, which is similar in shape for all polarization potentials, with very high impedance values in the range of 200 kΩ·cm~2~. This response corresponds to a charge transfer resistance in parallel with a constant phase element (CPE) representing the dielectric properties of the passive film. It is noteworthy that, as shown in Fig. 3, the impedance response (in amplitude) is slightly smaller only at 0.4 V~SCE~, while for the other passive potentials, the impedance responses almost overlap.
<figure><img src="image_6.png" /><figcaption>Fig. 3. Electrochemical impedance spectroscopy on the Cantor alloy in 0.5 M H₂SO₄ solution at different potentials on the passive domain.</figcaption></figure>

From the analysis of the EIS response, in particular the high frequency domain, the high-frequency capacitance ($C_∞$) can be obtained either from the capacitance plot [30,31] or from the measurement model analysis [32,33]. The high-frequency capacitance calculated using these two methods is remarkably similar. In this study, the measurement model was used. As outlined in references [33,34], the calculation process involves fitting the data by connecting an appropriate number of voigt elements in series. The measurement model then provides the total resistance and high-frequency capacitance values. Assuming that the dielectric contribution of the double layer can be neglected in the EIS analysis for the system formed by the passive film in series with the double layer, the value of $C_∞$ allows the thickness of the passive film to be readily estimated as:

$$ \delta = \frac{\varepsilon\varepsilon_0}{C_\infty} \qquad (3) $$

where $\delta$ is the thickness of passive film, $\varepsilon_0$ the vacuum permittivity ($\varepsilon_0 = 8.85 \times 10^{-14} F \cdot cm^{-1}$), and $\varepsilon$ the relative permittivity of the passive film. The permittivity of the passive film formed on the Cantor alloy is 13.5, as reported in a previous study [29]. The value of $\delta$ is corrected by the ratio $S_{eff}/S_{geo}$, where $S_{eff}$ is the effective surface area of the passive film, which is about three times the geometric area, $S_{geo}$ [35,36]. The results of the thickness calculation are presented in Table 1. It can be observed that the thickness of the
passive film initially decreased with increasing polarization potential, decreasing from 1.7 nm at 0.3 V~SCE~ to 1.1 nm at 0.4 V~SCE~. Subsequently, the thickness significantly increased, reaching about 2.4 nm at 0.5 V~SCE~, which is twice the value at 0.4 V~SCE~. For higher potentials on the passive domain, the thickness thus remained relatively constant. In a previous study, Haupt et al. [37] prepared passive films on FeCr alloys in sulfuric acid solutions by applying different potentials (all within the passive range) and used X-ray photoelectron spectroscopy (XPS) to calculate the passive film thickness. They concluded that the thicknesses of the passive films on Fe15Cr alloys in 0.5 M H~2SO~4 solution increased linearly with the polarization potentials. However, this trend was not observed in the present study, likely due to the influence of five elements (Co, Cr, Fe, Mn, Ni) in the alloy matrix on metal dissolution and passivation behavior at various potentials.

<table><caption>**Table 1.** Values of C~∞~ and calculated thicknesses of passive film formed on the Cantor alloy in 0.5 M H~2SO~4 for different passive potentials.</caption><thead><tr><th></th><th>0.3 V<sub>SCE</sub></th><th>0.4 V<sub>SCE</sub></th><th>0.5 V<sub>SCE</sub></th><th>0.6 V<sub>SCE</sub></th><th>0.7 V<sub>SCE</sub></th></tr></thead><tbody><tr><td>C<sub>∞</sub> /μF·cm<sup>-2</sup></td><td>19.7±1.9</td><td>32.2±2.3</td><td>14.4±1.4</td><td>13.7±2.6</td><td>14.5±1.8</td></tr><tr><td>d /nm</td><td>1.7±0.2</td><td>1.1±0.1</td><td>2.4±0.2</td><td>2.5±0.5</td><td>2.4±0.3</td></tr></tbody></table>

## 3.2 Electrochemical behavior of single pit

**Fig. 4** shows the evolution of the current measured for a Cantor alloy electrode in a 0.5 M H~2SO~4 solution at different potentials during Cl~⁻~ injection. For each experiment, the initial time ($t = 0$) corresponds to the time of Cl~⁻~ injection. Initially, during the first moment of Cl~⁻~ ion injection, no current increase was observed, corresponding to the pitting incubation period [38]. As the Cl~⁻~ injection was sustained, the passive film began to break down, and the current increased rapidly, indicating the onset of the pitting initiation phase [39]. Once the current reached a certain value, it stabilized and fluctuated slightly, indicating that the pitting propagation phase had been reached. In this domain, the current followed Ohm's law: the higher the polarization potential, the higher the current. After a 90-minute Cl~⁻~ injection, the injection was stopped and the current progressively dropped, indicating the repassivation of the material [40]. In roughly 20 to 30 minutes, the single pit site completed the repassivation process, and the current dropped back to extremely low levels, corresponding to a return to the passive state. This result shows that in acidic condition, the pit propagation on Cantor
alloy requires a continuous supply in chloride ions, otherwise it repassivates.

<figure><img src="image_7.png" /><figcaption>**Fig. 4.** Current evolution measured for the Cantor alloy during the Cl⁻ injection at different polarization potentials in 0.5 M H₂SO₄. The injected solution was 1 M NaCl + 0.5 M H₂SO₄ with an injection rate of 0.1 µL/min.</figcaption></figure>

**3.3 3D pictures and description of the pits**

After 90 minutes of Cl⁻ corrosion followed by 30 minutes of repassivation at different polarization, the samples showed single pits of different sizes, as shown in **Fig. 5**. This figure presents 3D images of the single pit on the surface of the Cantor alloy, observed from both top and side of the electrode. The top view images clearly show that the area of the single pits increased with the polarization, while the depth showed no significant variation. The characteristics, including diameter, depth, and volume of each single pit are given in **Table 2**, the errors in the pit diameter and depth correspond to the uncertainties in the measurement process, where the volume is calculated assuming that the pits are elliptical cylinders. To better illustrate the evolution of single pit radius and depth as a function of the polarization potential, the relevant parameters are presented in **Fig. 6 (a)**. The pit diameters increased almost linearly with the polarization potential, showing only a slight decrease at 0.7 V~SCE~. The pit depths range from 0.23 to 0.33 mm as shown in **Table 2**, while the volume of the pit increased with the potential, from 0.19 mm³ at 0.3 V~SCE~ to 0.32 mm³ at 0.5 V~SCE~, and further to 0.41 mm³ at 0.7 V~SCE~.
The ratio of pit depth to the pit radius was also calculated and presented in Fig. 6 (b). It decreased slightly with increasing polarization potential, but it remained relatively stable between 0.45 and 0.5. When this ratio is 1, the pit shape is hemispherical. However, in this study, pits were shallower, with a ratio of about 0.5, thus indicating that the pit was in the form of flattened cylinders or a disc-shaped [28].

<figure><img src="image_8.png" /><figcaption>**Fig. 5.** Optical images of the top surface and 3D reconstruction of the shape of single pits generated on the Cantor alloy at different polarization potentials with the injection of Cl⁻ for 90 min: (a1) (a2): 0.3 V<sub>SCE</sub>, (b1) (b2): 0.4 V<sub>SCE</sub>, (c1) (c2): 0.5 V<sub>SCE</sub>, (d1) (d2): 0.6 V<sub>SCE</sub>, (e1) (e2): 0.7 V<sub>SCE</sub>.</figcaption></figure>

<figure><img src="image_9.png" /><figcaption>**Fig. 6.** Diameter and depth of a single pit as a function of the polarization potential (a), and ratio of the pit depth to the pit radius as a function of the polarization potential (b).</figcaption></figure>

<table><caption>**Table 2.** Parameters measured from optical observation of single pit performed at different polarization potentials on the Cantor alloy in 0.5 M H₂SO₄ with injection of Cl⁻ for 90 min.</caption><tr><td>Polarization potential / V<sub>SCE</sub></td><td>0.3</td><td>0.4</td><td>0.5</td><td>0.6</td><td>0.7</td></tr><tr><td>Average diameter / mm</td><td>1.04±0.03</td><td>1.12±0.05</td><td>1.29±0.04</td><td>1.35±0.08</td><td>1.29±0.07</td></tr></table>
<table><tr><td>Depth / mm</td><td>0.23±0.03</td><td>0.33±0.04</td><td>0.29±0.04</td><td>0.32±0.04</td><td>0.26±0.03</td></tr><tr><td>Volume / mm³</td><td>0.19±0.01</td><td>0.32±0.01</td><td>0.37±0.01</td><td>0.46±0.01</td><td>0.41±0.01</td></tr></table>

The volume of the pit can be calculated using two different methods: the first method uses optical results and assumes that the single pits are cylinder shaped,

$$V = Sh \quad (4)$$

The parameter *S* represents the base area of the elliptical cylinder, which is obtained using a 3D microscope, and *h* denotes the pitting depth of the elliptical cylinder.

Whereas the second method uses electrochemical results and is based on the use of the Faraday's equation from which, the volume can be expressed as:

$$V = \frac{m}{\rho} = \frac{Q \cdot M}{n \cdot F \cdot \rho} \quad (5)$$

In this equation, *V* is the volume of the single pit, *m* is mass of the metal dissolved (g), *Q* is total charge consumed from the pit initiation to its repassivation, which is obtained from the integration of the current, *I*(*t*), with respect to time. *M* is the molar mass of the metal (g/mol), *n* number of electrons involved in the oxidation reaction, and *F* the Faraday constant (96485 C/mol). For an alloy, the number of electrons exchanged during dissolution or passivation is not necessarily straightforward. In this work, we assumed a homogeneous dissolution of each constituent of the alloy, and the parameters used are listed in **Table 3**. As a result, the molar mass and number of electrons are average values calculated from the five elements constituting the alloy. It should also be mentioned that due to discrepancies for the value of the density of the Cantor alloy, a value of 7.96 g/cm³ was chosen [41].

<table><caption>**Table 3.** Molar mass, density and electron number parameters of Co, Cr, Fe, Mn, Ni and Cantor alloy.</caption><thead><tr><td>Elements</td><td>Molar mass g/mol</td><td>Density g/cm³</td><td>n</td></tr></thead><tbody><tr><td>Co</td><td>58.93</td><td>8.86</td><td>2</td></tr><tr><td>Cr</td><td>51.99</td><td>7.15</td><td>3</td></tr><tr><td>Fe</td><td>55.85</td><td>7.87</td><td>2</td></tr></tbody></table>
<table><tr><td>Mn</td><td>54.95</td><td>7.3</td><td>2</td></tr><tr><td>Ni</td><td>58.71</td><td>8.9</td><td>2</td></tr><tr><td>Cantor alloy</td><td>56.10</td><td>7.96</td><td>2.2</td></tr></table>

The calculation results are shown in **Fig. 7**. The volumes calculated based on the elliptical cylinder assumption are represented by black squares, with error bars reflecting measurement uncertainties in the single pit radius and depth. The volumes calculated using the Faraday's equation are shown using red spheres. It can be observed that for the lower polarization potentials, the two sets of data are largely in agreement. However, for higher polarization potentials, the volumes calculated using the elliptical cylinder assumption are higher than those derived from the Faradaic formula, with a discrepancy in the range of 20 %. This suggests that the elliptical cylinder assumption is reasonable for calculating the pit volume for potentials close to the corrosion potential, whereas, at higher potentials, this assumption becomes less accurate, and the actual pit volume is smaller, possibly resembling a conical shape, which is rather difficult to assess from optical observation of a metallic substrate.

<figure><img src="image_10.png" /><figcaption>**Fig. 7.** Volumes of single pits performed at different polarizations for the Cantor alloy in 0.5 M H₂SO₄ with Cl⁻ injection for 90 min. Black squares: values based on elliptical cylinder assumption; red spheres: values based on the use of the Faraday's law and the parameters presented in Table 3.</figcaption></figure>

As shown in **Fig. 5**, the top of the pit is covered by a lacy metal cover, which complicates microscopic observation. Even after removing the lacy cover, it remains
challenging to obtain a cross-section of the pit along its depth, as the pit cavity can be either
larger or smaller than the diameter of the pit mouth. To address this point, a stable pit at 0.3
V<sub>SCE</sub> for 30 minutes was selected and closely studied by optical microscopy. The pit
diameter at different depths was determined through sequential polishing [28], thus allowing
the longitudinal cross-section of the pit to be observed at various steps of the pit depth, as
shown in **Fig. 8**. The diameter inside the pit was found to be larger than the pit mouth (e.g.,
the length bb' is larger than aa'), indicating that the pit extends not only longitudinally but
also laterally, which may explain the formation of the lacy cover observed in **Fig. 5**, as
reported by Ernst et al [17]. Additionally, **Fig. 8** shows that the bottom of the pit
approximates a conical shape, which explains why assuming an elliptical cylinder shape for
the pit results in an overestimation of its volume.

<figure><img src="image_11.png" /><figcaption>**Fig. 8.** Shape of pit observed after different steps of polishing for an experiment performed at +0.3 V<sub>SCE</sub> in 0.5 M H<sub>2</sub>SO<sub>4</sub> and a 30 minutes Cl<sup>-</sup> injection.</figcaption></figure>

**3.4 Different periods in the single pit growth process**

**3.4.1 Incubation and initiation of single pit**

It's particularly interesting to study the incubation and initiation periods of single pit
formation for different polarization potentials on the Cantor alloy during Cl⁻ injection. As
shown in **Fig. 9**, the current remains very low at the beginning of Cl⁻ injection,
corresponding the incubation period. During this period, there is no significant change in the
current. As illustrated in Fig. 9, at 0.3 V$_{SCE}$, 9 minutes of Cl⁻ injection are required to initiate pit, while at 0.4 and 0.5 V$_{SCE}$, it only takes 2 minutes. For larger potential, e.g., at 0.7 V$_{SCE}$, only 1 minute is needed. It is evident that the incubation time for pit decreases with the increase in polarization potential.

Once the Cl⁻ concentration is sufficient to locally break down the passive film, the current increases rapidly, indicating the initiation of the pit. A typical feature of the initiation period is that the sharp rise in current, and the amount of Cl⁻ required to trigger it, depend on the polarization of the Cantor alloy. The slope of this period represents the growth rate of the single pit, which can be calculated using the following formula:

$$k = \left| \frac{I_n - I_{n-1}}{t_n - t_{n-1}} \right| \qquad (6)$$

where k represents the growth rate of the pit, I$_n$ and I$_{n-1}$ are current values at times t$_n$ and t$_{n-1}$, respectively. The growth rate of the single pit increases with the polarization potential, as shown in Table 4. It rises from 0.94 µA/min at 0.3 V$_{SCE}$ to 2.4 µA/min at 0.5 V$_{SCE}$, and reaches 12 µA/min at 0.7 V$_{SCE}$, corresponding to an increase by a factor of approximately 13.

<figure><img src="image_12.png" /><figcaption>Fig. 9. Current variations as a function of time for various polarizations of the Cantor alloy in 0.5 M H$_2$SO$_4$ during the Cl⁻ injection.</figcaption></figure>

<caption>Table 4. the rates of single pits initiation with various polarization potential.</caption>
<table><tr><td>V<sub>SCE</sub></td><td>0.3</td><td>0.4</td><td>0.5</td><td>0.6</td><td>0.7</td></tr><tr><td>k / μA·min<sup>-1</sup></td><td>0.94</td><td>9.1</td><td>2.4</td><td>12</td><td>12</td></tr></table>

There are several possible reasons why the incubation time becomes shorter and the growth rate increases as the polarization potential increases. One reason could be the properties of the passive film at different polarization potentials, such as its thickness. The thickness of the passive film may decrease with increasing polarization potential, which could lead to a shorter initiation time for pitting corrosion and a faster pit growth rate. However, as shown in **Table 1**, the thickness of the passive film formed on the Cantor alloy in 0.5 M H₂SO₄ actually increases with higher polarization potentials. This suggests that the accelerated pit initiation rate with increasing polarization potential is not due to a reduction in film thickness. In fact, an increase in film thickness tends to slow down the pit initiation rate.

Another possible reason is that the increase in polarization potential enhances the dissolution kinetics of the alloy. Hou et al. [29] studied the corrosion mechanism of Cantor alloy, where the five elements in the alloy can be generalized as "M". According to McCafferty's study [42], the corrosion mechanisms of the Cantor alloy in 0.5 M H₂SO₄ with Cl⁻ can be expressed as follows:

$$M + H_2O \leftrightarrow M \cdot H_2O_{ads} \qquad (7)$$

$$\leftrightarrow MCl_{ads}^{-} + H_{2}O \qquad (8)$$

$$M \cdot H_{2}O_{ads} + Cl^{-} \leftrightarrow MOH_{ads}^{-} + H^{+} + Cl^{-} \qquad (9)$$

$$MCl_{ads}^{-} + MOH_{ads}^{-} \rightarrow MOH^{+} + M + Cl^{-} + 2e^{-} \qquad (10)$$

Eqs. 8 and 9 represent competition processes. In concentrated acidic solutions, Cl⁻ adsorption predominates over OH⁻ adsorption. The dissolution of the Cantor alloy is primarily described by Eq. 10, which is the rate determining step. Therefore, for a given amount of Cl⁻, the polarization potential accelerates the pit initiation by enhancing the kinetics of passive film failure, as expressed in Eq. 10.
### 3.4.2 Propagation of single pit

Once the single pit initiates with a high growth rate, it reaches a steady-state propagation phase that can be monitored by a stable current. Electrochemical impedance spectroscopy was thus performed during this period, corresponding to 60 minutes of Cl⁻ injection for various polarization potentials of the Cantor alloy (Nyquis plots in Fig. 10 and Bode plots in Fig. S5). The EIS results show two time-constants: the first one is a capacitive loop in the high-frequency domain, which corresponds to the charge transfer resistance in parallel with the interfacial capacitance. Interestingly, high frequency capacitive loop overlay each other within experimental error, indicating that this time constant is essentially independent of the polarization potential. The second time-constant appears as a short line as the beginning of a second capacitive loop, which may correspond to the diffusion of species or the resistance of the oxide film in single pit. It should be noted at this point the current is not sufficiently stable during the propagation phase of the pit to allow accurate impedance measurements to be performed at frequencies lower than 100 mHz. The measured impedance reflects the total impedance of the system, which includes both the impedance of the single pit and the surrounding passive film on the rest of the electrode surface. The impedance of the single pit can be extracted from the total impedance using following equations:

$$ \frac{1}{Z_{tot}} = \frac{1}{Z_{pit}} + \frac{1}{Z_{film}} \qquad (11) $$

Where $Z_{tot}$ is the impedance of the whole electrode, $Z_{pit}$ is the impedance of the single pit, and $Z_{film}$ is the impedance of the passive film.

Given that $Z_{film} \gg Z_{pit}$, the following equation can be derived based on Eq. 11:

$$ Z_{pit} \approx Z_{tot} \qquad (12) $$

Therefore, the impedance is primarily attributed to the contribution of a single pit. This conclusion can also be drawn from pit experiments conducted on samples with different surface areas. For details, refer to the supplementary materials. The impedance diagrams at different potentials nearly overlap and exhibit the same characteristic frequency, implying that the propagation of the single pit is independent of the polarization potential. This is a striking result for a dissolution process. However, this can be interpreted by a diffusion limited process in the solution inside the pit during the propagation step.
<figure><img src="image_13.png" /><figcaption>**Fig. 10.** EIS spectra of single pit at different polarization potentials measured during the propagation period in 0.5 M H₂SO₄ during the Cl⁻ injection.</figcaption></figure>

To investigate the mechanism of the pit propagation under different polarization potentials, EIS was performed as shown in **Fig. 11**. The impedance was measured for one hour every ten minutes on a limited frequency domain.

<figure><img src="image_14.png" /><figcaption>**Fig. 11.** EIS evolution with propagation of single pit at different polarization potentials in 0.5 M H₂SO₄ during the Cl⁻ injection.</figcaption></figure>

As presented in **Fig. 11**, the impedance response consists of two time-constants, the
high-frequency region displays a typical capacitive loop that slightly varies with times. The low-frequency part of the impedance varies with the polarization potential. At lower polarization potentials (0.3 and 0.4 V~SCE~), the low-frequency impedance is hardly distinguishable. Here again, it should be noted that reaching frequency below 1 Hz is challenging since the system must remain in steady-state during the whole duration of the measurement. For higher polarization potentials (0.5-0.7 V~SCE~), the low-frequency impedance exhibits a second capacitive loop, which is related to slower electrochemical processes at the interface. In this case, the formation of adsorbate intermediates may contribute to this time-constant. It is important to mention that the comparison of impedance values without taking into account the exposed surface of the alloy must be carried out with caution, therefore it is not possible to measure the evolution of the pitting size during an experiment at a fixed potential.

Another observation is that, under different polarization potentials, the impedance spectra exhibit the same shape regardless of pit propagation time. This indicates that the mechanism of single pit propagation does not change on this potential domain. From these results and the optical observation discussed in the previous section, the propagation of a single pit is along its depth rather than its mouth. Alternatively, it may proceed through lateral expansion within the interior of the pit, as illustrated in **Fig. 8**. This behavior for a single pit is in agreement with our previous work on pitting corrosion of Cantor alloy [29]. Indeed, the fit of the EIS data can be readily obtained by using the dissolution mechanism of the alloys as further developed in the Supporting Information.

### 3.4.3 Repassivation of single pit

After approximately 90 minutes, the chloride ion injection was stopped, but the polarization was maintained. At this point, repassivation spontaneously occurred, and the evolution of the current is shown in **Fig. 12** (the stop of the injection was chosen as the reference time, *t* = 0, for this figure). The repassivation process is clearly divided into three parts, as indicated in **Fig. 12**. The first and third parts are approximately linear, with the slopes of these lines representing the repassivation rate. The calculated results are presented in **Table 5**. Although there is no clear numerical pattern in the repassivation rate while increasing the polarization potential, a general trend of increasing repassivation rate can be observed as the polarization potential increases. For instance, in the first stage, repassivation rate increases from -1.86 µA·min⁻¹ at 0.3 V~SCE~ to -1.78 µA·min⁻¹ at 0.6 V~SCE~, and to -2.1 µA·min⁻¹ at 0.7 V~SCE~. In the third region, it varies from -1.34 µA·min⁻¹ at 0.3 V~SCE~ to -1.14
µA·min⁻¹ at 0.6 V<sub>SCE</sub>, and -2.63 µA·min⁻¹ at 0.7 V<sub>SCE</sub>.

<figure><img src="image_15.png" /><figcaption>**Fig. 12.** Evolution of single pit current as a function of time during the repassivation period for various polarization potential after 90 min Cl⁻ injection in 0.5 M H₂SO₄.</figcaption></figure>
<table><caption>**Table 5.** Slope of the curves recorded during the repassivation process for the periods I and III, and relation between current and square root of time for the period II.</caption><thead><tr><th></th><th>I / μA·min<sup>-1</sup></th><th>II</th><th>III/μA·min<sup>-1</sup></th></tr></thead><tbody><tr><td>0.3</td><td>k<sub>1</sub> = 1.86</td><td>n = 0.57 ± 0.005</td><td>k<sub>3</sub> = 1.34</td></tr><tr><td>0.4</td><td>k<sub>1</sub> = 1.36</td><td>n = 0.93 ± 0.024</td><td>k<sub>3</sub> = 0.97</td></tr><tr><td>0.5</td><td>k<sub>1</sub> = 1.11</td><td>n = 0.73 ± 0.014</td><td>k<sub>3</sub> = 1.62</td></tr><tr><td>0.6</td><td>k<sub>1</sub> = 1.78</td><td>n = 0.59 ± 0.006</td><td>k<sub>3</sub> = 1.14</td></tr><tr><td>0.7</td><td>k<sub>1</sub> = 2.10</td><td>n = 0.85 ± 0.020</td><td>k<sub>3</sub> = 2.63</td></tr></tbody></table>

For the second (or intermediate) stage, the repassivation curve is no longer linear, and the repassivation parameters can be obtained following the work of Kim et. al [43], who expressed the current as a power-law function:

$$i = A * |t - b|^n \qquad (13)$$

where *i* is the current measured during the oxide film formation (repassivation), *A* a constant, *t* the time, *b* the repassivation initial time, with *b*<*t*, and *n* represents the repassivation rate during the second stage. As shown in **Table 5**, the value of *n* increases from 0.57 at 0.3 V<sub>SCE</sub> to 0.95 at 0.7 V<sub>SCE</sub>.

The repassivation process was divided into three stages, with the repassivation rates in the first and third stages being faster than in the second stage. This is likely due to insufficient hydrogen ion diffusion into the single pit during the second stage, which slows the reaction. Once the concentration of hydrogen ions reaches a certain level, the rate of oxide film formation accelerates again. Alternatively, this could be attributed to the formation of a gel-like substance during the repassivation process of the single pit, which inhibits the repassivation reaction.

## 4. Conclusions

This study systematically investigated the formation, growth, and repassivation mechanisms of single pits on the surface of the Cantor alloy under different polarization potentials. Using electrochemical impedance spectroscopy (EIS), 3D microscopy, and other experimental techniques, we explored the electrochemical behavior and morphological changes of single pits during the incubation, initiation, propagation, and repassivation stages, revealing the kinetic characteristics of corrosion at each stage.
Firstly, during the incubation and initiation stages, it was found that the incubation time shortened and the pit growth rate significantly increased with the polarization potential. The higher polarization potentials accelerate the dissolution kinetics of the alloy, leading to rapid pit formation, which was confirmed by electrochemical measurements. The rapid rise in current during the initiation phase marks the localized breakdown of the passive film and the formation of a corrosion pit.

During the propagation phase, the EIS plots showed similar shapes at different potentials, indicating that the propagation mechanism of single pits is independent of the polarization potential. However, the variations in current observed at different potentials reflect differences in pit size, suggesting that while the propagation mechanism remains the same, the pit size varies with the polarization potential. Further morphological observations revealed that during propagation, the single pit mainly extends in the depth direction, while the pit surface area remains relatively unchanged. In addition, the pit volumes showed that the volumes of single pits based on the elliptical cylinder assumption were slightly higher than those calculated using the Faradaic formula. This discrepancy was attributed to the conical shape of the pit bottom, rather than the assumed elliptical cylindrical shape.

The repassivation process was divided into three stages, with the repassivation rates in the first and third stages being faster than in the second stage.

## Acknowledgements

The authors acknowledge the support of the Centre National de la Recherche Scientifique (CNRS) and the funding from the ANR (ANR-20-CE08-0031) - project TAPAS.

## Credit authorship contribution statement

**Yaojun Hou**: Methodology, Investigation, Conceptualization, Data curation, Validation, Formal analysis, Writing - original draft, Writing - review & editing.

**Oumaïma Gharbi, Kevin Ogle, Fan Sun, Mireille Turmine, Vincent Vivier**: Supervision, Project administration, Conceptualization, Methodology, Data curation, Validation, Formal analysis, Writing - original draft, Writing - review & editing.
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