## 3 Results and Discussion
### Spontaneous Growth of Passive Films on Stainless Steels and Inconel 600  
#### 3.2.1 Electrochemical Impedance Spectroscopy  
The evolution of the Nyquist diagrams as a function of the immersion time in the solution simulating reinforced concrete for the three alloys is shown in Figure 4. For the three alloys, the capacitive loop has a diameter that increases with the exposure time, meaning that the resistance of the passive films increases with the immersion time, which is in agreement with the literature [9; 26; 44]. All authors [9; 44; 26] suggest that the steady state of the steels exposed to alkaline media is well established after 3 days of immersion. Therefore, we chose to collect EIS data only during this time-lapse [9; 26]. For both AISI 304 and AISI 316, the impedance measurements were performed to show that the capacitive loop has a linear behavior at low-frequency ranges after 72 h of immersion. Suggesting that the film formed is stable and protective. This tendency is less clear for Inconel 600, meaning that the amplitude of the capacitive loops is less than that for the AISI 304 and \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **AISI 304** & **AISI 316** & **Inconel 600** \\ \hline Residual current & & & \\ (\(\mu\)A\(\cdot\)cm\({}^{-2}\)) cycle 1 & 14.55 & 11.57 & 15.60 \\ Residual current & & & \\ (\(\mu\)A\(\cdot\)cm\({}^{-2}\)) cycle 12 & 6.88 & 3.95 & 4.86 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The residual current of the passivity domain of both types of stainless steel (AISI 304 and AISI 316) and Inconel 600 was determined from the cyclic voltammograms. Figure 3: Bode plots (\(\log|\) Z 1) of AISI 304, AISI 316 and Inconel 600 in NaOH solution after twelve cyclic voltammograms. AISI 316 stainless steel. This result indicates that the films formed on Inconel 600 are less effective than those formed on stainless steel. The results of EIS measurements were exploited using an equivalent electrical circuit (EEC). Several equivalent circuits have been tested, and the circuit depicted in Figure 5 with two times constant was selected to fit the experimental data because it gave more reliable results and allowed the simulation of EIS data with the same circuit for all three samples, which allows for easy comparison. This circuit was applied in other studies to describe passivation for AISI304 [44], AISI316 [26] and Inconel [45], which is why it seems we adapted it to our electrochemical system. The EEC fitting parameters are described in Tables 3-5. The use of EEC suggests that the passive film contains porosities in which the electrolyte penetrates [39; 46]. The expression of the total impedance of the EEC is given by Equation (4). The half circles observed on the Nyquist diagrams are more or less flattened, which is explained by the non-ideality (roughness) of the electrode surface. So, it would be  
Figure 4: Experimental and simulated Nyquist plots as a function of immersion time obtained for (**A**) AISI 316. (**B**) AISI 304. (**C**) Inconel 600 in a NaOH (pH = 13) solution at OCP (from 100 kHz down to 5 mHz). better, as shown in Equation (5), to replace the pure capacities of the circuit with constant phase elements CPE: CPE\({}_{1}\) with a capacitance C\({}_{1}\) and an exponent \(\alpha_{1}\) and CPE\({}_{2}\) with a capacitance C\({}_{2}\) and an exponent \(\alpha_{2}\). The properties of the CPE depend on the values of \(\alpha\). When \(\alpha\) is equal to 1, the CPE behaves as a pure capacity and when \(\alpha\) is equal to 0.5, the CPE behaves like an impedance of Warburg (diffusional control during the film formation). \[Z(\omega)=R_{e}\frac{R_{1}}{\frac{1}{1+(Z_{2}(\omega)/R_{1})}+(j\omega R_{1}C_ {1})^{\alpha_{1}}} \tag{4}\]  
\[Z_{2}(\omega)=\frac{R_{2}}{1+(j\omega R_{2}C_{2})^{\alpha_{2}}} \tag{5}\]  
In our case, the literature [1; 26] suggests that the first time constant is associated with the charge transfer process where R\({}_{1}\) is the charge transfer resistance, and CPE\({}_{1}\) is the capacitance of the double layer at high frequencies.