## Materials and Methods  
### Materials  
In this work, two types of stainless steel and nickel-based alloy were provided by Goodfellow; their chemical composition is given in Table 1.  
The samples (size: 1 \(\times\) 1 cm\({}^{2}\)) were embedded in an epoxy resin, then abraded with wet SiC paper of decreasing grit size (1000, 2400 and 4000) and polished with a diamond paste (particle size: 3 and 1 \(\upmu\)m). The polisher is marketed by PERSI company, allowing for the control of the rotation speed (\(\omega\) in rad/s), the time (t in s) and the force (F in N) applied on the sample. The different polishing steps were quickly controlled by an optical microscope and then by AFM. After polishing, the sample was extracted from the epoxy resin and then rinsed in ultrasound baths with acetone, ethanol, and deionized water, then air-dried. The final substrate surface was checked for the three alloys by AFM, as shown in Figure 1. Low roughness surfaces (RMS: AISI 304 = 3.0 \(\pm\) 0.1 nm, AISI316 = 2.70 \(\pm\) 0.1 nm, Inconel 600 = 2.8 \(\pm\) 0.2 nm) were obtained. Since the roughness values are very close together, we could not distinguish and characterize the surface topography from one sample compared to another by using only this parameter. As can be seen in Figure 1, proper polishing grooves appear parallel at this micrometer scale. To obtain a physical parameter other than the RMS roughness to characterize each substrate, we calculate the self-correlation function G defined as:  
\[G(k_{1},k_{2})=\sum_{i=1}^{512}\sum_{j=1}^{512}h(i,j)\times h(i+k_{1},j+k_{2}) \tag{1}\]  
From the geometric point of view, this function probes the correlation between the original image and an image shifted by a distance \(k_{1}\) (\(k_{2}\)) in the x (y) direction with respect to the center of the original image. This function always reaches its maximum at the center of its image, and the shape of the central peak gives access to the grains' mean geometrical shape [14]. If there is a periodicity in the image, it will also appear in the self-correlation image. In our case, trenches due to polishing are parallel and separated by a mean distance 1 that is determined using the sections associated with each self-correlation image. The sections show maximums corresponding to the periodicity due to parallel trenches. By measuring the distance between two maxima, we obtain the characteristic parameter 1 corresponding to the mean distance separating two trenches (for example, see the section of image A1 in Figure 1). To obtain a more precise value of l, we measured the distance between 10 maximums and divided the measured value by 10 to obtain l for each substrate. We obtain l = 110 \(\pm\) 10 nm for the Inconel 600 substrate, l = 193 \(\pm\) 20 nm for AISI304, and l = 83 \(\pm\) 15 nm for AISI316 substrates. To conclude, the several lengths l obtained are different for each substrate, and l is a parameter that allows for the characterization of the differences between the surface topographies due to our polishing technique before the passivation process starts.  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**Elements** & **Cr** & **Ni** & **C** & **N** & **Si** & **Mn** & **Mo** & **Cu** & **S** \\ \hline AISI 304 & 18 & 10 & 0.053 & 0.04 & 0.48 & 1.42 & 0.39 & 0.14 & 0.024 \\ AISI 316 & 18 & 10 & 0.053 & 0.025 & 0.75 & 1.24 & 3.0 & 0.2 & 0.027 \\ \hline
**Elements** & **Cr** & **Fe** & **C** & **N** & **Si** & **Mn** & **P** & **Ti** & **S** \\ \hline Inconel & & & & & & & & & & \\
600 & 29 & 10 & 0.033 & 0.007 & 0.28 & 0.65 & 0.007 & 0.28 & 0.003 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Chemical composition of two types of stainless steel (AISI 304 and AISI 316) and Inconel 600.