## 3 Results and Discussion
### Spontaneous Growth of Passive Films on Stainless Steels and Inconel 600
#### 3.2.2 Atomic Force Microscopy
\begin{table}
\begin{tabular}{l c c c c c c} \hline \multicolumn{6}{c}{**Inmersion Time (min)**} \\ \hline
**Samples** & **0** & **30** & **60** & **180** & **216** & **1440** & **4320** \\ \hline AISI304 & 1 = 193 \(\pm\) 20 nm & l\({}_{1}\) = 180 \(\pm\) 10 nm & l\({}_{1}\) = 170 \(\pm\) 20 nm & l\({}_{1}\) = 280 \(\pm\) 10 nm & No periodicity & No periodicity & No periodicity \\  & d = 32 \(\pm\) 5 nm & d = 75 \(\pm\) 5 nm & d = 90 \(\pm\) 10 nm & d = 100 \(\pm\) 10 nm & d = 110 \(\pm\) 10 nm & d = 110 \(\pm\) 10 nm \\ \hline AISI316 & 1 = 83 \(\pm\) 15 nm & l\({}_{1}\) = 90 \(\pm\) 10 nm & l\({}_{1}\) = 100 \(\pm\) 10 nm & l\({}_{1}\) = 180 \(\pm\) 10 nm & No periodicity & No periodicity \\  & d = 100 \(\pm\) 10 nm & d = 72 \(\pm\) 5 nm & d = 85 \(\pm\) 5 nm & d = 90 \(\pm\) 5 nm & d = 95 \(\pm\) 5 nm & d = 100 \(\pm\) 5 nm \\ \hline \end{tabular}
\end{table} 
Table 6: Periodicity l\({}_{1}\) and mean oxide grain diameter d as a function of immersion time for the three substrates, as deduced from self-correlation function image calculations (for examples, see Figures 7–9 and related cross-sections). The time t = 0 corresponds to the bare substrate after the polishing steps and l to the mean distance between two trenches, as determined in Figure 1.  
Figure 8: AFM images (500 nm \(\times\) 500 nm) of passive films grown on AISI 316 substrates after polishing as a function of immersion time. (**A**) 1/2 h, (**B**) 3 h 1/2, and (**C**) 72 h. (**A1**), (**B1**), and (**C1**) are self-correlation images calculated using images (**A**), (**B**), and (**C**), respectively, as input with typical cross-sections allowing to determine a periodicity named l\({}_{1}\) and the mean oxide grain diameter d.  
Figure 10: Evolution of the RMS roughness as a function of immersion time for the AISI304, AISI316, and Inconel 600 samples. Figure 9: AFM images (0.5 μm \(\times\) 0.5 μm) of the passive film grown on Inconel 600 substrates after polishing (Figure 1C) as a function of immersion time: (**A**) 1/2 h, (**B**) 3 h 1/2, and (**C**) 72 h. (**A1**), (**B1**), and (**C1**) are self-correlation images calculated using respectively images (**A**), (**B**), and (**C**) as input with typical cross-sections allowing to determine a periodicity named l\({}_{1}\) and the mean oxide grain diameter d.  
At immersion times less than 30 min, the oxide islands are separated, and coalescence along the trenches occurs at t = 30 min (for example, see image A in Figures 7 and 9). At this time, the mean diameter d is large enough and the density of nucleation great enough to allow the neighboring islands to touch each other, conducting to lines of islands separated by a periodicity l\({}_{1}\) equal to l. Afterward, the mean diameter d increases and remains lower than 1/2. At an immersion time corresponding to t\({}_{\text{coal}}\), as determined previously, the oxide islands coalescence also in the direction of the periodicity because d became near to 1/2. At this time, we notice, experimentally, that l\({}_{1}\) became 2 \(\times\) l, showing that the growth remains under the influence of the substrate polishing steps. It is only after an immersion time longer and equal to 3 h that the periodicity l\({}_{1}\) disappears. After this time, the growth is not more under the control of the trenches, i.e., under the control of the bare substrate topography. Afterwards, d increases slowly. The only difference between the samples is that the coalescence in the direction perpendicular to the trenches occurs at a longer immersion time for AISI316 than for the AIS304 and Inconel 600 samples, as observed on the RMS roughness variations as a function of immersion time, as shown in Figure 10.