## 3 Results and Discussion
### Spontaneous Growth of Passive Films on Stainless Steels and Inconel 600
#### 3.2.2 Atomic Force Microscopy
When the immersion time reaches t = 3 h 1/2, the same characteristics are found as for the stainless steel, the presence of round oxide grains that develop until they reach coalescence. The obtained film covers the polishing grooves, and the effect of the substrate on the RMS becomes less important. At immersion times of t = 24 h and t = 72 h, the RMS is almost identical, and polishing scratches are less and less visible (Figure 9C). According to the literature [9], this can be due to the thickening of the oxide film with increasing immersion time. From Figure 10 and the above discussion, we can determine the coalescence time of the oxide grains, noting \(\rm t_{coal}\) corresponding to the immersion time where the RMS reaches a minimum before increasing again and corresponds to a substrate completely covered by an oxide layer that can act as an efficient barrier against corrosion. This affirmation will be confirmed by the SKFPM measurements (Section 3.2.3). For Inconel 600 and AISI316 substrates, we obtain the same value of \(\rm t_{coal}\) = 60 min. For AISI304, \(\rm t_{coal}\) = 210 min is slightly longer than for the two other substrates. Moreover, the roughness of the oxide formed on Inconel 600 evolves slowly after 24 h of immersion. The results of the AFM measurements seem to confirm those obtained by EIS and the analysis of Figure 3C, which shows that the Nyquist diagrams obtained at t = 24 h and t = 72 h are almost identical. The value of the resistance \(\rm R_{2}\) of the film was found to be almost identical to the one measured at t = 24 h and t = 72 h. Therefore, there is a correlation between electrochemical impedance measurements and the morphology modification of the oxide surface. To obtain a better inside into the growth mode of the oxide islands on the trenches of the several substrates, we again calculated the self-correlation function images of each topographic image in Figures 7-9. From these images, we can extract two characteristic lengths. Since we observe a periodicity in the cross-sections (see Figures 7A1-C1, 8A1-C1 and 9A1-C1), we determine a periodicity \(\rm l_{1}\). The width of the central peak at half-maximum taken in the direction of the periodicity gives us access to the mean diameter d of the oxide grains. In fact, since clearly the islands grow and coalesce first in the direction perpendicular to the periodicity that corresponds to parallel trenches due to the polishing steps, we can determine only a mean diameter in the direction of the periodicity. In the perpendicular direction, the oxide islands are contiguous since the density of nucleation centers for oxide islands is so important for  
Figure 7: AFM images (500 nm \(\times\) 500 nm) of passive films grown on AISI 304 substrates after polishing as a function of immersion time(t). (**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 \(\rm l_{1}\) and the mean oxide grain diameter d.  
the trenches. Therefore, for an immersion time shorter or equal to 30 min (see Figure 7A), the diameter of an island is great enough to allow the overlapping of neighborings islands along each trench. The results for l\({}_{1}\) and d as a function of immersion time for the three substrates using self-correlation images, such as Figures 7 and 8 (not all images showed), are given in Table 6.  
As can be deduced from the evolution of d and l\({}_{1}\) with the immersion time, the growth mechanism is always the same, whatever the substrate. The first oxide islands grow on the trenches, acting as a source for the nucleation centers. In this case, the mean diameter d is smaller than the average distance l between the trenches, and thus, we observe a periodicity l\({}_{1}\) that corresponds to l. Therefore, the bare substrate remains visible in the topography image.