## 3 Results and Discussion
### Spontaneous Growth of Passive Films on Stainless Steels and Inconel 600
#### 3.2.2 Atomic Force Microscopy  
Some AFM images (500 nm \(\times\) 500 nm) of the passive films formed on the polished substrates (see Figure 1 for the memory of the bare substrate) as a function of the immersion time in an alkaline solution simulating reinforced concrete (NaOH at pH = 13) are given in Figures 7-9 for the two types of stainless steel, AISI 304 and AISI 316, and Inconel 600 samples respectively. In Figures 7A and 8D, representing the surfaces of the stainless steel after 30 min immersion, polishing grooves can be observed and the first stage of passivation, which consists of the formation of small circular oxide grains distributed over the entire active surface and growing along trenches due to the polishing steps. The size of these grains increases with the immersion time until coalescence at t = 3 h1/2, which can be seen on the AFM images (see Figures 7B and 8E). Coalescence generates the covering of the whole surface, and the growth becomes less and less visible. On the surface of Inconel 600, we do not observe the same behavior as for stainless steel. Indeed, in Figure 9A, which represents the surface Inconel 600 after t = 1/2 h immersion, the polishing grooves are less visible than for stainless steel because the oxide film may be thicker. We noticed that the small oxide structures do not have a well-defined shape on the entire surface. As for AISI 304 and 316 at an immersion time of t = 3 h1/2, Inconel 600 shows the formation of oxide grains that cover its entire surface (Figure 9B). To quantify these observations, we determine the Root Mean Square (RMS) surface roughness parameter for the different immersion times using the following expression (The used formula is one of the mathematical definitions of RMS surface roughness). \[\text{RMS}\sqrt{\left(\frac{\sum_{i=1}^{512}\sum_{j=1}^{512}h_{ij}^{2}}{512^{ 2}}-\left\langle\eta\right\rangle^{2}\right)} \tag{6}\]  
where \(\left\langle\eta\right\rangle\) is the mean height of the height distribution \(h_{ij}\). In Figure 10, we show the variation of the RMS roughness as a function of the square root of the immersion time. The square root of time was used only out of better data presentation matter. For all three alloys, the RMS value increases at t = 1/2 h, consistent with the value of the bare substrate and decreases until reaching a minimum at t = 1 h for the AISI 316 and Inconel 600 and at t = 3 h1/2 for the AISI 304. At longer immersion times, the roughness increases again for the three alloys; for the AISI 316, a maximum is reached at t = 24 h, then will decrease until t = 72 h. The decrease of the RMS for Inconel 600 is between t = 3 h1/2 and t = 24 h after, the RMS seems to be constant. For the three alloys, when the immersion time is low, it is reasonable to say that the RMS may be controlled by the surface roughness of the bare substrate. On the surface of the stainless steel (Figures 7A and 8A), we observed the formation of small oxide grains isolated on the entire surface that will promote the increase of RMS at t = 1/2 h. We noticed that the size of these grains is much smaller than the ones observed in [PERSON]. [PERSON] et al. 's work [26] on carbon steel. With the expansion of immersion time in the alkaline solution, the grain size will tend to increase until coalescence (Figures 7B and 8E); this will cause the RMS to decline. This decrease results from the fact that the size of the grains increases progressively with the time of immersion, causing a covering of the trenches. Therefore, the oxide film has thickened. The influence of the substrate is then lost, and the RMS parameter is essentially controlled by the future growth of the passive film. Unlike stainless steel, the Inconel 600 at t = 1/2 h (Figure 9A) shows a porous film that covers entirely the substrate. This film is constituted of oxide grains of a larger size and round or elongated shapes.