Passivation-induced physicochemical alterations of the native surface oxide film on 316L austenitic stainless steel

Time of Flight Secondary Ion Mass Spectroscopy, X-Ray Photoelectron Spectroscopy, in situ Photo-Current Spectroscopy and electrochemical analysis were combined to characterize the physicochemical alterations induced by electrochemical passivation of the surface oxide film providing corrosion resistance to 316L stainless steel. The as-prepared surface is covered by a ~2 nm thick, mixed (Cr(III)-Fe(III)) and bi-layered hydroxylated oxide. The inner layer is highly enriched in Cr(III) and the outer layer less so. Molybdenum is concentrated, mostly as Mo(VI), in the outer layer. Nickel is only present at trace level. These inner and outer layers have band gap values of 3.0 and 2.6-2.7 eV, respectively, and the oxide film would behave as an insulator. Electrochemical passivation in sulfuric acid solution causes the preferential dissolution of Fe(III) resulting in the thickness decrease of the outer layer and its increased enrichment in Cr(III) and Mo(IV-VI). The further Cr(III) enrichment of the inner layer causes loss of photoactivity and improved corrosion protection with the anodic shift of the corrosion potential and the increase of the polarization resistance by a factor of ~4. Aging in the passive state promotes the Cr enrichment in the inner barrier layer of the passive film.


Introduction
Stainless steels (SS) are widely used thanks to their excellent mechanical properties and corrosion resistance. Surface analytical studies, including X-Ray Photoelectron Spectroscopy (XPS), performed on ferritic Fe-Cr(-Mo) [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19] and austenitic Fe-Cr-Ni(-Mo)  SS substrates have shown that a continuous and protective surface oxide/hydroxide layer, the passive film, markedly enriched in Cr(III) and only a few nanometers thick when formed at ambient temperature, provides the corrosion resistance. The Cr enrichment in the passive film, which is the key factor for the corrosion resistance, is strong in acid aqueous environment because of the competitive dissolution of the iron and chromium oxide species and comparatively small dissolution rate of Cr(III) oxide. In alkaline aqueous solutions, the lower solubility of Fe(II)/Fe(III) oxides mitigates the Cr enrichment. For Ni-bearing SS, there is no or very little Ni(II) in the passive films and the metallic alloy region underneath the oxide is enriched with Ni(0) [20][21][22][27][28][29][30]. Mo-bearing SS, including austenitic AISI 316L, have better corrosion resistance in chloride-containing environments, where passive film breakdown can be followed by the initiation of localized corrosion by pitting. Mo(IV) or Mo(VI) oxide species enter the passive film composition at a few at% level without markedly altering the thickness [10,21,22,27,30,32,35,37]. Molybdenum has been proposed to mitigate passive film breakdown or to promote passive film repair.
The Cr(III) enrichment may not be homogeneous in the passive film, as suggested by recent studies performed at the nanometer scale [27,41], and the heterogeneities may cause the local failure of the corrosion resistance and of the initiation of localized corrosion [42]. These heterogeneities of Cr enrichment would find their origin in the mechanisms of pre-passivation leading to the initial formation, most often in air, of the native oxide and in the subsequent modifications of the oxide film induced by immersion in solution. The better understanding of the mechanisms governing the Cr enrichment requires to thoroughly investigate both the initial stages of oxidation leading to pre-passivation of the SS surface [43] and the modifications brought by electrochemical passivation of the native oxide-covered SS surface.
Here we report on the properties of the native oxide layer formed on a polycrystalline austenitic 316L SS surface in air and modified by electrochemical passivation in acid solution. Time-of-Flight Secondary Ion Mass Spectroscopy (ToF-SIMS) and XPS surface analysis were used to characterize the layered structure, thickness and composition of the oxide film and their modifications. Photocurrent Spectroscopy (PCS), applied in situ and combined with electrochemical analysis [44][45][46][47], was used to obtain direct information on the electronic properties of the thin photo-conducting surface films. Linear Scan Voltammetry and Electrochemical Impedance Spectroscopy were applied to discuss the corrosion resistance.

Experimental
Polycrystalline AISI 316L austenitic SS samples were used. The bulk wt% composition of the main alloying elements was Fe-19Cr-13Ni-2.7Mo (Fe-20Cr-12Ni-1.6Mo at%). Surface preparation was performed by mechanical polishing first with emery paper of successive 1200 and 2400 grades and then with diamond suspensions of successive 6, 3, 1 and 0.25 μm grades.
Cleaning and rinsing was performed after each polishing step in successive ultrasonicated baths of acetone, ethanol and Millipore® water (resistivity > 18 MΩ cm). Depth profile elemental analysis of the oxide-covered surfaces was performed using a ToF-SIMS 5 spectrometer (Ion ToF -Munster, Germany) operated at about 10 -9 mbar. The depth profile analysis interlaced topmost surface analysis in static SIMS conditions using a pulsed 25 keV Bi + primary ion source delivering 1.2 pA current over a 100 × 100 m 2 area with sputtering using a 1 keV Cs + sputter beam giving a 32 nA target current over a 300 × 300 m 2 area. Analysis was centered inside the eroded crater to avoid edge effects. The profiles were recorded with negative secondary ions that have higher yield for oxide matrices than for metallic matrices. The Ion-Spec software was used for data acquisition and processing.
Surface chemical analysis was performed by XPS with a Thermo Electron ESCALAB 250 spectrometer operating at about 10 -9 mbar. The X-ray source was an AlK monochromatized radiation (h = 1486.6 eV). Survey spectra were recorded with a pass energy of 100 eV at a step size of 1 eV. High resolution spectra of the Fe 2p, Cr 2p, Ni 2p, Mo 3d, O 1s, and C 1s core level regions were recorded with a pass energy of 20 eV at a step size of 0.1 eV. The take-off angles of the analyzed photoelectrons were 40° and 90°. The binding energies (BE) were calibrated by setting the C 1s signal corresponding to olefinic bonds (-CH2-CH2-) at 285.0 eV. Reconstruction of the spectra (curve fitting) was performed with CasaXPS, using a Shirley type background. Asymmetry was taken into account for the metallic components (Cr 0 , Fe 0 , Mo 0 , Ni 0 ) by using the peak shape of LA(α, β, m) [48]. Lorentzian/Gaussian (70%/30%) peak shapes and a broader envelope was used to account for the multiplet splitting of the oxide components (Cr III , Fe III , Mo IV , Mo VI ) [48,49].
Photoelectrochemical and electrochemical analysis was performed using a Zennium electrochemical workstation (ZAHNER, Germany) operated with the Thales software. The measurements were performed in 0.1 M Na2B4O7 electrolyte (di-Sodium tetraborate , pH ~9.5) prepared from pure chemicals (R.P.NORMAPUR®) and Millipore® water using a standard 3-electrode cell with a Pt spiral as the counter electrode and an Ag/AgCl (in 3.5 M KCl) electrode as reference electrode. This buffer solution was selected in order to provide stability to the oxide films during measurements and thus to minimize their alteration. The photocurrent spectra were recorded in the wavelength range from 310 to 700 nm with the Zahner Zennium CIMPS system (TLS-03) at a 3.16 Hz frequency. The electrochemical impedance spectra were generated by applying a sinusoidal signal of 10 mV amplitude over the frequency range 0.1 Hz-100 kHz. The spectra were analyzed with the Zview software

Results and discussion
3.1 Surface analysis

Native oxide film
The ToF-SIMS negative ion depth profiles of the 316L stainless steel sample covered by the native oxide film are shown in Fig. 1. In Fig. 1a, the intensity profiles of secondary ions characteristic for the oxide film ( 18 O -, 18 OH -, CrO2 -, FeO2 -, NiO2and MoO2 -) and the substrate (Cr2 -, Fe2and Ni2 -) are plotted in logarithmic scale versus sputtering time. As proposed previously [50], the profile of the Ni2ions is used to define the position of the "modified alloy" region between the oxide film and the metallic bulk substrate regions, where Ni is found enriched as observed previously on austenitic and duplex stainless steels [20][21][22][27][28][29][30]50]. This region is measured from 20 to 48 s of sputtering time, meaning that the oxide film region is from 0 to 20 s and the metallic substrate region after 48 s. The sputtering rate can be estimated to 0.1 nm s -1 based on the thickness of the oxide film of 2 nm determined by XPS as discussed below. In the surface oxide region, the most predominant profiles of the oxidized metals are those of the CrO2 -, FeO2and to a lesser extent MoO2ions while that of the NiO2ions has much lower intensity, suggesting that only traces of oxidized nickel are present in the native oxide film as supported by the XPS analysis discussed below and in agreement with previous data [20][21][22][27][28][29][30].  Fig. 1b shows that the profiles of FeO2and CrO2ions peak at different positions, at 6 and 10 s, respectively. This is consistent with the native oxide film having a bilayer structure with iron and chromium oxides more concentrated in the outer and inner layers, respectively, as previously reported for oxide films on stainless steels [7,17,27,29,46]. The interface between outer and inner layer can be positioned at 8 s which is the median sputtering time position of the two intensity maxima. In   2 shows the angle-resolved XPS Cr 2p3/2, Fe 2p3/2, Mo 3d, Ni 2p3/2 and O 1s core level spectra recorded at 90 and 40° take-off angles. For the Cr 2p3/2, Fe 2p3/2 and Mo 3d core levels, the intensity ratio of the oxide peaks at higher BE (see below) to the metal peaks at lower BE (see below) increases with decreasing take-off angles, confirming that the oxide film lies above the metallic alloy substrate. The Ni 2p3/2 core level spectra show no oxide peaks at higher BE and an intensity decrease at lower take-off angle of the metal peaks. This is because Ni, only present in the metallic alloy, is increasingly attenuated by the surface oxide film. For the O 1s core level, the intensity ratio of the higher BE peak associated to OHligands (see below) to the lower BE peak associated to O 2ligands (see below) is slightly higher at 90° than at 40°. This indicates some stratification in the depth distribution of the oxide/hydroxide ligands according to the bilayer structure of the oxide film with the hydroxide species more concentrated in the outer layer and the oxide species in the inner layer.
This stratification was repeatedly observed and more marked in the passive films.  Table. 1. The Cr 2p3/2 spectrum (Fig. 3a) was reconstructed using one peak (Cr1) at 574.1 eV, assigned to metallic Cr 0 in the substrate and a series of five peaks (Cr2-Cr6), assigned to Cr III oxide in the surface oxide layer, as proposed previously [48,49]. It was verified that such a series of five peaks could fit the spectrum for an anhydrous thermal Cr oxide film grown by exposing a Cr substrate to gaseous oxygen in the XPS preparation chamber. In the present case, one additional peak (Cr7) at 577.2 eV, was necessary to optimize the fit with the experimental envelope. Given the lower relative intensity of this Cr7 component, it was deliberately chosen to use a single but wider peak rather than a series of five narrower peaks as done for the oxide component. This broad and relatively weak Cr7 component was assigned to Cr III hydroxide in the oxide film [2,16,20], No additional Cr VI component at a BE of 579.5 eV [48] was needed. Similarly, in the Fe 2p3/2 spectrum (Fig. 3b), the peak at 706.8 eV (Fe1) relates to metallic Fe 0 in the substrate and the series of five peaks (Fe2-Fe6) to Fe III in the surface oxide layer [7,23,34,48,51,52]. The additional peak needed at 711.9 eV (Fe7) is assigned to Fe III hydroxide in the oxide film. No series of five peaks associated to Fe II in the surface oxide layer was needed for reconstruction [48]. In the Mo 3d5/2-3/2 core level spectrum ( [22,27,31,33,36,53]. The intensity ratio of the Mo VI to Mo IV doublets is ~8, indicating that Mo VI species are mostly present. The O 1s spectrum (Fig. 3d) was reconstructed with three components at 530.3 (O1), 531.6 (O2) and 532.9 (O3) eV assigned to the oxide (O 2-), hydroxide (OH -) and water (H2O) ligands in the oxide film [11,34]. The broader O3 component may be explained by surface contamination by species including double bonded oxygen. The OH -/O 2intensity ratio is 0.9 for the native oxide. The Ni 2p3/2 spectrum (Fig. 2e) could be reconstructed with a single peak at 852.9 eV BE corresponding to metallic Ni 0 in the substrate [24], evidencing that the Ni oxide species, measured in the oxide film region by ToF-SIMS, were at trace level below the detection limit of XPS (~0.5 at%).
Based on the partition of the oxide film evidenced by the ToF-SIMS data and the depth distribution of the oxygen ligands measured by angle-resolved XPS, a bilayer model was built for quantitative processing of the XPS measured intensities [27]. The model, shown in Fig. 4, assumes a mixed chromium-iron oxide inner layer, neglecting any molybdenum content, and a mixed iron-chromium-molybdenum oxide/hydroxide outer layer. The equivalent thickness and composition of the outer and inner layers and the composition of the alloy underneath were calculated from the intensities of the oxidized and metallic components used for reconstruction: Cr2-Cr6 assigned to inner layer and Cr7 assigned to outer layer, Fe2-Fe4 assigned to inner layer and Fe5-Fe7 assigned to outer layer, Mo2-Mo3 assigned to outer layer, and Cr1, Fe1, Mo1 and Ni1 all assigned to modified alloy substrate. A classical model of intensity attenuation by continuous layers was used. The results are presented in Table. 2. The total thickness is found to be 2 nm, slightly larger than that (1.7 nm calculated using a similar model) reported for the native oxide film formed in air on a Fe-17Cr-14.5Ni-2.3Mo (wt%) single-crystalline surface prepared by mechanical polishing, electropolishing and high temperature annealing in reducing hydrogen atmosphere [27]. This difference might be due, at least partially, to the different surface preparation and the remaining presence of a coldworked layer on the polycristalline mechanically polished surface. In the present case , the thicknesses of the outer and inner layers of the surface oxide are 0.8 and 1.2 nm, respectively.
Their ratio of 2/3 is in agreement with the value of ~8/12 obtained from sputtering time in the ToF-SIMS depth profiles, not far from the 41/59 value found on the single-crystalline surface [27].
The overall composition of the oxide film, obtained by weighting the cation concentration value of each element by the fractional thickness of the inner and outer layers, as well as the composition of the modified alloy beneath the oxide film are also shown in Table. 2.
Chromium is found markedly enriched with Cr III ions representing 55% of the metal cations in the film and slightly depleted (18 at% instead of 20 at% in the bulk alloy) in the modified alloy underneath the oxide film. The overall Cr/Fe ratio in the oxide film is 1.4 vs. 0.3 in the modified alloy. This ratio is found higher in the inner layer than in the outer layer of the oxide film, reproducing the trend evidenced by the ToF-SIMS depth profiles. Nickel, not found in measurable amount in the oxide film, is enriched in the alloy underneath the oxide film (28 at% instead of 12 at% in the bulk alloy), also in agreement with the ToF-SIMS depth profiles.
These enrichments are quite similar to the results for the single-crystalline surface [27].
Concerning molybdenum, it is found enriched in the native oxide film (6 at% of Mo IV/VI instead of 1.6 at% of Mo 0 in the bulk alloy), more significantly than on the single-crystalline surface (2 at%) but also enriched in the alloy underneath the oxide film (3 at%), in contrast to the absence of enrichment found on the single-crystalline surface (1.5 at%), possibly also owing to the different surface preparation and/or microstructure effects.

Passive films
The ToF-SIMS negative ion depth profiles for the 316L stainless steel samples passivated in  (Table 1).
For the 1 h passivated sample, the profiles of the FeO2and CrO2secondary ions and FeO2and MoO2secondary ions are compared in Fig. 5b and Fig. 5c, respectively, using the same intensity scales as in Fig. 1. The FeO2and CrO2profiles also peak at different positions, 5 and 10 s, respectively, showing a bilayer structure also for the passive film with Fe and Cr oxides more concentrated in the outer and inner layers, respectively. By using the same method, we assign the outer/inner layer interface at 7 s. The FeO2and MoO2profiles both peak at 5 s and superimpose at longer sputtering time (Fig. 5c). The partition of the passive film is confirmed in Fig. 5d presenting the variation of the intensity ratio of CrO2to FeO2ions. The tendency of the curve is the same as for the native oxide film but with a higher Cr/Fe ratio, meaning that the passive oxide film has a higher chromium enrichment both in the outer and inner layers.
For the 20 h passivated sample, the FeO2and CrO2profiles, shown in Fig. 6b, also peak at different positions, 5 and 8 s, confirming the bilayer structure for the 20 h passive film with Fe and Cr oxides more concentrated in the outer and inner layers, respectively (interface is placed at 6 s). The FeO2and MoO2profiles both peak at 5 s and superimpose at longer sputtering time (Fig. 6c). The partition of the passive film is confirmed in Fig. 6d presenting the variation of the intensity ratio of CrO2to FeO2ions. The Cr/Fe ratio is slightly higher than that for the 1 h passive film, suggesting further Cr enrichment under the effect of aging in the passive state. Fig. 7 compares the ToF-SIMS data for native oxide-covered and passivated samples. As expected under identical analytical conditions of the same substrate in all samples, the intensity of the Fe2ions is the same in the metallic substrate region beyond 50 s (Fig. 7a).
This means that no normalization is necessary to compare the profiles of the three samples.
The shift towards shorter sputtering time of the increase in intensity of the Fe2ions reflects the decrease in thickness of the surface oxide film; it is noticeable for the 20 h passive film only. The Cr content in the inner layer is higher on the two passivated samples, indicating increased Cr oxide enrichment after electrochemical passivation and a promoting effect of aging (Fig. 7b). In the outer layer, the Fe content is slightly decreased (Fig. 7c), indicating that preferential iron oxide dissolution in acid solution is the cause of the increasing Cr enrichment. A small increase of Mo oxide content in the outer layer is suggested after 20 h passivation but not confirmed after 1 h (Fig. 7d).
The XPS spectra recorded for the 1 h passivated sample are similar to those for the native oxide-covered sample ( Fig. 8). The fitting results are also presented in Table. 1. The Cr 2p3/2 components associated to metallic Cr 0 in the substrate (Cr1), Cr III oxide (Cr2-Cr6) and Cr III hydroxide (Cr7) in the passive film are observed at 574.1 eV, 576.2-579.4 eV and 577.2 eV respectively (Fig. 8a) [13,16,33,48,49]. The Fe 2p3/2 components associated to metallic Fe 0 in the substrate (Fe1), Fe III oxide (Fe2-Fe6) and Fe III hydroxide (Fe7) in the passive film are observed at 707 eV, 708.8-712.8 eV and 711.9 eV respectively (Fig. 8b) [7,22,23,34,48,51,52]. The Mo 3d5/2-3/2 doublet components associated to metallic Mo 0 in the substrate and Mo IV and Mo VI in the passive film are observed at 227.8-230.9 eV, 229.6-232.7 eV and 232.7-235.8 eV, respectively (Fig. 8c) [31,33,36,53]. Since passivation was performed in sulfuric acid, a S 2s peak at 232.6 eV had to be considered. The presence of sulfate was confirmed by the S 2p spectrum (signal at 168.9 eV not shown here). The intensity ratio of the Mo VI to Mo IV doublets is ~6. The three O 1s components assigned to the oxide (O 2-), hydroxide (OH -) and water (H2O) ligands in the oxide film are observed at 530.3, 531.8 and 532.7 eV, respectively (Fig. 8d) [11,34]. The intensity ratio of OH -/O 2is 1.2 for the 1 h passivated sample, higher than for the native oxide-covered sample (0.9). It was confirmed by comparing the C 1s spectra that the increase of this component is not related to a higher carbonate contamination on the passivated sample, so that it can be concluded that the passive film is indeed more hydroxylated than the native oxide film as expected after formation in the aqueous solution.  [2,20,27] Using the same model of the bilayer structure (Fig. 4), thickness and composition of the 1 h and 20 h passive films were calculated (Table. 2). Compared with the native oxide film, the slight decrease of the thickness suggested by ToF-SIMS is confirmed and concentrated in the outer layer. We calculate values of 0.7 nm for 1 h and 0.6 nm for 20 h passivation instead of 0.8 nm for the native oxide. The composition of outer layer is calculated as 26%Fe III -56%Cr III -18%Mo IV/VI for 1 h and 32%Fe III -49%Cr III -19%Mo IV/VI for 20 h passivation instead of 41%Fe III -44%Cr III -15%Mo IV/VI for the native oxide, confirming chromium and molybdenum enrichment after passivation. The inner layer composition is 26%Fe III -74%Cr III for 1 h and 23%Fe III -77%Cr III for 20 h passivation instead of 36% Fe III -64% Cr III for the native oxide. It reproduces the increased balance in favor of chromium also observed by ToF-SIMS ( Fig. 5d and Fig. 6d) and reflected by the increase of the Cr/Fe ratio calculated from the XPS data (Table. 2). The global composition of the film also reflects the increase of the chromium enrichment induced by passivation. The Cr III concentration increases to 67% in the oxide film after 1 h passivation versus 55% in the native oxide but remains constant after 20 h passivation (68%). The passivation-induced Mo IV/VI enrichment of the oxide film outer layer is not marked when considering the global composition of the oxide. The alloy underneath the oxide film is found still markedly enriched in nickel and only slightly in molybdenum after passivation. The slight chromium depletion observed underneath the native oxide seems vanished after 1 h passivation and would reappear after longer passivation.
These modifications of the oxide film composition are consistent with the preferential iron oxide dissolution induced by passivation in acid solution [16,27,30,32,37]. Comparing with the results reported for the single-crystalline surface [27], the differences observed in the present case are the absence of variation of thickness of the inner layer of the oxide film after passivation whereas an increase was observed on the single-crystalline surface. The decrease in chromium depletion in the alloy underneath the film observed after 1 h passivation was also observed on the single-crystalline surface. The effect of aging in the passive state is to increase the Cr enrichment in the inner layer of the oxide film, considered as the barrier layer, but not in the outer layer, considered as an exchange layer with the electrolyte. It confirms previous findings on Mo-free austenitic [20] and ferritic [2,12] SS. Concerning molybdenum, its enrichment in the outer layer as well as its overall concentration in the oxide film do not seem to be promoted by aging in the passive state, nor its enrichment in the modified alloy underneath the passive film. The confinement of Mo IV/VI enrichment in the outer layer of the passive film is in agreement with previous works in the presence of molybdates [22,30,32]. It is supportive of the bipolar model developed to explain how molybdenum would mitigate passive film breakdown [34][35][36].

Native oxide film
The photoelectrochemical study was conducted in 0.1 M Na2B4O7 electrolyte (pH ~ 9. where h is the photon energy and Eg is the optical band gap (or mobility gap for amorphous materials); n is assumed to be 0.5 for non-direct optical transitions [54,55]. The photocurrent yield Qph is assumed to be proportional to the light absorption coefficient. It is defined as: where Iph is the collected photocurrent and e the electron charge. The incident photon flux on the interface 0 is corrected for the reflection at the metal/oxide/electrolyte interface with R being the total reflectivity of the junction. A two-region partition of the photocurrent spectra was also found for thermal oxide films formed on bright-annealed ferritic stainless steel [46], and on passive films formed on austenitic stainless after immersion in high pressurized water [45] and after electrochemically-induced rouging [47]. both anodic and cathodic photocurrents can be measured [47]. Since for insulating layers the flat band potential can be assumed to be close to the inversion photocurrent potential, we can estimate the flat band potential of the native oxide film formed on 316L SS to be about -0.4 V vs Ag/AgCl at pH ~9.5. This value is in agreement with the value reported for passive films grown on pure chromium [55]. Due to the very low thickness of the oxide film, we cannot exclude that the cathodic photocurrent arises from electron photoemission processes [45]. In this case the oxide would behave as a thin n-type semiconductor.
In order to confirm the sign of the generated photocurrent, current vs time plots were recorded at different UE values under constant wavelength while manually chopping the irradiation (Fig. 11). The generated photocurrent changes from anodic to none when the applied potential changes from 0.1 to -0.4 V vs Ag/AgCl. The drop to zero at UE= -0.4 V is consistent with the data reported in Fig. 7c and the determination of the flat band potential. The cathodic current expected at lower applied potential cannot be detected because the background current is too high.

Passive films
The is also mostly concentrated in the outer layer as shown by the angle-resolved XPS data (Fig.   2e). As for the Mo enrichment, it increases in the outer layer as discussed above. In contrast, the Cr enrichment increases in both layers after passivation as discussed and it may be at the origin of the loss of photo-activity observed after passivation. Besides, its slight increase with passivation time is also in agreement with increase loss of photo-activity after 20 h passivation.

Modeling
In order to get a more precise estimate of the optical band gap and photo-generated carriers transport properties of the two in-series layers of the oxide films, we have applied a model previously proposed to simulate the photoelectrochemical behavior of bilayered films [56,57].
According to this model, the collected photocurrent can be calculated as the sum of the contributions coming from each layer for the bilayered structure. The following equation is used for interpolating the experimental data: In this equation, the subscripts "inn" and "out" refer to the inner and outer layers, respectively, G and T to the generation and transport term in each layer, respectively, αout to the absorption coefficient of photon by the outer layer, and Dout to the thickness of the outer layer. The photon flux impinging the inner layer surface is assumed to be 0e -outDout .
The expressions for the G and T terms are [57]: where ηg (, F) is the generation efficiency, lower than 1 as result of geminate recombination effects in disordered materials at low electrode potentials with respect to the flat band potential [58]. α is the absorption coefficient at the given wavelength, D the total film thickness (D = Dout + Dinn) and F the electric field inside the film. μ and τ are the mobility and lifetime of the photogenerated carriers (holes, h, and electrons, e), respecting the following equation: In order to take into account possible multiple reflection effects at the metal/oxide interface, an average value of the total reflectivity, R, of the electrolyte/surface oxide film/metal junction has been estimated under the hypothesis of a single absorbing layer on an absorbing substrate [59]. The refractive indexes relating to water [60], the composition of surface oxide [61] and stainless steel [62] were used. of in the range 10 5 -10 3 cm -1 for the Fe-rich outer layer and 10 4 -10 2 cm -1 for the Cr-rich inner layer are in quite good agreement with the values usually reported for iron and chromium oxides [63][64]. Table 3 presents the other fitting parameters. For the native oxide film, the band gap of the inner layer is 3.3 eV and the band gap of the outer layer is 2.4 eV.
These two values are in reasonable good agreement with those obtained by linear fitting of the (Qph·hν) 0.5 vs hν plots (Fig. 10). For the passive films, no fits of the experimental curves could be achieved due to the weak measured photo currents (Fig. 12).
According to previous works [64][65][66], the bandgap value of mixed oxides AaBbOo depends on the electronegativity of the oxide. For d-metal oxides, the relationship is the following: Eg -Eam (eV) = 1.35 (av -O) 2 -1.49 (7) where O is the oxygen electronegativity (3.5 in the Pauling scale) and av an average electronegativity parameter defined as the arithmetic mean between the electronegativity of the metal partners in the oxides, i.e.: if the lattice disorder affects the density of states distribution both near the valence and conduction band edges [58].
In our case, we can develop Eq. (9) based on Eq. (8): For the native oxide film the composition of the outer and inner layers are taken as 41%Fe-44%Cr-15%Mo and 36%Fe-64%Cr, respectively, from the XPS data (Table 2). We assume components of the impedance [67]. This has been discussed as related to the influence of the frequency on the overall surface oxide capacitance caused by gap states for amorphous or strongly disordered thin oxide layers [58] and by surface states and adsorption phenomena [47]. The simplified equivalent circuit shown in the inset was used to fit the EIS data. It introduces a constant phase element to model the frequency-dependent equivalent capacitance and to calculate the polarization resistance RP as a rough estimate of the corrosion resistance.
The values of best fit parameters are compiled in Table. 4. The polarization resistance increases for the pre-passivated samples whereas the other parameters remain essentially unchanged. This means that despite the passivation-induced slight thickness decrease of the surface oxide film, evidenced by surface analysis, the corrosion resistance is higher than for the native oxide-covered sample film in agreement electrochemical polarization measurements. This confirms the effect associated with the enhanced Cr-enrichment of the surface oxide measured by surface analysis. No effect of aging in the passive state is detected on the polarization resistance.

Conclusion
ToF             Tables   Table. 1 BE, FWHM and relative intensity values of the peak components used for reconstruction of the XPS spectra on polycrystalline 316L SS after formation in ambient air of the native oxide film and after passivation at 0.  Table. 2 Thickness and composition of the native and passive oxide films on polycrystalline 316L SS as calculated form the XPS data based on the model in Fig. 4. Table 3. Best fit parameters for fitting, according to eq. (3) the photo current plots in Fig. 10.  Table. 4 Best fit parameters of the EIS spectra shown in Fig. 14b.