# Protection of Stainless Steels by Mo against Cl Attack: A DFT Study

Xian Huang, Dominique Costa, Boubakar Diawara, Vincent Maurice, Philippe Marcus

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Xian Huang, Dominique Costa, Boubakar Diawara, Vincent Maurice, Philippe Marcus. Protection of Stainless Steels by Mo against Cl Attack: A DFT Study. Journal of Physical Chemistry C, 2025, 129 (7), pp.3913-3919. 10.1021/acs.jpcc.4c08056. hal-04958415

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# Protection of Stainless Steels by Mo against Cl Attack: A DFT Study

Published as part of *The Journal of Physical Chemistry C* special issue "Francesc Illas and Gianfranco Pacchioni Festschrift".

Xian Huang, Dominique Costa,* Boubakar Diawara, Vincent Maurice, and Philippe Marcus*

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Cite This: https://doi.org/10.1021/acs.jpcc.4c08056

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**ABSTRACT:** We report a DFT study of (0001)-oriented Cr₂O₃ and Fe₂O₃ surfaces addressing the beneficial effects of Mo on the passivity breakdown of stainless steels in Cl-rich environments. Compared to Cr-rich zones, Fe-rich zones of the oxide barrier layer of the passive film are more prone to adsorbing Cl ions. Mo substitutes preferentially in these Fe-rich zones and favors the cationic vacancy formation to promote selective dissolution, thus curing the weak sites, sensitive to localized corrosion attack. In the Fe-rich weak sites with adsorbed Cl, Mo increases the barrier of O vacancy formation, thus mitigating passivity breakdown by inhibiting Cl penetration.

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## 1. INTRODUCTION

The excellent corrosion resistance of Cr-containing stainless alloys (such as stainless steels) relies on the nanometer-thick passive films formed on the surface, commonly composed of an inner Cr-rich oxide barrier layer and an outer exchange layer containing oxides and hydroxides.¹⁻³ Breakdown of the passive film, leading to pitting corrosion of the alloy, is an important issue for service in Cl-rich environments.

Several mechanisms, summarized in Figure 1, have been proposed in the literature⁴,⁵ to explain how Cl can lead to passivity breakdown after being adsorbed on the passive film surface. In the local thinning mechanism (Figure 1(a)), adsorbed Cl⁻ can accelerate oxide dissolution at the external interface and finally lead to passivity breakdown. In the voiding and collapse mechanism (Figure 1(b)), oxide dissolution at the external interface creates cationic vacancies that diffuse toward the alloy/oxide interface. The accumulation of vacancies at the internal interface forms voids resulting in the passive film collapse. In the Cl penetration mechanism (Figure 1(c)), the adsorbed aggressive anions penetrate the passive film and are transported to the alloy/oxide interface to form a metal chloride phase that induces stress cracking of the passive film. These phenomena may be locally more severe at the defects of passive films such as grain boundaries due to higher potential drops.⁵

On stainless steel, it has been reported that Fe (instead of Cr) can be locally enriched in the oxide barrier layer as a result of the deficient local supply of Cr during the initial stages of oxide growth.⁶,⁷ Such defects can be weak sites where the

<figure><img src="image_8.png" /><figcaption>**Figure 1.** (a) Local thinning, (b) voiding and collapse, and (c) Cl penetration mechanisms of passive film breakdown.</figcaption></figure>

**Received:** November 29, 2024

**Revised:** January 23, 2025

**Accepted:** January 27, 2025
<figure><img src="image_9.png" /><figcaption>**Figure 2.** Structures of fully covered (0001)-oriented Cr₂O₃ and Fe₂O₃ surfaces with different Cl coverages.</figcaption></figure>

passivity breakdown is triggered by one of the above mechanisms.

The addition of Mo to the alloy helps combat the problem. In a recent study of Mo-bearing multiprincipal element alloys (Cr-Fe-Co-Ni-Mo) that showed enhanced passivity in concentrated Cl-containing environments,⁸,⁹ it was suggested that the Fe-rich weak sites of corrosion protection could be cured by the enrichment of Mo. However, the exact role of Mo at the atomic scale is still under investigation.

Density functional theory (DFT), which is a powerful technique for investigating materials at the atomic scale, has been used to study the adsorption of Cl and its effects on the surfaces of chromium and iron oxides. The adsorption of Cl was simulated on anhydrous single-Cr-, chromyl-, and O-terminating Cr₂O₃ surfaces¹⁰ and single-Fe-terminating Fe₂O₃ surfaces.¹¹ We note that the calculated Bader charge of the adsorbed Cl in these studies was relatively low (−0.3 to −0.4 e) compared to half of the Bader charge of O in the bulk (−0.6 e). It was found that the adsorption energy increases about 1.4 eV as the Cl coverage increases from 0.08 to 1 ML (monolayer) on the anhydrous Fe₂O₃ surface.¹¹ On hydrous Cr₂O₃ surfaces, the increase in the energy of substitution of OH/H₂O by Cl is 2.4 eV as the Cl coverage increases from 0.17 to 1 ML.¹² Most of these studies were performed by using surface/vacuum models without considering solvation. Exceptionally, the adsorption of Cl in solution on O-terminating Cr₂O₃ surfaces has been simulated by joint density functional theory,¹³ which is an advanced method combining classical DFT and continuum liquid models to simulate surfaces in aqueous environments rather than in vacuum. This study suggests an ionic bond between Cl and the surface in aqueous solution as in vacuum.

Vacancy formation and Cl insertion were studied on single-Fe-terminating Fe₂O₃ surfaces.¹⁴ The formation energies of Fe and O vacancies on the surface were found to be lowered by Cl adsorption, resulting in lower differences of the vacancy formation energy between the surface and bulk. Cl insertion in the subsurface was tested by occupying an anionic vacancy or substituting an anion. It was found that the insertion is favored by the presence of O vacancies in Fe₂O₃, in agreement with another study on hydroxylated Cr₂O₃ surfaces.¹² Moreover, it was found that the energy of insertion by occupying anionic vacancies was higher for deeper occupied sites on Fe₂O₃ surfaces.¹⁴ As Cl coverage increased, the energy required to insert Cl into the subsurface diminished. In another study on Cr₂O₃ and Fe₂O₃ surfaces,¹⁵ the Cl insertion into cation vacancies and unoccupied cation sites of the corundum

structure was also simulated, and the same conclusion was reached: the insertion energy was lower when occupying a site on the surface than in the bulk. In this study, it was also found that the energy barrier for the migration of Cl occupying O vacancies from the surface to the bulk was higher in Fe₂O₃ than in Cr₂O₃.¹⁵

In contrast to Mo-free oxide surfaces, fewer DFT studies addressed Mo-containing Cr₂O₃ and Fe₂O₃ surfaces. A study on hydroxylated Cr₂O₃ and Fe₂O₃ surfaces reported that the substitution of Cr or Fe by Mo increased the activation energy of the oxygen reduction reaction.¹⁶ This suggests that the presence of Mo can mitigate the corrosion of the metallic anode by slowing down the counterpart cathodic reaction. In our previous studies on anhydrous and hydroxylated surfaces,¹⁷,¹⁸ the substitution of a metal cation by Mo was found to be more exothermic on Fe₂O₃ than on Cr₂O₃ surfaces, suggesting that Mo may be preferentially more enriched in the Fe-rich than in the Cr-rich zones of the oxide barrier layer of the passive film. On anhydrous surfaces,¹⁷ the presence of substitutional Mo was found to disfavor anionic vacancies and favor cationic vacancies, more significantly in Fe₂O₃ than in Cr₂O₃, suggesting that the Cl penetration via anionic vacancies could be limited and that the selective dissolution of the Fe-rich weak sites could be promoted. These results were already integrated in a discussion of the beneficial effects of molybdenum at the atomic scale on the stabilization of the passive films in a Cl-containing environment,¹⁹ even though Cl adsorption was not considered in the calculations.

In the present study, we further developed and completed the DFT approach by considering adsorbed Cl on hydroxylated surfaces of chromium (chromia) and iron (hematite) oxides, with the objective of understanding in more detail the stabilizing effects of Mo on the passivity of Cr-containing stainless alloys. Hereafter, vacancy-free surfaces are presented first, followed by surfaces with cationic and anionic vacancies so as to investigate Mo effects on Cl adsorption, oxide dissolution, and Cl penetration.

## 2. METHODS

Methods, surface models, energetics, and calculation details have been described in our previous papers and are reported in detail in SI section S1.

## 3. RESULTS AND DISCUSSION

Cl⁻ adsorption on the passive film surface is a prerequisite for Cl-induced passivity breakdown and the initiation of pitting corrosion. Cl⁻ adsorption is then discussed in this part. The
formation of cationic and anionic vacancies is presented in the second and third parts, respectively, since Cl⁻ may favor cation dissolution at the external interface or penetrate the oxide and diffuse to the internal interface via anion vacancies.

**3.1. Cl⁻ Adsorption.** On fully hydroxylated surfaces, which are thermodynamically stable for both Cr₂O₃ and Fe₂O₃ in aqueous environments,¹⁸ the substitution of OH⁻ by Cl⁻ is presented first. However, as unsaturated hydroxylation can locally occur during kinetic processes, Cl⁻ adsorption by substitution or direct addition is discussed second in this section on highly but not fully hydroxylated surfaces. The Mo effect on Cl⁻ adsorption is subsequently presented.

**3.1.1. Substitution of OH⁻ by Cl⁻ on Fully Hydroxylated Surfaces.** Figure 2 shows the structures of surfaces fully covered by OH⁻ and Cl⁻ with different Cl coverages. The lowest simulated Cl coverage (0.25 Cl + 2.75 OH) was realized by substituting 1 OH⁻ by Cl⁻ on 2 × 2 surface cells, and the highest one (3 Cl + 0 OH), by substituting all three OH⁻ by Cl⁻ on 1 × 1 surface cells. On Cl-free surfaces (0 Cl + 3 OH), circular -O-H- networks (marked by black circles in Figure 2) are formed, as reported previously.¹⁸ The presence of Cl⁻ breaks the -O-H- networks. Cr₂O₃ and Fe₂O₃ surfaces have similar structures except for the surfaces with the lowest Cl coverage, in which case only the circle with the substitutional Cl⁻ is broken on the Cr₂O₃ surface, while Cl⁻ disrupts all -O-H- networks on the Fe₂O₃ surface.

In a first test, we verified that substituting neutral hydroxyl groups with Cl atoms can simulate the substitution of hydroxyl ions with Cl ions (see SI section S2).

Figure 3 shows the energies of substitution of OH⁻ by Cl⁻ calculated using eq (2) in the SI for an acid solution (pH = 1)

<figure><img src="image_10.png" /><figcaption>**Figure 3.** Energies of substitution of OH⁻ by Cl⁻ on fully hydroxylated (0001)-oriented Cr₂O₃ and Fe₂O₃ surfaces with and without substitutional Mo with a high concentration (1 per unit surface cell).</figcaption></figure>

containing Cl⁻ (0.001 M) at room temperature (25 °C). The substitution is always endothermic on Cr₂O₃ surfaces, even for the lowest Cl coverage (0.25 Cl + 2.75 OH). On Fe₂O₃ surfaces, the energies of substitution are comparable to those on Cr₂O₃ surfaces for high Cl coverages. For low Cl coverages, the energies are lower on Fe₂O₃ than those on Cr₂O₃ surfaces. Moreover, the Cl adsorption becomes exothermic on the Fe₂O₃ surface (0.25 Cl + 2.75 OH), suggesting that Fe-rich zones of the oxide barrier layer of the passive film are more prone to adsorbing Cl than the Cr-rich zones.

These differences in energetics may be related to that in the surface structures shown in Figure 2. Indeed, the Cr₂O₃ and Fe₂O₃ surfaces with substitutional Cl⁻ have similar structures, except for the surfaces with the lowest Cl coverage (0.25 Cl + 2.75 OH). The surfaces in Figure 2 were obtained by

optimization from initial configurations, where the Cl atoms and the O atoms of the OH groups were in the bulk positions of the O groups in Cr₂O₃ and Fe₂O₃. However, when substituting a hydroxyl group on the relaxed fully hydroxylated surface with the circle-like -O-H- networks, the relaxed Fe₂O₃ surface (0.25 Cl + 2.75 OH) is more regular, like that of Cr₂O₃ shown in Figure 2. The Cl substitution energy calculated using such a relatively regular Fe₂O₃ surface was about 1.2 eV higher than that calculated using the irregular surface in Figure 3. This difference is close to the difference in substitution energy between the Cr₂O₃ and Fe₂O₃ (0.25 Cl + 2.75 OH) surfaces (Figure 3), suggesting that the low Cl substitution energy on Fe₂O₃ (0.25 Cl + 2.75 OH) surfaces is related to the reconstruction of -O-H- networks.

Lower acidity or Cl⁻ concentration yields higher energies of substitution (eq (2) in the SI). The change of one magnitude of H⁺ or Cl⁻ concentration yields a change of about 0.06 eV (ln(10)kₚT) in the energies of substitution, suggesting that the Cl substitution on the Fe₂O₃ (0.25 Cl + 2.75 OH) surface is still energetically favored under seawater conditions (pH = 8 and 0.6 M Cl⁻).

Experimentally, the quantities of Cl⁻ detected on the passive films of Mo-bearing multiprincipal element alloys in solutions containing 0.2 and 4.7 M Cl⁻ are about 10¹⁸ and 6 × 10¹⁸ m⁻², respectively.⁹ The surface concentration of adsorbed Cl on the (0.25 Cl + 2.75 OH) surface is about 1 × 10¹⁸ m⁻², which is consistent with the Cl amount measured experimentally on the passive films.

**3.1.2. Cl Substitution and Addition on Highly but Not Fully Hydroxylated Surfaces.** The not fully hydroxylated surfaces have also been considered and are shown in SI section S3.

Table 1 shows the energies of substitution of OH⁻ by Cl⁻ on the highly but not fully hydroxylated surface (0 Cl + 2 OH).

<table><caption>**Table 1. Energies of Substitution of OH⁻ by Cl on Highly but Not Fully Hydroxylated (0001)-Oriented Cr₂O₃ and Fe₂O₃ Surfaces (0 Cl + 2 OH) at 25 °C for pH = 1 and 0.001 M Cl⁻**</caption><thead><tr><th></th><th>Cr₂O₃</th><th>Fe₂O₃</th></tr></thead><tbody><tr><td>1 Cl + 1 OH</td><td>0.23</td><td>0.28</td></tr><tr><td>2 Cl + 0 OH</td><td>0.62</td><td>0.58</td></tr></tbody></table>

The positive substitution energies suggest that these Cr₂O₃ and Fe₂O₃ surfaces will not adsorb Cl⁻ by the substitution of OH⁻.

Cl addition on not fully hydroxylated surfaces was found to be exothermic in each case (see Figure S4 in the SI), indicating that not fully hydroxylated surfaces can adsorb Cl⁻ by direct addition in Cl-containing environments. As a result, only the surfaces fully covered by OH and Cl will be discussed in the following.

**3.1.3. Mo Effect on Cl Adsorption.** Mo was introduced to the surfaces by substituting a Cr or Fe atom. The case of high Mo concentration, in which one substitutional Mo is added on each surface unit cell (i.e., four on 2 × 2 surface supercells), is presented first. The Cl adsorption on Mo-substituted surfaces can be conversely investigated by studying Mo substitution on Cl-adsorbed surfaces.

Mo substitution does not significantly alter the surface structures. The substitution was studied in different sites, and it was found that the M1dn position is, in many cases, the most
stable configuration. More details and an exhaustive study are presented in SI section S4.

We consider only substitution at sites “M1dn” to simplify the analyses in the following.

The substitution energies at sites “M1dn” are plotted as a function of Cl coverage in Figure 4. The energies of

<figure><img src="image_11.png" /><figcaption>**Figure 4.** Energies of substitution by Mo at “M1dn” sites on (0001)-oriented Cr₂O₃ and Fe₂O₃ surfaces with different Cl coverages.</figcaption></figure>

substitution by Mo are always more exothermic on Fe₂O₃ than on Cr₂O₃ surfaces, which confirms the previous results obtained on anhydrous and hydroxylated surfaces.¹⁸ The effect of adsorbed Cl⁻ on the substitution by Mo or, conversely, the effect of substitutional Mo on the Cl adsorption is not remarkable according to Figure 4.

The case of lower Mo concentration in which one substitutional Mo is added on each 2 × 2 surface supercell (i.e., 0.25 Mo per surface unit) was also investigated (see section S6 and Figure S7 in the SI). No significant effect of the Mo concentration on Cl adsorption was observed.

**3.2. Cationic Dissolution.** Cl⁻ adsorbed on the oxide barrier surface can accelerate the dissolution of the oxide by facilitating the formation of cationic vacancies. In the following, the formation of cationic vacancies on Mo-free surfaces with different Cl coverages is first discussed, followed by that on Mo-substituted surfaces in order to study the Mo effect.

**3.2.1. Cationic Vacancies on Mo-Free Surfaces.** One cationic vacancy was created on each surface unit cell. In this case, creating vacancies at sites “M1up” on the double-M-terminating surfaces studied here is equivalent to simulating perfect single-M-terminating surfaces. Different sites were envisaged for the location of the cationic vacancy. The details are reported in SI section S5.

Table 2 compiles the nature of the most stable sites on surfaces with different Cl coverages. It shows that the

<table><caption>**Table 2.** Most Stable Sites for Cationic Vacancies on Mo-Free (0001)-Oriented Cr₂O₃ and Fe₂O₃ Surfaces with Different Cl Coverages</caption><thead><tr><th></th><th>0 Cl + 3 OH</th><th>1 Cl + 2 OH</th><th>2 Cl + 1 OH</th><th>3 Cl + 0 OH</th></tr></thead><tbody><tr><th>Cr<sub>2</sub>O<sub>3</sub></th><td>Cr2dn</td><td>Cr1up</td><td>Cr1up</td><td>Cr1up</td></tr><tr><th>Fe<sub>2</sub>O<sub>3</sub></th><td>Fe2dn</td><td>Fe2dn</td><td>Fe1up</td><td>Fe1up</td></tr></tbody></table>

subsurface is preferred for the formation of cationic vacancies in the case of the fully hydroxylated Cl-free surfaces but that the oxide/hydroxide interface may become preferential in the case of local Cl adsorption. For the surfaces with low Cl coverage (0.25 Cl + 2.75 OH), one can consider that the cationic vacancies are most stable at sites “Cr1up” for Cr₂O₃ and “Fe2dn” for Fe₂O₃ according to Table 2.

**3.2.2. Cationic Vacancies on Mo-Substituted Surfaces.**

The formation of cationic vacancies at different surface and subsurface sites was also investigated on surfaces with one Mo per surface unit cell. As discussed above, Mo preferentially substitutes for the cations at “M1dn” sites for all surfaces. Figure 5 shows the formation energies of cationic vacancies at different sites for the Mo-substituted surfaces. With the presence of substitutional Mo, the most stable site for cationic vacancies is “M1up”, regardless of Cl coverage. For the surfaces with low Cl coverage (0.25 Cl + 2.75 OH) with substitutional Mo at sites “M1dn”, one can consider that the cationic vacancies are most stable at sites “M1up” as for the other surfaces.

An additional test was performed for the low Cl-covered Cr₂O₃ surface (1 Cl + 2 OH) with substitutional Mo at sites “Cr2up”. The formation energies on such a surface are shown in the SI (Figure S10).

**3.2.3. Mo Effect on Cationic Vacancy Formation and Its Cl Dependency.** Figure 6 shows the formation energies of cationic vacancies on Mo-free and Mo-substituted surfaces with different Cl coverages. The vacancies are at the most stable sites determined above. On low-Cl-covered surfaces, including thermodynamically favored surfaces (0.25 Cl + 2.75 OH) and (1 Cl + 2 OH), the presence of adsorbed Cl does not significantly influence the formation of cationic vacancies. This suggests that Cl adsorption does not promote oxide dissolution by cation release at the external interface and thus local thinning of the oxide barrier layer of the passive film. At higher Cl coverages, including surfaces (2 Cl + 1 OH) and (3 Cl + 0 OH), the formation energies of cationic vacancies decrease on surfaces without substitutional Mo. One can then expect local oxide dissolution and thus oxide thinning to be accelerated by locally enhanced Cl adsorption, which is not, however, thermodynamically favored. The Cl dependency of the formation energies of cation vacancies disappears totally on Mo-substituted surfaces, indicating that Mo may mitigate passivity breakdown by preventing local thinning otherwise accelerated by locally enhanced Cl adsorption.

Figure 6 also shows that the presence of substitutional Mo lowers the formation energies of cationic vacancies, regardless of Cl coverage and more significantly in Fe₂O₃ than in Cr₂O₃, verifying the result obtained on anhydrous surfaces.¹⁷ Combined with preferential substitution by Mo in Fe₂O₃, it is suggested that the presence of Mo can accelerate the selective dissolution of Fe-rich oxide zones of the passive film and convert them into Mo-rich oxide zones, thus curing the less-corrosion-resistant sites.

We also considered the case of low vacancy concentration in which one vacancy is created on each 2 × 2 surface supercell (i.e., 0.25 vac per surface unit). For Mo-substituted surfaces, the case of a low Mo concentration (0.25 Mo per surface unit) was also considered. The surfaces with low Cl coverage (0.25 Cl + 2.75 OH) were studied here since they are the most stable Cl-covered surfaces. The cation vacancy was created at the site closest to the adsorbed Cl⁻ and substitutional Mo since we are interested in the effects of Mo and Cl.

Table 3 compiles the formation energies of cationic vacancies with low vacancy and Mo concentrations compared with those with high concentrations. It is confirmed that the vacancy formation is favored by the increase in the Mo concentration. In contrast, there is no significant effect of the vacancy concentration as opposed to that of the Mo concentration.
<figure><img src="image_12.png" /><figcaption>**Figure 5.** Formation energies of cationic vacancies at different sites on (0001)-oriented Cr₂O₃ and Fe₂O₃ surfaces substituted by Mo at "M1dn" sites.</figcaption></figure>

<figure><img src="image_13.png" /><figcaption>**Figure 6.** Formation energies of cationic vacancies on Mo-free and Mo-substituted (0001)-oriented Cr₂O₃ and Fe₂O₃ surfaces with different Cl coverages.</figcaption></figure>

<table><caption>**Table 3.** Formation Energies of Cationic Vacancies on (0001)-Oriented Cr₂O₃ and Fe₂O₃ Surfaces (0.25 Cl + 2.75 OH) at T = 25 °C and U = 0 V/SHE with a Mq⁺ (Cr³⁺ or Fe²⁺) Concentration of 10⁻⁶ M in Solutions</caption><thead><tr><th rowspan="2"></th><th colspan="2">Cr<sub>2</sub>O<sub>3</sub></th><th colspan="2">Fe<sub>2</sub>O<sub>3</sub></th></tr><tr><th>0.25 vac</th><th>1 vac</th><th>0.25 vac</th><th>1 vac</th></tr></thead><tbody><tr><td>0 Mo</td><td>4.80</td><td>4.80</td><td>5.64</td><td>5.45</td></tr><tr><td>0.25 Mo</td><td>3.49</td><td></td><td>3.68</td><td></td></tr><tr><td>1 Mo</td><td></td><td>2.26</td><td></td><td>2.53</td></tr></tbody></table>

**3.3. Cl Penetration.** Cl⁻ adsorbed on the external interface can penetrate the oxide barrier and diffuse toward the internal interface, leading to the formation of chloride particles that can induce passivity breakdown by stress cracking. Since the presence of oxygen vacancies can accelerate the diffusion of Cl⁻,¹² the formation energies of oxygen vacancies were calculated on Mo-free and Mo-substituted surfaces with different Cl coverages to investigate the effects of Cl and Mo.

**3.3.1. Oxygen Vacancy Formation on Mo-Free Surfaces.**
One oxygen vacancy was created on each surface unit cell. Each oxygen atomic layer has three sites per surface unit cell for the vacancy creation. The most stable sites for oxygen vacancy formation were searched, and detailed results are given in SI section S6. Oxygen vacancies are the most stable at the "O1" layer except for surfaces (0 Cl + 3 OH) where the formation energies of oxygen vacancies at the "O2" layer are nearly the same as those at the "O1" layer, indicating that adsorbed Cl favors the formation of surface compared to subsurface oxygen vacancies. We observed a more marked effect of Cl on the O vacancy formation in Fe₂O₃ than in Cr₂O₃, again suggesting that the Fe-rich zones of passive films are weak points for passivity.

**3.3.2. Mo Effect on Oxygen Vacancy Formation and Its Cl Dependency.** The formation energies of an anionic vacancy at

different sites, with Mo substituted at the "M1dn" site, are shown in detail in SI section S7. On Cr₂O₃ surfaces, the oxygen vacancy formation is not significantly influenced by the presence of Mo at the "M1dn" sites. On Fe₂O₃ surfaces, the most stable site of vacancies is at the "O1" layers in the presence of Cl.

**Figure 7** shows the formation energies of oxygen vacancies on surfaces with different Cl coverages. The vacancies are at

<figure><img src="image_14.png" /><figcaption>**Figure 7.** Formation energies of oxygen vacancies on Mo-free and Mo-substituted (0001)-oriented Cr₂O₃ and Fe₂O₃ surfaces with different Cl coverages.</figcaption></figure>

their most stable sites for each Cl coverage. On Mo-free surfaces, the formation energies decrease and then increase as the Cl coverage increases.

The formation energies of oxygen vacancies are always lower in Fe₂O₃ than in Cr₂O₃, suggesting that Cl is more prone to penetrate the oxide barrier via oxygen vacancies in the Fe-rich weak sites than in Cr-rich zones of the passive film.

The presence of substitutional Mo does not significantly affect the oxygen vacancy formation in Cr₂O₃. However, a marked influence is observed on the Cl-covered Fe₂O₃ surfaces, for which the oxygen vacancy formation energies are higher on Mo-substituted surfaces than on Mo-free surfaces, except for the fully Cl-covered surfaces. For the low-Cl-covered Fe₂O₃ surface (0.25 Cl + 2.75 OH), which is the thermodynamically favored case of interest, the increase in formation energy suggests that the presence of Mo may inhibit the Cl penetration by diminishing the concentration of its penetration sites.

In the case of lower vacancy concentration in which one vacancy is created on each 2 × 2 surface supercell (i.e., 0.25 vac per surface unit), the effect of a low Mo concentration (0.25 Mo per surface unit) was considered. The surfaces with low Cl coverage (0.25 Cl + 2.75 OH) were studied, since they are the most stable Cl-covered surfaces. The vacancy was formed at the site the closest to the adsorbed Cl⁻ and substitutional Mo since we are interested in the effects of Mo and Cl.
The results show no marked effect of the concentrations of vacancies and Mo on the formation energies of oxygen vacancies in Cr₂O₃ (Table 4). For Fe₂O₃, a higher vacancy

<table><caption>**Table 4.** Formation Energies of Oxygen Vacancies on Mo-Free and Mo-Substituted (0001)-Oriented Cr₂O₃ and Fe₂O₃ Surfaces (0.25 Cl + 2.75 OH) at T = 25 °C and U = 0 V/ SHE at pH = 1</caption><thead><tr><th rowspan="2"></th><th colspan="2">Cr₂O₃</th><th colspan="2">Fe₂O₃</th></tr><tr><th>0.25 vac</th><th>1 vac</th><th>0.25 vac</th><th>1 vac</th></tr></thead><tbody><tr><th>0 Mo</th><td>2.42</td><td>2.38</td><td>1.05</td><td>0.55</td></tr><tr><th>0.25 Mo</th><td>2.43</td><td></td><td>1.52</td><td></td></tr><tr><th>1 Mo</th><td></td><td>2.37</td><td></td><td>1.00</td></tr></tbody></table>

concentration yields a lower formation energy. The formation energy of oxygen vacancies increases once Mo substitutes for Fe on the surfaces, but the effect of Mo concentration is not very important since the formation energies increase by about 0.5 eV for the two Mo concentrations investigated here.

## 4. CONCLUSIONS

In the present work, DFT was applied to study the effects of substitution by Mo on (0001)-oriented hydroxylated Cr₂O₃ and Fe₂O₃ surfaces on Cl adsorption and the combined effects of adsorbed Cl and substitutional Mo on cationic and anionic vacancy formation. This work deepens the atomistic insights into the mechanisms of the Cl-induced initiation of passivity breakdown of stainless steels and how it is counteracted by Mo.

The results show that Cl adsorption by the substitution of hydroxyls is endothermic on most of the investigated Cr₂O₃ and Fe₂O₃ surfaces and exothermic only on the Fe₂O₃ surface at low Cl coverage (0.25 Cl + 2.75 OH) corresponding to that experimentally measured on passive films. This suggests that Fe-rich weak sites present in the oxide barrier layer of the passive film are more prone to being attacked by Cl than the Cr-rich zones. The energies of cation substitution by Mo are always more exothermic on Fe₂O₃ than on Cr₂O₃ surfaces, confirming the previous results obtained on anhydrous and hydroxylated surfaces.

On low-Cl-covered surfaces, adsorbed Cl does not significantly influence the formation energies of cationic vacancies, while a decrease is observed at higher Cl coverages. This suggests that adsorbed Cl does not promote local thinning of the oxide barrier by accelerating the dissolution reaction unless Cl is locally concentrated, which is not a thermodynamically favored case. The Cl coverage dependency of the formation energies of cation vacancies disappears on Mo-substituted surfaces, indicating that Mo may prevent passivity breakdown by inhibiting local thinning of the oxide barrier accelerated by locally concentrated Cl. The cationic vacancy formation is decreased by the presence of substitutional Mo, more markedly for high Mo concentrations. The effect of Mo is stronger for Fe₂O₃ than for Cr₂O₃, indicating that, in addition to the preferential location of Mo on Fe rich zones, the presence of Mo may promote the selective dissolution of the Fe-rich oxide zones and their transformation into Mo-rich zones, thus curing the weak sites of passive films.

Regarding oxygen vacancies, their formation energies are always lower in Fe₂O₃ than in Cr₂O₃, suggesting that Cl is more prone to penetrate the oxide barrier and diffuse via oxygen vacancies in the Fe-rich sites than in Cr-rich zones, thus

initiating passivity breakdown in the Fe-rich weak sites of passivity. On surfaces of low Cl coverage, adsorbed Cl strongly decreases the barrier for O vacancy formation in Fe₂O₃ but not in Cr₂O₃, pointing out the detrimental effect of adsorbed Cl in Fe-rich zones. Most importantly, the presence of substitutional Mo does not significantly affect the oxygen vacancy formation in Cr₂O₃, while in Fe₂O₃ it significantly increases the formation energies on surfaces with low Cl coverages. This suggests that Mo inhibits Cl penetration in the inner part of the passive film by diminishing the oxygen vacancy concentration in Fe-rich zones.

Finally, we conclude that the beneficial roles of Mo for enhancing the resistance to Cl-induced passivity breakdown are the following:

* by locating preferentially in Fe-rich zones of the oxide barrier layer and promoting cationic dissolution, Mo cures the weak sites of passive films,

* when Cl adsorbs on Fe-rich weak sites of passivity, Mo increases the barrier for O vacancy formation and mitigates Cl penetration, thus increasing the resistance to passivity breakdown.

## ■ ASSOCIATED CONTENT

### ● Supporting Information

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.jpcc.4c08056.

Methods; substitution of OH by Cl; not fully hydroxylated surfaces; Mo effect on Cl adsorption; cationic vacancies; oxygen vacancies; and Mo effect on oxygen vacancy formation (PDF)

## ■ AUTHOR INFORMATION

### Corresponding Authors

Dominique Costa – PSL Research University, CNRS - Chimie ParisTech, Institut de Recherche de Chimie Paris, 75005 Paris, France; Email: dominique.costa@chimieparistech.psl.eu

Philippe Marcus – PSL Research University, CNRS - Chimie ParisTech, Institut de Recherche de Chimie Paris, 75005 Paris, France; ● orcid.org/0000-0002-9140-0047; Email: philippe.marcus@chimieparistech.psl.eu

### Authors

Xian Huang – PSL Research University, CNRS - Chimie ParisTech, Institut de Recherche de Chimie Paris, 75005 Paris, France

Boubakar Diawara – PSL Research University, CNRS - Chimie ParisTech, Institut de Recherche de Chimie Paris, 75005 Paris, France

Vincent Maurice – PSL Research University, CNRS - Chimie ParisTech, Institut de Recherche de Chimie Paris, 75005 Paris, France

Complete contact information is available at: https://pubs.acs.org/10.1021/acs.jpcc.4c08056

### Funding

Project Equip@Meso (reference ANR-10-EQPX-29-01) HPC resources under allocation A0120802217 made by GENCI. This work was supported by the European Research Council (ERC) under the European Union's Horizon 2020 research
and innovation program (ERC Advanced Grant agreement No. 741123).

### Notes

The authors declare no competing financial interest.

## ACKNOWLEDGMENTS

The authors acknowledge the HPC resources of MesoPSL financed by the Region Ile de France and the project Equip@ Meso (reference ANR-10-EQPX-29-01) of the program Investissements d'Avenir of the Agence Nationale pour la Recherche. We were granted access to HPC resources under the allocation A0120802217 made by GENCI.

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