Use of the Critical Acidification Model to Estimate the Influence of W in the Localized Corrosion Resistance of 25Cr Super Duplex Stainless Steels

Two super duplex stainless steels (SDSS) with different W content, namely UNS S32750 (W-free) and UNS S39274 (2.1 wt.% W), were tested in simulated crevice corrosion environments to determine the influence of W on their corrosion resistance. Anodic potentiodynamic polarization experiments were performed in two different crevice-like-solutions: 1 M HCl (as reference for a pH = 0 environment), and 7 M LiCl, adjusted to the same pH value. Galvele’s critical acidification model was used to estimate the theoretical critical potential (Ecrit) and comparatively evaluate the corrosion resistance of the two SDSS. The anodic potentiodynamic polarization results showed a statistically significant difference between the two materials in only one test condition, i.e., 7 M Cl− at 60 ◦C. Additionally, the quantification of chemical dissolution of the metal cations after the tests suggested a surface enrichment in W only in the 7 M chloride solution. Scanning electron microscope (SEM) analysis indicated a uniform dissolution experienced by UNS S32750 in this environment, whereas UNS S39274 suffered selective corrosion of the ferrite-phase. These observations were reflected in a slight increase in the Ecrit values of UNS S32974 estimated with Galvele’s model.


Introduction
Super duplex stainless steels (SDSS) have excellent corrosion resistance in neutral chloride-containing environments thanks to their high content of alloying elements such as Cr, Mo, and N [1][2][3][4]. Tungsten (W) is another element that has been shown to improve corrosion resistance. However, the effect of W on localized corrosion resistance is still disputed, as discussed in detail elsewhere [5,6].
A recent publication reviewed and studied the influence of W additions to SDSS on the precipitation kinetics of tertiary phases. In this regard, tertiary phases such as σand χ-phase are well known to be deleterious to both mechanical properties and corrosion resistance [5]. The authors showed that about 2 wt.% W reduced the total concentration of deleterious phases, and retarded the precipitation of σ-phase, favoring the formation of χ-phase at grain and phase boundaries. When W was added at approximately 0.6 wt.%, W promoted deleterious phase precipitation and impacted the localized corrosion resistance of the material negatively.
Another recent publication [6] examined the influence of W as a solid solution element, i.e., in the absence of tertiary phases, on the crevice corrosion resistance of the same SDSS. The authors compared the critical crevice repassivation temperature (T R,Crev ) obtained by the potentiodynamic-galvanostatic-potentiodynamic (PD-GS-PD) technique with critical crevice available alloys. Others [7,[10][11][12]14] have also successfully distinguished the effect of other alloy elements by conducting anodic polarizations in acidic chloride environments.
The objective of this work was to investigate the possible role of W in a propagating localized attack as a function of temperature in simulated crevice electrolytes. For this purpose, two commercial SDSS differing mainly in their W content were tested in two different crevice-like environments as a function of temperature. Galvele's critical acidification model was employed to estimate theoretical E crit values, which were compared with E R,Crev results obtained in neutral chloride solutions.

Materials
Two SDSS, differing mainly in their W composition, were studied in this work, namely UNS S32750 (W-free) and UNS S39274 (2.1 wt.% W). Table 1 summarizes their composition given by the provider and confirmed by EDS. Both materials were produced as extruded pipes with 30 mm wall thickness and 203.2 mm in diameter. Round samples were machined by first extracting cylinders along the length of the pipe. The thickness of the coin-shaped specimens was 3 mm and the diameter 25 mm for UNS S32750 and 30 mm for UNS S39274. UNS S39274 was received in the solution annealed condition (heat-treated at 1085 • C for 10 min). UNS S32750 was solution annealed after machining, in an air-furnace at 1100 • C for 15 min and quenched in water, following the recommendations from the supplier.
Specimens were wet-ground down to 600 US-grit SiC paper, rinsed in acetone, followed by distilled water and ethanol, and cleaned in an ultrasonic bath for 5 min while they were immersed in ethanol.
Specimens of the two SDSSs were etched following Statoil technical note MAT-2010080 [19] to reveal the microstructure and distinguish the austenite (γ) and ferrite (α) phases by light optical microscopy (LOM) and scanning electron microscopy (SEM). The etching procedure consisted of two different steps. In the first step, a 15 wt.%. KOH solution was used, and a potential of 3 V was applied for 12 s. In the second step, the solution was 20 wt.%. NaOH with an applied potential of 1.5 V for 10 s. Figure 1 shows the microstructure of each material after the heat treatments. The γ and α ratio in these materials was measured by electron backscatter diffraction (EBSD) in a previous work [5], obtaining a 57.2 and 47.6 vol.% α for UNS S32750 and UNS S39274, respectively. These values are within the acceptable 40 to 60 vol.% range for each phase in SDSS. The average austenite region size of each material was determined by measuring the area of each austenite region in a minimum of three different areas and calculating the mean value by an open-access image processing software. The average austenite region size results for UNS S32750 and UNS S39274 were 577.9 µm 2 and 395.0 µm 2 , respectively. The ohmic potential drop term was estimated after Bocher et al. (Equation (3)) [11,14]: where ρ is the resistivity in the solution and is assumed to be 10 Ω·cm [14], w is the crevice gap which was given a value of 1 μm [11], x is the diffusion distance considered to be 10 -4 cm [23], and icrit was obtained from the pit stability product (Equation (4)) [24]: where k is a constant that is a function of the metal and pH of the solution. In this work and based on Kappes et al., the value of 10 −6 A/cm was adopted [23]. Equations (3) and (4) yield an icrit = 10 −2 A/cm 2 and ϕ = 5 μV. Since the ϕ << Ecorr * , Ecrit can be obtained as: Ecorr * can be found by measuring the corrosion potential in an electrolyte simulating the inside of a corroding pit or crevice. Consequently, the Ecrit can be obtained from Equation (5) by performing anodic potentiodynamic polarizations in crevice-like-solutions and obtaining the Ecorr and η (i.e., the applied overpotential needed to reach icrit = 10 −2 A/cm 2 ).

Crevice-Like-Solutions
Anodic potentiodynamic polarization experiments were conducted in solutions simulating pit/crevice environments. Two different crevice-like-solutions were used: 1 M HCl (as a reference solution at pH = 0) and 7 M LiCl, which was chosen based on Kappes et al. [11] as 7 N Cl − presented the highest current density before salt precipitation occurred. The 7 M LiCl solution was adjusted to 0 pH by adding concentrated HCl, following the relationship between H + and Cl − activity coefficients given by Bocher et al. [14]. The volume used in each experiment was 160 mL, which was measured by a graduated cylinder. The solution resistances varied from the less conductive to the more conductive solutions from 0.3 to 0.1 Ω, which was also confirmed using OLI simulations (OLI SYSTEMS INC., Parsippany, NJ, USA) and in line with the work of Artemov et al. [25], who studied the conductivity of aqueous HCl, NaOH and NaCl solutions. Thus, the effect of IR drop was considered negligible for the comparative assessment of the two SDSSs.
A three electrode-cell consisting of an Ag/AgCl KCl saturated reference electrode (RE) (−199 mV vs. Standard Hydrogen Electrode-SHE-) immersed in the solution through a glass tube and kept at room temperature was used to carry out the anodic polarization tests. The counter electrode (CE) consisted of a Pt mesh. A commercially available electrochemical Avesta cell was used to avoid crevice corrosion [26], which was modified, as shown in Figure 2. In the original design of the Avesta cell, the distilled water required to avoid crevice corrosion flows into the main chamber, which might affect the pH and Cl − concentration at the surface. The modification consisted of creating an

Galvele's Critical Acidification Model
Galvele's critical acidification model [13], described in Equation (1), can be used to estimate the E crit when the concentration of aggressive specimens in the electrolyte is known. Henceforth, to simplify the model, E inh is considered negligible to the contribution of E crit [11]. Despite the release of potential inhibiting species such as molybdates and tungstates from the alloys during dissolution [20][21][22], it is considered acceptable as the E crit value estimated in this manner is more conservative, i.e., lower E crit . Thus, E crit can be expressed as: The ohmic potential drop term was estimated after Bocher et al. (Equation (3)) [11,14]: where ρ is the resistivity in the solution and is assumed to be 10 Ω·cm [14], w is the crevice gap which was given a value of 1 µm [11], x is the diffusion distance considered to be 10 -4 cm [23], and i crit was obtained from the pit stability product (Equation (4)) [24]: where k is a constant that is a function of the metal and pH of the solution. In this work and based on Kappes et al., the value of 10 −6 A/cm was adopted [23]. Equations (3) and (4) yield an i crit = 10 −2 A/cm 2 and φ = 5 µV. Since the φ << E corr * , E crit can be obtained as: E corr * can be found by measuring the corrosion potential in an electrolyte simulating the inside of a corroding pit or crevice. Consequently, the E crit can be obtained from Equation (5) by performing anodic potentiodynamic polarizations in crevice-like-solutions and obtaining the E corr and η (i.e., the applied overpotential needed to reach i crit = 10 −2 A/cm 2 ).

Crevice-Like-Solutions
Anodic potentiodynamic polarization experiments were conducted in solutions simulating pit/crevice environments. Two different crevice-like-solutions were used: 1 M HCl (as a reference solution at pH = 0) and 7 M LiCl, which was chosen based on Kappes et al. [11] as 7 N Cl − presented the highest current density before salt precipitation occurred. The 7 M LiCl solution was adjusted to 0 pH by adding concentrated HCl, following the relationship between H + and Cl − activity coefficients given by Bocher et al. [14]. The volume used in each experiment was 160 mL, which was measured by a graduated cylinder. The solution resistances varied from the less conductive to the more conductive solutions from 0.3 to 0.1 Ω, which was also confirmed using OLI simulations (OLI SYSTEMS INC., Parsippany, NJ, USA) and in line with the work of Artemov et al. [25], who studied the conductivity of aqueous HCl, NaOH and NaCl solutions. Thus, the effect of IR drop was considered negligible for the comparative assessment of the two SDSSs.
A three electrode-cell consisting of an Ag/AgCl KCl saturated reference electrode (RE) (−199 mV vs. Standard Hydrogen Electrode-SHE-) immersed in the solution through a glass tube and kept at room temperature was used to carry out the anodic polarization tests. The counter electrode (CE) consisted of a Pt mesh. A commercially available electrochemical Avesta cell was used to avoid crevice corrosion [26], which was modified, as shown in Figure 2. In the original design of the Avesta cell, the distilled water required to avoid crevice corrosion flows into the main chamber, which might affect the pH and Cl − concentration at the surface. The modification consisted of creating an additional outlet for the distilled water supplied by the peristaltic pump ( Figure 2) to avoid contact with the electrolyte.  Consequently, the distilled water did not leak into the electrolyte, but circulated through the Oring sealing, wetting the filter paper and, then, circulated outside the cell through a new vent. The area of the working electrode was 1.54 cm 2 .
Anodic polarization experiments were performed at different temperatures: room temperature (22 ± 1 °C), 40 °C, 50 °C, and 60 °C. The temperature was controlled using a water bath connected to the double glass wall of the cell, except for the room temperature condition in which testing was done at the temperature of the lab.
The tests were performed in an oxygen-free electrolyte since the localized environment inside active pits and crevices has a low oxygen content, as it is consumed during the initial stages [27]. The electrolyte was purged with nitrogen gas for 1 h before exposing the specimen to ensure a low dissolved oxygen concentration. Since the specimen is placed at the bottom of the cell (Figure 2), the electrolyte had to be purged in a tight glass vessel mounted on top of the Avesta cell, as illustrated in Figure 2. The main Avesta cell chamber was simultaneously purged with N2 to remove all air and Consequently, the distilled water did not leak into the electrolyte, but circulated through the O-ring sealing, wetting the filter paper and, then, circulated outside the cell through a new vent. The area of the working electrode was 1.54 cm 2 .
Anodic polarization experiments were performed at different temperatures: room temperature (22 ± 1 • C), 40 • C, 50 • C, and 60 • C. The temperature was controlled using a water bath connected to the double glass wall of the cell, except for the room temperature condition in which testing was done at the temperature of the lab. The tests were performed in an oxygen-free electrolyte since the localized environment inside active pits and crevices has a low oxygen content, as it is consumed during the initial stages [27]. The electrolyte was purged with nitrogen gas for 1 h before exposing the specimen to ensure a low dissolved oxygen concentration. Since the specimen is placed at the bottom of the cell (Figure 2), the electrolyte had to be purged in a tight glass vessel mounted on top of the Avesta cell, as illustrated in Figure 2. The main Avesta cell chamber was simultaneously purged with N 2 to remove all air and ensure an O 2 -free atmosphere from the moment the solution came in contact with the specimen. The tight glass vessel was connected through a valve directly into the Avesta cell, to avoid contact of the deaerated electrolyte with the air when transferring the solution from the vessel to the main cell. Deaeration of the electrolyte continued during the tests. The dissolved oxygen concentration was monitored continuously using a fiber optic oxygen meter, and its content was always below 10 ppb from the moment the material came in contact with the test solution.
The sequence of the anodic polarization tests was as follows. First, the E corr * was measured for 1 h (the asterisk indicates that E corr was measured in a simulated crevice solution), followed by the anodic potentiodynamic polarization, starting at E corr * and finishing at 1.2 V Ag/AgCl , with a sweep rate of 0.167 mV/s. All tests were performed at least in duplicate. The passive current density (i pass ), the critical passive current density (i cp ), the corrosion potential (E corr * ), the transpassive potential (E Trans ), and the primary passive potential (E pp ) were obtained from each anodic potentiodynamic polarization curve.

Characterization
After the tests, the electrolyte was stored in tight plastic containers and the ions released from the specimens were quantified using Inductively Coupled Plasma Mass Spectrometry (ICP-MS).
Congruent or incongruent dissolution was verified with the ICP-MS results by calculating the dissolution ratio of each metallic element M (d' M ). d' M was defined as the ratio between the experimental dissolution (d experimental ) quantified by the ICP-MS analysis and the congruent dissolution (d congruent ) value. d congruent was calculated as the proportional dissolution of Fe, as it is the bulk element for the two materials, as shown in Equation (6): where d M (in ppb) is the dissolution quantity of metal M measured by ICP-MS, C M (in wt.%) is the concentration in solid solution of metal M in the material (shown in Table 1), C Fe (in wt.%) is the concentration in solid solution of Fe in the material (shown in Table 1), and d Fe (in ppb) is the dissolution quantity of Fe obtained by ICP-MS for the same condition as that of the measured metal M. In this regard, a d' M > 1 suggests selective metal M dissolution [28]. Contrarily, a d' M < 1 implies a relative surface enrichment in M [28]. Finally, d' M = 1 indicates congruent dissolution [28]. The specimens were analyzed after the tests with an infinite focus microscope (IFM) used as a LOM, which can simultaneously acquire the 3D surface profile, enabling the estimation of the depth of localized attacks. The specimens were also analyzed by SEM together with energy-dispersive x-ray spectroscopy (EDS). An accelerated voltage of 20 kV, with a 50 µm diameter aperture and a spot size of 5 was employed, giving a beam current of approximately 7.2 nA. The point analysis tool was used to acquire the composition of the full area taken by the SEM. At least five measurements were performed per specimen.

Statistical Analysis
A statistical study of the data was performed to examine whether the metal cations quantity released at the end of the electrochemical test was related to any of the polarization curve parameters or the two parameters, η and E crit , used in Galvele's model. The statistical study consisted of calculating the Kendall correlation coefficient [29] in a pairwise comparison between all the mentioned variables. In contrast to other more known correlation parameters such as Pearson's, the Kendall correlation coefficient does not assume a normal distribution [30]. Thus, Kendall's coefficient indicates a general monotonic relationship, i.e., if both variables increase or decrease together [29]. Consequently, Kendall's coefficient will show a strong relationship even for non-linear relationships such as exponential behaviors.
For this reason, this coefficient is becoming more popular within the scientific community [29,31]. The closer the coefficient is to 1 (in absolute value), the stronger the variables are connected. The sign of the coefficient indicates the type of relationship: (i) positive; both variables increase or decrease together, or (ii) negative, one variable increases as the other decreases.  Figure 4 summarizes the anodic potentiodynamic polarization curves obtained for one specimen of each alloy tested at each temperature, while Figure 5 presents all the critical parameters extracted from Figure 4. As indicated in Figure 3, i pass was calculated as the average value between the intersections between lines 1 and 2 at low potentials and the intersection of lines 3 and 4 at high potentials. Although the limiting currents after the active/passive transition do not imply true passivation given the high values, i pass was calculated as the average value of the current density measured during the pseudopassive region following the same criteria as for the normal passive range. In agreement with others [11,32], i cp was obtained as the maximum current density measured before the active/passive transition. Similarly, E pp was defined as the potential at which the transition from active to passive took place. E corr * was considered as the value measured at the end of the 1 h open circuit potential measurement before polarization. After the active/passive transition, potentials reached values more positive than the oxygen evolution reaction and within the transpassive area [33]. Consequently, the inflection point seen at high anodic potentials (the intersection between lines 3 and 4 in Figure 3) was defined as E Trans . As shown in Figures 4 and 5, a clear difference was observed between the two solutions. In this regard, the active/passive transition in 1 N Cl − was only observed at T ≥ 40 • C and T = 60 • C for UNS S32750 and UNS S39274, respectively. In contrast, active dissolution followed by a high diffusion-limited current (i lim ≈ i cp ) and passivation at E pp occurred in 7 M LiCl for all specimens at all temperatures. Even though the current density did not achieve typical passive values, this area will be referred to as passive hereunder to compare i pass between the solutions. Additionally, lower current densities (both i cp and i pass ) were obtained in 1 M HCl for potentials below the oxygen evolution reaction or below the transpassive region [33]. In contrast, i pass was, in most cases, as high in 1 M HCl as in 7 M LiCl for UNS S32750. In 7 M LiCl, the E pp values were nobler than in 1 M HCl. In fact, due to the high E corr * values in 1 M HCl, the E pp was not observed in several tests, as indicated in Figure 5.

Crevice-Like-Solutions
density measured before the active/passive transition. Similarly, Epp was defined as the potential at which the transition from active to passive took place. Ecorr * was considered as the value measured at the end of the 1 h open circuit potential measurement before polarization. After the active/passive transition, potentials reached values more positive than the oxygen evolution reaction and within the transpassive area [33]. Consequently, the inflection point seen at high anodic potentials (the intersection between lines 3 and 4 in Figure 3) was defined as ETrans.   density measured before the active/passive transition. Similarly, Epp was defined as the potential at which the transition from active to passive took place. Ecorr * was considered as the value measured at the end of the 1 h open circuit potential measurement before polarization. After the active/passive transition, potentials reached values more positive than the oxygen evolution reaction and within the transpassive area [33]. Consequently, the inflection point seen at high anodic potentials (the intersection between lines 3 and 4 in Figure 3) was defined as ETrans.   temperatures. Even though the current density did not achieve typical passive values, this area will be referred to as passive hereunder to compare ipass between the solutions. Additionally, lower current densities (both icp and ipass) were obtained in 1 M HCl for potentials below the oxygen evolution reaction or below the transpassive region [33]. In contrast, ipass was, in most cases, as high in 1 M HCl as in 7 M LiCl for UNS S32750. In 7 M LiCl, the Epp values were nobler than in 1 M HCl. In fact, due to the high Ecorr * values in 1 M HCl, the Epp was not observed in several tests, as indicated in Figure 5.  Differences between the two materials were also observed. In 1 M HCl, UNS S32750 had a higher i pass than UNS S39274, whereas the E pp of UNS S32750 was more positive in 7 M LiCl, especially at 60 • C. At that same temperature, there was a significant difference in i cp between both materials in 7 M LiCl. Figure 6 illustrates the surface of two specimens after exposure, as observed by LOM. No crevice corrosion was found along the edges of the filter paper by both high IFM magnifications and SEM analysis. No evident corrosion attack was seen on the surface of the specimens tested in 1 M HCl. In this case, the surface was slightly etched, revealing the grain structure of the samples. In contrast and as expected [11], the specimens tested in 7 M LiCl experienced uniform dissolution.
Differences between the two materials were also observed. In 1 M HCl, UNS S32750 had a higher ipass than UNS S39274, whereas the Epp of UNS S32750 was more positive in 7 M LiCl, especially at 60 °C. At that same temperature, there was a significant difference in icp between both materials in 7 M LiCl. Figure 6 illustrates the surface of two specimens after exposure, as observed by LOM. No crevice corrosion was found along the edges of the filter paper by both high IFM magnifications and SEM analysis. No evident corrosion attack was seen on the surface of the specimens tested in 1 M HCl. In this case, the surface was slightly etched, revealing the grain structure of the samples. In contrast and as expected [11], the specimens tested in 7 M LiCl experienced uniform dissolution. Figure 6. Optical visualization of UNS S39274 specimens after anodic potentiodynamic polarization at room temperature exposed to (a) 1 M HCl, and (b) 7 M LiCl. The exposed area, the circle, is equal in the two pictures.
The surface analysis performed by SEM and EDS of the corroded specimens in 7 M LiCl revealed a clear difference in the attack morphology between both SDSS. Figure 7 shows the morphology of the attack after testing, as observed by SEM. While both phases corroded uniformly in the case of UNS S32750, S39274 suffered selective dissolution of the α-phase. In this regard, ferrite can be distinguished easily from austenite using EDS due to its lower Ni and higher Cr and Mo concentration [6,34]. The surface chemical composition of each phase for both materials obtained by EDS before and after the corrosion testing is presented in Table 2. The W-free material showed a relative enrichment in O, Ni, and Mo and an impoverishment in Cr and, especially Fe, when comparing the values before and after the corrosion testing. This behavior was observed for both austenite and ferrite phases. On the other hand, the W-rich material was richer in O and Mo, but poorer only in Fe. In comparison, Cr and Ni concentration was similar before and after corrosion. Nevertheless, there was a difference in the W content between the austenite and ferrite phases. W was enriched in the ferrite phase, but not in austenite after corrosion. Figure 8 shows the concentration of dissolved metal cations as measured by ICP-MS after testing. As expected, the concentration of dissolved metal cations was larger in 7 M LiCl than in 1 M HCl for both materials, which increased with increasing temperature (except for UNS S39274 at 60 °C in 7 M LiCl). The amount of released metal cations by both materials in 1 M HCl was similar. Contrarily, in 7 M LiCl, the dissolved concentration of metal cations released by UNS S39274 was larger than that Figure 6. Optical visualization of UNS S39274 specimens after anodic potentiodynamic polarization at room temperature exposed to (a) 1 M HCl, and (b) 7 M LiCl. The exposed area, the circle, is equal in the two pictures.
The surface analysis performed by SEM and EDS of the corroded specimens in 7 M LiCl revealed a clear difference in the attack morphology between both SDSS. Figure 7 shows the morphology of the attack after testing, as observed by SEM. While both phases corroded uniformly in the case of UNS S32750, S39274 suffered selective dissolution of the α-phase. In this regard, ferrite can be distinguished easily from austenite using EDS due to its lower Ni and higher Cr and Mo concentration [6,34]. The surface chemical composition of each phase for both materials obtained by EDS before and after the corrosion testing is presented in Table 2. The W-free material showed a relative enrichment in O, Ni, and Mo and an impoverishment in Cr and, especially Fe, when comparing the values before and after the corrosion testing. This behavior was observed for both austenite and ferrite phases. On the other hand, the W-rich material was richer in O and Mo, but poorer only in Fe. In comparison, Cr and Ni concentration was similar before and after corrosion. Nevertheless, there was a difference in the W content between the austenite and ferrite phases. W was enriched in the ferrite phase, but not in austenite after corrosion.    Table 3 shows the calculated dissolution ratio (d'M) of each element for all specimens. Cr, Ni, and Mo showed dissolutions ratios close to 1, suggesting congruent dissolution with Fe. On the other hand, there were significant differences regarding the dissolution ratio of W. In 1 M HCl, d'W was close to 1; however, in 7 M LiCl, the results indicated a possible surface enrichment of W on the surface, as d'W < 1.   Figure 8 shows the concentration of dissolved metal cations as measured by ICP-MS after testing. As expected, the concentration of dissolved metal cations was larger in 7 M LiCl than in 1 M HCl for both materials, which increased with increasing temperature (except for UNS S39274 at 60 • C in 7 M LiCl). The amount of released metal cations by both materials in 1 M HCl was similar. Contrarily, in 7 M LiCl, the dissolved concentration of metal cations released by UNS S39274 was larger than that of UNS S32750, apart from the tests performed at 60 • C, where UNS S39274 experienced a much lower dissolution than UNS S32750.    Figure 9 illustrates the Ecorr * and η obtained from the anodic potentiodynamic polarization curves used for Galvele's critical acidification model, together with the estimated Ecrit calculated using Equation (5). Even though both materials differed in the Ecorr * and η, the resulting Ecrit was similar for both materials in 1 M HCl. Additionally, the estimated Ecrit values were over the reversible potential of the oxygen evolution reaction and within the transpassive region [33], suggesting transpassive dissolution. As a result, in neutral chloride solutions, it could be expected that Ecrit ≈ ETrans at all temperatures. In 7 N Cl − , there were no differences in most cases, apart from 60 °C where UNS S39274 obtained a slightly nobler Ecrit than UNS S32750, due to the difference in η between materials. In all  Table 3 shows the calculated dissolution ratio (d' M ) of each element for all specimens. Cr, Ni, and Mo showed dissolutions ratios close to 1, suggesting congruent dissolution with Fe. On the other hand, there were significant differences regarding the dissolution ratio of W. In 1 M HCl, d' W was close to 1; however, in 7 M LiCl, the results indicated a possible surface enrichment of W on the surface, as d' W < 1.  Figure 9 illustrates the E corr * and η obtained from the anodic potentiodynamic polarization curves used for Galvele's critical acidification model, together with the estimated E crit calculated using Equation (5). Even though both materials differed in the E corr * and η, the resulting E crit was similar for both materials in 1 M HCl. Additionally, the estimated E crit values were over the reversible potential of the oxygen evolution reaction and within the transpassive region [33], suggesting transpassive dissolution. As a result, in neutral chloride solutions, it could be expected that E crit ≈ E Trans at all temperatures. In 7 N Cl − , there were no differences in most cases, apart from 60 • C where UNS S39274 obtained a slightly nobler E crit than UNS S32750, due to the difference in η between materials. In all other conditions, E crit decreased slightly with temperature, although the differences were within the experimental error.

Galvele's Acidification Model
Metals 2020, 10, x FOR PEER REVIEW 12 of 19 other conditions, Ecrit decreased slightly with temperature, although the differences were within the experimental error.

Statistical Analysis
Tables 4 and 5 contain Kendall's correlation coefficients calculated for the pairwise parameters shown in the column and row of each cell for 1 M HCl and 7 M LiCl crevice-like-solutions, respectively. Additionally, statistically significant (p-value < 0.05) values are indicated in bold font.
In both electrolytes, the concentration of released metal cations of each element seemed to follow the same trend, either increasing or decreasing in quantity altogether. The only exception was W in 7 M LiCl, which did not present any relationship with any parameter. The other elements had a strong significant positive relationship with icp and Epp in 7 M LiCl. In contrast, in 1 M HCl, only a strong

Statistical Analysis
Tables 4 and 5 contain Kendall's correlation coefficients calculated for the pairwise parameters shown in the column and row of each cell for 1 M HCl and 7 M LiCl crevice-like-solutions, respectively. Additionally, statistically significant (p-value < 0.05) values are indicated in bold font.
In both electrolytes, the concentration of released metal cations of each element seemed to follow the same trend, either increasing or decreasing in quantity altogether. The only exception was W in 7 M LiCl, which did not present any relationship with any parameter. The other elements had a strong significant positive relationship with i cp and E pp in 7 M LiCl. In contrast, in 1 M HCl, only a strong positive correlation was seen between the dissolution of the chemical elements and i cp . The low correlation values obtained for E pp were most likely due to the low number of tests where the E pp could be measured, as it was mentioned above. E crit was correlated to the concentration of dissolved elements, especially in 1 M HCl, indicating an increment of released cations of all elements, the more negative the E crit . However, even though the correlation was weaker in 7 M LiCl, there was a significant exception since W was the only element with no relationship to E crit .

Choice of Parameters for the Critical Acidification Model
During stable pit and crevice propagation, Cl − anions migrate inside the pit/crevice to maintain electroneutrality as the metal cations are released at the bottom of the attack and undergo hydrolysis [27,35]. Therefore, different Cl − concentrations simulate different propagation degrees. The Cl − concentration is limited by the metallic cation saturation concentration, above which a metallic salt film precipitates [11]. Some authors have reported maximum Cl − concentration values in artificial and real pits of 6 N [9] and 12 N Cl − [36], respectively. Additionally, Kappes et al. [11] reported the precipitation of the salt film in a 22Cr DSS and UNS S32750 to occur between 7 N and 9 N Cl − , representing the 58% and 75% Cl − saturation concentration, respectively. Other authors [15,37] calculated the critical saturation concentration to be 50% for UNS S31600, i.e., approximately 7 N Cl − concentration required for stability of localized corrosion. Kappes and coauthors [11] observed as well that the maximum current density (i cp ) decreased with higher Cl − content above the saturation concentration. On the other hand, i cp increased with Clconcentration in the range below salt film formation. In this regard, the 7 N Cl − concentration solution was chosen in this work to study the effect of W for being the crevice-like-solution with the highest i cp . Similarly, the pH inside artificial pits has been reported to be close to 0 [9], becoming the pH value employed by Kappes et al. [11] and the chosen pH value in this work.
Galvele [13] developed the critical acidification model for pure metals; hence, the choice of parameters, especially for the stability product, must differ when estimating E crit in alloys. Bocher et al. [14] employed a stability product value of x·i crit = 0.01 A/cm, with x = 0.001 cm for Ni-alloys. This choice of parameters results in i crit = 10 A/cm 2 , a current density value four orders of magnitude larger than the i crit determined by Kappes [11] and in this work. Additionally, 10 A/cm 2 in the anodic potentiodynamic curves can only be reached in transpassive potentials, as seen in Figures 4 and 5, erroneously implying that both SDSS would be immune to crevice corrosion at all temperatures. In this regard, the i crit obtained in this work, similar to the one calculated by Kappes [11], were considered to be more appropriate for the estimation of E crit in DSS.

Role of W in Crevice-Like-Solutions
The theoretical E crit values obtained from Galvele's critical acidification model demonstrate the large difference in the aggressiveness of the solutions, as expected. The E crit values obtained in 1 M HCl where all more positive than the oxygen evolution reaction [33], implying that stable localized corrosion requires a higher chloride concentration and, thus, the material will suffer transpassive dissolution, i.e., E crit in 1 N Cl − is, in reality, an E Trans . In contrast, E crit values for 7 N Cl − were low, suggesting that crevice corrosion could be possible in neutral chloride environments at all the temperatures investigated. Interestingly, Figure 8 clearly shows a significant difference in the concentration of dissolved ions in the two solutions, with much higher values for all elements in 7 M LiCl.
Both materials behaved similarly in the 1 N Cl − environment. All parameters from the anodic potentiodynamic polarizations were in the same range (Figures 4 and 5), with the only exception of E corr * and i pass , which were lower and higher, respectively, for UNS S32750, indicating a lower corrosion resistance in the pit/crevice solution. However, the concentration of dissolved metal cations was similar in both SDSSs ( Figure 8). Since the anodic potentiodynamic polarization in all tests reached the transpassive region, it is suspected that most of the ions were released at these high potentials, causing negligible dissolution in the passive region or at E corr * .
In the more aggressive 7 M LiCl solution, both materials showed larger differences, especially at 60 • C. Even though all parameters extracted from the anodic potentiodynamic polarization curves ( Figure 4) were in the same range up to 50 • C, the concentration of released ions was higher in UNS S39274 than in UNS S32750. Nevertheless, at 60 • C, UNS S39274 showed a somewhat better corrosion resistance as indicated by i cp , E pp, and the lower concentration of dissolved cations.
Based on the concentration of dissolved metal cations, the d' M reported in Table 3 indicates an important difference that can be related to the difference achieved in E crit for the two solutions. The only values that changed significantly between the solutions were d' W at all temperatures. In 1 M HCl, d' W was between 0.9 and 1, suggesting congruent W dissolution, similar to the other elements. In contrast, in 7 M LiCl, d' W fluctuated between 0.25 and 0.66, depending on the temperature, suggesting a surface enrichment in W. Indeed, W was the only element displaying incongruent dissolution, as all the other elements dissolved approximately uniformly at all temperatures. According to the Pourbaix diagrams [33], W is the only element capable of forming an oxide layer, WO 3 , at pH 0. Indeed, a yellow (the color of WO 3 [33]) reflection was seen on UNS S39274 after the tests. Even though W is a ferrite stabilizer [38], ferrite dissolved selectively for UNS S39274, as seen in Figure 7. The dissolved W, in the form of tungstate ions, can precipitate forming a WO 3 layer, shown to reduce the corrosion rate [39]. A small enrichment was measured by EDS (Table 2) in ferrite, but not on austenite. Most likely, given the small thickness of the deposit, a more surface-sensitive technique such as x-ray photoelectron spectroscopy (XPS) or Auger electron spectroscopy (AES) would be needed to confirm this assumption. On the other hand, the W-free material showed a uniform attack, as illustrated in Figure 7.
The analysis of the chemical composition of the phases before corrosion included in Table 2 showed that both α and γ phases of UNS S32750 are richer in Cr (>1 wt.%) and Mo (approximately 0.5 wt.%) than the phases in UNS S39274. The total wt.% (Cr + Mo) difference between the two SDSSs for each phase was approximately the same as the content of W in UNS S39274 of that phase. Nevertheless, variances in chemical composition alone cannot explain the difference in the corrosion morphology observed by SEM (Figure 7). Local probe technique studies of passive film have concluded that, despite the higher PRE value of the ferrite phase in SDSS, austenite shows a more noble behavior, i.e., austenite is more corrosion resistant than ferrite [40]. However, when the material was exposed to a very aggressive environment (i.e., concentrated nitric acid), both austenite and ferrite adopted similar passive film properties and their differences disappeared. This observation is in line with the uniform corrosion observed in 7 M LiCl solution at 60 • C of UNS S32750 in this work. Nevertheless, the selective dissolution of ferrite observed for UNS S39274 is not in line with the SKPFM results obtained by Rahimi et al. [41], where ferrite showed a nobler behavior than austenite. On the other hand, selective dissolution of ferrite of SDSS was observed by Långberg et al. [42] as the data obtained by synchrotron XRR, XRF, and XRD showed a higher dissolution quantity of Fe from ferrite than austenite. Additionally, this work observed the following order in element dissolution in UNS S32750 as the potentiodynamic polarization applied higher potentials: only Fe at E < 1 V Ag/AgCl , then dissolution of Fe and Cr at E > 1.2 V Ag/AgCl causing an enrichment of Mo and Ni and, finally, dissolution of all elements at E > 1.3 V Ag/AgCl . This dissolution order fits the behavior seen for UNS S32750 in Table 2, where the surface was enriched in Ni and Mo and depleted in Cr and, especially, Fe. However, Rahimi et al. [41] stated that W promotes the stability of Mo, Cr and Fe. This statement can explain why the W-rich material experimented no Cr impoverishment and a much lower dissolution of Fe than the W-free material.
The improved localized corrosion resistance of UNS S39274 at 60 • C, indicated by the lower metallic cation dissolution (Figure 8), the lower i cp , and higher E pp (Figures 4 and 5), resulted in a higher E crit calculated by Galvele's critical acidification model (Figure 9). The E crit value obtained was nobler (approximately 100 mV) than that of UNS S32750, and nobler than the E crit at previous temperatures. The increase of E crit at 60 • C was mainly due to the shift of η to more noble potentials. As stated by Galvele et al. [7], an increment of η indicates a slower dissolution rate.
Kendall's correlation coefficient calculated in Tables 4 and 5 also showed a significant difference between the quantity of W dissolved into the electrolyte and E crit in 7 M LiCl. The correlation between the dissolution of Cr, Fe, Ni, and Mo and E crit is seen in Figures 8 and 9. Up to 50 • C, the dissolution of these elements increased, whereas the E crit decreased. However, at 60 • C, this behavior changed for both parameters. The dissolution of the elements was reduced, whereas E crit increased. In other words, at all temperatures, the dissolution quantity and the E crit followed exactly the opposite trend, reflected by a strong negative value of Kendall's coefficient.
The fact that W was not correlated in the same way as the other elements might suggest that; either (i) W dissolution increased even though E crit was nobler for UNS S39274 than for UNS S32750, or (ii) W dissolution decreased as E crit decreases for UNS S39274. Even though Figure 8 shows that W dissolution decreased at 60 • C in 7 M LiCl, as the other elements, whereas d' W (Table 3) indicated that W was released in higher amounts at that condition. The only plausible explanation is that the dissolution of W was reduced, but not as much as the other elements at 60 • C in 7 M LiCl. This increment in d' W despite the nobler E crit at this particular condition for UNS S39274 is most likely the reason why the dissolution of W and E crit were not correlated. Consequently, the combination of d' W and Kendall's coefficient parameters infer a significant role of W on the improvement of corrosion resistance in propagating localized attacks, i.e., 7 N Cl − acidic environments, only at 60 • C.

Prediction of Crevice Corrosion Repassivation Potential
In this work, Galvele's model was used to estimate the theoretical E crit in different crevice-like-solutions and to study the validity of the model to predict crevice corrosion potentials, more specifically E R,Crev as it is widely used to define a protection potential [6]. Figure 10 compares E crit values estimated by the critical acidification model in this work and by Kappes et al. [11] with experimental E R,Crev results of UNS S32750 and UNS S39274 measured by the PD-GS-PD technique in 3.5% NaCl (pH = 6.5) by Torres et al. [6]. In this regard, Torres et al. established a T R,Crev = 55 • C for UNS S39274 in 3.5 wt.% NaCl by the PD-GS-PD technique. In the same study, UNS S39274 polarized at +600 mV Ag/AgCl (simulating chlorinated seawater [43,44]) gave a CCT of 55 • C in natural seawater. For UNS S32750, that same work measured a CCT of 45 • C and a T R,Crev of 42.5 • C in natural seawater polarized at +600 mV Ag/AgCl .
In this work, the Ecrit values obtained using Galvele's model were independent of temperature and suggested the possibility of crevice corrosion at T ≥ 22 °C. In contrast, PD-GS-PD results gave Ecrit values in the transpassive range for T < TR,Crev, which was 40 °C for UNS S32750 and 55 °C for S39274. The discrepancy can be reconciled by the fact that Galvele's model describes stable localized corrosion propagation. The high potentials measured by the PD-GS-PD method in 3.5 wt.% NaCl suggested that crevice corrosion initiation is controlled by the breakdown of the passive film at T ≤ TR,Crev (or CCT) as suggested by the Li-Scully-Frankel framework [50,51]. In this regard, while crevice corrosion could propagate stably if the concentration of the crevice environment reaches 7 N Cl − , in practice, the stability of the passive film at T < Tcrit is rate-determining, preventing the development of the critical environment required for crevice corrosion propagation. To our knowledge, the effect of temperature on the critical acidification model has not been addressed to date. Despite these discrepancies, the Ecrit obtained by Galvele's critical acidification model was in excellent agreement with ER,Crev values measured by the PD-GS-PD method in 3.5 wt.% NaCl (pH = 6.5) as seen in Figure  10, i.e., 33 mV difference at 60 °C and a 66 mV difference at 50 °C for UNS S32750, and no difference for UNS S39274 at 60 °C. These findings, therefore, also suggest that the use of the critical acidification model to estimate the theoretical Ecrit might require prior knowledge of Tcrit.  As seen in Figure 10, the E crit estimate by Kappes et al. [11] for UNS S32750 at room temperature in 7 M LiCl was approximately 70 mV less noble than the one obtained in this work. Additionally, the difference between the E crit value reported by Kappes and the E R,Crev of UNS S32750 in 1 wt.% NaCl environment at 30 • C reported by Martinez et al. [45] is only of 20 mV, whereas the difference increases to 90 mV when compared to the E crit obtained in this work. Nevertheless, many studies have tested SDSS, in particular UNS S32750, obtaining critical temperatures (T crit ) for localized corrosion well above 30 • C [43,[46][47][48][49], i.e., E crit is within the transpassive region at T ≤ 30 • C, differing significantly from the E crit values measured by Kappes and Martinez et al. In this work, the E crit values obtained using Galvele's model were independent of temperature and suggested the possibility of crevice corrosion at T ≥ 22 • C. In contrast, PD-GS-PD results gave E crit values in the transpassive range for T < T R,Crev , which was 40 • C for UNS S32750 and 55 • C for S39274. The discrepancy can be reconciled by the fact that Galvele's model describes stable localized corrosion propagation. The high potentials measured by the PD-GS-PD method in 3.5 wt.% NaCl suggested that crevice corrosion initiation is controlled by the breakdown of the passive film at T ≤ T R,Crev (or CCT) as suggested by the Li-Scully-Frankel framework [50,51]. In this regard, while crevice corrosion could propagate stably if the concentration of the crevice environment reaches 7 N Cl − , in practice, the stability of the passive film at T < T crit is rate-determining, preventing the development of the critical environment required for crevice corrosion propagation. To our knowledge, the effect of temperature on the critical acidification model has not been addressed to date. Despite these discrepancies, the E crit obtained by Galvele's critical acidification model was in excellent agreement with E R,Crev values measured by the PD-GS-PD method in 3.5 wt.% NaCl (pH = 6.5) as seen in Figure 10, i.e., 33 mV difference at 60 • C and a 66 mV difference at 50 • C for UNS S32750, and no difference for UNS S39274 at 60 • C. These findings, therefore, also suggest that the use of the critical acidification model to estimate the theoretical E crit might require prior knowledge of T crit .

Conclusions
In this work, simulated crevice environments were tested, and Galvele's critical acidification model applied to estimate E crit values as a function of temperature and study the effect of W as an alloying element in solid solution. The following conclusions were drawn: • A 7 N Cl − (pH = 0) crevice-like solution was necessary to simulate stable crevice propagation, suggesting that W additions could be beneficial only in situations of localized corrosion propagation under a salt film.

•
The dissolution morphology was different between materials in 7 N Cl − . UNS S32750 experienced uniform corrosion of austenite and ferrite phases, whereas α-phase selectively dissolved in UNS S39274. • E crit values obtained using the critical acidification model were independent of temperature, which contrasted with previous findings in simulated seawater environments. In line with the new Li-Scully-Frankel framework, the discrepancy was attributed to the stability of the passive film as a rate-determining step below a T crit . Conversely, E crit values obtained by the critical acidification model were in good agreement with E R,Crev results obtained by the PD-GS-PD technique in 3.5 wt.% NaCl for temperatures above T R,Crev . Funding: This research received no external funding.