Inverse Crevice Corrosion of Carbon Steel: Effect of Solution Volume to Surface Area

Crevice corrosion of carbon steel was investigated in different exposure environments by performing coupon exposure and electrochemical tests. The extent of corrosion on the bold surface of a carbon steel crevice coupon was more severe at 80◦C than at 21◦C, in aerated rather than dearated solutions, and with γ-radiation present. In contrast to normal crevice corrosion, we observed ‘inverse crevice corrosion’ behavior, the phenomenon where it is the corrosion on the bold surface that is accelerated when coupled, rather than that on the crevice surface. The coupling current measured between a crevice and a bold electrode in an electrochemical cell was also negative. This inverse crevice corrosion behavior is attributed to a significantly lower metal cation dissolution capacity of the small occluded water volume in the crevice, compared to that of the bulk water volume over the bold surface. The reduction in dissolution capacity results in faster and earlier formation of a protective oxide layer. Corrosion of the bold and crevice surfaces evolves at different rates, leading to galvanically accelerated corrosion of the bold surface. The effect of γ-radiation on corrosion evolution in different solution environments leading to inverse crevice corrosion is discussed. © The Author(s) 2017. Published by ECS. This is an open access article distributed under the terms of the Creative Commons Attribution 4.0 License (CC BY, http://creativecommons.org/licenses/by/4.0/), which permits unrestricted reuse of the work in any medium, provided the original work is properly cited. [DOI: 10.1149/2.0511709jes] All rights reserved.

Many countries, including Canada, are exploring long-term disposal of used nuclear fuel in a deep geological repository (DGR) using a multiple-barrier system, with a key barrier being the used fuel container (UFC). [1][2][3][4][5][6][7] Certain UFC designs considered for disposal in a DGR consist of an inner vessel made of carbon steel (CS) or cast iron for structural strength, with an outer Cu shell or coating as an external corrosion barrier (e.g. the Swedish and Canadian UFC designs). 3,8 The current Canadian UFC design consists of a pressure-vessel-grade CS pipe pre-coated with Cu. The vessel would be sealed by laser welding on site, in air, by attaching a pre-Cu-coated hemispherical CS head at one end. This would be followed by applying a Cu coating over the welded regions. 9,10 A concern regarding the structural integrity of the inner CS vessels of this UFC design is localized corrosion. 11 Moisture trapped inside a UFC could condense on the stressed regions near the welds and, for the Canadian design, within the gap between the hemispherical head and the body. This could lead to localized corrosion, a potential failure mechanism of the container.
The environment inside the UFC will be initially humid and it will include a flux of ionizing radiation (and particularly γ-radiation), emitted from the decay of radionuclides in the used fuel. For the current Canadian UFC design the dose rate at the inner surface of a UFC is anticipated to be less than 100 Gy·h -1 (1 Gy = 1 J·kg -1 ). The dose rate is calculated to be 51 Gy·h -1 for 10-year old fuel and the dose rate will steadily decreases to 4.9 Gy·h -1 after the used fuel ages for 100 years. 12 Interaction of matter with high energy photons or particles usually results in the absorbed energy being dissipated predominantly as heat (increasing the material's temperature slightly), with the important exception of high dielectric media, notably water. [13][14][15][16][17] Absorption by water of high energy radiation induces ionization and decomposition of water molecules to produce a number of redox active species. For example, γ-irradiation of liquid water produces oxidants such as H 2 O 2 , 14,15,18 while humid air radiolysis produces NO x and HNO 3 that will dissolve in any condensed water that is available. 12,[19][20][21] Thus, the chemical environment in water in a UFC will be very different from the relatively benign chemical environment expected in water in the absence of ionizing radiation.
Carbon steel generally does not exhibit localized corrosion behavior without ionizing radiation present and localized corrosion is observed only in chemical environments that promote the break-down of a passive oxide film. Such environments include water with strongly alkaline pHs 22 and solutions containing certain anions such as carbonate/bicarbonate, 23 chromate 24,25 and halides. [26][27][28] However, it has been observed that γ-radiation can increase the corrosion potential for CS significantly, alter the kinetic pathways of CS corrosion 29 and cause pitting on CS even in Ar-purged seawater. 23 Our current understanding of the impact of γ-driven water radiolysis on localized corrosion of CS is limited. Due to the highly chemically active environment irradiation induces, water radiolysis is known to increase the rate of metal oxidation at the early stages of corrosion. However, because metal oxidation leads to both solid oxide formation and metal dissolution, and the oxide formed on the surface influences the subsequent metal oxidation, a change in the early oxidation rate, and hence the corrosion pathway, can have a profound effect on long-term corrosion behavior. [30][31][32] In the weld region of a UFC there will be two different corrosion environments associated with the crevice at the weld and the adjoining boldly exposed metal surfaces. This work explores the possibility of galvanically coupled corrosion between the crevice and bold CS surfaces in the presence of γ-radiation. Two sets of experiments have been performed. In the first set of experiments, water droplets were placed over crevices formed between CS and quartz plates in sealed vials, and the test assemblies were then exposed to γ-radiation. The results showed different extents of corrosion on the crevice and the bold surfaces, raising the possibility of inverse crevice corrosion, i.e., galvanic coupling that accelerates the corrosion on the boldly exposed surfaces covered with water. We investigated this possibility in a second set of electrochemical experiments by monitoring the coupling current between two electrodes, one electrode mimicking the bold surface and the other mimicking the crevice surface. The post-test electrodes were examined by surface analysis.

Experimental
Crevice coupon exposure tests.-The CS used was A516 Gr.70 CS purchased from Metal Samples Company, containing 0.23% carbon. The CS test coupons were cuboids of 1.0 cm × 1.5 cm × 0.7 cm. A notch with a volume of 0.02 cm 3 was fabricated on the 10-mm edge to hold a water droplet over the crevice mouth, as shown in Fig. 1a. The CS coupons were polished manually using a series of silicon carbide papers with grits of 400, 800 and finally 1200. The polished coupons were then sonicated in acetone and dried under flowing argon.
A crevice was created between a CS coupon and a quartz plate by binding them in a polyester holder (Fig. 1a). The gap between the coupon and the quartz plate was estimated to be ∼50 μm based on the roughnesses of the two surfaces. This gap is not as narrow as a crevice typically used in a corrosion study (a few μm), but will nevertheless be referred to as a crevice in this paper. The quartz crevice former allowed visual inspection of corrosion in the crevice without opening the crevice. The quartz plates did not appear to have any chemical effect on the CS corrosion process because the post-test surface analysis by X-ray photoelectron spectroscopy (XPS) found no Si on the CS crevice surfaces. A crevice assembly was placed on a glass pedestal inside a 40-mL glass corrosion test cell (Fig. 1b). A small volume (1.5 mL) of purified water (Type 1, 18.2 M · cm) was added to the bottom of the cell to maintain 100% relative humidity in the cell without having a direct contact with the crevice coupon assembly. A water droplet of 0.05 mL was used to fill the notch over the mouth of the crevice and to wet the crevice by the capillary effect. The water droplet also partially covered the surface outside the notch (Fig. 1a). Depending on the type of cover gas used to fill the cell, the assembly was prepared either in an argon-filled glove box using deaerated water, or under ambient conditions using aerated water. The glass corrosion test cell was sealed and placed in an autoclave (Fig. 1c) and the temperature of the whole assembly was maintained either at room temperature or at 80 • C. Room temperature was 21 ± 3 • C during the tests and 21 • C is used to represent room temperature throughout this paper. For irradiation tests, the autoclave was placed inside a 60 Co γ-irradiation cell (Fig. 1c) which provided a dose rate of 3.2 kGy·h -1 at the time of the tests. This is about 60 times higher than the anticipated dose rate inside a UFC.
Following a 20-h exposure, the crevice assembly was taken apart inside an argon-filled glove box to minimize air oxidation and the CS coupon was transferred to a post-test surface analysis laboratory in a container filled with argon.
Electrochemical galvanic coupling tests.-Galvanic coupling between the crevice and boldly exposed surfaces was explored using two electrode types representing the different geometries of the crevice and boldly exposed surfaces. They are referred to as the 'crevice electrode' and the 'bold electrode', respectively, hereafter.
The crevice electrodes were prepared as follows. One face on each of two CS coupons was polished using 1200 grit SiC paper and the other faces were coated with insulating paint (Amercoat 90 HS, PPG Protective & Marine Coatings). This epoxy-phenolic paint is stable under γ-irradiation at room temperature over the exposure durations used in this study. The crevice electrode was assembled by placing the two CS coupons in a polyester holder, as shown in Fig. 2, with the two polished surfaces facing each other, forming a crevice with a total geometric crevice surface area of 3 cm 2 . The bold-surface electrode was a flat CS coupon with a surface area of 0.785 cm 2 .
The electrolyte was prepared from 0.01 M Na 2 B 4 O 7 · 10H 2 O (analytical grade, EMD Inc.), with the addition of H 3 BO 3 (analytical grade, Caledon Laboratories Ltd.) to achieve the desired pH of 7. The borate buffer was chosen to match the initial pH of the water droplet used in the coupon exposure tests while minimizing the buffer's influence on corrosion reactions. Borate is stable under γ-radiation, has a good buffer capacity near neutral pH and does not incorporate into the oxide film of Fe. 33 The 500-mL electrolyte solution was purged with argon continuously throughout the experiment.
The electrochemical cell setup for coupling current measurement is schematically shown in Fig. 2. The bold and crevice electrodes were connected through a potentiostat (Solartron, model 1287) configured as a zero-resistance ammeter (ZRA). 34 The measured coupling currents were verified using an ammeter (Keithley model 6514 System Electrometer). In a different set of experiments, a crevice electrode and a bold electrode in the same electrochemical cell were not coupled but allowed to corrode independently for 3 h or 48 h.
All electrochemical experiments were performed at room temperature with or without radiation present. Radiation experiments were conducted in the 60 Co γ-cell at 3.2 kGy·h −1 .
Surface analyses.-The X-ray photoelectron spectroscopy (XPS) analyses were carried out with a Kratos Axis Ultra spectrometer using a monochromatic Al Kα source. The spectrometer dispersion was adjusted to give a binding energy of 932.63 eV for metallic Cu-2p 3/2 . High-resolution spectra were collected using an analysis area of ∼300 μm × 700 μm for Fe-2p 3/2 and C-1s using a pass energy of 20 eV. The pass energy corresponds to an Ag 3d 5/2 peak with a full width at half maximum (FWHM) of 0.55 eV. All spectra were analyzed using Casa XPS software. Peak shifts due to any apparent charging were adjusted using calibration with the C-1s peak set to 284.8 eV. The Fe-2p 3/2 high resolution spectra were fitted using Gupta-Sen multiplet peaks. 35 The FWHM was generally fixed between 1.0 and 1.2 eV. A detailed description of binding energies and the spectral deconvolution method can be found elsewhere. 36 A LEO (Zeiss) 1540XB scanning electron microscope (SEM) equipped with focused ion beam (FIB) was used to examine the surface morphology and cross section of the coupons. Raman spectra of the coupons were taken using a Renishaw model 2000 Raman spectrometer with a Melles Griot 35 mW HeNe laser at 633 nm and a Peltier cooled charge-coupled device (CCD) detector. The focused laser beam was ∼2 μm in diameter. The coupon spectra were compared with Raman spectra of standard iron oxide samples from Alfa Aesar. . Optical images of the CS crevice coupons exposed for 20 h to water droplets under Ar or air cover gas in the absence of radiation (no Rad), or with radiation (Rad) at 21 • C. exposure conditions crevice surfaces remained relatively clean while bold surfaces were more corroded. For a given exposure condition, corrosion on a bold surface was not limited to the area initially covered with a water droplet (labelled wet-bold), but also included the rest of the surface (labelled dry-bold). The amount and the color of the corrosion deposits on a wet-bold surface varied depending on whether the surface was outside or inside the notch. These results indicate that for a given exposure condition the amount and type of oxides formed during stagnant water-droplet corrosion may strongly depend on the local thickness of a water layer or condensed water film. At room temperature the extent of corrosion on a bold surface ranged from the least to the most extensive in the following order of exposure environments:

Experimental Results and Discussion
Ar + no Rad < air + no Rad < Ar + Rad < air + Rad where 'no Rad' and 'Rad' represent tests without or with radiation present, respectively. The color of oxide deposits also depended on exposure environment. The color of the oxide formed in Ar + no Rad is difficult to see due to the thinness of the oxide layer present. On a dry-bold surface corroded in other environments the color of the oxide deposits varies from light green (in air + no Rad), to dark green (or mixture of green and black) (in Ar + Rad), and to dark orange (black and orange) (in air + Rad). On a wet bold-surface the color of oxide deposits formed outside the notch varies from dark red (in air + no Rad), to black and orange (in Ar + Rad), and to orange (in air + Rad). Iron oxides and hydroxides have distinct colors: mixed ferrousferric hydroxides are green, magnetite (Fe 3 O 4 ) is black, lepidocrocite (γ-FeOOH) is orange, and hematite (α-Fe 2 O 3 ) is red. 37 The chemical compositions of oxide deposits on wet-bold surfaces outside the notches were characterized by Raman spectroscopy. The Raman results, discussed in more detail below, are summarized in Table I. The Raman spectra of the surfaces corroded in different exposure environments are compared with the reference spectra of standard powdered iron oxide samples in Fig. 4. The Raman spectrum of a surface corroded in Ar + no Rad at 21 • C shows no discernible iron oxide peaks as there is only a very thin layer of oxide present. The Raman spectrum of a surface corroded in air + no Rad shows three major peaks at 250, 380 and 530 cm −1 that correspond to the three main peaks of lepidocrocite (γ-FeOOH). However, the relative intensity of the peak at 670 cm −1 to the intensities of the two other peaks is higher in the spectrum of the corroded surface than in that of reference standard γ-FeOOH. The higher intensity at 670 cm -1 is attributed to the additional presence of magnetite (Fe 3 O 4 ), which has its main Raman peak at 670 cm -1 . The Raman characterization of the oxide deposits on the wet-bold surface outside the notch is consistent with the dark orange color of the oxides seen in the optical image of this surface in Fig. 3. Magnetite is black while lepidocrocite is orange. Magnetite, being black, also has a low Raman scattering probability. 38 These results indicate that the oxide deposits present on coupons corroded for 20 h in air + no Rad consist mainly of Fe 3 O 4 and γ-FeOOH.
The Raman spectrum of a wet-bold surface corroded in Ar + Rad shows major peaks near 300, 400 and 700 cm -1 . This spectrum does not exactly match the reference spectrum of any individual iron oxide/hydroxide. The reference Raman spectra of hematite (α-Fe 2 O 3 ), goethite (α-FeOOH) and γ-FeOOH, all have peaks at 300 and 400 cm -1 . However, the ratio of the observed peak intensities at 300 cm -1 Figure 4. Raman spectra of the wet-bold surfaces of the CS coupons the optical images of which are shown in Fig. 3.
Journal of The Electrochemical Society, 164 (9) C539-C553 (2017) C543 to 400 cm -1 in the spectrum of the wet-bold surface does not match with those in the reference spectra of any of the Fe III oxides. In addition, green rusts, which are a group of Fe II -Fe III hydroxides with some of the OH sites in the oxide lattice replaced by other anions, have a main peak at 420 cm −1 . 37 Green rusts do not exist as a pure solid phase and are not stable in air. Hence, no standard sample is available from which a reference spectrum can be taken. Based on the known Raman peaks for iron oxides, we have assigned the peaks at 300 and 400 cm −1 to Raman scattering associated with the vibrational modes of the Fe III − O bond of an oxide(s) that has not formed to a specific oxide phase. The peak near 700 cm -1 is assigned to spinel oxides, magnetite and/or maghemite (γ-Fe 2 O 3 ). Maghemite has a major, broad peak over the range of 670 to 718 cm -1 , has the same oxide structure as magnetite, and also has a low Raman scattering probability. 38,39 The bold-surface spectrum is very similar to that of iron-oxide nanoparticles formed by γ-irradiation of a solution initially containing ferrous ions. 17 Those iron-oxide nanoparticles were identified as magnetite with a hydrated and hydrolyzed surface (i.e. as ferrous and ferric hydroxides and oxyhydroxides): The Raman analysis indicates that the oxide deposits on coupons corroded in Ar + Rad consist of green Fe II -Fe III hydroxides, black Fe 3 O 4 and possibly γ-Fe 2 O 3 , consistent with the colors of the deposits seen in the optical image shown in Fig. 3.
The Raman spectrum of a wet-bold surface corroded in air + Rad at room temperature compares well with that of γ-FeOOH, but it also contains an additional broad peak at 670 to 720 cm -1 suggesting the presence of Fe 3 O 4 and γ-Fe 2 O 3 as well. The Raman analysis is consistent with the dark orange color of the deposits seen in an optical image.
The optical images in Fig. 3 demonstrate that the formation of corrosion products on a bold surface during 20 h of corrosion at 80 • C are significantly more extensive than those formed at room temperature. At 80 • C, the oxide deposits formed on a bold-surface are mainly black with some green color when corrosion occurred in Ar + no Rad, mostly black in Ar + Rad, while mostly black with some orange to red in air + no Rad or in air + Rad. The Raman spectra of these oxides (Fig. 4) indicate that the black oxides formed in Ar + no Rad or Ar + Rad are mostly Fe 3 O 4 . Based on the Raman spectra and the deposit colors, the oxides formed on a surface corroded in Ar + no Rad at 80 • C are characterized as Fe 3 O 4 , and those formed in Ar + Rad are characterized as mainly a mixture of Fe 3 O 4 and γ-Fe 2 O 3 .
The Raman spectra of bold surfaces corroded in air + No Rad or air + Rad at 80 • C indicate the presence of a mixture of γ-FeOOH and α-Fe 2 O 3 , in addition to Fe 3 O 4 and γ-Fe 2 O 3 . The Raman results are consistent with the mainly black deposits with orange to red tints seen in the optical micrographs (Fig. 3). The color of the oxide deposits formed with radiation present is darker and mostly black compared to the deposits formed without radiation present, further indicating that the oxides formed with radiation present contain more Fe 3 O 4 and γ-Fe 2 O 3 while the oxides formed without radiation present contain more γ-FeOOH and α-Fe 2 O 3 .
The optical imaging and the Raman spectroscopic analyses indicate that iron oxidation progresses to form iron hydroxides/oxides with different oxidation states depending on the exposure environment. At room temperature without radiation, iron oxidation in Ar progresses very slowly and oxide formation is negligible. Iron oxidation in air forms granular Fe 3 O 4 and γ-FeOOH deposits. With radiation present, iron oxidation in Ar forms mixed Fe II /Fe III hydroxides and Fe 3 O 4 and γ-Fe 2 O 3 , and iron oxidation in air forms Fe 3 O 4 , γ-Fe 2 O 3 and γ-FeOOH. Increasing temperature from 21 • C to 80 • C accelerates the formation and growth of oxides. At 80 • C the formation of mixed Fe II /Fe III hydroxides and particularly Fe 3 O 4 is seen in all studied environments. As Fe(OH) 2

Intensity
Binding Energy (eV) Figure 5. Examples of high-resolution XPS spectra and the deconvoluted components for the Fe-2p region from crevice surfaces on coupons exposed at 21 • C with radiation and with air as the cover gas. The Fe-2p 3/2 peak was fitted with peaks for Fe metal, FeO, Fe 3 O 4 , Fe 2 O 3 (average of α and γ) and FeOOH (average of α and γ). 36 thus depend on the corrosion environment, as discussed further in the Effect of solution redox property on oxide formation section.
Oxides formed on crevice surfaces.-Crevice surfaces were examined primarily using XPS because of the very thin oxide deposits on these surfaces. High resolution XPS spectra of the O-1s and Fe-2p 2/3 bands were deconvoluted to obtain the oxidation-state compositions and the hydroxide/oxide ratios in the top 9 nm of the oxide layers (the analysis depth of the XPS instrument used in this study). The reference spectra of single-phase metals and metal oxides (Fe 0 , FeO, Fe 3 O 4 , γ-FeOOH, α-FeOOH, α-Fe 2 O 3 and γ-Fe 2 O 3 ) were used for the deconvolution following a method developed by Biesinger et al. 36 Note that the multiple-peak spectra of standard γ-FeOOH and α-FeOOH are nearly the same and hence separation of the contributions of these two phases of ferric oxyhydroxides is not possible. Separation of two phases of ferric oxide (α-Fe 2 O 3 and γ-Fe 2 O 3 ) is not possible for the same reason. Similarly, separation of the FeO contribution from that of Fe 3 O 4 to the overall spectrum is difficult due to the similarities of their multiple-peak spectra. Thus, only the sum of their contributions (as Fe II & Fe II /Fe III oxides) is considered in the following discussion.
Example XPS spectra, presented in Fig. 5, were taken from the crevice and wet-bold surface of coupons corroded in air + Rad at 21 • C. The metallic fraction (Fe 0 ) in the spectrum of the bold surface is negligible, indicating that the oxide layer on this surface is thicker than 9 nm. The XPS analysis indicates that the oxides in the top 9 nm on the bold surface are Fe 3 O 4 , Fe 2 O 3 and FeOOH, consistent with the Raman analysis results (Table I). On the other hand, the XPS Fe-2p 3/2 spectrum of the crevice surface includes a large contribution of Fe 0 (∼25 at.%), indicating that the oxide layer is very thin (<9 nm). The deconvolution of the spectrum indicates that the oxides present on the crevice surface are mainly Fe II & Fe II /Fe III oxides and Fe 2 O 3 but lacking FeOOH.
The XPS results for crevice surfaces corroded under different conditions are summarized in Fig. 6. Also shown in this figure is the XPS analysis of a freshly-polished surface with only an air-formed oxide. Compared to the freshly-polished surface, all crevice surfaces have smaller Fe 0 components, indicating that additional or potentially different oxides from the air-formed oxide have formed on the crevice surfaces. At a given temperature the metallic (Fe 0 ) fraction in the XPS Fe-2p 3/2 band on a crevice surface corroded for 20 h in air is nearly the same as that found on a crevice corroded in Ar with or without radiation. However, the Fe III (FeOOH + Fe 2 O 3 ) fraction in the oxide layer is higher on a crevice surface corroded in air than on one corroded in Ar. A thinner layer of oxide is formed and the fraction of Fe 3 O 4 present in the layer is higher for corrosion with radiation present than without radiation at room temperature. This could be attributed to the faster formation of a uniform layer of Fe 3 O 4 with radiation present, as the presence of this oxide can suppress the later growth of Fe(OH) 2 and its subsequent oxidation to Fe(OH) 3 and γ-FeOOH. Oxidative conversion of Fe 3 O 4 to γ-FeOOH is more difficult than its conversion to γ-Fe 2 O 3 . The oxidation of Fe 3 O 4 to γ-Fe 2 O 3 is relative fast because both oxides share the same oxide structure. 29,37,40 As the outer layer of conductive Fe 3 O 4 is converted to an insulating layer of γ-Fe 2 O 3 , further metal oxidation can be quickly suppressed. 31 Increasing temperature from 21 • C to 80 • C decreases the Fe 0 fraction in the surface layer on a crevice surface corroded in Ar or air and with or without radiation. The Fe 0 fraction on the surfaces corroded in either cover gas with radiation present at 80 • C is negligible, indicating that the oxide layers on these surfaces are thicker than 9 nm. Since the XPS only analyses the top 9 nm layer, it does not convey information on any thicker oxides present on these surface.
The XPS analysis results indicate that the decrease in the Fe 0 fraction with increase in temperature is primarily associated with an increase in the Fe 3 O 4 fraction in the oxide layer on a surface corroded in Ar, while it is primarily associated with an increase in the Fe III (FeOOH + Fe 2 O 3 ) fraction on a surface corroded in air. In a given cover-gas environment at 80 • C, the oxide fraction in the XPS Fe-2p 3/2 band is higher with radiation present than without radiation, and the fraction of FeOOH in the oxide layer is also higher with radiation present. These results are opposite to the trends observed at room temperature.
Effect of solution redox property on oxide formation.-The observed effects of cover gas, radiation and temperature on the types of oxide formed on CS surfaces during 20-h corrosion are consistent with the thermodynamics of iron oxidation reactions. The electrochemical equilibrium potentials (E eq ) of the redox half-reactions of iron hydroxides/oxides are well established. Their values at pH 7.0 are indicated on a potential scale with respect to that of the saturated calomel electrode (V SCE ) in Fig. 7. The equilibrium potentials of (Fe 0 Fe 2+ (aq) + 2 e − ) and (Fe 2+ Fe 3+ (aq) + e − ) are not indicated in the E eq diagram because they depend on the concentrations of dis-solved ferrous and ferric ions. When the aqueous concentrations of these ions are at their saturation limits their E eq values are the same as those of (Fe 0 + 2 H 2 O Fe(OH) 2 The driving force for an electrochemical oxidation is the difference between the corrosion potential and the oxidation equilibrium potential (E eq ). The corrosion potential of a metal-solution system depends on how oxidizing the solution is; the overpotential does not dictate the overall rate of metal oxidation. The relative positions of the E eq values of different iron redox reactions indicate that in a less oxidizing environment (such as Ar + no Rad) corrosion products would be limited to ferrous ions dissolved in water, green rust (mixed ferrous and ferric hydroxides) and FeO/Fe 3 O 4 . In a more oxidizing environment (e.g., in the presence of O 2 or γ-radiation), the Fe(OH) 2  With γ-radiation present the main oxidants are H 2 O 2 produced from liquid water radiolysis, 15,18,29 and HNO 3 produced from humid air radiolysis. 12,19,20 Gamma-radiation affects metal corrosion primarily via production of oxidizing species in the solution phase. 29,41-43 Exposed to  It is also worthwhile discussing here whether the overall corrosion extent depends purely on the total dose (D R · t) of radiation input, or also on the dose rate (D R ), as there is some confusion around this issue in the radiolytic corrosion literature. Corrosion involves surface oxidation, the rate of which depends on the surface state (the chemical and morphological nature of the metal substrate and any oxide layer present) and the aqueous concentration of the oxidant at the surface. If an oxidant generated from radiolytic processes did not undergo any chemical reactions other than corrosion reactions, the net radiolytic production rate of the oxidant in solution would be linearly proportional to D R . And if the surface state of the metal did not change as corrosion progresses, the overall corrosion damage might depend on the total dose (D R · t), and not on dose rate. In this study, the rate of surface oxidation by a radiolytically produced oxidant is determined by competition kinetics of the surface oxidation with all other reactions of the oxidant. Therefore, in this study, using dose rate rather than total dose is a more accurate approach. Using total dose rather than dose rate is a shortcut that can be used only for very short irradiation times (pulse radiolysis) or when the bulk phase chemical reactions of radiolysis products are not important.
For the corrosion of CS the main oxidant produced by γ-radiolysis of liquid water is H 2 O 2 , 15,18,29 while humid air radiolysis produces HNO 3 12,19,20 that can be absorbed easily in water droplets. Hydrogen peroxide and nitric acid are strong and kinetically facile oxidants. In addition, nitric acid lowers the pH of the water. The continuous radiolytic production of H 2 O 2 and HNO 3 in solution by a steady flux of ionizing radiation will not only push the overall oxidation of Fe 0 to iron oxides with higher oxidation states but will also increase the rates of individual oxidation steps.
Electrochemical study of inverse crevice corrosion.-The different corrosion kinetics observed on crevice and bold surfaces raise the possibility that galvanic coupling between a bold and a crevice electrode may be accelerating water-droplet corrosion of the bold surface, an effect we refer to as 'inverse crevice corrosion'. Corrosion kinetics on these surfaces and the possibility of galvanic coupling were explored using two electrode types representing the different geometries of the crevice and bold surfaces (Fig. 2).
Two sets of experiments were performed. In the first set, a crevice electrode and a bold electrode were galvanically coupled through a zero-resistance ammeter, and the coupling current (I cp ) between the two electrodes was monitored. In the second set, a crevice electrode and a bold electrode were not coupled but allowed to corrode independently for the same durations, 3 h and 48 h. To determine the effect of coupling on corrosion evolution the electrode surfaces corroded while coupled and those corroded independently were examined by SEM and XPS and compared. The electrode tests were only performed in Ar-purged solutions at 21 • C with or without radiation present.
Coupling current.-The coupling currents observed between the crevice and bold electrodes in Ar-purged solutions with or without γradiation are shown in Fig. 8. Two sets of data with different coupling durations (3 h and 48 h) are shown in the figure. The currents plotted here are not normalized to unit surface area due to the different sizes of the two electrodes (3 cm 2 for a crevice electrode and 0.785 cm 2 for a bold electrode). The coupling currents observed with or without γ-radiation are all negative; i.e. the electrons flow from a bold electrode to a crevice electrode. The negative current does not mean that metal oxidation occurs exclusively on a bold electrode while solution reduction occurs exclusively on a crevice electrode, but that the net redox process on the bold electrode is more anodic (i.e. there is faster overall oxidation than reduction) than on the crevice electrode.
The magnitude of the initial coupling current varies from one experiment to another, but it decreases rapidly to a near steady-state value of −1.0 ± 0.2 μA within 30 min in all cases. Gamma-radiation of an Ar-purged solution affects the time to reach steady state but has a negligible effect on the steady-state coupling current that is reached and, if anything, slightly reduces it.
A coupling current of −1.0 μA corresponds to an electron transfer rate per unit area of 3.5 × 10 −12 mol·cm −2 ·s −1 at the crevice surface/solution interface and 1.3 × 10 −11 mol·cm −2 ·s −1 at the bold electrode/solution interface. The latter value corresponds to metal oxidation rate of 0.7 × 10 −11 mol·cm −2 ·s −1 if the metal oxidation involves only the conversion of Fe 0 to Fe 2+ (aq) -the most conservative assumption in terms of the possible rate of Fe 0 loss from the metal phase. The maximum metal dissolution from the bold surface with a surface area of 0.785 cm 2 over 48 h, due to the galvanic coupling, is then 0.9 × 10 −6 mol. The molar mass of iron is 56 g · mol -1 and its density is 7.9 g·cm −3 . Using these values the maximum rate of metal loss from the bold surface with area of 0.785 cm 2 is 0.29 ng·s −1 or 4.7 × 10 −4 nm·s −1 . The maximum total metal loss due to the galvanic coupling over 48 h is then 50 μg in weight or 81 nm in dissolution depth.
The coupling current does not necessarily represent either a purely anodic reaction current on the bold electrode or a purely cathodic reaction current on the crevice electrode. On each electrode both anodic (metal oxidation) and cathodic (solution reduction) reactions occur. The negative coupling current only means that the sum of the anodic and cathodic currents is slightly more positive on the bold electrode while the sum is slightly more negative on the crevice electrode. If the electrodes are not coupled, the anodic and the cathodic reaction currents on each electrode should be the same and the total current would be zero, irrespective of the rate of the oxidation reaction. This would allow the rate of metal oxidation on the crevice electrode to be very different from that on the bold electrode. When the electrodes are coupled, if there is no galvanic coupling between the two electrodes there would be no coupling current in spite of different corrosion rates. The small negative coupling current observed means that the coupling increases the metal oxidation rate slightly on the bold electrode, while it increases the solution reduction rate slightly on the crevice electrode. The coupling current does not represent the overall oxidation rate on the bold electrode or the overall reduction rate on the crevice electrode.
Evolution of surfaces. -Fig. 9 compares the low magnification SEM images of the electrode surfaces corroded while coupled with those corroded independently. Corresponding higher magnification SEM images of these surfaces are presented later. Whether the electrodes are coupled or un-coupled, the morphologies of the surfaces of both crevice and bold electrodes evolve with time, but they evolve differently. The morphologies of both surfaces evolve faster when the electrodes are coupled than un-coupled. Gamma-radiation also affects the morphological evolutions of both surfaces.
The SEM images of corroded bold electrodes (Figs. 9 and 10) show the lamellar morphology of cementite layers on the surfaces of  Figure 10. High magnification SEM images of the bold electrodes whose low magnification SEM images are shown in Fig. 9.  pearlite grains. The iron in the cementite phase is strongly coordinated to carbon and inert to further oxidation. Thus, at early stages of corrosion iron dissolution will occur preferentially from the active α-Fe phases. This oxidative dissolution will leave cementite layers on the surfaces of the pearlite grains, 16 but smooth surfaces on the pure α-Fe grains.

h 3 h h 3 h
In Fig. 11, the SEM images of FIB cut cross sections of the bold electrodes corroded while coupled to the crevice electrodes for 20 h with radiation present are compared with the image of a CS electrode independently corroded for the same duration at the same temperature and with radiation present, but in an aerated solution at pH 6.0. The preferential dissolution of α-Fe at early stages of CS corrosion can be more easily observed at a lower pH and in more oxidizing (aerated and radiation present) environments because of more extensive and prolonged dissolution of ferrous ions at a lower pH. The cross-section image of a CS electrode corroded at pH 6.0 clearly demonstrates that at early stages of corrosion iron dissolution occurs preferentially from the active α-Fe phases. In contrast to this, at pH 7.0 in deaerated solutions, the difference in the dissolution depth between the α-Fe and the cementite sites is much smaller, and there is significant buildup of hydroxide/oxide particles on these surfaces.
The SEM images of the cross sections of the bold electrodes corroded for 48 h with radiation present are shown in Fig. 12. Comparison of Fig. 11 and Fig. 12 reveals that the difference in the dissolution depth between the α-Fe and the cementite sites is greater and the quantity of oxide deposits is also greater on the bold electrodes corroded for longer times (Fig. 12). On these surfaces the metal-oxide interface on the ferrite grains is depressed compared to that on the pearlite grains. The observed topologies indicate that, due to faster oxide buildup, iron dissolution from the α-Fe sites in pearlite is suppressed at a faster rate and hence at an earlier time than dissolution from the ferrite sites. The oxide deposits formed on the bold electrode corroded without coupling are slightly thicker but more porous, while those formed on the coupled electrode are more compact and more uniformly spread across the surface.
The SEM images in Figs. 9 and 10 indicate that iron dissolution is less extensive with radiation present than without radiation. This is attributed to faster surface coverage by oxides driven by the radiolytically produced oxidants. Similarly, for a given radiation environment, the surface coverage is faster with coupling than without coupling (Fig. 12). The faster coverage of the surface leads to growth of a more compact oxide layer as corrosion progresses. Because of the variations in oxide coverage and oxide porosity across the surface the XPS results for these surfaces were not analyzed to obtain the different oxide fractions.
The surfaces of crevice electrodes corroded with or without radiation are all relatively smooth. Nevertheless, small changes due to radiation and coupling were observed. The surface morphology (Figs. 9 Figure 12. SEM micrographs of the cross sections of the ferrite/pearlite interfacial region and the ferrite region on bold electrodes corroded for 48 h while coupled (with coupling) to the crevice electrodes or independent (without coupling) in deaerated water at neutral pH with radiation present. and 13) and the surface composition (metal oxidation states, Fig. 14) of an independently corroded crevice electrode are closer to those observed for a coupled crevice electrode corroded for 48 h than for a coupled crevice electrode corroded for only 3 h. This suggests that without radiation present the metal oxidation has progressed faster on an independently corroded crevice electrode. In addition, on an independently corroded crevice electrode the surface morphology and metal oxidation composition do not change significantly after 3 h. This indicates that there may be rapid metal formation of a protective oxide layer within 3h. On a coupled crevice electrode, the formation of a protective oxide layer appears to be slower and corrosion continues to progress over a longer time period.
The effect of coupling on crevice electrode corrosion with radiation present is similar to that observed without radiation. The low magnification SEM image of a coupled crevice electrode corroded for 3 h shows dark circular spots that correspond to pits generated from dissolution of inclusions. After 48 h, the surface is covered by a uniform, albeit thin, layer of oxide, and the metal grain structures underneath the oxide layer are clearly visible. Crevice electrodes corroded independently do not show these features indicating that there is less dissolution and more oxide formation compared to coupled electrodes.
Interestingly  Figure 13. High magnification SEM images of the crevice electrodes whose low magnification SEM images are shown in Fig. 9. Ar-purged solutions (with or without radiation) are nearly the same as those observed for the coupons corroded using droplets under the same conditions, although the corresponding bold surfaces (Fig. 4 versus Fig. 9) show very different corrosion extents. These comparisons suggest that the most critical parameter controlling the rate of corrosion is the ratio of water volume to surface area. A small occluded water volume can be quickly saturated with dissolved metal ions. The presence of these ions, when they approach the saturation limit, can suppress further dissolution, while promoting oxide formation. 45 The faster formation of a uniform protective oxide layer can in turn suppress overall metal oxidation and the net result is a cleaner surface with a thinner oxide layer within the crevice than on a boldly exposed surface.
The presence of a protective oxide layer may suppress metal oxidation but it can still support water reduction. Hence, if the crevice surface is coupled with a boldly exposed surface that could corrode easily the crevice surface can provide more cathodic sites and accelerate the metal oxidation on the boldly exposed surface.

Proposed Mechanism for Evolution of CS Corrosion
The experimental results show that different types of oxides are formed and grow in different solution environments. The types of oxides observed are consistent with those expected based on the thermodynamics of individual metal-solution redox reactions. However, the composition and morphology of the oxides evolve with time, and the rate of oxide evolution depends on the solution environment, which includes the ratio of water volume to surface area, pH and temperature as well as the type and concentration of oxidants present in solution. The effect of a particular solution parameter on corrosion evolution varies depending on the state of other parameters. As a result, solution parameters can affect differently the individual elementary processes involved in the overall corrosion process and this can lead to the system following different corrosion pathways.
To determine the integrated effect of different solution parameters on the overall corrosion rate and its evolution, the overall corrosion process must be deconvoluted into the key elementary kinetic processes and the separate effects of individual solution parameters on the rate of each elementary process must be determined. The results from this study suggest that the key elementary processes are a series of iron oxidation steps, with each oxidation step followed by dissolution and oxide formation, as schematically shown in Fig. 15. This kinetic scheme is based on the mass and charge balance (MCB) model that has successfully simulated the observed corrosion behavior of passive alloys. 46,47 The corrosion kinetic scheme can also explain many seemingly contradictory observations reported in the literature, some of which are discussed below. Firstly, however, the corrosion kinetic scheme (Fig. 15) and the effect of solution parameters on the individual kinetic steps will be described.
Carbon steel corrosion pathways.-Corrosion involves metal oxidation coupled with the reduction of solution species on the metal surface. This is an electrochemical process, requiring interfacial electron transfer between metal and solution species, e.g., However, unlike other electrochemical processes on inert surfaces, for corrosion to proceed the electron transfer must be accompanied by metal cation transfer from the metal to the solution phase due to  Figure 15. Schematic of CS corrosion reaction pathways. The red arrows represent interfacial charge transfer steps at rates of R OX# , the blue arrows represent metal cation dissolution steps at rates of R Diss# and the green arrows represent metal hydroxide/oxide formation steps at rates of R MO# . The large black arrow at the bottom of the schematic indicates that corrosion progresses further along the corrosion pathway and faster in a more oxidizing solution environment. charge conservation. The metal cation transfer requires lattice-bond breaking followed by solvation (or hydration) of the cation: where Fe II (hyd) represents the hydrated ferrous ion (Fe II ·nH 2 O) on the metal surface, and not yet diffused into the bulk solution phase. The overall interfacial charge transfer process that produces Fe II (hyd) in deaerated water is then: Hereafter, Fe II (hyd) will be simply referred to as Fe II . In the presence of another oxidant, the metal oxidation coupled with the reduction of the oxidant should be included. For example, in an aerated solution the overall charge transfer rate is the sum of the rates of Reactions 5 and 6: In Fig. 15, the overall charge transfer process that produces Fe II (Fe → Fe II ) is schematically represented by a red arrow with a rate of R OX1 . The overall rate of Reaction 5 is controlled by the slowest of the two charge transfer processes (Reactions 2 and 4). The type and concentration of oxidant present in solution (referred to as the solution redox environment) affects the rate of interfacial electron transfer strongly but does not directly affect the solvation of a metal cation. Temperature (in the studied range of 21 to 80 • C) and pH have minor effects on the electron transfer rate, but significant effects on surface hydration (Reaction 4). The ratio of solution volume to surface area should not affect either of the interfacial charge transfer processes.
The hydrated ferrous species can now diffuse from the surface into the bulk solution phase. As ferrous ions are hydrated and diffuse into solution, they also undergo hydrolysis equilibrium reactions: At high pHs (> 12) the hydrolysis equilibrium can shift far to the right to produce Fe(OH) 3 − in addition to the above species. The hydrolysis equilibria are acid-base equilibria of the ferrous hydroxide salt, and the equilibria are established very fast compared to aqueous diffusion of the ferrous ions. Thus, the dissolved ferrous ion encompasses all of the solvated ferrous species involved in the equilibria. The dissolved ferrous species collectively will be represented by Fe II (aq) hereafter: The relative concentrations of the different solvated ferrous species depend on pH and temperature.
It has been suggested by Bockris et al., that the first step of iron dissolution from Fe electrode is the formation of Fe(OH) (ad) followed by the formation of Fe(OH) + which then dissolves into solution as Fe 2+ . 48 Because of the fast hydrolysis equilibria, it is impossible to determine experimentally the exact kinetic pathway for the oxidation of Fe 0 to dissolved ferrous species. However, the exact pathway to reach the equilibria has negligible influence on the subsequent corrosion pathway that is followed. The total amount of dissolved ferrous iron and the relative concentrations of ferrous species can have a significant effect on the subsequent corrosion processes.
Initially, the concentration of Fe II near the surface will be zero and hence the oxidation of Fe 0 to Fe II coupled with solution reduction proceeds immediately irrespective of solution conditions. The predominant corrosion pathway following the metal oxidation of Fe 0 to Fe II is the diffusion of Fe II into the bulk solution. However, as corrosion progresses, [Fe II (aq) ] will increase and approach its saturation limit, and at that point the predominant corrosion pathway switches from dissolution to primarily the formation of Fe(OH) 2(s) . The time to reach this kinetic stage depends on the solution environmental parameters.
Note that an Fe II (aq) concentration gradient exists in the diffusion layer at the solid/solution interface, and hence the rate of formation of Fe(OH) 2(s) also varies with distance from the metal surface. Hydroxide formation near the surface can be substantial under stagnant (non-turbulent) conditions even if the bulk solution is not saturated. Experimentally measurable quantities for corrosion, such as corrosion current, metal loss, dissolved metal concentration, and oxide thickness, are bulk phase properties. Thus, although the transition from dissolution to metal oxide formation at a specific point in the diffusion layer may be abrupt, the average changes in the bulk properties are more gradual.
Irrespective of the exact rates of aqueous diffusion and hydroxide formation, the Fe II formed on the metal surface by Reaction 5 will end up either in the solution as dissolved ferrous ions (Fe II (aq) ) or in the solid hydroxide phase as Fe(OH) 2(s) . In Fig. 15, these two corrosion paths are schematically represented using a blue arrow for dissolution at an overall rate of R Diss1 and a green arrow for solid hydroxide formation at an overall rate of R MO1 . The rates, R Diss1 and R MO1 , are not independent of R OX1 at any given time during corrosion because of mass conservation; the total amount of oxidized metal produced by coupling with solution reduction must be the same as the sum of the amounts of metal in the solution and the hydroxide/oxide phase: The relative rates of R Diss1 and R MO1 are very sensitive functions of pH and temperature because of their influence on the hydrolysis and phase equilibria of ferrous ions. The rates also change with time as corrosion progresses.
Under acidic and high flow conditions, dissolution is the predominant corrosion path and the overall corrosion reaction is: [10] In this case, the overall corrosion rate equals the dissolution rate (R Diss1 ) and these rates are the same as the interfacial charge transfer rate, R OX1 . A more oxidizing solution environment can increase the interfacial electron transfer rate. However, because electron transfer must accompany metal cation transfer, the overall metal oxidation rate is largely controlled by the slowest of the two processes, the metal cation transfer (Reaction 4), and the overall rate of metal oxidation depends strongly on pH and temperature.
Under most conditions corrosion leads to both dissolution (overall Reaction 10) and metal hydroxide/oxide formation (overall Reaction 11).
Fe 0 + 2H 2 O →→ Fe(OH) 2(s) + 2H 2 [11] In this case the overall corrosion rate is the sum of the rates of dissolution (R Diss1 ) and solid hydroxide formation (R OX1 ). As discussed above, the rates R Diss1 and R MO1 are very sensitive functions of pH and temperature, and their rates also change with time as corrosion progresses and the solution becomes saturated with Fe II (aq) . For a given pH and temperature, the interfacial charge transfer rate (R OX1 ) is independent of the ratio of the solution volume to surface area (V sol /A m|sol ). However, the rate of increase in [Fe II (aq) ], and hence the rate of approach to the saturation limit, is very sensitive to V sol /A m|sol . The [Fe II (aq) ] increases faster and approaches its saturation limit earlier with a smaller V sol /A m|sol . This forces the overall corrosion pathway to switch to the deposition and the growth of Fe(OH) 2(s) faster. As Fe(OH) 2(s) is growing, some of the Fe II present on the surface of the Fe(OH) 2(s) particles can further oxidize to Fe III , coupled with solution reduction reactions. The ferric ion produced from Fe(OH) 2(s) is also subject to hydration. The overall process is, in deaerated water: 2Fe(OH) 2 + 2H 2 O → 2Fe III (hyd) + 6OH − + H 2 [12] and in aerated water: The interfacial charge transfer process involving partial oxidation of Fe(OH) 2 is schematically shown as (Fe(OH) 2 → Fe II /Fe III ) in Fig.  15 with a red arrow and with an overall rate of R OX2 . R OX1 depends simply on the solution redox environment, i.e., the oxidant type and concentration. However, R OX2 also depends on the rate of production of Fe(OH) 2 .
The ferrous and ferric ions present on the surface of Fe(OH) 2(s) can also undergo hydrolysis reactions. These species either dissolve into solution (Fe II (aq) and Fe III (aq) ) or precipitate as mixed hydroxides (Fe II (OH) 2 ·nFe III (OH) 3  The overall reactions of ferric iron dissolution and the mixed oxide formation that follow the interfacial charge transfer process with rate R OX2 are then: Hereafter, the phase designations of the iron hydroxides/oxides are omitted.
Reactions 15 and 16 are schematically represented using two corrosion pathways in Fig. 15: dissolution of the mixed hydroxide at an overall rate of R Diss2 and magnetite particle growth at an overall rate of R MO2 . These are competing processes whose rates must total the rate of the preceding step: The relative rates of R Diss2 and R MO2 are also very sensitive functions of pH and temperature due to the hydrolysis equilibria. The growth of a metal oxide into a distinct crystal phase from dissolved ions, such as the growth of magnetite particles during corrosion, is very sensitive to temperature because the lattice bond formation is a high activation energy process. At temperatures above 60 • C the transformation of Fe(OH) 2 to Fe 3 O 4 via the Schikorr reaction, 49 can also occur at an accelerated rate. Hence, temperature can have a more significant impact on R Diss2 and R MO2 than on R Diss1 and R MO1 .
There has been some debate as to whether Fe 0 oxidation in pure anoxic water can progress beyond the formation of Fe(OH) 2 at room temperature. 50,51 The formation of Fe 3 O 4 in pure water is thermodynamically possible; the electrochemical equilibrium potential of the metal oxidation half reaction of Fe(OH) 2 to Fe 3 O 4 lies below that of water (or proton via H 2 O H + + OH − ) reduction to H 2 . However, in the absence of other oxidants such as O 2 the overall oxidation rate of Fe 0 to Fe II (R OX1 ) would be very slow and saturation of a large water volume with Fe II (aq) would take a long time. In a flowing solution, rapid saturation near the surface would be also prevented. Consequently, the precipitation and growth of Fe(OH) 2(s) on the metal surface would be negligible. The oxidation of Fe II (aq) to Fe III (aq) in the solution phase requires a much stronger oxidant than water. Without the formation of Fe(OH) 2(s) on the surface, further formation of Fe 3 O 4 on CS, while possible, would be very slow at room temperature. However, Fe 3 O 4 formation is readily observed at a temperature higher than 60 • C where the Schikorr reaction can occur. 52 In the presence of a stronger oxidant than water (such as O 2 or H 2 O 2 ), Fe(OH) 2 and Fe 3 O 4 can more readily oxidize to ferric compounds (Fe III ). In Fig. 15 the charge transfer steps involving Fe II to Fe III and Fe II /Fe III to Fe III (coupled with solution reduction) are represented by red arrows with overall rates R OX3 and R OX4 , respectively. The oxidation to Fe III is followed by hydration, hydrolysis and precipitation of the ferric ion, resulting in either dissolution of the ferric ion into solution at a rate of R Diss3 or R Diss4 , or precipitation as hydroxides which then grow into an oxyhydroxide or oxide of a specific phase such as γ-FeOOH (lepidocrocite) or γ-Fe 2 O 3 (maghemite) at a rate of R MO3 or R MO4 .
The proposed corrosion mechanism includes iron oxidation that occurs in sequence to higher oxidation states progressively (Fe 0 to Fe II , Fe II to Fe II /Fe III , Fe II and Fe II /Fe III to Fe III ). Each oxidation leads to dissolution and hydroxide/oxide formation of the oxidized metal. Such progressive formation and growth of different oxides has been also proposed by Misawa et al., 53,54 who suggested that lepidocrocite (γ-FeOOH) is formed via oxidation of Fe II (aq) and subsequent precipitation. It may be possible that dissolved ferrous ions can be oxidized in the solution phase. However, solution reactions typically have a higher activation energy than surface reactions and require a more powerful oxidant. The surface oxidation of the ferrous ion should occur at a faster rate than the solution oxidation. Experimentally these processes cannot be differentiated. Our proposed mechanism is also consistent with the observation made by other groups that Fe 3 O 4 is usually observed in the inner layer of a rust whereas mainly Fe III oxide/oxyhydroxide is seen in the outer layer. 55,56 The more commonly observed Fe III oxides/oxyhydroxides formed during CS corrosion are γ-Fe 2 O 3 and γ-FeOOH. These ferric species can slowly rearrange their lattice structure and convert to a more thermodynamically stable oxide/hydroxide. Conversions between different ferric oxides/hydroxides have been observed during synthesis of ferric oxyhydroxide from dissolved ferric ions; γ-FeOOH is formed at early stages of particle formation and is then gradually converted into the more stable α-FeOOH. 53,57 The formation of the most stable ferric oxide, α-Fe 2 O 3 (hematite), is rarely observed during aqueous corrosion at room temperature. In this study, we observed α-Fe 2 O 3 formation only at 80 • C under air (Table I). This is due to the fact that high temperature accelerates the dehydration of FeOOH. 37 Some of the individual reactions involved in corrosion occur in sequence while others occur in parallel, as schematically shown in Fig.  15. For sequential reactions, the rate of the overall reaction is controlled by the slowest step in the sequence. For parallel reactions, more than one product is formed and the rate of the overall process is the sum of the rates of reactions in parallel. For parallel reactions, the yields of their products are proportional to their relative rates. 42,46,47,58,59 For CS corrosion the oxidation of iron to progressively higher oxidation state cations (Fe II to Fe II /Fe III and to Fe III ) occurs in sequence, while each oxidized iron species can follow two parallel reaction pathways, dissolution into solution or solid oxide formation. Thus, the rates of dissolution and oxide formation of each metal cation (R Diss# and R MO# , respectively) formed from metal oxidation are not independent of each other and are related to the oxidation rate that produces the metal cation (R OX# ): [18] What complicates the CS corrosion kinetics further is the fact that metal hydroxides/oxides formed on the metal surface can have a profound impact on subsequent iron oxidation reactions that lead to the production of those hydroxides/oxides. The more oxidizing the solution environment is, the faster the initial rates of individual oxidation reactions. But such fast rates can increase the rate of formation of a protective (not necessarily passive for electron transfer but passive for cation transfer) oxide layer, leading to earlier suppression of further corrosion. Alternatively, it can induce a rapid change in local water chemistry, leading to accelerated corrosion. The type of oxide that grows and the rate of its growth are extremely important parameters in predicting long-term corrosion behavior. The corrosion path that is followed will depend on not only the oxidizing potential of the solution but also on the other parameters that affect the competing kinetics of oxide formation and dissolution of metal cations. Quantitative modeling of the CS corrosion is beyond the scope of this paper and will be published elsewhere.
Inverse crevice corrosion.-Crevice corrosion is a form of galvanic corrosion and initiates because the local chemistry inside the crevice develops differently from that of the bulk solution. 60,61 Our results show that galvanic coupling between crevice and bold surfaces may occur on CS, but the result is that corrosion of the bold surface is accelerated, rather than crevice corrosion, a process we refer to as inverse crevice corrosion. Our work also indicates that the main factor driving this behavior is the local ratio of solution volume to surface area that determines the local metal cation dissolution capacity.
For corrosion of any metal, if there is no clear separation of anodic and cathodic sites the rate of proton consumption should be related to the rate of increase in the dissolved metal cation concentration, irrespective of type of oxidant or other chemicals present. Due to mass and charge conservation during corrosion: two H + ions are required to produce one Fe 2+ ; one proton to produce Fe(OH) + , etc. Therefore, if corrosion produces mainly dissolved ferrous ions in the form of Fe 2+ or Fe(OH) + , pH would increase as corrosion progresses. On the other hand, if corrosion produces mainly neutral metal hydroxide or oxide such as Fe(OH) 2 and Fe 3 O 4 the pH of the solution would not change. At a very basic pH (> 12), the predominant form of dissolved ferrous ion is Fe(OH) 3 − and in this case the overall oxidation of Fe 0 leading to metal dissolution would consume OH − , decreasing pH. Thus, if there is no clear separation of anodic and cathodic sites, a pH change occurs during the period when corrosion leads primarily to metal dissolution. At pHs lower than 12 iron dissolution leads to an increase, not a decrease, in pH. Subsequent formation and growth of additional neutral Fe hydroxide or oxide does not change the pH of the solution any further.
The local pH of a solution can be lowered if the anodic and cathodic sites become separated. In normal crevice corrosion this happens on passive alloys such as stainless steel. 62 Once O 2 is depleted in the crevice solution, metal oxidation occurs primarily on the crevice surface while solution reduction occurs primarily on the bold surface. This process has anodic and cathodic sites that are separated but connected galvanically: The galvanically coupled reactions cannot propagate without migration of cations out of the crevice and anions into the crevice due to charge conservation.
There are two additional processes that can induce a pH change in the crevice solution. The migration of OH − into the crevice (or H + out of the crevice) would increase the pH inside the crevice, while the hydrolysis of M 2+ (aq) to form M(OH) 2 (Reaction 21) would decrease the pH inside the crevice. Most crevice corrosion studies are performed in NaCl solutions where [Cl − ] and [Na + ] are much higher than [OH − ] and [H + ]. In these solutions the main ions that migrate into and out of the crevice to maintain charge balance would be Cl − and Na + rather than OH − and H + . Therefore, a pH change in these solutions due to OH − or H + migration is negligible. Migration of Cl − into the crevice allows the galvanically coupled reactions to propagate and metal hydrolysis decreases the pH (acidification). 61,62 The presence of Cl − also allows formation of complexes of ferrous and ferric ions together with OH − (such as Fe x+y (OH) 2x Cl 2y , green rust), 63 thereby accelerating local acidification.
In our electrochemical experiments, none of the conditions required for the initiation and propagation of crevice corrosion were present. As discussed in Carbon steel corrosion pathway section water or proton is an effective oxidant for the oxidation of Fe 0 to Fe II and Fe II /Fe III oxides/hydroxides, and cannot be depleted. The pH of the solution was initially neutral and anions such as Cl − were absent. Therefore, dissolution of Fe would lead to an increase in pH. The borate buffer concentration in the electrochemical cell was 10 −2 M. The pH change inside or outside the crevice should be negligible unless the dissolved Fe 2+ concentration reaches a level comparable to the concentration of the buffer. The solubility limit of Fe(OH) 2 is ∼10 −3 M at pH 7.0 and lower at a higher pH. 64 It is more likely that the saturation level of Fe 2+ would be reached at a concentration below that which would affect the pH of the crevice solution. If the buffer was not effective, the pH in the crevice solution would have increased. This would promote the hydrolysis reactions and the precipitation of Fe(OH) 2 would have occurred earlier. Thus, a change in pH inside the crevice is ruled out as a contributing factor for the galvanic current seen in our experiment.
In our study, the galvanic coupling between the oxidation of bold and crevice surfaces arises from the different rates of evolution of metal oxidation on the two surfaces. The metal oxidation fluxes from the crevice and bold surfaces are initially the same. However, the rate of increase in [Fe 2+ (aq) ] is initially faster inside than outside the crevice due to the smaller water volume to surface area ratio. Therefore, the precipitation of Fe(OH) 2 occurs much earlier in the crevice solution than in the bulk solution. Unlike stainless steel, a passive film is absent on CS, and hence metal oxidation on the bold surface continues to result in dissolution of ferrous ions.
On the crevice surface the earlier precipitation of Fe(OH) 2 accelerates the lateral growth of a gelatinous hydroxide layer, which then converts to a uniform layer of Fe 3 O 4 . The earlier formation of this uniform protective oxide film slows down subsequent metal oxidation on the crevice electrode. However, magnetite is a near conductor (with a bandgap of 0.1 eV) 37 and hence the crevice surface can still facilitate water reduction if the water reduction can be coupled with metal oxidation on the bold surface. Therefore, when the crevice surface is connected to the bold surface, the CS crevice surface does not act as an anode, which is expected in normal crevice corrosion, but as a cathode.

Conclusions
Crevice corrosion of carbon steel was investigated in different exposure environments, in aerated and deaerated solutions, at 21 and 80 • C, and with and without γ-radiation present. The extent of corrosion on the bold surface of a carbon steel crevice coupon was more severe at 80 • C than at 21 • C, in aerated rather than deaerated solutions, and with γ-radiation present. The crevice surface showed minimal corrosion under all studied conditions, exhibiting inverse crevice corrosion behavior. The coupling current measured between a crevice and a bold electrode in an electrochemical cell was also negative, i.e., the opposite direction to that seen in normal crevice corrosion. These results indicate that the metal oxidation rate is increased on the bold surface while the solution reduction rate is increased on the crevice surface when the bold and crevice surfaces are galvanically coupled, with respect to those rates when the surfaces are not coupled but corrode independently in the same solution environment.
The inverse crevice corrosion behavior is attributed to the significantly lower metal cation dissolution capacity of the small occluded water volume in the crevice, compared to that of the bulk water volume over the bold surface. The reduction in dissolution capacity results in the faster and earlier formation of a protective oxide layer. Corrosion of the bold and crevice surfaces evolve at different rates, and this can lead to galvanically accelerated corrosion of the bold surface and not the crevice surface.
A CS corrosion mechanism that can explain the different corrosion observed on the bold and crevice surfaces, and the effects of different exposure environments was proposed. Carbon steel corrosion involves many oxidation steps that lead to the formation and growth of different oxides as well as metal dissolution. The type and thickness of the oxide that is formed can influence the subsequent oxidation processes, and the type of the oxide that is formed and its growth rate depend on the ratio of water volume to surface area as well as the solution chemical environment.
The results indicate that accelerated crevice corrosion is not anticipated to occur for a welded carbon steel container under long-term nuclear waste storage conditions.