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. 2023 Feb 15;8(8):7395–7406. doi: 10.1021/acsomega.2c05615

Sulfide (H2S) Corrosion Modeling of Cr-Doped Iron (Fe) Using a Molecular Modeling Approach

Mohammad Asif †, Faisal Khan ‡,*, Kelly Hawboldt †, Shams Anwar †
PMCID: PMC9979321  PMID: 36872987

Abstract

graphic file with name ao2c05615_0009.jpg

This work presents the use of density functional theory to study the adsorption/dissociation mechanism of the H2S molecule at the Cr-doped iron (Fe(100)) surface. It is observed that H2S is weakly adsorbed on Cr-doped Fe; however, the dissociated products are strongly chemisorbed. The most feasible path for disassociation of HS is favorable at Fe compared to Cr-doped Fe. This study also shows that H2S dissociation is a kinetically facile process, and the hydrogen diffusion follows the tortuous path. This study helps better understand the sulfide corrosion mechanism and its impact, which would help design effective corrosion prevention coatings.

1. Introduction

Steel containing Cr, an iron alloy produced from iron, is widely used to transport crude oil and gas due to its ductility, excellent stress absorbing abilities, and cost-effectiveness. However, iron loses its mechanical properties in acidic environments1−3 as the iron crystal acts as an electron conductor resulting in corrosion. In the oil and gas industry, corrosion is typically found in pipelines and the process equipment.4 Pipelines are crucial for long-distance transportation of crude oil and natural gas at a low cost and are capable of handling large volumes.5

The consequences of corrosion include increased maintenance and operating costs, breakdowns, and failures.6 In 2015, corrosion losses at the global level amounted to $US 2.5 trillion.7 Corrosion can take many forms including biocorrosion where microorganisms present at the metal surface combined with environmental conditions impact the corrosion rate.8 An estimated 20% of the annual losses is attributed to microbiologically influenced corrosion.9,10

The electrochemical reactions associated with biocorrosion occur in the biofilm11 in which microorganisms stick to the surface. The possible reactions in the biofilm at the metal surface include electron transfer between species such as H2S, S2–, Fe2+, FeS, SO42–, H2O, CO2, and Cl–. Hydrogen sulfide (H2S), carbon dioxide (CO2), and chloride ions (Cl–) are highly corrosive and have the potential to rapidly degrade petroleum equipment in humid environments, seriously compromising the safety and reliability of these systems.12 H2S is generated via a number of mechanisms; however, sulfate-reducing bacteria are the primary source in seawater-injected oil and gas fields and sewage systems.13 H2S is capable of widespread corrosion, local corrosion, and pitting corrosion of many metals.14,15 Shoesmith et al.16 studied the electrochemical behavior of iron in alkaline sulfide solutions.

Natural protection against corrosion can be achieved by either alloying the metal or the formation of a metal oxide layer on the surface. The Fe2O3 and Fe3O4 layers provide enough protection in a mild corrosive environment (<500 °C). If the temperature rises or the environment becomes more corrosive, other steel grades may be employed or another coating was applied.17 Several different oxide layers, composed of Cr2O3, Ni2O3, and Mn3O4, provide corrosion resistance to the steel.18,19 An oxide layer is formed when sulfide is not present as the presence of sulfur inhibits oxide growth. With sufficient anodic potential, the oxide layer II is attacked, producing ferric sulfide because of a breakdown in passivity. By oxidizing the sulfide ion, a deposit of elemental sulfur is formed on the electrodes. Levy and Yong-Fa20 reported that the most significant surface degradation mechanism was formed by the erosion of oxide scale on a steel surface. Analyzing the adsorption phenomenon of corrosion products (HS, S, hydrogen) can give the means to explore the subsequent reactions occurring in the presence of H2S. Das et al.21 studied anisotropic structure of H2S with the help of microwave spectroscopy. They found that (H2S) will also form a hydrogen-bonded system like water.

High-chromium alloys provide better protection than simple iron steel at higher temperatures and in more aggressive conditions. These include ferrite steel alloys, austenitic steel alloys, and ferritic high alloy steels. In the case of steels with chromium, there was a significant difference between the scale loss mechanism, for instance steels with Cr between 5 and 9 wt % Cr lose metal at a much lower rate than steels below 5 wt % Cr. However, the morphology of the ferritic steel scales is a more important factor than the composition in the rate of metal loss. Cr helps to decrease scale formation and removal, as well as metal loss through scale formation and removal when it is present in the austenitic steel scales. There is a correlation between the drop-in corrosion rate and abnormal surface segregation of Cr resulting from the complex interaction between atoms in bulk and surfaces.22−25 The corrosion behavior of steel containing Cr is significant for understanding the passivation effect in the presence of strong oxidizing elements/compounds.

The mechanism of reactions that occurs at Fe/S/H2S interfaces is central to sulfide corrosion processes in an acidic environment.26 The environment is acidified by H2S, and steel pipes are pitted. The corrosion contributing reactions in H2S systems are27

H2S reduction:

1.

HS– dissolution:

1.

FeS formation by precipitation:

1.

Recently due to advancement in computational power, density functional theory (DFT) has been used as a tool to estimate reaction parameters such as activation energy barrier, heat of reaction, and structural parameters.28

In an atomistic level study,29 the electronics and structural properties of oxygen adsorptions on Fe(100) and Fe(110) surfaces were investigated. Studies from Błoński et al.,30 Tan et al.,31 and Ossowski and Kiejna32 investigated the effect of oxygen coverage (passivation effect) on electronic and magnetic properties for low-index surfaces such as Fe(100) and Fe(110). Adsorption and dissociation mechanisms of H2S at FeS, Rh(100), and Fe(110)26,33,34 are well studied from the DFT.

The corrosion of iron doped with Cr has attracted considerable attention in scientific literature35−38 in part as it is an economically important material. There is a lack of atomic-level knowledge of how the sulfide layer forms on Fe–Cr surfaces and the process of oxidation. Computational studies have primarily investigated cases of pure Cr and Fe in the initial oxidation process. Yuan et al.39 investigated the effect of segregating alloying elements on oxygen adsorption on Fe(100) surfaces employing DFT with generalized gradient approximation (GGA).

In this paper, adsorption/dissociation of H2S on Cr-doped Fe(100) is performed using DFT. The findings (adsorption characteristic, reaction parameters, diffusion of hydrogen) of Cr-doped Fe(100) surfaces are compared with those of the pure iron. The adsorption occurs at the sites namely top (T), bridge (B), and hollow (H) shown in Figure 1. There are a number of reaction paths; however, in this paper, dissociation from the most stable sites T at Fe(100) and B at Cr-doped Fe(100) is considered. A number of diffusional paths for hydrogen on the surface and subsurface (bulk) between a wide range of sites are estimated to understand the embrittlement problems in alloys. These microscale findings will help to protect iron/alloy from corrosion in real operational condition.

Figure 1.

Figure 1

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(a) Four kinds of sites at the surface; T (top), B (bridge), H (hollow), and TFH (threefold hollow) are shown with respect to locations, (b) free H2S molecule, and (c) side view of free slab with d12 is the distance between layers 1 and 2; d23 is the distance between layers 2 and 3. Second-layer Fe atoms are red in color.Inline graphic

2. Molecular Model Development

This study has adopted the DFT approach with the generalized gradient approximation with the Perdew–Burke–Ernzerhof (GGA-PBE)40 function using the DMol341 module in BIOVIA materials studio 2017 software. Dmol3 includes either a Fermi occupation scheme (electronic occupation scheme suitable for covalent bonded system) or a thermal occupation procedure (to compute fractional occupation of orbitals suitable for metallic systems), which is sometimes necessary for converging electronic density.42

The four-layer Fe(100) surfaces with a 3 × 3 supercell with 36 atoms were used for the first-principle calculations. The four-layer model is well tested and used widely for quantum calculations.43,44 The vacuum for the slab was set to 14 Å in the direction normal to the sheet for sufficient space between two cleaved surfaces, such that they did not interact with each other.

A double numerical plus polarization (DNP) was used as a basis set (representation of electronic wave function), which employs a d-type polarization function to heavier atoms (Fe, Cr) and p-type polarization functions to hydrogen atoms; this gives better accuracy than Gaussian 6-31G(d,p).45 The DNP corresponding to the double zeta quality basis set has comparable or less basis set superposition error (BSSE) than Gaussian 6-31G(d,p).46 To ensure the accuracy of the model, we performed a convergence test for the total ground-state energy of the Fe(100) with varying k point using different basis sets. The total ground-state energy is shown in Appendix Tables A3 and A4. For the selection of k point from Table A3, we chose to mesh size 3 × 3 × 1 as a balanced option (between computational cost and precision of results) given 2 × 2 × 1 and 4 × 4 × 1 have similar energy levels.

Table A3. Ground-State Energy of Fe(100) for the Different k Points.

k point basis set total energy (Ha)
2 × 2 × 1 DNP 45496.726
3 × 3 × 1 DNP 45496.727
4 × 4 × 1 DNP 45496.727
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Table A4. Ground-State Energy of Fe(100) for the Different Basis Sets.

basis set total energy (Ha) DFT-D correction (Ha)
DNP 45496.727 0.318
MIN 45492.937 0.389
DND 45496.723 0.317
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All the atoms were allowed to relax until convergence in cut off energy, force, and displacement reached to 1 × 10–5 Ha (2.72 × 10–4 eV),0.004 Ha/Å (0.1088 eV/Å) and 0.005 Å, respectively. In all calculations, Grimme density function dispersion correction (DFT-D) is applied.47

The slab is optimized using the spacing of 16 × 16 × 16 for bulk iron and 3 × 3 × 1 for surface (with adsorbate ) of Monkhorst–Pack for k-point Brillouin zone sampling.48 The calculated lattice constant for BCC iron (took from software directory) was a = b = c = 2.860 Å after optimization in excellent agreement to the experimental value of 2.866 Å.49

The adsorption energy of reactants/products is calculated by the following expression50

2.

where ER/P(slab) is the energy of reactants/products in binding state, Eslab is the energy of the slab, and ER/P is the energy of the reactants/product in free state.

The relaxation between layers is calculated by the following:51

2.

where Δij is the relaxation between i and j layers of the Fe(100) slab, dij(ad) the distance between i and j layers of the Fe(100) slab when species is adsorbed (can be seen in Figure 1c), and dij(bulk) is the distance between i and j layers of an Fe(100) slab without any adsorption. Positive/negative values of relaxation between first and second layers (Δ12) indicate that the surface moves outward/inward (compared with bulk) after geometric optimization.

The activation energy barriers (Ea) and the reaction energy (ΔE) for dissociation of H2S → HS + H → S+ 2H are defined as follows:52

2.
2.

where ETS is the energy of the transition state, EIS is the energy of the initial state, and EFS is the energy of the final state.

The transition state (TS) for all reaction/diffusion pathways is performed by the nudge elastic band (NEB) method. This method works on optimizing several images along the reaction paths. The run is repeated until the stationary point is reached.53 To confirm the minimum energy pathway, we used the TS confirmation tool available in the DMol3.

3. Results and Discussion

3.1. Adsorption of Reactants and Products

Hu et al.57 studied the adsorption behavior of H2O, H+, Cl–, and OH– on the clean and Cr-doped Fe(110). In their work, only one Fe atom is replaced with Cr. In this work, three Fe atoms are replaced with Cr (7.8 wt %) at Fe(100) as the corrosion rate in alloy steel drops rapidly as Cr content approaches 8%.58 The calculation of Cr wt % is shown in Appendix. The Fe atom can be replaced with the Cr atom via (i) random replacement, (ii) replacing the second layer iron atoms, (iii) replacing the combination of the first layer and second layer iron atoms, and (iv) replacing only the top layer atoms. For this work, replacement scheme (iii), in which Cr atoms are accumulated, is chosen based on minimum ground state energy. A study done by Bradley59 also shows, at low temperature atoms of similar kind stay together; however, at higher temperature this trend disappears.

The most stable adsorption state of the individual component at Fe(100) and Cr-doped Fe(100) surfaces must be established before the disassociation can be modeled. In this work, many adsorption locations/orientation of components were analyzed, such as (i) adsorption over the Fe or Cr (ii) hydrogen atom orientation (flat, upward, or downward) but only a few sites led to the feasible optimization shown in Figures 2 and 3.

Figure 2.

Figure 2

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Top view and side view of the optimized geometries for the stable adsorption for (a) H2S (b) HS (c) S, and (d) hydrogen at Fe(100). T is the top site; B is the bridge site, and H is the hollow site. The H in bracket corresponding to hydrogen atom orientation such as B (H up) is the bridge site with hydrogen atom facing upward direction. The bond length for H–S, Fe–S, and Fe–H are indicated with alphabets a, b, and c. The values are shown in Appendix Table A5. Second-layer Fe atoms are red in color.Inline graphic

Figure 3.

Figure 3

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Top view and side view for optimized geometries for stable adsorption for (a) H2S (b) HS (c) S, and (d) hydrogen for Cr-doped Fe(100). T is the top site; B is the bridge site, and H is the hollow site. The H in bracket corresponds to hydrogen atom orientation such as B (H up) is the bridge site with hydrogen atom facing upward direction. The bond length for H–S, Fe–S, and Fe–H are indicated with alphabets a, b, and c. The values are shown in Appendix Table A6. Second-layer Fe atoms are red in color.Inline graphic

The adsorption energy for Fe(100) and Cr-doped Fe(100) is shown in Tables 1 and 2. The microadsorption mechanism can be seen by calculating the bond length, distance from the surface, and angle between hydrogen atoms at these surfaces.

Table 1. Adsorption Energy and Geometric Parameters for the Adsorption of Reactants and Products at the Fe(100)a.

species adsorption site d (surf-S)/Å d (S–H)/Å ØHSH/° –Ead/eV Δ12/% Δ23/%
H2S T (H flat) 2.310 (2.422)c 1.437, 1.455 (1.431)c 89.222 (89.167)c 0.999 (0.763)c –0.782 2.078
B (H up) 1.891 1.426, 1.427 94.791 0.947 –0.112 3.335
HS B (H flat) 1.931 (2.326)d 1.429 (1.361)d   4.457 (3.60)d –0.168 3.335
H (H up) 1.367 (2.343)d 1.438 (1.385)d   4.329 (3.98)d –0.503 2.679
S H 1.419     6.661 (6.87)b –0.782 2.242
hydrogen T 1.685     2.357 (2.21)e –0.056 0.164
B 1.167     2.659 (2.71)e 0.000 0.711
H 0.212     2.610 (2.68)e –0.056 0.164
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a

d (surf-S)/Å is the distance of sulfur atom from the surface. d (S–H)/Å is the bond length of S–H, ØHSH (°) is the angle between hydrogen atoms in H2S, Ead (eV) is the adsorption energies, Δ12 ( % ) is the relaxation between first and second layer, and Δ23 ( % ) is the relaxation between second and third layer.

b

Ref (54).

c

Ref (55).

d

Ref (56).

e

Ref (44).

Table 2. Adsorption Energy and Geometric Parameters for the Adsorption of Reactants and Products at Cr-Doped Fe(100)a.

species adsorption site d (surf-S)/Å d (S–H)/Å ØHSH/° –Ead/eV Δ12/% Δ23/%
H2S B (Cr–Cr, H up) 2.150 1.421, 1.422 94.637 0.967 –0.055 0.167
T (Cr, H flat) 2.443 1.428, 1.513 88.905 0.917 –0.829 0.835
T (Fe, H flat) 2.343 1.429, 1.455 89.584 0.944 –0.774 1.169
HS B (Cr–Cr, H flat) 2.151 1.429   4.400 –0.332 0.612
H (Cr, H up) 1.464 1.432   4.346 –0.608 0.056
B (Cr–Fe, H flat) 2.055 1.437   4.398 –0.106 0.445
S H (Cr) 1.475     6.688 –0.719 0.445
H (Fe) 1.504     6.682 –0.663 0.390
hydrogen B (Cr–Cr) 1.405     2.651 –0.387 0.947
H (Cr) 0.208     2.689 –0.111 0.501
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a

d (surf-S)/Å is the distance of sulfur atom from the surface. d (S–H)/Å is the bond length of S–H, ØHSH (°) is the angle between hydrogen atoms in H2S, Ead (eV) is the adsorption energies. Δ12 ( % ) is the relaxation between first and second layer and Δ23 ( % ) is the relaxation between second and third layer.

The most stable adsorption of H2S occurs at the top (H flat) shown in Figure 2a; and the least stable adsorption is the bridge (H up) at the Fe(100) surface. The adsorption energy for the most stable adsorption of H2S at Fe(100) is found to be 0.999 eV. Ren et al.55 reported the adsorption energy range of 0.461–2.298 eV for H2S at various sites. HS adsorbed at location bridge B (H flat) with adsorption energy 4.457 eV at Fe(100). Wen et al.56 reported adsorption energy for HS as 3.98 eV for the most stable site at Fe(100).

All adsorption energies calculated at the Fe(100) and Cr-doped Fe(100) surfaces are negative, indicating exothermic nature for the reactants and products. This indicates that these species act as corrosive media for Fe(100) and Cr-doped Fe(100). Among H2S, hydrogen, HS, and S, the adsorption energy of H2S is the lowest at both Fe(100) and Cr-doped Fe(100) surface, and the adsorption energy of S is the highest among these species. This trend is in good agreement with the previous work.34,60,61 The mechanism of adsorption is the same for all species at Fe(100) and Cr-doped Fe(100). The H–S bond length for the H2S at Fe(100) varied from 1.426–1.455 Å and angle varied from Inline graphic of 89.222° – 94.791°, which is in good agreement with Ren et al.55 They reported that the H–S bond length varied from 1.427–1.491 Å and Inline graphic of 86.071° – 94.696°. The experimental H–S length is 1.328 Å and Inline graphic of 93.556° for the free state of H2S molecules.51 The larger bond length further confirms the likelihood of dissociation of H2S at the Fe(100) surface with a small activation barrier.

For the Cr-doped Fe(100) surface, the most stable adsorption occurs at the B (Cr–Cr, H up) site of H2S (Figure 3a) with an adsorption energy of 0.967 eV. The H2S molecule sits at a distance of 2.150 Å (Table 2) at the most stable adsorption for the Cr-doped Fe(100). The adsorption of these species changes the geometric structure of the slab, which can also be observed by the relaxation between layers shown in Tables 1 and 2. It is observed that relaxation between layers significantly decreases for the adsorption of H2S, HS, S after the addition of Cr atoms into the Fe(100) slab however, for the adsorption of hydrogen atom, the relaxation between layers does not change significantly with addition of Cr. These results are in good agreement with the experiment62 and other studies shown in Table A1. The S atom is most stable at the H site for Fe(100) and H (Cr) site for Cr-doped Fe(100). Legg et al.63 confirmed by experiment the S atom prefers to sit on the H site. Placing the S atom at a T site or B site results in the S atom migrating to the H site. The adsorption energy of the S atom for Cr-doped Fe(100) at sites H (Cr) found to be 6.688 eV is highest among species studied in this work.

Table A1. Interlayer Relaxation for Irona.

method layer number Δ12 ( % ) Δ23 ( % ) reference
PAW-GGA (PBE) 4b –0.782 2.078 present work (for most stable sites)
4c –0.168 3.335
4d –0.782 2.242
4e 0.00 0.711
PAW-GGA (PBE) 5 –2.2 4.3 (51)
7 –2.9 3.0 (51)
USPP-GGA (PW91) 5 –4.3 3.1 (66)
7 –3.8 2.7 (66)
USPP-GGA (PW91) 5 –3.5 2.3 (67)
FLAPW-GGA (PBE) 5 –4.0 1.5 (68)
LEED Experiment   1.4 ± 3   (62)
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a

Δ12 ( % ) is relaxation between layer 1 and 2, Δ23 ( % ) is relaxation between layer 2 and 3.

b

Adsorption of H2S on T (H flat) site.

c

Adsorption of HS on B (H flat).

d

Adsorption S on H site.

e

Adsorption hydrogen on B site.

3.2. Dissociation of H2S

H2S disassociation is made up of a series of reactions as the gas dissolves and dissociates into individual components on the metal surface. The decomposition of H2S at the Fe(100) surface involves a series of reactions:34

3.2. 1
3.2. 2
3.2. 3

The calculation of transition state (TS) at different sites demonstrates the different dissociation behavior of H2S is related not only to adsorption energy but also to activation energy (reaction barrier).

The corrosive H2S gas dissolves to bisulfide (HS) and hydrogen ions with further degradation to hydrogen and S at Fe(100) and Cr-doped Fe(100) surfaces. Previous work on adsorption of H2S demonstrates that dissociative interactions are thermodynamically favored on Fe2O3(001) and at Fe(100),56,64 The full dissociation process on the Fe(100) slab and Cr-doped Fe(100) slab is shown in Figures 4 and 5 respectively. Dissociation of H2S can occur from any site but in this work, dissociation is studied from the most stable sites, the T (H flat) at Fe(100) and B (Cr–Cr, H up) at Cr-doped Fe(100). The whole process can be divided into five steps (1) the incoming H2S gas adsorbs on the stable sites, (2) the adsorbed H2S gas disassociates to HS and releases one hydrogen atom, (3) the (HS) ion shifts toward the B site for Fe(100) and B (Cr–Cr) site for Cr-doped Fe(100) with a further drop in energy (4) dissociation of (HS) into hydrogen and S by crossing the activation energy barrier at both surfaces, and (5) shift of both hydrogen and S to other stable sites.

Figure 4.

Figure 4

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Whole reaction path for the dissociation of H2S at Fe(100). The top view geometries are shown. Second-layer Fe atoms are red in color.Inline graphic

Figure 5.

Figure 5

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Whole reaction path for the dissociation of H2S at Cr-doped Fe(100). The top view geometries are shown. Second-layer Fe atoms are red in color.Inline graphic

By following the trajectory of the reaction process (Figures 4 and 5), it has been observed that the H2S bond link to the surface slightly rotates and breaks into hydrogen + HS with low activation energy barriers of 0.013 eV for Fe(100) and 0.362 eV at Cr-doped Fe(100). Akande et al.34 also showed a small dissociation barrier for H2S at Fe(110), implying easy dissociation of H2S at iron surfaces. The dissociative adsorption of H2S is confirmed by X-ray photoelectron spectroscopy,34,65 from 190 K up to room temperature; however at lower temperatures molecular adsorption occurs. The activation energy barrier for disassociation of HS is 0.402 eV for the Fe(100) and 0.436 eV for the Cr-doped Fe(100), respectively. Wen et al.56 calculated an activation energy barrier of 0.35 eV for dissociation of HS on an Fe(100) slab. The difference in the activation barrier can be attributed to the distinct path chosen or starting position.

After dissociation, both hydrogen atoms prefer to sit at a B site; however, the sulfur atom prefers to sit on a H site at Fe(100) (see the final step in Figure 4). The preference of the S atom to sit on the H site at Fe(100) is confirmed by experiment.63 The first hydrogen atom moves to the B site (Fe–Cr), while the second hydrogen atom sits at a H (above Fe atom); however, the S atom sits at a H site (above Cr) for Cr-doped Fe(100) as depicted in Figure 5.

The dissociation barrier in the Cr-doped Fe(100) slab is higher indicating resistance to the dissociation process. The total energy gain for the (HS + hydrogen) is 1.889 eV at the Fe(100) surface and 1.811 eV at the Cr-doped Fe(100) surface with respect to free molecule (H2S) after the dissociation process (Figures 4 and 5). Wen et al.56 reported the total energy gain for HS + hydrogen on the defect-free Fe(100) surface as 1.92 eV.

In Figure 6, three kinds of sites are shown T (top), B (bridge), and H (hollow). The sites in the bulk are B, B1 is the site below B, and B2 is the site below B1 Similarly, T1 is the site below T. Subscripts 1 and 2 denote bulk locations below the surface sites. Second-layer Fe atoms are red in color. The order of the depths is as follows: T < B < H < B1 < T1 < B2 < H1.

Figure 6.

Figure 6

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Schematic diagram (top view and side view) of hydrogen atom diffusion sites at the surface and bulk of Fe (100).Inline graphic

In Figure 7, the curve corresponds to the minimum energy path (MEP) of single hydrogen atom diffusion until the point B2; however, there are number of paths to reach this point. The arrows indicate a diffusion barrier for hydrogen atoms. TS represents the transition state. R represents routes for which values are taken from Table 3. T and B sites are taken as reference for Fe(100) and for Fe(100)–Cr, respectively.

Figure 7.

Figure 7

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Energy profile of hydrogen atom diffusion at (a) Fe(100) surface via path 1 and 2 (b) Cr-doped Fe(100) surface.

Table 3. Activation Energy Ea (eV) and Heat of Reaction ΔE (eV) for the Diffusion of Hydrogen Atoms from Various Sites at the Fe(100) Surface and Cr-Doped Fe(100).

Fe(100)
 Fe(100)–Cr
diffusion routes ΔE (eV) Ea (eV) diffusion routes ΔE (eV) Ea (eV)
R1 : T → B N/A N/A R1 : T → B N/A N/A
R2: T → H N/A N/A R2 : T → H N/A N/A
R3 : T → T1 –0.020 0.385 R3 : T → T1 N/A N/A
R4 : T → B1 N/A N/A R4 : T → B1 N/A N/A
R5 : T → B2 N/A N/A R5 : T → B2 N/A N/A
R6 : T → H1 N/A N/A R6 : T → H1 N/A N/A
R7 : B → H 0.034 0.085 R7 : B → H –0.053 0.076
R8 : B → T1 0.307 0.648 R8 : B → T1 0.204 0.519
R9 : B → B1 0.295 0.423 R9 : B → B1 0.155 0.506
R10 : B → B2 0.348 0.781 R10 : B → B2 0.286 0.511
R11 : B → H1 0.306 0.045 R11 : B → H1 N/A N/A
R12 : H → T1 0.273 0.76 R12 : H → T1 0.257 0.774
R13 : H → B1 0.261 0.317 R13 : H → B1 0.208 0.394
R14 : H → B2 0.313 0.733 R14 : H → B2 –0.339 0.858
R15 : H → H1 N/A N/A R15 : H → H1 0.329 1.047
R16 : B1 → T1 0.012 0.273 R16 : B1 → T1 0.049 0.272
R17 : B1 → B2 0.052 0.474 R17 : B1 → B2 0.130 0.605
R18 : B1 → H1 0.011 0.531 R18 : B1 → H1 0.121 0.697
R19 : T1 → B2 0.040 0.231 R19 : T1 → B2 0.081 0.283
R20 : T1 → H1 0.00 0.566 R20 : T1 → H1 0.072 0.711
R21 : B2 → H1 –0.041 0.186 R21 : B2 → H1 –0.009 0.222
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3.3. Diffusion of Hydrogen

The spontaneous dissociation of H2S adsorbed at the Fe(100) surface results in two hydrogen atoms. The hydrogen atom diffuses over the surface from the top site to the bridge or hollow site; in addition it also migrates toward the subsurface layer (bulk) of the slab. The effect of the vacancy defect on hydrogen diffusion is discussed by Wen et al.56 However, the effect of chromium doping of Fe(100) requires study. Therefore, all the feasible routes for MEPs are explored. The activation energy barrier and heat released/absorbed during migration of hydrogen atoms were calculated employing NEB methods. The illustrative diagram for the diffusion of hydrogen among various sites is shown in Figure 6. The four-layer model shown in Figure 6 was symmetrical, so the diffusion of hydrogen atoms was done up to the third inner layer only.

The DFT calculations for hydrogen diffusion over the surface and subsurface give context to hydrogen embrittlement at the microscopic level. Hydrogen diffusion consists of three steps (i) diffusion at the upper surface layer, (ii) dissolution to the lower surface (second layer) at interstitial locations, and (iii) diffusion in the bulk Fe(100). There are a large number of energetically stable sites available for dissolution of H atoms in bulk Fe(100), increasing the number of possible diffusion paths. Activation energy Ea (eV) and heat of reaction ΔE (eV) for the diffusion/dissolution of single hydrogen atoms from the various sites at simple Fe(100) slab and Cr-doped Fe(100) slab are shown in Table 3. As noted above, the order of the depths is as follows: T < B < H < B1 < T1 < B2 < H1. The hydrogen atom can also combine with another hydrogen atom to produce H2, but this was not considered in this work with respect to diffusion. The diffusion barrier at surface (R7 : B → H) is 0.085 eV for Fe(100) and 0.076 eV for Cr-doped Fe(100) which is in good agreement with experimental68 and other studies shown in Table A2. Out of several possible paths, B → H → B1 → T1 → B2 is chosen (following the minimum activation energy barrier from Table 3) for the hydrogen atom to reach to the site B2 (third layer). The energy profile of hydrogen atom diffusion is shown in Figure 7. The largest activation energy (steps B → H → B1 → T1 → B2) will be the rate-limiting step for the diffusion of hydrogen atoms to the site B2. The connection between H → B1 has the highest barrier, 0.317 eV at Fe(100), and 0.394 eV at Cr-doped Fe(100) and therefore is the rate-limiting step for hydrogen atom diffusion. It is worthwhile noting that hydrogen atoms are not stable at the T site at Cr-doped Fe(100).

Table A2. Activation Energy Barrier for Diffusion of Hydrogen.

metal temperature range (°C) experimental method –Ead (eV) reference
Fe(100)   DFT 0.085a present work
0.076b
0.317c
0.394d
∝-iron 350–900 DFT 0.049 (69)
350–700 0.213
∝-iron 126–693 gas phase, time lag 0.047 (70)
∝-iron 25–780 vacuum degassing 0.139 (70)
carbon steel 10–100 acid attack, time lag 0.399 (70)
Open in a new tab
a

R7 : B → H at Fe(100).

b

R7 : B → H at Cr-doped Fe(100).

c

R13 : H → B1 at Fe(100).

d
R13 : H → B1 at Cr-doped Fe(100).
graphic file with name ao2c05615_m014.jpg

The diffusion barrier for R11 : B → H1 at Fe(100) and R7 : B → H at Cr-doped Fe(100) is the minimum among the paths studied for migration of hydrogen atoms at the surface, implying that the hydrogen atom prefers to diffuse through the B site into the subsurface. The Ea for the first layer diffusion from R9 : B → B1 is 0.423 eV and for the Cr-doped Fe(100) from R9 : B → B1 is 0.506 eV. Diffusion of the hydrogen atom from R3 : T → T1 is exothermic (−0.02 eV); however, R8 : B → T1 is endothermic (0.307 eV) at Fe(100).

The diffusion barrier from the H site for R12, R13, R14, and R15 at Cr-doped Fe(100) is more than Fe(100), indicating that diffusion of hydrogen atoms from the H site is difficult on Cr-doped Fe(100). The migration of hydrogen atoms at the Fe(100) for the route R21 : B2 → H1 is preferred compared to a similar path, R21 : B2 → H1 at the Cr-doped Fe(100) with an activation barrier of 0.186 and 0.222 eV, respectively. Route R10 at Fe(100) and R15 at Cr-doped Fe(100) has the highest energy barriers of 0.781 and 1.047 eV, respectively (diffusion into the bulk), but the order of Ea (1.047 eV) is low to not inhibit diffusion of the hydrogen atom. The diffusion pathways of hydrogen will clarify the mechanism of embrittlement/hydrogen-induced deterioration.

4. Conclusions

This study presents understanding of the corrosion mechanism using the GGA-PBE)40 function with the DMol341 module. The corrosion mechanism is studied considering the adsorption mechanism of species H2S, hydrogen, HS, and S as well as feasible dissociation pathways for Fe(100) and Cr-doped Fe(100). The H2S is weakly adsorbed for the top (flat hydrogen) site at Fe(100) and bridge (Cr–Cr, hydrogen up) site at Cr-doped Fe(100) with adsorption energies of −0.999 and −0.967 eV, respectively. The most stable adsorption for HS occurs at bridge (hydrogen flat) site for Fe(100) and bridge (Cr–Cr, hydrogen flat) site for Cr-doped Fe(100) with their adsorption energies −4.457 and −4.400 eV respectively. The order of the adsorption energies is Ead(H2S) < Ead(H) < Ead(HS) < Ead(S) at both surfaces (Fe(100) and Cr-doped Fe(100)), which is in good agreement with previous studies.

The activation energy barrier at Fe(100) for H2S dissociation is almost negligible; however, for HS dissociation it is 0.402 eV. In addition, the activation energy barrier at Cr-doped Fe(100) for H2S dissociation is 0.362 eV, and for HS dissociation it is 0.436 eV, respectively. The higher activation barrier for Cr-doped Fe(100) may be due to variable charge density, or the path chosen in this study.

The hydrogen atom diffuses over the surface from the top site to the bridge or hollow site, in addition it also migrates toward the subsurface layer (bulk) of the slab. A large number of diffusion paths are available, but only feasible paths are considered. The diffusion barrier from hollow sites for R12, R13, R14, and R15 at Cr-doped Fe(100) is more than Fe(100) shown in Table 3; this implies that the diffusion of hydrogen atoms from the hollow site is difficult in the presence of Cr.

This study will help in understanding the corrosion mechanism due to H2S for pure metals/alloys. In addition, it will help for investigating the diffusion/formation of H2 gas inside the bulk (embrittlement) of the metals/alloys.

Acknowledgments

The authors acknowledge the financial support provided by Genome Canada and their supporting partners and the Canada Research Chair (CRC) Tier I Program in Offshore Safety and Risk Engineering.

Appendix A

Interlayer relaxation for iron; activation energy barrier for diffusion of hydrogen; ground-state energy of Fe(100) for the different k points; ground-state energy of Fe(100) for the different basis sets; bond length for H–S, Fe–S, and Fe–H mentioned in Figure 2 for Fe(100); and bond length for H–S, Fe–S, and Fe–H mentioned in Figure 3 for Cr-doped Fe(100) are presented in Tables A1A2A3A4A5A6.

Table A5. Bond Length for H–S, Fe–S, and Fe–H Mentioned in Figure 2 for Fe(100).

species site A b c d e
H2S T (H flat) 1.437 1.455 2.408    
B (H up) 1.427 1.426 2.389 2.384  
HS B (H flat) 1.429 2.415 2.412    
H (H up) 2.463 2.463 2.462 2.462 1.438
S H 2.453 2.451 2.452 2.452  
hydrogen T 1.655        
B 1.799 1.765      
H          
Open in a new tab

Table A6. Bond Length for H–S, Fe–S, and Fe–H Mentioned in Figure 3 for Cr-Doped Fe(100).

species adsorption site a b c d e
H2S B (Cr–Cr, H up) 2.460 2.460 1.422 1.421  
T (Cr, H flat) 1.513 1.428 2.500    
T (Fe, H flat) 1.455 1.429 2.418    
HS B (Cr–Cr, H flat) 2.465 2.465 1.429    
H (Cr, H up) 2.526 2.459 2.458 2.526 1.432
B (Cr–Fe, H flat) 1.437 2.470 2.397    
S H (Cr) 2.506 2.437 2.441 2.510  
H (Fe) 2.439 2.503 2.503 2.439  
hydrogen B (Cr–Cr) 1.843 1.845      
H (Cr)          
Open in a new tab

The authors declare no competing financial interest.

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