Exploring the Evolution Mechanism of Sulfur Vacancies by Investigating the Role of Vacancy Defects in the Interaction between H2S and the FeS(001) Surface.

Vacancy defects are inherent point defects in materials. In this study, we investigate the role of Fe vacancy (VFe) and S vacancy (VS) in the interaction (adsorption, dissociation, and diffusion) between H2S and the FeS(001) surface using the dispersion-corrected density functional theory (DFT-D2) method. VFe promotes the dissociation of H2S but slightly hinders the dissociation of HS. Compared with the perfect surface (2.08 and 1.15 eV), the dissociation energy barrier of H2S is reduced to 1.56 eV, and HS is increased to 1.25 eV. Meanwhile, S vacancy (VS) significantly facilitates the adsorption and dissociation of H2S, which not only reduces the dissociation energy barriers of H2S and HS to 0.07 and 0.11 eV, respectively, but also changes the dissociation process of H2S from an endothermic process to a spontaneous exothermic one. Furthermore, VFe can promote the hydrogen (H) diffusion process from the surface into the matrix and reduce the energy barrier of the rate-limiting step from 1.12 to 0.26 eV. But it is very hard for H atoms gathered around VS to diffuse into the matrix, especially the energy barrier of the rate-limiting step increases to 1.89 eV. Finally, we propose that VS on the FeS(001) surface is intensely difficult to form and exist in the actual environment through the calculation results.

Introduction

H2S corrosion is the most dangerous factor in the corrosion of equipment in oil and gas fields with high sulfur content. As a highly toxic gas, H2S not only seriously threatens the routine use of equipment and pipeline steel but also directly threatens the safety of human life.[1,2] When steel is used in the H2S environment, pitting corrosion, local corrosion, uniform corrosion, linear corrosion, stress corrosion cracking, and hydrogen-induced cracking occur easily.[3] In the 1980s, Canadian scholars found that corrosion products in H2S environments were more complex than other corrosion environments. Especially, when iron-base alloys contacted the wet H2S environment, corrosion product films would immediately form on the surface. The types of corrosion products were intricate and varied, and they often existed in the form of mixed crystals, mainly iron sulfide compounds with nonstoichiometry.[4,5]

Mackinawite (FeS) is an exceptionally crucial iron sulfide compound. It is the initial metastable corrosion product formed by steel in a humid H2S environment at low temperatures, while it is also the main corrosion product.[6] Due to the strong reducibility, FeS is readily oxidized and converted into other more stable iron sulfide compounds.[7] Consequently, FeS is regarded as the forerunner of other iron sulfide compounds formed in deposition and hydrothermal systems, including pyrite (FeS2), pyrrhotite (Fe7S8), and greigite (Fe3S4).[8] Besides, recent studies have shown that FeS exhibits typical metallic characteristics.[9] In a wet H2S environment, the reaction at the iron sulfide compounds/H2S interface has a vast influence on the formation of subsequent corrosion products and the transition between corrosion products.[10−13] A prior study discovered that in the Fe–H2S–H2O environment at a high temperature, the crystal evolution sequence of iron sulfide compounds is as follows: mackinawite → pyrrhotite → pyrite; troilite → pyrrhotite → pyrite.[14] In addition, FeS gradually transforms into pyrrhotite as the temperatures increase.[15] The H atoms generated by H2S dissociation further diffuse from the surface to the interior of the matrix and gather at H traps such as defects and inclusions to form H2, thus generating hydrogen bubbling or cracking.[16] Bai et al. studied the hydrogen escape behavior of FeS under different hydrogen charging conditions through the pyrolysis adsorption test, and the results showed that H diffused from grain boundary/dislocation to vacancies in the metal and that FeS had no obstruction to hydrogen permeation.[17]

The formation and transformation of FeS and its hydrogen resistance properties in the H2S environment have been studied in detail experimentally. However, it is difficult to determine the interaction between H2S and the low-dimensional surface of FeS from a microscopic point of view through the existing experimental techniques. Density functional theory (DFT) can provide an understanding of the interactions between small molecules and surfaces at the molecular level. In recent years, DFT has been widely used to study the adsorption/dissociation process of molecules and charge transfer between molecules and substrates. An FeS crystal has a tetragonal structure. Fe atoms are connected to four equidistant S atoms in a tetragonal lattice by tetrahedral coordination to form an equilateral tetrahedral layered structure stacked along the z-axis and stabilized by vdW force.[18] FeS is usually layered, so FeS is characterized by surface activity and high specific surface area like other two-dimensional layered materials.[19] In the past, some scholars have studied the interaction between some small molecules and diverse low-dimensional surfaces of FeS by the DFT method. Dzade et al. systematically studied the adsorption/dissociation of various small molecules on diverse low-dimensional surfaces of FeS.[20−24] The adsorption energy of small molecules at different adsorption sites on diverse low-dimensional surfaces was investigated, and the dissociation of small molecules was analyzed. The calculation results reported that NO, CO2, H2O, C3H7NO2S, and C4H4S are more likely to dissociate on the most unstable FeS(111) surface. Meanwhile, the dissociation energy barrier of these molecules is the largest on the FeS(001) surface. Whereafter, further studies found that preadsorption of O2/O atoms on diverse low-dimensional surfaces would promote the subsequent adsorption and dissociation of H2O.[25] Moreover, Krishnamoorthy of MIT suggested the effect of the insertion of H2 and H atoms in the gap between the FeS layers and the insertion of H atoms in the Fe vacancy on the tensile strength and elastic modulus of the matrix.[26] Recently, Wen et al. calculated the adsorption and dissociation processes of H2S on diverse low-dimensional surfaces of FeS in corrosive environments.[27] The results demonstrated that H2S had the lowest dissociation energy barrier on the FeS(011) surface and the highest on the FeS(001) surface.

It is widely known that crystal defects exist in any material.[28] Vacancy is an inherent point defect in a crystal structure. The existence of vacancy defects has a considerable effect on the reactivity of a surface.[29] For instance, the presence of S vacancies on the pyrite(100) surface not only promoted the adsorption of formamide but also facilitated the transition of amino acid from a zwitterionic species to an anionic species.[30,31] Sahraei et al. found that the vacancy defects on the ZnS(110) surface can change the hydrophilicity of the surface and also prompt the conversion of amino acid from neutral to zwitterionic.[32,33] Ward et al. revealed that pure FeS could be described by FeS0.94.[34] Furthermore, crystallographic evidence found by Taylor and Finger et al. confirmed that FeS was sulfur-deficient (FeS1–, typically 0 ≤ x ≤ 0.07).[35] This may be caused by the existence of VS or the incorporation of interstitial metal atoms. In most calculations, a perfect FeS surface has been emphasized with attention. However, the influence of vacancy defects on the adsorption, dissociation, and H diffusion behavior of H2S on the FeS surface is rarely reported. In view of the metastable nature of FeS, surface defects are very possible to form in the actual environment. Exploring the adsorption/dissociation and diffusion processes of H2S on the vacancy-defective FeS surface by the DFT method can be used to guide the experiment. Besides, this allows us to further enhance the understanding of the hydrogen barrier properties of FeS and the influence of vacancy defects on the subsequent formation and transformation of iron sulfide compounds from the microscopic perspective.

In this work, we investigated the impact of VFe and VS on the adsorption and dissociation processes of H2S on the most stable (001) surface of FeS. Besides, the diffusion energy barrier of the H atom from the surface into the matrix was calculated. In the end, according to the calculation results, we found that VS on the FeS(001) surface is extremely difficult to form and exist in the actual environment.

Results and Discussion

Properties of FeS(001) Surfaces

First, according to the vacancy formation energy formula, we calculate the formation energies of VFe and VS of the FeS(001) surface. The results indicate that the formation energies of VFe and VS are 1.34 and 3.91 eV, respectively. The top and front views of perfect and vacancy-defective FeS(001) surfaces are shown in Figure a–c. The red dotted lines represent VFe and VS. Among them, VFe is in the second atomic layer and VS is in the first atomic layer. Since vacancy defects are vacant in different layered positions, the charge density distribution is carried out to assess the change of the surface electronic structure. The charge density distribution of perfect and vacancy-defective FeS(001) surfaces is shown in Figure d–f. Blue and red represent the areas with lower and higher charge densities, respectively. The red dotted lines in the figure represent the location of vacancy defects. It can be clearly seen that a region with considerably low charge density is formed around the vacancy defects. Besides, the charge density around VS decreases more obviously, which has a greater influence on the charge density distribution of the FeS(001) surface.

Figure 1

Top and front views (a–c) of the surface structures of perfect and vacancy-defective FeS(001) surfaces. Red dotted lines represent VFe and VS, respectively. The charge density of perfect (d), vacancy-defective-Fe (e), and vacancy-defective-S (f) FeS(001) surfaces.

Moreover, we also calculated that the formation energy of the VS of the third atomic layer is equal to that of the first atomic layer, but the result shows that VS in the third atomic layer has almost no effect on the surface charge density distribution and the adsorption of H2S. Therefore, our study focused on the VS located in the first atomic layer and the VFe located in the second atomic layer, which are relatively close to the surface.

Adsorption of H2S

Figure S1b–d shows the possible adsorption sites of different FeS(001) surfaces and dissolution sites in the matrix. Table S1 lists the related parameters of different adsorbents after they are stably adsorbed on different surfaces. Table lists the structural parameters of the most stable adsorption configurations, where d (Å) expresses the distance between adsorbents and the surface. Figure shows the top view, front view, DCD, and adsorption energy of H2S stably adsorbed on perfect and vacancy-defective FeS(001) surfaces. The yellow and blue areas in the DCD represent the areas of charge increase and loss, respectively.

Table 1

Structural Parameters of Different Adsorbates Stably Adsorbed on Different FeS(001) Surfaces

adsorbate	adsorption spot	d (Å)	αHSH (deg)	d (H–S) (Å)	Eads (eV)
Perfect FeS(001)
H2S	Fe-Ba	2.794	91.346	1.352; 1.352	–0.23
HS	S-Tb	2.157	–	1.357	–1.27
H + HS	Fe-B + S-T	1.665; 2.191	–	1.357	1.63
H + S	Fe-B + S-T	1.681; 1.942	–	–	–0.36
Vacancy-Defective-Fe FeS(001)
H2S	Fe-B	2.781	91.570	1.352; 1.352	–0.19
HS	S-T	2.188	–	1.359	–1.43
H + HS	Fe-B + S-T	1.509; 2.187	–	1.355	1.33
H + S	Fe-Vc + S-T	1.936; –	–	–	–0.48
Vacancy-Defective-S FeS(001)
H2S	S-V	–	87.169	1.402; 1.403	–1.21
HS	S-V	–	–	1.376	–4.83
H + HS	Fe-B + S-V	1.601; –	–	1.377	–1.84
H + S	Fe-B + S-V	1.668; –	–	–	–4.96

B: represents the bridge site.

T: represents the top site.

V: represents the location of the vacancy defect.

Figure 2

Different views of the stable adsorption texture of H2S on perfect (a), vacancy-defective-Fe (b), and vacancy-defective-S (c) FeS(001) surfaces. (d–f) The corresponding DCD.

The stable adsorption site of H2S on perfect and vacancy-defective-Fe FeS(001) surfaces are all Fe-B sites. However, on the vacancy-defective-Fe FeS(001) surface, the adsorption energy of H2S decreases slightly, which reveals that the existence of VFe slightly decreases the adsorption capacity of H2S. Nevertheless, the presence of VFe does not change the stable adsorption location and configuration of H2S. The bond length, bond angle, and the distance between H2S and the surface are almost identical to those of the perfect surface after H2S was stably adsorbed on the vacancy-defective-Fe FeS(001) surface. Since the adsorption of H2S on the FeS(001) surface itself is weak physical adsorption, and VFe is in the second atomic layer, so it is arduous to affect the adsorption process of H2S on the surface. Besides, it can also be seen from the DCD that the charge transfer between H2S and the vacancy-defective-Fe FeS(001) surface is basically the same as that between H2S and the perfect FeS(001) surface.

On the vacancy-defective-S FeS(001) surface, H2S is stably and vertically adsorbed at the S-V site and has evident hybridization with the surface. The adsorption energy of H2S increases to −1.21 eV. As one can see from the DCD, the H atom in H2S takes some electrons from the S atom in H2S, which is different from the charge transfer of H2S after it is stably adsorbed on other surfaces. In addition, part of the charge from the S atom in H2S is also transferred to the Fe atom of FeS. The transfer of charge further proves that there is a strong interaction between H2S and the vacancy-defective-S FeS(001) surface, which may be caused by the reduction of the charge density prompted by VS as mentioned above.

On the other hand, it can be seen from the structural parameters, compared with the perfect and vacancy-defective-Fe FeS(001) surfaces, the bond length of H2S increases and the bond angle decreases on the vacancy-defective-S FeS(001) surface, proposing that these states may be the precursors of H2S dissociation. This also provides some evidence from the side that the existence of VS may promote the dissociation process of H2S.

Dissociation of H2S

In this work, CI-NEB is applied to calculate the maximum dissociation barrier Ea and the minimum energy paths (MEPs) of H2S and HS. The adsorption energies and related parameters of HS + H and S + H after stable co-adsorption on different surfaces were calculated, as shown in Table . The top views of the ISi, FSi, and TSi configurations of MEPs where H2S and HS dissociate on the vacancy-defective FeS(001) surface are shown in Figures and 4. Meanwhile, Table lists the Ea and ΔE of the H2S dissociation reaction. The energy barriers Ea1 and Ea2 as well as the transition state configurations on the perfect FeS(001) surface in this work are consistent with the previous calculations of our group (2.06 and 1.23 eV),[27] which also proves the validity of our work.

Figure 3

Most beneficial path for the dissociation of H2S on the vacancy-defective-Fe FeS(001) surface.

Figure 4

Most beneficial path for the dissociation of H2S on the vacancy-defective-S FeS(001) surface.

Table 2

Reaction Heat (ΔE) and Dissociation Energy (Ea) of the Dissociation Steps of H2S on the Perfect and Vacancy-Defective FeS(001) Surfaces

	perform ZPE		no ZPE
reaction coordinate	Ea-ZPE (eV)	ΔE-ZPE (eV)	Ea (eV)	ΔE (eV)
Perfect FeS(001)
P1: IS1 → TS1 → FS1	2.08	1.77	2.19	1.86
P2: IS2 → TS2 → FS2	1.15	0.83	1.19	0.91
Vacancy-Defective-Fe FeS(001)
P1: IS1 → TS1 → FS1	1.56	1.49	1.90	1.56
P2: IS2 → TS2 → FS2	0.34	–0.06	0.29	–0.05
P3: IS3 → TS3 → FS3	1.25	0.90	1.32	0.95
Vacancy-Defective-S FeS(001)
P1: IS1 → TS1 → FS1	0.07	–0.69	0.13	–0.63
P2: IS2 → TS2 → FS2	0.11	–0.19	0.18	–0.13

The MEPs of H2S dissociated on the vacancy-defective-Fe FeS(001) surface are shown in Figure . The dissociation process of H2S goes through four steps: (a) H2S is stably adsorbed at the Fe-B site near VFe by releasing an energy of 0.19 eV. (b) H2S rotates horizontally, breaking an H–S bond away from VFe. Then, the H atom breaks off from H2S, diffusing to the nearest Fe atom and forms a bond with it, while HS diffuses directly to the nearest S-T position. The energy barrier to be overcome for this process is 1.57 eV. (c) The isolated H atom diffuses from VFe to the interior of the matrix by overcoming an energy barrier of 0.34 eV. Meanwhile, HS does not change and still adsorbs at the original S-T site. (d) HS further overcomes an energy barrier of 1.25 eV and decomposes into S + H. After TS3, the H atom continues to diffuse into the matrix through VFe and the S atom is still adsorbed at the S-T site. The stable dissolution site is the same as that of the H atom separated by H2S in the first order. It can be seen from Table that compared with the perfect surface, the dissociation energy barriers Ea1 of H2S decrease and Ea2 increase to some extent, but the change is not conspicuous. The results imply that VFe has little influence on the dissociation reaction of H2S. It is worth mentioning that although the energy barrier of H2S dissociation does not change observably, we found that all H atoms dissociated from H2S can diffuse into the matrix through VFe, which provides some guidance for our subsequent study on the H diffusion process from the surface into the matrix.

The MEPs of H2S completely dissociated on the vacancy-defective-S FeS(001) surface are shown in Figure . In this process, the dissociation of H2S can be divided into three steps: (a) H2S is stably adsorbed at the S-V site and the adsorption energy is −1.21 eV. (b) H2S directly rotates 45° in the horizontal direction at S-V, and then a H–S bond breaks. The liberated H atom diffuses to the nearest Fe-B site and gets adsorbed stably, while HS continues to be adsorbed stably at the original S-V site. The energy barrier to be overcome for this process is 0.07 eV. (c) HS further overcomes an energy barrier of 0.11 eV and decomposes into S + H. Similar to the first H atom, the H atom split from HS also diffuses to the nearest Fe-B site for stable adsorption, while the S atom continues to be adsorbed stably at the S-V site.

Compared with the perfect surface, the dissociation energy barriers Ea1 and Ea2 of H2S on the vacancy-defective-S FeS(001) surface are intensely reduced, and the whole dissociation process changes from endothermic to exothermic. The existence of VS greatly promotes the dissociation process of H2S. Also, H2S can be dissociated directly through two dehydrogenation processes at the original adsorption site, making the dissociation process more concise. The calculations demonstrate that VS has a strong adsorption capacity for H2S, which is also caused by the extreme decrease of charge density around VS. The decrease of charge density may also cause the dissociation of H2S to change into an exothermic process that can occur spontaneously. In addition, we found that after H2S is completely disintegrated, the S atom fills the previous VS, thus forming the perfect surface. According to this characteristic, we later put forward an evolution mechanism of sulfur vacancies on the FeS(001) surface.

Diffusion of H Atoms

H atoms generated by H2S dissociation adsorb on the FeS(001) surface. By studying the diffusion mechanism of H atoms from the surface into the matrix by the DFT method, we can not only explore the hydrogen resistance performance of FeS but also further examine the influence mechanism of vacancy defects on H diffusion from the microscopic perspective.

Tables S2 and S3 list the Eads and Edis of H atoms and all possible diffusion paths of individual H atoms on the perfect FeS(001) surface. Table shows the Eads and Edis of H atoms on vacancy-defective FeS(001) surfaces and the matrix. Except for the S-V site, the Eads and Edis of H atoms on the perfect and vacancy-defective surfaces are both positive, which indicates that the adsorption/dissolution process of H atoms is not stable. At the S-V site, the adsorption energy of the H atom reaches −0.84 eV, which indicates that VS has a great adsorption capacity for H atoms. As mentioned above, this is also caused by the decrease of the charge density around VS.

Table 3

Adsorption Energy of the H Atom at Different Adsorption and Dissolution Sites on the Vacancy-Defective FeS(001) Surfaces

surfaces	adsorption site	Eads (eV)
vacancy-defective-Fe FeS(001)	S-T	0.69
	Fe-B	0.71
	Fe-L	0.68
	S-L	0.59
vacancy-defective-S FeS(001)	S-T	0.94
	S-V	–0.84
	S-L	0.73

Subsequently, we calculate all possible diffusion paths for H atoms on vacancy-defective FeS(001) surfaces. Figures S2, 5, and 6 show the MEPs of individual H atoms diffusing from the surface to the matrix on vacancy-defective FeS(001) surfaces. The illustration shows top and front views of the corresponding adsorption/dissolution locations and the configuration of the transition state. Table lists Ea and ΔE with and without ZPE correction for all possible diffusion paths of H atoms on the FeS(001) surface. The bold fonts in Table are Ea and ΔE of the rate-limiting steps for the H diffusion process into the matrix.

Figure 5

MEPs of the H diffusion process on the vacancy-defective-Fe FeS(001) surface.

Figure 6

MEPs of the H diffusion process on the vacancy-defective-S FeS(001) surface.

Table 4

Reaction Heat (ΔE) and Dissolution Energy Barrier (Edif) for All Possible H Diffusion Paths on Vacancy-Defective FeS(001) Surfaces

	perform ZPE		no ZPE
diffusion pathway steps	Edif-ZPE (eV)	ΔE-ZPE (eV)	Edif (eV)	ΔE (eV)
Vacancy-Defective-Fe FeS(001)
P1: S-T → Fe-B	0.45	–0.05	0.51	0.02
P2: S-T → Fe-L	0.49	–0.07	0.55	–0.01
P3: Fe-B → Fe-L	0.26	–0.03	0.27	–0.03
P4: Fe-L → S-L	0.24	–0.03	0.22	–0.09
Vacancy-Defective-S FeS(001)
P1: S-T → S-V	0.12	–1.82	0.14	–1.78
P2: S-V → S-L	1.89	1.61	1.96	1.57

On the perfect FeS(001) surface, the MEPs of H diffusion are S-T to Fe-B to Fe-L to S-L. The diffusion energy barrier Ea of the rate-limiting step of H diffusing into the matrix is 1.12 eV, which is not very large, thus H atoms can diffuse from the perfect FeS(001) surface into the matrix under certain conditions. The diffusion process of H atoms on the vacancy-defective-Fe FeS(001) surface is shown in Figure . According to the diffusion barrier, the MEPs of H diffusion are S-T to Fe-B to Fe-L to S-L, which is the same as H diffusion on the perfect surface. However, the energy barrier Ea of the rate-limiting step of diffusion is only 0.26 eV, which is overwhelmingly lower than that of the perfect surface (1.12 eV). It can be clearly seen from Figure that the existence of VFe provides an expedited path for H atoms in the diffusion process. Thus, the diffusion process of H atoms is smoother and the diffusion energy barrier is lower. This is consistent with the steps of H diffusion in the H2S dissociation process on the vacancy-defective-Fe FeS(001) surface calculated above, which further proves the rationality of this theory.

The H diffusion process on the vacancy-defective-S FeS(001) surface is shown in Figure . The adsorption sites of H atoms on the vacancy-defective-S FeS(001) surface are S-T and S-V. After calculation, we found that the diffusion of H atoms from S-T to S-V only needs to overcome a very small energy barrier of 0.12 eV, and unlike the S-T site, the adsorption of H atoms at the S-V site is an exothermic process. Therefore, it can be inferred that H atoms are very easy to aggregate near VS on the vacancy-defective-S FeS(001) surface. The energy barrier of H atom diffusion from S-V into the matrix is 1.89 eV, which is higher than that of the rate-limiting step on the perfect FeS(001) surface (1.12 eV). Different from VFe, the existence of VS does not provide a smoother path for H diffusion. VS binds the H atom to the vacancy defect, thus making the diffusion behavior of H atoms into the matrix more difficult, which is also caused by the decrease of charge density around VS.

In summary, compared with the perfect FeS(001) surface, VFe and VS have different influence mechanisms on the H atom diffusion process. VFe provides a smoother path for H atoms and considerably reduces the energy barrier of H diffusion into the matrix. On the other hand, the presence of VS binds H atoms to VS and hinders the diffusion of H atoms from the surface to the matrix.

Energy Barrier Split

The influence of vacancy defects on the H2S dissociation and H diffusion process is shown in Figure . Compared with the perfect surface, VFe can promote the dissociation process of H2S but hinder the dissociation of HS, while VS has an extremely significant promoting effect on both H2S and HS. In particular, VS can also change the dissociation process of H2S from an endothermic reaction, which is difficult to occur, to an exothermic reaction, which can proceed spontaneously. Furthermore, both VFe and VS can promote the H diffusion process into the matrix, and the promotion effect of VFe is particularly significant.

Figure 7

Diffusion barrier (Edif) of H atoms and the dissociation barrier (Ea) of H2S on perfect, vacancy-defective-Fe, and vacancy-defective-S FeS(001) surfaces.

According to the energy barrier splitting formula, each part contributes to the dissociation barrier Ea, as shown in Table . Compared with the perfect surface, the change of ΔEslab, ETS1HS, ETS1H, EIS1H, and Eint-H···HS on the vacancy-defective-Fe FeS(001) surface is small, but the change of ΔEdef-H is obvious, which decreases by 0.46 eV. This is the main reason for the decrease of the dissociation barrier Ea of H2S. On the vacancy-defective-S FeS(001) surface, the changes of ETS1HS, ETS1H, EIS1H, and Eint-H···HS are all significant, and their contribution together reduces the dissociation barrier Ea of H2S. It is worth mentioning that compared with the perfect and vacancy-defective-Fe FeS(001) surfaces, the contribution of ΔEslab and ΔEdef-H to dissociation barrier Ea is very small, which indicates that the slab model and H2S can move from the initial state to the transition state with little energy absorption. This also proves from the side that the configuration of H2S after stable adsorption at the S vacancy defect mentioned above may be the precursor of H2S dissociation. For the dissociation of HS, on the vacancy-defective-Fe surface, ΔEdef-HS decreases by 1.48 eV, which contributes the most to the dissociation barrier Ea. However, the interaction energy between H and S has a great positive contribution to the dissociation barrier Ea, which can almost cancel out the negative contribution of ΔEdef-H, so that the change of Ea is not very obvious. On the vacancy-defective-S surface, the changes of each part are manifested, which together lead to the decrease of the dissociation barrier Ea.

Table 5

Contribution of Each Part to the Dissociation Ea of H2S and HS

ΔEslab (eV)	ΔEdef-H2S (eV)	ETS1HS (eV)	ETS1H (eV)	EIS1H2S (eV)	Eint-H···HS (eV)
Perfect FeS(001)
0.24	3.44	–0.76	0.66	–0.23	1.73
Vacancy-Defective-Fe FeS(001)
0.22	2.98	–0.95	0.57	–0.19	1.45
Vacancy-Defective-S FeS(001)
–0.02	0.02	–4.47	2.16	–1.21	–1.17

Based on the research results, we proposed an evolution mechanism of sulfur vacancies on the FeS(001) surface, as shown in Figure . In our opinion, VS is very difficult to exist on the FeS(001) surface due to the following reasons: (a) The formation energy of VS is very large and reaches 3.91 eV, which indicates that in the actual environment, it is difficult to form VS on the FeS(001) surface under external conditions such as temperature and pressure. (b) Even if VS was formed on the surface, H2S in the environment would continue to spontaneously adsorb and dissociate at VS, so as to fill VS and form the perfect surface. Therefore, according to the calculation results, we propose that there is almost no VS on the FeS(001) surface in a corrosive environment and the vast majority of VS may exist within the matrix.

Figure 8

Evolution mechanism of S vacancies on the FeS(001) surface.

Computational Details

Models

The perfect and vacancy-defective FeS(001) surfaces are created through an utterly relaxed volume structure using Materials Studio (MS).[36] As shown in Figure S1a, the slab model of the FeS(001) surface adopts a 2 × 2 supercell structure and is equipped with nine atomic layers to adapt to the relaxation expansion of the first layer. An additional 15 Å vacuum layer is placed to ensure separation.[37,38] Zero-point energy (ZPE) correction is performed for the adsorption energy and dissociation energy barriers.[39,40] In all calculations involving the interaction of H2S and the dissociated atoms with the FeS(001) surface, the adsorbate and top three layers of atoms are totally allowed to relax, while the remaining atomic layers are fixed.

Methods

All of the calculations are executed using the Vienna Ab-initio Simulation Package (VASP).[41−45] The Perdew–Burke–Ernzerhof (PBE) generalized gradient approximation (GGA) exchange–correlation functional using the projector augmented wave method is applied.[46,47] We added the spin polarization parameters in the calculation process, which had little effect on the calculation of the perfect and vacancy-defective-Fe FeS(001) surfaces but had a great influence on the calculation of the vacancy-defective-S FeS(001) surface. Since the conventional DFT method cannot accurately describe the weak vdW force between atoms separated by vacuum, the DFT-D2 method is used to correct the weak vdW force between FeS layers in this study, which has been confirmed in other research studies.[27] When a cut-off energy of 400 eV is used, the total energy of FeS(001) converges. The K-points are set to be 11 × 11 × 11 for H2S in vacuum and bulk FeS optimizations, while 5 × 5 × 1 is applied for FeS(001) surface calculations. The convergence standards of energy and force are 10–5 eV and 0.05 eV·Å–1, respectively.

The formation energy of vacancy defects is defined by the following formula[48]Here, EV and EFeS denote the total energy of the FeS(001) model containing VFe/VS and the perfect surface, respectively. The μi represents the atomic chemical potential introduced by the formation of VFe/VS.

The transition state of the dissociation process of H2S/HS and the H diffusion process is probed by a climbing image nudged elastic band (CI-NEB) method,[49] and the frequency of the transition state is checked to make sure there is only one virtual frequency. The formulas for adsorption/dissolution energy (Eads/dis), ZPE correction, differential charge density (DCD), activation energy barrier (Ea), reaction heat (ΔE), and energy barrier splitting are all described in our published papers.[50]

Conclusions

Vacancy defects are inherent point defects of materials. Two kinds of vacancy defects on the FeS(001) surface can affect the adsorption/dissociation of H2S and the H diffusion process. In our work, the impact of VFe and VS on the adsorption/dissociation and diffusion of H2S was calculated using the DFT-D2 method. In our calculation, VFe did not change the stable adsorption site and adsorption configuration of H2S but promoted the dissociation process of H2S. Compared with the perfect surface (2.08 eV), the dissociation energy barrier of H2S was reduced to 1.56 eV. Meanwhile, VFe also slightly hindered the dissociation process of HS. VS significantly promotes the adsorption and dissociation process of H2S, which not only reduces the dissociation energy barriers of H2S and HS to 0.07 and 0.11 eV, respectively, but also changes the dissociation process of H2S from an endothermic process to a spontaneous exothermic one. In addition, VFe and VS have different influence mechanisms on the H atom diffusion process. VFe provides a barrier-free diffusion channel for the diffusion process of H atoms, so the H diffusion process is more accessible. But the presence of VS binds H atoms to VS and hinders the diffusion of H atoms from the surface to the matrix. Compared with the perfect FeS(001) surface, the energy barriers of the rate-limiting step of H diffusion from the surface into the matrix on the vacancy-defective-Fe and vacancy-defective-S FeS(001) surfaces are 0.26 and 1.89 eV, respectively. In the end, according to the calculation results, we propose that there is almost no S vacancy defect existing on the FeS(001) surface in a corrosive environment. Our research provides a theoretical basis for understanding the influence of vacancy defects on the adsorption, dissociation, and diffusion processes of H2S in FeS. Meanwhile, it can also provide a theoretical basis for the formation, transformation, and further corrosion of iron sulfide compounds. This may encourage scholars to conduct further experimental research and verification.