First ‐ Principles Study on the Adsorption Characteristics of Corrosive Species on Passive Film TiO 2 in a NaCl Solution Containing H 2 S and CO 2

: The adsorption characteristics of corrosive anions (Cl − , HS − , S 2 − , HCO 3 − and CO 32 − ) on TiO 2 of TC4 titanium alloy in a NaCl solution containing H 2 S and CO 2 were studied by density functional theory (DFT). The stable adsorption configuration of each corrosive species on the TiO 2 (110) surface was obtained by geometric optimization, and the electronic structure and interface binding energy were calculated and analyzed. The results showed that the optimal adsorption positions of Cl − , HS − , S 2 − , HCO 3 − and CO 32 − on TiO 2 (110) were all bridge positions. There was a strong charge interaction between the negatively charged Cl, S and O atoms in Cl − , HS − , S 2 − , HCO 3 − and CO 32 − and the posi ‐ tively charged Ti atoms of TiO 2 . The interface bonding was mainly caused by charge movement from around Ti atoms to around Cl, O, S atoms. The energy levels were mainly caused by the elec ‐ tron orbital hybridization of Cl ‐ 3p 5 , S ‐ 3p 4 , O ‐ 2p 4 and Ti ‐ 3d 2 . All adsorption configurations were chemical adsorption. The order of influence of the five ions on the stability of TiO 2 was S 2 − > CO 32 − > Cl − > HS − > HCO 3 − . Finally, a novel corrosion mechanism was proposed to illustrate the dynamic evolution processes of pits.


Introduction
In the process of oil and gas exploitation and transportation, corrosive media such as H2S, CO2 and Cl − are often encountered, oil country tubular goods (OCTGs) will suffer from corrosion, which is sometimes serious, and the cost of corrosion is increasing daily [1]. According to statistics, the consumption of the petroleum industry is approximately CNY 10 billion for OCTG every year in China, and most of these expenses are caused by corrosion [2,3]. With the rapid development of the petroleum industry, drilling conditions are becoming increasingly severe. The common materials used in oil and gas fields, such as carbon steel and conventional stainless steel, have been unable to meet the needs for the technical development of modern drilling and the extraction and transportation of oil and gas [4][5][6].
Titanium alloy has been widely used in many fields because of its high strength-toweight ratio, its excellent mechanical properties and its good corrosion resistance [7][8][9][10][11][12][13][14][15]; among them, the excellent corrosion resistance is attributed to the spontaneous oxide passive film (TiO2) on the surface of titanium alloy [16,17]. The stability of the passive film on the surface of titanium alloy exposed to the working environment depends on its electronic properties, which are closely related to the electrochemical reactivity and the redox reaction at the metal/oxide interface [9].
The passive film on titanium alloy is only a few nanometers thick, and the adsorption characteristics of corrosive species such as Cl − , HS − and HCO3 − on the surface of corrosionresistant alloys have only been studied on a limited basis. Therefore, it is difficult to study the thermodynamic stability of the interface between the passive film and the solution and to further study the electronic structure, bonding type and bonding strength after adsorption on the surface of passive film only by experimental means. First-principles calculations, especially the density functional theory (DFT) method, can link the microscopic properties of metal materials with their structural and thermodynamic properties, providing a powerful tool for the study of adsorption systems [18]. Fu [19] found that the adsorption capacity of H2S at the top and bridge positions on the Mo2C (001) surface was also weak, with adsorption energies of 23.23 kcal/mol and 26.12 kcal/mol, respectively. Lin [20] believed that when CO molecules were adsorbed on the surface of SiC (111), the adsorption of O atoms in CO molecules in the vertical direction of Si atoms was the most stable, and the adsorption energy was −1.24 eV. Lin [21] argued that there was almost no charge transferred from the SiC (111) surface to the CH4 molecule during the adsorption of CH4 on the SiC (111) surface, and it could be seen that the adsorption mechanism was physical adsorption based on the diagram of the electron density difference and the density of states.
Therefore, the adsorption characteristics (electronic structure and interfacial binding energy) of corrosive ions (Cl − , HS − , S 2− , HCO3 − and CO3 2− ) on the passive film (TiO2) of TC4 titanium alloy were investigated by using the CASTEP module in the first-principles Materials Studio simulation software based on density functional theory, and the thermodynamic stability characteristics of the passive film interface on TC4 titanium alloy were obtained. Finally, the corrosion resistance mechanism of TC4 titanium alloy in a harsh corrosion environment (CO2-H2S-Cl − medium system) was revealed from the micro perspective to provide a theoretical basis for the development of titanium alloy and its applicability in oil and gas fields.

Modeling and Computing
TiO2 is a metal oxide semiconductor with polycrystalline properties [22], and it has three types of crystalline structures: rutile, anatase and brookite. They are all composed of octahedral structures, but their arrangement, linkage and lattice structure are different [23]. Rutile TiO2 belongs to the tetragonal crystal system structure, and its space group is P42/MNM [24], as shown in Figure 1a, around which each octahedron is connected to ten octahedrons, with two common edges and eight common apex angles. Each protocell consists of two TiO2 molecules, and thus, the molecular formula is Ti2O4. Anatase TiO2 belongs to the tetragonal crystal system structure, as shown in Figure 1b. Each octahedron is connected to eight octahedrons, with four common sides and four common apical angles. Each primitive cell consists of four TiO2 molecules, and thus, the molecular formula is Ti4O8. Brookite TiO2 belongs to the orthorhombic crystal system, as shown in Figure 1c. Each primitive cell consists of six TiO2 molecules, and thus, the molecular formula is Ti6O12.
The rutile phase is stable under atmospheric conditions and is also the main component phase of passive films on titanium alloys. Burnside and Labat [25,26] simulated the relative energy of rutile TiO2 (110), (100) and (001) crystal faces and found that the relative energy of the TiO2 (110) crystal face was the lowest and most stable. Studies have shown that the (110) crystal face of TiO2 was the close-packed surface and the thermodynamically stable surface with the lowest energy [27,28]. Zhao [29] also obtained that the rutile phase characteristic peak was the (110) face by XRD analysis and found that the 0.320 nm lattice fringes shown in the sample correspond to the (110) face of the rutile phase through HR-TEM. Therefore, the (110) crystal face of rutile TiO2 was selected for the first-principles calculation in this paper.

Modeling
The interface characteristics of all the adsorption models were calculated by the CASTEP module based on density functional theory (DFT) in Material Studio software [30,31]. Taking full account of the degree of conformity with the actual situation, the actual calculation strength of the server and the calculation requirements of CASTEP, the supercell structure of the TiO2 (110) face in three-dimensional space with 2 × 1 × 1 periodic boundary conditions was established. To avoid the interaction between the plates, a vacuum region of 15 Å was added between the plates. Figure 2 shows the interface models of different corrosive species (Cl − , HS − , S 2− , HCO3 − and CO3 2− ) at three adsorption positions (top, bridge and hole) on the TiO2 (110) crystal face.

Computational Methods
The PBE functional form under the generalized gradient approximation (GGA) was used for all calculations, and the ultrasoft pseudopotential self-consistent field (SCF) was used to construct the pseudopotential [32][33][34]. The plane wave cutoff energy was 425 eV, and the self-consistent iteration was 500 times. The convergence accuracy was 2 × 10 −6 eV/atom, the force converged to 0.03 eV/atom, the stress deviation was less than 0.08 GPa, the tolerance deviation was less than 0.005 and the value of the k point in the Brillouin zone was 4 × 4 × 1.

Optimum Structure and Stable Adsorption Configuration
(1) Optimum structure Table 1 is a comparison of the lattice constants of the rutile TiO2 in this paper to those in the literature [35]. The errors of "a" and "c" were only ±0.02% and ±0.07%, respectively, indicating that the constructed model conformed to the actual requirements. (2) Stable adsorption configuration Since each atom in the nonrelaxation state of TiO2 is fixed, it is equivalent to the mechanical accumulation in a specific position. However, the atoms in the relaxation state of TiO2 can move within the crystal cell. After the geometric optimization of the adsorption structures with corrosive species adsorbed on the surface of TiO2, an optimal position was needed, in which the energy of the system was the lowest-that is, the system was the most stable at this time. Therefore, the geometries of all adsorption positions were optimized to select the most stable adsorption configuration. Table 2 shows the final energies of Cl − , HS − , S 2− , HCO3 − and CO3 2− at each adsorption position (top, bridge and hole) on the TiO2 (110) crystal face after geometric optimization.
The final energies of Cl − , HS − , S 2− , HCO3 − and CO3 2− at the bridge position on the TiO2 (110) crystal face were the lowest; the lower the total cell energy is, the more stable the cell structure is [36]. Therefore, the optimal adsorption positions of Cl − , HS − , S 2− , HCO3 − and CO3 2− on the TiO2 (110) surface were all bridge positions, and the final energy order of the corrosive species at the bridge position on the TiO2 (110) crystal face was S 2− > HS − > Cl − > CO3 2− > HCO3 − . Figure 3 shows the charge density distributions of Cl − , HS − , S 2− , HCO3 − and CO3 2− at the bridge position on the TiO2 (110) crystal face, which can directly reflect the bonding characteristics between atoms [37].

Electron Density
As shown in Figure 3, when the adsorption of corrosive species on the TiO2 (110) surface reached a stable state, there was a strong charge interaction between the Cl atoms in Cl − , the S atoms in HS -, the S atoms in S 2− , the O atoms in HCO3 − , the O atoms in CO3 2− and the Ti atoms on TiO2 [38]. The red region represents a large density of electrons, which is an active region available for chemical reactions. The deeper the color of the red, the larger the charge density [39]. Interface bonding [40] mainly occurred between the negatively charged atoms in the anion and the positively charged Ti atoms in the TiO2 (110) crystal face. Table 3 shows the charge number of the negatively charged atoms in each corrosive species. The absolute value order of the charge number of Cl atoms in the Cl − , S atoms in HS − , the S atoms in S 2− , the O atoms in HCO3 − and the O atoms in CO3 2− was S 2− > CO3 2− > Cl − > HS − > HCO3 − . The charge density represents the number of valence electrons in a volume of pure physical space, and the larger the charge density is, the easier the ions are adsorbed on the metal surface, resulting in the stronger corrosive effect of the ions on the passive film. Therefore, the stability of TiO2 in the medium containing S 2− was the worst, followed by CO3 2− , Cl − , HS − and HCO3 − .

Electron Density Difference
The electron density difference can verify the relevant conclusions of the charge density diagram and more intuitively observe the charge transfer before and after adsorption [41] and the bonding situation [42]. The analysis of the electron density difference was conducted on the steady-state adsorption configuration of Cl − , HS − , S 2− , HCO3 − and CO3 2− adsorbed at the crystal plane bridge position of TiO2 (110), as shown in Figure 4. When the adsorption of corrosive species on the TiO2 (110) surface reached a stable state, there was an obvious charge transfer phenomenon between the Cl atoms in Cl − , the S atoms in HS − , the S atoms in S 2− , the O atoms in HCO3 -, the O atoms in CO3 2− and the Ti atoms on the surface of TiO2. In addition, the charge accumulation and electronegativity around the negatively charged atoms in the species decreased, while the charge dissipation and electronegativity around the Ti atoms increased. The interface bonding mainly existed between the Cl atoms in Cl − , the S atoms in HS -, the S atoms in S 2− , the O atoms in HCO3 − , the O atoms in CO3 2− and the Ti atoms. The bonding was mainly caused by the charge moving from around the Ti atom to around the Cl atom in Cl − , the S atom in HS − , the S atom in S 2− , the O atoms in HCO3 − and the O atoms in CO3 2− .

Density of States
The electron transfer of the interaction between atoms mainly occurs with the valence electrons of each atom. To further investigate the nature of electronic interactions in interface bonding after adsorption and understand the contribution of the electrons of each element to the total density of states of the alloy [43], partial density of states (PDOS) analysis of the steady-state adsorption configurations of Cl − , HS − , S 2− , HCO3 − and CO3 2− at the bridge position of the TiO2 (110) crystal face was carried out, as shown in Figure 5.  Figure 5 shows that there was a certain degree of charge interaction between the Cl atoms in Cl − , the S atoms in HS − , the S atoms in S 2− , the O atoms in HCO3 − and the O atoms in CO3 2− with the Ti atoms on the surface of TiO2, indicating that the adsorption processes were all chemisorption [44]. The charge interactions took place near −6 eV and 0.5 eV~1.5 eV, 0.5 eV~1.5 eV, −6 eV and 0.5 eV, 1 eV, −10.5 eV and −6 eV and 0.5 eV, respectively, which were mainly formed by the hybrid orbitals between the 3d 2 electrons of Ti and the 3p 5 electrons of Cl, the 3p 4 electrons of S and the 2p 4 electrons of the O atoms. Therefore, after the adsorption of Cl − , HS − , S 2− , HCO3 − and CO3 2− on the TiO2 (110) crystal surface, the interface bonding was mainly caused by the electronic orbital hybridization of Cl-3p 5 , S-3p 4 , O-2p 4 and Ti-3d 2 , and the bonding energy levels of the Cl − , HS − , S 2− , HCO3 − and CO3 2− ions were mainly located near the corresponding charge position mentioned above.

Interface Binding Energy
The stability of the interface can be quantitatively determined by the interface binding energy to determine the corrosion attack of corrosive species in the solution on metallic materials. The calculation equation of the interface binding energy is as follows [35]: (1) where Et is the total energy of the entire adsorption system after geometric optimization, Em is the energy of the TiO2 (110) system and Ei is the energy of the corrosive medium system (Cl − , HS − , S 2− , HCO3 − and CO3 2− ). Table 4 shows the final energies of the single Cl − , HS − , S 2− , HCO3 − , CO3 2− and TiO2 (110) models after geometric optimization. The binding energies of the Cl − , HS − , S 2− HCO3 − , CO3 2− and TiO2 (110) surfaces at bridge positions were obtained by Tables 2 and 4, as shown in Table 5. Table 5 shows that, compared with Cl − , HS − , HCO3 − and CO3 2− , it was easier for S 2− to bind and react with TiO2, indicating that S 2− had strong adsorption on the TiO2 (110) surface. The interface binding energy is an important parameter to characterize the interface thermodynamic stability; the smaller the value is, the more stable the interface structure is [35]. Therefore, the stability of TiO2 in this environment containing S 2-was the poorest. The binding energy order of Cl − , HS − , S 2− , HCO3 − and CO3 2− with the TiO2 (110) surface was S 2− > CO3 2− > Cl − > HS − > HCO3 − . The stability of TiO2 in the environments containing Cl − , HS − , S 2− , HCO3 − and CO3 2− was S 2− < CO3 2− < Cl − < HS − < HCO3 − , which is in good accordance with the electron density results.

Corrosion Mechanism
According to the above study, when corrosive ions (Cl − , HS − , S 2− , HCO3 − and CO3 2− ) adsorbed on the TiO2 (110) surface, their order of corrosion attack on the TiO2 (110) surface was S 2− > CO3 2− > Cl − > HS − > HCO3 − . The corrosion resistance of TiO2 in the environment containing H2S was the worst, followed by CO2, and the stability of TiO2 in the environment containing Cl − was better than the former two. In addition, the TC4 titanium alloy would suffer more serious corrosion in the CO2-H2S-Cl − system due to the interaction between corrosive ions. The corrosion mechanism of the TC4 titanium alloy in the NaCl solution containing H2S and CO2 is shown in Figure 6. The following is the specific reaction process of each corrosive ion (Cl − , HS − , S 2− , HCO3 − and CO3 2− ) on the passive film of the TC4 titanium alloy surface. The specific oxidation process of titanium is as follows [45,46]: Ti 3+ e →Ti 4+ The total reaction equation is: Ti 4+ + 2O 2 →TiO 2 (7) The oxide film formed is mainly TiO2. In the environment where titanium alloy is in service, H2S will undergo an ionization reaction to ionize HS − , S 2− and H + , and the specific ionization process is as follows [47]: HS (aq) ⇌S 2 + H + (9) Obviously, the local concentration of HS − increases with increasing sulfide concentrations, and the concentration of S 2− increases with increasing HSconcentrations. The specific formation process of TiS2 is mainly manifested in two situations [46]. The first one is shown in Equation (10), and the second one may be caused by chemical reaction after the electron transfer reaction. The specific reaction process is shown in Equation (11).
Ti 4+ + 2S 2 ⇌TiS 2 (11) The corrosion of titanium alloy in a saturated CO2 water environment is also electrochemical corrosion. CO2 is dissolved in water to form H2CO3. After ionization, H2CO3 generates HCO3 − and CO3 2− . The specific reaction steps are as follows [47]:  (14) According to Equations (2)- (14) and the binding energy between the corrosive ions and the corrosive ions with the rutile TiO2 (110) surface, when the initial corrosion system only contains the NaCl medium, Cl − has a strong penetration, which can destroy the passive film TiO2 on the titanium alloy surface. However, when H2S and CO2 are introduced into the system, although Cl − has a superadsorption effect, the interfacial binding energy of Cl − between TiO2 is lower than those of S 2− and CO3 2− , and the interfacial binding energy of S 2− between TiO2 is higher than that of CO3 2− . The literature showed that, in a corrosive environment where CO2 and H2S coexisted, the chemical adsorption capacity of HS − was stronger than that of HCO3 − [48].
Therefore, S 2− will first exclude Cl − and show a high concentration on the surface of the passive film. At this time, the damage of S 2− on the titanium alloy surface passive film TiO2 is stronger than that of Cl − . Therefore, TiO2 firstly reacts with H2S (or its hydrolysate) in the interface between the bulk solution and the metal matrix to form TiS2. At the same time, HSand S 2− ionized by H2S can promote the formation of TiS2 compounds [45]. TiS2 is mainly contained in the outer layer of the passive film. However, the source of some TiS2 can be attributed to the competition of sulfur and oxygen for titanium bond orbitals, which is actually a central issue [49]. Since S and O are elements in the same main group, S more easily replaces O in passive film TiO2. That is, the nucleation and growth of partial TiS2 is a process of replacing Ti-O bonds with Ti-S bonds [49]. Some researchers believe that the formation of sulfides on metals is much faster than the formation of corresponding oxides [50].
When the formed corrosion scale TiS2 is deposited on the substrate surface and reaches a certain saturation state, the formation of the corrosion scale TiS2 gradually replaces the passive film TiO2. At the moment, CO3 2− ionized from H2CO3 formed by CO2 dissolved in water will act on TiO2 to generate titanium carbonate. As a typical weak acid and alkali salt, titanium carbonate is easily hydrolyzed, but it will cause the dissolution of passive film or corrosion product film. Therefore, the existence of CO2 will promote the dissolution of the TiS2 film, destroy the structure of the TiS2 film as well as the integrity of the passive film and corrosion scale and further erode the metal matrix.
H2CO3 formed by CO2 dissolved in water provides a further acidified environment for Cl − corrosion attack, resulting in a significant decrease in the stability of the passive film (or corrosion product film) in an acidic medium. At the same time, Cl − itself has a corresponding influence on the formation of the corrosion product layer [51]. With the influence of H2CO3, Cl − further destroys the integrity of TiS2 on the metal matrix and accelerates the dissolution of the matrix [52], resulting in an increase in the number and depth of corrosion pits. The above discussion is consistent with the experimental results in the relevant literature: compared with the CO2 corrosion environment in formation water, the passive film on the surface of titanium alloy is more vulnerable to damage in the water solution containing the H2S corrosion medium [35]. Therefore, TC4 titanium alloy will suffer serious corrosion in the environment containing H2S, followed by the environment containing CO2, and it has relatively good corrosion resistance to Cl − . When the corrosions H2S, CO2 and Cl − coexist in the corrosion medium, TC4 titanium alloy will suffer more serious corrosion. Data Availability Statement: Not applicable.