Oxidation and hydrogenation of monolayer MoS2 with compositing agent under environmental exposure: The ReaxFF Mo/Ti/Au/O/S/H force field development and applications

An atomistic modeling tool is essential to an in-depth understanding upon surface reactions of transition metal dichalcogenides (TMDs), such as molybdenum disulfide (MoS₂), with the presence of compositing agents, including Ti and Au, under different environmental exposures. We report a new ReaxFF reactive force field parameter set for Mo, Ti, Au, O, S, and H interactions. We apply the force field in a series of molecular dynamics (MD) simulations to unravel the impact of the Ti dopant on the oxidation/hydrogenation behaviors of MoS₂ surface. The simulation results reveal that, in the absence of Ti clusters, the MoS₂ surface is ruptured and oxidized at elevated temperatures through a process of adsorption followed by dissociation of the O₂ molecules on the MoS₂ surface during the temperature ramp. When the MoS₂ surface is exposed to H₂O molecules, surface hydrogenation is most favored, followed by oxidation, then hydroxylation. The introduction of Ti clusters to the systems mitigates the oxidation/hydrogenation of MoS₂ at a low or intermediate temperature by capturing the O₂/H₂O molecules and locking the O/H-related radicals inside the clusters. However, OH⁻ and H₃O⁺ are emitted from the Ti clusters in the H₂O environment as temperature rises, and the accelerating hydrogenation of MoS₂ is consequently observed at an ultra-high temperature. These findings indicate an important but complex role of Ti dopants in mitigating the oxidation and hydrogenation of MoS₂ under different environmental exposures. The possible mechanisms of oxidation and hydrogenation revealed by MD simulations can give an insight to the design of oxidation resistant TMDs and can be useful to the optical, electronic, magnetic, catalytic, and energy harvesting industries.

1 Introduction

Lamellar solids exhibit low friction due to the low shear strength resulting from weak van der Waals interactions between lamellae (Spalvins, 1987; Scharf and Prasad, 2013; Ouyang et al., 2022). Lamellar solids, such as transition metal dichalcogenides (TMDs), are not only candidates for solid lubricants utilized in extreme environments, but also considered promising semiconductor materials (Street, 2009; Liu et al., 2011; Radisavljevic et al., 2011; Marian et al., 2022). The stability of the two-dimensional (2D) structure of lamellar solids is important in terms of maintaining their desired properties and long-term functionalities, e.g., tribological response (Hilton and Fleischauer, 1992; Curry et al., 2016; Vazirisereshk et al., 2019). However, the mechanism of lamellar degradation is still not well understood. This work aims to reveal the mechanisms of the thermal degradation of molybdenum disulfide (MoS₂), a typical solid lubricant material, in the presence of oxygen (O₂) and water molecules (H₂O).

Several thermal etching mechanisms have been proposed to explain the oxidation of MoS₂ crystals (Szoszkiewicz, 2021). Oxidation products, such as MoO₃, were detected at room temperature at the edges of layered MoS₂ flakes (Walter et al., 2017). In the basal planes of MoS₂, the O atoms could directly bond with Mo atoms at temperatures higher than 300°C (Yamamoto et al., 2013; Wu et al., 2013; Zhou et al., 2013; Ukegbu and Szoszkiewicz, 2019). In the presence of H₂O, however, the volatile species, such as MoO₂(OH)₂, were expected to emerge at temperatures higher than 300°C, leading to more rapid MoS₂ oxidation compared to that in dry air conditions (Walter et al., 2017). In addition to volatile oxidation products, the presence of H₂SO₄ as well as sulfur oxides at temperatures above 400°C was proposed (Ross and Sussman, 1955). The passivation layer of MoO₃ forms at temperatures lower than 500°C, while amorphous Mo oxides and MoO_x clusters appeared above 500°C (Szoszkiewicz et al., 2020; Rogala et al., 2021; Park et al., 2021a). These alterations to the MoS₂ surface upon oxidation in humid environments were detrimental to desired tribological behaviors of MoS₂ thin films. Curry et al. (2017) investigated the oxidation behavior of various microstructures of MoS₂ thin films and the effects on the shear strength between MoS₂ basal planes. It was shown that films with ordered microstructures were resistant to both O atoms and O₂ molecules at even elevated temperatures, while amorphous microstructures provided more edge sites for O atoms and O₂ to penetrate and react throughout the depth of the film. Such findings imply that controlling the number of edges during the epitaxial growth of TMD thin films leads to robust stability of as-grown 2D materials. Apart from growth control, the introduction of compositing agents, such as Ti and Au, has been demonstrated to mitigate the detrimental effects of oxidation to TMD thin films in humid environments (Colas et al., 2015; Li et al., 2017). The underlying mechanism responsible for the improved resistance to the oxidation and humidity has been reported to be a sacrificial effect of dopant metals, protecting the MoS₂ from interacting with O₂ and H₂O molecules.

Since the microstructure of MoS₂ as well as the presence of Ti in the system, plays an important role in resistance to oxidation and humidity, we developed a new ReaxFF parameter set describing Mo, Ti, O, S, and H interactions. A series of molecular dynamics (MD) simulations were performed at different temperatures with the presence of O₂ and H₂O molecules. The simulation results reveal several possible kinetic pathways of the oxidation of the MoS₂ surface when exposed to O₂ molecules, and the hydrogenation or hydroxylation when exposed to H₂O molecules. The same series of simulations were also performed with the introduction of Ti clusters to the systems to identify the mechanisms responsible for the prevention of oxidation/hydrogenation by the Ti clusters.

2 Computational methods

2.1 ReaxFF force field

Reactive force field (ReaxFF) uses the bond order formalism to treat reactive chemical systems, where bond order is described as a continuous function of interatomic distance (van Duin et al., 2001). Unlike classical force fields that adopt a static bond assumption, ReaxFF updates bond orders at every iteration and allows energetic contributions to disappear upon bond dissociation. Thus, ReaxFF can describe reactive events involving bond formation and breakage with no energy discontinuities over the course of simulations. The potential energy of the system is described as a sum of several partial terms (Senftle et al., 2016),

$E_{system}=E_{bond}+E_{over}+E_{val}+E_{tor}+E_{vdWaals}+E_{Coulomb}+E_{specific}(1)$

The simplest form of $E_{system}$ consists of a bond formation energy $E_{bond}$, an energetic penalty due to over-coordination $E_{over}$ based on valence rule, valence angle energy $E_{val}$, torsion energy $E_{tor}$, and nonbonded contributions from van der Waals $E_{vdWaals}$ and Coulomb $E_{Coulomb}$ interactions. The term $E_{speicific}$ captures properties tied to specific systems, such as corrections for lone pairs, hydrogen binding etc. The empirical parameters of ReaxFF are trained against quantum mechanical (QM) calculations, that allow for transferring the accuracy of QM methods to much larger systems with a much lower computational cost.

Recent ReaxFF force fields have been validated and extensively applied to modeling carbon materials (Mao et al., 2022; Mao et al., 2020; Kowalik et al., 2019; Rajabpour et al., 2021a; Zhang et al., 2020; Vashisth et al., 2020), 2D materials (Curry et al., 2021; Rajabpour et al., 2021b; Nayir et al., 2020; Nayir et al., 2021a; Nayir et al., 2021b; Ostadhossein et al., 2017; Lele et al., 2022; Mojtabavi et al., 2021; Ganeshan et al., 2020), oxidation kinetics of MXenes (Zhao et al., 2020a; Zhao et al., 2019; Lotfi et al., 2018; Zheng et al., 2021) and multiple other materials.

2.2 Force field parameterization for ReaxFF C/H/O/S/Mo/Ti/Au

We developed a new ReaxFF reactive force field for C/H/O/S/Mo/Ti/Au interactions to study the thermal degradation, oxidation, and hydrogenation of MoS₂ in the presence of compositing agents, i.e., Ti and Au. Prior to the force field training, three ReaxFF force fields were combined for an initial attempt at parameterization. Particularly, the Ti/O/H interactions from the force field ReaxFF Ti/O/H (Raju et al., 2013) and the Au/O/S/C/H interactions from the force field ReaxFF C/H/O/S/Au (Monti et al., 2016) were incorporated into a refitted force field based on ReaxFF Mo/S/O/H (Islam et al., 2014) on the aqueous branch. Then, we trained the C/H/O/S/Mo/Ti/Au parameter set against non-periodic DFT data using Jaguar (Bochevarov et al., 2013) at the B3LYP/LACV3P++** level of theory due to the presence of heavy atoms, i.e., Mo, Au, specifically on bond dissociations of Ti-S, Au-S, and S-H as well as angular distortions of S-Ti-S, Ti-S-H, Ti-S-Ti, Ti-S-Mo, Au-S-Mo, Au-S-H, and H-S-H, drawn from the single molecules of Ti(SH)₄, Ti(SH)₃-S-Ti(SH)₃, Ti(SH)₃-S-Mo(SH)₃, AuSH, Au-S-Mo(SH)₃, and H₂S. In addition, the dissociation energy of Ti(SH)₃ and SH radicals from Ti(SH)₄ and the reaction energies of Ti(SH)₃-S-Ti(SH)₃, Ti(SH)₃-S-Mo(SH)₃, and Au-S-Mo(SH)₃ with H₂S were computed at the DFT level by using Eqs 2–5

$E_{{\mathrm{T}\mathrm{i}\left(\mathrm{S}\mathrm{H}\right)}_4}-\left(E_{{\mathrm{T}\mathrm{i}\left(\mathrm{S}\mathrm{H}\right)}_3}+E_{\mathrm{S}\mathrm{H}}\right)(2)$

$\left(E_{{\mathrm{T}\mathrm{i}\left(\mathrm{S}\mathrm{H}\right)}_3-\mathrm{S}-{\mathrm{T}\mathrm{i}\left(\mathrm{S}\mathrm{H}\right)}_3}+E_{{\mathrm{H}}_2\mathrm{S}}\right)-{2E}_{{\mathrm{T}\mathrm{i}\left(\mathrm{S}\mathrm{H}\right)}_4}(3)$

${(E}_{{\mathrm{T}\mathrm{i}\left(\mathrm{S}\mathrm{H}\right)}_3-\mathrm{S}-{\mathrm{M}\mathrm{o}\left(\mathrm{S}\mathrm{H}\right)}_3}+E_{{\mathrm{H}}_2\mathrm{S}})--(E_{{\mathrm{T}\mathrm{i}\left(\mathrm{S}\mathrm{H}\right)}_4}+E_{{\mathrm{M}\mathrm{o}\left(\mathrm{S}\mathrm{H}\right)}_4})(4)$

${(E}_{\mathrm{A}\mathrm{u}-\mathrm{S}-{\mathrm{M}\mathrm{o}\left(\mathrm{S}\mathrm{H}\right)}_3}+E_{{\mathrm{H}}_2\mathrm{S}})--(E_{\mathrm{A}\mathrm{u}\mathrm{S}\mathrm{H}}+E_{{\mathrm{M}\mathrm{o}\left(\mathrm{S}\mathrm{H}\right)}_4})(5)$

During the parameterization, a single-parameter search technique was utilized to minimize the error of the sum of squares (Chenoweth et al., 2008). The comparisons of relative bond and angle energies between the parameterized ReaxFF data and DFT data are depicted in Figure 1, showing good agreement around their equilibrium positions. The ReaxFF and DFT predicted dissociation and reaction relative energies are shown in Supplementary Figure S1, where the energy difference between DFT and ReaxFF falls within 5 kcal/mol. It should be noted that the basis set superposition error (BSSE) may be a problem when small basis sets, such as LACV3P++** for our systems, are used. However, as reported by Schneebeli et al. (Schneebeli et al., 2011), the average BSSE on a gigantic data set is ∼4 kcal/mol for B3LYP/LACVP. For this reason, we typically assume that DFT methods can overestimate/underestimate the energies within the range of 5 kcal/mol due to intrinsically present errors. Since we reach an energy difference between ReaxFF and DFT calculated data within 5 kcal/mol, we assume the energies meet sufficient accuracy.

FIGURE 1

FIGURE 1. Comparisons of relative bond and angle energies between ReaxFF and QM computed data for (A) Ti-S bond in Ti(SH)₄, (B) S-Ti-S angle in Ti(SH)₄, (C) Ti-S-H angle in Ti(SH)₄, (D) H-S-H angle in H₂S, (E) Ti-S-Ti angle in Ti(SH)₃-S-Ti(SH)₃, (F) Ti-S-Mo angle in Ti(SH)₃-S-Mo(SH)₃, (G) Au-S bond in Au-S-H, (H) Au-S-H angle in Au-S-H, and (I) Au-S-Mo angle in Au-S-Mo(SH)₃.

The accuracy and transferability of this newly developed force field were validated by benchmarking small MD simulations on surface reactions of MoS₂ with compositing Ti and Au clusters at ambient conditions in order to compare with experimental measurements and DFT calculations in the literature (Wu et al., 2019; Freedy et al., 2019; Szoszkiewicz, 2021; Merida et al., 2018; Liu et al., 2020). In addition, the developed force field exhibits better performance of describing M/O crystalline systems than that using the previously reported parameters (Ostadhossein et al., 2017; Hong et al., 2017; Chen et al., 2020).

2.3 ReaxFF molecular dynamics simulation steps

In this work, we investigated the surface reactions of monolayer MoS₂ with Ti clusters exposed to gas-phase molecules at elevated temperatures. We used two MoS₂ substrates, pristine MoS₂ (P-MoS₂) and defective MoS₂ with 5% S-vacancies (D-MoS₂). The defects we created are neutral S-vacancies, which are the most stable MoS₂ defects experimentally measured in low-pressure conditions. Note that although ReaxFF allows for charge transfer between defected sites and gas phase molecules or compositing agents with Electronegativity Equalization Method, it is typically used to describe neutral defects in MD simulations.

We designed the following eight systems to study the impact of defects, gas-phase molecules, i.e., O₂ and H₂O, and Ti clusters on the oxidation and hydrogenation behaviors of MoS₂. Details of the eight systems and the nomenclatures are given in Table 1.

TABLE 1

TABLE 1. The eight systems designed to study the oxidation and hydrogenation mechanisms of the MoS₂ surface with respect to the effects of defects, gas-phase environments, and compositing agents (Ti clusters).

The monolayer 2H-phase MoS₂ contained 225 Mo atoms and 450 S atoms in a periodic hexagonal supercell (α = β = 90°, γ = 120°) with the lattice parameters of a = b = 49.8 Å, c = 80.0 Å for the systems without Ti clusters and c = 97.0 Å for the systems with Ti clusters. The length of c for the systems with Ti clusters was elongated in order to ensure consistency of gas densities among the systems. We deleted 22 S atoms from the P-MoS₂ to create a D-MoS₂, with 11 S atoms randomly removed from the top surface and another 11 S atoms randomly removed from the bottom surface, amounting to 5% vacancies. The 10 Ti₂₀ clusters were placed near the MoS₂ surface, with 5 clusters randomly distributed within a 5–10 Å spacing from the top surface and another 5 clusters randomly distributed within a 5–10 Å spacing from the bottom surface. The initial configuration of a Ti₂₀ cluster was obtained via an annealing treatment. For this, we randomly placed 20 elemental Ti atoms in an orthogonal box (a = b = c = 80.0 Å, α = β = γ = 90°), heated at 1,800 K for 200 ps in an NVT ensemble, allowing the Ti atoms to cluster and reorganize, and finally we ran an energy minimization after cooling to 300 K, to release internal stresses. We introduced 200 O₂ or H₂O gas molecules to the systems, evenly distributed on the top and bottom surfaces of the monolayer MoS₂. For the systems without Ti clusters, the gas density was kept at ∼0.062 g/cm³ for O₂-containing systems and at ∼0.035 g/cm³ for H₂O-containing systems. These densities of O₂ and H₂O are one order of magnitude higher than the atmospheric air density (at 101.325 kPa and 15°C). However, since we aim to understand the MoS₂ surface reactions individually with O₂ or H₂O, it is crucial to place the MoS₂ in each gas-phase environment with a relatively high density to enable more extensive surface-gas interactions in our nanosecond-scale simulations.

After energy minimization, we equilibrated the systems at 300 K in an NVT ensemble for 500 ps so that they could be fully relaxed. Subsequently, these eight systems were heated to 3,000 K with a rate of 10 K/ps in an NVT ensemble. The time step was set to be 0.1 fs in order to prevent unphysically wide oscillations of covalent bonds at high temperatures. It should be noted that the temperature-dependent measurements of oxidation of monolayer MoS₂ usually take place at a temperature below 1,500 K in experiments (Park et al., 2021b; Grønborg et al., 2019; Walter et al., 2017). However, exposure to extreme space-terrestrial environments or operating conditions can lead to instantaneous ultra-high temperatures for MoS₂ (Voevodin and Zabinski, 2005; Li et al., 2021). On the other hand, such a wide temperature range provides a better insight into temperature-dependent oxidation and hydrogenation mechanisms of MoS₂, as MoS₂ readily reacts with O₂ but does not volatilize above 1,500 K from MD simulations (Rahman et al., 2021; Farigliano et al., 2020; Jo et al., 2020). For the statistical calculations, the six configurations, represented by different coordinates and velocities, were saved every 10 ps prior to the temperature ramp for each of the eight systems. In post-processing, we computed the mean values and the standard deviations from the forty-eight trajectories that were recorded during the temperature ramp.

We also performed size-dependent studies of the Ti clusters, with an aim of understanding the mechanisms mitigating oxidation and hydrogenation in O₂- and H₂O-rich environments. We designed six models by randomly inserting an increased number of O₂ or H₂O molecules around a Ti cluster with varying size. Details of the six models and the nomenclatures are given in Table 2. The six Ti clusters were placed in an orthogonal box, with a_1,4 = b_1,4 = c_1,4 = 20.0 Å, a_2,5 = b_2,5 = c_2,5 = 50.0 Å, a_3,6 = b_3,6 = c_3,6 = 100.0 Å, and α = β = γ = 90°, so that all systems have a comparable density. The six systems were separately annealed at 300 K for 500 ps in an NVT ensemble and then heated up from 300 K to 1,000 K with a rate of 10 K/ps. Lastly, these systems were annealed at 1,000 K for another 500 ps in an NVT ensemble. All courses of ReaxFF MD simulations were carried out with the use of Amsterdam Modeling Suite (AMS) (ReaxFF 2022.1 and SCM, 2022).

TABLE 2

TABLE 2. The six models designed to study the anti-oxidation and anti-hydrogenation mechanisms of Ti clusters of varying size.

From the ReaxFF literature, a bond order cutoff of 0.3–0.5 is commonly used for the recognition of molecule fragmentation (Wang et al., 2020; Wang et al., 2022; Hahn et al., 2018; Liu et al., 2021). We determine the cutoff bond lengths through the bond scan technique with an increment of 0.1 Å, where a cutoff bond length is computed as the bond order between the two target atoms is reduced to 0.5. Therefore, the cutoff bond lengths for Mo-S, Mo-O, Mo-H, Ti-S, Ti-O, S-H, and O-H can be derived and applied to data post-processing. Namely, cutoff_Mo-S = 3.0 Å, cutoff_Mo-O = 2.1 Å, cutoff_Mo-H = 2.3 Å, cutoff_Ti-S = 3.5 Å, cutoff_Ti-O = 2.2 Å, cutoff_S-H = 2.1 Å, and cutoff_O-H = 1.5 Å. The Visual Molecular Dynamics (VMD) (Humphrey et al., 1996) and the Open Visualization Tool (OVITO) (Stukowski, 2009) were used to display molecular structures and perform trajectory analyses.

3 Results and discussion

3.1 Thermal degradation, oxidation and hydrogenation of MoS₂

We investigate the roles of O₂ and H₂O individually in MoS₂ surface reactions, both with and without Ti₂₀ clusters. Mo, S, O, and H atoms are tracked over a temperature ramp course, from 300 K to 3,000 K. We present top-down views of the eight models listed in Table 1 to illustrate the MoS₂ lattice degradation, as also evidenced by the changes in the coordination number of Mo atoms (Figures 2, 3, Supplementary Figures S2, S3), Mo-S bond dissociation and formation, and Mo-O and Mo-H bond formation (Supplementary Figures S4, S5).

FIGURE 2

FIGURE 2. Variation of Mo atom coordination numbers during the temperature ramp with a rate of 10 K/ps, for pristine MoS₂ with O₂ (P-MoS₂ + O₂) at (B) 500 K, (C) 1,000 K, and (D) 2,000 K; pristine MoS₂ with O₂ and Ti clusters (P-MoS₂ + O₂ + Ti) at (E) 500 K, (F) 1,000 K, and (G) 2,000 K; defective MoS₂ with O₂ (D-MoS₂ + O₂) at (I) 500 K, (J) 1,000 K, and (K) 2,000 K; and defective MoS₂ with O₂ and Ti clusters (D-MoS₂ + O₂ + Ti) at (L) 500 K, (M) 1,000 K, and (N) 2,000 K. The coordination numbers for the initial configurations (at 0 K) of P-MoS₂ and D-MoS₂ are presented in (A) and (H) for reference.

FIGURE 3

FIGURE 3. Variation of Mo atom coordination numbers during the temperature ramp with a rate of 10 K/ps, for pristine MoS₂ with H₂O (P-MoS₂ + H₂O) at (B) 500 K, (C) 1,000 K, and (D) 2,000 K; pristine MoS₂ with H₂O and Ti clusters (P-MoS₂ + H₂O+ Ti) at (E) 500 K, (F) 1,000 K, and (G) 2,000 K; defective MoS₂ with H₂O (D-MoS₂ + H₂O) at (I) 500 K, (J) 1,000 K, and (K) 2,000 K; and defective MoS₂ with H₂O and Ti clusters (D-MoS₂ + H₂O+ Ti) at (L) 500 K, (M) 1,000 K, and (N) 2,000 K. The coordination numbers for the initial configurations (at 0 K) of P-MoS₂ and D-MoS₂ are presented in (A) and (H) for reference.

3.1.1 Lattice degradation and miscoordination of Mo atoms

In Figure 2, we show the lattice distortion and the coordination number variation of Mo atoms in a monolayer of MoS₂ exposed to O₂ at temperatures of 500, 1,000, and 2,000 K. The coordination numbers of the initial configurations P-MoS₂ and D-MoS₂ (i.e., prior to gas-phase exposure) are given in Figures 2A,H for comparison. The distribution of coordination numbers of Mo atoms at these temperatures can be viewed in Supplementary Figures S6A,B,D. The equilibrated monolayer MoS₂ (2H-MoS₂) lattice has hexagonal symmetry, where Mo atoms have a coordination number of six and form trigonal prismatic geometry with nearby S atoms. Thus, under-coordination (coordination number below 6) of Mo atoms indicates distortion of the MoS₂ lattice as a consequence of the Mo-S bond dissociation. On the other hand, over-coordination (coordination number above 6) of Mo atoms is used to identify reactions such as chemisorption accompanying bond formation. The variation of Mo atom coordination numbers of P-MoS₂ and D-MoS₂ in vacuum and in the absence of compositing agents is also provided as a base line for comparison, as shown in Supplementary Figures S2(a₁)–(a₁₀) and Supplementary Figures S3(a₁)–(a₁₀) respectively. The P-MoS₂ and D-MoS₂ systems present lower degree of miscoordination and better structure integrity at low and intermediate temperatures compared to the systems with gas phase molecules and Ti clusters. However, P-MoS₂ + O₂ + Ti system exhibits more 6-coordinated Mo atoms and higher crystallinity than P-MoS₂ at 900 K, where the MoS₂ plane stays flat in the former system yet the rippling of MoS₂ is found in the latter system, resulting from the dissipation of internal stress of MoS₂ with the presence of Ti_xO_y clusters. The miscoordination of Mo atoms and the lattice distortion are similar in all cases when temperature reaches 2,400 K, regardless of the presence of gas phase molecules or Ti clusters.

From Figures 2B,I, we observe that P-MoS₂ outperforms D-MoS₂ in sustaining lattice integrity in the O₂ environment at 500 K. Specifically, D-MoS₂ in Figure 2I exhibits disturbed atomic arrangement with grouped under-coordinated Mo atoms at 500 K, indicating that initially isolated S-vacancies migrate into line defects or vacancy clustering, which is energetically favored (Zhao et al., 2020b; Garcia-Esparza et al., 2022). The presence of Ti₂₀ clusters, as shown in Figure 2L, significantly reduces the oxidation-related lattice distortion, leading to the recovery of the coordination number of Mo atoms in the initial configuration of D-MoS₂. This suggests that Ti₂₀ clusters alleviate S-vacancy driven lattice degradation of MoS₂ and help keep the original Mo coordination in the O₂ environment. The higher binding energies of O and O₂ adsorbed to a Ti₂₀ cluster than to a mono S-vacancy from a monolayer MoS₂ (Supplementary Table S1) also implies that O and O₂ molecules are more prone to capture by Ti clusters than binding to S-vacancies on MoS₂. From Figures 2B–D and Figures 2I–K, we note that the lattice structure is further disturbed as temperature increases for both P-MoS₂ and D-MoS₂. The presence of Ti₂₀ clusters also mitigates thermal degradation of the lattice and the miscoordination of Mo atoms at low or intermediate temperatures (<2,000 K), as shown by the comparisons of Figures 2E–G to Figures 2B–D and Figures 2L–N to Figures 2I–K, or as can be seen more clearly in Supplementary Figures S2(c₁)–(c₆) compared with Supplementary Figures S2(b₁)–(b₆) and Supplementary Figures S3(c₁)–(c₆) compared with Supplementary Figures S3(b₁)–(b₆). However, when the temperature is raised to 2,700 K, the lattice distortion and the miscoordination of Mo atoms are similar in all cases with the presence of O₂, as shown in Supplementary Figures S2, S3(b₉), (b₁₀), (c₉), and (c₁₀).

The conclusions are similar for the H₂O environment, namely that 1) the migration and clustering behaviors of S-vacancies occur at elevated temperatures; 2) Ti₂₀ clusters are capable of constraining the fluctuation of Mo coordination number; 3) Ti₂₀ clusters maintain the lattice structure of P-MoS₂ and attenuate the miscoordination of Mo atoms when temperature does not exceed 2,000 K, as shown both by the comparison of Figures 3E–G to Figures 3B–D and more clearly from Supplementary Figures S2(d₁)–(d₆) and Supplementary Figures S2(e₁)–(e₆). Additionally, the distribution of coordination numbers of Mo atoms below 2,000 K in the H₂O environment can be viewed in Supplementary Figures S6E–H. Other crucial findings drawn from the simulations are that 1) D-MoS₂ has more over-coordinated Mo atoms in the H₂O environment than that in the O₂ environment below 2,000 K, as shown by the comparison of Figures 3I–K to Figures 2I–K and Figures 3L–N to Figures 2L–N. 2) the over-coordination of Mo atoms in the H₂O environment due to hydrogenation barely disturbs the ordered structures, while the under-coordination in the O₂ environment degrades the ordered structures below 2,000 K. We find that the under-coordination of Mo atoms at low or intermediate temperatures primarily results from crystallographic defects. O₂ molecules stay inert and do not decompose to O-radicals on the surface during the temperature ramp process even in the proximity of S-vacancies. Nevertheless, one should expect the oxidation of Mo atoms to happen extensively in just a few hundred picoseconds of annealing or at much higher applied temperatures. 3) The presence of Ti₂₀ clusters distorts the ordered structures of MoS₂ in the H₂O environment below 2,000 K, shown by the comparison of Supplementary Figures S2(e₁)–(e₆) to Supplementary Figures S2(d₁)–(d₆) or by the comparison of Supplementary Figures S3(e₁)–(e₆) to Supplementary Figures S3(d₁)–(d₆); this is ascribed to attack by H₂ emitted from Ti_xH_yO_z clusters with increased temperatures. The addition of Ti₂₀ clusters, however, helps sustain the ordered structures of MoS₂ in the O₂ environment, shown by the comparison of Figures 2E–G to Figures 2B–D and Figures 2L–N to Figures 2I–K, or by the comparison of Supplementary Figures S2(c₁)–(c₆) to Supplementary Figures S2(b₁)–(b₆) and Supplementary Figures S3(c₁)–(c₆) to Supplementary Figures S3(b₁)–(b₆). These results suggest that 1) H atoms form extra bonds with Mo atoms in the H₂O environment that are initially 6-coordinated at low temperatures; 2) the interaction between H₂O and S-vacancies is less detrimental to the lattice structure than that with O₂; 3) H atoms barely affect the S-Mo-S substructure and can even stabilize the original atomic arrangement.

3.1.2 Oxidation and hydrogenation effects on MoS₂

From the previous analyses, there is a clear increase in the number of under-coordinated Mo atoms for the systems in the O₂ environment below 2,000 K, as a consequence of the thermally driven S-vacancy migration in the basal plane of MoS₂. By contrast, over-coordination of Mo atoms for systems in the H₂O environment below 2,000 K originates from the hydrogenation of Mo atoms, while the hydroxylation of Mo atoms is barely observed regardless of the presence of S-vacancy. In this section, we discuss the temperature-dependent effects of crystallographic defects as well as the associated reactions at the MoS₂-gas interface at elevated temperatures. As such, we present the bonding of S, O, and H with Mo atoms in Supplementary Figures S4, S5. The O and H atoms that bond with the MoS₂ surface are magnified, so as to highlight the locally oxidized and hydrogenated regions of MoS₂ in the O₂ and H₂O environments from 300 K to 3,000 K with a temperature increment of 300 K. The representative O- and H-containing products drawn from the onset of oxidation for each system are displayed by the side, as shown in Supplementary Figures S4(z₁)–(z₄) and Supplementary Figures S5(z₁)–(z₄).

In Supplementary Figures S4(a₃)–(a₆), there are buckled areas in triangular- and chain-shape in the free-standing monolayer MoS₂, which can be ascribed to the out-of-plane movements of atoms to release the thermal and defect-induced lattice strain. It is also noteworthy that we do not observe a 2H-1T phase transition in these buckled areas, for their lattice still displays distorted hexagonal pattern and comprises trigonal prismatic coordinated Mo atoms. Oxidation occurs particularly in the buckled areas, where the initiation as well as propagation of cracks increase the chemical reactivity of the surface exposed to gas-phase molecules. For instance, the oxidation of Mo atoms in Supplementary Figure S4(a₈) occurs on the wrinkle ridges of chain-shape buckled regions, and the crack formed on the top left of Supplementary Figure S4(a₈) leads to the further oxidation at higher temperatures, as can be seen in Supplementary Figures S4(a₉)–(a₁₀). In comparison with Supplementary Figures S4(a₇)–(a₁₀), Supplementary Figures S4(b₇)–(b₁₀) demonstrate that the oxidation of D-MoS₂ triggers collaborative atomic displacement and further disorganizes the atomic arrangement. The presence of Ti₂₀ clusters constrains O₂ from disintegrating ordered structures for both P-MoS₂ and D-MoS₂ at all selected temperatures, as can be seen from the comparisons of Supplementary Figures S4(c₁)–(c₁₀) to Supplementary Figures S4(a₁)–(a₁₀) and Supplementary Figures S4(d₁)–(d₁₀) to Supplementary Figures S4(b₁)–(b₁₀). In other words, Ti₂₀ clusters can effectively seize the O₂ molecules that are detrimental to the original S-Mo-S substructure, so that the collaborative displacement zones and buckled areas in both P-MoS₂ and D-MoS₂ maintain their shape. In addition to the formation of Mo-O bonds, shown by Supplementary Figures S4(z₁) and (z₂), sulfur oxides such as SO, SO₂, SO₃ are detected near the MoS₂ surface, as shown in Supplementary Figures S4(z₃) and (z₄). These products are qualitatively comparable with those reported in the experiment over elevated temperatures (Walter et al., 2017; Szoszkiewicz, 2021).

For systems in the H₂O environment, oxidation and hydrogenation reactions of Mo atoms take place due to the decomposition of H₂O molecules, whereas hydroxylation is rarely found in our simulations. This is because the binding strength of the OH radical to the MoS₂ surface is weaker than that of H or O radical. The binding energy of an OH radical to a surface Mo atom of P-MoS₂ is 65.30 and 59.07 kcal/mol lower than those of H and O radicals, drawn from the ReaxFF minimization results. The hydroxylation of an Mo atom can be seen in Supplementary Figure S5(z₁). Comparing Supplementary Figures S5(b₁)–(b₁₀) with Supplementary Figures S4(b₁)–(b₁₀), we find that D-MoS₂ is better able to maintain its lattice structure in the H₂O environment than that in the O₂ environment at the same temperature. Meanwhile, we observe that hydrogenation occurs in D-MoS₂ over the entire temperature range, while oxidation occurs to a much smaller extent only as temperature reaches the intermediate level, which signifies that oxidation degrades the lattice structure more than hydrogenation. Hydrogenation even appears to stabilize ordered structures of D-MoS₂ from 600 K to 1,500 K, as can be seen from the comparison of Supplementary Figures S5(b₂)–(b₅) and Supplementary Figures S5(d₂)–(d₅). When Ti₂₀ clusters interact with H₂O and reduce the hydrogenation of Mo atoms, the D-MoS₂ in Supplementary Figures S5(d₂)–(d₆) exhibits less ordered atomic arrangement than without the presence of Ti₂₀, as shown in Supplementary Figures S5(b₂)–(b₆). Similarly, we observe S-containing products such as S₂ and SO, as shown in Supplementary Figure S5(z₃) at 2,100 K. From Supplementary Figures S4(z₃) and (z₄) and Supplementary Figure S5(z₃), we conclude that oxidation of S usually occurs in the high temperature range (>2,000 K) regardless of environment, when the systems undergo thermal shock that severely ruptures the MoS₂ lattice structure, causing S to dissociate from the Mo and bond with O or the neighboring S atoms.

3.1.3 O₂ and H₂O adsorption on Ti clusters

In the previous discussion, we can understand the role of Ti clusters in anti-oxidation and anti-hydrogenation for the monolayer MoS₂ systems. For systems in the O₂ environment, Ti clusters effectively capture O₂ and thus prevent the MoS₂ lattice from O₂ attack and oxidation. For systems in the H₂O environment, on the other hand, Ti clusters lock the dissociated OH and H radicals inside the clusters, so that the MoS₂ appears less ordered than without Ti clusters. The absence of Ti clusters allows faster hydrogenation of Mo atoms, inducing a conversion to a trigonal planar geometry (1 H atom with 3 Mo atoms) and helping to stabilize the original atomic arrangement of MoS₂. Here, we study the effects of the size of Ti clusters on the prevention of oxidation and hydrogenation. To this end, we investigate the adsorption of O₂ and H₂O onto a Ti cluster for the six models described in Table 2. The snapshots of these models at the end of 300 K annealing are presented in Figures 4A–F. The numbers of Ti atoms that bond with O or OH are color projected to the x-y plane, as can be seen in Figures 4G–L, for a better visualization of the oxidation states from core to shell.

FIGURE 4

FIGURE 4. Adsorption of O₂ and H₂O molecules on Ti cluster with varying size. The molecular snapshots showing Ti₂₀ cluster with (A) 20 O₂ molecules (Ti₂₀ + 20 O₂) and (D) 20 H₂O molecules (Ti₂₀ + 20 H₂O), Ti₂₀₀ cluster with (B) 200 O₂ molecules (Ti₂₀₀ + 200 O₂) and (E) 200 H₂O molecules (Ti₂₀₀ + 200 H₂O), as well as Ti₂₀₀₀ cluster with (C) 2000 O₂ molecules (Ti ₂₀₀₀ + 2000 O₂) and (F) 2000 H₂O molecules (Ti ₂₀₀₀ + 2000 H₂O), are extracted at t = 500 ps during NVT simulations at 300 K. Accordingly, Ti atoms constituting Ti-O or Ti-OH that are projected onto the x-y plane are given to identify the size-dependent oxidation states of core and shell of Ti clusters, as can be seen in (G) for Ti₂₀ + 20 O₂, (H) for Ti₂₀ + 20 H₂O, (I) for Ti₂₀₀ + 200 O₂, (J) Ti₂₀₀ + 200 H₂O, (K) Ti ₂₀₀₀ + 2000 O₂, and (L) Ti ₂₀₀₀ + 2000 H₂O. The solid circles represent the numbers of Ti atoms constituting Ti-O or Ti-OH within the core (i.e., r $\le$ $\frac{R}{2}$, where R is the radius of the Ti cluster). The hollow circles represent the numbers of Ti atoms constituting Ti-O or Ti-OH within the entire cluster. The core is projected to the center of x-y plane and colored red for the cases with O₂ and colored blue for the cases with H₂O.

As depicted in Figures 4A,G, the smaller Ti₂₀ clusters effectively react with all gas-phase molecules in the environment by consuming 20 O₂ or 20 H₂O within 500 ps, leading to the compositional mixing of Ti₂₀O_y and Ti₂₀O_yH_z, respectively. In addition, there is one Ti atom coordinated with 6 O atoms for the Ti₂₀ + 20 O₂ system, and two Ti atoms coordinated with 5 O atoms fall within the core, defined as a sphere with a radius r $\le$ $\frac{R}{2}$, where R is the radius of the whole Ti cluster, as shown in Figure 4G. This indicates a local transformation of Ti₂₀ to TiO₂ or quasi-TiO₂ for Ti₂₀ + 20 O₂. In contrast, the Ti₂₀ + 20H₂O system has less than 4 O or OH coordinated with Ti atoms, with H₂ molecules being ejected from the Ti_xH_yO_z surface due to the excess kinetic energy from the exothermic reaction. For the bigger Ti clusters in both environments, e.g., Ti₂₀₀ and Ti₂₀₀₀, we observe that phase segregation becomes favored. In the larger systems with the presence of O₂, we find the TiO₂ or quasi-TiO₂ phase is formed towards the outer surface of the cluster; while in those with the presence of H₂O, the Ti_x phase starts to appear in the center. Particularly, the large populations of yellow solid circles within the cores of Ti_xH_yO_z clusters, as shown in Figures 4J,L, suggest that the Ti_x phase dominates the core, yet without the presence of O or OH. Nevertheless, O atoms can always penetrate the core of Ti clusters in the O₂ environment regardless of the cluster size, hence the occurrence of 3–6 O atoms coordinated with the Ti atoms within the core in Figures 4G,I,K. In analogy to the Ti₂₀ + 20 H₂O system, the Ti₂₀₀ cluster captures all the H₂O molecules and releases H₂. However, Figure 4F shows an excess of H₂O molecules clustered by the side of the Ti₂₀₀₀H_yO_z cluster, leaving an intact core and quasi-TiO₂ phase shell, as shown in Figure 4L. Unlike the Ti clusters in the O₂ environment, those in the H₂O environment become disordered and non-spherical. Our simulations suggest that a Ti cluster under the O₂ or H₂O exposure is expected to form a core-shell segregated structure, where Ti_xO_y or Ti_xO_yH_z dominates the shell and Ti_x primarily in the core. Another finding drawn from our simulations is that the interaction between Ti clusters and O₂ and H₂O molecules is temperature driven. Therefore, the Ti clusters not only are capable of seizing O₂ and H₂O at room temperature, but also exhibit a sustained-capture path at elevated temperatures, as can be seen in Supplementary Figures S7G,H.

3.2 Statistical investigation of bond formation and gas production

In this section, we statistically evaluate the bond formation and the gas production for the eight systems (Table 1) exposed to the O₂ and H₂O environments to quantify the observations presented in Section 3.1. To this end, Figure 5 and Supplementary Figure S8 show the numbers of oxidized Mo, S, and Ti for the eight systems in the O₂ and H₂O environments and the numbers of hydrogenated Mo and hydroxylated Ti only for the systems in the H₂O environment as a function of temperature. Similarly, the numbers of Mo-O, S-O, and Ti-O bonds as well as Mo-H bonds are profiled in Supplementary Figure S9 for the respective systems. In addition, we plot the numbers of volatile gas molecules, O₂, H₂, and H₂O in Figure 6, in order to shed light on the interaction mechanisms between O₂ or H₂O gas phase molecules and the monolayer MoS₂.

FIGURE 5

FIGURE 5. Evolution of oxidized Mo, S, and Ti atoms in the systems of (A), (E), and (I) pristine MoS₂ with O₂ (P-MoS₂ + O₂); (B), (F), and (J) defective MoS₂ with O₂ (D-MoS₂ + O₂); (C), (G), and (K) pristine MoS₂ with H₂O (P-MoS₂ + H₂O); (D), (H), and (L) defective MoS₂ with H₂O (D-MoS₂ + H₂O) quantifying the reactions during the temperature ramp. Evolution of hydrogenated Mo and hydroxylated Ti atoms in the systems of (M,O) P-MoS₂ + H₂O as well as (N,P) D-MoS₂ + H₂O quantifying hydrogenation and hydroxylation reactions during the temperature ramp. The percentages of O₂ and H₂O molecules adsorbed by Ti clusters during the 300 K NVT annealing are shown in (Q,R). The heights of bars and the error bars represent the mean values and the standard deviations derived from six configurations for each system, respectively.

FIGURE 6

FIGURE 6. Evolution of the number of (A) O₂ gas molecules for the systems with O₂ at elevated temperatures; evolution of the numbers of (B) O₂ gas molecules, (C) H₂ gas molecules, and (D) H₂O gas molecules for the systems with H₂O at elevated temperatures. The light green, dark green, light gray, dark gray, light blue, dark blue, light purple, and dark purple squares represent the mean values of gas molecule numbers for the cases of P-MoS₂ + O₂, D-MoS₂ + O₂, P-MoS₂ + O₂ + Ti, D-MoS₂ + O₂ + Ti, P-MoS₂ + H₂O, D-MoS₂ + H₂O, P-MoS₂ + H₂O+ Ti, D-MoS₂ + H₂O+ Ti, respectively. The error bars indicate the standard deviations. The mean values and the standard deviations are derived from six configurations for each system, respectively.

3.2.1 Bond formation

In Figure 5, the numbers of oxidized Mo, S, and Ti at the ramped temperatures from 300 K to 3,000 K are presented. Figures 5A,B indicate that in the O₂ environment, detectable oxidation of Mo starts to happen to P-MoS₂, P-MoS₂ + Ti, D-MoS₂, and D-MoS₂ + Ti systems around 2,100, 2,400, 900, and 1,500 K, respectively. The number of oxidized Mo in D-MoS₂ is much larger than the other systems at the same temperature, whereas the number of oxidized Mo in D-MoS₂ is reduced to a level similar to that of P-MoS₂, as Ti₂₀ clusters are introduced. This is consistent with the conclusion from Section 3.1, that Ti₂₀ clusters mitigate lattice degradation by attenuating the oxidation of D-MoS₂.

Figures 5I,J indicate a stable oxidation state of Ti over the whole temperature range for both P-MoS₂ and D-MoS₂ systems, where all Ti atoms are bonded with O atoms. Further, from Supplementary Figure S8C and Supplementary Figure S9C, we can conclude that most Ti atoms are coordinated with 4 O atoms on average, aligning well with the oxidation state studies of small and medium-sized Ti clusters presented in Figures 4G,I and in Supplementary Figures S7A,C. The snapshots shown in Supplementary Figures S10A–D indicate a partial transformation of Ti_xO_y to a rutile crystal (Ti in 6-fold coordination and O in 3-fold coordination), where the tetragonal crystal formation can be seen in Supplementary Figures S10B,D. Unlike the metal oxides that are major oxidation products over a wide temperature range, we only observe sulfur oxides when the temperature is above 2,000 K. Particularly, Figure 5E shows that the oxidation of S occurs from 2,400 K to 3,000 K. This is consistent with the analysis in Section 3.1 that the distortion of S layer is not caused by S-O bonding but caused by the interference of O₂ in the S-Mo-S substructure.

In the H₂O environment, comparing Figures 5C,D with Figures 5A,B shows that the oxidation of Mo is largely suppressed over the whole temperature range. However, Ti atoms still form bonds with 1.5–2.5 O atoms on average throughout the temperature ramp, as shown in Supplementary Figure S8F and Supplementary Figure S9F. The snapshots in Supplementary Figures S10F,H further confirm the occurrence of tetragonal Ti₂O (O atoms in 6-fold coordination and Ti atoms in 3-fold coordination), in good agreement with the oxidation state studies of small and medium-sized Ti clusters presented in Figures 4H,J and in Supplementary Figures S7B,D. Moreover, Mo atoms prefer to bond with H atoms. Even though the D-MoS₂ is extensively hydrogenated throughout the process, the hydrogenation of Mo is greatly reduced by the presence of Ti₂₀ below 1,500 K, as shown in Figure 5N. One interesting observation from Figures 5M,N is that the presence of Ti₂₀ clusters favors the hydrogenation of Mo above 1500 K, for both P-MoS₂ and D-MoS₂. For instance, P-MoS₂ + Ti experiences an increased number of hydrogenated Mo with a slope steeper than that of P-MoS₂ above 1,500 K. At 3,000 K, both P-MoS₂+Ti and D-MoS₂+Ti have more hydrogenated Mo atoms than those without Ti clusters.

3.2.2 Gas production

Figure 6A indicates that for the systems exposed to O₂, the number of O₂ gas molecules stays stable in the absence of Ti-clusters, where D-MoS₂ has fewer O₂ gas molecules than P-MoS₂. Recall that in Supplementary Figure S9A, there are very few Mo-O bonds forming below 900 K in D-MoS₂, yet the number of Mo-O bonds increases significantly from 900 to 2,100 K and then reaches a plateau. The discrepancy between the trend of Mo-O bond formation and the trend of changing amount of O₂ molecules suggests that at low temperatures, O₂ molecules are physiosorbed to the D-MoS₂ surface; whereas, as temperature increases, the adsorbed O₂ molecules dissociate to O radicals and start to bond with Mo atoms until the initially adsorbed O₂ molecules are fully consumed. For P-MoS₂ + O₂ + Ti and D-MoS₂ + O₂ + Ti systems, the number of O₂ grows slowly from 0 at 300 K yet increases rapidly at 1,200 K and then reaches a plateau at 2,100 K. This suggests that as temperature goes above 1,200 K, O atoms are released from Ti_xO_y clusters and trigger the detectable oxidation of MoS₂.

On the other hand, D-MoS₂ in the H₂O environment in the absence of Ti clusters shows different chemical behavior than that in the O₂ environment, i.e., MoS₂ is functionalized by H₂O with no O₂ gas produced, as shown in Figure 5N and Figures 6B–D. The near-constant difference of H₂O molecules between D-MoS₂ and P-MoS₂ in Figure 6D suggests that in the proximity of the surface, H atoms dissociate from H₂O and saturate Mo atoms by leaving O_mH_n radicals at low and intermediate temperatures. Nevertheless, the O_mH_n radicals interact further with the surface to hydrogenate and oxidize Mo atoms above 1,500 K.

When Ti clusters are introduced, the number of H₂O molecules decreases constantly, which indicates that the presence of Ti-clusters catalyzes the H₂ gas formation from H₂O, while the remaining O_mH_n radicals are absorbed by Ti clusters, forming Ti_xH_yO_z clusters, as shown in Figures 6B–D. Moreover, it is found from Figures 5M–P and Figures 6C,D that, in the early stage of H₂O reduction, the hydroxylation of Ti increases, yet the hydrogenation of Mo is suppressed to a stable lower level until 1,500 K. At a temperature below 2,100 K, Ti clusters extensively react with H₂O molecules, resulting in the emission of H₂ gas molecules, O_mH_n radicals, as well as Ti_xH_yO_z clusters. Meanwhile, the Ti_xH_yO_z clusters are more reactive towards the radicals of low molecular weight than D-MoS₂, thus inhibiting the hydrogenation and oxidation of Mo atoms. As temperature increases to 2,100 K and above, the number of Ti-OH bonds starts to decrease because of the H and O_pH_q radicals released from Ti_xH_yO_z clusters, leading to a rapid increase in the hydrogenation/oxidation for Mo atoms. From these observations, we can suggest the following reaction mechanisms in MoS₂ + Ti system in the H₂O environment: (i) H₂O interacts with Ti-clusters to produce H₂ and O_mH_n radicals, i.e., (z + m) H₂O+ x Ti → Ti_xH_yO_z + [z + m-(y + n)/2] H₂ + O_mH_n. (ii) The Ti_xH_yO_z clusters decompose to Ti_xH_bO_c, O_pH_q, and H₂, i.e., Ti_xH_yO_z → Ti_xH_bO_c + [(y-b-(z-c) q/p)/2] H₂ + (z-c)/p O_pH_q. As such, O_mH_n and O_pH_q radicals can functionalize Mo atoms gradually as temperature rises.

3.3 Reaction pathways in O₂ and H₂O environments

In order to substantiate the reaction mechanisms we suggested in the previous subsections, we inspect the MD trajectories for the D-MoS₂ + Ti systems in the O₂ and H₂O environments. The three representative reactions of (i) oxidation of Mo atoms in the O₂ environment, (ii) hydrogenation of Mo atoms in H₂O environment, and (iii) hydrogen gas formation near the MoS₂ surface in H₂O environment are visualized and detailed in Figure 7.

FIGURE 7

FIGURE 7. Representative reaction pathways during the temperature ramp, such as (A–E) oxidation of Mo atoms with Ti_xO_y clusters delivering O radicals drawn from the D-MoS₂ + O₂ + Ti system, (F–J) hydrogenation of Mo atoms with Ti_xH_yO_z clusters delivering H radicals drawn from the D-MoS₂ + H₂O+ Ti system, and (K–O) hydrogen gas formation with the presence of Ti_xH_yO_z clusters drawn from the D-MoS₂ + H₂O+ Ti system.

3.3.1 Oxidation of Mo atoms in O₂ environment

The oxidation of Mo atoms for the systems without Ti clusters typically occurs at a region with S-vacancies or a region with locally distorted S-Mo-S lattice structures due to thermal degradation. The presence of Ti clusters effectively inhibits oxidation of the MoS₂ substrate at low temperatures, yet at sufficiently high temperatures, we can still detect the oxidation of Mo for the systems with Ti clusters. Figures 7A–E show that the MoS₂ surface oxidation results from O-transfer from Ti_xO_y clusters to the S-defects in the vicinity of Mo atoms. During the 300 K annealing, prior to the temperature ramp, the formation of Ti_xO_y clusters takes place as the majority of volatile O₂ gas molecules are captured by Ti clusters. Thus, when temperature is increased to 320 K, as shown in Figure 7A, the dangling O1 and O2 atoms from a large Ti_xO_y cluster start to bond with each other. As temperature is increased to 1,160 K, the buckling of MoS₂ plane is observed, yielding chemically reactive local regions facing towards O1 and O2, as shown in Figure 7B. At 1,340 K, shown by Figure 7C, O1 and O2 approach the MoS₂ surface and interact with dangling Mo atoms on the surface. At 1,600 K, shown by Figure 7D, O1 is the first to bind to a 4-coordinated Mo atom, followed by O2 binding to a 3-coordinated Mo atom at 1,630 K, shown by Figure 7E.

3.3.2 Hydrogenation of Mo atoms in H₂O environment

The presence of dangling Mo bonds drives the surface hydrogenation for the D-MoS₂ systems even at a temperature as low as 300 K. Nonetheless, the Mo-H bonds are barely observed for the P-MoS₂ systems in the H₂O environment at low temperatures. Figures 7F–J depict the H-transfer from a Ti_xH_yO_z cluster to the MoS₂ surface, with the H atom travelling along the path paved by the adjacent S-defects.

At 1,140 K, an H atom dissociating from an H₂O molecule bonds with a small Ti_xH_yO_z cluster, as shown in Figure 7F. In Figure 7G at 1,620 K, the small Ti_xH_yO_z cluster and the other clusters coalesce into a larger Ti_xH_yO_z cluster, with the H atom moving towards the S-defects. At 1,750 K shown by Figure 7H, the H radical passivates an S-defect site and bond with two Mo atoms. In Figure 7I, at the temperature of 1,790 K, the two Mo-H bonds break, and the H atom shifts slightly upwards and connects with two under-coordinated Mo atoms. The Mo-H bonds are not as stable as Mo-O bonds, presented in Figures 7D,E. Lastly, the H atom moves downwards and dwells at the new S-defect connecting with two Mo atoms, as shown in Figure 7J.

3.3.3 H₂ gas formation near Ti_xH_yO_z clusters

In Figure 6C, we detect an increase in the number of H₂ molecules during the temperature ramp for systems with Ti clusters in the H₂O environment. In an effort to reveal the mechanism of H₂ formation in the presence of Ti clusters, we examine the reaction pathway of two H atoms, H1 and H2 from the D-MoS₂ + H₂O+ Ti system, as shown in Figures 7K–O. At the temperature of 420 K, as shown in Figure 7K, H1 and H2 are bonded with a Ti_xH_yO_z cluster. When temperature ramps up to 2,100 K, shown by Figure 7L, H1 dissociates from the Ti_xH_yO_z cluster and evolves to an H₂O molecule, while H2 remains bound to the Ti_xH_yO_z cluster. As can be seen in Figure 7M, at 2,420 K, H1 dissociates from the H₂O molecule into an H radical, and H2 is eventually released from the Ti_xH_yO_z cluster, forming another H₂O molecule due to the high temperature. Further, at 2,490 K, shown by Figure 7N, H1 transforms into an H₃O radical, whereas H2 forms an OH radical as a consequence of the decomposition of the H₂O molecule. Lastly, at 2,560 K, H1 and H2 bind together to form an H₂ molecule. In the meantime, the residual OH and H radicals are adsorbed by the Ti_xH_yO_z cluster, as shown in Figure 7O.

4 Conclusion

In this work, we have developed a new ReaxFF reactive force field for Mo, Ti, Au, O, S, and H (ReaxFF Mo/Ti/Au/O/S/H-2022) to investigate the role of Ti clusters in preventing the oxidation and hydrogenation of a monolayer MoS₂ surface in O₂- and H₂O-rich environments, respectively. Our ReaxFF MD simulations reveal the oxidation and the hydrogenation mechanisms for the MoS₂ surfaces exposed to O₂ and H₂O environments with and without the presence of Ti clusters.

The coordination number analysis for Mo atoms in the monolayer MoS₂ demonstrates that D-MoS₂ under H₂O exposure possesses more over-coordinated Mo atoms than that under O₂ exposure, and that the H₂O-induced over-coordination does not disturb the S-Mo-S lattice but rather stabilizes the original atomic arrangement at low or intermediate temperatures. The presence of Ti₂₀ clusters can significantly mitigate the defect-induced lattice degradation of MoS₂ in the O₂ environment and sustain the original Mo coordination in both the O₂ and H₂O environments. In addition, the study of the effects of size of the Ti clusters indicates that Ti clusters regardless of size are promising antioxidants or anti-hydrogenation agents and can effectively capture O₂ or H₂O molecules within a wide temperature range. Finally, the statistical calculations on the bond formation of Mo-O, Mo-H, S-O, Ti-O, and Ti-H as well as the gas formation of O₂, H₂, and H₂O reveal the stoichiometry of oxidation and hydrogenation in response to elevated temperatures. We suggest three reaction pathways: (i) oxidation of Mo atoms with O-transfer by Ti_xO_y clusters; (ii) hydrogenation of Mo atoms with H-transfer by Ti_xH_yO_z clusters; (iii) hydrogen gas formation near the MoS₂ surface due to the catalytic role of Ti_xH_yO_z clusters. In other words, in the O₂ environment, the O radicals or O₂ gas molecules are released from Ti_xO_y clusters, leading to thermal degradation and oxidation of MoS₂ at elevated temperatures. On the other hand, in the H₂O environment, the H and H_mO_n radicals that dissociate from Ti_xH_yO_z clusters initiate more extensive hydrogenation and oxidation of Mo atoms as temperature rises. In particular, the pathway of H-transfer along the S-vacancies in the MoS₂ due to the reversible adsorption of H and H_mO_n radicals from Ti_xH_yO_z clusters is identified during the hydrogenation reaction.

To conclude, this work offers a new ReaxFF force field to describe the Mo/Ti/Au/O/S/H interactions for the materials modeling society with an interest in 2D materials and nanotechnologies. Our MD simulations uncover the impact of the Ti dopant on the oxidation/hydrogenation behaviors of MoS₂ surface. These results provide a theoretical basis for engineering the oxidation and anti-oxidation properties of MoS₂ thin films and other TMDs, which can benefit 2D material designs in automotive, aerospace, semiconductor, and nanotechnology industries.

Data availability statement

The original contributions presented in the study are included in the article/Supplementary Material, further inquiries can be directed to the corresponding author.

Author contributions

QM: modeling, investigation, data curation, visualization, writing, and editing; YZ: modeling, writing, and editing; MK: literature review, Introduction drafting, and reviewing; NN: reviewing and editing; MC: reviewing, editing, and supervision; AD: reviewing, editing, project supervision, funding acquisition, project administration.

Funding

The authors acknowledge the funding from the National Science Foundation 2D Crystal Consortium Materials Innovation Platform (NSF 2DCC-MIP) under cooperative agreement DMR-1539916. Computations for this research were performed on the PSU’s Institute for Cyber Science Advanced Cyber Infrastructure (ICS-ACI). This work was funded by the Laboratory Directed Research and Development program at Sandia National Laboratories, a multi-mission laboratory managed and operated by National Technology and Engineering Solutions of Sandia, LLC., a wholly owned subsidiary of Honeywell International, Inc., for the US. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525. Any subjective views or opinions that might be expressed in the paper do not necessarily represent the views of the US. Department of Energy or the United States Government.

Conflict of interest

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Publisher’s note

All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.

Supplementary material

The Supplementary Material for this article can be found online at: https://www.frontiersin.org/articles/10.3389/fnano.2022.1034795/full#supplementary-material

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