Oxidation of the titanium(0001) surface: diffusion processes of oxygen from DFT

Abstract

The initial oxidation process of the Ti(0001) surface is investigated based on the diffusion of oxygen with a potential barrier by first-principles methods. The results show that oxygen molecules can dissociate freely at the Ti surface without an energy barrier and oxygen atoms are chemisorbed on the face-centered cubic (FCC) site of the surface. At low oxygen coverage on the surface, the nearest-neighbor oxygen can assist the diffusion of oxygen from the surface into the sublayer, due to the decrease in the energy barrier. Based on the analysis of the adsorption energy and diffusion barrier, the double-layer model of oxygen adsorption is proposed. With this model, the change in work function is analyzed by following the increase in adsorbed oxygen from 0 to 200%, and is consistent with the experimental results.

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1. Introduction

Oxidation of metal surfaces is a rather complicated, but research-worthy topic. The related knowledge is important to the physical and chemical properties of surfaces and the different kinds of application of surfaces, such as heterogeneous catalysis, fuel cells, sensors, supercapacitors, corrosion resistance, and so on. To understand the processes of oxidation, the interaction between oxygen and the metal surface and the diffusion of oxygen atoms in the sub-surface are crucial.^1,2 When exposed to oxygen atmosphere, the metal surface easily forms the different structures and oxidation states, depending on environmental pressure, temperature, and other conditions. Initially chemisorbed oxygen on the surface or oxygen diffusing into the surface has been witnessed by experiments for most metal surfaces.^3–5 However, the microcosmic mechanism of initial oxidation is not universal among the surfaces of different metals. For example, on the surface of Ag(111) and Pd(111), oxygen tends to form on-surface chemisorbed adlayers on the surface and then the thin layer of surface oxide.^6,7 For the surfaces of Ru(0001) and Rh(111), the on-surface chemisorbed adlayers due to oxygen adsorption are found to transform directly into bulk oxide phases without the formation of surface oxides.⁸ For the Cu(111) surface, the surface oxide is found to form directly without the on-surface oxygen adlayer formation process.^1,6

Owing to its outstanding chemical and electronic properties, titanium and its corresponding oxides have been researched for years, both experimentally^9–13 and theoretically.^14–18 The oxidation processes of the Ti(0001) surface are of great interest, and the complexity of the processes causes it to still be under debate. In the early years, researchers found that the oxidation products were a mixture of different oxidation states, depending on the experimental temperature and Ti substrate thickness.^19–22 Besides the oxidation process, the work function change in the process also attracts researchers' attention. Bignolas et al.²³ studied the influence of temperature on the oxygen adsorption and the work function of the oxidation products. In both low and high temperature cases, the decrease of work function in the beginning was witnessed. The decrease is considered to be due to the penetration of the oxygen atoms into the titanium surface. This is supported by the experimental results that the higher the temperature, the faster the decrease of work functions. This phenomenon was also observed by other research groups.^24,25 Moreover, no oxygen is detected at the Ti surface at temperatures over 400 °C, indicating that temperature can enhance the diffusability into bulk Ti.²¹ However, the microcosmic mechanism of the oxidation process may be complicated and it has been in debate for years. Azoulay and his colleagues²⁶ pointed out that initially the oxygen accumulates on the topmost atomic layer. This is totally different from other studies, where the initially chemisorbed oxygen is incorporated into the subsurface and interlayers.^23,24,27 They also argued that the initial decrease of the work function can be explained by other factors, such as changes in electronic charge distribution in the topmost layer due to smoothing or roughening effects, or polarization of the adsorbed electronegative atoms instead of subsurface penetration.^28,29 Moreover, for lower oxygen exposure, some researchers have found that the work function is constant or shows very minor variations.^30,31

In the theoretical part, some works towards the oxidation process of Ti(0001) surface have been taken out recently.^32–35 The realistic oxidization processes are difficult to simulate, since the structures of the oxidized titanium surface are complex.^21,26,36 With molecular dynamics simulations, Schneider et al.³³ tried to obtain the model of amorphous TiO_x layers for the oxidized Ti(0001) surface. Ohler et al.³⁴ studied the interfaces formed between the Ti and TiO₂ layer by building the TiO₂ with rutile and anatase structures on the titanium surface. The metal work function was found to be changed as the oxidation layer (TiO₂) formed, but the change of work function is positive for rutile and negative for anatase. For the oxygen adsorption on the Ti(0001) surface, Liu et al.³² have adopted a model of multiple-layer adsorption and found the change of the work function is consistent with experimental results. Li et al.³⁵ tried to explain the change of work function with the bond–band–barrier correlation model.³⁷ However, to our best knowledge, the dynamical processes of oxygen adsorption and oxygen diffusion with the formation of an oxidation layer are still elusive.

In the present study, we have investigated the initial oxidation process of the Ti(0001) surface with the diffusion of oxygen, based on first-principle calculations. We focus on the interactions among oxygen atoms and the Ti(0001) top three layers, with the energy barrier method and we analyze how the oxygen molecule is decomposed on the titanium surface. Based on the analysis of the favorite sites of the surface on which the oxygen atom is adsorbed, we study the relationship between the coverage ratio of oxygen and the change of work function. For the oxygen diffusion into the sublayer of the surface, the energy barrier and work function are analyzed with the effect of oxygen coverage. With the analysis of the density of states due to the oxygen insertion in the sublayer, we finally discuss the initial state of the formation of TiO_x.

2. Computational details and theoretical models

In this study, all the calculations are performed on the basis of density functional theory with projector augmented wave (PAW) formalism, as implemented using the Vienna ab initio simulation package (VASP) code.^38,39 The Perdew–Burke–Ernzerhof (PBE) approximation is used for the exchange–correlation functional. A kinetic energy cutoff of 500 eV for the plane wave expansion and a proper k-point spacing with the Monkhorst–Pack grid method⁴⁰ are found to be sufficient to ensure that the total energy is converged at the 1 meV per atom level. The convergence criterion for the self-consistent field energy is set to be 10⁻⁶ eV. For bulk Ti with the primitive cell, a k-point mesh of 10 × 10 × 10 is used. For the analysis of the processes of oxygen adsorption on the Ti(0001) surface, the surface model of a 2 × 2 supercell with a large vacuum layer along the z-axis is constructed and the k-point mesh of 4 × 4 × 1 is used to perform the structural relaxation. The calculated lattice parameters (a and c) of the bulk titanium are 2.946 Å and 4.638 Å, respectively. The results are consistent with the results of previous calculations and experimental values.^16,32,41

To simulate the Ti(0001) surface, we have built a slab system with seven atomic layers of Ti and a vacuum region, up to 15 Å, by the supercell method. For the adsorption of oxygen on the Ti(0001) surface, oxygen is placed on one side of the seven-layer slab of Ti, and the dipole correction is considered for all calculations.⁴² For both the clean Ti(001) surface and the O/Ti(0001) system, the last two-layers of Ti atoms are fixed with the value of bulk Ti in the simulation in the process of structural relaxation. In the case of calculating the oxygen diffusion barrier, the nudged elastic band method (NEB) is used. The energy barriers are found by building the potential reaction path for the selected diffusion oxygen atom with a series of intermediate images and relaxing the structures of intermediate images in which the z coordinate of the selected oxygen atom is fixed and the others (x and y coordinates) with the nearby atoms are relaxed. In order to study the effect of adsorbed oxygen on the electronic structures and properties of substrate Ti, we have considered the change of oxygen coverage from 0% to 200%. The 11.1% coverage is calculated in the surface mode of a 3 × 3 supercell, with a 3 × 3 × 1 k-point mesh, while the rest of the calculations are performed with the surface model of a 2 × 2 supercell.

For the oxygen-adsorbed Ti(0001) surface, the dynamic barriers in the diffusion processes of oxygen are analyzed within the multiple-layer adsorption model. For the surface adsorption sites, both the surface face-centered cubic (FCC) site and the surface hexagonal close-packed (HCP) site are considered based on the previous results in the literature.^32,35 For the diffusion of oxygen atoms into the sublayer or bulk, these oxygen atoms are found to prefer octahedral (Oct) sites instead of tetrahedral (Tet) sites. All these possible sites are shown in Fig. 1. The adsorption energies for different coverage and adsorption sites are calculated by the following formula:

where ΔE_ad is the adsorption energy, and E_O/Ti, E_clean, and E_O2 represent the total energies per unit cell of the oxygen-adsorbed Ti system, the clean Ti slab and the O₂ molecule, respectively. N represents the total number of oxygen atoms in the calculated unit cell.

Fig. 1 Illustration of the possible oxygen adsorption sites in the O/Ti(0001) system with the 2 × 2 surface supercell and 7-layer slab of Ti atoms. Note that the red balls represent oxygen atoms and the grey balls represent Ti atoms. The FCC, HCP, Oct and Tet represent face-centered cubic, hexagonal close-packed, octahedral and tetrahedral sites, respectively. (i, j) mean the oxygen atom is located between the i^th and j^th layer.

3. Results and discussion

3.1 Dissociation of oxygen molecule (gas) on Ti(0001)

For the clean Ti(0001) surface, we used a 2 × 2 surface supercell with a slab of 7-layer Ti atomic layers. After the structural relaxation, the distance between the layers for the first three layers was obviously changed, with respect to the bulk spacing value d = 2.319 Å. The changes Δ_ij = (d_ij − d)/d, between the layer i and j are Δ₁₂ = −7.7%, Δ₂₃ = +2.6% and Δ₃₄ = −1.5%, respectively. The results are consistent with previous calculations and experimental results.^16,24 The minus sign means that the spacing values of the Ti interlayers are contracted compared to that of bulk Ti. In particular, the contraction of the distance between the first layer and second layer (Δ₁₂) is obvious. This phenomenon is popular for the metallic surface and can be attributed simply to the Coulomb trapping due to the surface formation.

Before considering the adsorption and diffusion of oxygen atoms on the Ti(0001) surface, the interaction between oxygen molecules and the clean Ti(0001) surface was first investigated. For oxygen molecules far from the Ti(0001) surface, two typical configurations, including that perpendicular to the Ti surface (O⊥S–Ti) and parallel to the Ti surface (O∥S–Ti) are shown in Fig. 2. Oxygen molecules are then shifted towards the Ti(0001) surface gradually, to simulate the dissociation process of oxygen on the surface with the typical NEB method. The changes in energy and distance between oxygen atoms were analyzed with respect to the distance to the surface, as shown in Fig. 3. It was found that the change in adsorption energy is related to the bond length of molecular oxygen, which becomes larger at distances from the surface less than 5 Å for O∥S–Ti and less than 3.5 Å for O⊥S–Ti. This may be due to the formation of electric dipole moments under the induction of surface electrons in the model of O∥S–Ti being easier than that in the model of O⊥S–Ti.

Fig. 2 Illustration of two typical initial configurations about the oxygen molecule sites far from the Ti surface, including those (a) perpendicular to the Ti(0001) surface and (b) parallel to the Ti(0001) surface. The red balls represent oxygen and the grey balls represent titanium. The distance to the surface is defined as the distance between the lower oxygen atom and the Ti surface, as presented by the dashed line.

Fig. 3 The change in energy and O–O bond length, following the change in distance between the O₂ molecule and the surface of the Ti, based on the models in Fig. 2, including (a) parallel to the Ti(0001) surface and (b) perpendicular to the Ti(0001) surface. In both cases, the oxygen molecule is found to dissociate without the dynamic barrier.

Following the decrease in distance between oxygen molecules and the surface, the oxygen molecules begin to dissociate into two separate oxygen atoms for both models. There is no energy barrier in the processes of the dissociation of the oxygen molecules. This proves that the adsorption of oxygen on Ti(0001) is chemisorption instead of physical adsorption. This result is similar to the dissociation adsorption of oxygen on other metal surfaces, such as Al(111)⁴³ and Pd(111).⁵ The absence of a dynamic barrier on the Ti(0001) surface and the exothermal character of the dissociation means the processes of oxygen adsorption can be completed even without the heat energy from the environment.

3.2 Adsorption of oxygen on the surface and diffusion of oxygen in the sublayer

The analysis of the diffusing barrier of adsorbed oxygen atoms into the sublayer is obviously essential to understanding the dynamic processes of surface oxidation. Firstly, we consider the adsorption of oxygen atoms since the oxygen molecules have been dissociated on the Ti surface. Two possible surface adsorption sites, including the face-centered cubic (FCC) site and hexagonal close-packed (HCP) site, are considered, as shown in Fig. 1. The adsorption energies of FCC and HCP are 5.53 eV and 5.41 eV, respectively, which are similar to the previous reports.^32,35 It is obvious that FCC is more favorable than HCP for the occupation of oxygen atoms on the surface.

The initial site of the oxygen atom is proposed to be the FCC site. As shown in Fig. 4a, the oxygen atom diffusion is controlled from the surface to the second layer and then to the third layer and fourth layer gradually, by the NEB method. The diffusing barrier is defined to be the difference in the lowest energy in the initial states and the highest energy in the process when passing through each layer. The calculated barrier values shown in Fig. 4b are 1.55 eV, 2.42 eV and 2.24 eV for the surface, second layer and third layer, respectively, and the barriers are high. This means oxygen atoms will accumulate at the surface of Ti(0001), by following the increase in adsorbed oxygen.

Fig. 4 (a) An illustration of the proposed model of oxygen diffusion from the surface to the fourth layer; (b) the change in energy from the path of oxygen diffusion. The corresponding energy barriers for a single oxygen atom diffusing through the 1^st, 2^nd and 3^rd layers of Ti(0001) are indicated. The diffusing oxygen atom is initially placed on the surface face-centered cubic (FCC) site.

In order to figure out initially whether or not and how oxygen atoms diffuse into the Ti subsurface region, we analyzed the effect of the oxygen surface coverage on the diffusion barrier. The simulation models are shown in Fig. 5a and b and all the surface adsorption sites and corresponding barrier values are listed in Table 1. Here, the surface coverage is defined as the concentration of oxygen atoms adsorbed on the surface of Ti, except for the selected diffusion atoms. For example, there are four sites of FCC in the model of the (2 × 2) surface supercell. The 75% oxygen coverage represents the case that there are four oxygen atoms in the O/Ti(0001) system as shown in Fig. 5c. In order to consider the low oxygen coverage, the (3 × 3) surface supercell is adopted for the case of surface adsorption with 11.1%. As shown in Fig. 5c and Table 1, there is a minimal value (0.14 eV) for the diffusion barrier of the first layer when the oxygen coverage is 25%. This means the accumulation of oxygen atoms on the surface in low content can promote the diffusion of oxygen. This may be attributed to the near-neighbor oxygen atoms around the diffusion oxygen atom trapping the free electrons of nearby Ti atoms. The decrease in electronic concentration along the diffusion path results in the decrease in the diffusion barrier. By following the increase in concentration of the adsorption oxygen atoms, the Ti surface may form different oxidized Ti states. In the region of the surface, the interaction between oxygen and Ti results in the Ti atom being difficult to relax in the network of the Ti–O surface with the diffusion of oxygen atoms. Therefore, the diffusion barrier is increased due to the formation the Ti–O network with a high concentration of oxygen on the surface.

Fig. 5 Illustration of the structural models with adsorption sites for (a) 3 × 3 surface supercell (11.1% adsorption) and (b) 2 × 2 surface supercell and the calculated diffusion barriers through (c) the first Ti layer and (d) the second Ti layer (subsurface) with the concentration of surface adsorption varying from 0% to 75% (100%). The corresponding adsorption sites for different oxygen coverage are listed in Tables 1 and 2. The smallest values of barriers for each coverage amount are connected with the black line. The red circles indicate the oxygen diffusion sites.

Table 1 The calculated diffusion barriers from the surface to the second layer with the surface adsorption model. The corresponding FCC sites and HCP sites are defined in Fig. 5a and b

Coverage	Adsorption site	Barrier (eV)
0%	—	1.55
11.1%	FCC1	1.36
	FCC2	2.95
25%	HCP1	0.61
	FCC1	0.14
	FCC4	1.13
50%	HCP1 + FCC1	0.38
	FCC1 + FCC4	1.10
	HCP1 + HCP2	1.47
75%	FCC1 + FCC2 + FCC3	4.42

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How about the effect of the adsorption of oxygen on the surface on the diffusion from the second layer to the third layer? Similar models were adopted and the results are shown in Fig. 5d and Table 2. Here, the definition of oxygen coverage is the same as in Fig. 5c. For example, in the case of 100% oxygen coverage, there are five oxygen atoms with four atoms on the surface and the last one under the first layer is selected as the diffusion atom. The energy barrier is decreased to the lowest value at the oxygen coverage of 25%, with the value down to 0.55 eV. However, the further increase of oxygen adsorption on the surface results in a larger diffusion barrier. It is also noticed that different adsorption sites under the same oxygen coverage influence the diffusion barrier dramatically, as shown in Fig. 5. For example, for the three different adsorption sites considered for the oxygen coverage of 25% on the surface, the diffusion barrier values about the surface change from 0.14 eV to 1.13 eV, as shown in Table 1. In addition, the lowest barrier (0.55 eV) for going through the second layer is relatively high, compared with that for the first layer (0.14 eV).

Table 2 The calculated diffusion barriers from the second layer to the third layer with the surface adsorption model. The corresponding FCC sites and HCP sites are defined in Fig. 5a and b

Coverage	Adsorption site	Barrier (eV)
0%	—	2.42
11.1%	FCC1	1.66
	FCC2	2.73
25%	HCP1	1.26
	FCC1	0.98
	FCC4	0.51
50%	HCP1 + FCC1	2.16
	FCC1 + FCC4	0.72
75%	FCC1 + FCC2 + FCC3	0.89
100%	FCC1 + FCC2 + FCC3 + FCC4	1.21

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Next we considered sublayer adsorption and calculated the diffusion barriers with the change in oxygen coverage and adsorption sites. The multiple-layer model of adsorption was adopted. We considered the oxygen coverage from 11.1% to 100% for surface adsorption and the oxygen coverage from 0% to 75% for the sublayer (second layer) adsorption. The calculated results are shown in Table 3. Surprisingly, the oxygen can diffuse into the third layer with no barrier in most of the cases with the low oxygen coverage for the second layer. This means the oxygen atoms, with the assistance of other near-neighbor oxygen in the second layer, diffuse easily into the third layer. This implies that oxygen atoms tend to occupy the sites with a double-layer of Ti atoms. From the calculation, the way that oxygen atoms like to occupy the octahedral interstitial sites with the double-layer model is more stable in energy, which is similar to the previous reoprts.^32,35 It also implies that oxygen diffuses easily into the core of the titanium piece. For the high oxygen concentration at the surface and second layer, the unusual barrier values imply that the formation of surface oxide will hinder the diffusion process.

Table 3 The calculated diffusion barriers from the second layer to the third layer, considering the increase in oxygen coverage in the sublayer (between the first layer and the second layer of Ti) and that on the surface

Sublayer^b	Surface^a
	11.1%	25%	50%	75%	100%
a Represents the face-centered cubic (FCC) sites on the surface as the adsorption sites.b Represents the octahedral (Oct) sites in the sublayer as the adsorption sites.
0%	1.84	0.51	0.72	0.89	1.21
11.1%	0.00	0.00	1.24	0.00	0.00
25%	—	0.00	0.81	0.00	0.00
50%	—	—	1.86	3.07	2.45
75%	—	—	—	3.52	4.43

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From the above analysis, it was found that after oxygen molecules dissociate on the Ti surface, the separated oxygen atoms first accumulate on the surface before diffusing into the subsurface layer. Once oxygen atoms diffuse into the second layer, they tend to diffuse into the third layer, due to strong repulsive interactions with the oxygen atoms on the surface. We can regard this as a diffusion cycle for oxygen atoms diffusing into the Ti interlayers.

3.3 Density of states and changes of work functions

The detection of work function is an important way to analyze the oxidization of a surface. It has been found experimentally that the work function is decreased at the very beginning and then increases until a subsequent plateau is reached.^21,23 This is witnessed by most research groups, while a few others do not observe the initial decreasing trend.^30,31 For pure Ti metal surfaces, the calculated work function is 4.44 eV, which agrees well with other DFT calculations and experimental results.^16,24 In order to verify the proposed double-layer model of adsorption, we calculated the work function for oxygen coverage varying from 0% to 200%. Here, 100% oxygen coverage represents four oxygen atoms chemisorbed in the O/Ti(0001) system. The possible sites based on the double-layer adsorption and the adsorption energy of the corresponding configurations are shown in Fig. 6 and Table 4.

Fig. 6 The calculated work functions of the configurations with different oxygen coverage amounts and possible adsorption sites of oxygen. In (a), the points connected by the black solid line represent the most probable adsorption configurations, based on the double-layer model of adsorption shown in Fig. 7. In (b), the points connected by the black dotted line represent the adsorption configurations based on the adsorption energy for reference. The corresponding adsorption sites are listed in Table 4.

Table 4 The calculated adsorption energy and work function for various adsorption sites and oxygen coverage. With the double-layer model of adsorption (in Fig. 7), the most probable adsorption sites for various adsorption concentrations are in bold. Note that ‘Sur’, ‘Sub’ and ‘third’ represent the sites on the surface, sublayer (second layer) and the third layer, adsorbed by oxygen atoms, respectively. The number before the adsorption site stands for the number of oxygen atoms adsorbed on the corresponding sites

Adsorption concentration	Adsorption site	Adsorption energy/eV	Work function/eV
0%	—	—	4.44
25%	1Sur	6.27	4.37
	1Sub	5.01	4.30
50%	2Sur	5.81	4.48
	1Sur + 1Sub	5.65	4.45
	1Sur + third	6.17	4.20
	2Sub	5.23	4.30
75%	3Sur	5.63	4.80
	2Sur + 1Sub	5.72	4.47
	2Sur + 1third	6.00	4.57
	1Sur + 1Sub + 1third	5.71	4.77
	1Sur + 2Sub	5.54	5.18
	1Sur + 2third	5.99	4.27
100%	4Sur	5.44	6.14
	3Sur + 1Sub	5.72	4.80
	2Sur + 2Sub	5.71	4.99
	2Sur + 2third	6.02	5.14
	2Sur + 1Sub + 1third	5.82	4.50
	1Sur + 3third	5.94	4.47
125%	2Sur + 3third	5.94	4.95
150%	3Sur + 3third	5.86	5.02
175%	3Sur + 4third	5.79	5.09
200%	4Sur + 4third	5.67	5.15

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It is found that that under the same oxygen coverage, different adsorption sites result in various work functions with different adsorption energies in Table 4, suggesting that the work function is sensitive to oxygen adsorption sites. Based on the idea that the higher adsorption energy makes the configuration more stable and the diffusion barrier is lower at low surface oxygen coverage, we have proposed the proper structure for each concentration as the most probable site, as shown in Fig. 7. In this model, it implies that the oxygen atoms on the surface are likely to diffuse into the third layer of Ti. The work functions of these structures are plotted with the connection of the black solid line in Fig. 6a. It shows that the work function first decreases to 4.20 eV at 50% oxygen coverage and then increases to 4.47 eV at 100% oxygen coverage. This trend is in accordance with the experimental results. As shown in Fig. 6b, the black dotted line represents the work functions for the structures only based on adsorption energy for reference. We noticed that at low oxygen coverage, the dotted line coincides with the solid line. However, for oxygen coverage larger than 50%, the dotted line has a sudden dramatic increase to 5.14 eV at 100% coverage of oxygen. This implies that by simply considering adsorption energy, the result is not fully consistent with the experiments at higher oxygen coverage (>50%). In addition, the energy difference of the two configurations (the stable state in the double-layer model in Fig. 7 and that with lowest energy) is very small at each level of oxygen coverage. In the cases of 75% and 100% coverage, the differences are 0.01 eV and 0.08 eV, respectively. Considering the diffusion barriers, at low oxygen coverage, the oxygen atom tends to diffuse into the subsurface region rather than be chemisorbed on the surface. This suggests that the proposed double-layer model may be popular in experiments.

Fig. 7 Illustration of the configurations with the most probable adsorption sites, based on the adsorption energy (listed in Table 4) and diffusion barrier for oxygen coverage varying from 0% to 200%.

In Fig. 8a, the density of states (DOS) for O/Ti(0001) with the oxygen concentration from 0% to 100% are shown. The calculated models are from that in Fig. 7. When the oxygen atom is located at the Ti surface, a peak shows up at around −5.5 eV. An additional peak located at around −7 eV comes out when oxygen diffuses into the subsurface, which is clearly seen at the adsorption concentrations of 50% and 75%. When the adsorption concentration is high (100%), two peaks merge together. It is also noticed that a dip is located around the Fermi level in DOS, due to the oxygen adsorption. With the increase in the oxygen concentration, the dip has a trend to deepen from the ΔDOS in Fig. 8b. This trend implies that the metallic surface of Ti(0001) will turn into a semi-conductive surface by following the oxidation processes of the surface. The change of DOS is also an indicator for the oxidation processes.

Fig. 8 (a) Density of states (DOS) of the O–Ti(0001) skin (three outer Ti layers) for oxygen coverage ranging from 0% to 100%; (b) the difference between the DOS of the O–Ti(0001) skin and Ti(0001) skin for oxygen coverage ranging from 25% to 100%. The dashed line represents the Fermi level.

4. Conclusion

The oxidation process of the Ti(0001) surface has been investigated using the first-principles methods, by the analysis of the oxygen adsorption on the surface and the diffusion of oxygen into the sublayer with the diffusion barrier. The calculation results confirm that oxygen molecules (gas) can dissociate automatically on the Ti(0001) surface without any potential barrier. The chemisorbed oxygen atom prefers the face-centered cubic site of the surface at the beginning of the oxidation processes, before diffusing into the interlayers.

It was found that the diffusion barrier of isolated oxygen diffusing from the surface into the bulk is very high. However, with the help of the other near-neighbor oxygen atoms, the dynamic barrier is largely decreased. For example, at low oxygen coverage (25%), with the assistance of the nearest-neighbor oxygen, the barrier from the surface to the second layer is reduced dramatically to 0.14 eV. At the same time, the higher oxygen coverage on the surface will impede the process of diffusion, due to the formation of the Ti–O network. At the low oxygen coverage, the surface oxygen is also found to assist the diffusion of oxygen from the second layer to the third layer. Interestingly, under the assistance of the nearest-neighbor oxygen in the second layer, the diffusion barrier is reduced to zero. Based on this result, with the stability of different configurations from the analysis of the adsorption energy, the double-layer adsorption model is proposed for the initial process of surface oxidation. With this model, the work functions of different configurations with the concentration from 0% to 200% were analyzed and the results are in accordance with the experimental results. We expect that this double-layer adsorption model on the Ti(0001) surface with the analysis of the diffusion barrier can help to shine some light on the complex processes of surface oxidation.

Acknowledgements

The authors would like to acknowledge the support by Nanyang Technological University under Grant No. RG97/15 and RG101/14 and National Natural Science Foundation of China under Grant No. 11504123 for this research.

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