First-Principles Investigation on the Adsorption and Diffusion of Oxygen at the B2(110)–O(001) Interface in Ti₂AlNb Alloys

Abstract

The adsorption and diffusion of oxygen at the B2(110)[$\overline{1}$11]||O(001)[1$\overline{1}$0] interface in Ti₂AlNb alloys were investigated via first-principles calculations. Only a 2.6% interfacial mismatch indicates that B2(110)–O(001) is basically a stable coherent interface. The calculated adsorption energies and diffusion energy barriers show that oxygen prefers to occupy the Ti-rich interstitial sites, and once trapped, it hardly diffuses to other interstitial sites, thus promoting the preferential formation of Ti oxides. Under the premise of a Ti-rich environment, a Nb-rich environment is more favorable for oxygen adsorption than an Al-rich environment. The electronic structures suggest that O 2p orbitals mainly occupy the energy region below −5 eV, bonding with its coordinated atoms of Ti, Al, and Nb. However, Al 3p and Nb 4d orbitals near the Fermi level couple with sparsely distributed O 2p orbitals, forming anti-bonding, which is not conducive to oxygen adsorption. Because Nb 4d electrons are more localized than Al 3p electrons are, Nb–O anti-bonding is weaker. O–Ti has almost no contribution to anti-bonding, suggesting good bonding between them. This is consistent with the experimental observations that TiO₂ is the main oxidation product.

1. Introduction

Ti₂AlNb alloys are regarded as the next generation of the most promising lightweight high-temperature aerospace structural materials due to their excellent mechanical properties, such as their good creep resistance, high strength-to-weight ratio, and satisfactory hot workability [1,2,3]. Ti₂AlNb alloys are composed of an order of the orthorhombic (O) phase (space group: Cmcm, Pearson symbol: oS16), B2 phase (space group: Pm$\overline{3}$m, Pearson symbol: cP2), and α₂ phase (space group: P6₃/mmc, Pearson symbol: hP8) [4,5]. As a high-temperature alloy, the oxidation resistance of Ti₂AlNb alloy is not good above 750 °C [6,7,8]. This is because the competitive oxidation of Ti and Al occurs at high temperatures, failing to produce a dense oxide layer to protect the alloy matrix [9,10].

In order to improve the high-temperature oxidation resistance of Ti₂AlNb alloys, an in-depth study of the high-temperature oxidation mechanism is necessary. The experimental studies of the high-temperature oxidation behavior of Ti₂AlNb alloys currently focus on oxidation kinetic testing, oxidation product and oxidation layer structure analysis, etc. It is shown that the oxide layer of the alloy consists of a mixture of TiO₂ and Al₂O₃, of which TiO₂ is the main oxidation product [11], because TiO₂ is the preferred oxidation product of B2, α₂, and orthorhombic (O) phases [12]. The oxidation process of Ti₂AlNb alloys is controlled by the microstructure of the initial B2–O two-phase interface, and the extremely lamellar morphology restricts the diffusion of oxygen [13]. In our previous experiments on the oxidation mechanisms of Ti₂AlNb alloys at 800 °C, the TEM observations revealed that the O phase and B2 phase followed a crystallographic-orientation relationship of [$\overline{1}11$]B2//[$1\overline{1}0$]O and (110)B2//(001)O [14], which was also observed in other studies related to Ti₂AlNb alloys [15,16].

Constrained by the experimental characterization scale, some theoretical studies have also been conducted to investigate the oxidation mechanism of Ti–Al–Nb alloys based on the electronic structure calculated via the first-principles density functional theory (DFT). The surface phase diagrams for oxygen adsorption on γ–TiAl low-index surfaces reveal that oxygen may induce surface segregations of Ti and Al in Ti-rich and Al-rich surface environments, respectively [17]. In α₂-Ti₃Al alloy, the driving force for the adsorption of oxygen atoms on the (0001) surface is provided by the O–Ti bonding strength, and the diffusion coefficients of oxygen in the alloy are anisotropic in different directions [18,19]. The study of oxygen adsorption on Ti₂AlNb alloy surfaces indicates that the bonding strength of the O–Ti and O–Nb bonds is stronger than that of the O–Al bond [20]. In addition to the surfaces of the alloy, the interfaces also play an important role in oxidation behavior. Excellent interfacial stability means better mechanical properties and also increases the resistance to oxidation [21,22,23]. In the γ-TiAl–α₂-Ti₃Al interface, oxygen tends to occupy the Ti-rich octahedral sites, and the occupancy tendency of oxygen in the γ–α₂ interface from high to low is α₂–Ti₃Al to the interface and γ-TiAl. Oxygen adsorption at the interface destabilizes the interface, leading to a reduction in the mechanical properties of the alloy [24].

However, first-principles studies on the oxidation mechanism of Ti₂AlNb alloys, especially at the interface between different phases, are lacking. In this study, we investigated the adsorption and diffusion of oxygen at the B2(110)[$\overline{1}11$]||O(001)[$1\overline{1}0$] interface, which is normally observed in Ti₂AlNb alloys.

2. Computational Methods and Models

2.1. Computational Details

All first-principles calculations were performed using Vienna Ab-initio Simulation Packages (VASP.5.4.4) [25], based on the framework of Kohn–Sham density functional theory (DFT) [26]. The projector-augmented wave (PAW) method proposed by Blöchl and implemented by Kresse and Joubert was used with a cutoff energy of 560 eV [27]. The exchange correlation function was determined via generalized gradient approximation as formulated by Perdew, Burke, and Ernzerhof (GGA-PBE) [28]. Monkhorst–Pack k-point meshes were used for integration over the Brillouin zone [29], where the k-point mesh setting as a uniform mesh grid with a spacing of 0.03 Å was used to sample the complete Brillouin zone and calculate the density of states for all calculated systems. Brillouin zone integrations were carried out with the Methfessel–Paxton technique with a 0.1 eV smearing of the electron levels [30]. The PAW pseudopotentials considered were Ti 3s²3p⁶3d³4s¹, Al 3s²3p¹, Nb 4s²4p⁶4d⁴5s¹, and O 2s²2p⁴. Full relaxation structure optimization was used for the bulk and surface of B2 and O phases to obtain the ground state crystal structure. With a precision test, a partial relaxation method with the lattice parameters fixed and internal atomic positions relaxed simultaneously was used for the interface B2(110)–O(001). The total energy convergence parameter during optimization was 1 × 10⁻⁵ eV/atom, the Hermann–Feynman force convergence parameter was 0.01 eV/Å, the tolerance shift was less than 0.002 Å, and the stress deviation per atom was less than 0.1 GPa.

We utilized the climbing image nudged elastic band (CI-NEB) method to identify the minimum energy pathway (MEP) for oxygen diffusion at the B2(110)–O(001) interface. The CI-NEB method was derived from the conventional search transition state nudged elastic band (NEB) method combined with climbing image [31]. As one of the most efficient methods, it requires just a few points to locate the transition state accurately. In the framework of the CI-NEB method, the atomic positions of all considered images were relaxed until the force on each atom was less than 0.03 eV/Å. Crystal orbital Hamilton population (COHP) calculations were performed for analyzing the interaction between oxygen atoms and the nearest coordinated atoms by means of LOBSTER [32]. LOBSTER reconstructs the chemical information in terms of local, auxiliary atomic orbitals outputted from DFT computations (VASP.5.4.4). The orbital bonding information between atoms can be visualized very well via COHP analysis; those that contribute positively to the bonding of atoms are called bonding components, and those that contribute negatively are called anti-bonding components [32].

2.2. Structural Models

The orthorhombic (O) phase has an orthogonal structure (Cmcm) (Figure 1a), with the experimental lattice parameters a = 6.090 Å, b = 9.570 Å, and c = 4.670 Å [4]. Ti atoms occupy 8g sites, while Al and Nb atoms are located at 4c1 and 4c2 sites, respectively. The B2 phase has a cubic structure with a space group of Pm$\overline{3}$m (Figure 1b), and the experimental lattice parameters are 3.229 Å [4]. Ti and Al atoms occupy 8g sites and 4c sites, respectively. Their chemical formulas are Ti₂AlNb and TiAl for the orthorhombic (O) phase and B2 phase, respectively.

Based on the surface energy tests and previous theoretical reports [33,34], a five-layer slab is sufficient to show the bulk characteristics for both B2(110) and O(001) surfaces. Therefore, five layers of B2(110) slabs and O(001) slabs were used to construct the interface structure of B2(110)[$\overline{1}11$]||O(001)[$1\overline{1}0$], with a 15 Å vacuum layer along the c axis in order to block the periodic effects (Figure 1c). Subsequently, the relative position between B2(110) and O(001) was tested in the three axial directions in order to find the configuration with the lowest energy as the initial interface structure. The final interface configuration was obtained after structural optimization, and had an interfacial distance of 2.2 Å. As shown in Figure 1c, the two-phase interface was divided into five regions: the B2-phase bulk, B2-phase sub-interface, interface, O-phase sub-interface, and O-phase bulk. Only the B2-phase sub-interface, interface, and O-phase sub-interface were considered for oxygen adsorption and diffusion calculations (Figure 1d).

3. Results and Discussion

3.1. B2(110)/O(001) Interface

The lattice parameters of the full-relaxed crystal structures are a = 3.187 Å for the B2 phase, and a = 6.053 Å, b = 9.520, Å and c = 4.679 Å for the orthorhombic (O) phase, all being in good agreement with the experimental values. The interfacial mismatch parameter ξ is usually used to describe the stability of interface structure [35]:

$$\xi =1-\frac{2\Omega }{A_1+A_2},$$

(1)

where Ω is the area of the B2(110)/O(001) interface structure, and A₁ and A₂ are the areas of B2(110) slabs and O(001) slabs, respectively. Based on the optimized interface and slab structures, we obtained Ω = 57.588 Ų, A₁ = 60.636 Ų, and A₂ = 57.634 Ų, leading to a value of 2.6% for ξ. It is usually assumed that the interface satisfies the stabilizing relationship characteristics when the mismatch is less than 5%. The small interfacial mismatch degree also implies that the B2(110)/O(001) interface is basically coherent, which is often observed in Ti₂AlNb alloys in experiments [14].

In order to investigate the bonding characteristics of the B2(110)/O(001) interface, the partial density of states (PDOS), charge density differences, and corresponding planar average charge density were calculated. The charge density difference (e/ų) is defined as $\Delta \rho =\Delta {\rho }_{interface}-\Delta {\rho }_{B2-slab}-\Delta {\rho }_{O-slab}$; here, $\Delta {\rho }_{interface}$ is the charge density of the B2–O two-phase interface, and $\Delta {\rho }_{B2-slab}$ and $\Delta {\rho }_{O-slab}$ represent the charge density of the isolated B2(110) and O(001) slabs, respectively. The planar average charge density difference (e/Å) is obtained by taking a planar average of $\Delta \rho$ in the ab plane (parallel to the contacting interface), which can reflect the characteristic charge fluctuation vertical to the interfacial direction (the c direction).

One can find from Figure 2a,b that the PDOS of Ti 3d, Al 3p, and Nb 4d orbitals of the B2-phase sub-interface and O-phase sub-interface have a smaller distribution at the Fermi level than those of B2-phase bulk and O-phase bulk, indicating much stronger bonding for the atoms in the sub-interfaces. This can also be observed from the charge density differences in Figure 2c. The red part represents the regions of electron accumulation, and the blue part represents those of electron depletion. Combining the charge density difference and the corresponding planar-averaged charge density difference plot, we can see that electron accumulation and depletion mainly happen at the interface with a little occurring in the next layers adjacent to it. In other words, only the atoms in the B2-phase sub-interface and O-phase sub-interface take part in bonding in forming the B2(110)–O(001) interface.

Compared with O phase, the electrons in B2 phase are more delocalized, i.e., Ti 3d orbitals cover −5 eV to E_f and Al 3p orbitals extend from E_f to −7.5 eV, creating strong hybridization with 3s orbitals (Figure 2a). As a result, Ti 3d orbitals interact with Al sp hybridized orbitals in the B2 phase. However, Al 3s and 3p orbitals are almost separated in the O phase, so the main interaction in the O phase takes place among the Al 3p, Ti 3d, and Nb 4d orbitals near E_f.

3.2. Oxygen Adsorption at B2(110)–O(001) Interface

We considered all possible octahedral interstitial sites for single-oxygen-atom adsorption at the B2(110)–O(001) interface. As shown in Figure 1d, they are O1a-b (2Ti–4Al coordination) and O2a-c (4Ti–2Al) at the B2-phase sub-interface, O3a-b (2Ti–3Al–1Nb), O4a-b (4Ti–2Al) and O5a-b (4Ti–1Al–1Nb) at the interface, and O6a-b (2Ti–2Al–2Nb), O7a-b (4Ti–1Al–1Nb), O8a (4Ti–2Al), and O9a (4Ti–2Nb) at the O-phase sub-interface.

Table 1. The calculated total energies, E_(O–system), and oxygen adsorption energies (E_ads) of the B2(110)/O(001) interface corresponding to the coordination environment of oxygen adsorption sites (Coord.).

Location	Site (Coord.)	E(O-system) (eV)	Eads (eV)
B2-phase sub-interface	O1a (2Ti-4Al)	−548.205	-
	O1b (2Ti-4Al)	−548.377	-
	O2a (4Ti-2Al)	−548.090	−3.460
	O2b (4Ti-2Al)	−548.380	−3.750
	O2c (4Ti-2Al)	−548.394	−3.764
Interface	O3a (2Ti-3Al-1Nb)	−548.698	-
	O3b (2Ti-3Al-1Nb)	−547.340	−2.710
	O4a (4Ti-2Al)	−548.195	−3.565
	O4b (4Ti-2Al)	−548.596	−3.966
	O5a (4Ti-1Al-1Nb)	−548.379	−3.749
	O5b (4Ti-1Al-1Nb)	−548.701	−4.071
O-phase sub-interface	O6a (2Ti-2Al-2Nb)	−548.915	-
	O6b (2Ti-2Al-2Nb)	−547.820	−3.190
	O7a (4Ti-1Al-1Nb)	−548.306	−3.676
	O7b (4Ti-1Al-1Nb)	−548.377	−3.747
	O8a (4Ti-2Al)	−548.747	−4.117
	O9a (4Ti-2Nb)	−548.917	−4.287

lists the total energies and adsorption energies of all oxygen-absorbed interface structures. The adsorption energies of oxygen atoms were calculated via the following equation:

$$E_{ads}=E_{(O-system)}-(E_{(system)}-\frac{1}{2}{E}_{(O_2)}),$$

(2)

where E_(O-system) and E_(system) are the total energies of the interfaces with and without oxygen, respectively, and $E_{(O_2)}$ is the total energy of an oxygen molecule, which was calculated in a cubic box with 12 Å edges. Our calculated $E_{(O_2)}$ is −9.854 eV, in which is good agreement with that of −9.860 eV in the previous report [19]. The obtained value of E_(system) is −539.703 eV.

Lower adsorption energy means a more stable oxygen adsorption site. In the B2-phase sub-interface (Figure 1d), the most stable oxygen adsorption site is O2c, as shown in Table 1. It is followed by O2b, with the adsorption energy being 10 meV higher. Both of them are coordinated by four Ti atoms and two Al atoms. The small energy difference probably originates from the influence of the adjacent interface layer. The O2a site is also coordinated by four Ti atoms and two Al atoms but has a total energy that is about 0.3 eV higher. The value of the adsorption energy is strongly linked to the bonding strength of the oxygen atom with the nearest neighboring atoms in the site. The local structures show that for O2b site, the average bond lengths of Al–O and Ti–O bonds are 2.031 Å and 2.129 Å, while for the O2a site, they are 1.879 and 2.207 Å. Obviously, a shorter Ti–O bond supports a higher stability of oxygen atom adsorption. The O1a and O1b sites coordinated by two Ti atoms and four Al atoms were too unstable to shift to the 4Ti–2Al coordination sites after optimization. Obviously, oxygen atoms prefer the 4Ti–2Al coordination environment in the B2-phase sub-interface, and a shorter Ti–O bond is more supportive for oxygen adsorption.

In the O-phase sub-interface (Figure 1d), O9a (4Ti-2Nb) is the most stable oxygen adsorption site with the lowest E_ads of −4.287 eV (Table 1), and is also most stable in the whole B2(110)–O(001) two-phase interface structure. The next site is the 4Ti–2Al-coordinated O8a site, with an E_ads that is 0.17 eV higher than that of O9a. Apparently, the adsorption sites with 4Ti–2Al coordination (O8a) in the O-phase sub-interface have a much lower E_ads than do those (O2a-c) in the B2-phase sub-interface, and the max energy difference is up to 0.6 eV (between O2a and O8a). The local structures show that the average bond lengths of T–-O at the O8a site are 2.075 Å, which is much shorter than that of 2.207 Å at the O2c site. 4Ti–1Al–1Nb-coordinated O7a and O7b sites have similar E_ads values of around −3.7 eV, which is very close to the values of 4Ti–2Al-coordinated O2b and O2c sites in the B2-phase sub-interface. The most unstable sites in the O-phase sub-interface are 2Ti–2Al–2Nb-coordinated O6a and O6b. The oxygen atoms absorbed at the O6a site move to the 4Ti–2Nb site after optimization. Obviously, oxygen atoms prefer Ti-rich and Nb-rich coordination environments in the O-phase sub-interface.

At the interface (Figure 1d), the 4Ti–1Al–1Nb-coordinated O5b site is the most stable site with an E_ads of −4.071 eV. Next is 4Ti–2Al coordinated O4b with an E_ads of −3.966 eV. Here, O5a and O4a sites, which have the same coordination environment as O5b and O4b, respectively, have higher adsorption energies with differences of up to 0.3 eV and 0.4 eV. The local structures show that the average bond length of Ti–O at O4b is 2.130 Å, which is shorter than that of 2.150 Å at O4a, as mentioned above. The shorter Ti–O bond is more constructive for oxygen adsorption, and so the adsorption energy of O4b is 0.4 eV, which is lower than that of O4a. Comparing the local structures of O5a and O5b (4Ti-1Al-1Nb), we find that the bond lengths of Al–O and Nb–O at the O5b site (E_ads = −4.071 eV) are 1.854 Å and 2.126 Å, respectively, which are shorter than those of 1.879 and 2.134 Å at the O5a site (E_ads = −3.749 eV), while the average Ti–O bond length at O5b is 2.173 Å, which is longer than that of 2.148 Å at O5a. Apparently, Ti–O bonds no longer play a decisive role in the stability of oxygen adsorption at the 4Ti–1Al–1Nb-coordinated site at the interface.

Generally, the adsorption stability of oxygen atoms at the octahedral interstitial positions is mainly determined by their coordination environment, i.e., oxygen atoms prioritize occupying the Ti-rich and Nb-rich interstitial positions. Next, the local structure also affects the stability of oxygen adsorption, e.g., for the 4Ti–2Al-coordinated site, Ti–O bond strength plays a more important role than does the Al–O bond. As a whole, for the same coordination environment, the stability of the oxygen adsorption site is O-phase sub-interface > interface > B2-phase sub-interface in the B2(110)–O(001) interface system.

3.3. Oxygen Diffusion at B2(110)–O(001) Interface

Based on Table 1, possible diffusion pathways were designed for the interface, B2-phase, and O-phase sub-interfaces, as well as the place between the interface and sub-interface, in order to understand the oxygen diffusion at the B2(110)/O(001) interface, as summarized in

Table 2. The calculated energy barriers (eV) of oxygen atom diffusion from one site (Initial) to another site (Final) in the B2-phase sub-interface (B2-phase sub-int.) and O-phase sub-interface (O-phase sub-int.), at the interface, and between the interface and sub-interface in the B2(110)–O(001) interface system, corresponding to the coordination environment of oxygen adsorption sites (Coord.).

Location	Initial (Coord.)	Final (Coord.)	Energy Barrier (eV)
B2-phase sub-int.	O2a (4Ti–2Al)	O2b (4Ti–2Al)	1.580
	O2b (4Ti–2Al)	O2c (4Ti–2Al)	1.844
Interface	O3b (2Ti–3Al–1Nb)	O5a (4Ti–1Al–1Nb)	0.199
	O4a (4Ti–2Al)	O4b (4Ti–2Al)	1.698
	O5a (4Ti–1Al–1Nb)	O5b (4Ti–1Al–1Nb)	1.518
O-phase sub-int.	O6b (2Ti–2Al–2Nb)	O7a (4Ti–1Al–1Nb)	0.568
	O7a (4Ti–1Al–1Nb)	O8a (4Ti–2Al)	1.427
	O8a (4Ti–2Al)	O9a (4Ti–2Nb)	1.667
B2-phase sub-int.—Interface	O2c (4Ti–2Al)	O5b (4Ti–1Al–1Nb)	1.632
	O2b (4Ti–2Al)	O4b (4Ti–2Al)	1.825
Interface—O-phase sub-int.	O5b (4Ti–1Al–1Nb)	O9a (4Ti–2Nb)	1.773
	O4b (4Ti–2Al)	O9a (4Ti–2Nb)	1.584

.

It can be seen from Table 2 that the coordination environment of oxygen adsorption sites plays an important role in oxygen diffusion. Whether at the interface, the B2-phase sub-interface and O-phase sub-interface, or between the interface and sub-interface, the diffusion between Ti-rich sites has a high energy barrier, such as O2b → O2c (1.844 eV), O4a → O4b (1.698 eV), O8a → O9a (1.667 eV), O2c → O5b (1.632 eV), and O5b → O9a (1.773 eV). However, the diffusion from Ti-poor sites to Ti-rich sites has a much lower energy barrier, e.g., 0.199 eV for O3b (2Ti–3Al–1Nb) → O5a (4Ti–1Al–1Nb) at the interface, and 0.568 eV for O6b (2Ti–2Al–2Nb) → O7a (4Ti–1Al–1Nb) at the O-phase sub-interface. Moreover, the oxygen atom at O3b (2Ti–3Al–1Nb) diffuses more easily than that at O6b (2Ti–2Al–2Nb) to a Ti-rich site. This is consistent with the result of adsorption energy in Table 1, where O3b shows a higher E_ads than O6b does, and the Ti-rich and Nb-rich coordination environments are more attractive for the adsorption of oxygen atoms. It is clear that the diffusion from the Ti-rich site to other sites requires crossing a high energy barrier, which makes the Ti-rich site an oxygen trap and hinders the diffusion of oxygen. As a result, oxygen atoms trapped at the Ti-rich site react with Ti atoms to produce Ti oxides preferentially.

Figure 3 shows the minimum energy paths of oxygen diffusion from a Ti-rich site, O8a (4Ti–2Al), to another Ti-rich site, O9a (4Ti–2Nb), and from a Ti-poor site, O3b (2Ti–3Al–1Nb), to Ti-rich site, O5a (4Ti–1Al–1Nb), with the corresponding partial density of states of the oxygen atom and its coordinated atoms of Ti, Al, and Nb. In order to obtain insights into bonding and anti-bonding, which are closely related to the stability of the local structure of oxygen adsorption, crystal orbital Hamilton population (COHP) calculations were performed for the bond between the oxygen atom and the nearest coordinated atom; the results are shown in Figure 4.

It can be seen from Figure 3a that it is hard for oxygen diffusion to happen between two stable oxygen adsorption sites because of the presence of a too-high energy barrier. The PDOS at the O8a site shows that O 2p orbitals divide into two peaks at −8.5 eV and −7.3 eV, which mainly interact with Al 3s orbitals, and Ti 3p, 3d, and 4s orbitals, respectively, while the PDOS of O 2p orbitals at the O9a site only have one peak at −7.3 eV and couples with Ti 3s, 3p, and 3d orbitals, and Nb 4d orbitals. As shown in Figure 4a,b, the bonding for both O8a and O9a sites’ oxygen adsorption originates from the O 2p orbital and its coordinated atoms’ orbitals in the energy region away from the Fermi level (<−5.0 eV). The anti-bonding for O8a site oxygen adsorption mainly stems from the O–Al bond, which is very delocalized, distributed from −7.0 eV to E_f, while the anti-bonding for O9a site oxygen adsorption comes from a more localized O–Nb bond and is weaker than the O–Al anti-bonding at O8a. For both O8a and O9a sites, the O–Ti bond has almost no contribution to anti-bonding, suggesting good bonding between them. This is consistent with the idea that oxygen atoms prefer a Ti-rich adsorption site.

Figure 3d shows that oxygen diffuses much more easily from a Ti-poor site (O3b, 2Ti–3Al–1Nb) to a Ti-rich site (O5a, 4Ti–1Al–1Nb) with a low energy barrier of 0.199 eV. The PDOS in Figure 3e shows that compared to those at O8a and O9a, O 2p electrons at the O8a site are more delocalized, with a wide peak ranging from −9.1 eV to −5 eV, and couple with Al 3s electrons, and Ti 3d, 3p, and 4s electrons. As shown in Figure 3f, the PDOS of O 2p orbitals at O5a has two peaks located at −8.2 eV and −7.3 eV, but these are different from those at O8a, which are not completely separated. The former mainly interact with Al 3s orbitals, but the latter couples with Ti 3d, 3p, and 4d orbitals, and Nb 4d orbitals. The COHP in Figure 4c,d indicates that for both O3b and O5a sites, bonding originates from the O 2p orbital and its coordinated atom orbitals in the energy region away from the Fermi level (<−5.0 eV), while anti-bonding mainly stems from the delocalized O–Al bond distributed from −7.0 eV to the Fermi level and the localized O–Nb bond distributed near the Fermi level. Also, the O–Ti bond has a very small contribution to anti-bonding just as in the case of the O8a and O9a sites. Too-large O–Al anti-bonding makes the O3b (2Ti–3Al–1Nb) site less stable than the O5a site (4Ti–1Al–1Nb).

Clearly, for oxygen adsorption at the B2(110)–O(001) interface, the oxygen atom at the Ti-rich site is more stable because of the strong bonding and very weak anti-bonding between Ti and oxygen atoms. Compared with Ti, more delocalized Al 3p electrons create strong anti-bonding with O 2p electrons, which is not conducive to oxygen adsorption. The Nb 4d electrons near E_f also create anti-bonding with O 2p electrons, but this is much weaker than Al–O anti-bonding because of the more localized 4d electrons.

4. Conclusions

First-principles density functional theory (DFT) was employed to study the adsorption and diffusion of oxygen at the B2(110)–O(001) interface in Ti₂AlNb alloys. The extremely low interfacial mismatch parameter suggests that B2(110)[$\overline{1}11$]||O(001)[$1\overline{1}0$] is a fairly stable coherent interface, consistent with the experimental report. The calculated adsorption energies indicate that the stability of the oxygen atom at the adsorption site is mainly determined by its coordination environment, i.e., the Ti-rich and Nb-rich interstitial sites are more supportive for oxygen adsorption. Moreover, for the same coordination environment, the stability of oxygen adsorption sites is O phase > interface > B2 phase in the B2(110)/O(001) interface system. The coordination environment also plays an important role in oxygen diffusion. In the B2(110)–O(001) interface, the diffusion between the Ti-rich sites needs to overcome a high energy barrier of over 1.5 eV, while only a much lower energy barrier of ~0.5 eV needs to be surmounted from Ti-poor sites to Ti-rich sites. The partial density of states with the corresponding crystal orbital Hamilton population suggests that O 2p orbitals mainly occupy the energy region below −5 eV and bond well with their coordinated atoms of Ti, Al, and Nb, supporting the stability of the oxygen atom at the absorption site. However, Al 3p electrons and Nb 4d electrons near the Fermi level interact with sparsely distributed O 2p electrons to create anti-bonding, weakening the stability of oxygen adsorption. Because Al 3p electrons are more delocalized, Al–O anti-bonding is stronger than Nb–O anti-bonding.