# Effect of refractory elements and of aluminium on oxygen diffusion and solubility in Titanium alloys: experiments and first-principles calculations

Kevin Gautier, Damien Connétable, Enrica Epifano, Thomas Gheno, Daniel Monceau

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Kevin Gautier, Damien Connétable, Enrica Epifano, Thomas Gheno, Daniel Monceau. Effect of refractory elements and of aluminium on oxygen diffusion and solubility in Titanium alloys: experiments and first-principles calculations. 15th World Conference on Titanium 2023, 2023, Edinbourg, United Kingdom. pp.47, 10.7490/f1000research.1119888.1. hal-04736603

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# EFFECTS OF REFRACTORY ELEMENTS AND OF ALUMINIUM ON OXYGEN DIFFUSION AND SOLUBILITY IN TITANIUM ALLOYS: EXPERIMENTS AND FIRST-PRINCIPLES CALCULATIONS

Kevin Gautier¹, Damien Connétable¹, Enrica Epifano¹, Thomas Gheno², Daniel Monceau¹

1 CIRIMAT, Université de Toulouse, CNRS, INP-ENSIACET, 4 allée Emile Monso - BP44362, 31030 Toulouse cedex 4, France

2 DMAS, ONERA, Université Paris-Saclay, 92322 Chatillon, France

Titanium alloys are widely used in aerospace applications due to their high specific strength. However, titanium alloys are limited to service temperatures below 600 °C due to insufficient creep resistance and oxygen embrittlement. These properties can be improved by adding alloying elements. In this study, the effects of refractory alloying elements (Hf, Ta, and W) in binary (Ti-X) and ternary (Ti-Al-X) on the oxidation resistance during 500 h at 650 °C in air were assessed. Oxidation tests were also performed in Ar-20%O₂ to dissociate the effects of oxygen and nitrogen. In air, the global oxidation kinetics decreased in air by adding Ta, Hf and W, with the largest effect observed for W. Oxygen dissolution was also reduced in ternary Ti-Al-W alloys. The oxygen uptake of this ternary alloy was lower than in Ti6242s, a reference alloy for high temperature applications. However, this effect was not explained by a direct effect of W addition on O dissolution or diffusion. This beneficial effect of W was linked to nitrogen uptake and to the enhanced formation of nitrides at the metal/oxide interface. The interfacial N-rich layer decreased the oxygen dissolution in the bulk alloy. First-principles calculations were conducted to calculate oxygen diffusivities in pure titanium and to evaluate the effect of aluminium on the oxygen solubility limit. Even if aluminium has a destabilizing effect on oxygen most stable site (octahedral site), this effect is not very strong and it cannot be measured experimentally.

**Keywords:** high-temperature oxidation, diffusion, solubility, tungsten, DFT

## 1. Introduction

Reducing the weight of aircraft in order to reduce fuel consumption is an important lever to achieve low-carbon mobility. The use of titanium alloys as lighter metals is now widely spread in structural parts [1]. However, in aircraft engines, nickel-based alloys or steels are still used due to their better oxidation resistance and creep resistance. Replacing some of these alloys with titanium alloys is one of the proposals to lighten aircraft.

Nevertheless, titanium alloys are limited to temperatures below 600 °C because of insufficient creep resistance [2] and oxygen embrittlement [3-6]. The most detrimental effect that occurs during oxidation is oxygen penetration to form an oxygen-affected zone (OAZ), which is about 10 times thicker than the oxide layer at 650 °C [7] and thus has a greater effect on mechanical properties. Indeed, the oxygen solubility is about 33 at.% in α-Ti [8] and the brittle-to-ductile transition induced by oxygen is about 1 at.% at room temperature for Ti-64 [9]. One of the solutions to improve mechanical properties and oxidation resistance, and also to reduce the OAZ extent is to add alloying elements. Some alloying elements such as Al [10, 11], Nb [12] or Si [13, 14] are known to improve the global oxidation resistance. Huvelin et al. showed that the simultaneous addition of refractory (Ta, W and Ge) in IMI834 improves creep resistance at 600 °C [15].

In the present paper, the oxidation behaviour of binary (Ti-X) and ternary (Ti-Al-X) alloys with X=Hf, Ta and W is presented. Oxidation tests were performed at

650 °C, in both air and Ar-20%O₂ up to 500 h. Commercial materials (Ti-50, Ti6242s and Ti64) were also tested for comparison. Oxygen diffusivities were measured by Electron Probe Micro-Analysis (EPMA). First-principles calculations were conducted to calculate oxygen diffusivity in pure titanium and to estimate the effect of Al on oxygen solubility limit.

## 2. Material and methods

### 2.1. *Experiments*

Titanium alloys were elaborated in an electric arc furnace. Their compositions were measured by inductively coupled plasma-optical emission spectroscopy (Spectro Ciros) for the major elements and by fusion/gas analysis (Inductar) for oxygen and nitrogen; the results are listed in Table 1. Experiments were also performed on forged reference materials (Ti-50, Ti6242s and Ti64).

Oxidation samples were cut from ingots as thin plates of approximately 13x8x2 mm³ and a 2.5 mm diameter hole was drilled to hang each sample in the furnace. Before oxidation, samples were ground using P600 SiC paper on faces, edges and corners to limit the oxide scale spallation. They were finally cleaned in ethanol in an ultrasonic bath and dried in air. Just before and after oxidation, samples were weighed three times using a SARTORIUS LA75 3200D balance with an accuracy of ±20 µg. Oxidation treatments under laboratory air were performed in a CARBOLITE CWF1300 furnace for 500 h at 650 °C with natural convection. Oxidation treatments in Ar-20%O₂ (gas
velocity of 1.2*10⁻⁴ m/s) were performed in an oxidation bench developed in the laboratory.

<table><caption>**Table 1: Alloys studied and their composition.**</caption><thead><tr><td>Alloys</td><td>Composition (wt.%)</td></tr></thead><tbody><tr><td>Ti-6Al</td><td>Al: 5.9, O: 0.15, N: &lt;0.01</td></tr><tr><td>Ti-6Al-2Ta</td><td>Al: 5.8, Ta: 1.8, O: 0.11, N: &lt;0.01</td></tr><tr><td>Ti-6Al-8Ta</td><td>Al: 5.5, Ta: 7.7, O: 0.15, N: &lt;0.01</td></tr><tr><td>Ti-6Al-2W</td><td>Al: 5.8, W: 2.0, O: 0.11, N: &lt;0.01</td></tr><tr><td>Ti-6Al-8W</td><td>Al: 5.4, W: 7.9, O: 0.17, N: &lt;0.01</td></tr><tr><td>Ti-6Al-2Hf</td><td>Al: 5.9, Hf: 1.8, O: 0.13, N: &lt;0.01</td></tr><tr><td>Ti-2Ta</td><td>Ta: 1.8, O: 0.11, N: &lt;0.01</td></tr><tr><td>Ti-8Ta</td><td>Ta: 7.2, O: 0.11, N: &lt;0.01</td></tr><tr><td>Ti-2W</td><td>W: 1.9, O: 0.11, N: 0.01</td></tr><tr><td>Ti-8W</td><td>W: 7.3, O: 0.12, N: 0.01</td></tr></tbody></table>

After oxidation, a copper deposition was realized to protect the oxide layer before cutting. The cross-section was then ground using P600 and P1200 SiC paper and automatically polished using STRUERS DiaPro 9, 3 and 1 µm diamond solutions. They were finally rinsed with water between each diamond solution, cleaned into ethanol under ultrasounds and dried in air. EPMA was carried out to measure composition profiles from the oxide scale to the bulk material. Samples were metalized with C and inserted in the EPMA (in vacuum condition) at most one hour after the final polishing step. Oxygen pollution at the titanium surface is always present and the analysis results need to be corrected by removing the signal induced by the native oxide layer. To do so, oxygen concentration is measured 5 times in the bulk on the cross-section and corrected to equal the known O concentration in the bulk of the alloy [16]. The same correction is applied to all points of the EPMA profiles.

## 2.2. First-principles calculation methods

The Vienna Ab initio Simulation Package (VASP) [17], was used to perform density functional theory calculations [18, 19]. Simulations were carried out within the Perdew-Burke-Ernzerhof generalized gradient approximation of the exchange and correlation functional (PBE) [20]. Projector-augmented wave (PAW) pseudopotentials (Ti-pv with 10 electrons as valence electrons) were used [21]. A kinetic energy cut-off of 600 eV for the plane-wave basis set was used to compute energies, and the Brillouin zones were sampled using 20×20×18 k-mesh grids for the hcp primitive cell containing 2 atoms.

4×4×3 supercells, which contain 96 Ti atoms, were used to calculate insertion and migration energies.

Ionic relaxations were introduced by using a conjugate-gradient algorithm, and all calculations were realized without supercell relaxations (keeping volume and shape fixed during computations).

Investigations of migration paths were conducted using CLIMB-NEB calculations [22, 23]. Three intermediate positions were used for each trajectory. Frequencies were calculated using Agarwal et al. methodology [24]: forces induced on O were determined by applying small displacements (±0.01 Å) in 3 directions (x, y and z) from their equilibrium positions (see further detail in [25]).

# 3. Results

## 3.1. Air oxidation

Figure 1 shows the mass changes obtained after oxidation at 650 °C in lab air. It can be seen that alloy Ti64 loses mass after 200 h; this is due to oxide spalling that has been observed when removing samples from the furnace. In the model alloys, the alloying elements greatly affect the mass change. The alloys can be ordered from their global oxidation kinetics as follows: Ti-50>Ti-2Ta>Ti-6Al>Ti-2W≈Ti-8Ta>Ti-6Al-2Ta>Ti-6Al-2Hf>Ti-6Al-8Ta≈Ti-8W>Ti-6Al-2W>Ti6242s>Ti-6Al-8W.

<figure><img src="image_2.png" /><figcaption>Figure 1. Mass variation vs. time for alloys listed in Table 1 and reference materials (Ti-50, TA6V and Ti6242s) oxidized at 650 °C in air.</figcaption></figure>

Parabolic constants $k_p$, defined in Equation (1) and given in Table 3 for air oxidation, indicate the global kinetics, i.e., the kinetics of mass change due to both oxide growth and oxygen dissolution in the alloy. Only one alloy, Ti-6Al-8W, has a smaller oxidation kinetics than the oxidation reference material (Ti6242s).

$$ \left(\frac{\Delta m}{S}\right)_{tot} = \sqrt{k_p t} \qquad (1) $$

By measuring oxide scale thicknesses, the mass change due to the oxygen uptake necessary to grow the
oxide scale can be calculated and subtracted from the total mass gain to obtain the main gain due to oxygen dissolution in the metal (see Vaché et al. for details [7]). Figure 2 shows the variation in the quantity of oxygen dissolved in the alloys as a function of the weight fraction of refractory elements. It can be seen that adding refractory elements reduces oxygen dissolution for the binary alloys (Ti-Ta and Ti-W). Three ternary alloys, namely Ti-6Al-2Hf, Ti-6Al-2W and Ti-6Al-8W, dissolved less oxygen than the industrial alloys, with a decrease of almost 30% of this quantity for Ti-6Al-8W compared to Ti6242s.

<figure><img src="image_3.png" /><figcaption>Figure 2. Variation of the quantity of oxygen dissolved vs. weight fraction of refractory element after oxidation at 650 °C in air during 500 h. TA6V and Ti6242s values extracted from Vaché et al. [7] for comparison.</figcaption></figure>

Oxygen concentration profiles obtained by EPMA are presented in Figure 3 for air oxidation at 650 °C during 500 h. Most oxygen profiles have an “erf”-type shape (Equation 2) consistent with a constant oxygen concentration at the metal/oxide interface (about 25 at%) and a constant oxygen diffusivity. This is not the case for the Ti-Al-W ternary and Ti-W binary alloys, for which the profiles shape is more complex. In these alloys, the oxygen concentration is low just below the oxide scale (0 to 10 at.%); it then sharply increases to about 8 to 15 at.%, and slowly decreases toward the bulk. The low-oxygen area below the oxide scale can be due to nitrogen uptake in the alloys. Indeed, XRD analysis showed the presence of Ti₂N in these alloys. This suggests that the solubility of oxygen was modified by the presence of the nitride.

$$C(x) = C_0 + (C_s - C_0) * \left(1 - \operatorname{erf}\left[\frac{x}{2\sqrt{Dt}}\right]\right) \quad (2)$$

Equation (2) was fitted to the oxygen concentration profiles to obtain the oxygen diffusivities presented in Table 2. These values show that there are no large variations of oxygen diffusivity by adding refractory alloying elements.

<figure><img src="image_4.png" /><figcaption>Figure 3. Oxygen concentration profiles obtained by EPMA for air oxidation at 650 °C during 500 h.</figcaption></figure>

<table><caption>Table 2: Oxygen diffusivities for each alloy after oxidation in air at 650 °C during 500 h.</caption><thead><tr><th>Alloys</th><th>Air - D (×10<sup>-17</sup>m<sup>2</sup>.s<sup>-1</sup>)</th></tr></thead><tbody><tr><td>Ti-6Al</td><td>6.8±0.5</td></tr><tr><td>Ti-6Al-2Ta</td><td>7.9±0.6</td></tr><tr><td>Ti-6Al-8Ta</td><td>16±1</td></tr><tr><td>Ti-6Al-2W</td><td>15±1</td></tr><tr><td>Ti-6Al-8W</td><td>9.5±1.7</td></tr><tr><td>Ti-6Al-2Hf</td><td>10±1</td></tr><tr><td>Ti-2Ta</td><td>18±1</td></tr><tr><td>Ti-8Ta</td><td>17±1</td></tr><tr><td>Ti-2W</td><td>22±1</td></tr><tr><td>Ti-8W</td><td>26±2</td></tr><tr><td>Ti-50</td><td>20±1</td></tr><tr><td>Ti6242s</td><td>12±1</td></tr></tbody></table>

### 3.2. Ar-20%O₂ oxidation

Figure 4 shows the mass changes obtained after oxidation at 650 °C in Ar-20%O₂. The alloys can be ordered from their global oxidation kinetics as follows: Ti-8W>Ti-2W>Ti-8Ta≈Ti-50>Ti-2Ta≈Ti-6Al-2Hf>Ti-6Al-2W≈Ti-6Al≈Ti-6242s≈Ti-6Al-8W≈Ti-6Al-2Ta≈Ti-6Al-8Ta. This order is completely modified compared to oxidation in air. Indeed, the binary Ti-W alloys follow linear kinetics with a large mass gain (four times more than in air), while the ternary Ti-6Al-W alloys maintain the same global oxidation kinetics as Ti-6242s, as in air oxidation. Table 3 summarizes the parabolic rate constants obtained for Ar-20O₂ oxidation. All the oxygen concentration profiles measured by EPMA (not shown here) all have the same shape, with a maximum of 25-30 at.% below the scale, i.e. slightly higher than in air, even in the W-containing alloys.
<figure><img src="image_5.png" /><figcaption>Figure 4. Mass variation vs. time for alloys listed in Table 1 and reference materials (Ti-50 and Ti6242s) oxidized at 650 °C in 80Ar-20O₂.</figcaption></figure>

<table><caption>**Table 3:** Parabolic rate constants *k*<sub>p</sub> for each alloy after oxidation in air or in Ar-20O<sub>2</sub> at 650 °C during 500 h.</caption><thead><tr><th rowspan="2">Alloys</th><th>Air –</th><th>Ar-20%O<sub>2</sub> –</th></tr><tr><th><i>k</i><sub>p</sub> (10<sup>-7</sup> mg<sup>2</sup>.cm<sup>-4</sup>.s<sup>-1</sup>)</th><th><i>k</i><sub>p</sub> (10<sup>-7</sup> mg<sup>2</sup>.cm<sup>-4</sup>.s<sup>-1</sup>)</th></tr></thead><tbody><tr><td>Ti-6Al</td><td>12</td><td>12</td></tr><tr><td>Ti-6Al-2Ta</td><td>7.2</td><td>8.2</td></tr><tr><td>Ti-6Al-8Ta</td><td>5.4</td><td>6.8</td></tr><tr><td>Ti-6Al-2W</td><td>3.7</td><td>9.9</td></tr><tr><td>Ti-6Al-8W</td><td>2.2</td><td>8.9</td></tr><tr><td>Ti-6Al-2Hf</td><td>5.6</td><td>12</td></tr><tr><td>Ti-2Ta</td><td>24</td><td>12</td></tr><tr><td>Ti-8Ta</td><td>8.9</td><td>27</td></tr><tr><td>Ti-2W</td><td>12</td><td>N/A</td></tr><tr><td>Ti-8W</td><td>6.0</td><td>N/A</td></tr><tr><td>Ti-50</td><td>26</td><td>25</td></tr><tr><td>Ti6242s</td><td>3.5</td><td>8.4</td></tr></tbody></table>

### 3.3. Compute oxygen insertion: from pure Ti to dilute alloy modelling

#### 3.3.1. Oxygen diffusivity in pure Ti

Different interstitial configurations were tested to find the stable site for oxygen insertion in pure titanium. Only 3 of all tested configurations correspond to a stable insertion site for oxygen. The most stable site is the octahedral site (labelled OC), located in the 2a Wyckoff position (0,0,0). Then the second most stable site is the projection of the tetrahedral site on the basal plane (BT), which is located in 2d site (2/3,1/3,1/4). The last stable site is the crowdion site (CN), located in 6g (1/2,1/2,1/2). Figure 5 (left) shows interstitial stable sites in the Ti hcp primitive cell.

<figure><img src="image_6.png" /><figcaption>Figure 5. Stable interstitial positions for oxygen in the primitive cell of hcp Ti (left) and corresponding migration paths between stable sites (right).</figcaption></figure>

Solubility energies can be calculated using the Equation (3) as follows:

$$E_s[O] = E_{DFT}[96Ti + O] - E_{DFT}[96Ti] - \mu_{ref}[O] \quad (3)$$

with $E_{DFT}[96Ti + O]$ corresponds to the DFT energy of the supercell containing one oxygen, $E_{DFT}[96Ti]$ without oxygen, and $\mu_{ref}[O]$ is the chemical potential of oxygen, calculated from the DFT energy of the O₂ molecule. It can be noticed that the oxygen atom prefers to be located in octahedral sites. Indeed, solubility energies are equal to -5.55, -4.38 and -3.93 eV for OC, BT and CN respectively. These values are in good agreement with previous studies [26, 27]. These values show the large stability of the octahedral site, with a gap of almost 1.2 eV with the BT site. This means that oxygen in titanium always occupies OC sites.

Then, elementary paths are identified by listing all possible connections between stable sites, and migration energies are calculated by the NEB method. All migration paths that contribute to oxygen migration are presented in Figure 5. Although the CN-CN site could be a possible migration pathway, this is not included in the diffusion mechanism. In fact, the NEB calculation shows that there is no transition state, oxygen is diverted by the nearest OC or BT site. Then, frequencies are calculated and oxygen diffusivities in both basal and c-axis directions are computed by the Multi-State Diffusion (MSD) formalism [28, 29]. This formalism gives explicit formulas of oxygen diffusivities as a function of temperature, migration energies and frequencies of each site and transition state.

The calculated oxygen diffusivities are presented in Figure 6 with experimental data and previous results from *ab initio* studies for comparison. The values obtained in this study are close to the work of Wu et al. [27], without significant anisotropy along the a and c axes, whereas the study of Scotti et al. shows a strong anisotropic diffusion and is closer to experimental measurements. Gautier et al. discussed these differences in further details in [25].
<figure><img src="image_7.png" /><figcaption>Figure 6. Oxygen diffusivities in basal (dotted lines) and c-axis (continuous lines) directions obtained in this study (blue) and previous studies, with experimental data for comparison.</figcaption></figure>

### 3.3.2. Extension to dilute binary alloy: Effect of Al on oxygen solubility

Adding a substitutional solute element greatly

<figure><img src="image_8.png" /><figcaption>Figure 7. The possible insertion site of oxygen in binary alloy Ti-1at%Al.</figcaption></figure>

complexifies the study of oxygen insertion and migration. Indeed, adding an alloying element (in our case, one Al atom) reduces the symmetry of the crystal and thus increases the number of non-equivalent stable sites for oxygen and migration paths, even if we only consider a 1st nearest-neighbour (1NN) alloying element interaction.

To study the Al effect on oxygen insertion and diffusivity, a 4×4×3 supercell was considered by replacing one Ti atom with Al, which represents a dilute binary alloy Ti-1at%Al. The binding energy of Al in Ti is equal to -849 meV, which means that the insertion of Al in Ti to form Ti-1at%Al alloy is energetically favourable. Then, the O atom is inserted in stable sites identified in the Ti-O calculations (OC, CN and BT). However, some of the equivalent sites in pure Ti are not equivalent in a binary alloy. For example, the BT site can be located in the plane containing Al, or along the c-axis direction (see Figure 7), and thus gives two different BT sites (BT-B and BT-C resp.). A similar argumentation gives two different CN sites (CN-near and CN-far), while OC sites are not impacted by this break of symmetry induced by alloying element.

After calculating solubility energies, only the CN-near site becomes unstable. Similar results have been obtained by Wu et al., although they obtain the CN-far

site as an unstable site [30]. The effect of aluminium on oxygen stability can be quantified by calculating the oxygen-aluminium interaction energy, which is the difference of energies for O near and far from Al. These energies are equal to 0.70, 0.47, 0.28 and 0.12 eV for OC, BT-B, BT-C and CN-far sites respectively. These values, in good agreement with the study of Wu et al. [30], are all positives, which means the Al-O interaction is repulsive.

## 4. Discussion

Among the tested refractory elements, the addition of W strongly reduces oxidation kinetics in air in term of mass gain (Figure 1) but also in term of O dissolution in the metallic substrate (Figures 2 and 3). This beneficial effect of W is larger than the effect of Hf and Ta for the same concentrations. On the contrary, the global oxidation kinetics increase considerably for binary Ti-W alloys in Ar-20%O₂, when nitrogen is absent from the atmosphere. This comparison shows that the beneficial effect of W is related to the reaction of nitrogen with these alloys. In air, the oxygen concentration profile has the same error function shape in all alloys. The maximum oxygen concentration is about 25-30 at.%, except in alloys with W, for which this value is strongly decreased to about 15 and 10 at% for Ti-(6Al)-2W and Ti-(6Al)-8W respectively. This is likely due to the presence of nitrogen, forming nitrides and/or a solid solution with Ti, as observed previously for cp-Ti by Chaze et al. [31] and for Ti6242s by Dupressoire et al. for 1000 h oxidation in air at 650 °C [16] and further proved using atomic probe tomography (APT) [32]. Further analyses on Ti-(6Al)-W alloys will be performed to validate this hypothesis.

Regarding first-principle calculations, OC sites are found to be the most stable sites for pure Ti, as reported by Wu et al. and Scotti et al. [26, 30]. The gap between the OC and the 2nd most stable site (BT) is huge (1.17 eV). BT sites cannot be filled by thermal excitation (300 K represents around 25 meV), only OC sites contribute to the solubility of oxygen. By adding an Al atom, OC sites near Al are so destabilized that they can no longer contribute to the oxygen solubility. For pure Ti, the solubility limit of O is known to be 33 at% [8]. This corresponds to half of OC sites filled with O. Adding one Al atom blocks 6 OC sites around the solute atom, i.e. three sites involved in the solubility limit. For a 4×4×3 supercell with only one Al atom, i.e. in Ti-1at%Al, the oxygen solubility changes from 33 at% to 31.9 at%. By extension, the estimated solubility limit in the binary alloy studied experimentally Ti-10%atAl (Ti-6wt%Al), in the approximation of non-interacting Al solute atoms would be 15.8 at%. This low value is far from the observed
oxygen concentration at the interface which is about 25 at%. This could be because with 10 at% of Al, the solute atoms interact with each other. Further work is in progress to improve both the calculation and experimental measurements of the oxygen solubility.

## 5. Conclusions

The effect of refractory alloying elements (W, Ta and Hf) on oxidation resistance and oxygen diffusivity was studied at 650 °C for 500 h in air and in Ar-20%O₂. The results showed that W has the greatest effect on the reduction of oxidation kinetics in air. Combined with Al, which also has a beneficial effect, the ternary Ti-6Al-W has lower oxidation kinetics than Ti6242s in terms of mass gain and also in terms of dissolving oxygen in the metal. Without nitrogen, the positive effect of W disappears and the oxidation kinetics becomes linear. The difference of behaviour can be explained by the formation of titanium nitride Ti₂N during the oxidation of alloys containing W.

Adding Al in pure titanium reduces by a factor of 3 the oxygen diffusivity. The other alloying elements tested in the work do not change significantly oxygen diffusivity by comparison with pure titanium. However, tungsten reduces the maximum oxygen concentration after oxidation in air, which may be due to nitrogen insertion. Several hypotheses, related to both thermodynamics or kinetics, could explain this W-N coupling effect and they are currently under investigation.

## 6. Acknowledgements

This work was performed using HPC resources from CALMIP (Grant 2021-p0749) and GENCI-TGCC (Grant A0090912003). It has also been carried out within the framework of the PHYDOM project and has received funding from the DGAC. The authors gratefully acknowledge Cédric Lopez and Etienne Rimpot (ONERA-DMAS) and Sophie Gouy (UMS Castaing) for alloy elaboration with arcmelting furnace, chemical analysis and EPMA measurements, respectively.

## 7. References

1. Peters, M., et al., *Advanced Engineering Materials* 5-6 (2003) 419-427.

2. Boyer, R.R., *Advanced Performance Materials* 2-4 (1995) 349-368.

3. Yan, M., et al., *Powder Metallurgy* 57-4 (2014) 251-257.

4. Shenoy, R.N., J. Unnam, and R.K. Clark, *Oxidation of Metals* 26-1-2 (1986) 105-124.

5. Casadebaigt, A., J. Hugues, and D. Monceau, *Corrosion Science* 175- (2020) 108875.

6. Fukai, H., et al., *ISIJ International* 45-1 (2005) 133-141.

7. Vaché, N., et al., *Corrosion Science* 178- (2021) 109041.

8. Okamoto, H., *Journal of Phase Equilibria and Diffusion* 32-5 (2011) 473.

9. Ebel, T., et al., *Key Engineering Materials* 520- (2012) 153-160.

10. Chaze, A.M. and C. Coddet, *Journal of the Less-Common Metals* 157- (1990) 55-70.

11. Chaze, A.M., C. Coddet, and G. Béranger, *Journal of the Less Common Metals* 83- (1982) 49-70.

12. Gobel, M., V.A.C. Haanappel, and M.F. Stroosnijder, *Oxidation of Metals* 55-1-2 (2001) 137-151.

13. Vojtěch, D., B. Bártová, and T. Kubatík, *Materials Science and Engineering: A* 361-1 (2003) 50-57.

14. Chaze, A.M. and C. Coddet, *Oxidation of Metals* 27-1-2 (1987) 1-20.

15. Huvelin, Z., et al., *Role of refractory elements in near-alpha titanium alloys on high temperature mechanical properties*. in *Titanium 2019*. 2019. NANTES, France.

16. Dupressoire, C., et al., *Oxidation of Metals* vol. 87-nº 3-4 (2017) pp. 343-353.

17. Kresse, G. and J. Hafner, *Physical Review B* 47-1 (1993) 558-561.

18. Hohenberg, P. and W. Kohn, *Physical Review* 136-3B (1964) B864-B871.

19. Kohn, W. and L.J. Sham, *Physical Review* 140-4A (1965) A1133-A1138.

20. Perdew, J.P., K. Burke, and M. Ernzerhof, *Physical Review Letters* 77-18 (1996) 3865-3868.

21. Kresse, G. and D. Joubert, *Physical Review B* 59-3 (1999) 1758-1775.

22. Henkelman, G., B.P. Uberuaga, and H. Jónsson, *The Journal of Chemical Physics* 113-22 (2000) 9901-9904.

23. Henkelman, G. and H. Jónsson, *The Journal of Chemical Physics* 113-22 (2000) 9978-9985.

24. Agarwal, R. and D.R. Trinkle, *Physical Review B* 94-5 (2016) 054106.

25. Gautier, K., et al., submitted- (2023).

26. Scotti, L. and A. Mottura, *The Journal of Chemical Physics* 144-8 (2016) 084701.

27. Wu, H.H. and D.R. Trinkle, *Physical Review Letters* 107-4 (2011) 045504.

28. Landman, U. and M.F. Shlesinger, *Physical Review B* 19-12 (1979) 6207-6219.

29. Landman, U. and M.F. Shlesinger, *Physical Review B* 19-12 (1979) 6220-6237.

30. Wu, H.H. and D.R. Trinkle, *Journal of Applied Physics* 113-22 (2013) 223504.

31. Chaze, A.M. and C. Coddet, *Journal of the Less Common Metals* 124- (1986) 73-84.

32. Dupressoire, C., et al., *Acta Materialia* 216- (2021) 117134.