Thermodynamic Study on Initial Oxidation Behavior of TiAl-Nb Alloys at High Temperature

: The initial oxidation behavior of TiAl-Nb alloys was systematically investigated against the composition, temperature, and partial pressure of O 2 with the CALculation of PHAse Diagrams (CALPHAD) technique. The mole fraction of each oxidation product at the initial oxidation stage of the alloys at the corresponding temperatures was predicted. The initial oxidation products of the alloys are oxides of Al, Ti, and Nb, with the oxidation order of Al, Ti, and Nb. As P(O 2 ) increases, the Ti and Nb oxidation products move towards a high oxygen content, and the mole fractions of the Al and Ti oxides gradually decrease and increase, respectively. It was found that the temperature and partial pressure of O 2 determined the types of the oxides and the oxidation order, while the concentration of Nb and Al determined the mole fraction of the oxides. The CALPHAD results are in good agreement with the experiments.


Introduction
The TiAl alloy is widely used in aerospace, automobiles, and other fields because of its high specific strength, low density, good fracture toughness, and creep resistance [1][2][3][4][5].Because of these excellent properties, it is often considered as an ideal substitute for nickel-based superalloys for some aerospace structural parts [6,7].However, due to the lack of oxidation resistance of the TiAl alloy at high temperature, the service life of the TiAl alloy at high temperatures is severely affected and its range of use is limited [8][9][10][11].Therefore, in order to improve the high-temperature oxidation resistance of TiAl alloys, a lot of experimental research has been conducted on their oxidation behavior and the improvement of their oxidation resistance [9,[11][12][13][14][15][16].However, oxidation is a very complicated process, and it is difficult to trace in situ experimentally.Although there have been many recent studies on the formation and evolution mechanisms of oxide films during the oxidation of TiAl alloys [17][18][19], thermodynamic information on the oxidation behavior of TiAl alloys at relatively high temperatures is lacking.
In recent years, thermodynamic calculations have been widely used in the field of materials science and engineering [20].The CALculation of PHAse Diagrams (CALPHAD) technique, as one of the development directions of material thermodynamic calculation, is one of the most effective method to calculate the properties of multicomponent and multiphase systems at present and has become an effective tool for the development and design of new materials [21][22][23][24].It is used to obtain the oxidation thermodynamic information of materials to predict the material properties, as well as to develop new materials [25][26][27][28][29].
Niobium is a doping element with a higher valence than titanium.It has been suggested that the addition of niobium decreases the oxygen vacancy concentration, thus inhibiting rutile growth, increasing the activity of Al, and reducing the solubility of oxygen Metals 2023, 13, 485.https://doi.org/10.3390/met13030485https://www.mdpi.com/journal/metals in the alloy [30][31][32].Therefore, in this paper, the initial oxidation behavior of TiAl-based alloys with the compositions Ti-42Al-xNb, Ti-45Al-xNb, and Ti-48Al-xNb (x = 0~10 at.%) at high temperatures was thermodynamically calculated using the CALPHAD technique with the PanTiAl high-quality titanium alloy thermodynamic database in combination with the well-established computational phase diagram software PANDAT 2021 (CompuTherm, LLC, Wisconsin, WI, USA).The three alloy systems are selected to have a wide range of Al content, while covering the two commercial TiAl alloys, i.e., Ti45XD and Ti4822.
The formation and transformation of the oxidation products and the mole fraction of each phase in the alloy in the initial oxidation stage were predicted, and the thermodynamic factors were discussed, which provides theoretical support for the optimization of TiAl-based alloys.

Method
The CALculation of PHAse Diagrams (CALPHAD) technique uses thermodynamic models to describe the thermodynamic characteristics of multicomponent systems as functions under different conditions, such as temperature, composition, and pressure [33].CALPHAD has three key elements: the thermodynamic model, the database, and the software [34].The thermodynamic description of the phase in the research system is carried out through the thermodynamic model, and then, the parameters in the thermodynamic model are optimized through key experiments and first-principles theoretical calculations so as to establish the database using the CALPHAD-based software [35].The existing thermodynamic databases provide information such as stable and metastable phase equilibria, phase fractions, phase transition characteristic temperatures, and various thermodynamic quantities, which can play an important role in the development and design of materials [36].Finally, based on the thermodynamic model, the multicomponent system in the system is described thermodynamically and combined with the corresponding thermodynamic database and the use of the thermodynamic software to calculate the various phase generation and phase content changes with the temperature and other processes of the phase diagram and thermodynamic functions.
PANDAT is a computational software package developed based on the CALPHAD method and integrated with the PanPhaseDiagram, PanPrecipitation, PanDiffusion, PanSolidification and PanPhaseField modules for the thermodynamic/phase diagram calculation, precipitation simulation, diffusion simulation, solidification simulation, and phase field simulation of multivariate systems.Combining PANDAT software with thermodynamic, kinetic, and thermophysical databases enables an integrated workspace for the phase diagram calculations and material property simulations of multivariate systems.The results of the simulations, which contain thermodynamic, kinetic, thermophysical and microstructurerelated information, are important in the development and design of materials and in the selection of parameters for process steps such as heat treatment, property prediction, and failure analysis [37].In recent years, the PANDAT software and the database have become increasingly sophisticated and have been well used through the combination of this software and the database, which has provided researchers with a lot of useful information [38,39].Therefore, this paper calculates the initial oxidation products of Ti-42Al-xNb, Ti-45Al-xNb, and Ti-48Al-xNb alloys oxidized at the corresponding temperatures and predicts the transformation and mole fraction of each oxide in the initial stage of oxidation of the alloys based on the well-established computational phase diagram software PANDAT, the high-quality PanTiAl titanium alloy thermodynamic database.
The initial oxidation behavior of the TiAl-based alloys was calculated with the aid of the high-quality PanTiAl thermodynamic database accumulated in the previous stage.The calculation conditions are listed in the following Table 1.

Oxidation Products
The initial oxidation products of Ti-42Al-xNb at 700 °C, 800 °C, and 900 °C are shown in Figure 1.At 700 °C (Figure 1a), the alloy was oxidized at P(O2), and the oxidation products were Al2O3 and Ti2O3.As P(O2) increases, the oxide of Nb appears, and the alloy enters a fully oxidized state.As P(O2) continues to increase, the Ti and Nb oxidation products move towards a high oxygen content, and the final oxidation products are Al2O3, TiO2, and Nb2O5.At 800 °C (Figure 1b), the alloy also undergoes oxidation at low P(O2), and the oxidation products are Al2O3 and TiO.As P(O2) continues to increase, there is a transition from Ti 2+ to Ti 3+ , while the oxides of Nb appear and the alloy enters a fully oxidized state.As P(O2) further increases, Ti 3+ becomes Ti 4+ , Nb 2+ becomes Nb 3+ , Nb 5+ , and the final oxidation products are Al2O3, TiO2, and Nb2O5.At 900 °C (Figure 1c), the alloy was not oxidized even at low P(O2).The Nb content was in the range of 0 to 5.8% for TiAl + Ti3Al and in the range of 5.8% to 10% for TiAl + Ti3Al + Nb2Al.With the increase in P(O2), the alloy starts to oxidize and Al2O3 preferentially appears.With the P(O2) further increases, the Ti 2+ oxides start to appear.As P(O2) continues to increase, there is a transition from Ti 2+ to Ti 3+ , while the oxides of Nb appear and the alloy enters a fully oxidized state.Finally, as P(O2) increases, Ti 3+ becomes Ti 4+ , Nb 2+ becomes Nb 3+ , Nb 5+ , and the final oxidation products are Al2O3, TiO2, and Nb2O5.The initial oxidation products of Ti-45Al-xNb at 700 °C, 800 °C, and 900 °C are shown in Figure 2. At 700 °C (Figure 2a), the initial oxidation products are basically similar to those of Ti-42Al-xNb (Figure 1a), and the oxidation products and their corresponding P(O2) are basically unchanged.At 800 °C (Figure 2b), the initial oxidation products are basically similar to those of Ti-42Al-xNb (Figure 1b), and the oxidation products and their corresponding P(O2) are basically unchanged.At 900 °C (Figure 2c), when the alloy is not oxidized at low P(O2), the Nb content is in the range of 0 to 7.8% for TiAl + Ti3Al and 7.8% to 10% for TiAl + Ti3Al + Nb2Al.As P(O2) increases, the subsequent changes are essentially similar to those of Ti-42Al-xNb (Figure 1c), with the oxidation products remaining essentially constant with their corresponding P(O2).The initial oxidation products of Ti-45Al-xNb at 700 • C, 800 • C, and 900 • C are shown in Figure 2. At 700 • C (Figure 2a), the initial oxidation products are basically similar to those of Ti-42Al-xNb (Figure 1a), and the oxidation products and their corresponding P(O 2 ) are basically unchanged.At 800 • C (Figure 2b), the initial oxidation products are basically similar to those of Ti-42Al-xNb (Figure 1b), and the oxidation products and their corresponding P(O 2 ) are basically unchanged.At 900 • C (Figure 2c), when the alloy is not oxidized at low P(O 2 ), the Nb content is in the range of 0 to 7.8% for TiAl + Ti 3 Al and 7.8% to 10% for TiAl + Ti 3 Al + Nb 2 Al.As P(O 2 ) increases, the subsequent changes are essentially similar to those of Ti-42Al-xNb (Figure 1c), with the oxidation products remaining essentially constant with their corresponding P(O 2 ).
The initial oxidation products of Ti-48Al-xNb at 700 • C, 800 • C, and 900 • C are shown in Figure 3.At 700 • C (Figure 3a), the initial oxidation products are basically similar to those of Ti-42Al-xNb (Figure 1a) and Ti-45Al-xNb (Figure 2a), and the oxidation products and their corresponding P(O 2 ) are basically unchanged.At 800 • C (Figure 3b), the initial oxidation products are basically similar to those of Ti-42Al-xNb (Figure 1b) and Ti-45Al-xNb (Figure 2b), and the oxidation products and their corresponding P(O 2 ) are basically unchanged.At 900 • C (Figure 3c), the initial oxidation product is similar to that of Ti-42Al-xNb (Figure 1c) and Ti-45Al-xNb (Figure 2c).At low P(O 2 ), the alloy matrix is TiAl + Ti 3 Al.The other oxidation products and their corresponding P(O 2 ) are essentially unchanged.The initial oxidation products of Ti-48Al-xNb at 700 °C, 800 °C, and 900 °C are shown in Figure 3.At 700 °C (Figure 3a), the initial oxidation products are basically similar to those of Ti-42Al-xNb (Figure 1a) and Ti-45Al-xNb (Figure 2a), and the oxidation products and their corresponding P(O2) are basically unchanged.At 800 °C (Figure 3b), the initial oxidation products are basically similar to those of Ti-42Al-xNb (Figure 1b) and Ti-45Al-xNb (Figure 2b), and the oxidation products and their corresponding P(O2) are basically unchanged.At 900 °C (Figure 3c), the initial oxidation product is similar to that of Ti-42Al-xNb (Figure 1c) and Ti-45Al-xNb (Figure 2c).At low P(O2), the alloy matrix is TiAl + Ti3Al.The other oxidation products and their corresponding P(O2) are essentially unchanged.The initial oxidation products of Ti-48Al-xNb at 700 °C, 800 °C, and 900 °C are shown in Figure 3.At 700 °C (Figure 3a), the initial oxidation products are basically similar to those of Ti-42Al-xNb (Figure 1a) and Ti-45Al-xNb (Figure 2a), and the oxidation products and their corresponding P(O2) are basically unchanged.At 800 °C (Figure 3b), the initial oxidation products are basically similar to those of Ti-42Al-xNb (Figure 1b) and Ti-45Al-xNb (Figure 2b), and the oxidation products and their corresponding P(O2) are basically unchanged.At 900 °C (Figure 3c), the initial oxidation product is similar to that of Ti-42Al-xNb (Figure 1c) and Ti-45Al-xNb (Figure 2c).At low P(O2), the alloy matrix is TiAl + Ti3Al.The other oxidation products and their corresponding P(O2) are essentially unchanged.

Mole Fractions of the Oxides
Further calculations were performed to obtain the variation of the mole fraction of the oxidation products with oxygen partial pressure at the early oxidation stage.Three compositions of Ti-42Al-8Nb, Ti-45Al-4Nb, and Ti-48Al-2Nb were selected, and the calculations were performed at 900 °C; the results are shown in Figure 4. Before oxidation, Ti-42Al-8Nb was initially dominated by the Ti3Al + TiAl + Nb2Al phase at 900 °C (Figure 4a).As the alloy increases with oxygen partial pressure, the matrix phase content starts to decrease and the Al2O3 content starts to gradually increase.As the partial pressure of O2 continues to increase, Ti begins to oxidize preferentially to form TiO. Al and Ti are oxidized almost simultaneously.Thermodynamically, the stability of Al2O3 and TiO of the metals Al and Ti is very similar [40].From the affinity energy, the affinity energy of the TiO formed by Ti and O is −28.27 eV; the affinity energy of the Al2O3 formed by Al and O

Mole Fractions of the Oxides
Further calculations were performed to obtain the variation of the mole fraction of the oxidation products with oxygen partial pressure at the early oxidation stage.Three compositions of Ti-42Al-8Nb, Ti-45Al-4Nb, and Ti-48Al-2Nb were selected, and the calculations were performed at 900 • C; the results are shown in Figure 4. Before oxidation, Ti-42Al-8Nb was initially dominated by the Ti 3 Al + TiAl + Nb 2 Al phase at 900 • C (Figure 4a).As the alloy increases with oxygen partial pressure, the matrix phase content starts to decrease and the Al 2 O 3 content starts to gradually increase.As the partial pressure of O 2 continues to increase, Ti begins to oxidize preferentially to form TiO. Al and Ti are oxidized almost simultaneously.Thermodynamically, the stability of Al 2 O 3 and TiO of the metals Al and Ti is very similar [40].From the affinity energy, the affinity energy of the TiO formed by Ti and O is −28.27 eV; the affinity energy of the Al 2 O 3 formed by Al and O is −30.00 eV; and the affinity energies of Al 2 O 3 and TiO are also very similar [41].As the partial pressure of O 2 increases, there is a transition from Ti 2+ to Ti 3+ , Ti 4+ and the mole fraction gradually increases, while the mole fraction of Al 2 O 3 gradually decreases, and the mole fraction of Nb oxide also gradually increases, but all are relatively low, and finally, the mole fraction of TiO 2 is higher.Before oxidation, Ti-45Al-4Nb was dominated by the Ti 3 Al + TiAl phases at 900 • C (Figure 4b).As the alloy increases with oxygen partial pressure, the matrix phase content begins to decrease and the Al 2 O 3 content begins to gradually increase.As the partial pressure of O 2 continues to increase, the subsequent change process is basically consistent with Figure 4a.However, the mole fractions of TiAl and Al 2 O 3 have increased and the mole fractions of the Ti 3 Al and Nb oxides have decreased compared with Figure 4a.Before oxidation, Ti-48Al-2Nb was also dominated by the Ti 3 Al + TiAl phases at 900 • C (Figure 4c).As the alloy increases with the oxygen partial pressure, the matrix phase content begins to decrease and the Al 2 O 3 content begins to gradually increase.As the partial pressure of O 2 continues to increase, the subsequent change process is basically consistent with Figure 4a and b.However, compared with Figure 4a and b partial pressure of O2 increases, there is a transition from Ti 2+ to Ti 3+ , Ti 4+ and the mole fraction gradually increases, while the mole fraction of Al2O3 gradually decreases, and the mole fraction of Nb oxide also gradually increases, but all are relatively low, and finally, the mole fraction of TiO2 is higher.Before oxidation, Ti-45Al-4Nb was dominated by the Ti3Al + TiAl phases at 900 °C (Figure 4b).As the alloy increases with oxygen partial pressure, the matrix phase content begins to decrease and the Al2O3 content begins to gradually increase.As the partial pressure of O2 continues to increase, the subsequent change process is basically consistent with Figure 4a.However, the mole fractions of TiAl and Al2O3 have increased and the mole fractions of the Ti3Al and Nb oxides have decreased compared with Figure 4a.Before oxidation, Ti-48Al-2Nb was also dominated by the Ti3Al + TiAl phases at 900 °C (Figure 4c).As the alloy increases with the oxygen partial pressure, the matrix phase content begins to decrease and the Al2O3 content begins to gradually increase.As the partial pressure of O2 continues to increase, the subsequent change process is basically consistent with Figure 4a and b.However, compared with Figure 4a and b, the mole fractions of TiAl and Al2O3 increased, and the mole fractions of Ti3Al and Nb oxides decreased.

Relevance with the Experiments
The presence of Ti oxides at high O2 partial pressure is often detrimental to the formation of a protective Al2O3 outer layer, resulting in the poor oxidation resistance of the alloy [42].The initial oxidation behavior of TiAl was also studied experimentally [43,44].The results show that Al2O3 is formed preferentially at the initial stage of oxidation, followed by the formation of low-valent oxides (Ti2O3, TiO) at the interface between Al2O3 and the substrate, and finally, the low-valent Ti ions are oxidized to TiO2 by diffusion to the outer layer.In addition, the low-valent oxides (Ti2O3 and TiO) are more readily oxidized to TiO2 than Ti [45].Therefore, TiO2 rather than TiO is usually found in the experiment because the surface partial pressure of the oxide layer is very high, and the intermediate state is often further oxidized to the highest value state in the atmos-

Relevance with the Experiments
The presence of Ti oxides at high O 2 partial pressure is often detrimental to the formation of a protective Al 2 O 3 outer layer, resulting in the poor oxidation resistance of the alloy [42].The initial oxidation behavior of TiAl was also studied experimentally [43,44].The results show that Al 2 O 3 is formed preferentially at the initial stage of oxidation, followed by the formation of low-valent oxides (Ti 2 O 3 , TiO) at the interface between Al 2 O 3 and the substrate, and finally, the low-valent Ti ions are oxidized to TiO 2 by diffusion to the outer layer.In addition, the low-valent oxides (Ti 2 O 3 and TiO) are more readily oxidized to TiO 2 than Ti [45].Therefore, TiO 2 rather than TiO is usually found in the experiment because the surface partial pressure of the oxide layer is very high, and the intermediate state is often further oxidized to the highest value state in the atmosphere.For Nb oxides the appearance of early Nb oxides was also confirmed experimentally, but for several reasons, such as the low Nb content, the oxides of the alloy in the laboratory were mainly Al and Ti oxides [46,47].Liu et al. [48] studied the oxide film generated by the oxidation of Ti-42Al-8Nb in 900 • C air for 20 h.The results show that the outermost oxide layer is TiO 2 , and the secondary layer is composed of Al 2 O 3 , TiO, Ti 2 O 3 , TiO 2 and a small amount of TiN.In addition, the oxide content of Ti increases gradually along the matrix to the outer surface of the oxide film.Chen et al. [49] experimentally carried out XPS feature mapping analysis on TiAl-based alloy powders oxidized for only 5 min at the initial oxidation stage.It was found that the oxides formed at the initial 5 min of oxidation already contained TiO 2 , Ti 2 O 3 , and Al 2 O 3 , with the TiO 2 form being the predominant one.This further indicates the formation of Al 2 O 3 and the rapid transformation of low-valent oxides of Ti to high-valent TiO 2 at the early stage of oxidation and the gradual increase in content.The experimental results are basically in agreement with the calculation.In the early stage, the O 2 partial pressure was relatively high in the air, and the Al 2 O 3 and TiO 2 oxidation layers formed on the surface of the alloys.At high temperature, the density of the Al 2 O 3 layer was insufficient, and Ti continued to oxidize.At the same time, the O 2 partial pressure at the interface between the matrix and the oxide film was reduced, thus low-valent titanium oxides are formed.

Conclusions
For the early oxidation stage of Ti-42Al-xNb, Ti-45Al-xNb, and Ti-48Al-xNb at 700 • C, 800 • C, and 900 • C, the oxidation products are the oxides of Al, Ti, and Nb, and the oxidation order is Al, Ti, and Nb.When the O 2 partial pressure reaches a certain range, Al is oxidized preferentially to produce Al 2 O 3 , followed by oxides of Ti 2+ .As the O 2 partial pressure increases, there is a transition from Ti 2+ to Ti 3+ , Ti 4+ , and Nb also starts to oxidize.
For the same alloy oxidized at different high temperatures, the O 2 partial pressure required to initiate the oxidation and for the transformation of the oxidation products is relatively high.For different alloys oxidized at the same temperature, the initial oxidation products are generally the same at 700 • C and 800 • C, while they are slightly different at 900 • C.
Regarding the oxidation products at 900 • C, the mole fraction of Al 2 O 3 is higher, while that of the Nb oxides is lower at the early stage; as P(O 2 ) increases, the mole fraction of Al 2 O 3 gradually decreases and that of the Ti oxides gradually increases in all three alloys, with the subsequent domination of TiO 2 .The calculations are in good agreement with the experiments.

Table 1 . 3 .Table 1 .
Composition, Pressure, temperature, and partial pressure of O 2 in the present calculation.Results and Discussion 3.1.Oxidation Products The initial oxidation products of Ti-42Al-xNb at 700 • C, 800 • C, and 900 • C are shown in Figure 1.At 700 • C (Figure 1a), the alloy was oxidized at P(O 2 ), and the oxidation products were Al 2 O 3 and Ti 2 O 3 .As P(O 2 ) increases, the oxide of Nb appears, and the alloy enters a fully oxidized state.As P(O 2 ) continues to increase, the Ti and Nb oxidation products move towards a high oxygen content, and the final oxidation products are Al 2 O 3 , TiO 2 , and Nb 2 O 5 .At 800 • C (Figure 1b), the alloy also undergoes oxidation at low P(O 2 ), and the oxidation products are Al 2 O 3 and TiO.As P(O 2 ) continues to increase, there is a transition from Ti 2+ to Ti 3+ , while the oxides of Nb appear and the alloy enters a fully oxidized state.As P(O 2 ) further increases, Ti 3+ becomes Ti 4+ , Nb 2+ becomes Nb 4+ , Nb 5+ , and the final oxidation products are Al 2 O 3 , TiO 2 , and Nb 2 O 5 .At 900 • C (Figure 1c), the alloy was not oxidized even at low P(O 2 ).The Nb content was in the range of 0 to 5.8% for TiAl + Ti 3 Al and in the range of 5.8% to 10% for TiAl + Ti 3 Al + Nb 2 Al.With the increase in P(O 2 ), the alloy starts to oxidize and Al 2 O 3 preferentially appears.With the P(O 2 ) further increases, the Ti 2+ oxides start to appear.As P(O 2 ) continues to increase, there is a transition from Ti 2+ to Ti 3+ , while the oxides of Nb appear and the alloy enters a fully oxidized state.Finally, as P(O 2 ) increases, Ti 3+ becomes Ti 4+ , Nb 2+ becomes Nb 4+ , Nb 5+ , and the final oxidation products are Al 2 O 3 , TiO 2 , and Nb 2 O 5 .Composition, Pressure, temperature, and partial pressure of O₂ in the present calculation.~10 −20 Ti-45Al-xNb Ti-48Al-xNb (x = 0-10 at.%)
, the mole fractions of TiAl and Al 2 O 3 increased, and the mole fractions of Ti 3 Al and Nb oxides decreased.