Comparison of the Magnesiothermic Reduction Behavior of Nb2O5 and Ti2Nb10O29

Abstract

Nb-Ti binary alloys are widely employed as high value-added materials in the manufacture of super heat-resistant alloys, biomaterials, and superconductors. Therefore, there is significant interest to produce Nb-Ti master alloys in a cost-effective manner. In this study, we investigated the magnesiothermic reduction of Nb₂O₅ and Ti₂Nb₁₀O₂₉ over the temperature range of 1073 to 1223 K and comparatively evaluated the reaction outcomes. The reduction product was composed of metal (Nb or Nb-Ti) particles and MgO, which covered the surface of the reduced metal particles. After the reduction reaction, the surface MgO phase was removed by pickling with hydrochloric acid (HCl) to finally recover the Nb metal or Nb-Ti alloy as a pure product. Scanning electron microscopy and X-ray diffraction analyses of the pure Nb metal and Nb-Ti alloy powders revealed that the reduction of both raw materials was successful at temperatures exceeding 1173 K. Reaction kinetics analysis revealed that the activation energy for the reduction of the mixed metal oxide (Ti₂Nb₁₀O₂₉) is lower than that of Nb₂O₅ reduction. This is because of the different reaction mechanism behaviors during reduction and the different thermodynamic stabilities of the precursors.

1. Introduction

Niobium, a metal with a very high melting point of 2741 K, is often used as an additive in the manufacture of commercial alloys such as iron- and titanium-based alloys because of its excellent ductility, corrosion resistance, and high strength [1]. Among Nb-based materials, Nb-Ti binary alloys are widely used as high value-added materials for manufacturing super heat-resistant alloys, biomaterials, and superconductors [2]. Consequently, the efficient fabrication of Nb-Ti master alloys is the focus of extensive research.

The most commonly used conventional commercial production process for Nb-Ti alloys is the direct preparation of high-purity Nb and Ti metals by arc melting [3]. However, this method is expensive and requires high-purity raw metals. As a low-cost process, the thermite reaction using aluminum powder to reduce low-cost raw oxides has been commercialized. However, it is not economical to use high-purity, expensive fine aluminum powder as a reducing agent [4]. Furthermore, methods using calcium, sodium, and magnesium as reducing agents, instead of aluminum, are also being actively studied. Among them, calcium has the advantage of reduction at approximately 1273 K, with easy removal of calcium oxide, a by-product, after the reduction process [5]. However, handling calcium at high temperatures requires caution due to its pronounced affinity for oxygen [6,7]. The reduction process using sodium allows for lower reduction temperatures, facilitating the production of finely crystalline powders and straightforward by-product removal [8,9]. But the dilution materials used are toxic [10,11].

The use of magnesium as a reducing agent has several advantages [12], such as a relatively low reduction temperature [13], no mutual solid solubility of Nb and Ti with Mg in the reduction temperature range, easy extraction of pure Nb-Ti alloys [14], and easy removal of the MgO by-product [15,16]. Mg can be used as a reductant in both gas and liquid phases. In liquid-phase reduction using Mg, it may be difficult to control the reaction rate, owing to the possibility of direct contact of the Mg liquid with metal oxide, resulting in a violent reaction [17]. In contrast, when gas-phase Mg is used, the reaction time is slightly longer, but the intense exothermic reaction is avoided, as observed in many studies. Our group has also investigated the extraction of pure metals, such as Ta, Nb, and V, through gas-phase Mg reduction [12].

The direct extraction of Nb-Ti alloys using magnesium gas reduction requires an initial oxide feedstock containing Nb and Ti. Although some studies have been reported on this method, the reduction reaction was performed at a single temperature of 1073 K, and no study on the extraction of the Nb-Ti alloy by removing MgO produced as a secondary product has been reported [18]. Especially, the reduction behavior and kinetic energy variations in the reduction of Nb₂O₅ and a Nb-Ti multiple oxide using Mg have not been studied.

Therefore, in this study, we examined the Mg gas reduction of two materials, i.e., pure Nb₂O₅ and a Nb-Ti composite oxide. The properties of the reduced materials, such as the phase and microstructure [19,20], were compared according to different reduction temperatures. In particular, the reaction behaviors were analyzed from the thermodynamic and kinetic aspects of the Mg reduction reaction [21].

2. Materials and Methods

Nb-20 wt.%Ti was selected as the target alloy. To extract this alloy, Nb-Ti composite oxides were prepared separately as initial raw materials. Niobium oxide (Nb₂O₅, 99.99%, ~300 nm, JiuJiang Ltd., JiuJiang, China) and titanium oxide (TiO₂, 99.99%, ~200 nm, YEE YOUNG TTC CO., Seoul, Republic of Korea) were mixed uniformly according to the target ratio. Then, heat treatment was performed at 1573 K for 10 h in air to form the composite oxide phase [22].

To extract Nb from 1 mol of Nb₂O₅, 5 mol of Mg is required, and the mass ratio in this case is 266:120. Typically, 20 g of Nb₂O₅ was used in this study, and the theoretical amount of Mg required for reducing it is 9 g. However, 20 g of Mg was added to the reactor to ensure an adequate reduction of the oxide. In addition, the excess Mg required for reducing the complex oxide was calculated and used in the same way.

The prepared oxide powder and magnesium pieces were placed in a stainless steel (STS304, AJUVACUUM, Daegu, Republic of Korea) reactor using a graphite crucible. Therefore, the gaseous Mg reacted with the oxide to form MgO and metal. Then, the reactor was evacuated to 6 × 10⁻⁴ kPa using a mechanical vacuum pump, and argon gas (99.999% purity) was injected to reach the atmospheric pressure. The mixture was then heated to the reduction temperature of 1073, 1123, 1173, or 1223 K at a rate of 10 K/min and maintained at the final temperature for 10 h before terminating the reduction reaction. The chamber was maintained at a pressure exceeding 110 kPa throughout the heating, reducing, and cooling processes.

After the completion of the reduction reaction, the final metallic material was obtained by pickling the formed MgO component in a 10% aqueous hydrochloric acid solution to remove it [12].

The microstructure, phase, and composition of the obtained metal powders were evaluated using a scanning electron microscope (MIRA3 LM, TESCAN, Brno, Czech Republic), an X-ray diffractometer (Rigaku, Tokyo, Japan), an ONH analyzer (ELTRA ONH-P, Haan, Germany), and an elemental analyzer (Flash 2000, Thermo Fisher Scientific, Waltham, MA, USA), in addition to an Inductively Coupled Plasma Mass Spectrometer (Varian 820 ICP-MS, Varian, Mulgrave, Australia).

3. Results and Discussion

The scanning electron microscopy (SEM) images in Figure 1 show the microstructures of Nb₂O₅ and TiO₂ powders used as metal precursors. Both powders were in general composed of spherical particles, which were slightly agglomerated.

Figure 2 shows an SEM image of the composite oxide obtained by the heat treatment of the metal oxide mixture (Nb₂O₅ and TiO₂) at 1573 K for 10 h in air. It exhibits a morphology that expanded significantly with heat treatment. The X-ray diffraction (XRD) pattern of this material (Figure 3) revealed the absence of pure Nb₂O₅ and TiO₂ phases. Instead, a new complex phase of Ti₂Nb₁₀O₂₉ was observed, indicating successful complexation.

Figure 4 shows a schematic of the magnesium gas reduction of the metal oxide. The free energy changes for the reduction of Nb₂O₅ and TiO₂ at 1173 K as the average temperature are shown in Equations (1) and (2), respectively, which indicate that the two reactions are thermodynamically favorable.

Nb₂O₅ (s) + 5Mg (g) = 2Nb (s) + 5MgO (s)   ΔG_1173K = −1132.04 kJ/mole(1)

TiO₂ (s) + 2Mg (g) = Ti (s) + 2MgO (s)   ΔG_1173K = −275.80 kJ/mole(2)

The reduction with Mg gas starts from the surface of the Nb₂O₅ or Ti₂Nb₁₀O₂₉ particles. If the reduction is successful, a MgO film can eventually form on the surface of the particles while the Nb metal or Nb-Ti alloy is formed inside the particles. After the reaction, the surface MgO phase can be removed by pickling to finally recover the Nb metal or Nb-Ti alloy as a pure product.

Figure 5a,b show representative SEM images and the XRD pattern of the Nb powder obtained through magnesium reduction of Nb₂O₅ at 1173 K. First, as determined through XRD analysis, only Nb metals and MgO phases were present after the reaction, indicating a successful reduction process. This result suggests that the reduced material particles shown in Figure 5a had an Nb-core and MgO-shell structure. The particle size after reduction was approximately 200 nm, comparable to the size of the initial metal oxide particles.

Figure 6 shows the results obtained after the Mg reduction of Ti₂Nb₁₀O₂₉. Because the particles of the composite oxide were very coarse (see Figure 2), the particles obtained after reduction were also highly coarse. In addition, some extraneous particles were adsorbed onto the surface of the coarse particles, which are speculated to be MgO particles formed during the reduction reaction. Furthermore, the XRD pattern in Figure 6b indicates that the Nb, Ti metal phases are in the same position, which makes sense considering that Nb and Ti have complete solid-solution properties with the same crystal structure and similar atomic radii.

Figure 7 shows a representative SEM image and XRD pattern of the final pure Nb powder obtained by pickling the reduction product at 1173 K. The particles were fine in the range of 100–200 nm, and the XRD results confirmed that the MgO shell layer was removed sufficiently. However, some undesired niobium hydride (NbH_0.89) phases were observed, which were probably formed by the reaction of Nb particles with hydrogen ions during pickling in the aqueous hydrochloric acid solution.

Figure 8 shows the SEM microstructure and XRD results of the Nb-Ti alloy powder obtained after pickling. First, the SEM image reveals that the grains are slightly coarse and agglomerated compared with those of the pure Nb metal particles in Figure 7a. This is because the melting point of the Nb-20 wt.%Ti alloy is 2073 K, which is significantly lower than that of pure Nb metal (2740 K). After the nucleation of alloy grains, grain growth and agglomeration were relatively more prominent in the alloy than in pure Nb. The XRD pattern of the Nb-Ti alloy (Figure 8b) is similar to that of the pure Nb metal powder (Figure 7b).

The individual metal/alloy particles were maintained at a similar size as the corresponding precursors, but the agglomeration of the reduced metal/alloy powders differed slightly. This is because the applied reduction temperature was significantly lower than the melting points of the reactants, and no significant grain growth occurred after nucleation.

Figure 9 shows the XRD patterns of the final Nb powders obtained after Mg gas reduction at different temperatures. The reduced powder obtained at the lowest temperature of 1073 K contained a mixture of unreduced oxide phases of Nb₂O₅, NbO₂, and NbO, indicating inadequate reduction at this temperature. These unreduced oxide phases were not found when the reduction temperature was greater than 1173 K, suggesting that the reduction reaction was successful at temperatures exceeding 1173 K [23].

The results obtained using Ti₂Nb₁₀O₂₉ as the raw material at different reduction temperatures are shown in Figure 10. Although some unreduced oxide phases remained after reduction at the lowest temperature of 1073 K, they were not intermediate oxide phases, as shown in Figure 9, but were initial complex oxide phases. Furthermore, as in the case of Nb reduction, the reduction of the mixed oxide occurred adequately at temperatures exceeding 1173 K. Remarkably, in the reduction of the Nb-Ti alloy, there was a direct phase transformation to Nb-Ti metal without the formation of an intermediate phase, unlike in the Nb reduction process. This phenomenon suggests that the reduction of mixed oxides occurs via an easier and simpler route than the reduction of pure oxides. Therefore, the difference between the reduction behaviors of Nb₂O₅ and Ti₂Nb₁₀O₂₉ requires further investigation.

The mean size of niobium hydride (NbH_0.89), as shown in Figure 9 and Figure 10, was larger in the material obtained from the low-temperature reduction reaction. This can be attributed to the formation of finer reduced particles in the low-temperature reduction reaction and the relatively greater reactivity with hydrogen during the pickling process. These hydrides could be easily dehydrogenated via vacuum heat treatment at approximately 973 K. In this study, effective removal of hydrogen was achieved through vacuum heat treatment, resulting in the production of pure Nb and NbTi. After vacuum heat treatment, Mg content in the range of 100–200 ppm (ICP) and hydrogen concentrations were not detected.

Next, we examined the differences between the reduction behaviors of Nb₂O₅ and Ti₂Nb₁₀O₂₉. For this, the oxygen concentration of the powders obtained after reduction was analyzed by an ONH analyzer. The decrease in the amount of oxygen could be determined as the difference between the oxygen contents of the product and oxide precursor. Furthermore, from this value, the reduction rate values, k and ln k, could be calculated, and the obtained results are summarized in Table 1. The activation energy for Mg reduction was determined from the plot of ln k and the reciprocal of the reduction temperature, 1/T (Figure 11) [14,24,25,26]. As shown in Figure 11, the activation energies for the Mg reduction of Nb₂O₅ and Ti₂Nb₁₀O₂₉ reaction are 109.61 and 63.95 kJ/mole, respectively.

The ~50% lower activation energy for Nb-Ti alloy production indicates that the reduction reaction is faster and more effective when a mixed oxide is used. Herein, two causes for this result are discussed: (1) the difference in the phase change behavior of the reduced material and (2) the difference in the thermodynamic stability of the initial oxide during the magnesium reduction reaction.

First, pure Nb₂O₅ is reduced through intermediate phases such as NbO and NbO₂, as determined from the XRD results in Figure 9. Thus, the presence of newly produced intermediate oxides during reduction is likely to inhibit the reduction reaction, resulting in an increase in the activation energy of the reduction reaction [23]. In contrast, when Ti₂Nb₁₀O₂₉ is used as the raw material, the reduction progressed directly to the alloy phase without the formation of new intermediate phases (Figure 10). Hence, the reduction occurred relatively fast, and the activation energy was lower [18].

The second cause is the difference between the thermodynamic stabilities of the initial oxides. In general, oxides with a higher thermodynamic stability are more difficult to reduce due to the stronger interatomic bonding between the metal and oxygen. Therefore, the more effective reduction of Ti₂Nb₁₀O₂₉ can be attributed to the lower thermodynamic stability of Ti₂Nb₁₀O₂₉ compared with that of Nb₂O₅. This also suggests a slightly weaker bond between the metal and oxygen in the mixed oxide. According to some studies, when single-phase oxides of Nb₂O₅ and TiO₂ were mixed to form TiNb_xO_y, the interatomic irregularity increased. As a result, the enthalpy of the material increased while the thermodynamic stability decreased [27], which is consistent with the results of this study to some degree. In other words, the thermodynamic stability of the system decreased with the formation of the composite oxide phase, and this promoted the reduction reaction with Mg.

Another reason for the lower thermodynamic stability of Ti₂Nb₁₀O₂₉ is its melting point. The melting point of Ti₂Nb₁₀O₂₉ is known to be 1713 K, whereas the melting point of the mixed oxide obtained by simply mixing Nb₂O₅ and TiO₂ at a ratio of 1:10 wt.% is 1818 K, indicating a lower melting point of the composite phase [21]. Similarly, the melting point of FeTiO₃ is 1673 K, whereas the melting point of the FeO-TiO₂ mixture is 1883 K [19]. Considering the proportional relationship between the melting point of a material and its interatomic bonding strength, a lower melting point of a composite oxide indicates weaker interatomic bonding and thus a lower thermodynamic stability. Additionally, another mechanism is postulated to exist, indicating the presence of potential differences. Hence, it is deemed essential to conduct research on Nb₂O₅ and Ti₂Nb₁₀O₂₉ multiple oxides to further investigate it.

Finally, given the differences between the phase change behaviors of the two systems during reduction, the thermodynamic stabilities of the initial raw materials, and the melting points of the raw materials, we could infer that the magnesiothermic reduction of Ti₂Nb₁₀O₂₉ as the raw material is promoted owing to decreased activation energy [28].

4. Conclusions

A magnesium reduction reaction was performed using Nb₂O₅ and Ti₂Nb₁₀O₂₉ as raw materials in the temperature range of 1073 to 1223 K. The XRD results revealed that the reduction of both raw materials was inadequate at 1073 K, whereas the reduction was successful at temperatures exceeding 1173 K. SEM studies revealed that the Nb-Ti alloy particles were smaller than those of pure Nb. In addition, the Nb-Ti alloy particles were slightly coarser and more agglomerated than the pure Nb particles. The activation energy for the Mg reduction reaction could be calculated from the oxygen concentration results of the reduced powders. The activation energies for the reduction of Nb₂O₅ and Ti₂Nb₁₀O₂₉ to Nb and Nb-Ti alloy, respectively, were determined to be 109.61 and 63.95 kJ/mole, respectively. The reasons for the lower activation energy of the Mg reduction of the complex oxide were qualitatively examined and were attributed to the different phase change behaviors of the reduced materials and the different thermodynamic stabilities of the initial oxides.

Author Contributions

J.H. and D.L.; data curation: J.H. and N.K.; formal analysis: J.H. and S.H.; investigation: J.H. and D.L.; resources: D.L.; writing—original draft preparation: J.H., writing—review and editing: D.L. and N.K.; visualization: J.H. and D.L.; supervision: D.L. and N.K.; project administration: D.L.; funding acquisition: D.L. All authors have read and agreed to the published version of the manuscript.

Data Availability Statement

Not applicable.

Acknowledgments

The authors wish to thank Dong-Won Lee from the Titanium Department at KIMS.

Conflicts of Interest

The authors declare no conflict of interest.

Footnotes

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content.

Figures and Table

Figure 1. SEM microstructures of (a) [Forumla omitted. See PDF.] and (b) [Forumla omitted. See PDF.] powders used as starting material.

Figure 2. SEM microstructure of powder heat-treatment at 1573 K for 10 h with [Forumla omitted. See PDF.] mixed powder.

Figure 3. X-ray diffraction patterns of (a) [Forumla omitted. See PDF.], (b) Nb2O5 powder of starting materials and (c) multiple powder at 1573 K.

Figure 4. Schematic concept of magnesiothermic reduction behavior from pure Nb2O5 or compound oxide (Nb-Ti-O) to Nb and NbTi alloy.

Figure 5. (a) SEM microstructure and (b) X-ray diffraction pattern of [Forumla omitted. See PDF.] powder obtained by Mg reduction at 1173 K for 10 h before acid leaching.

Figure 5. (a) SEM microstructure and (b) X-ray diffraction pattern of [Forumla omitted. See PDF.] powder obtained by Mg reduction at 1173 K for 10 h before acid leaching.

Figure 6. (a) SEM microstructure and (b) X-ray diffraction pattern of multiple powders obtained by Mg reduction at 1173 K for 10 h before acid leaching.

Figure 6. (a) SEM microstructure and (b) X-ray diffraction pattern of multiple powders obtained by Mg reduction at 1173 K for 10 h before acid leaching.

Figure 7. (a) SEM microstructure and (b) X-ray diffraction pattern of [Forumla omitted. See PDF.] powder obtained by Mg reduction at 1173 K for 10 h after acid leaching.

Figure 7. (a) SEM microstructure and (b) X-ray diffraction pattern of [Forumla omitted. See PDF.] powder obtained by Mg reduction at 1173 K for 10 h after acid leaching.

Figure 8. (a) SEM microstructure and (b) X-ray diffraction pattern of multiple powders obtained by Mg reduction at 1173 K for 10 h after acid leaching.

Figure 8. (a) SEM microstructure and (b) X-ray diffraction pattern of multiple powders obtained by Mg reduction at 1173 K for 10 h after acid leaching.

Figure 9. X-ray diffraction patterns of Mg-reduced Nb powder at different reduction temperatures after acid leaching.

Figure 10. X-ray diffraction patterns of Mg-reduced multiple powders at different reduction temperatures after acid leaching.

Figure 11. Plot of ln k − 1/T × 103 for the estimation of the activation energies by the metal powders at various reduction temperatures.

Table 1

Oxygen contents of Mg-reduced powder at various reduction temperatures used for calculating ln k to draw a conclusion about activation energies.

		Nb			Nb-Ti
T, K	O, wt.%	R.A. wt.%	ln k	O, wt.%	R.A. wt.%	ln k
1073	24.22	5.78	−0.54	18.13	13.01	0.26
1123	10.10	19.90	0.69	11.08	20.22	0.70
1173	7.23	22.77	0.82	4.41	26.73	0.99
1223	1.46	28.54	1.05	0.49	30.65	1.12

R.A.: Reduction amount of oxygen.

References

1. Soisson, D.J.; McLafferty, J.J.; Pierret, J.A. Staff-industry collaborative report tantalum and niobium. Ind. Eng. Chem.; 1961; 53, pp. 861-868. [DOI: https://dx.doi.org/10.1021/ie50623a016]

2. Yu, H.; Wu, K.; Dong, B.; Yu, L.; Liu, J.; Liu, Z.; Xiao, D.; Jing, X.; Liu, H. Effect of niobium content on the microstructure and mechanical properties of simulated coarse-grained heat-affected zone (CGHAZ) of high-strength low-alloy (HSLA) steels. Materials; 2022; 15, 3318. [DOI: https://dx.doi.org/10.3390/ma15093318] [PubMed: https://www.ncbi.nlm.nih.gov/pubmed/35591649]

3. Jackson, M.; Dring, K. A review of advances in processing and metallurgy of titanium alloys. Mater. Sci. Technol.; 2006; 22, pp. 881-887. [DOI: https://dx.doi.org/10.1179/174328406X111147]

4. Juneja, J.M. Preparation of niobium-aluminium alloys by aluminothermic reduction of Nb₂O₅. High Temp. Mater. Process.; 2011; 24, pp. 1-6. [DOI: https://dx.doi.org/10.1515/HTMP.2005.24.1.1]

5. Baba, M.; Ono, Y.; Suzuki, R.O. Tantalum and Nb powder preparation from their oxides by calciothermic reduction in the molten CaCl₂. J. Phys. Chem. Solids; 2005; 66, pp. 466-470. [DOI: https://dx.doi.org/10.1016/j.jpcs.2004.06.042]

6. Baba, M.; Kikuchi, T.; Suzuki, R.O. Niobium powder synthesized by calciothermic reduction of Nb hydroxide for use in capacitors. J. Phys. Chem. Solids; 2015; 78, pp. 101-109. [DOI: https://dx.doi.org/10.1016/j.jpcs.2014.11.014]

7. Vershinnikov, V.I.; Ignat’eva, T.I.; Aleshin, V.V.; Mikhailov, Y.M. Fine Ti powders through metallothermic reduction in TiO₂–Mg–Ca mixtures. Int. J. Self-Propagating High-Temp. Synth.; 2018; 27, pp. 55-59. [DOI: https://dx.doi.org/10.3103/S1061386218010120]

8. Wang, N.; Huang, K.; Hou, J.; Zhu, H. Preparation of Nb nanoparticles by sodiothermic reduction of Nb₂O₅ in molten salts. Rare Metals; 2012; 31, pp. 621-626. [DOI: https://dx.doi.org/10.1007/s12598-012-0569-5]

9. Yoon, J.-S. The fabrication of Nb powder by sodiothermic reduction process. Int. J. Refract. Met. Hard Mater.; 2010; 28, pp. 265-269. [DOI: https://dx.doi.org/10.1016/j.ijrmhm.2009.10.009]

10. Fang, Z.Z.; Froes, F.H.; Zhang, Y. Chapter 8—Metallothermic reduction of TiO₂. Extractive Metallurgy of Titanium; 1st ed. Elsevier: Amsterdam, The Netherlands, 2020; pp. 131-164.

11. Sokolov, V.M.; Babyuk, V.D.; Zhydkov, Y.A.; Skok, Y.Y. Aluminothermic studies of a liquid partial reduced ilmenite. Miner. Eng.; 2008; 21, pp. 143-149. [DOI: https://dx.doi.org/10.1016/j.mineng.2007.08.010]

12. Park, S.-J.; Hwang, S.-M.; Wang, J.-P.; Son, Y.-G.; Lee, D.-W. Metallic niobium powder reduced by atmospheric magnesium gas with niobium pentoxide powder. Mater. Trans.; 2021; 62, pp. 34-40. [DOI: https://dx.doi.org/10.2320/matertrans.MT-M2020241]

13. Choi, K.; Choi, H.; Sohn, I. Understanding the magnesiothermic reduction mechanism of TiO₂ to produce Ti. Metall. Mater. Trans. B; 2017; 48, pp. 922-932. [DOI: https://dx.doi.org/10.1007/s11663-016-0912-6]

14. Choi, S.H.; Ali, B.; Choi, K.S.; Hyun, S.K.; Sim, J.J.; Choi, W.J.; Joo, W.; Lim, J.H.; Lee, T.H.; Kim, T.S. et al. Reaction kinetics and morphological study of TiNb₂O₇ synthesized by solid-state reaction. Arch. Metall. Mater.; 2017; 62, pp. 1051-1056. [DOI: https://dx.doi.org/10.1515/amm-2017-0152]

15. Bolivar, R.; Friedrich, B. Magnesiothermic reduction from titanium dioxide to produce titanium powder. J. Sustain. Metall.; 2019; 5, pp. 219-229. [DOI: https://dx.doi.org/10.1007/s40831-019-00215-z]

16. Worcester, S.A.; Case, P.L. Direct Production of niobium TITANIUM Alloy During Niobium Reduction. Available online: https://www.osti.gov/ (accessed on 11 October 2023).

17. Luidold, S.; Antrekowitsch, H.; Ressel, R. Production of Nb powder by magnesiothermic reduction of Nb oxides in a cyclone reactor. Int. J. Refract. Met. Hard Mater.; 2007; 25, pp. 423-432. [DOI: https://dx.doi.org/10.1016/j.ijrmhm.2006.11.002]

18. Choi, K.; Lee, K.H.; Ali, B.; Choi, S.-H.; Park, K.-T.; Sohn, I. Magnesiothermic reduction for direct synthesis of Ti-Nb alloy at 1073 K (800 °C). Met. Mater. Int.; 2017; 23, pp. 1037-1044. [DOI: https://dx.doi.org/10.1007/s12540-017-7010-4]

19. Roth, R.S.; Coughanour, L.W. Phase equilibrium relations in the systems titania-niobia and zirconia-niobia. J. Res. Natl. Bur. Stand.; 1955; 55, pp. 209-213. [DOI: https://dx.doi.org/10.6028/jres.055.023]

20. Liu, C.; Luo, P.; Feng, Y.; Gong, W.; Zhang, F. Phase equilibria in the TiO₂–Nb₂O₅ system: New experiments and thermodynamic modeling. Ceram. Int.; 2023; 49, pp. 30471-30480. [DOI: https://dx.doi.org/10.1016/j.ceramint.2023.06.311]

21. Wang, C. Titanium Niobium Oxides. Master’s Thesis; Alfred University: New York, NY, USA, 2014.

22. Adhami, T.; Ebrahimi-Kahrizsangi, R.; Bakhsheshi-Rad, H.R.; Majidi, S.; Ghorbanzadeh, M.; Berto, F. Synthesis and Electrochemical Properties of TiNb₂O₇ and Ti₂Nb₁₀O₂₉ Anodes under Various Annealing Atmospheres. Metals; 2021; 11, 983. [DOI: https://dx.doi.org/10.3390/met11060983]

23. Nico, C.; Monteiro, T.; Graça, M.P.F. Niobium oxides and niobates physical properties: Review and prospects. Prog. Mater. Sci.; 2016; 80, pp. 1-37. [DOI: https://dx.doi.org/10.1016/j.pmatsci.2016.02.001]

24. Logan, S.R. The origin and status of the Arrhenius equation. J. Chem. Ed.; 1982; 59, 279. [DOI: https://dx.doi.org/10.1021/ed059p279]

25. Laidler, K.J. The development of the Arrhenius equation. J. Chem. Ed.; 1984; 61, 494. [DOI: https://dx.doi.org/10.1021/ed061p494]

26. Hwang, S.-M.; Hong, J.-W.; Park, Y.-H.; Lee, D.-W. Synthesis of tantalum carbide using purified hexane by titanium powder. Materials; 2022; 15, 7510. [DOI: https://dx.doi.org/10.3390/ma15217510] [PubMed: https://www.ncbi.nlm.nih.gov/pubmed/36363105]

27. Fan, H.; Wang, R.; Xu, Z.; Duan, H.; Chen, D. Structural and transport properties of FeO-TiO₂-SiO₂ systems: Insights from molecular dynamics simulations. J. Non-Cryst. Solids; 2021; 571, 121049. [DOI: https://dx.doi.org/10.1016/j.jnoncrysol.2021.121049]

28. Stoklosa, A.; Laskowska, B. The bond energy and the composition of metal oxides. High Temp. Mater. Process.; 2007; 26, pp. 93-102. [DOI: https://dx.doi.org/10.1515/HTMP.2007.26.2.93]