Efficient Design of Quinary Alumina-Forming Refractory Multi-Principal Element Alloys

1. J. R. Nicholls, Advances in Coating Design for High-Performance Gas Turbines, (2003). [Online]. Available: www.mrs.org/publications/bulletin10.1557/mrs2003.194 ↗

2. A.G. Evans, D.R. Clarke, and C.G. Levi, The Influence of Oxides on the Performance of Advanced Gas Turbines, J. Eur. Ceram. Soc., 2008, 28(7), p 1405–1419. https://doi.org/10.1016/j.jeurceramsoc.2007.12.02310.1016/j.jeurceramsoc.2007.12.023 ↗

3. R.C. Reed, The Superalloys: Fundamentals And Applications. Cambridge University Press, 2008.

4. R. Darolia, Development of Strong, Oxidation and Corrosion Resistant Nickel-Based Superalloys: Critical Review of Challenges, Progress and Prospects, Int. Mater. Rev., 2019, 64(6), p 355–380.10.1080/09506608.2018.1516713 ↗

5. M. Perrut, P. Caron, M. Thomas, and A. Couret, High Temperature Materials for Aerospace Applications: Ni-Based Superalloys and γ-TiAl Alloys, C. R. Phys., 2018, 19(8), p 657–671. https://doi.org/10.1016/j.crhy.2018.10.00210.1016/j.crhy.2018.10.002 ↗

6. T.M. Pollock, Alloy Design for Aircraft Engines, Nature Mater, 2016, 15(8), p 809–815. https://doi.org/10.1038/nmat470910.1038/nmat4709 ↗

7. J. Sato, T. Omori, K. Oikawa, I. Ohnuma, R. Kainuma, and K. Ishida, Cobalt-Base High-Temperature Alloys, Science, 2006, 312(5770), p 90–91. https://doi.org/10.1126/science.112173810.1126/science.1121738 ↗

8. T.M. Pollock, J. Dibbern, M. Tsunekane, J. Zhu, and A. Suzuki, New Co-Based γ-γ′ High-Temperature Alloys, JOM, 2010, 62(1), p 58–63. https://doi.org/10.1007/s11837-010-0013-y10.1007/s11837-010-0013-y ↗

9. M.S. Titus, A. Suzuki, and T.M. Pollock, High temperature creep of new L12 containing cobalt‐base superalloys, in Superalloys 2012, 1st ed. E.S. Huron, R.C. Reed, M.C. Hardy, M.J. Mills, R.E. Montero, P.D. Portella, and J. Telesman, Eds., Wiley, 2012, p823–832. https://doi.org/10.1002/9781118516430.ch9110.1002/9781118516430.ch91 ↗

10. R.W. Jackson, M.S. Titus, M.R. Begley, and T.M. Pollock, Thermal Expansion Behavior of New Co-Based Alloys and Implications for Coatings, Surf. Coat. Technol., 2016, 289, p 61–68. https://doi.org/10.1016/j.surfcoat.2015.12.08310.1016/j.surfcoat.2015.12.083 ↗

11. D.B. Miracle, and O.N. Senkov, A Critical Review of High Entropy Alloys and Related Concepts, Acta Mater., 2017, 122, p 448–511. https://doi.org/10.1016/J.ACTAMAT.2016.08.08110.1016/J.ACTAMAT.2016.08.081 ↗

12. S.A. Kube, C. Frey, C. McMullin, B. Neuman, K.M. Mullin, and T.M. Pollock, Navigating the BCC-B2 Refractory Alloy Space: Stability and Thermal Processing with Ru-B2 Precipitates, Acta Mater., 2024, 265, p 119628. https://doi.org/10.1016/j.actamat.2023.11962810.1016/j.actamat.2023.119628 ↗

13. C. Frey, H. You, S.A. Kube, G.H. Balbus, K.M. Mullin, S. Oppenheimer, C.S. Holgate, and T.M. Pollock, High Temperature B2 Precipitation in Ru-Containing Refractory Multi-Principal Element Alloys, Metall. Mater. Trans. A, 2024, 55(6), p 1739–1764. https://doi.org/10.1007/s11661-024-07368-x10.1007/s11661-024-07368-x ↗

14. L. Northcott, Some Features of the Refractory Metals, J. Less-Common Met., 1961, 3(2), p 125–148. https://doi.org/10.1016/0022-5088(61)90004-210.1016/0022-5088(61)90004-2 ↗

15. R.A. Perkins, and G.H. Meier, The Oxidation Behavior and Protection of Niobium, JOM, 1990, 42(8), p 17–21. https://doi.org/10.1007/BF0322104610.1007/BF03221046 ↗

16. R.A. Perkins, and K.T. Chiang, Formation of Alumina on Nb-Al Alloys, Scripta Metall., 1988, 22(3), p 419–424. https://doi.org/10.1016/S0036-9748(88)80217-510.1016/S0036-9748(88)80217-5 ↗

17. B. Gorr, S. Schellert, F. Müller, H.J. Christ, A. Kauffmann, and M. Heilmaier, Current Status of Research on the Oxidation Behavior of Refractory High Entropy Alloys, Adv. Eng. Mater., 2021. https://doi.org/10.1002/ADEM.20200104710.1002/ADEM.202001047 ↗

18. T.M. Pollock, D.M. Lipkin, and K.J. Hemker, Multifunctional Coating Interlayers for Thermal-Barrier Systems, MRS Bull., 2012, 37(10), p 923–931. https://doi.org/10.1557/mrs.2012.23810.1557/mrs.2012.238 ↗

19. J. Smialek and G. M. Meier, High Temperature Oxidation in Superalloy, High-temperature oxidation. Superalloys II, 2, Jan. 1987.

20. H.W. Lavendel, and A.G. Elliot, Evaluation of Silicide Coatings on Columbium and Tantalum and a Means for Improving their Oxidation Resistance, Trans. Metall. Soc. AIME, 1967, 239, p 143.

21. P. Lublin, and L. Sama, Analysis of Modified Silicide Coatings for Oxidation Protection of Columbium and Tantalum, Amer. Ceram. Soc. Bull., 1967, 46, p 1083–1090.

22. M. D. Novak and C. G. Levi, Oxidation and volatilization of silicide coatings for refractory niobium alloys, in Proceedings of the ASME 2007 International Mechanical Engineering Congress and Exposition. Volume 1: Advances in Aerospace Technology. Seattle, (Washington, USA. November 11–15, 2007). pp. 261-267, https://doi.org/10.1115/IMECE2007-42908.10.1115/IMECE2007-42908 ↗

23. General Electric (GE) Global Research | arpa-e.energy.gov. [Online]. Available: https://arpa-e.energy.gov/technologies/projects/ultimate-refractory-alloy-innovations-superior-efficiency-raise

24. C.S. Holgate, C. Frey, M.A. Endsley, A. Suzuki, C.G. Levi, and T.M. Pollock, Design of an Alumina Forming Coating for Nb-Base Refractory Alloys, Mater. Des., 2025, 251, p 113652. https://doi.org/10.1016/j.matdes.2025.11365210.1016/j.matdes.2025.113652 ↗

25. C. M. Austin, J.R. Dobbs, H.L. Fraser, D.G. Konitzer, D.J. Miller, M. J. Parks, J.C. Schaeffer, and J.W. Sears, Rapidly solidified oxidation resistant niobium base alloys. Final Report, WL-TR-93-4059, Wright Laboratory, 1992, https://apps.dtic.mil/sti/html/tr/ADA273211/

26. B. Gorr, F. Müller, M. Azim, H.-J. Christ, T. Müller, H. Chen, A. Kauffmann, and M. Heilmaier, High-Temperature Oxidation Behavior of Refractory High-Entropy Alloys: Effect of Alloy Composition, Oxid. Met., 2017, 88(3–4), p 339–349. https://doi.org/10.1007/S11085-016-9696-Y/TABLES/110.1007/S11085-016-9696-Y/TABLES/1 ↗

27. M. Ghadyani, C. Utton, and P. Tsakiropoulos, Microstructures and Isothermal Oxidation of the Alumina Scale Forming Nb1.45Si2.7Ti2.25Al3.25Hf0.35 and Nb1.35Si2.3Ti2.3Al3.7Hf0.35 Alloys, Materials, 2019. https://doi.org/10.3390/ma1205075910.3390/ma12050759 ↗

28. M. Ghadyani, C. Utton, and P. Tsakiropoulos, Microstructures and Isothermal Oxidation of the Alumina Scale Forming Nb1.7Si2.4Ti2.4Al3Hf0.5 and Nb1.3Si2.4Ti2.4Al3.5Hf0.4 Alloys, Materials, 2019. https://doi.org/10.3390/ma1202022210.3390/ma12020222 ↗

29. The interactive Ellingham diagram. Accessed: Mar. 24, 2026. [Online]. Available: https://www.tpoms.ac.uk/tlplib/ellingham_diagrams/interactive.php

30. Thermo-Calc Software TCHEA5. [Online]. Available: https://thermocalc.com/products/databases/high-entropy-alloys/

31. The TC-Python API Programmer Guide 2023a. [Online]. Available: https://thermocalc.com/support/documentation/

32. C.R. Harris, K.J. Millman, S.J. van der Walt, R. Gommers, P. Virtanen, D. Cournapeau, E. Wieser, J. Taylor, S. Berg, N.J. Smith, R. Kern, M. Picus, S. Hoyer, M.H. van Kerkwijk, M. Brett, A. Haldane, J. Fernández del Río, M. Wiebe, P. Peterson, P. Gérard-Marchant, K. Sheppard, T. Reddy, W. Weckesser, H. Abbasi, C. Gohlke, and T.E. Oliphant, Array Programming with Numpy, Nature, 2020, 585(7825), p 357–362. https://doi.org/10.1038/s41586-020-2649-210.1038/s41586-020-2649-2 ↗

33. T. Pandas development team, pandas-dev/pandas: Pandas. (Nov. 2022). Zenodo. https://doi.org/10.5281/zenodo.7344967.10.5281/zenodo.7344967 ↗

34. M.L. Waskom, Seaborn: Statistical Data Visualization, J. Open Source Softw., 2021, 6(60), p 3021. https://doi.org/10.21105/joss.0302110.21105/joss.03021 ↗

35. A.R. Ericks, F.W. Zok, D.L. Poerschke, and C.G. Levi, Protocol for Selecting Exemplary Silicate Deposit Compositions for Evaluating Thermal and Environmental Barrier Coatings, J. Am. Ceram. Soc., 2022, 105(6), p 3665–3688. https://doi.org/10.1111/jace.1841310.1111/jace.18413 ↗

36. I.T. Jolliffe, and J. Cadima, Principal Component Analysis: A Review and Recent Developments, Phil. Trans. R. Soc. A, 2016, 374(2065), p 20150202. https://doi.org/10.1098/rsta.2015.020210.1098/rsta.2015.0202 ↗

37. M. Steinbach, L. Ertöz, and V. Kumar, The challenges of clustering high dimensional data, in New Directions in Statistical Physics: Econophysics, Bioinformatics, and Pattern Recognition. L.T. Wille, Ed., Springer, Berlin, Heidelberg, 2004, p273–309. https://doi.org/10.1007/978-3-662-08968-2_1610.1007/978-3-662-08968-2_16 ↗

38. J. Landgrebe, W. Wurst, and G. Welzl, Permutation-Validated Principal Components Analysis of Microarray Data, Genome Biol., 2002, 3(4), p research0019.1-research0019.11. https://doi.org/10.1186/gb-2002-3-4-research001910.1186/gb-2002-3-4-research0019 ↗

39. F. Pedregosa, G. Varoquaux, A. Gramfort, V. Michel, B. Thirion, O. Frisel, M. Blondel, P. Prettenhofer, R. Weiss, V. Dubourg, J. Vanderplas, A. Passos, D. Cournapeau, M. Brucher, M. Perrot, and É. Duchesnay, Scikit-Learn: Machine Learning in Python, J. Mach. Learn. Res., 2011, 12(85), p 2825–2830.

40. O.N. Senkov, S.V. Senkova, D.M. Dimiduk, C. Woodward, and D.B. Miracle, Oxidation Behavior of a Refractory NbCrMo0.5Ta0.5TiZr Alloy, J. Mater. Sci., 2012, 47, p 6522–6534. https://doi.org/10.1007/s10853-012-6582-010.1007/s10853-012-6582-0 ↗

41. M. Garg, H.S. Grewal, and H.S. Arora, Effect of Microwave Processing on the Oxidation Behavior of Refractory High Entropy Alloy, Mater. Chem. Phys., 2021, 262, p 124256. https://doi.org/10.1016/j.matchemphys.2021.12425610.1016/j.matchemphys.2021.124256 ↗

42. N. Yurchenko, E. Panina, S. Zherebtsov, and N. Stepanov, Oxidation Behaviour of Eutectic Refractory High-Entropy Alloys at 800–1000 °C, Corros. Sci., 2022, 205, p 110464. https://doi.org/10.1016/j.corsci.2022.11046410.1016/j.corsci.2022.110464 ↗

43. Thermo-Calc Software TCHEA7. [Online]. Available: https://thermocalc.com/products/databases/high-entropy-alloys/

44. R. J. G. B. Campello, D. Moulavi, and J. Sander, Density-Based Clustering Based on Hierarchical Density Estimates, in Advances in Knowledge Discovery and Data Mining, vol. 7819, J. Pei, V. S. Tseng, L. Cao, H. Motoda, and G. Xu, Eds., in Lecture Notes in Computer Science, vol. 7819, (Berlin, Heidelberg: Springer Berlin Heidelberg, 2013), pp. 160–172. https://doi.org/10.1007/978-3-642-37456-2_14.10.1007/978-3-642-37456-2_14 ↗

45. E.J. Opila, Oxidation and Volatilization of Silica Formers in Water Vapor, J. Am. Ceram. Soc., 2003, 86(8), p 1238–1248. https://doi.org/10.1111/j.1151-2916.2003.tb03459.x10.1111/j.1151-2916.2003.tb03459.x ↗

46. E.J. Opila, and R.E. Hann, Paralinear Oxidation of CVD SiC in Water Vapor, J. Am. Ceram. Soc., 1997, 80(1), p 197–205. https://doi.org/10.1111/j.1151-2916.1997.tb02810.x10.1111/j.1151-2916.1997.tb02810.x ↗

47. D.L. Poerschke, R.W. Jackson, and C.G. Levi, Silicate Deposit Degradation of Engineered Coatings in Gas Turbines: Progress Toward Models and Materials Solutions, Annu. Rev. Mater. Res., 2017, 47(1), p 297–330. https://doi.org/10.1146/annurev-matsci-010917-10500010.1146/annurev-matsci-010917-105000 ↗

48. R.G. Munro, Evaluated Material Properties for a Sintered Alpha‐Alumina, J. Am. Ceram. Soc., 1997, 80(8), p 1919–1928. https://doi.org/10.1111/j.1151-2916.1997.tb03074.x10.1111/j.1151-2916.1997.tb03074.x ↗