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Stabilization of the hcp structure in the ruthenium-substituted high-entropy Cantor alloys Cr20Mn20(Fe20−xRux)Co20Ni20 (0 ≤ x ≤ 20) and their magnetic and structural properties

Yaşar Orbay1, David Koch2, Benedikt Eggert3, Aslı Çakır1, Katharina Ollefs4, Heiko Wende3, Michael Farle3, and Mehmet Acet3

  • 1Department of Metallurgical and Materials Engineering, Muğla Sıtkı Koçman University, 48000 Muğla, Turkey
  • 2Fachbereich Material und Geowissenschaften, TU-Darmstadt, D-64287 Darmstadt, Germany
  • 3Faculty of Physics and Center for Nanointegration (CENIDE), Universität Duisburg-Essen, D-47048 Duisburg, Germany
  • 4Kirchhoff Institut für Physik, Universität Heidelberg, 69120 Heidelberg, Germany

Phys. Rev. B 114, 024401 – Published 6 July, 2026

DOI: https://doi.org/10.1103/3p5b-qlgx

Abstract

While the valence electron concentration (VEC) of the system Cr20Mn20(Fe20−xRux)Co20Ni20 (0≤x≤20), where Fe is partially substituted by Ru, remains at eight electrons per atom (e/a), the structure undergoes a change from single-phase fcc (x=0) to a two-phase fcc/hcp system as x increases, with the VEC of both phases remaining at or very close to 8 e/a. The hcp phase forms already at 5 at% Ru substitution. From studies on thermal expansion determined through x-ray diffraction, magnetization, and Mössbauer spectroscopy, we find that the fcc phase is magnetically active and possesses moment-volume instabilities with energetically close-lying low-spin and high-spin states, while the hcp phase is nonmagnetic in accordance with the predictions of theory. The results show that the hcp phase can be stabilized at a volume fraction of up to 80% under ambient conditions in a predominantly 3-d alloy with VEC=8 e/a.

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References (74)

  1. B. Cantor, I. T. H. Chang, P. Knight, and A. J. B. Vincent, Microstructural development in equiatomic multicomponent alloys, Mater. Sci. Eng. A 375-377, 213 (2014).
  2. J.-W. Yeh, S.-K. Chen, S.-J. Lin, J.-Y. Gan, T.-S. Chin, T.-T. Shun, C.-H. Tsau, and S.-Y. Chang, Nanostructured high-entropy alloys with multiple principal elements: Novel alloy design concepts and outcomes, Adv. Eng. Mater. 6, 299 (2004).
  3. M. C. Troparevsky, J. R. Morris, P. R. C. Kent, A. R. Lupini, and G. M. Stocks, Criteria for predicting the formation of single-phase high-entropy alloys, Phys. Rev X. 5, 011041 (2015).
  4. E. J. Pickering and N. G. Jones, High-entropy alloys: A critical assessment of their founding principles and future prospects, Intl. Mater. Rev. 61, 183 (2016).
  5. A. Takeuchi, K. Amiya, T. Wada, K. Yabuta, and W. Zhang, High-entropy alloys with a hexagonal close-packed structure designed by equi-atomic alloy strategy and binary phase diagrams, JOM 66, 1984 (2014).
  6. N. Tang, L. Quigley, W. L. Boldman, C. S. Jorgensen, R. Koch, D. O'Leary, H. R. Medal, P. D. Rack, and D. A. Gilbert, Magnetism in metastable and annealed compositionally complex alloys, Phys. Rev. Mater. 5, 114405 (2021).
  7. Ö. Özgün, D. Koch, A. Çakír, T. Tavşanoğlu, W. Donner, M. Farle, and M. Acet, Magnetic properties of FCC and σ phases in equiatomic and off-equiatomic high-entropy Cantor alloys, Phys. Rev. B 106, 214422 (2022).
  8. M. Moschetti, L. Perrière, J.-P. Couzinié, J. J. Kruzic, and B. Gludovatz, A novel strategy for the design of compositionally complex alloys for advanced nuclear applications, Appl. Mater. Today 38, 102164 (2024).
  9. Y. Zou, H. Ma, and R. Spolenak, Ultrastrong ductile and stable high-entropy alloys at small scales, Nat. Commun. 6, 7748 (2015).
  10. B. Gludovatz, A. Hohenwarter, D. Catoor, E. H. Chang, E. P. George, and R. O. Ritchie, A fracture-resistant high-entropy alloy for cryogenic applications, Science 345, 1153 (2014).
  11. H. Kou, J. Lu, and Y. Li, High-strength and high-ductility nanostructured and amorphous metallic materials, Adv. Mater. 26, 5518 (2014).
  12. C. P. Lee, Y. Y. Chen, C. Y. Hsu, J. W. Yeh, and H. C. Shih, The effect of boron on the corrosion resistance of the high entropy alloys Al0.5CoCrCuFeNiBx, J. Electrochem. Soc. 154, C424 (2007).
  13. G. Laplanche, P. Gadaud, O. Horst, F. Otto, G. Eggeler, and E. P. George, Temperature dependencies of the elastic moduli and thermal expansion coefficient of an equiatomic, single-phase CoCrFeMnNi high-entropy alloy, J. Alloys Compd. 623, 348 (2015).
  14. O. Schneeweiss, M. Friák, M. Dudová, D. Holec, M. Sob, D. Kriegner, V. Holý, P. Beran, E. P. George, J. Neugebauer, and A. Dlouhý, Magnetic properties of the CrMnFeCoNi high-entropy alloy, Phys. Rev. B 96, 014437 (2017).
  15. P. Koželj, S. Vrtnik, M. Krnel, A. Jelen, D. Gacnik, M. Wencka, Z. Jaglicice, A. Meden, F. Danoix, J. Ledieu, M. Feuerbacher, and J. Dolinsek, Spin-glass magnetism of the non-equiatomic CoCrFeMnNi high-entropy alloy, J. Magn. Magn. Mater. 523, 167579 (2021).
  16. L. Zhu, H. He, M. Naeem, X. Sun, J. Qi, P. Liu, S. Harjo, K. Nakajima, B. Li, and X.-L. Wang, Antiferromagnetism and phase stability of CrMnFeCoNi high-entropy alloy, Phys. Rev. Lett. 133, 126701 (2024).
  17. H.-P. Chou, Y.-S. Chang, S.-K. Chen, and J.-W. Yeh, Microstructure, thermophysical and electrical properties in AlxCoCrFeNi (0≤x≤2) high-entropy alloys, Mater. Sci. Eng. B 163, 184 (2009).
  18. V. A. Bykov, T. V. Kulikova, I. S. Sipatov, E. V. Sterkhov, D. A. Kovalenko, and R. E. Ryltsev, Transport properties of equiatomic CoCrFeNi high-entropy alloy with a single-phase face-centered cubic structure, Crystals 13, 1567 (2023).
  19. J.-W. Chen, S.-H. Chen, P. Shafer, W.-Y. Tzeng, Y.-C. Chen, C.-W. Luo, W.-W. Wu, J.-W. Yeh, and Y.-H. Chu, Role of the structure order in the transport and magnetic properties of high-entropy alloy films, NPG Asia Mater. 15, 72 (2024).
  20. F. Tian, L. K. Varga, N. Chen, L. Delczeg, and L. Vitos, Ab initio investigation of high-entropy alloys of 3d elements, Phys. Rev. B 87, 075144 (2013).
  21. Z. Leong, J. S. Wróbel, S. L. Dudarev, R. Goodall, I. Todd, and D. Nguyen-Manh, The effect of electronic structure on the phases present in high entropy alloys, Sci. Rep. 7, 39803 (2017).
  22. Z. Dong, S. Schönecker, W. Li, D. Chen, and L. Vitos, Thermal spin fluctuations in CoCrFeMnNi high entropy alloy, Sci. Rep. 8, 12211 (2019).
  23. D. Ma, B. Grabowski, F. Körmann, J. Neugebauer, and D. Raabe, Ab initio thermodynamics of the CoCrFeMnNi high entropy alloy: Importance of entropy contributions beyond the configurational one, Acta Mater. 100, 90 (2015).
  24. J. Wang, H. Kwon, H. S. Kim, and B.-J. Lee, A neural network model for high entropy alloy design, npj Comput. Mater. 9, 60 (2023).
  25. X. Liu, J. Zhang, and Z. Pei, Machine learning for high-entropy alloys: Progress, challenges and opportunities, Prog. Mater. Sci. 131, 101018 (2023).
  26. X. Tan, W. Trehern, A. Sundar, Y. Wang, S. San, T. Lu, F. Zhou, T. Sun, Y. Zhang, Y. Wen, Z. Liu, M. Gao, and S. Hu, Machine learning and high-throughput computational guided development of high temperature oxidation-resisting Ni-Co-Cr-Al-Fe based high-entropy alloys, npj Comput. Mater. 11, 93 (2025).
  27. W. Pepperhoff and M. Acet, Constitution and Magnetism of Iron and its Alloys, Engineering Materials and Processes (Springer, New York, 2001).
  28. E. F. Wassermann, M. Acet, P. Entel, and W. Pepperhoff, Basic understanding of the relations between Invar, anti-Invar, and martensite in Fe-based alloys, J. Magn. Soc. Jpn. 23, 385 (1999).
  29. M. Acet, B. Gehrmann, E. F. Wassermann, H. Bach, and W. Pepperhoff, Relevance of magnetic instabilities to the properties of interstitial solid solutions and compounds of Fe, J. Magn. Magn. Mater. 232, 221 (2001).
  30. A. Çakír, L. Righi, F. Albertini, M. Acet, and M. Farle, Intermartensitic transitions and phase stability in Ni50Mn50−xSnx Heusler alloys, Acta Mater. 99, 140 (2015).
  31. J. Wang, Z. Kou, S. Fu, S. Wu, S. Liu, M. Yan, Z. Ren, D. Wang, Z. You, S. Lan, H. Hahn, X.-L. Wang, and T. Feng, Ultrahard BCC-AlCoCrFeNi bulk nanocrystalline high-entropy alloy formed by nanoscale diffusion-induced phase transition, J. Mater. Sci. Technol. 115, 29 (2022).
  32. F. Liu, P. K. Liaw, and Y. Zhang, Recent progress with BCC-structured high-entropy alloys, Metals 12, 501 (2022).
  33. A. Smekhova, A. Kuzmin, K. Siemensmeyer, C. Luo, K. i Chen, F. Radu1, E. Weschke1, U. Reinholz, A. Guilherme Buzanich, and K. V. Yusenko, Al-driven peculiarities of local coordination and magnetic properties in single-phase Alx-CrFeCoNi high-entropy alloys, Nano Res. 15, 4845 (2022).
  34. M. Feuerbacher, M. Heidelmann, and C. Thomas, Hexagonal high-entropy alloys, Mater. Res. Lett. 3, 1 (2015).
  35. Y. J. Zhao, J. W. Qiao, S. G. Ma, M. C. Gao, H. J. Yang, M. W. Chen, and Y. Zhang, A hexagonal close-packed high-entropy alloy: The effect of entropy, Mater. Des. 96, 10 (2016).
  36. R. Devanathan1, W. Jiang, K. Kruska1, M. A. Conroy, T. C. Droubay, and J. M. Schwantes, Hexagonal close-packed high-entropy alloy formation under extreme processing conditions, J. Mater. Res. 34, 709 (2019).
  37. J. W. Qiao, M. L. Bao, Y. J. Zhao, H. J. Yang, Y. C. Wu, Y. Zhang, J. A. Hawk, and M. C. Gao, Rare-earth high entropy alloys with hexagonal close-packed structure, J. Appl. Phys 124, 195101 (2018).
  38. S. Vrtnik, J. Lužnik, P. Koželj, A. Jelen, J. Luzar, M. Krnel, Z. Jagličić, A. Meden, M. Feuerbacher, and J. Dolinšek, Magnetic phase diagram and magnetoresistance of Gd–Tb–Dy–Ho–Lu hexagonal high-entropy alloy, Intermetallics 105, 163 (2019).
  39. T. Nagase, M. Todai, and T. Nakano, Development of Ti–Zr–Hf–Y–La high-entropy alloys with dual hexagonal-close-packed structure, Scr. Mater. 186, 242 (2020).
  40. S. Uporov, S. Kh Estemirova, V. A. Bykov, D. A. Zamyatin, and R. E. Ryltsev, A single-phase ScTiZrHf high-entropy alloy with thermally stable hexagonal close-packed structure, Intermetallics 122, 106802 (2020).
  41. S. Huang, J. Cheng, L. Liu, W. Li, H. Jin, and L. Vitos, Thermo-elastic behavior of hexagonal Sc–Ti–Zr–Hf high-entropy alloys, J. Phys. D: Appl. Phys. 55, 235302 (2022).
  42. X. Yang, X. Shi, H. Yang, J. Qiao, P. K. Liaw, and Y. Wu, Entropy versus enthalpy in hexagonal-close-packed high-entropy alloys, Rare Metals 41, 2906 (2022).
  43. G. M. Muralikrishna, S. Sen, S. K. Ayyappan, S. Sankaran, K. Guruvidyathri, J. Schell, L. Rogal, X. Zhang, J. Mayer, B. Grabowski, G. Wilde, and S. V. Divinski, Microstructure stability and self-diffusion in the equiatomic HfScTiZr HCP multi-principal element alloy, J. Alloys Compd. 976, 173196 (2024).
  44. A. Takeuchi, T. Wada, and H. Kato, High-entropy alloys with hexagonal close-packed structure in Ir26Mo20Rh22.5Ru20W11.5 and Ir25.5Mo20Rh20Ru25W9.5 alloys designed by sandwich strategy for the valence electron concentration of constituent elements in the periodic chart, Mater. Trans. 60, 1666 (2019).
  45. A. Ter-Isahakyan, J. S. Rau, and T. J. Balk, High entropy alloys with hexagonal close-packed structure derived from thin film combinatorial approach, J. Alloys Compd. 893, 162293 (2022).
  46. S. Sen, X. Zhang, L. Rogal, J. Schell, G. Wilde, B. Grabowski, and S. V. Divinski, Sc diffusion in HCP high entropy alloys, Scr. Mater. 242, 115917 (2024).
  47. X. An, Z. Wang, S. Ni, and M. Song, The tension-compression asymmetry of martensite phase transformation in a metastable Fe40Co20Cr20Mn10Ni10 high-entropy alloy, Sci. China Mater. 63, 1797 (2020).
  48. K.-T. Hsieh, Y.-Y. Lin, C.-H. Lu, J.-R. Yang, P. K. Liaw, and C.-L. Kuo, Atomistic simulations of the face-centered-cubic-to-hexagonal-close-packed phase transformation in the equiatomic CoCrFeMnNi high entropy alloy under high compression, Comput. Mater. Sci. 184, 109864 (2020).
  49. X.-T Chen, H.-H. Jiang, C.-R. Xu, T.-W. Fan, and B.-Y. Tang, Ab initio study of mechanical properties of hexagonal high-entropy ceramic (Mo0.25Nb0.25Ta0.25V0.25)(Al0.5Si0.5)2 with dual mixing of cation and anion sublattice, J. Phys. Chem. Solids 165, 110701 (2022).
  50. P. Koželj, S. Vrtnik, A. Jelen, S. Jazbec, Z. Jagličić, S. Maiti, M. Feuerbacher, W. Steurer, and J. Dolinšek, Discovery of a superconducting high-entropy alloy, Phys. Rev. Lett. 113, 107001 (2014).
  51. M. C. Gao, B. Zhang, S. M. Guo, J. W. Qiao, and J. A. Hawk, High-entropy alloys in hexagonal close-packed structure, Metall. Mater. Trans. A 47, 3322 (2016).
  52. S. Marik, K. Motla, M. Varghese, K. P. Sajilesh, D. Singh, Y. Breard, P. Boullay, and R. P. Singh, Superconductivity in a new hexagonal high-entropy alloy, Phys. Rev. Mater. 3, 060602(R) (2019).
  53. B. Liu, J. Wu, Y. Cui, Q. Zhu, G. Xiao, S. Wu, G. Cao, and Z. Ren, Superconductivity in hexagonal Nb-Mo-Ru-Rh-Pd high-entropy alloys, Scr. Mater. 182, 109 (2020).
  54. Q. Zhu, G. Xiao, Y. Cui, W. Yang, S. Song, G.-H. Cao, and Z. Ren, Structural transformation and superconductivity in carbon-added hexagonal high-entropy alloys, J. Alloys Compd. 909, 164700 (2022).
  55. K. Motla, Arushi, S. Jangid, P. K. Meena, R. K. Kushwaha, and R. P. Singh, Superconducting properties of new hexagonal and noncentrosymmetric cubic high entropy alloys, Supercond. Sci. Technol. 36, 115024 (2023).
  56. R. Li, J.-W. Qiao, P. K. Liaw, and Y. Zhang, Preternatural hexagonal high-entropy alloys: A review, Acta Metall. Sin. (Engl. Lett.) 33, 1033 (2020).
  57. C. L. Tracy, S. Park, D. R. Rittman, S. J. Zinkle, H. Be, M. Lang, R. C. Ewing, and W. L. Mao, High pressure synthesis of a hexagonal close-packed phase of the high-entropy alloy CrMnFeCoNi, Nat. Commun. 8, 15634 (2017).
  58. M. Acet, Inducing strong magnetism in Cr20Mn20Fe20Co20Ni20 high-entropy alloys by exploiting its anti-Invar property, AIP Adv. 9, 095037 (2019).
  59. J. Kübler, Metastable magnetic ground-state HCP-Fe, Solid State Commun. 72, 631 (1989).
  60. M. Podgórny and J. Goniakowski, Metamagnetism of hexagonal iron, Il Nuovo. Cimento. D 13, 311 (1991).
  61. H. C. Herper, E. Hoffmann, and P. Entel, Ab initio full-potential study of the structural and magnetic phase stability of iron, Phys. Rev. B 60, 3839 (1999).
  62. K. Shimizu, T. Kimura, S. Furomoto, K. Takeda, K. Kontani, Y. Onuki, and K. Amaya, Superconductivity in the nonmagnetic state of iron under pressure, Nature (London) 412, 316 (2001).
  63. T. Faske and W. Donner, X-ray diffractometer for the investigation of temperature- and magnetic field-induced structural phase transitions, J. Appl. Cryst. 51, 761 (2018).
  64. V. Petricek, M. Dusek, and L. Palatinus, Crystallographic computing system JANA2006: General features, Z. Kristallogr. 229, 345 (2014).
  65. U. von Hörsten, pi program package, A windows program for the evaluation of Mössbauer spectra, https://udue.de/Pi.
  66. W. Stieler, M. Hillberg, F. J. Litterst, Ch Böttger, and J. Hesse, Numerical evaluation of Mössbauer spectra from thick absorbers, Nucl. Instrum. Methods Phys. Res. Sect. B 95, 235 (1995).
  67. S. Kamusella and H.-H. Klauss, Moessfit: A free Mössbauer fitting program, Hyperfine Interact. 237, 82 (2016).
  68. M. Acet, H. Zahres, E. F. Wassermann, and W. Pepperhoff, High-temperature moment-volume instability and anti-Invar of γ-Fe, Phys. Rev. B 49, 6012 (1994).
  69. W. Bendick, H. H. Ettwig, and W. Pepperhoff, Anomalies in specific heat and thermal expansion of FCC iron alloys, J. Phys. F: Met. Phys. 8, 2525 (1978).
  70. V. L. Moruzzi, P. M. Marcus, and J. Kübler, Magnetovolume instabilities and ferromagnetism versus anti ferromagnetism in bulk FCC iron and manganese, Phys. Rev. B 39, 6957 (1989).
  71. W. Keune, R. Halbauer, U. Gonser, J. Lauer, and D. L. Williamson, Antiferromagnetism of FCC Fe thin films, J. Appl. Phys. 48, 2976 (1977).
  72. W. A. A. Macedo and W. Keune, Magnetism of epitaxial FCC-Fe(100) films on Cu(100) investigated in situ by conversion-electron Mössbauer spectroscopy in ultrahigh vacuum, Phys. Rev. Lett. 61, 475 (1988).
  73. W. Keune, T. Ezawa, W. A. A. Macedo, U. Glos, K. P. Schletz, and U. Kirschbaum, Magneto-volume effects in γ-Fe ultrathin films and small particles, Physica B 161, 269 (1990).
  74. D. I. C. Pearson and J. M. Williams, Fe57 Mossbauer study of hexagonal phase iron alloys, J. Phys. F: Met. Phys. 9, 1797 (1979).

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