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Vacancy formation and migration energies in 15-15Ti and FeCrAl: A study from first principles

Nils Wikström1,*, Ruihuan Li2, Stephan Schönecker2, Xiaoqing Li2, and Pär Olsson1,†

  • *Contact author: nilwik@kth.se
  • †Contact author: polsson@kth.se

Phys. Rev. Materials 10, 103608 – Published 23 October, 2026

DOI: https://doi.org/10.1103/tz5y-dzyb

Abstract

Lead-cooled fast reactors impose harsh environments on the structural materials, including high damage doses, high temperatures and corrosive liquid lead. To withstand these environments, advanced steel concepts, such as a composite of 15-15Ti and FeCrAl, have been proposed as fuel cladding. Microstructural evolution of alloys is governed by fundamental properties, including the vacancy formation and migration energies, yet such data for novel alloy compositions is sparse. In this work, an extensive set of vacancy formation and migration energies in two alloys, 15-15Ti and FeCrAl, was calculated from first principles, employing density functional theory. Special quasirandom structures were generated for both alloys, and different magnetic states of the alloys were simulated. It was found that the vacancy formation energy is highly influenced by the chemical and magnetic environment in 15-15Ti, while in FeCrAl the size mismatch between Fe and the alloying elements dominates. The vacancy formation energy was calculated by two different density functional theory formulations, showing excellent agreement. The vacancy migration energy was found to be governed by changes in the magnetic and chemical environment as the atom migrates. Based on these findings, temperature-averaged behaviors of vacancies in the alloys are derived, which can be further used to define effective vacancy formation and migration energies at reactor-relevant temperatures. The effective vacancy formation and migration energies can be used to predict temperature-variable shifts needed to accommodate the higher dose rate when using ion irradiation to emulate neutron irradiation.

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References (65)

  1. U.S. DOE Nuclear Energy Research Advisory Committee and the Generation IV International Forum, A technology roadmap for Generation IV nuclear energy systems, Technical Report No. GIF-002-00 (U.S. DOE/Generation IV International Forum, 2002).
  2. T. R. Allen and D. C. Crawford, Lead-cooled fast reactor systems and the fuels and materials challenges, Sci. Technol. Nucl. Install. 2007, 097486 (2007).
  3. International Atomic Energy Agency, Status of Fast Reactor Research and Technology Development, IAEA-TECDOC-1691, IAEA, Vienna (2013).
  4. C. Petersson, P. Szakálos, and D. Dietrich Stein, Slow strain rate testing of Fe-10Cr-4Al ferritic steel in liquid lead and lead–bismuth eutectic, Nucl. Mater. Energy 34, 101403 (2023).
  5. F. Garner, Irradiation performance of cladding and structural steels in liquid metal reactors, Materials Science and Technology (John Wiley & Sons, New York, 2006).
  6. F. Dehlin, J. Wallenius, and S. Bortot, An analytic approach to the design of passively safe lead-cooled reactors, Ann. Nucl. Energy 169, 108971 (2022).
  7. P. H. Gruber, J. Frostevarg, and F. Akhtar, FeCrAl/15-15Ti composite tubes as LFR fuel cladding, J. Nucl. Mater. 631, 156823 (2026).
  8. P. Yvon, M. Le Flem, C. Cabet, and J. L. Seran, Structural materials for next generation nuclear systems: Challenges and the path forward, Nucl. Eng. Des. 294, 161 (2015).
  9. J. Ejenstam and P. Szakálos, Long term corrosion resistance of alumina forming austenitic stainless steels in liquid lead, J. Nucl. Mater. 461, 164 (2015).
  10. H. Liu, G.-H. Lei, and H.-F. Huang, Review on synergistic damage effect of irradiation and corrosion on reactor structural alloys, Nucl. Sci. Tech. 35, 57 (2024).
  11. P. Scott, A review of irradiation assisted stress corrosion cracking, J. Nucl. Mater. 211, 101 (1994).
  12. K. S. Mao, C. P. Massey, Y. Yamamoto, K. A. Unocic, M. N. Gussev, D. Zhang, S. A. Briggs, O. Karakoc, A. T. Nelson, K. G. Field, and P. D. Edmondson, Improved irradiation resistance of accident-tolerant high-strength FeCrAl alloys with heterogeneous structures, Acta Mater. 231, 117843 (2022).
  13. C. Liu, H. Ma, P. Fan, K. Li, Q. Zhang, A. Du, W. Feng, X. Su, S. Zhu, and D. Yuan, Cavity swelling of 15-15Ti steel at high doses by ion irradiation, Materials 17, 925 (2024).
  14. K. A. Terrani, N. A. Capps, M. J. Kerr, C. A. Back, A. T. Nelson, B. D. Wirth, S. L. Hayes, and C. R. Stanek, Accelerating nuclear fuel development and qualification: Modeling and simulation integrated with separate-effects testing, J. Nucl. Mater. 539, 152267 (2020).
  15. P. E. Blöchl, Projector augmented-wave method, Phys. Rev. B 50, 17953 (1994).
  16. G. Kresse and D. Joubert, From ultrasoft pseudopotentials to the projector augmented-wave method, Phys. Rev. B 59, 1758 (1999).
  17. J. B. Piochaud, T. P. C. Klaver, G. Adjanor, P. Olsson, C. Domain, and C. S. Becquart, First-principles study of point defects in an fcc Fe-10Ni-20Cr model alloy, Phys. Rev. B 89, 024101 (2014).
  18. R. Hafner, D. Spisák, R. Lorenz, and J. Hafner, Does density-functional theory predict a spin-density-wave ground state for Cr? J. Phys.: Condens. Matter 13, L239 (2001).
  19. H. Amara, C. C. Fu, F. Soisson, and P. Maugis, Aluminum and vacancies in α-iron: Dissolution, diffusion, and clustering, Phys. Rev. B 81, 174101 (2010).
  20. H. Pitkänen, M. Alatalo, A. Puisto, M. Ropo, K. Kokko, M. P. J. Punkkinen, P. Olsson, B. Johansson, S. Hertzman, and L. Vitos, Ab initio study of the phase stability in paramagnetic duplex steel alloys, Phys. Rev. B 79, 024108 (2009).
  21. I. A. Abrikosov, A. E. Kissavos, F. Liot, B. Alling, S. I. Simak, O. Peil, and A. V. Ruban, Competition between magnetic structures in the Fe rich fcc FeNi alloys, Phys. Rev. B 76, 014434 (2007).
  22. D. Costa, G. Adjanor, C. Becquart, P. Olsson, and C. Domain, Vacancy migration energy dependence on local chemical environment in Fe–Cr alloys: A density functional theory study, J. Nucl. Mater. 452, 425 (2014).
  23. E. del Rio, J. M. Sampedro, H. Dogo, M. J. Caturla, M. Caro, A. Caro, and J. Manuel Perlado, Formation energy of vacancies in FeCr alloys: Dependence on Cr concentration, J. Nucl. Mater. 408, 18 (2011).
  24. J. Ejenstam, M. Thuvander, P. Olsson, F. Rave, and P. Szakalos, Microstructural stability of Fe–Cr–Al alloys at 450–550°C, J. Nucl. Mater. 457, 291 (2015).
  25. 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).
  26. 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).
  27. J. Rogal, S. V. Divinski, M. W. Finnis, A. Glensk, J. Neugebauer, J. H. Perepezko, S. Schuwalow, M. H. F. Sluiter, and B. Sundman, Perspectives on point defect thermodynamics, Physica Status Solidi (B) 251, 97 (2014).
  28. T. Schuler, M. Nastar, K. Li, and C.-C. Fu, Towards accurate thermodynamics from random energy sampling, Acta Mater. 276, 120074 (2024).
  29. Y. Zhang, A. Manzoor, C. Jiang, D. Aidhy, and D. Schwen, A statistical approach for atomistic calculations of vacancy formation energy and chemical potentials in concentrated solid-solution alloys, Comput. Mater. Sci. 190, 110308 (2021).
  30. L. Vitos, H. L. Skriver, B. Johansson, and J. Kollár, Application of the exact muffin-tin orbitals theory: The spherical cell approximation, Comput. Mater. Sci. 18, 24 (2000).
  31. A. Zunger, S.-H. Wei, L. G. Ferreira, and J. E. Bernard, Special quasirandom structures, Phys. Rev. Lett. 65, 353 (1990).
  32. G. Kresse and J. Hafner, Ab initio molecular-dynamics simulation of the liquid-metal–amorphous-semiconductor transition in germanium, Phys. Rev. B 49, 14251 (1994).
  33. G. Kresse and J. Furthmüller, Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set, Comput. Mater. Sci. 6, 15 (1996).
  34. G. Kresse and J. Furthmüller, Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set, Phys. Rev. B 54, 11169 (1996).
  35. B. L. Gyorffy, Coherent-potential approximation for a nonoverlapping-muffin-tin-potential model of random substitutional alloys, Phys. Rev. B 5, 2382 (1972).
  36. L. Vitos, I. A. Abrikosov, and B. Johansson, Anisotropic lattice distortions in random alloys from first-principles theory, Phys. Rev. Lett. 87, 156401 (2001).
  37. J. P. Perdew, K. Burke, and M. Ernzerhof, Generalized gradient approximation made simple, Phys. Rev. Lett. 77, 3865 (1996).
  38. E. R. Davidson, in Methods in Computational Molecular Physics, edited by G. H. F. Diercksen and S. Wilson, NATO Advanced Study Institute, Series C, Vol. 113 (Plenum, New York, 1983), pp. 95–115.
  39. B. Liu, in Numerical Algorithms in Chemistry: Algebraic Methods, edited by C. Moler and I. Shavitt (Lawrence Berkeley Laboratory, University of California, 1978), pp. 49–54.
  40. J. S. Wróbel, M. R. Zemła, D. Nguyen-Manh, P. Olsson, L. Messina, C. Domain, T. Wejrzanowski, and S. L. Dudarev, Elastic dipole tensors and relaxation volumes of point defects in concentrated random magnetic Fe-Cr alloys, Comput. Mater. Sci. 194, 110435 (2021).
  41. D. Gehringer, M. Friák, and D. Holec, Models of configurationally-complex alloys made simple, Comput. Phys. Commun. 286, 108664 (2023).
  42. A. Stukowski, Visualization and analysis of atomistic simulation data with OVITO-the Open Visualization Tool, Modell. Simul. Mater. Sci. Eng. 18, 015012 (2010).
  43. L. Vitos, Computational Quantum Mechanics for Materials Engineers: The EMTO Method and Applications (Springer, Berlin, 2007).
  44. B. L. Gyorffy, A. J. Pindor, J. Staunton, G. M. Stocks, and H. Winter, A first-principles theory of ferromagnetic phase transitions in metals, J. Phys. F: Met. Phys. 15, 1337 (1985).
  45. P. Olsson, I. Abrikosov, L. Vitos, and J. Wallenius, Ab initio formation energies of Fe–Cr alloys, J. Nucl. Mater. 321, 84 (2003).
  46. A. J. Pindor, J. Staunton, G. M. Stocks, and H. Winter, Disordered local moment state of magnetic transition metals: A self-consistent KKR CPA calculation, J. Phys. F: Met. Phys. 13, 979 (1983).
  47. A. Kissavos, S. Simak, P. Olsson, L. Vitos, and I. Abrikosov, Total energy calculations for systems with magnetic and chemical disorder, Comput. Mater. Sci. 35, 1 (2006).
  48. H. King, Quantitative size-factors for metallic solid solutions, J. Mater. Sci. 1, 79 (1966).
  49. P. Olsson, T. P. C. Klaver, and C. Domain, Ab initio study of solute transition-metal interactions with point defects in bcc Fe, Phys. Rev. B 81, 054102 (2010).
  50. D. Sheppard, P. Xiao, W. Chemelewski, D. D. Johnson, and G. Henkelman, A generalized solid-state nudged elastic band method, J. Chem. Phys. 136, 074103 (2012).
  51. G. Henkelman, B. P. Uberuaga, and H. Jónsson, A climbing image nudged elastic band method for finding saddle points and minimum energy paths, J. Chem. Phys. 113, 9901 (2000).
  52. L. Messina, M. Nastar, N. Sandberg, and P. Olsson, Systematic electronic-structure investigation of substitutional impurity diffusion and flux coupling in bcc iron, Phys. Rev. B 93, 184302 (2016).
  53. R. Soulairol, C.-C. Fu, and C. Barreteau, Structure and magnetism of bulk Fe and Cr: From plane waves to lcao methods, J. Phys.: Condens. Matter 22, 295502 (2010).
  54. A. R. Warwick, J. B. J. Chapman, D. Nguyen-Manh, P.-W. Ma, and S. L. Dudarev, Ab initio relaxation volumes of transition metal solutes in iron and tungsten, Phys. Rev. Mater. 10, 045402 (2026).
  55. S. S. Shapiro and M. B. Wilk, An analysis of variance test for normality (complete samples), Biometrika 52, 591 (1965).
  56. P. Olsson, C. Domain, and J. Wallenius, Ab initio study of Cr interactions with point defects in bcc Fe, Phys. Rev. B 75, 014110 (2007).
  57. E. Mansouri and P. Olsson, First-principles predictions of structural and magnetic phase stability in irradiated α-Fe, Mater. Res. Lett. 12, 477 (2024).
  58. I. Miháliková, M. Friák, N. Koutná, D. Holec, and M. Šob, An ab initio study of vacancies in disordered magnetic systems: A case study of Fe-rich Fe-Al phases, Materials 12, 1430 (2019).
  59. J.-H. Ke and A. M. Jokisaari, Effects of aluminum and molybdenum on the phase stability of iron-chromium alloys: A first-principles study, JOM 75, 3208 (2023).
  60. A. Galler, C. Taranto, M. Wallerberger, M. Kaltak, G. Kresse, G. Sangiovanni, A. Toschi, and K. Held, Screened moments and absence of ferromagnetism in feal, Phys. Rev. B 92, 205132 (2015).
  61. I. R. Magalhães, L. V. G. Chaves, V. F. de Castro, P. A. L. Reis, A. L. Costa, M. A. F. Veloso, and C. Pereira, Comparative analysis of different FeCrAl alloys in pressurized water reactors, Nucl. Eng. Des. 422, 113109 (2024).
  62. A. Vasilyev, S. Sokolov, N. Kolbasnikov, and D. Sokolov, Effect of alloying on the self-diffusion activation energy in γ-iron, Phys. Solid State 53, 2194 (2011).
  63. S.-L. Shang, B.-C. Zhou, W. Y. Wang, A. J. Ross, X. L. Liu, Y.-J. Hu, H.-Z. Fang, Y. Wang, and Z.-K. Liu, A comprehensive first-principles study of pure elements: Vacancy formation and migration energies and self-diffusion coefficients, Acta Mater. 109, 128 (2016).
  64. J. Kučera, B. Million, J. Růžičková, V. Foldyna, and A. Jakobová, Self-diffusion of iron in alpha-phase of iron and Fe-Cr alloys, Acta Metall. 22, 135 (1974).
  65. L. Mansur, Correlation of neutron and heavy-ion damage: II. the predicted temperature shift if swelling with changes in radiation dose rate, J. Nucl. Mater. 78, 156 (1978).

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