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MD Simulations of Collision Cascades in α-Ti. The Residual Number of Radiation Defects, Cascade Relaxation Time, and Displacement Cascade Region Morphology

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Abstract

Molecular dynamics (MD) simulations were applied to study primary damage formation in collision cascades initiated by the recoil of primary knock-on atoms (PKAs) with PKA energies \({{E}_{{{\text{PKA}}}}}\) = 5, 10, 15, 20, and 25 keV in α-Ti at temperature T = 100, 300, 600, and 900 K. A statistical sample of 24 collision cascades per set of parameters \(\left( {{{E}_{{{\text{PKA}}}}},~T} \right)\) was generated in order to assure statistical reliability of the obtained results. The size of the sampling set was justified posteriori using a simple procedure. The number of Frenkel pairs, \({{N}_{{{\text{FP}}}}}\), and cascade relaxation time were obtained as functions of \(\left( {{{E}_{{{\text{PKA}}}}},~T} \right)\). It was found that the average \(\left\langle {{{N}_{{{\text{FP}}}}}\left( {{{E}_{{{\text{PKA}}}}},~T} \right)} \right\rangle \) values fit into ≈0.3NRT if the threshold displacement energy is selected in the range of 28–40 eV depending on the irradiation temperature. At high PKA energies/low temperatures, collision cascades in α-Ti tend to break up into subcascades elongated along the trajectories of high-energy recoil atoms and their relaxation time does not depend on \({{E}_{{{\text{PKA}}}}}\). At low PKA energies/high temperatures, equiaxed collision cascades dominate and their relaxation time increases monotonically with increasing PKA energy \({{E}_{{{\text{PKA}}}}}\).

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REFERENCES

  1. S. S. Ushkov and O. A. Kozhevnikov, “Experience of application and value of titanium alloys for development of Russia nuclear power engineering,” (2009), Vol. 59, pp. 172–187.

  2. A. S. Oryshchenko, A. S. Kudryavtsev, V. I. Mikhaylov, and V. P. Leonov, “Titanium alloys for marine engineering and nuclear power engineering,” Vopr. Materialoved. 65 (1), 60–74 (2011).

    Google Scholar 

  3. I. V. Gorynin, V. V. Rybin, S. S. Ushkov, and O. A. Kozhevnikov, “Titanium alloys as perspective reactor materials,”, 37–45 (2002).

  4. W. Cai, J. Li, B. Uberuaga, and S. Yip, “Molecular dynamics,” in Comprehensive Nuclear Materials, Ed. by J. M. Konings and R. E. Stoller (Elsevier, Amsterdam, 2020), Vol. 1, pp. 573–594. https://doi.org/10.1016/b978-0-12-803581-8.11724-2

    Book  Google Scholar 

  5. R. E. Stoller and E. Zarkadoula, “Primary radiation damage formation in solids,” in Comprehensive Nuclear Materials, Ed. by J. M. Konings and R. E. Stoller (Elsevier, Amsterdam, 2020), Vol. 1, pp. 620–662. https://doi.org/10.1016/b978-0-12-803581-8.00661-5

    Book  Google Scholar 

  6. S. J. Wooding, D. J. Bacon, and W. J. Phythian, “A computer simulation study of displacement cascades in α-titanium,” Philos. Mag. A 72, 1261–1279 (1995). https://doi.org/10.1080/01418619508236254

    Article  CAS  Google Scholar 

  7. R. E. Voskoboinikov, “A study of primary damage formation in collision cascades in titanium,” Inorg. Mater.: Appl. Res. 13, 1736–1745 (2022). https://doi.org/10.1134/s2075113322060314

    Article  Google Scholar 

  8. R. E. Voskoboinikov, “MD simulations of collision cascades in α-Ti. Cluster statistics and governing mechanisms of point defect cluster formation”, Phys. Met. Metallogr. 124, 751–757 (2023). https://doi.org/10.1134/S0031918X23601154

    Article  Google Scholar 

  9. M. S. Daw and M. I. Baskes, “Embedded-atom method: Derivation and application to impurities, surfaces, and other defects in metals,” Phys. Rev. B 29, 6443–6453 (1984). https://doi.org/10.1103/physrevb.29.6443

    Article  CAS  Google Scholar 

  10. R. R. Zope and Y. Mishin, “Interatomic potentials for atomistic simulations of the Ti-Al system,” Phys. Rev. B 68, 24102–24103 (2003). https://doi.org/10.1103/physrevb.68.024102

    Article  Google Scholar 

  11. K. Gärtner, D. Stock, B. Weber, G. Betz, M. Hautala, G. Hobler, M. Hou, S. Arite, W. Eckstein, J. J. Jiménez-Rodríguez, A. M. C. Pérez-Martín, E. P. Andribet, V. Konoplev, A. Gras-Marti, M. Posselt, M. H. Shapiro, T. A. Tombrello, H. M. Urbassek, H. Hensel, Y. Yamamura, and W. Takeuchi, “Round robin computer simulation of ion transmission through crystalline layers,” Nucl. Instrum. Methods Phys. Res., Sect. B 102, 183–197 (1995). https://doi.org/10.1016/0168-583x(95)80139-d

    Article  Google Scholar 

  12. J. F. Ziegler, J. P. Biersack, and U. Littmark, The Stopping and Range of Ions in Solids (Pergamon, Oxford, 1985).

    Google Scholar 

  13. C. G. Shirley and R. L. Chaplin, “Evaluation of the threshold energy for atomic displacements in titanium,” Phys. Rev. B 5, 2027–2029 (1972). https://doi.org/10.1103/physrevb.5.2027

    Article  Google Scholar 

  14. G. Sattonnay, F. Rullier-Albenque, and O. Dimitrov, “Determination of displacement threshold energies in pure Ti and in γ-TiAl alloys by electron irradiation,” J. Nucl. Mater. 275, 63–73 (1999). https://doi.org/10.1016/s0022-3115(99)00109-9

    Article  CAS  Google Scholar 

  15. V. A. Fok, Origins of Quantum Mechanics (Nauka, Moscow, 1976).

    Google Scholar 

  16. A. M. Russell and B. A. Cook, “Coefficient of thermal expansion anisotropy and texture effects in ultra-thin titanium sheet,” Scr. Mater. 37, 1461–1467 (1997). https://doi.org/10.1016/s1359-6462(97)00312-6

    Article  CAS  Google Scholar 

  17. http://www.srim.org/SRIM/SRIM-2013-Std.e.

  18. H. Paul, “Nuclear stopping power and its impact on the determination of electronic stopping power,” AIP Conf. Proc. 1525, 309–313 (2013). https://doi.org/10.1063/1.4802339

    Article  CAS  Google Scholar 

  19. M. P. Allen and D. J. Tildesley, Computer Simulation of Liquids (Clarendon, Oxford, 1987). https://doi.org/10.1093/oso/9780198803195.001.0001

    Book  Google Scholar 

  20. L. A. Marqués, J. E. Rubio, M. Jaraíz, L. Enríquez, and J. Barbolla, “An improved molecular dynamics scheme for ion bombardment simulations,” Nucl. Instrum. Methods Phys. Res., Sect. B 102, 7–11 (1995). https://doi.org/10.1016/0168-583x(95)80108-x

    Article  Google Scholar 

  21. R. E. Voskoboinikov, Yu. N. Osetsky, and D. J. Bacon, “Statistics of primary damage creation in high-energy displacement cascades in copper and zirconium,” Nucl. Instrum. Methods Phys. Res., Sect. B 242, 68–70 (2006). https://doi.org/10.1016/j.nimb.2005.08.166

    Article  CAS  Google Scholar 

  22. R. E. Voskoboinikov, “Radiation defects in aluminum: MD simulations of collision cascades in the bulk of material,” Phys. Met. Metallogr. 120, 1–8 (2019). https://doi.org/10.1134/S0031918X18110212

    Article  CAS  Google Scholar 

  23. R. Voskoboinikov, “A contribution of L10 ordered crystal structure to the high radiation tolerance of γ-TiAl intermetallics,” Nucl. Instrum. Methods Phys. Res., Sect. B 460, 92–97 (2019). https://doi.org/10.1016/j.nimb.2019.04.080

    Article  CAS  Google Scholar 

  24. R. Voskoboinikov, “An insight into radiation resistance of D019 Ti3Al intermetallics,” J. Nucl. Mater. 519, 239–246 (2019). https://doi.org/10.1016/j.jnucmat.2019.03.046

    Article  CAS  Google Scholar 

  25. R. Voskoboinikov, “MD simulations of primary damage formation in L12 Ni3Al intermetallics,” J. Nucl. Mater. 522, 123–135 (2019). https://doi.org/10.1016/j.jnucmat.2019.05.009

    Article  CAS  Google Scholar 

  26. P. Lindemann, “Über die Berechnung molekularer Eigenfrequenzen,” Phys. Z. 11, 609–612 (1910).

    CAS  Google Scholar 

  27. K. Nordlund and R. S. Averback, “Point defect movement and annealing in collision cascades,” Phys. Rev. B 56, 2421–2431 (1997). https://doi.org/10.1103/physrevb.56.2421

    Article  CAS  Google Scholar 

  28. R. E. Voskoboinikov, Yu. N. Osetsky, and D. J. Bacon, “Computer simulation of primary damage creation in displacement cascades in copper. I. Defect creation and cluster statistics,” J. Nucl. Mater. 377, 385–395 (2008). https://doi.org/10.1016/j.jnucmat.2008.01.030

    Article  CAS  Google Scholar 

  29. K. Nordlund, A. E. Sand, F. Granberg, S. J. Zinkle, R. Stoller, R. S. Averback, T. Suzudo, L. Malerba, F. Banhart, W. J. Weber, F. Willaime, S. Dudarev, and D. Simeone, Primary Radiation Damage in Materials: Review of Current Understanding and Proposed New Standard Displacement Damage Model to Incorporate In-cascade Mixing and Defect Production Efficiency Effects (OECD Nuclear Energy Agency, Paris, 2015).

    Google Scholar 

  30. D. J. Bacon, Yu. N. Osetsky, R. Stoller, and R. E. Voskoboinikov, “MD description of damage production in displacement cascades in copper and α‑iron,” J. Nucl. Mater. 323, 152–162 (2003). https://doi.org/10.1016/j.jnucmat.2003.08.002

    Article  CAS  Google Scholar 

  31. M. J. Norgett, M. T. Robinson, and I. M. Torrens, “A proposed method of calculating displacement dose rates,” Nucl. Eng. Des. 33, 50–54 (1975). https://doi.org/10.1016/0029-5493(75)90035-7

    Article  Google Scholar 

  32. D. J. Bacon, F. Gao, and Yu. N. Osetsky, “The primary damage state in fcc, bcc and hcp metals as seen in molecular dynamics simulations,” J. Nucl. Mater. 276, 1–12 (2000). https://doi.org/10.1016/s0022-3115(99)00165-8

    Article  CAS  Google Scholar 

  33. R. E. Voskoboinikov, “Simulation of primary radiation damage in nickel,” Phys. Met. Metallogr. 121, 14–20 (2020). https://doi.org/10.1134/S0031918X20010196

    Article  CAS  Google Scholar 

  34. I. G. Aramanovich and V. I. Levin, Equations of Mathematical Physics (Nauka, Moscow, 1969).

    Google Scholar 

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ACKNOWLEDGMENTS

MD simulations were conducted using facilities of NRNU MEPhI high-performance computing center and computing resources of the federal collective usage center Complex for Simulation and Data Processing for Mega-science Facilities at NRC “Kurchatov Institute,” http://ckp.nrcki.ru/.

Funding

The work was supported in part by the Ministry of Science and Higher Education of the Russian Federation, grant no. 075-11-2021-085.

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Correspondence to R. E. Voskoboinikov.

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Voskoboinikov, R.E. MD Simulations of Collision Cascades in α-Ti. The Residual Number of Radiation Defects, Cascade Relaxation Time, and Displacement Cascade Region Morphology. Phys. Metals Metallogr. 124, 743–750 (2023). https://doi.org/10.1134/S0031918X2360121X

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