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Atomistic Modeling of Symmetric and Asymmetric Σ5 \(\left\langle {{\text{001}}} \right\rangle \) Tilt Grain Boundaries in Niobium: Structure, Energy, Point Defects, and Grain-Boundary Self-Diffusion

  • STRUCTURE, PHASE TRANSFORMATIONS, AND DIFFUSION
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Abstract

Symmetric and three asymmetric Σ5 \(\left\langle {001} \right\rangle \) tilt grain boundaries in niobium were studied by computer-aided modeling methods. The structure and energy of considered boundaries and the formation energy of point defects in them were calculated by molecular static modeling. The dependences of the formation energy of point defects on the distance from the plane of grain boundary were analyzed. The grain-boundary self-diffusion coefficients were calculated for the considered boundaries by the molecular dynamics method.

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REFERENCES

  1. A. P. Sutton and R. W. Balluffi, Interfaces in Crystalline Materials (Clarendon Press, Oxford, 1995).

    Google Scholar 

  2. Z.-H. Liu, Ya-X. Feng, and J.-X. Shang, “Characterizing twist grain boundaries in BCC Nb by molecular simulation: Structure and shear deformation,” Appl. Surf. Sci. 370, 19–24 (2016). https://doi.org/10.1016/j.apsusc.2016.02.097

    Article  CAS  Google Scholar 

  3. D. Singh and A. Parashar, “Effect of symmetric and asymmetric tilt grain boundaries on the tensile behaviour of bcc-niobium,” Comput. Mater. Sci. 143, 126–132 (2018). https://doi.org/10.1016/j.commatsci.2017.11.005

    Article  CAS  Google Scholar 

  4. D. Singh, P. Sharma, and A. Parashar, “Atomistic simulations to study point defect dynamics in bi-crystalline niobium,” Mater. Chem. Phys. 255, 123628 (2020). https://doi.org/10.1016/j.matchemphys.2020.123628

    Article  CAS  Google Scholar 

  5. D. Singh and A. A. Parashar, “A comparison between ∑3 asymmetrical tilt grain boundary energies in niobium obtained analytically and through molecular dynamics based simulations,” Mater. Sci. Forum 998, 179–184 (2020). https://doi.org/10.4028/www.scientific.net/msf.998.179

  6. V. V. Popov, M. E. Stupak, and M. G. Urazaliev, “Atomistic simulation of grain boundaries in niobium: Structure, energy, point defects and grain-boundary self-diffusion,” J. Phase Equilib. Diffus. 43, 401–408 (2022). https://doi.org/10.1007/s11669-022-00981-6

    Article  CAS  Google Scholar 

  7. A. G. Lipnitskii, I. V. Nelasov, E. V. Golosov, Yu. R. Kolobov, and D. N. Maradudin, “A molecular-dynamics simulation of grain-boundary diffusion of niobium and experimental investigation of its recrystallization in a niobium–copper system,” Russ. Phys. J. 56, 330–337 (2013). https://doi.org/10.1007/s11182-013-0036-2

    Article  CAS  Google Scholar 

  8. S. Plimton, “Fast parallel algorithms for short-range molecular dynamics,” J. Comput. Phys. 117, 1–19 (1995). https://doi.org/10.1006/jcph.1995.1039

    Article  Google Scholar 

  9. M. A. Tschopp and D. L. Mcdowell, “Structures and energies of Σ3 asymmetric tilt grain boundaries in copper and aluminium,” Philos. Mag. 87, 3147–3173 (2007). https://doi.org/10.1080/14786430701255895

    Article  CAS  Google Scholar 

  10. M. G. Urazaliev, M. E. Stupak, and V. V. Popov, “Structure and energy of symmetric tilt boundaries with the 〈110〉 axis in Ni and the energy of formation of vacancies in grain boundaries,” Phys. Met. Metallogr. 122, 665–672 (2021). https://doi.org/10.1134/s0031918x21070139

    Article  CAS  Google Scholar 

  11. Y. Zhang, R. Ashcraft, M. I. Mendelev, C. Z. Wang, and K. F. Kelton, “Experimental and molecular dynamics simulation study of structure of liquid and amorphous Ni62Nb38 alloy,” J. Chem. Phys. 145, 204505 (2016). https://doi.org/10.1063/1.4968212

    Article  CAS  Google Scholar 

  12. A. Stukowski, “Visualization and analysis of atomistic simulation data with OVITO–the Open Visualization Tool,” Modell. Simul. Mater. Sci. Eng. 18, 015012 (2010). https://doi.org/10.1088/0965-0393/18/1/015012

    Article  Google Scholar 

  13. B. T. Polyak, “The conjugate gradient method in extremal problems,” USSR Comput. Math. Math. Phys. 9, 94–112 (1969). https://doi.org/10.1016/0041-5553(69)90035-4

    Article  Google Scholar 

  14. S. Nosé, “A unified formulation of the constant temperature molecular dynamics methods,” J. Chem. Phys. 81, 511–519 (1984). https://doi.org/10.1063/1.447334

    Article  Google Scholar 

  15. W. G. Hoover and B. L. Holian, “Kinetic moments method for the canonical ensemble distribution,” Phys. Lett. A 211, 253–257 (1996). https://doi.org/10.1016/0375-9601(95)00973-6

    Article  CAS  Google Scholar 

  16. I. I. Novoselov, A. Y. Kuksin, and A. V. Yanilkin, “Energies of formation and structures of point defects at tilt grain boundaries in molybdenum,” Phys. Solid State 56, 1401–1407 (2014). https://doi.org/10.1134/s1063783414070282

    Article  CAS  Google Scholar 

  17. M. I. Mendelev, H. Zhang, and D. J. Srolovitz, “Grain boundary self-diffusion in Ni: Effect of boundary inclination,” J. Mater. Res. 20, 1146–1153 (2005). https://doi.org/10.1557/jmr.2005.0177

    Article  CAS  Google Scholar 

  18. E. W. Hart, “On the role of dislocations in bulk diffusion,” Acta Metall. 5, 597 (1957). https://doi.org/10.1016/0001-6160(57)90127-x

    Article  CAS  Google Scholar 

  19. S. V. Divinski and B. S. Bokstein, “Recent advances and unsolved problems of grain boundary diffusion,” Defect Diffus. Forum 309–310, 1–8 (2011). doi 10.4028/www.scientific.net/ddf.309-310.1

  20. M. Köppers, Yu. Mishin, and Ch. Herzig, “Fast diffusion of cobalt along stationary and moving grain boundaries in niobium,” Acta Metall. Mater. 42, 2859–2868 (1994). https://doi.org/10.1016/0956-7151(94)90227-5

    Article  Google Scholar 

  21. D. Faken and H. Jónsson, “Systematic analysis of local atomic structure combined with 3D computer graphics,” Comp. Mater. Sci. 2, 279–286 (1994). https://doi.org/10.1016/0927-0256(94)90109-0

    Article  CAS  Google Scholar 

  22. P. M. Larsen, “Revisiting the common neighbour analysis and the centrosymmetry parameter,” (2020). https://doi.org/10.48550/arXiv.2003.08879

  23. M. R. Fellinger, H. Park, and J. W. Wilkins, “Force-matched embedded-atom method potential for niobium,” Phys. Rev. B 81, 144119 (2010). https://doi.org/10.1103/physrevb.81.144119

    Article  Google Scholar 

  24. M. A. Tschopp, K. N. Solanki, F. Gao, X. Sun, M. A. Khaleel, and M. F. Horstemeyer, “Probing grain boundary sink strength at the nanoscale: Energetics and length scales of vacancy and interstitial absorption by grain boundaries in α-Fe,” Phys. Rev. B 85, 64108 (2012). https://doi.org/10.1103/physrevb.85.064108

    Article  Google Scholar 

  25. L. E. Kar’kina, I. N. Kar’kin, and Yu. N. Gornostyrev, “Grain boundary sliding along special asymmetric grain boundaries in the Al bicrystals: Atomistic molecular dynamics simulation,” Phys. Met. Metallogr. 122, 1103–1111 (2021). https://doi.org/10.1134/S0031918X21110077

    Article  Google Scholar 

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ACKNOWLEDGMENTS

Computations were performed on the Uran supercomputer at the IMM UB RAS.

Funding

This study was supported by a grant from the Russian Scientific Foundation (project no. 21-13-00063; https://rscf.ru/project/21-13-00063/; Mikheev Institute of Metal Physics, Ural Branch, Russian Academy of Sciences).

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Authors and Affiliations

  1. Mikheev Institute of Metal Physics, Ural Branch, Russian Academy of Sciences, 620108, Ekaterinburg, Russia

    M. E. Stupak, M. G. Urazaliev & V. V. Popov

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  1. M. E. Stupak
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  2. M. G. Urazaliev
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  3. V. V. Popov
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Correspondence to V. V. Popov.

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Translated by E. Glushachenkova

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Stupak, M.E., Urazaliev, M.G. & Popov, V.V. Atomistic Modeling of Symmetric and Asymmetric Σ5 \(\left\langle {{\text{001}}} \right\rangle \) Tilt Grain Boundaries in Niobium: Structure, Energy, Point Defects, and Grain-Boundary Self-Diffusion. Phys. Metals Metallogr. 124, 801–806 (2023). https://doi.org/10.1134/S0031918X23601105

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