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Ab Initio Simulation of the Energy of the α-Fe/Fe3C Interphase Boundary with Bagaryatsky Orientation Relationships

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Abstract

Pearlite is one of the fundamental structural components of carbon and low-alloy steels. In pearlite, the orientation relationships of Bagaryatsky, Isaychev, and Pitsch can be observed between the body-centered cubic ferritic and rhombic cementite Fe3C phases. In low-temperature pearlite, which exhibits the highest strength, the first two predominate, and they are closely related, sometimes indistinguishable in experiments. In this study, ab initio simulation using density functional theory in the WIEN2k software package is conducted to investigate the structures and energies of coherent α-Fe/Fe3C interphase boundaries. The supercells undergo structural and volume optimization. Calculations of the interphase boundary surface energy yield values of 0.383 and 0.594 J/m2 for the Bagaryatsky and Isaychev orientation relationships, respectively. These results align well with existing experimental values and outcomes from other molecular dynamics and ab initio calculations. The difference in the surface energy may play a significant role in low-temperature pearlite with thin plates of ferrite and cementite and a large interphase-boundary area per unit volume.

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REFERENCES

  1. Cementite in Carbon Steels, Ed. by V. M. Schastlivtsev (Ural. Politekh. Univ., Yekaterinburg, 2017) [in Russian].

    Google Scholar 

  2. S. Nagakura, Y. Hirotsu, M. Kusunoki, T. Suzuki, and Y. Nakamura, Metall. Trans. A 14, 1025 (1983). https://doi.org/10.1007/BF02670441

    Article  CAS  Google Scholar 

  3. G. V. Kurdyumov, L. M. Utevskii, and R. I. Entin, Transformations in Iron and Steel (Nauka, Moscow, 1977) [in Russian].

    Google Scholar 

  4. L. I. Tushinskii, A. A. Bataev, and L. B. Tikhomirova, Pearlite Structure and Structural Strength of Steel (Nauka, Novosibirsk, 1993) [in Russian].

    Google Scholar 

  5. V. M. Schastlivtsev, D. A. Mirzaev, and I. L. Yakovleva, Structure of Heat Treated Steel (Metallurgiya, Moscow, 1994) [in Russian].

    Google Scholar 

  6. V. M. Schastlivtsev, D. A. Mirzaev, I. L. Yakovleva, K. Yu. Okishev, T. I. Tabatchikova, and Yu. V. Khlebnikova, Pearlite in Carbon Steels (Ural. Otd. Ross. Akad. Nauk, Yekaterinburg, 2006) [in Russian].

    Google Scholar 

  7. V. N. Gridnev, V. G. Gavrilyuk, and Yu. Ya. Meshkov, Strength and Ductility of Cold-Worked Steel (Naukova Dumka, Kiev, 1974) [in Russian].

    Google Scholar 

  8. Y. Li, D. Raabe, M. Herbig, P.-P. Choi, S. Goto, A. Kostka, H. Yarita, C. Borchers, and R. Kirchheim, Phys. Rev. Lett. 113, 106104 (2014). https://doi.org/10.1103/PhysRevLett.113.106104

    Article  CAS  PubMed  Google Scholar 

  9. V. G. Gavrilyuk, Carbon Distribution in Steel (Naukova Dumka, Kiev, 1987) [in Russian].

    Google Scholar 

  10. Yu. Ivanisenko, W. Lojkowski, R. Z. Valiev, and H.‑J. Fecht, Acta Mater. 51, 5555 (2003). https://doi.org/10.1016/S1359-6454(03)00419-1

    Article  CAS  Google Scholar 

  11. I. L. Yakovleva, L. E. Kar’kina, Yu. V. Khlebnikova, V. M. Schastlivtsev, and T. I. Tabatchikova, Fiz. Met. Metalloved. 96 (4), 44 (2003).

    CAS  Google Scholar 

  12. Y. T. Zhou, X. H. Shao, S. J. Zheng, and X. L. Ma, J. Mater.Sci. Technol. 101, 28 (2022). https://doi.org/10.1016/j.jmst.2021.05.061

    Article  CAS  Google Scholar 

  13. A. V. Makarov, R. A. Savrai, V. M. Schastlivtsev, T. I. Tabatchikova, I. L. Yakovleva, Yu. V. Khlebnikova, and L. Yu. Egorova, Fiz. Met. Metalloved. 97 (5), 94 (2004).

    CAS  Google Scholar 

  14. A. V. Makarov, V. M. Schastlivtsev, T. I. Tabatchikova, I. L. Yakovleva, and L. Yu. Egorova, Phys. Met. Metallogr. 111, 95 (2011).

    Article  Google Scholar 

  15. Yu. A. Bagaryatskii, Dokl. Akad. Nauk SSSR 73, 1161 (1950).

    CAS  Google Scholar 

  16. W. Pitsch, Acta Metall. 10, 897 (1962). https://doi.org/10.1016/0001-6160(62)90108-6

    Article  CAS  Google Scholar 

  17. N. J. Petch, Acta Crystallogr. 6, 96 (1953). https://doi.org/10.1107/S0365110X53000260

    Article  CAS  Google Scholar 

  18. G. D. Sukhomlin, Fiz. Met. Metalloved. 38 (4), 878 (1974).

    CAS  Google Scholar 

  19. Y. Ohmori, A. T. Davenport, and R. W. HoneycombeK, Trans. Iron Steel Inst. Jpn. 12, 128 (1972). https://doi.org/10.2355/isijinternational1966.12.128

    Article  CAS  Google Scholar 

  20. I. V. Isaichev, Zh. Tekh. Fiz. 17, 835 (1947).

    CAS  Google Scholar 

  21. D. S. Zhou and G. J. Shiflet, Metall. Trans. A 23, 1259 (1992). https://doi.org/10.1007/BF02665057

    Article  Google Scholar 

  22. M.-X. Zhangand P. M. Kelly, Scr. Mater. 37, 2009 (1997).

    Article  Google Scholar 

  23. V. M. Schastlivtsev and I. L. Yakovleva, Fiz. Met. Metalloved. 38, 571 (1974).

    CAS  Google Scholar 

  24. G. D. Sukhomlin, Fiz. Met. Metalloved. 42, 965 (1976).

    CAS  Google Scholar 

  25. I. L. Yakovleva, L. E. Kar’kina, Yu. V. Khlebnikova, V. M. Schastlivtsev, and T. I. Tabatchikova, Fiz. Met. Metalloved. 92 (6), 81 (2001).

    CAS  Google Scholar 

  26. Y. T. Zhou, S. J. Zheng, Y. X. Jiang, T. Z. Zhao, Y. J. Wang, and X. L. Ma, Philos. Mag. 97, 2375 (2017). https://doi.org/10.1080/14786435.2017.1332434

    Article  CAS  Google Scholar 

  27. Y. Ohmori, ISIJ Int. 41, 554 (2001). https://doi.org/10.2355/isijinternational.41.554

    Article  CAS  Google Scholar 

  28. H. K. D. H. Bhadeshia, J. Mater. Sci. Technol. 34, 1666 (2018). https://doi.org/10.1080/02670836.2018.1470746

    Article  CAS  Google Scholar 

  29. V. Kraposhin, I. Jakovleva, L. Karkina, G. Nuzhny, T. Zubkova, and A. Talis, J. Alloys Compd. 577, S30 (2013). https://doi.org/10.1016/j.jallcom.2011.10.102

    Article  CAS  Google Scholar 

  30. R. J. Dippenaar and R. W. HoneycombeK., Proc. R. Soc. London, Ser. A 333, 455 (1973). https://doi.org/10.1098/rspa.1973.0073

    Article  CAS  Google Scholar 

  31. M. A. Mangan and G. J. Shiflet, Metall. Mater. Trans. A 30, 2767 (1999). https://doi.org/10.1007/s11661-999-0114-9

    Article  Google Scholar 

  32. D. F. Lupton and D. H. Warrington, Metallography 5, 325 (1972).

    Article  CAS  Google Scholar 

  33. D. N. Shackleton and P. M. Kelly, J. Iron Steel Inst. 207, 1253 (1969).

    CAS  Google Scholar 

  34. R. Morgan and B. Ralph, J. Iron Steel Inst. 206, 1138 (1968).

    CAS  Google Scholar 

  35. I. L. Yakovleva, L. E. Kar’kina, I. G. Kabanova, V. M. Schastlivtsev, and T. A. Zubkova, Bull. Russ. Acad. Sci.: Phys. 74, 1537 (2010).

    Article  Google Scholar 

  36. S. W. Thompson and P. R. Howell, in Proc. Int. Conf. Solid-to-Solid Phase Transformations in Inorganic Materials (Nemacolin, PA, 1994), p. 1127.

  37. D. N. Shackleton and P. M. Kelly, Acta Metall. 15, 979 (1967).

    Article  CAS  Google Scholar 

  38. Y. Ohmori, A. T. Davenport, and R. W. K. Honeycombe, Trans. ISIJ 12, 112 (1972).

    Article  CAS  Google Scholar 

  39. J. Kim, H. Ghaffarian, S. Ryu, and K. Kang, Comput. Mater. Sci. 173. 109375 (2020). https://doi.org/10.1016/j.commatsci.2019.109375

    Article  CAS  Google Scholar 

  40. M. Guziewski, S. P. Coleman, and C. R. Weinberger, Acta Mater. 119, 184 (2016). https://doi.org/10.1016/j.actamat.2016.08.017

    Article  CAS  Google Scholar 

  41. M. Guziewski, S. P. Coleman, and C. R. Weinberger, Acta Mater. 155, 1 (2018). https://doi.org/10.1016/j.actamat.2018.05.051

    Article  CAS  Google Scholar 

  42. A. V. Verkhovykh, A. A. Mirzoev, and D. A. Mirzaev, Vestn. Yuzhno-Ural. Gos. Univ., Ser. Mat. Mekh. Fiz. 10 (4), 78 (2018). https://doi.org/10.14529/mmph180409

    Article  Google Scholar 

  43. K. W. Andrews, Acta Metall. 11, 939 (1963). https://doi.org/10.1016/0001-6160(63)90063-4

    Article  CAS  Google Scholar 

  44. E. J. Fasiska and G. A. Jeffrey, Acta Crystallogr. 19, 463 (1965). https://doi.org/10.1107/S0365110X65003602

    Article  CAS  Google Scholar 

  45. A. V. Ursaeva, G. E. Ruzanova, and A. A. Mirzoev, Vestn. Yuzhno-Ural. Gos. Univ., Ser. Mat. Mekh. Fiz. 9 (2), 97 (2010).

    Google Scholar 

  46. O. M. Barabash and Yu. N. Koval’, Structure and Properties of Metals and Alloys: Handbook. Crystal Structure of Metals and Alloys (Naukova Dumka, Kiev, 1986) [in Russian].

    Google Scholar 

  47. A. V. Verkhovykh, K. Yu. Okishev, A. A. Mirzoev, and D. A. Mirzaev, Vestn. Yuzhno-Ural. Gos. Univ., Ser. Mat. Mekh. Fiz. 6 (2), 49 (2014).

    Google Scholar 

  48. K. Schwarz and P. Blaha, Comput. Mater. Sci. 28, 259 (2003).

    Article  CAS  Google Scholar 

  49. A. V. Verkhovykh, K. Yu. Okishev, A. A. Mirzoev, and D. A. Mirzaev, Vestn. Yuzhno-Ural. Gos. Univ., Ser. Metall. 17 (1), 35 (2017). https://doi.org/10.14529/met170104

    Article  Google Scholar 

  50. A. A. Mirzoev, A. V. Verkhovykh, K. Yu. Okishev, and D. A. Mirzaev, Mol. Phys. 116, 482 (2018). https://doi.org/10.1080/00268976.2017.1406161

    Article  CAS  Google Scholar 

  51. M. W. Finnis, J. Phys.: Condens. Matter 8, 5811 (1996). https://doi.org/10.1088/0953-8984/8/32/003

    Article  CAS  Google Scholar 

  52. J. J. Kramer, G. M. Pound, and R. F. Mehl, Acta Metall. 6, 763 (1958). https://doi.org/10.1016/0001-6160(58)90051-8

    Article  CAS  Google Scholar 

  53. J. W. Martin, R. D. Doherty, and B. Cantor Stability of Microstructure in Metallic System (Cambridge Univ. Press, Cambridge, 1997).

    Book  Google Scholar 

  54. H. O. K. Kirchner, B. G. Mellor, and G. A. Chadwick, Acta Metall. 26, 1023 (1978). https://doi.org/10.1016/0001-6160(78)90052-4

    Article  CAS  Google Scholar 

  55. C. Y. Li, J. M. Blakely, and A. H. Feingold, Acta Metall. 14, 1397 (1966). https://doi.org/10.1016/0001-6160(66)90159-3

    Article  CAS  Google Scholar 

  56. X. Zhang, T. Hickel, J. Rogal, S. Fähler, R. Drautz, and J. Neugebauer, Acta Metall. 99, 281 (2015). https://doi.org/10.1016/j.actamat.2015.07.075

    Article  CAS  Google Scholar 

  57. M. Ruda, D. Farkas, and G. Garcia, Comput. Mater. Sci. 45, 550 (2009). https://doiorg/101016/jcommatsci200811020

  58. J. Kim, K. Kang, and S. Ryu, Int. J. Plast. 83, 302 (2016). https://doi.org/10.1016/j.ijplas.2016.04.016

    Article  CAS  Google Scholar 

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Funding

The study was supported by the Ministry of Science and Higher Education of the Russian Federation (State Assignment for fundamental scientific research no. FENU-2023-0011 (2023011GZ)).

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Authors and Affiliations

  1. Institute of Natural Sciences and Mathematics, South Ural State University, 454080, Chelyabinsk, Russia

    A. V. Verkhovykh, A. A. Mirzoev & N. S. Dyuryagina

  2. Institute of New Materials and Technologies, Ural Federal University, 620002, Yekaterinburg, Russia

    K. Yu. Okishev

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  1. A. V. Verkhovykh
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  2. A. A. Mirzoev
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  3. K. Yu. Okishev
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  4. N. S. Dyuryagina
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Correspondence to N. S. Dyuryagina.

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Translated by O. Zhukova

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Verkhovykh, A.V., Mirzoev, A.A., Okishev, K.Y. et al. Ab Initio Simulation of the Energy of the α-Fe/Fe3C Interphase Boundary with Bagaryatsky Orientation Relationships. J. Surf. Investig. 18, 40–46 (2024). https://doi.org/10.1134/S1027451024010208

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