Physics of Metals and Metallography

, Volume 119, Issue 6, pp 576–581 | Cite as

Ab initio Computer Simulation of Carbon–Carbon Interactions for Various Spacings in BCC and BCT Lattices of Ferrite and Martensite

  • Ya. M. RidnyiEmail author
  • A. A. Mirzoev
  • V. M. Schastlivtsev
  • D. A. Mirzaev
Structure, Phase Transformations, and Diffusion


The ab initio computer simulation of lattice parameters and local structure distortions caused by interstitial carbon atoms in the iron-carbon system has been carried out using WIEN2k software. For the calculations, the full-potential method of linearized augmented plane waves (LAPWs) taking into account the generalized gradient approximation of PBE–GGA was used in a supercell of 54 iron atoms with periodic boundary conditions. The carbon dissolution energy has been found to be 0.85 eV for bcc iron, and 0.79 eV for bct iron. The carbon–carbon interaction energies in the ferromagnetic bct iron have been calculated. It has been found that accounting for tetragonal distortions considerably changes the interaction energy of carbon atoms in comparison with that of the bcc iron. Both the maximum degree of tetragonality of iron and the maximum attraction of carbon atoms have been observed for the case of carbon atoms placed in octahedral pores of the same type. If carbon atoms are in different types of octahedral pores, the tetragonal distortion of the lattice is weak. The obtained results are in good agreement with the Zener–Khachaturyan hypothesis and experimental data of Kurdyumov.


ab-initio simulation bcc iron carbon impurities WIEN2k 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    S. Umanskii, Yu. A. Skakov, A. N. Ivanov, and L. I. Rastorguev, Crystallography, X-ray Diffraction, and Electron Microscopy (Metallurgiya, Moscow, 1982).Google Scholar
  2. 2.
    G. V. Kurdyumov, L. M. Utevskii, and R. I. Entin, Transformations in Iron and Steel (Nauka, Moscow, 1977) [in Russian].Google Scholar
  3. 3.
    E. C. Bain, “The nature of martensite,” Trans. AIME, Steel Div. 70, 25–46 (1924).Google Scholar
  4. 4.
    C. Zener, “Theory of strain interaction of solute atoms,” Phys. Rev. 74, 639–647 (1948).CrossRefGoogle Scholar
  5. 5.
    A. G. Khachaturyan, Theory of Structural Transformations and Structure of Solid Solutions (Nauka, Moscow, USSR, 1974); A. G. Khachaturyan, Theory of Structural Transformations in Solids (Wiley, New York, 1983).Google Scholar
  6. 6.
    A. G. Khachaturyan and G. A. Shatalov, “On the theory of ordering of carbon atoms in martensite crystal,” Fiz. Met. Metalloved. 32, 5–13 (1971).Google Scholar
  7. 7.
    R. Naraghi, M. Selleby, and J. Agren, “Thermodynamics of stable and metastable structures in Fe–C system,” CALPHAD 46, 148–158 (2014).CrossRefGoogle Scholar
  8. 8.
    A. Udyansky, J. Pezold, V. N. Bugaev, M. Friak, and J. Neugebauer, “Interplay between long-range elastic and short-range chemical interactions in Fe–C martensite formation,” Phys. Rev. 79, 224112 (2009).CrossRefGoogle Scholar
  9. 9.
    T. Lau and C. J. F. Forst, “Many-body potential for point defect clusters in Fe–C alloys,” Phys. Rev. Lett. 98, 215501 (2007).CrossRefGoogle Scholar
  10. 10.
    C. S. Becquart, J. M. Raulot, G. Bencteux, C. Domain, M. Perez, S. Garruchet, and H. Nguyen, “Atomistic modeling of an Fe system with a small concentration of C,” Comput. Mater. Sci. 40, 119–129 (2007).CrossRefGoogle Scholar
  11. 11.
    H. Ohtsuka, V. A. Dinh, T. Ohno, K. Tsuzaki, K. Tsuchiya, R. Sahara, H. Kitazawa, and T. Nakamura, “First-principles calculation of effects of carbon on tetragonality and magnetic moment in Fe–C system,” ISIJ Int. 55, 2483–2491 (2015).CrossRefGoogle Scholar
  12. 12.
    K. Schwarz, P. Blaha, and G. K. H. Madsen, “Electronic structure calculations of solids using the WIEN2k package for material science,” Comput. Phys. Commun. 147, 71–76 (2002).CrossRefGoogle Scholar
  13. 13.
    S. Cottenier, Density Functional Theory and the Family of (L)APW-Methods: A Step-by-Step Introduction (IKS, Leuven, 2004).Google Scholar
  14. 14.
    P. S. Kostenetskiy and A. Y. Safonov, SUSU Supercomputer Resources, PCT 2016, CEUR Workshop Proceedings (2016). pp. 561–573.Google Scholar
  15. 15.
    C. Domain, C. S. Becquart, and J. Foct,“Ab initio study of foreign interstitial atom (C, N) interactions with intrinsic point defects in α-Fe,” Phys. Rev. B 69, 144112 (2004).CrossRefGoogle Scholar
  16. 16.
    D. E. Jiang and E. A. Carter “Carbon dissolution and diffusion in ferrite and austenite from first principles,” Phys. Rev. B. 67, 214103 (2003).CrossRefGoogle Scholar
  17. 17.
    V. A. Ludsteck, “Bestimmung der Anderung der Gitterkonstanten und des Anisotropen Debye–Waller-Faktors yon Graphit mittels Neutronenbeugung im Ternperaturbereich von 25°C bis 1850°C,” Acta Crystallogr. 28, 59–65 (1972).CrossRefGoogle Scholar
  18. 18.
    B. M. Mogutnov, N. A. Tomilin, and L. A. Shvartsman, Thermodynamics of Iron–Carbon Alloys of Iron (Metallurgiya, Moscow, 1984) [in Russian].Google Scholar
  19. 19.
    W. W. Dunn and R. B. McLellan, “The thermodynamic properties of carbon in body-centered cubic iron,” Metall. Trans. 2, 1079–1086 (1971).CrossRefGoogle Scholar
  20. 20.
    J. A. Lobo and G. H. Geiger, “Thermodynamics and solubility of carbon in ferrite and ferritic Fe–Mo alloys,” Metall. Trans. A 7A, 1347–1357 (1976).CrossRefGoogle Scholar
  21. 21.
    M. Shumilov, A. Kozak, L. Yakushechkina, and K. Sokolov, “Solubility of carbon in ferrite,” Phys. Met. Metallogr. 47, 2169–2178 (1973).Google Scholar
  22. 22.
    E. Schlirmann, T. Schmidt, and F. Tillmann, “Carburisation equilibria of alpha-iron with methane–hydrogen mixtures in the 600–800C range,” Giesserei-Forschung 19, 35–41 (1967).Google Scholar
  23. 23.
    J. C. Fisher, “Elastic interaction of interstitial atoms in body-centered cubic crystals,” Acta Metall. 6, 13–18 (1958).CrossRefGoogle Scholar
  24. 24.
    Y. Mou and H. I. Aaronson, “The carbon–carbon interaction energy in alpha Fe–C alloys,” Acta Metall. 37, 757–765 (1989).CrossRefGoogle Scholar
  25. 25.
    A. H. Cottrell, Chemical Bonding in Transition Metal Carbides (Institute of Materials., London, 1995).Google Scholar
  26. 26.
    A. Udyansky, J. Pezold, A. Dick, and J. Neugebauer, “Orientational ordering of interstitial atoms and martensite formation in dilute Fe-based solid solutions,” Phys. Rev. B 83, 184112 (2011).CrossRefGoogle Scholar
  27. 27.
    Y. You, M. F. Yan, and H. T. Chen, “Interactions of carbon–nitrogen and carbon–nitrogen–vacancy in α-Fe from first-principles calculations,” Comput. Mater. Sci. 67, 222–228 (2013).CrossRefGoogle Scholar
  28. 28.
    A. Ruban, “Self-trapping of carbon atoms in α-Fe during the martensitic transformation: A qualitative picture from ab initio calculations,” Phys. Rev. B 90, 144106 (2014).CrossRefGoogle Scholar
  29. 29.
    C. Barouh, T. Schuler, C. Fu, and M. Nastar, “Interaction between vacancies and interstitial solutes (C, N, and O) in α-Fe: From electronic structure to thermodynamics,” Phys. Rev. B 90, 054112 (2014).CrossRefGoogle Scholar
  30. 30.
    V. V. Popov, Modeling of Transformations of Carbonitrides Under Heat Treatment of Steels (UrO RAN, Ekaterinburg, 2003) [in Russian].Google Scholar
  31. 31.
    P. Gustafson, “Thermodynamic evaluation of the Fe–C system,” Scand. J. Metall. 14, 259–267 (1985).Google Scholar
  32. 32.
    I. I. Gorbachev, V. V. Popov and A. Yu. Pasynkov, “Calculations of the influence of alloying elements (Al, Cr, Mn, Ni, Si) on the solubility of carbonitrides in low-carbon low-alloy steels,” Phys. Met. Metallogr. 117, 1226–1236 (2016).CrossRefGoogle Scholar
  33. 33.
    I. I. Gorbachev, V. V. Popov, and A. Yu. Pasynkov, “Thermodynamic calculations of carbonitride formation in low-alloy low-carbon steels containing V, Nb, and Ti,” Phys. Met. Metallogr. 115, 69–76 (2014).CrossRefGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  • Ya. M. Ridnyi
    • 1
    Email author
  • A. A. Mirzoev
    • 1
  • V. M. Schastlivtsev
    • 2
  • D. A. Mirzaev
    • 1
  1. 1.South Ural State UniversityChelyabinskRussia
  2. 2.Mikheev Institute of Metal Physics, Ural BranchRussian Academy of ScienceEkaterinburgRussia

Personalised recommendations