Advertisement

Greater diffusion rate of carbon atoms from nonlinear migration in micro-cell and spatially heterogeneous stable states in FCC iron

  • Jian Wang
  • Qing Tao
  • Liming Fu
  • Wei Lai
  • Chengjin Shen
  • Zhi Sun
  • Aidang Shan
Computation
  • 18 Downloads

Abstract

The nonlinear migration of C atom between nearest interstitial sites in fcc iron has been studied in the paper. It reveals an optimum migration pathway in the preferred crowdion direction in its infancy; the pathway is finally along the tetrahedral direction. This nonlinear tendency can be intensified by a repulsive force from another near neighbor C atom in the crowdion direction. We introduce an interaction model based on Coulomb’s force, which indicates that this nonlinear migration mechanism is a foregone conclusion with a certain atomic geometric configuration. However, for a multiple-C system, we find that there exists a typical preferred orientation, which is a continuously stable structure maintained by the C atoms migrating in the crowdion direction. The first neighbor migrated structure is the main formation as a result of this preferential orientation. Based on this, we derive a novel diffusion equation by introducing a proportionality coefficient \( K_{\rho } \), which can be closely related to the C structures absorbed on the surface during carburization. The diffusion coefficient will increase dramatically with a small perturbation of \( K_{\rho } \). Moreover, a spatially heterogeneous occupation is introduced on a much larger scale. The results not only show that it is a relatively stable state but that the C diffusion coefficient is significantly larger than that of the other disorder-free C states. Meanwhile, it provides a repulsive force for nonlinear migration in the micro-cell. As a result, a greater diffusion rate will be achieved from both spatial heterogeneity and the nonlinear migration of C atoms.

Notes

Acknowledgements

This research is financially supported by the National Natural Science Foundation of China (No. 51641109), the Fundamental Research Funds for the Central Universities (No. 2017XKZD08).

References

  1. 1.
    Sarıkaya Y, Önal M (2012) High temperature carburizing of a stainless steel with uranium carbide. J Alloy Compd 542:253–256CrossRefGoogle Scholar
  2. 2.
    Bhadeshia HKDH (2010) A commentary on: “Diffusion of carbon in austenite with a discontinuity in composition”. Metall Mater Trans A 41(7):1605–1615CrossRefGoogle Scholar
  3. 3.
    Cheeseman JR, Frisch MJ, Devlin FJ, Stephens PJ (1996) Ab initio calculation of atomic axial tensors and vibrational rotational strengths using density functional theory. Chem Phys Lett 252(3–4):211–220CrossRefGoogle Scholar
  4. 4.
    Fuchs M, Scheffler M (1999) Ab initio pseudopotentials for electronic structure calculations of poly-atomic systems using density-functional theory. Comput Phys Commun 119(1):67–98CrossRefGoogle Scholar
  5. 5.
    Jiang DE, Carter EA (2005) Carbon atom adsorption on and diffusion into Fe(110) and Fe(100) from first principles. Phys Rev B 71(4):045402CrossRefGoogle Scholar
  6. 6.
    Jiang DE, Carter EA (2003) Carbon dissolution and diffusion in ferrite and austenite from first principles. Phys Rev B 67(21):214103CrossRefGoogle Scholar
  7. 7.
    Simonetti S, Pronsato ME, Brizuela G, Juan A (2007) The C–C pair in the vicinity of a bcc Fe bulk vacancy: electronic structure and bonding. Physica Status Solidi (b) 244(2):610–618CrossRefGoogle Scholar
  8. 8.
    Asaro R, Farkas D, Kulkarni Y (2008) The Soret effect in diffusion in crystals. Acta Mater 56(6):1243–1256CrossRefGoogle Scholar
  9. 9.
    Hepburn DJ, Ackland GJ (2008) Metallic-covalent interatomic potential for carbon in iron. Phys Rev B 78(16):165115CrossRefGoogle Scholar
  10. 10.
    Ruda M, Farkas D, Garcia G (2009) Atomistic simulations in the Fe–C system. Comput Mater Sci 45(2):550–560CrossRefGoogle Scholar
  11. 11.
    Liu X, Huo C, Li Y, Wang J, Jiao H (2012) Energetics of carbon deposition on Fe(100) and Fe(110) surfaces and subsurfaces. Surf Sci 606(7–8):733–739CrossRefGoogle Scholar
  12. 12.
    Domain C, Becquart CS, Foct J (2004) Ab initio study of foreign interstitial atom (C, N) interactions with intrinsic point defects in α-Fe. Phys Rev B 69(14):144112CrossRefGoogle Scholar
  13. 13.
    Becquart CS, Domain C, Foct J (2005) Ab initio calculations of some atomic and point defect interactions involving C and N in Fe. Philos Mag 85(4–7):533–540CrossRefGoogle Scholar
  14. 14.
    Ohnuma T, Soneda N, Iwasawa M (2009) First-principles calculations of vacancy–solute element interactions in body-centered cubic iron. Acta Mater 57(20):5947–5955CrossRefGoogle Scholar
  15. 15.
    Hepburn DJ, Ferguson D, Gardner S, Ackland GJ (2013) First-principles study of helium, carbon, and nitrogen in austenite, dilute austenitic iron alloys, and nickel. Phys Rev B 88(2):024115CrossRefGoogle Scholar
  16. 16.
    Bhadeshia HKDH (2004) Carbon–carbon interactions in iron. J Mater Sci Technol 39(12):3949–3955Google Scholar
  17. 17.
    Barouh C, Schuler T, Fu C-C, Jourdan T (2015) Predicting vacancy-mediated diffusion of interstitial solutes in α-Fe. Phys Rev B 92(10):104102CrossRefGoogle Scholar
  18. 18.
    Tapasa K, Barashev A, Bacon D, Osetsky Y (2007) Computer simulation of carbon diffusion and vacancy–carbon interaction in α-iron. Acta Mater 55(1):1–11CrossRefGoogle Scholar
  19. 19.
    Forst CJ, Slycke J, Van Vliet KJ, Yip S (2006) Point defect concentrations in metastable Fe–C alloys. Phys Rev Lett 96(17):175501CrossRefGoogle Scholar
  20. 20.
    Paxton AT, Elsässer C (2013) Analysis of a carbon dimer bound to a vacancy in iron using density functional theory and a tight binding model. Phys Rev B 87(22):224110CrossRefGoogle Scholar
  21. 21.
    Liu P, Xing W, Cheng X, Li D, Li Y, Chen X-Q (2014) Effects of dilute substitutional solutes on interstitial carbon in α-Fe: interactions and associated carbon diffusion from first-principles calculations. Phys Rev B 90(2):024103CrossRefGoogle Scholar
  22. 22.
    Qiao L, Zhang X, Wang S, Yu S, Hu X, Wang L, Zeng Y, Zheng W (2014) First-principles investigations on the adsorption and diffusion of carbon atoms on the surface and in the subsurface of Co (111) related to the growth of graphene. RSC Adv 4(65):34237–34243CrossRefGoogle Scholar
  23. 23.
    Hu X, Björkman T, Lipsanen H, Sun L, Krasheninnikov AV (2015) Solubility of boron, carbon, and nitrogen in transition metals: getting insight into trends from first-principles calculations. J Phys Chem Lett 6(16):3263–3268CrossRefGoogle Scholar
  24. 24.
    Aguiar-Hualde J-M, Magnin Y, Amara H, Bichara C (2017) Probing the role of carbon solubility in transition metal catalyzing single-walled carbon nanotubes growth. Carbon 120:226–232CrossRefGoogle Scholar
  25. 25.
    Cao Y, Ernst F, Michal GM (2003) Colossal carbon supersaturation in austenitic stainless steels carburized at low temperature. Acta Mater 51(14):4171–4181CrossRefGoogle Scholar
  26. 26.
    Michal G, Ernst F, Kahn H, Cao Y, Oba F, Agarwal N, Heuer A (2006) Carbon supersaturation due to paraequilibrium carburization: stainless steels with greatly improved mechanical properties. Acta Mater 54(6):1597–1606CrossRefGoogle Scholar
  27. 27.
    Michal GM, Ernst F, Heuer AH (2006) Carbon paraequilibrium in austenitic stainless steel. Metall Mater Trans A 37(6):1819–1824CrossRefGoogle Scholar
  28. 28.
    Ernst F, Avishai A, Kahn H, Gu X, Michal GM, Heuer AH (2009) Enhanced carbon diffusion in austenitic stainless steel carburized at low temperature. Metall Mater Trans A 40(8):1768–1780CrossRefGoogle Scholar
  29. 29.
    Gu X, Michal GM, Ernst F, Kahn H, Heuer AH (2014) Concentration-dependent carbon diffusivity in austenite. Metall Mater Trans A 45(9):3790–3799CrossRefGoogle Scholar
  30. 30.
    Fernandes FAP, Christiansen TL, Winther G, Somers MAJ (2017) Measurement and tailoring of residual stress in expanded austenite on austenitic stainless steel. Mater Sci Eng A 701:167–173CrossRefGoogle Scholar
  31. 31.
    Li W, Guo W, Zhu X, Jin X, Li X, Dong H (2017) The effect of applied compressive stress on the diffusion of carbon in carbon supersaturated S-phase layer. Surf Coat Technol 331:1–6CrossRefGoogle Scholar
  32. 32.
    Peng Y, Gong J, Chen C, Liu Z, Jiang Y (2018) Numerical analysis of stress gradient and traps effects on carbon diffusion in AISI 316L during low temperature gas phase carburization. Metals 8(4):214CrossRefGoogle Scholar
  33. 33.
    Jespersen FN, Hattel JH, Somers MAJ (2016) Modelling the evolution of composition-and stress-depth profiles in austenitic stainless steels during low-temperature nitriding. Modell Simul Mater Sci Eng 24(2):025003CrossRefGoogle Scholar
  34. 34.
    Brink BK, Ståhl K, Christiansen TL, Oddershede J, Winther G, Somers MAJ (2017) On the elusive crystal structure of expanded austenite. Scripta Mater 131:59–62CrossRefGoogle Scholar
  35. 35.
    Jang JH, Bhadeshia HKDH, Suh D-W (2013) Solubility of carbon in tetragonal ferrite in equilibrium with austenite. Scripta Mater 68(3–4):195–198CrossRefGoogle Scholar
  36. 36.
    Cermak J, Kral L (2014) Carbon diffusion in carbon-supersaturated ferrite and austenite. J Alloy Compd 586:129–135CrossRefGoogle Scholar
  37. 37.
    Enomoto M, Hayashi K (2015) Simulation of the growth of austenite during continuous heating in low carbon iron alloys. J Mater Sci 50(20):6786–6793.  https://doi.org/10.1007/s10853-015-9234-3 CrossRefGoogle Scholar
  38. 38.
    Wang J, Li Z, Wang D, Qiu S, Ernst F (2017) Thermal stability of low-temperature-carburized austenitic stainless steel. Acta Mater 128:235–240CrossRefGoogle Scholar
  39. 39.
    Tao Q, Wang J, Fu L, Chen Z, Shen C, Zhang D, Sun Z (2017) Ultrahigh hardness of carbon steel surface realized by novel solid carburizing with rapid diffusion of carbon nanostructures. J Mater Sci Technol 33(10):1210–1218.  https://doi.org/10.1016/j.jmst.2017.04.022 CrossRefGoogle Scholar
  40. 40.
    Hohenberg P, Kohn W (1964) Inhomogeneous electron gas. Phys Rev 136(3B):B864–B871CrossRefGoogle Scholar
  41. 41.
    Sham LJ, Schlüter M (1983) Density-functional theory of the energy gap. Phys Rev Lett 51(20):1888–1891CrossRefGoogle Scholar
  42. 42.
    Segall MD, Lindan PJ, Probert MA, Pickard CJ, Hasnip PJ, Clark SJ, Payne MC (2002) First-principles simulation: ideas, illustrations and the CASTEP code. J Phys Condens Matter 14(11):2717–2744CrossRefGoogle Scholar
  43. 43.
    Clark SJ, Segall MD, Pickard CJ, Hasnip PJ, Probert MI, Refson K, Payne MC (2005) First principles methods using CASTEP. Zeitschrift für Kristallographie Cryst Mater 220(5/6):567–570Google Scholar
  44. 44.
    Perdew JP, Burke K, Ernzerhof M (1996) Generalized gradient approximation made simple. Phys Rev Lett 77(18):3865–3868CrossRefGoogle Scholar
  45. 45.
    Monkhorst HJ, Pack JD (1976) Special points for Brillouin-zone integrations. Phys Rev B 13(12):5188–5192CrossRefGoogle Scholar
  46. 46.
    Fischer TH, Almlof J (1992) General methods for geometry and wave function optimization. J Phys Chem 96(24):9768–9774CrossRefGoogle Scholar
  47. 47.
    Plimpton S (1995) Fast parallel algorithms for short-range molecular dynamics. J Comput Phys 117(1):1–19CrossRefGoogle Scholar
  48. 48.
    Lee BJ (2006) A modified embedded-atom method interatomic potential for the Fe–C system. Acta Mater 54(3):701–711CrossRefGoogle Scholar
  49. 49.
    Bonny G, Terentyev D, Pasianot RC, Poncé S, Bakaev A (2011) Interatomic potential to study plasticity in stainless steels: the FeNiCr model alloy. Modell Simul Mater Sci Eng 19(8):085008CrossRefGoogle Scholar
  50. 50.
    Lee SJ, Matlock DK, Van Tyne CJ (2013) Comparison of two finite element simulation codes used to model the carburizing of steel. Comput Mater Sci 68:47–54CrossRefGoogle Scholar
  51. 51.
    Eto Y, Umemoto M, Yoshida M (2015) Mechanism of abnormal surface carbon content reduction in Nb-bearing case hardening steel gas carburized after machining. ISIJ Int 55(1):227–234CrossRefGoogle Scholar
  52. 52.
    Kim DW, Cho HH, Lee WB, Cho KT, Cho YG, Kim SJ, Han HN (2016) A finite element simulation for carburizing heat treatment of automotive gear ring incorporating transformation plasticity. Mater Des 99:243–253CrossRefGoogle Scholar
  53. 53.
    Dal’Maz Silva W, Dulcy J, Ghanbaja J, Redjaïmia A, Michel G, Thibault S, Belmonte T (2017) Carbonitriding of low alloy steels: mechanical and metallurgical responses. Mater Sci Eng A 693:225–232CrossRefGoogle Scholar
  54. 54.
    Veiga RGA, Becquart CS, Perez M (2014) Comments on “Atomistic modeling of an Fe system with a small concentration of C”. Comput Mater Sci 82:118–121CrossRefGoogle Scholar
  55. 55.
    Restrepo OA, Mousseau N, El-Mellouhi F, Bouhali O, Trochet M, Becquart CS (2016) Diffusion properties of Fe–C systems studied by using kinetic activation–relaxation technique. Comput Mater Sci 112:96–106CrossRefGoogle Scholar
  56. 56.
    Restrepo OA, Becquart CS, El-Mellouhi F, Bouhali O, Mousseau N (2017) Diffusion mechanisms of C in 100, 110 and 111 Fe surfaces studied using kinetic activation-relaxation technique. Acta Mater 136:303–314CrossRefGoogle Scholar
  57. 57.
    Sahputra IH, Chakrabarty A, Restrepo O, Bouhali O, Mousseau N, Becquart CS, El-Mellouhi F (2017) Carbon adsorption on and diffusion through the Fe(110) surface and in bulk: developing a new strategy for the use of empirical potentials in complex material set-ups. Physica Status Solidi (b) 254(2):1600408CrossRefGoogle Scholar
  58. 58.
    Sheppard D, Terrell R, Henkelman G (2008) Optimization methods for finding minimum energy paths. J Chem Phys 128(13):134106CrossRefGoogle Scholar
  59. 59.
    Becquart CS, Raulot J, Bencteux G (2007) Atomistic modeling of an Fe system with a small concentration of C. Comput Mater Sci 40(1):119–129CrossRefGoogle Scholar
  60. 60.
    Liu WJ, Brimacombe JK, Hawbolt EB (1991) Influence of composition on the diffusivity of carbon in steels—I. Non-alloyed austenite. Acta Metallurgica Et Materialia 39(10):2373–2380CrossRefGoogle Scholar
  61. 61.
    McLellan RB (1996) The diffusion of heavy interstitial atoms in the absence of a particle density gradient. Acta Mater 44(10):4181–4185CrossRefGoogle Scholar
  62. 62.
    Tibbetts GG (1980) Diffusivity of carbon in iron and steels at high temperatures. J Appl Phys 51(9):4813–4816CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • Jian Wang
    • 1
  • Qing Tao
    • 1
  • Liming Fu
    • 2
  • Wei Lai
    • 1
  • Chengjin Shen
    • 1
  • Zhi Sun
    • 1
  • Aidang Shan
    • 2
  1. 1.School of Materials Science and EngineeringChina University of Mining and TechnologyXuzhouChina
  2. 2.School of Materials Science and EngineeringShanghai Jiao Tong UniversityShanghaiChina

Personalised recommendations