Skip to main content

Thank you for visiting You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Mechanism of collective interstitial ordering in Fe–C alloys


Collective interstitial ordering is at the core of martensite formation in Fe–C-based alloys, laying the foundation for high-strength steels. Even though this ordering has been studied extensively for more than a century, some fundamental mechanisms remain elusive. Here, we show the unexpected effects of two correlated phenomena on the ordering mechanism: anharmonicity and segregation. The local anharmonicity in the strain fields induced by interstitials substantially reduces the critical concentration for interstitial ordering, up to a factor of three. Further, the competition between interstitial ordering and segregation results in an effective decrease of interstitial segregation into extended defects for high interstitial concentrations. The mechanism and corresponding impact on interstitial ordering identified here enrich the theory of phase transitions in materials and constitute a crucial step in the design of ultra-high-performance alloys.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

Fig. 1: Disorder–order transition in Fe–C alloys.
Fig. 2: Strain-induced interaction.
Fig. 3: Impact of local anharmonicity on the disorder–order transition.
Fig. 4: Competition between C ordering and segregation.
Fig. 5: Comparison between theory and experiment.

Data availability

The datasets generated during the current study are available from the corresponding authors on request.

Code availability

The computer code developed during the current study is available from the corresponding authors on request.


  1. 1.

    Wuttig, M. et al. The role of vacancies and local distortions in the design of new phase-change materials. Nat. Mater. 6, 122–128 (2007).

    CAS  Google Scholar 

  2. 2.

    Guignard, M. et al. P2-NaxVO2 system as electrodes for batteries and electron-correlated materials. Nat. Mater. 12, 74–80 (2013).

    CAS  Google Scholar 

  3. 3.

    Sohn, S. S. et al. Ultrastrong medium-entropy single-phase alloys designed via severe lattice distortion. Adv. Mater. 31, 1807142 (2019).

    Google Scholar 

  4. 4.

    Siegrist, T. et al. Disorder-induced localization in crystalline phase-change materials. Nat. Mater. 10, 202–208 (2011).

    CAS  Google Scholar 

  5. 5.

    Li, X. et al. Direct visualization of the Jahn–Teller effect coupled to Na ordering in Na5/8MnO2. Nat. Mater. 13, 586–592 (2014).

    CAS  Google Scholar 

  6. 6.

    Ni, Y. & Khachaturyan, A. G. From chessboard tweed to chessboard nanowire structure during pseudospinodal decomposition. Nat. Mater. 8, 410–414 (2009).

    CAS  Google Scholar 

  7. 7.

    Lei, Z. et al. Enhanced strength and ductility in a high-entropy alloy via ordered oxygen complexes. Nature 563, 546–550 (2018).

    CAS  Google Scholar 

  8. 8.

    Seljakow, N. The nature of martensite. Nature 123, 204–205 (1929).

    Google Scholar 

  9. 9.

    Jack, K. H. Iron-nitrogen, iron-carbon and iron-carbon-nitrogen interstitial alloys: their occurrence in tempered martensite. Nature 158, 60–61 (1946).

    Google Scholar 

  10. 10.

    Li, Y. et al. Segregation stabilizes nanocrystalline bulk steel with near theoretical strength. Phys. Rev. Lett. 113, 106104 (2014).

    Google Scholar 

  11. 11.

    Zhang, X. et al. Structural transformations among austenite, ferrite and cementite in Fe-C alloys: a unified theory based on ab initio simulations. Acta Mater. 99, 281–289 (2015).

    CAS  Google Scholar 

  12. 12.

    Wang, H., Zhang, X., Yan, D., Somsen, C. & Eggeler, G. Interface dominated cooperative nanoprecipitation in interstitial alloys. Nat. Commun. 9, 4107 (2018).

    Google Scholar 

  13. 13.

    Zhang, X., Hickel, T., Rogal, J. & Neugebauer, J. Interplay between interstitial displacement and displacive lattice transformations. Phys. Rev. B 94, 104109 (2016).

    Google Scholar 

  14. 14.

    Honda, K. & Sekito, S. Two kinds of martensite. Nature 121, 744 (1928).

    CAS  Google Scholar 

  15. 15.

    Udyansky, A., von Pezold, J., Bugaev, V. N., Friák, M. & Neugebauer, J. Interplay between long-range elastic and short-range chemical interactions in Fe-C martensite formation. Phys. Rev. B 79, 224112 (2009).

    Google Scholar 

  16. 16.

    Udyansky, A., von Pezold, J., Dick, A. & Neugebauer, J. Orientational ordering of interstitial atoms and martensite formation in dilute Fe-based solid solutions. Phys. Rev. B 83, 184112 (2011).

    Google Scholar 

  17. 17.

    Naraghi, R., Selleby, M. & Ågren, J. Thermodynamics of stable and metastable structures in Fe-C system. Calphad 46, 148–158 (2014).

    CAS  Google Scholar 

  18. 18.

    Ruban, A. V. 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).

    Google Scholar 

  19. 19.

    Djaziri, S. et al. Deformation-induced martensite: a new paradigm for exceptional steels. Adv. Mater. 28, 7753–7757 (2016).

    CAS  Google Scholar 

  20. 20.

    Khachaturian, A. Theory of Structural Transformations in Solids (Wiley, 1983).

  21. 21.

    Kanzaki, H. Point defects in face-centred cubic lattice-II X-ray scattering effects. J. Phys. Chem. Solids 2, 107–114 (1957).

    Google Scholar 

  22. 22.

    Kanzaki, H. Point defects in face-centred cubic lattice-I Distortion around defects. J. Phys. Chem. Solids 2, 24–36 (1957).

    Google Scholar 

  23. 23.

    Lau, T. T. et al. Many-body potential for point defect clusters in Fe-C alloys. Phys. Rev. Lett. 98, 215501 (2007).

    Google Scholar 

  24. 24.

    Cochardt, A., Schoek, G. & Wiedersich, H. Interaction between dislocations and interstitial atoms in body-centered cubic metals. Acta Metall. 3, 533–537 (1955).

    CAS  Google Scholar 

  25. 25.

    Kamber, K., Keefer, D. & Wert, C. Interactions of interstitials with dislocations in iron. Acta Metall. 9, 403–414 (1961).

    CAS  Google Scholar 

  26. 26.

    Douthwaite, R. & Evans, J. Interaction between a tetragonal distortion and a 〈111〉 screw dislocation in an anisotropic cubic crystal. Scr. Mater. 7, 1019–1026 (1973).

    CAS  Google Scholar 

  27. 27.

    de Hosson, J. An atomic model for the interaction between a 12 〈111〉 {110} edge dislocation and carbon in α-Fe. Solid State Commun. 17, 747–750 (1975).

    Google Scholar 

  28. 28.

    Tapasa, K., Osetsky, Y. & Bacon, D. Computer simulation of interaction of an edge dislocation with a carbon interstitial in α-iron and effects on glide. Acta Mater. 55, 93–104 (2007).

    CAS  Google Scholar 

  29. 29.

    Clouet, E., Garruchet, S., Nguyen, H., Perez, M. & Becquart, C. S. Dislocation interaction with C in α-Fe: a comparison between atomic simulations and elasticity theory. Acta Mater. 56, 3450–3460 (2008).

    CAS  Google Scholar 

  30. 30.

    Lejček, P. Grain Boundary Segregation in Metals (Springer Berlin Heidelberg, 2010).

  31. 31.

    Speich, G. R. Tempering of low-carbon martensite. Trans. TMS-AIME 245, 2553–2564 (1969).

    CAS  Google Scholar 

  32. 32.

    Wilde, J., Cerezo, A. & Smith, G. D. W. Three-dimensional atomic-scale mapping of a cottrell atomosphere around a dislocation in iron. Scr. Mater. 43, 39–48 (2000).

    CAS  Google Scholar 

  33. 33.

    Fink, W. L. & Campbell, E. D. Influence of heat treatment and carbon contents on the structure of pure iron-carbon alloys. Trans. Am. Soc. Steel Treat. 9, 717–748 (1926).

    CAS  Google Scholar 

  34. 34.

    Bain, E. C. & Paxton, H. W. Alloying Elements in Steel (ASM, 1966).

  35. 35.

    Honda, E. & Nishiyama, Z. On the nature of the tetragonal and cubic martensites. Sci. Rep. Toh. Imper. Univ. 21, 299–331 (1932).

    CAS  Google Scholar 

  36. 36.

    Hägg, G. X-ray investigations on the structure and decomposition of martensite. J. Iron Steel Inst. 130, 439–451 (1934).

    Google Scholar 

  37. 37.

    Xiao, L. et al. Lattice-parameter variation with carbon content of martensite. I. X-ray-diffraction experimental study. Phys. Rev. B 52, 9970–9978 (1995).

    CAS  Google Scholar 

  38. 38.

    Krakauer, B. W. & Seidman, D. N. Absolute atomic-scale measurements of the Gibbsian interfacial excess of solute at internal interfaces. Phys. Rev. B 48, 6724–6727 (1993).

    CAS  Google Scholar 

  39. 39.

    Santodonato, L. J., Liaw, P. K., Unocic, R. R., Bei, H. & Morris, J. R. Predictive multiphase evolution in Al-containing high-entropy alloys. Nat. Commun. 9, 4520 (2018).

    CAS  Google Scholar 

  40. 40.

    King, G. & Woodward, P. M. Cation ordering in perovskites. J. Mater. Chem. 20, 5785–5796 (2010).

    Google Scholar 

  41. 41.

    Plimpton, S. Fast parallel algorithms for short-range molecular dynamics. J. Comput. Phys. 117, 1–19 (1995).

    CAS  Google Scholar 

  42. 42.

    Boeck, S., Freysoldt, C., Dick, A., Ismer, L. & Neugebauer, J. The object-oriented DFT program library S/PHI/nX. Comput. Phys. Commun. 182, 543–554 (2011).

    CAS  Google Scholar 

  43. 43.

    Kresse, G. & Furthmüller, J. Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys. Rev. B 54, 11169–11186 (1996).

    CAS  Google Scholar 

  44. 44.

    Blöchl, P. E. Projector augmented-wave method. Phys. Rev. B 50, 17953–17979 (1994).

    Google Scholar 

  45. 45.

    Perdew, J. P., Burke, K. & Ernzerhof, M. Generalized gradient approximation made simple. Phys. Rev. Lett. 77, 3865–3868 (1996).

    CAS  Google Scholar 

  46. 46.

    Monkhorst, H. J. & Pack, J. D. Special points for Brillouin-zone integrations. Phys. Rev. B 13, 5188–5192 (1976).

    Google Scholar 

  47. 47.

    Uebing, C. On the ordering of interstitials in bcc metals and bct martensites: a lattice gas approach. Scr. Metall. Mater. 30, 1183–1188 (1994).

    CAS  Google Scholar 

  48. 48.

    Finney, D. J. Bioassay and the practice of statistical inference. Int. Stat. Rev. 47, 1–12 (1979).

    Google Scholar 

Download references


We gratefully acknowledge the financial support from the German Research Foundation (DFG) under grant HI 1300/15-1 within the DFG-ANR project C-TRAM. H.W. thanks J. Westraadt at the Nelson Mandela University for help with measuring the TEM foil thickness by EELS. X.Z. thanks W. Wang for fruitful discussions.

Author information




X.Z., T.H. and J.N. designed the project. X.Z. performed all atomistic calculations under the supervision of T.H., J.R. and J.N. H.W. and Y.L. did the HRTEM characterization and APT analysis. All authors discussed the results and contributed to writing the manuscript.

Corresponding authors

Correspondence to Xie Zhang or Hongcai Wang.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary information

Supplementary Information

Supplementary Notes 1–5, Figs. 1–10 and Table 1.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Zhang, X., Wang, H., Hickel, T. et al. Mechanism of collective interstitial ordering in Fe–C alloys. Nat. Mater. 19, 849–854 (2020).

Download citation


Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing