Journal of Materials Science

, Volume 54, Issue 7, pp 5570–5583 | Cite as

Atomistic simulations of grain boundary energies in austenitic steel

  • Sutatch RatanaphanEmail author
  • Rajchawit Sarochawikasit
  • Noppadol Kumanuvong
  • Sho Hayakawa
  • Hossein Beladi
  • Gregory S. Rohrer
  • Taira Okita
Computation and theory


The energies of 388 grain boundaries with a range of misorientations and grain boundary plane orientations have been calculated using the meta-atom embedded atom method potential recently developed to simulate an austenitic twinning-induced plasticity (TWIP) steel. A comparison between the simulated grain boundary energies and the measured grain boundary population in an austenitic TWIP steel revealed that at fixed misorientations, there is a strong inverse correlation between the energy and the population. In addition, the Bulatov–Reed–Kumar five-parameter grain boundary energy function for face-centered cubic metals was used to produce a larger, more nearly continuous set of grain boundary energies. Interestingly, these interpolated grain boundary energies were consistent with the simulated energies and also inversely correlated with the measured grain boundary populations in an austenitic TWIP steel.



S.R. acknowledges the financial supports provided by the Skill Development Grant, King Mongkut’s University of Technology Thonburi (KMUTT), Research Strengthening Project of the Faculty of Engineering, KMUTT, and the Thailand Research Fund and Office of the Higher Education Commission (MRG6080253). G.S.R. acknowledges support from the National Science Foundation under grant DMR 1628994. The simulating machine supported by the Innovative Software and Computing Center at KMUTT. We also thank Prof. Tawee Tunkasiri and Prof. Poom Kumam for critical comment and suggestion, Dr. David Olmsted for the code used for grain boundary energy calculation, and Dr. Lucas Hale for iprPy calculation framework and the Interatomic Potential Repository Project (NIST).

Supplementary material

10853_2018_3297_MOESM1_ESM.xlsx (20 kb)
Supplementary material 1 (XLSX 20 kb)
10853_2018_3297_MOESM2_ESM.txt (34 kb)
Supplementary material 2 (TXT 34 kb)


  1. 1.
    Bouaziz O, Allain S, Scott CP et al (2011) High manganese austenitic twinning induced plasticity steels: a review of the microstructure properties relationships. Curr Opin Solid State Mater Sci 15:141–168. CrossRefGoogle Scholar
  2. 2.
    Beladi H, Timokhina IB, Estrin Y et al (2011) Orientation dependence of twinning and strain hardening behaviour of a high manganese twinning induced plasticity steel with polycrystalline structure. Acta Mater 59:7787–7799. CrossRefGoogle Scholar
  3. 3.
    Barr CM, Vetterick GA, Unocic KA et al (2014) Anisotropic radiation-induced segregation in 316L austenitic stainless steel with grain boundary character. Acta Mater 67:145–155. CrossRefGoogle Scholar
  4. 4.
    Gutierrez-Urrutia I, Zaefferer S, Raabe D (2010) The effect of grain size and grain orientation on deformation twinning in a Fe–22wt.% Mn–0.6wt.% C TWIP steel. Mater Sci Eng A 527:3552–3560. CrossRefGoogle Scholar
  5. 5.
    Michiuchi M, Kokawa H, Wang ZJ et al (2006) Twin-induced grain boundary engineering for 316 austenitic stainless steel. Acta Mater 54:5179–5184. CrossRefGoogle Scholar
  6. 6.
    Shimada M, Kokawa H, Wang ZJ et al (2002) Optimization of grain boundary character distribution for intergranular corrosion resistant 304 stainless steel by twin-induced grain boundary engineering. Acta Mater 50:2331–2341. CrossRefGoogle Scholar
  7. 7.
    Barr CM, Thomas S, Hart JL et al (2018) Tracking the evolution of intergranular corrosion through twin-related domains in grain boundary networks. NPJ Mater Degrad 2:14. CrossRefGoogle Scholar
  8. 8.
    Sakaguchi N, Endo M, Watanabe S et al (2013) Radiation-induced segregation and corrosion behavior on Σ3 coincidence site lattice and random grain boundaries in proton-irradiated type-316L austenitic stainless steel. J Nucl Mater 434:65–71. CrossRefGoogle Scholar
  9. 9.
    Bouaziz O, Allain S, Scott C (2008) Effect of grain and twin boundaries on the hardening mechanisms of twinning-induced plasticity steels. Scr Mater 58:484–487. CrossRefGoogle Scholar
  10. 10.
    Steinmetz DR, Jäpel T, Wietbrock B et al (2013) Revealing the strain-hardening behavior of twinning-induced plasticity steels: theory, simulations, experiments. Acta Mater 61:494–510. CrossRefGoogle Scholar
  11. 11.
    Rohrer GS (2011) Grain boundary energy anisotropy: a review. J Mater Sci 46:5881–5895. CrossRefGoogle Scholar
  12. 12.
    Beladi H, Nuhfer NT, Rohrer GS (2014) The five-parameter grain boundary character and energy distributions of a fully austenitic high-manganese steel using three dimensional data. Acta Mater 70:281–289. CrossRefGoogle Scholar
  13. 13.
    Jones R, Randle V, Engelberg D, Marrow TJ (2009) Five-parameter grain boundary analysis of a grain boundary–engineered austenitic stainless steel. J Microsc 233:417–422. CrossRefGoogle Scholar
  14. 14.
    Gertsman VY, Bruemmer SM (2001) Study of grain boundary character along intergranular stress corrosion crack paths in austenitic alloys. Acta Mater 49:1589–1598. CrossRefGoogle Scholar
  15. 15.
    Jones R, Randle V (2010) Sensitisation behaviour of grain boundary engineered austenitic stainless steel. Mater Sci Eng A 527:4275–4280. CrossRefGoogle Scholar
  16. 16.
    Shi F, Tian PC, Jia N et al (2016) Improving intergranular corrosion resistance in a nickel-free and manganese-bearing high-nitrogen austenitic stainless steel through grain boundary character distribution optimization. Corros Sci 107:49–59. CrossRefGoogle Scholar
  17. 17.
    Tokita S, Kokawa H, Sato YS, Fujii HT (2017) In situ EBSD observation of grain boundary character distribution evolution during thermomechanical process used for grain boundary engineering of 304 austenitic stainless steel. Mater Charact 131:31–38. CrossRefGoogle Scholar
  18. 18.
    Feng W, Yang S, Yan Y (2017) Dependence of grain boundary character distribution on the initial grain size of 304 austenitic stainless steel. Philos Mag 97:1057–1070. CrossRefGoogle Scholar
  19. 19.
    Hu C, Xia S, Li H et al (2011) Improving the intergranular corrosion resistance of 304 stainless steel by grain boundary network control. Corros Sci 53:1880–1886. CrossRefGoogle Scholar
  20. 20.
    Murr LE, Wong GI, Horylev RJ (1973) Measurement of interfacial free energies and associated temperature coefficients in 304 stainless steel. Acta Metall 21:595–604. CrossRefGoogle Scholar
  21. 21.
    Saylor DM, Rohrer GS (2001) Evaluating anisotropic surface energies using the capillarity vector reconstruction method. Interface Sci 9:35–42. CrossRefGoogle Scholar
  22. 22.
    Holm EA, Olmsted DL, Foiles SM (2010) Comparing grain boundary energies in face-centered cubic metals: Al, Au, Cu and Ni. Scr Mater 63:905–908. CrossRefGoogle Scholar
  23. 23.
    Olmsted DL, Foiles SM, Holm EA (2009) Survey of computed grain boundary properties in face-centered cubic metals: I. Grain boundary energy. Acta Mater 57:3694–3703. CrossRefGoogle Scholar
  24. 24.
    Rohrer GS, Holm EA, Rollett AD et al (2010) Comparing calculated and measured grain boundary energies in nickel. Acta Mater 58:5063–5069. CrossRefGoogle Scholar
  25. 25.
    Holm EA, Rohrer GS, Foiles SM et al (2011) Validating computed grain boundary energies in fcc metals using the grain boundary character distribution. Acta Mater 59:5250–5256. CrossRefGoogle Scholar
  26. 26.
    Shibuta Y, Takamoto S, Suzuki T (2008) A molecular dynamics study of the energy and structure of the symmetric tilt boundary of iron. ISIJ Int 48:1582–1591. CrossRefGoogle Scholar
  27. 27.
    Finnis MW, Sinclair JE (1984) A simple empirical N-body potential for transition metals. Philos Mag A 50:45–55. CrossRefGoogle Scholar
  28. 28.
    Wang P, Xu S, Liu J et al (2017) Atomistic simulation for deforming complex alloys with application toward TWIP steel and associated physical insights. J Mech Phys Solids 98:290–308. CrossRefGoogle Scholar
  29. 29.
    Pierce DT, Jiménez JA, Bentley J et al (2014) The influence of manganese content on the stacking fault and austenite/ε-martensite interfacial energies in Fe–Mn–(Al–Si) steels investigated by experiment and theory. Acta Mater 68:238–253. CrossRefGoogle Scholar
  30. 30.
    Chamati H, Papanicolaou NI, Mishin Y, Papaconstantopoulos DA (2006) Embedded-atom potential for Fe and its application to self-diffusion on Fe(100). Surf Sci 600:1793–1803. CrossRefGoogle Scholar
  31. 31.
    Allain S, Chateau J-P, Bouaziz O et al (2004) Correlations between the calculated stacking fault energy and the plasticity mechanisms in Fe–Mn–C alloys. Mater Sci Eng A 387:158–162. CrossRefGoogle Scholar
  32. 32.
    Bulatov VV, Reed BW, Kumar M (2014) Grain boundary energy function for fcc metals. Acta Mater 65:161–175. CrossRefGoogle Scholar
  33. 33.
    Ratanaphan S, Olmsted DL, Bulatov VV et al (2015) Grain boundary energies in body-centered cubic metals. Acta Mater 88:346–354. CrossRefGoogle Scholar
  34. 34.
    Ratanaphan S, Boonkird T, Sarochawikasit R et al (2017) Atomistic simulations of grain boundary energies in tungsten. Mater Lett 186:116–118. CrossRefGoogle Scholar
  35. 35.
    Sato K, Ichinose M, Hirotsu Y, Inoue Y (1989) Effects of deformation induced phase transformation and twinning on the mechanical properties of austenitic Fe–Mn–Al alloys. ISIJ Int 29:868–877. CrossRefGoogle Scholar
  36. 36.
    Plimpton SJ (2007) Large-scale atomic/molecular massively parallel simulator. Sandia Natl LabGoogle Scholar
  37. 37.
    Foiles SM (2010) Temperature dependence of grain boundary free energy and elastic constants. Scr Mater 62:231–234. CrossRefGoogle Scholar
  38. 38.
    Gupta D (2003) Diffusion, solute segregations and interfacial energies in some material: an overview. Interface Sci 11:7–20. CrossRefGoogle Scholar
  39. 39.
    Morawiec A, Glowinski K (2013) On “macroscopic” characterization of mixed grain boundaries. Acta Mater 61:5756–5767. CrossRefGoogle Scholar
  40. 40.
    Glowinski K (2014) On identification of symmetric and improperly quasi-symmetric grain boundaries. J Appl Crystallogr 47:726–731. CrossRefGoogle Scholar
  41. 41.
    Ratanaphan S, Raabe D, Sarochawikasit R et al (2017) Grain boundary character distribution in electroplated nanotwinned copper. J Mater Sci 52:4070–4085. CrossRefGoogle Scholar
  42. 42.
    Davison AC, Hinkley DV (1997) Bootstrap methods and their application. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  43. 43.
    Li J, Dillon SJ, Rohrer GS (2009) Relative grain boundary area and energy distributions in nickel. Acta Mater 57:4304–4311. CrossRefGoogle Scholar
  44. 44.
    Saylor DM, Morawiec A, Rohrer GS (2003) The relative free energies of grain boundaries in magnesia as a function of five macroscopic parameters. Acta Mater 51:3675–3686. CrossRefGoogle Scholar
  45. 45.
    Beladi H, Rohrer GS (2013) The relative grain boundary area and energy distributions in a ferritic steel determined from three-dimensional electron backscatter diffraction maps. Acta Mater 61:1404–1412. CrossRefGoogle Scholar
  46. 46.
    Ratanaphan S, Yoon Y, Rohrer GS (2014) The five parameter grain boundary character distribution of polycrystalline silicon. J Mater Sci 49:4938–4945. CrossRefGoogle Scholar
  47. 47.
    Gruber J, George DC, Kuprat AP et al (2005) Effect of anisotropic grain boundary properties on grain boundary plane distributions during grain growth. Scr Mater 53:351–355. CrossRefGoogle Scholar
  48. 48.
    Beladi H, Rohrer GS (2013) The distribution of grain boundary planes in interstitial free steel. Metall Mater Trans A 44:115–124. CrossRefGoogle Scholar
  49. 49.
    Ratanaphan S (2013) Grain boundary character distributions in isostructural materials. Ph.D. thesis, Dep Mater Sci Eng Carnegie Mellon UnivGoogle Scholar
  50. 50.
    Cantwell PR, Tang M, Dillon SJ et al (2014) Grain boundary complexions. Acta Mater 62:1–48. CrossRefGoogle Scholar
  51. 51.
    Raabe D, Herbig M, Sandlöbes S et al (2014) Grain boundary segregation engineering in metallic alloys: a pathway to the design of interfaces. Curr Opin Solid State Mater Sci 18:253–261. CrossRefGoogle Scholar
  52. 52.
    Kuzmina M, Ponge D, Raabe D (2015) Grain boundary segregation engineering and austenite reversion turn embrittlement into toughness: example of a 9 wt.% medium Mn steel. Acta Mater 86:182–192. CrossRefGoogle Scholar
  53. 53.
    Deng Y, Tasan CC, Pradeep KG et al (2015) Design of a twinning-induced plasticity high entropy alloy. Acta Mater 94:124–133. CrossRefGoogle Scholar
  54. 54.
    Frolov T, Olmsted DL, Asta M, Mishin Y (2013) Structural phase transformations in metallic grain boundaries. Nat Commun 4:1899. CrossRefGoogle Scholar
  55. 55.
    Frolov T, Asta M, Mishin Y (2015) Segregation-induced phase transformations in grain boundaries. Phys Rev B 92:020103. CrossRefGoogle Scholar
  56. 56.
    Kurtuldu G, Sicco A, Rappaz M (2014) Icosahedral quasicrystal-enhanced nucleation of the fcc phase in liquid gold alloys. Acta Mater 70:240–248. CrossRefGoogle Scholar
  57. 57.
    Thomas SL, Chen K, Han J et al (2017) Reconciling grain growth and shear-coupled grain boundary migration. Nat Commun 8:1764. CrossRefGoogle Scholar
  58. 58.
    Homer ER, Patala S, Priedeman JL (2015) Grain boundary plane orientation fundamental zones and structure-property relationships. Sci Rep 5:15476. CrossRefGoogle Scholar

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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Tool and Materials EngineeringKing Mongkut’s University of Technology ThonburiBangkokThailand
  2. 2.Department of Computer EngineeringKing Mongkut’s University of Technology ThonburiBangkokThailand
  3. 3.School of EngineeringThe University of TokyoTokyoJapan
  4. 4.Institute for Frontier MaterialsDeakin UniversityGeelongAustralia
  5. 5.Department of Materials Science and EngineeringCarnegie Mellon UniversityPittsburghUSA
  6. 6.Research into Artifacts, Center for EngineeringThe University of TokyoKashiwaJapan

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