Entropy-dominated grain boundary segregation

Abstract

The phenomenon of entropy-dominated grain boundary segregation is introduced and discussed. Numerous examples of the grain boundaries and solutes exhibiting this phenomenon are compiled and predicted for example of α-iron-based alloys and other host materials. Consequences of entropy-dominated grain boundary segregation for grain size stabilization and intergranular embrittlement are shown.

Graphical abstract

This is a preview of subscription content, access via your institution.

Figure 1
Figure 2
Figure 3

Data availability

The data sets generated and/or analyzed in the present study are available from the corresponding author on reasonable request.

Notes

  1. 1.

    The product \(T \times {\text{ln}}X_{I}^{*} \left( T \right)\) is independent of temperature in the ideal case.

  2. 2.

    Using the value ΔHI = – 92 kJ mol–1 referred in [31] which implies the value ΔSI = – 97 J mol–1 K–1 [21], two times larger difference of the values of ΔσI is obtained.

References

  1. 1

    Stølen S, Grande T (2003) Chemical thermodynamics of materials. Wiley, Chichester

    Google Scholar 

  2. 2

    Ewing RH (1971) An analytical approach to interfacial entropy. Acta Metall 19:1359–1362. https://doi.org/10.1016/0001-6160(71)90073-3

    CAS  Article  Google Scholar 

  3. 3

    Fultz B (2010) Vibrational thermodynamics of materials. Prog Mater Sci 55:247–352. https://doi.org/10.1016/j.pmatsci.2009.05.002

    CAS  Article  Google Scholar 

  4. 4

    George EP, Raabe D, Ritchie RO (2019) High-entropy alloys. Nat Rev Mater 4:515–534. https://doi.org/10.1038/s41578-019-0121-4

    CAS  Article  Google Scholar 

  5. 5

    Lejček P, Všianská M, Šob M (2018) Recent trends and open questions in grain boundary segregation. J Mater Res 33:2647–2660. https://doi.org/10.1557/jmr.2018.230

    CAS  Article  Google Scholar 

  6. 6

    Lejček P, Hofmann S, Všianská M, Šob M (2021) Entropy matters in grain boundary segregation. Acta Mater 206:116597. https://doi.org/10.1016/j.actamat.2020.116597

    CAS  Article  Google Scholar 

  7. 7

    duPlessis J, van Wyk GN (1988) A model for surface segregation in multicomponent alloys—part I: equilibrium segregation. J Phys Chem Solids 49:1441–1450. https://doi.org/10.1016/0022-3697(88)90118-7

    CAS  Article  Google Scholar 

  8. 8

    duPlessis J, van Wyk GN (1988) A model for surface segregation in multicomponent alloys—part II: comment of other segregation analyses. J Phys Chem Solids 49:1451–1458. https://doi.org/10.1016/0022-3697(88)90119-9

    CAS  Article  Google Scholar 

  9. 9

    Wagih M, Schuh CA (2019) Spectrum of grain boundary segregation energies in polycrystal. Acta Mater 181:228–237. https://doi.org/10.1016/j.actamat.2019.09.034

    CAS  Article  Google Scholar 

  10. 10

    McLean D (1957) Grain boundaries in metals. Oxford University Press, Oxford

    Google Scholar 

  11. 11

    Yang X, Zhang Y (2012) Prediction of high-entropy stabilized solid-solution in multicomponent alloys. Mater Chem Phys 132:233–238. https://doi.org/10.1016/j.matchemphys.2011.11.021

    CAS  Article  Google Scholar 

  12. 12

    Erhart H, Grabke HJ (1981) Equilibrium segregation of phosphorus at grain boundaries of Fe–P, Fe–C–P, Fe–Cr–P, and Fe–Cr–C–P alloys. Metal Sci 15:401–408. https://doi.org/10.1179/030634581790426877

    CAS  Article  Google Scholar 

  13. 13

    Briant CL (1999) The effect of grain boundary segregation on intergranular failures. In: Briant CL (ed) Impurities in engineering materials. Marcel Dekker, New York, pp 193–224

    Google Scholar 

  14. 14

    Lejček P, Hofmann S (2016) Interstitial and substitutional solute segregation at individual boundaries of α-iron: data revisited. J Phys Condens Matter 28:064001. https://doi.org/10.1088/0953-8984/28/6/064001

    CAS  Article  Google Scholar 

  15. 15

    Ishida Y, Yokoyama S, Nishizawa T (1985) Grain boundary segregation in ferromagnetic alloys. Acta Metall 33:255–264. https://doi.org/10.1016/0001-6160(85)90143-9

    CAS  Article  Google Scholar 

  16. 16

    Hänsel H, Grabke HJ (1986) Grain boundary segregation of phosphorus and carbon in ferritic iron. Scr Metall 20:1641–1644. https://doi.org/10.1016/0036-9748(86)90411-4

    Article  Google Scholar 

  17. 17

    Seah MP, Lea C (1975) Surface segregation and its relation to grain boundary segregation. Philos Mag A 31:627–645. https://doi.org/10.1080/14786437508226543

    CAS  Article  Google Scholar 

  18. 18

    Mast R, Viefhaus H, Grabke HJ (1999) Grain boundary segregation of antimony in iron base alloys and its effect on toughness. Steel Res 70:239–246. https://doi.org/10.1002/srin.199905633

    CAS  Article  Google Scholar 

  19. 19

    Lejček P (2004) Grain boundary segregation of antimony in α-iron: prediction and experiment. J Alloys Compd 378:85–88. https://doi.org/10.1016/j.jallcom.2003.10.076

    CAS  Article  Google Scholar 

  20. 20

    Lejček P, Pokluda J, Šandera P, Horníková J, Jenko M (2012) Solute segregation at 46.8°(111) twist grain boundary of a phosphorus doped Fe–2.3%V alloy. Surf Sci 606:258–262. https://doi.org/10.1016/j.susc.2011.10.002

    CAS  Article  Google Scholar 

  21. 21

    Lejček P, Hofmann S (2019) Modeling grain boundary segregation by prediction of all the necessary parameters. Acta Mater 170:253–567. https://doi.org/10.1016/j.actamat.2019.03.037

    CAS  Article  Google Scholar 

  22. 22

    Lejček P, Hofmann S (2008) Thermodynamics of grain boundary segregation and applications to anisotropy, compensation effect and prediction. Crit Rev Sol State Mater Sci 33:133–163. https://doi.org/10.1080/10408430801907649

    CAS  Article  Google Scholar 

  23. 23

    Ko WS, Kim NJ, Lee BJ (2012) Atomistic modeling of an impurity element and metal-impurity system: pure P and Fe–P system. J Phys Condens Matter 24:225002. https://doi.org/10.1088/0953-8984/24/22/225002

    CAS  Article  Google Scholar 

  24. 24

    Sutton AP, Balluffi RW (1995) Interfaces in crystalline materials. Clarendon, Oxford

    Google Scholar 

  25. 25

    Massalski TB (1986) Binary alloy phase diagrams. ASM, Metals Park

    Google Scholar 

  26. 26

    Di Stefano D, Mrovec M, Elsässer Ch (2015) First-principles investigation of hydrogen trapping and diffusion at grain boundaries in nickel. Acta Mater 98:306–312. https://doi.org/10.1016/j.actamat.2015.07.031

    CAS  Article  Google Scholar 

  27. 27

    Muzyk M, Kurzydlovski KJ (2011) Density functional theory calculations of properties of the grain boundaries in aluminum. MRS Symp Proc 1297:155–159. https://doi.org/10.1557/opl.2011.531

    CAS  Article  Google Scholar 

  28. 28

    Rajagopalan M, Bhatia MA, Tschopp MA, Srolovitz DJ, Solanki KN (2014) Atomic-scale analysis of liquid-gallium embrittlement of aluminum grain boundaries. Acta Mater 73:312–325. https://doi.org/10.1016/j.actamat.2014.04.011

    CAS  Article  Google Scholar 

  29. 29

    Razumovskii VI, Lozovoi AY, Razumovskiy IM (2015) First principles-aided design of a new Ni-base superalloy: influence of transition metal alloying elements on grain boundary and bulk cohesion. Acta Mater 82:369–377. https://doi.org/10.1016/j.actamat.2014.08.047

    CAS  Article  Google Scholar 

  30. 30

    Scheiber D, Pippan R, Puschnig P, Ruban A, Romaner L (2016) Ab-initio search for cohesion-enhancing solute elements at grain boundaries in molybdenum and tungsten. Int J Refract Metals Hard Mater 60:75–81. https://doi.org/10.1016/j.ijrmhm.2016.07.003

    CAS  Article  Google Scholar 

  31. 31

    Kirchheim R (2002) Grain coarsening inhibited by solute segregation. Acta Mater 50:413–419. https://doi.org/10.1016/S1359-6454(01)00338-X

    CAS  Article  Google Scholar 

  32. 32

    Darling A, Chan RN, Wong PZ, Semones JE, Scattergood RO, Koch CC (2008) Grain-size stabilization in nanocrystalline FeZr alloys. Scr Mater 59:530–533. https://doi.org/10.1016/j.scriptamat.2008.04.045

    CAS  Article  Google Scholar 

  33. 33

    Rice JR, Wang JS (1989) Embrittlement of interfaces by solute segregation. Mater Sci Eng A 107:23–40. https://doi.org/10.1016/0921-5093(89)90372-9

    Article  Google Scholar 

  34. 34

    Všianská M, Šob M (2011) The effect of segregated sp-impurities on grain-boundary structure, magnetism and embrittlement. Prog Mater Sci 56:817–840. https://doi.org/10.1016/j.pmatsci.2011.01.008

    CAS  Article  Google Scholar 

  35. 35

    Ma Y, Sun B, Schökel A, Song W, Ponge D, Raabe D, Bleck W (2020) Phase boundary segregation-induced strengthening and discontinuous yielding in ultrafine-grained duplex medium-Mn steels. Acta Mater 200:389–403. https://doi.org/10.1016/j.actamat.2020.09.007

    CAS  Article  Google Scholar 

  36. 36

    Furuhara T, Zhang Y, Miyamoto G (2019) Roles of transformation interfaces in the design of advanced high strength steels. IOP Conf Ser Mater Sci Eng 580:012005. https://doi.org/10.1088/1757-899X/580/1/012005

    CAS  Article  Google Scholar 

  37. 37

    Wicaksono AT, Militzer M (2017) Interaction of C and Mn in a Σ3 grain boundary of bcc iron. IOP Conf Ser Mater Sci Eng 219:012044. https://doi.org/10.1088/1757-899X/219/1/012044

    Article  Google Scholar 

Download references

Acknowledgements

Financial support was provided by the Czech Science Foundation (Project No. GA-20-08130S), by the Ministry of Education, Youth and Sports of the Czech Republic (CEITEC 2020-Project No. LQ1601), and by the Academy of Sciences of the Czech Republic (RVO:68378271).

Author information

Affiliations

Authors

Corresponding author

Correspondence to P. Lejček.

Ethics declarations

Conflict of interest

The authors declare that they have no known competing financial interest or personal relationships that could have appeared to influence the work reported in this paper.

Additional information

Publisher's Note

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

Handling Editor: N. Ravishankar.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Lejček, P., Hofmann, S. Entropy-dominated grain boundary segregation. J Mater Sci 56, 7464–7473 (2021). https://doi.org/10.1007/s10853-021-05800-w

Download citation