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.

Bismuth embrittlement of copper is an atomic size effect


Embrittlement by the segregation of impurity elements to grain boundaries is one of a small number of phenomena that can lead to metallurgical failure by fast fracture1. Here we settle a question that has been debated for over a hundred years2: how can minute traces of bismuth in copper cause this ductile metal to fail in a brittle manner? Three hypotheses for Bi embrittlement of Cu exist: two assign an electronic effect to either a strengthening3 or weakening4 of bonds, the third postulates a simple atomic size effect5. Here we report first principles quantum mechanical calculations that allow us to reject the electronic hypotheses, while supporting a size effect. We show that upon segregation to the grain boundary, the large Bi atoms weaken the interatomic bonding by pushing apart the Cu atoms at the interface. The resolution of the mechanism underlying grain boundary weakening should be relevant for all cases of embrittlement by oversize impurities.

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

Relevant articles

Open Access articles citing this article.

Access options

Rent or buy this article

Prices vary by article type



Prices may be subject to local taxes which are calculated during checkout

Figure 1: Internal energy as a function of strain as a unit cell based on a face-centred cubic lattice is sheared into itself on a (111) plane in a [112̄] crystal direction12.
Figure 2: Structure of a 1 ML Bi-segregated Σ19a grain boundary in Cu.
Figure 3: The local density of states (in arbitrary units) projected onto a Cu atom in a Σ19a GB to which 1 ML of Bi is segregated, the Σ19a in pure Cu and pure bulk copper.


  1. Gray, J. L. Investigation into the consequences of the failure of a turbine-generator at Hinkley Point ‘A’ power station. Proc. Inst. Mech. Eng. 186, 379–390 (1972)

    Article  CAS  Google Scholar 

  2. Hampe, W. Beiträge zu der Metallurgie des Kupfers. Berg-. Hütten- u. Salinenwesen 23, 93–137 (1874)

    Google Scholar 

  3. Haydock, R. The mobility of bonds at metal surfaces. J. Phys. C 14, 3807–3816 (1981)

    Article  ADS  CAS  Google Scholar 

  4. Messmer, R. & Briant, C. L. The role of chemical bonding in grain boundary embrittlement. Acta Metall. 30, 457–467 (1982)

    Article  CAS  Google Scholar 

  5. Sutton, A. P. & Vitek, V. An atomistic study of tilt grain boundaries with substitutional impurities. Acta Metall. 30, 2011–2033 (1982)

    Article  CAS  Google Scholar 

  6. Lawn, B. R. Fracture of Brittle solids Sect. 2.2, 2nd edn (Cambridge Univ. Press, Cambridge, 1993)

    Book  Google Scholar 

  7. Kelly, A. & Macmillan, N. H. Strong Solids Sect. 2.3.1 (Clarendon, Oxford, 1986)

    Google Scholar 

  8. Anderson, P. M. & Rice, J. R. Dislocation emission from cracks in crystals or along crystal interfaces. Scripta Metall. 20, 1467–1472 (1986)

    Article  CAS  Google Scholar 

  9. Rice, J. R. & Wang, J.-S. Embrittlement of interfaces by solute segregation. Mater. Sci. Eng. A 107, 23–40 (1989)

    Article  Google Scholar 

  10. Sigle, W., Chang, L.-S. & Gust, W. On the correlation between grain-boundary segregation, faceting and embrittlement in Bi-doped Cu. Phil. Mag. A 82, 1595–1608 (2002)

    Article  ADS  CAS  Google Scholar 

  11. Warke, W. R. in ASM Handbook Vol. 11, Failure Analysis and Prevention 861–867 (ASM International, Ohio, 2002)

    Google Scholar 

  12. Paxton, A. T., Gumbsch, P. & Methfessel, M. A quantum mechanical calculation of the theoretical strength of metals. Phil. Mag. Lett. 63, 267–274 (1991)

    Article  ADS  CAS  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

  14. Finnis, M. W. The energy and elastic constants of simple metals in terms of pairwise interactions. J. Phys. F 4, 1645–1656 (1974)

    Article  ADS  CAS  Google Scholar 

  15. Jokl, M. L., Vitek, V. & McMahon, C. J. Jr A microscopic theory of brittle fracture in deformable solids: a relation between ideal work to fracture and plastic work. Acta Metall. 28, 1479–1788 (1980)

    Article  Google Scholar 

  16. Finnis, M. W. The theory of metal–ceramic interfaces. J. Phys. Condens. Matter. 8, 5811–5836 (1996)

    Article  ADS  CAS  Google Scholar 

  17. Sutton, A. P. & Balluffi, R. W. Interfaces in Crystalline Materials Ch. 7 (Clarendon, Oxford, 1995)

    Google Scholar 

  18. Alber, U., Müllejans, H. & Rühle, M. Bismuth segregation at copper grain-boundaries. Acta Mater. 47, 4047–4060 (1999)

    Article  CAS  Google Scholar 

  19. Goodwin, L., Needs, R. J. & Heine, V. Effect of impurity bonding on grain-boundary embrittlement. Phys. Rev. Lett. 60, 2050–2053 (1988)

    Article  ADS  CAS  Google Scholar 

  20. Bruley, J., Keast, V. J. & Williams, D. B. An EELS study of segregation-induced grain-boundary embrittlement of copper. Acta Mater. 47, 4009–4017 (1999)

    Article  CAS  Google Scholar 

  21. Muller, D. A. Why changes in bond lengths and cohesion lead to core-level shifts in metals, and consequences for the spatial difference method. Ultramicroscopy 78, 163–174 (1999)

    Article  CAS  Google Scholar 

  22. Duscher, G., Chisholm, M., Alber, U. & Rühle, M. Bismuth-induced embrittlement of copper grain boundaries. Nature Mater. 3, 621–626 (2004)

    Article  ADS  CAS  Google Scholar 

  23. Özkaya, D., Yuan, J., Brown, L. M. & Flewitt, P. E. J. Segregation-induced hole drilling at grain-boundaries. J. Microsc. 180, 300–306 (1995)

    Article  Google Scholar 

  24. Saqi, M. A. S. & Pettifor, D. G. Role of impurity elements in metal–metal bond strengths. Phil. Mag. Lett. 56, 245–249 (1987)

    Article  ADS  Google Scholar 

  25. Powell, B. D. & Mykura, H. The segregation of bismuth to grain boundaries in copper-bismuth alloys. Acta Metall. 21, 1151–1156 (1973)

    Article  CAS  Google Scholar 

  26. 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)

    Article  ADS  CAS  Google Scholar 

  27. Rice, J. R. Dislocation nucleation from a crack tip: an analysis based on the Peierls concept. J. Mech. Phys. Solids 40, 239–271 (1992)

    Article  ADS  CAS  Google Scholar 

Download references


Financial support was provided by EPSRC.

Author information

Authors and Affiliations


Corresponding author

Correspondence to Anthony T. Paxton.

Ethics declarations

Competing interests

The authors declare that they have no competing financial interests.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Schweinfest, R., Paxton, A. & Finnis, M. Bismuth embrittlement of copper is an atomic size effect. Nature 432, 1008–1011 (2004).

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI:

This article is cited by


By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.


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