Skip to main content
Log in

A Computational Algorithm to Produce Virtual X-ray and Electron Diffraction Patterns from Atomistic Simulations

  • Published:
JOM Aims and scope Submit manuscript

Abstract

Electron and x-ray diffraction are well-established experimental methods used to explore the atomic scale structure of materials. In this work, a computational algorithm is developed to produce virtual electron and x-ray diffraction patterns directly from atomistic simulations. This algorithm advances beyond previous virtual diffraction methods by using a high-resolution mesh of reciprocal space that eliminates the need for a priori knowledge of the crystal structure being modeled or other assumptions concerning the diffraction conditions. At each point on the reciprocal space mesh, the diffraction intensity is computed via explicit computation of the structure factor equation. To construct virtual selected-area electron diffraction patterns, a hemispherical slice of the reciprocal lattice mesh lying on the surface of the Ewald sphere is isolated and viewed along a specified zone axis. X-ray diffraction line profiles are created by binning the intensity of each reciprocal lattice point by its associated scattering angle, effectively mimicking powder diffraction conditions. The virtual diffraction algorithm is sufficiently generic to be applied to atomistic simulations of any atomic species. In this article, the capability and versatility of the virtual diffraction algorithm is exhibited by presenting findings from atomistic simulations of 〈100〉 symmetric tilt Ni grain boundaries, nanocrystalline Cu models, and a heterogeneous interface formed between α-Al2O3 (0001) and γ-Al2O3 (111).

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

References

  1. P.D. Bristowe and S.L. Sass, Acta Metall. 28, 575 (1980).

    Article  Google Scholar 

  2. J. Budai, P.D. Bristowe, and S.L. Sass, Acta Metall. 31, 699 (1983).

    Article  Google Scholar 

  3. P.D. Bristowe and R.W. Balluffi, Surf. Sci. 144, 14 (1984).

    Article  Google Scholar 

  4. Y. Oh and V. Vitek, Acta Metall. 34, 1941 (1986).

    Article  Google Scholar 

  5. M.R. Fitzsimmons and S.L. Sass, Acta Metall. 36, 3103 (1988).

    Article  Google Scholar 

  6. S. Brandstetter, P.M. Derlet, S. Van Petegem, and H. Van Swygenhoven, Acta Mater. 56, 165 (2008).

    Article  Google Scholar 

  7. A. Stukowski, J. Markmann, J. Weissmüller, and K. Albe, Acta Mater. 57, 1648 (2009).

    Article  Google Scholar 

  8. J. Markmann, V. Yamakov, and J. Weissmüller, Scr. Mater. 59, 15 (2008).

    Article  Google Scholar 

  9. J. Markmann, D. Bachurin, L. Shao, P. Gumbsch, and J. Weissmüller, Europhys. Lett. 89, 66002 (2010).

    Article  Google Scholar 

  10. P.M. Derlet, S. Van Petegem, and H. Van Swygenhoven, Phys. Rev. B 71, 1 (2005).

    Article  Google Scholar 

  11. H. Van Swygenhoven, Ž. Budrovie, P.M. Derlet, A.G. Froseth, and S. Van Petegem, Mater. Sci. Eng. A 400, 329 (2005).

    Article  Google Scholar 

  12. S.P. Coleman, D.E. Spearot, and L. Capolungo, Model. Simul. Mater. Sci. Eng. 21, 055020 (2013).

    Article  Google Scholar 

  13. D.B. Williams and C.B. Carter, Transmission Electron Microscopy, Part 2 Diffraction, 2nd ed. (New York: Springer, 2009), pp. 211–219.

    Book  Google Scholar 

  14. S.J. Plimpton, J. Comput. Phys. 117, 1 (1995).

    Article  MATH  Google Scholar 

  15. B.E. Warren, X-Ray Diffraction, 1st ed. (New York: Dover Publications, 1990), pp. 1–389.

    Google Scholar 

  16. C. Colliex, J.M. Cowley, S.L. Dudarev, M. Fink, K. Gjønnes, R. Hilderbrandt, A. Howie, D.F. Lynch, L.-M. Peng, G. Ren, A.W. Ross, V.H. Smith Jr., J.C.H. Spence, J. Steeds, J. Wang, M.J. Whelan, and B.B. Zvyagin, International Tables Crystallography, Vol. C: Mathematical, Physical, and Chemical Tables, 3rd ed., ed. E. Prince (Norwell: Kluwer Academic Publishers, 2004), pp. 259–429.

    Google Scholar 

  17. L.-M. Peng, G. Ren, S.L. Dudarev, and M.J. Whelan, Acta Crystallogr. Sect. A 52, 257 (1996).

    Article  Google Scholar 

  18. P.J. Brown, A.G. Fox, E.N. Maslen, M.A. O’Keefe, and B.T.M. Willis, International Tables Crystallography, Vol. C: Mathematical, Physical, and Chemical Tables, 3rd ed., ed. E. Prince (Norwell: Kluwer Academic Publishers, 2004), pp. 554–595.

    Google Scholar 

  19. A.G. Fox, M.A. O’Keefe, and M.A. Tabbernor, Acta Crystallogr. Sect. A 45, 786 (1989).

    Article  Google Scholar 

  20. B.E. Warren, X-Ray Diffraction, ed. M. Cohen (Reading: Addison-Wesley Publishing Company, 1969), pp. 51–74.

    Google Scholar 

  21. S.M. Foiles and J.J. Hoyt, Acta Mater. 54, 3351 (2006).

    Article  Google Scholar 

  22. D.E. Spearot, K.I. Jacob, and D.L. McDowell, Acta Mater. 53, 3579 (2005).

    Article  Google Scholar 

  23. D.B. Williams and C.B. Carter, Transmission Electron Microscopy, Part 2 Diffraction, 2nd ed. ed. (New York: Springer, 2009), pp. 271–281.

    Book  Google Scholar 

  24. D.Y. Guan and S.L. Sass, Philos. Mag. A 39, 293 (1979).

    Article  Google Scholar 

  25. Y.M. Mishin, M. Mehl, D. Papaconstantopoulos, A.F. Voter, and J. Kress, Phys. Rev. B 63, 224106 (2001).

    Article  Google Scholar 

  26. G.K. Williamson and W.H. Hall, Acta Metall. 1, 22 (1953).

    Article  Google Scholar 

  27. M. Wojdyr, J. Appl. Crystallogr. 43, 1126 (2010).

    Article  Google Scholar 

  28. S. Simões, R. Calinas, M.T. Vieira, M.F. Vieira, and P.J. Ferreira, Nanotechnology 21, 145701 (2010).

    Article  Google Scholar 

  29. F.G. Sen, Y. Qi, A.C.T. van Duin, and A.T. Alpas, Appl. Phys. Lett. 102, 051912 (2013).

    Article  Google Scholar 

  30. C.L. Kelchner, S.J. Plimpton, and J. Hamilton, Phys. Rev. B 58, 11085 (1998).

    Article  Google Scholar 

  31. H. Tsuzuki, P.S. Branicio, and J.P. Rino, Comput. Phys. Commun. 177, 518 (2007).

    Article  Google Scholar 

  32. N. Ishizawa, T. Miyata, I. Minato, F. Marumo, and S. Iwai, Acta Crystallogr. Sect. B 36, 228 (1979).

    Article  Google Scholar 

  33. E.J.W. Verwey, Zeitschrift Für Krist. 91, 317 (1935).

    Google Scholar 

  34. A.P. Sutton and R.W. Balluffi, Monographs on the Physics and Chemistry of Materials, Vol. 51 (Oxford U.K.: Clarendon Press, 1995), p. 819.

    Google Scholar 

  35. T.C. Chou and T.G. Nieh, Thin Solid Films 221, 89 (1992).

    Article  Google Scholar 

Download references

Acknowledgements

The authors acknowledge support of the National Science Foundation under grant 0954505. Additional support is provided by the twenty-first century Professorship in Mechanical Engineering at the University of Arkansas. Most simulations in this work were performed on resources supported in part by the National Science Foundation under grants 0963249, 0959124, and 0918970, managed by the Arkansas High Performance Computing Center. Select simulations were performed using the National Science Foundation support XSEDE Network. The authors also acknowledge support of Y. Wang at the Pittsburgh Supercomputing Center and L. Cueva-Parra at Auburn University at Montgomery for assistance in parallelizing the reciprocal space mesh in the virtual diffraction compute.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Douglas E. Spearot.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Coleman, S.P., Sichani, M.M. & Spearot, D.E. A Computational Algorithm to Produce Virtual X-ray and Electron Diffraction Patterns from Atomistic Simulations. JOM 66, 408–416 (2014). https://doi.org/10.1007/s11837-013-0829-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11837-013-0829-3

Keywords

Navigation