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Entropy and Diffuse Scattering: Comparison of NbTiVZr and CrMoNbV

  • Symposium: High Entropy Alloys III
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Abstract

The chemical disorder intrinsic to high-entropy alloys inevitably creates diffuse scattering in their X-ray or neutron diffraction patterns. Through first principles hybrid Monte Carlo/molecular dynamics simulations of two BCC high-entropy alloy forming compounds, CrMoNbV and NbTiVZr, we identify the contributions of chemical disorder, atomic size, and thermal fluctuations to the diffuse scattering. As a side benefit, we evaluate the reduction in entropy due to pair correlations within the framework of the cluster variation method. Finally, we note that the preference of Ti and Zr for hexagonal structures at low temperature leads to a mechanical instability reducing the local BCC character of NbTiVZr, while preserving global BCC symmetry.

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References

  1. O.N. Senkov, S.V. Senkova, D.B. Miracle, C. Woodward, Mat. Sci. Eng. A 565, 51–62 (2013)

    Article  Google Scholar 

  2. M. Widom: in High Entropy Alloys: Fundamentals and Applications, M. Gao, J.-W. Yeh, P. Liaw, and Y. Zhang, eds., Springer, New York, 2015.

  3. M. Widom, W.P. Huhn, S. Maiti, W. Steurer, Mat. Met. Trans. A 45, 196–200 (2013)

    Google Scholar 

  4. G. Kresse, J. Furthmuller, Phys. Rev. B 54, 11169–86 (1996)

    Article  Google Scholar 

  5. G. Kresse, D. Joubert, Phys. Rev. B 59, 1758–75 (1999)

    Article  Google Scholar 

  6. J.P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 77, 3865–68 (1996)

    Article  Google Scholar 

  7. W. Guo, W. Dmowski, J.Y. Noh, P. Rack, P.K Liaw, and T. Egami, Mat. Trans. A 44, 1994–97 (2013)

    Article  Google Scholar 

  8. B. Borie, Acta Cryst. 10, 89–96 (1957)

    Article  Google Scholar 

  9. M. A. Krivoglaz, Diffuse Scattering of X-rays and Neutrons by Fluctuations (Springer, 1996)

    Book  Google Scholar 

  10. W. Schweika: Disordered Alloys: Diffuse Scattering and Monte Carlo simulations, Springer Tracts in Modern Physics, vol. 141, Springer, Berlin, 1998

    Google Scholar 

  11. T.R. Welberry: Diffuse X-ray Scattering and Models of Disorder, IUCR Monographs on Crystallography, vol. 16, Oxford University Press, Oxford, 2004

    Google Scholar 

  12. V. Blum, A. Zunger, Phys. Rev. B 72, 02010R (2005)

    Google Scholar 

  13. B.E. Warren, B.L. Averbach, and B.W. Roberts, J. Appl. Phys. 22, 1493–96 (1951)

    Article  Google Scholar 

  14. T. Egami and S. J. L. Billinge, Underneath the Bragg Peaks, vol. 16 of Pergamon Materials Series (Elsevier, 2013)

    Google Scholar 

  15. I.B. Ramsteiner, O. Shchyglo, M. Mezger, A. Udyansky, V. Bugaev, S. Schoder, H. Reichert, H. Dosch, Acta Mater. 56, 1298–305 (2008)

    Article  Google Scholar 

  16. D. de Fontaine: in Solid State Physics, H. Ehrenreich and D. Turnbull, eds., Academic Press, New York, 1979, vol. 34, pp. 73–274.

  17. D. de Fontaine: in Solid State Physics, H. Ehrenreich and D. Turnbull, eds., Academic Press, New York, 1994, vol. 47, pp. 33–176.

  18. W.L. Bragg, E.J. Williams, Proc. R. Soc. Lond. A 145, 699–730 (1934)

    Article  Google Scholar 

  19. E.A. Guggenheim, Proc. R. Soc. Lond. A 183, 213–27 (1944)

    Article  Google Scholar 

  20. H. Ackermann, G. Inden, R. Kikuchi, Acta Metall. 37, 1–7 (1989)

    Article  Google Scholar 

Download references

Acknowledgments

I thank Michael Gao, Marcel Sluiter, Soumyadipta Maiti, and Walter Steurer for useful discussions. This research was supported in part by the Department of Energy Grant DE-SC0014506.

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Correspondence to Michael Widom.

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Manuscript submitted April 28, 2015.

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Widom, M. Entropy and Diffuse Scattering: Comparison of NbTiVZr and CrMoNbV. Metall Mater Trans A 47, 3306–3311 (2016). https://doi.org/10.1007/s11661-015-3095-x

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  • DOI: https://doi.org/10.1007/s11661-015-3095-x

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