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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O.N. Senkov, S.V. Senkova, D.B. Miracle, C. Woodward, Mat. Sci. Eng. A 565, 51–62 (2013)
M. Widom: in High Entropy Alloys: Fundamentals and Applications, M. Gao, J.-W. Yeh, P. Liaw, and Y. Zhang, eds., Springer, New York, 2015.
M. Widom, W.P. Huhn, S. Maiti, W. Steurer, Mat. Met. Trans. A 45, 196–200 (2013)
G. Kresse, J. Furthmuller, Phys. Rev. B 54, 11169–86 (1996)
G. Kresse, D. Joubert, Phys. Rev. B 59, 1758–75 (1999)
J.P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 77, 3865–68 (1996)
W. Guo, W. Dmowski, J.Y. Noh, P. Rack, P.K Liaw, and T. Egami, Mat. Trans. A 44, 1994–97 (2013)
B. Borie, Acta Cryst. 10, 89–96 (1957)
M. A. Krivoglaz, Diffuse Scattering of X-rays and Neutrons by Fluctuations (Springer, 1996)
W. Schweika: Disordered Alloys: Diffuse Scattering and Monte Carlo simulations, Springer Tracts in Modern Physics, vol. 141, Springer, Berlin, 1998
T.R. Welberry: Diffuse X-ray Scattering and Models of Disorder, IUCR Monographs on Crystallography, vol. 16, Oxford University Press, Oxford, 2004
V. Blum, A. Zunger, Phys. Rev. B 72, 02010R (2005)
B.E. Warren, B.L. Averbach, and B.W. Roberts, J. Appl. Phys. 22, 1493–96 (1951)
T. Egami and S. J. L. Billinge, Underneath the Bragg Peaks, vol. 16 of Pergamon Materials Series (Elsevier, 2013)
I.B. Ramsteiner, O. Shchyglo, M. Mezger, A. Udyansky, V. Bugaev, S. Schoder, H. Reichert, H. Dosch, Acta Mater. 56, 1298–305 (2008)
D. de Fontaine: in Solid State Physics, H. Ehrenreich and D. Turnbull, eds., Academic Press, New York, 1979, vol. 34, pp. 73–274.
D. de Fontaine: in Solid State Physics, H. Ehrenreich and D. Turnbull, eds., Academic Press, New York, 1994, vol. 47, pp. 33–176.
W.L. Bragg, E.J. Williams, Proc. R. Soc. Lond. A 145, 699–730 (1934)
E.A. Guggenheim, Proc. R. Soc. Lond. A 183, 213–27 (1944)
H. Ackermann, G. Inden, R. Kikuchi, Acta Metall. 37, 1–7 (1989)
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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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