Abstract
Construction of suitable structural models in order to account for chemical short-range orders is the reason behind the difficult multi-scale computational simulation methods for solid solutions. Herein, using Ti–Mo alloys as representative, we used our cluster-plus-glue-atom model to address the chemical short-range orders for body-center cubic lattice. In accordance with the atomic interaction mode, an Mo solute atom would prefer 14 Ti solvent atoms as its nearest neighbors, forming a rhombic-dodecahedral cluster, and some next outer-shell Mo and Ti atoms would serve as the glue atoms, which is formulated as [Mo–Ti14](Mo,Ti)x. The number of glue atoms x corresponds to different spatial distribution of the clusters. One of the formula having good stability is [Mo–Ti14]Mo, i.e., with one Mo as the glue atom. To verify its stability, mechanical properties and electronic density of state are obtained using the first-principles calculations and the Young’s modulus agrees with the experimental values. Also the formulated structural unit [Mo–Ti14]Mo is indeed verified by the cluster expansion method. This work then confirms the existence of simple structural unit covering the nearest neighbors and a few next outer-shell atoms for the Ti–Mo alloy of high structural stability.
Similar content being viewed by others
References
A. van de Walle, P. Tiwary, M. de Jong, D.L. Olmsted, M. Asta, A. Dick, D. Shin, Y. Wang, L.Q. Chen, Z.K. Liu, CALPHAD 42, 13 (2013)
L. Vitos, in Computational Quantum Mechanics for Materials Engineers: The EMTO Method and Applications (Springer, London, 2007)
H.L. Hong, Q. Wang, C. Dong, P.K. Liaw, Sci. Rep. 4, 7065 (2014)
D.D. Dong, Dissertation, Dalian University of Technology (2017)
M. Niinomi, T. Hattori, K. Morikawa, T. Kasuga, A. Suzuki, H. Fukui, S. Niwa, Mater. Trans. 43, 2970 (2002)
M. Geetha, A.K. Singh, R. Asokamani, A.K. Gogia, Prog. Mater Sci. 54, 397 (2009)
Y.L. Hao, S.J. Li, S.Y. Sun, C.Y. Zheng, Q.M. Hu, R. Yang, Appl. Phys. Lett. 87, 091906 (2005)
D.Q. Martins, W.R. Oso’rio, M.E.P. Souza, R. Caram, A. Garcia, Electrochim. Acta 53, 2809 (2008)
L.J. Xu, Y.Y. Chen, J. Alloys Compd. 453, 320 (2008)
M. Abdel-Hady, K. Hinoshita, M. Morinaga, Scr. Mater. 55, 477 (2006)
P.J. Bania, in Beta Titanium Alloys in the 1990 s (TMS, Warrendale, 1993)
E.W. Collings, in Physical Metallurgy of Titanium Alloys (ASM, Metals Park, 1984)
Y. Zhang, Q. Wang, H.G. Dong, C. Dong, H.Y. Zhang, X.F. Sun, Acta Metall. Sin. (Engl. Lett.) 31, 127 (2018)
C. Zhang, H. Tian, C.P. Hao, J.J. Zhao, Q. Wang, E.X. Liu, C. Dong, J. Matter. Sci. 48, 3138 (2013)
C.P. Hao, Q. Wang, R.T. Ma, Y.M. Wang, J.B. Qiang, C. Dong, Acta Phys. Sin. 60, 116101 (2011)
Q. Wang, C. Ji, Y.M. Wang, J.B. Qiang, C. Dong, Metall. Mater. Trans. A 44, 1872 (2013)
B.B. Jiang, Q. Wang, D.H. Wen, F. Xu, G.Q. Chen, C. Dong, L. Sun, P.K. Liaw, Mater. Sci. Eng., A 687, 1 (2017)
J. Singh, P. Singh, S. Rattan, S. Prakash, Phys. Rev. B 49, 932 (1994)
H. Sharma, S. Prakash, Pramana 68, 655 (2007)
C. Pang, B.B. Jiang, Y. Shi, Q. Wang, C. Dong, J. Alloys Compd. 652, 63 (2015)
G. Kresse, D. Joubert, Phys. Rev. B 59, 1758 (1999)
J.P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 77, 3865 (1996)
G. Kresse, J. Furthmuller, Phys. Rev. B 54, 11169 (1996)
H.J. Monkhorst, J.D. Pack, Phys. Rev. B 13, 5188 (1976)
J.M. Sanchez, F. Ducastelle, D. Gratias, Physica 128A, 334 (1984)
A. van de Walle, G. Ceder, J. Phase Equilib. 23, 348 (2002)
A. van de Walle, M. Asta, G. Ceder, CALPHAD 26, 539 (2002)
Z.J. Wu, E.J. Zhao, H.P. Xiang, X.F. Hao, X.J. Liu, J. Meng, Phys. Rev. B 76, 054115 (2007)
J.Y. Dai, J.M. Yuan, P. Giannozzi, Appl. Phys. Lett. 95, 232105 (2009)
Acknowledgements
The work was financially supported by the National Key Research and Development Program of China (Grant No. 2016YFB0101206) and the Natural Science Foundation of China (Grant No. 11674045).
Author information
Authors and Affiliations
Corresponding author
Additional information
Available online at http://link.springer.com/journal/40195.
Rights and permissions
About this article
Cite this article
Jiang, F., Pang, C., Zheng, Z. et al. First-Principles Calculations for Stable β-Ti–Mo Alloys Using Cluster-Plus-Glue-Atom Model. Acta Metall. Sin. (Engl. Lett.) 33, 968–974 (2020). https://doi.org/10.1007/s40195-020-01006-2
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s40195-020-01006-2