Abstract
On basis of systematical ab initio study of mechanical properties of body-centered cubic NbTiZrM (M = Hf, Ta, W) refractory high entropy alloys, the correlation between mechanical properties and valence electron concentration (VEC) is appreciably revealed. The present investigation demonstrates that both the single-crystal elastic parameters and the elastic moduli of NbTiZrM alloys increase for M from Hf to W, similar to the variation trend of VEC. Hence, the strength and hardness of NbTiZrM alloys exhibit apparent correlation with the VEC. Because the Poisson's ratio and the Pugh’s ratio suggest the alloys are more ductile for M from W to Hf, the lower VEC obviously correlates with the better ductility of NbTiZrM alloys. Moreover, with increasing VEC, the elastic anisotropies of NbTiZrM alloys are predicted to decrease, whereas the Debye temperatures of these alloys show increasing tendency. Noticeably, the VEC is an effective adjusting parameter to obtain excellent mechanical properties.
Similar content being viewed by others
References
D.B. Miracle, O.N. Senkov, Acta Mater. 122, 448 (2017)
E.P. George, D. Raabe, R.O. Ritchie, Nat. Rev. Mater. 4, 515 (2019)
E.P. George, W.A. Curtin, C.C. Tasan, Acta Mater. 188, 435 (2020)
O.N. Senkov, G.B. Wilks, J.M. Scott, D.B. Miracle, Intermetallics 19, 698 (2011)
Y. Long, X.B. Liang, K. Su, H.Y. Peng, X.Z. Li, J. Alloys Compd. 780, 607 (2019)
O.N. Senkov, D.B. Miracle, K.J. Chaput, J.-P. Couzinie, J. Mater. Res. 33, 3092 (2018)
N.Y. Yurchenko, E.S. Panina, S.V. Zherebtsov, M.A. Tikhonovsky, G.A. Salishchev, N.D. Stepanov, Mater. Charact. 158, 109980 (2019)
D.-X. Qiao, H. Jiang, W.-N. Jiao, Y.-P. Lu, Z.-Q. Cao, T.-J. Li (2019) Acta Metall. Sin. Engl. Lett. 32: 925
O.N. Senkov, S. Rao, K.J. Chaput, C. Woodward, Acta Mater. 151, 201 (2018)
L.-Y. Tian, G. Wang, J.S. Harris, D.L. Irving, J. Zhao, L. Vitos, Mater. Des. 114, 243 (2017)
M. Liao, Y. Liu, L. Min, Z. Lai, T. Han, D. Yang, J. Zhu, Intermetallics 101, 152 (2018)
O.N. Senkov, S.V. Senkova, C. Woodward, D.B. Miracle, Acta Mater. 61, 1545 (2013)
Y. Zhang, X. Yang, P.K. Liaw, JOM 64, 830 (2012)
Y.X. Ye, Z.P. Lu, T.G. Nieh, Scripta Mater. 130, 64 (2017)
Y.X. Ye, B.L. Musico, Z.Z. Lu, L.B. Xu, Z.F. Lei, V. Keppens, H.X. Xu, T.G. Nieh, Intermetallics 109, 167 (2019)
J.H. Dai, W. Li, Y. Song, L. Vitos, Mater. Des. 182, 108033 (2019)
V.T. Nguyen, M. Qian, Z. Shi, T. Song, L. Huang, J. Zou, Intermetallics 101, 39 (2018)
Y. Lederer, C. Toher, K.S. Vecchio, S. Curtarolo, Acta Mater. 159, 364 (2018)
Z.L. Wang, W.J. Gao, Y.L. Liu, R. Li, F.S. Meng, J.P. Song, Y. Qi, J. Alloys Compd. 829, 154480 (2020)
K.-K. Tseng, C.-C. Juan, S. Tso, H.-C. Chen, C.-W. Tsai, J.-W. Yeh, Entropy 21, 15 (2019)
S. Guo, C. Ng, J. Lu, C.T. Liu, J. Appl. Phys. 109, 103505 (2011)
F. Tian, L.K. Varga, N. Chen, J. Shen, L. Vitos, J. Alloys Compd. 599, 19 (2014)
S. Sheikh, S. Shafeie, Q. Hu, J. Ahlström, C. Persson, J. Veselý, J. Zýka, U. Klement, S. Guo, J. Appl. Phys. 120, 164902 (2016)
L. Vitos, Computational Quantum Mechanics for Materials Engineers: The EMTO Method and Applications (Springer, London, 2007).
L. Vitos, Phys. Rev. B 64, 014107 (2001)
L. Vitos, I.A. Abrikosov, B. Johansson, Phys. Rev. Lett. 87, 156401 (2001)
S. Huang, W. Li, O. Eriksson, L. Vitos, Acta Mater. 199, 53 (2020)
H. Zhang, X. Sun, S. Lu, Z. Dong, X. Ding, Y. Wang, L. Vitos, Acta Mater. 155, 12 (2018)
X. Bai, Y. Li, B. Xiao, Y. Rao, H. Liang, L. He, J. Feng, Mater. Chem. Phys. 254, 123423 (2020)
J. Emsley, The Elements, 3rd edn. (Clarendon, Oxford, 1998).
S. Qiu, N. Miao, J. Zhou, Z. Guo, Z. Sun, Intermetallics 92, 7 (2018)
O.N. Senkov, J.M. Scott, S.V. Senkova, D.B. Miracle, C.F. Woodward, J. Alloys Compd. 509, 6043 (2011)
Y. Zhang, Y.J. Zhou, J.P. Lin, G.L. Chen, P.K. Liaw, Adv. Eng. Mater. 10, 534 (2008)
A. Takeuchi, A. Inoue, Mater. Trans 46, 2817 (2005)
M.C. Gao, C. Zhang, P. Gao, F. Zhang, L.Z. Ouyang, M. Widom, J.A. Hawk, Curr. Opin. Solid State Mater. Sci. 21, 238 (2017)
Y. Zhou, J.-M. Zhang, Appl. Phys. A 125, 800 (2019)
X.-Q. Chen, H. Niu, D. Li, Y. Li, Intermetallics 19, 1275 (2011)
J. Xu, S. Zhang, X. Lu, S. Jiang, P. Munroe, Z.-H. Xie, Ultrason. Sonochem. 59, 104742 (2019)
B. Djelti, S. Bentata, W. Benstaali, A. Abbad, W. Benosman, Y. Benmalem, S. Cherid, Appl. Phys. A 124, 622 (2018)
J. Zagorac, D. Zagorac, D. Jovanović, J. Luković, B. Matović, J. Phys. Chem. Solids 122, 94 (2018)
S. Kamran, K. Chen, L. Chen, Phys. Rev. B 79, 024106 (2009)
M.A. Hopcroft, W.D. Nix, T.W. Kenny, J. Microelectromech. Syst. 19, 229 (2010)
J.J. Wortman, R.A. Evans, J. Appl. Phys. 36, 153 (1965)
W. Brantley, J. Appl. Phys. 44, 534 (1973)
M.I. Naher, S.H. Naqib, J. Alloys Compd. 829, 154509 (2020)
S. Huang, X. Li, H. Huang, E. Holmström, L. Vitos, Mater. Chem. Phys. 210, 37 (2018)
Acknowledgements
This work was gratefully supported by National Natural Sciences Foundation of China under Grant no. 51461002, Key Project of Guangxi Scientific Foundation under Grant no. 2018GXNSFDA281010 and Innovation Project of Guangxi Graduate Education under Grant no. YCBZ2020010.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The authors declare that they have no conflict of interest.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Yang, M., Shao, L., Duan, JM. et al. Correlation between mechanical properties and valence electron concentration for NbTiZrM (M = Hf, Ta, W) refractory high entropy alloys: an ab initio study. Appl. Phys. A 127, 341 (2021). https://doi.org/10.1007/s00339-021-04449-1
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s00339-021-04449-1