Abstract
The effect of zirconium alloying on the crystal structures and mechanical properties of binary tungsten–zirconium alloys is investigated in this study using the first-principles method. Firstly, we investigate the cell volumes, lattice constants, and formation energies of binary W1−xZrx (x = 0, 0.0625, 0.125, 0.1875, 0.25, and 0.5) alloys. It is shown that binary tungsten–zirconium alloys maintain BCC structures. When the concentration of zirconium atoms is lower than 12.5%, the structures of binary tungsten–zirconium alloys can be thermodynamically stable. The elastic constants of binary tungsten–zirconium alloys are calculated based on the optimized atomic lattice. Then, the elastic modulus and other mechanical parameters are deduced according to the relevant formulas. It is shown that the mechanical strength of binary tungsten–zirconium alloy decreases with an increasing concentration of zirconium atoms, which is lower than the mechanical strength of pure tungsten metal. However, the mechanical strength of binary tungsten–zirconium alloys is higher than that of pure zirconium metal. In addition, zirconium alloying can be effective in improving the ductility of pure tungsten metal.
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T. Tanabe, N. Noda, and H. Nakamura: Review of high Z materials for PSI applications. J. Nucl. Mater. 196, 11 (1992).
C. Garcia-Rosales: Erosion processes in plasma-wall interactions. J. Nucl. Mater. 211, 202 (1994).
V.A. Chuyanov: ITER EDA project status. J. Nucl. Mater. 233, 4 (1996).
H. Kurishita, S. Kobayashi, K. Nakai, H. Arakawa, S. Matsuo, T. Takida, K. Takebe, and M. Kawai: Current status of ultra-fine grained W–TiC development for use in irradiation environments. Phys. Scr. T128, 76–80 (2007).
M.Z. Tokar, J.W. Coenen, V. Philipps, and Y. Ueda: Tokamak plasma response to droplet spraying from melted plasma-facing components. Nucl. Fusion 52, 013013 (2012).
S.W. Zhang, Y. Wen, and H.J. Zhang: Low temperature preparation of tungsten nanoparticles from molten salt. Powder Technol. 253, 464–466 (2014).
M.T. Kajioka, T. Sakamoto, K. Nakai, S. Kobayashi, H. Kurishita, S. Matsuo, and H. Arakawa: Effects of plastic working and MA atmosphere on microstructures of recrystallized W–1.1% TiC. J. Nucl. Mater. 417, 512–515 (2011).
O. El-Atwani, J.A. Hinks, G. Greaves, S. Gonderman, T. Qiu, M. Efe, and J.P. Allain: In situ TEM observation of the response of ultrafine- and nanocrystalline-grained tungsten to extreme irradiation environments. Sci. Rep. 4, 4716 (2014).
A. Xu, C. Beck, D.E.J. Armstrong, K. Rajan, G.D.W. Smith, P.A.J. Bagot, and S.G. Roberts: Ion-irradiation-induced clustering in W–Re and W–Re–Os alloys: A comparative study using atom probe tomography and nanoindentation measurements. Acta Mater. 87, 121 (2015).
Y.D. Kim, N.L. Oh, S.T. Oh, and I.H. Moon: Thermal conductivity of W–Cu composites at various temperatures. Mater. Lett. 51, 420 (2001).
G.A. Dosovitskiy and S.V. Samoilenkov: Thermal expansion of Ni–W, Ni–Cr, and Ni–Cr–W alloys between room temperature and 800 °C. Int. J. Thermophys. 30, 1931 (2009).
H.L. Ren, X.J. Liu, and J.G. Ning: Microstructure and mechanical properties of W–Zr reactive materials. Mater. Sci. Eng., A 660, 205 (2016).
P.G. Luo, Z.C. Wang, C.L. Jiang, L. Mao, and Q. Li: Experimental study on impact-initiated characters of W/Zr energetic fragments. Mater. Des. 84, 72 (2015).
H.M. Fu, N. Liu, A.M. Wang, H. Li, Z.W. Zhu, H.W. Zhang, H.F. Zhang, and Z.Q. Hu: High-temperature deformation behaviors of W/Zr based amorphous interpenetrating composite. Mater. Des. 58, 182 (2014).
E. McCafferty: Graph theory and the passivity of binary alloys more examples. J. Electrochem. Soc. 151, B82 (2004).
Z.M. Xie, T. Zhang, R. Liu, Q.F. Fang, S. Miao, X.P. Wang, and C.S. Liu: Grain growth behavior and mechanical properties of zirconium micro-alloyed and nano-size zirconium carbide dispersion strengthened tungsten alloys. Int. J. Refract. Met. Hard Mater. 51, 180 (2015).
H.Y. Chen, L.M. Luo, J.B. Chen, X. Zan, X.Y. Zhu, Q. Xu, G.N. Luo, J.L. Chen, and Y.C. Wu: Effects of zirconium element on the microstructure and deuterium retention of W–Zr/Sc2O3 composites. Sci. Rep. 6, 32678 (2016).
V.K. Kharchenko and V.V. Bukhanovskii: High-temperature strength of refractory metals, alloys and composite materials based on them. Part 1. tungsten, its alloys, and composites. Strength Mater. 44, 512 (2012).
Z.M. Xie, R. Liu, Q.F. Fang, Y. Zhou, X.P. Wang, and C.S. Liu: Spark plasma sintering and mechanical properties of zirconium micro-alloyed tungsten. J. Nucl. Mater. 444, 175 (2014).
S.L. Wen, K.H. He, H.N. Cui, M. Pan, Z. Huang, and Y. Zhao: Migration properties of mono-vacancy in W-4d/5d transition metal alloys. J. Alloys Compd. 728, 363 (2017).
W. Setyawan and R.J. Kurtz: Effects of transition metals on the grain boundary cohesion in tungsten. Scr. Mater. 66, 558 (2012).
X.S. Kong, X.B. Wu, Y.W. You, C.S. Liu, Q.F. Fang, J.L. Chen, G.N. Luo, and Z.G. Wang: First-principles calculations of transition metal-solute interactions with point defects in tungsten. Acta Mater. 66, 172 (2014).
S.Q. Shi, S. Tanaka, and M. Kohyama: First-principles study of the tensile strength and failure of α-A1203(0001)/Ni(111) interfaces. Phys. Rev. B 76, 075431 (2007).
S.Q. Shi, H. Zhang, X.Z. Ke, C.Y. Ouyang, M.S. Lei, and L.Q. Chen: First-principles study of lattice dynamics of LiFePO4. Phys. Lett. A 373, 4096 (2009).
S.L. Shang, L.G. Hector, Jr., S.Q. Shi, Y. Qi, Y. Wang, and Z.K. Liu: Lattice dynamics, thermodynamics and elastic properties of monoclinic Li2CO3 from density functional theory. Acta Mater. 60, 5204 (2012).
X.K. Feng, S.Q. Shi, J.Y. Shen, S.L. Shang, M.Y. Yao, and Z.K. Liu: Lattice dynamics, thermodynamics and elastic properties of C22-Zr6FeSn2 from first-principles calculations. J. Nucl. Mater. 479, 461 (2016).
Y.H. Yang, Q. Wu, Y.H. Cui, Y.C. Chen, S.Q. Shi, R.Z. Wang, and H. Yan: Elastic properties, defect thermodynamics, electrochemical window phase stability, and Li+ mobility of Li3PS4: Insights from first-principles calculations. ACS Appl. Mater. Interfaces 8, 25229 (2016).
S.Q. Shi, J. Gao, Y. Liu, Y. Zhao, Q. Wu, W.W. Ju, C.Y. Ouyang, and R.J. Xiao: Multi-scale computation methods: Their applications in lithium-ion battery research and development. Chin. Phys. B 25, 018212 (2016).
G. Kresse and J. Hafner: Ab initio molecular dynamics for open-shell transition metals. Phys. Rev. B 48, 13115 (1993).
G. Kresse and J. Furthmüller: Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys. Rev. B 54, 11169 (1996).
P.E. Blöchl: Projector augmented-wave method. Phys. Rev. B 50, 17953 (1994).
Y. Wang and J.P. Perdew: Correlation hole of the spin-polarized electron gas, with exact small-wave-vector and high-density scaling. Phys. Rev. B 44, 13298 (1991).
H.J. Monkhorst and J.D. Pack: Special points for Brillouin-zone integrations. Phys. Rev. B 13, 5188 (1976).
S. Jin, Y.L. Liu, H.B. Zhou, Y. Zhang, and G.H. Lu: First-principles investigation on the effect of carbon on hydrogen trapping in tungsten. J. Nucl. Mater. 415, S709 (2011).
B.C. Kittel: Introduction to Solid State Physics, 7th ed. (Wiley, New York, 1996).
D.C. Wallace: Thermoelastic theory of stressed crystals and higher-order elastic constants. Solid State Phys. 25, 301 (1970).
J.J. Zhao, J.M. Winey, and Y.M. Gupta: First principles calculations of second- and third-order elastic constants for single crystals of arbitrary symmetry. Phys. Rev. B 75, 094105 (2007).
W. Voigt: über die Beziehungzwischen den beiden Elasticitäts constantenisotroper Körper. Ann. Phys. 38, 573 (1889).
A. Reuss: Berechnung der Flieβgrenze von Mischkristallen auf Grupd der Plastizitäts bedingung für Einkristalle. Z. Angew. Math. Mech. 9, 49 (1929).
R. Hill: The elastic behaviour of a crystalline aggregate. Proc. Phys. Soc., London, Sect. A 65, 349 (1952).
R. Hill: Elastic properties of reinforced solids: Some theoretical principles. J. Mech. Phys. Solids 11, 357 (1963).
Y.J. Hu, S.L. Shang, Y. Wang, K.A. Darling, B.G. Butler, L.J. Kecskes, and Z.K. Liu: Effects of alloying elements and temperature on the elastic properties of W-based alloys by first-principles calculations. J. Alloys Compd. 671, 267 (2016).
P. Söderlind, O. Eriksson, J.M. Wills, and A.M. Boring: Theory of elastic constants of cubic transition metals and alloys. Phys. Rev. B 48, 5844 (1993).
S.S. Kushwah, M.P. Sharma, and Y.S. Tomar: An equation of state for molybdenum and tungsten. Phys. B 339, 193 (2003).
H. Meradji, S. Drablia, and S. Ghemid: First-principles elastic constants and electronic structure of BP, BAs, and BSb. Phys. Status Solidi B 241, 2881 (2004).
S.F. Pugh: Relations between the elastic moduli and the plastic properties of polycrystalline pure metals. Philos. Mag. 45, 823 (1954).
Y.C. Lin, S.C. Luo, M.S. Chen, D.G. He, and C.Y. Zhao: Effects of pressure on anisotropic elastic properties and minimum thermal conductivity of D022-Ni3Nb phase: First-principles calculations. J. Alloys Compd. 688, 285 (2016).
S. Kamran, K.Y. Chen, and L. Chen: Ab initio examination of ductility features of fcc metals. Phys. Rev. B 79, 024106 (2009).
ACKNOWLEDGMENTS
This work was sponsored by the National Natural Science Foundation of China (No. 61762045), the Science and Technology Key Project of Jiangxi Provincial Department of Education (GJJ151146), the Natural Sciences Project of Jiangxi Science and Technology Department (20151BBE50079), and the Patent Transformation Project of Intellectual Property Office of Jiangxi Province (the application and popularization of the digital method to distinguish the direction of rotation photoelectric encoder in identification).
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Diyou, J., Li, X., Xuemei, H. et al. Effect of Zr additions on crystal structures and mechanical properties of binary W–Zr alloys: A first-principles study. Journal of Materials Research 34, 290–300 (2019). https://doi.org/10.1557/jmr.2018.426
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DOI: https://doi.org/10.1557/jmr.2018.426