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Electronic structure and elasticity of the Ta-W solid solution
Phys. Rev. Materials 10, 053605 – Published 26 May, 2026
DOI: https://doi.org/10.1103/ph3y-8lnq
Abstract
The brittleness or ductility of metals has long been attributed to their elastic constants, with a high Poisson ratio, or equivalently, a high Pugh ratio, favoring greater ductility. Growing evidence links ductility with their electronic structure. Consequently, it is desirable to understand how the electronic structure affects the elastic constants. Here, we examine the Ta-W binary alloy system, which evolves from ductile character at Ta-rich compositions to brittleness at high W. We show that a change in slope of the composition-dependent shear modulus near the equiatomic composition coincides with an abrupt change in the Fermi level density of states. We relate the behaviors of the elastic constants to the characters of occupied electronic orbitals close to the Fermi level. Finally, we consider additional alloy systems from groups V and VI and show that qualitatively similar behavior occurs more broadly.
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References (38)
- S. Wang, Z. Wu, M. Xie, D. Si, L. Li, C. Chen, Z. Zhang, and Y. Wu, The effect of tungsten content on the rolling texture and microstructure of Ta-W alloys, Mater. Charact. 159, 110067 (2020).
- X. Duan, Y. Huang, W. Liu, Q. Cai, W. Liu, and Y. Ma, Effect of Ta on the microstructure and mechanical properties of W-Ta alloys prepared by arc melting, Mater. Charact. 188, 111823 (2022).
- C. Chen, Y. Chen, K. Li, S. Yang, J. Wang, S. Wang, Y. Mao, L. Luo, and Y. Wu, The ductile-brittle transition behaviors of W/Ta multilayer composites, J. Alloys Compd. 946, 169377 (2023).
- H. Liu, S. Tang, Y. Ma, W. Liu, and C. Liang, Short-range ordering governs brittleness and ductility in W-Ta solid solution: Insights from Pugh's shear-to-bulk modulus ratio, Scr. Mater. 204, 114136 (2021).
- H. Hu, C. Zhang, R. Yue, B. Hu, and S. Chen, Unraveling ductility enhancement mechanisms in W-Ta alloys using machine-learning potential, Int. J. Mech. Sci. 286, 109911 (2025).
- R. Thompson and W. Clegg, Predicting whether a material is ductile or brittle, Curr. Opin. Solid State Mater. Sci. 22, 100 (2018).
- S. Pugh, XCII. Relations between the elastic moduli and the plastic properties of polycrystalline pure metals, London, Edinburgh, Dublin Philos. Mag. J. Sci. 45, 823 (1954).
- J. R. Rice and R. Thomson, Ductile versus brittle behaviour of crystals, Philos. Mag. 29, 73 (1974).
- M. C. Gao, Ö. N. Doğan, P. King, A. D. Rollett, and M. Widom, The first-principles design of ductile refractory alloys, JOM 60, 61 (2008).
- R. Hill, The elastic behaviour of a crystalline aggregate, Proc. Phys. Soc. A 65, 349 (1952).
- D. G. Pettifor and M. Aoki, Bonding and structure of intermetallics: A new bond order potential, Phil. Trans. Roy. Soc. A 334, 439 (1991).
- M. E. Eberhart and T. E. Jones, Cauchy pressure and the generalized bonding model for nonmagnetic bcc transition metals, Phys. Rev. B 86, 134106 (2012).
- O. N. Senkov and D. B. Miracle, Generalization of intrinsic ductile-to-brittle criteria by Pugh and Pettifor for materials with a cubic crystal structure, Sci. Rep. 11, 4531 (2021).
- C. Kittel, Introduction to Solid State Physics, 8th ed. (John Wiley & Sons, Hoboken, NJ, 2005).
- P. Hohenberg and W. Kohn, Inhomogeneous electron gas, Phys. Rev. 136, B864 (1964).
- W. Kohn and L. J. Sham, Self-consistent equations including exchange and correlation effects, Phys. Rev. 140, A1133 (1965).
- K. Abdelmaqsoud, D. Sinclair, V. S. S. A. Karra, S. M. Taheri-Mousavi, M. Widom, B.and A. Webler J. R. Kitchin, Computational design of ductile additively manufactured tungsten-based refractory alloys, Comp. Mat. Sci. 270, 114735 (2026).
- J. P. Perdew, K. Burke, and M. Ernzerhof, Generalized gradient approximation made simple, Phys. Rev. Lett. 77, 3865 (1996).
- R. Dronskowski and P. E. Blöchl, Crystal orbital Hamilton populations (COHP): Energy-resolved visualization of chemical bonding in solids based on density-functional calculations, J. Phys. Chem. 97, 8617 (1993).
- J. Qi, X. Fan, D. I. Hoyos, M. Widom, P. K. Liaw, and J. Poon, Integrated design of aluminum-enriched high-entropy refractory B2 alloys with synergy of high strength and ductility, Sci. Adv. 10, eadq0083 (2024).
- D. G. Pettifor, Theoretical predictions of structure and related properties of intermetallics, Mater. Sci. Technol. 8, 345 (1992).
- A. Samanta, M. Widom, J. Berry, A. Perron, and J. McKeown, Analysis of correlations between intrinsic ductility and electronic density of states in refractory alloys, Scr. Mater. 265, 116728 (2025).
- P. P. P. O. Borges, R. O. Ritchie, and M. Asta, Electronic descriptors for dislocation deformation behavior and intrinsic ductility in bcc high-entropy alloys, Sci. Adv. 10, eadp7670 (2024).
- Y.-J. Wang and C.-Y. Wang, A comparison of the ideal strength between (Al,W) and under tension and shear from first-principles calculations, Appl. Phys. Lett. 94, 261909 (2009).
- D. Pant, S. Varshney, and D. S. Aidhy, Dominant role of second nearest-neighbor bonding in strength-ductility tradeoff of bcc refractory high entropy alloys, Acta Mater. 309, 122091 (2026).
- J. Wang, A. Barooni, and M. Ghazisaeidi, Stability of the B2 phase among refractory metals, Acta Mat. 279, 120323 (2024).
- G. Kresse and D. Joubert, From ultrasoft pseudopotentials to the projector augmented-wave method, Phys. Rev. B 59, 1758 (1999).
- R. Nelson, C. Ertural, J. George, V. L. Deringer, G. Hautier, and R. Dronskowski, LOBSTER: Local orbital projections, atomic charges, and chemical-bonding analysis from projector-augmented-wave-based density-functional theory, J. Comput. Chem. 41, 1931 (2020).
- R. Feenstra and M. Widom, https://www.andrew.cmu.edu/user/feenstra/wavetrans/.
- V. Wang, N. Xu, J.-C. Liu, G. Tang, and W.-T. Geng, VASPKIT: A user-friendly interface facilitating high-throughput computing and analysis using VASP code, Comput. Phys. Commun. 267, 108033 (2021).
- B. Feng and M. Widom, Band structure theory of the bcc to hcp Burgers distortion, Phys. Rev. B 98, 174108 (2018).
- V. Raghuraman, M. Widom, and M. C. Gao, Nonlinear deformation and elasticity of bcc refractory metals and alloys, Phys. Rev. Mater. 6, 053601 (2022).
- T. E. Jones, M. E. Eberhart, D. P. Clougherty, and C. Woodward, Electronic selection rules controlling dislocation glide in bcc metals, Phys. Rev. Lett. 101, 085505 (2008).
- W. P. Huhn and M. Widom, Prediction of A2 to B2 phase transition in the high-entropy alloy Mo-Nb-Ta-W, JOM 65, 1772 (2013).
- A. van de Walle and G. Ceder, Automating first-principles phase diagram calculations, J. Phase Equilib. 23, 348 (2002).
- A. van de Walle, Multicomponent multisublattice alloys, nonconfigurational entropy and other additions to the alloy theoretic automated toolkit, Calphad 33, 266 (2009), tools for Computational Thermodynamics.
- A. Zunger, S.-H. Wei, L. G. Ferreira, and J. E. Bernard, Special quasirandom structures, Phys. Rev. Lett. 65, 353 (1990).
- G. Grimvall, B. Magyari-Köpe, V. Ozoliņš, and K. A. Persson, Lattice instabilities in metallic elements, Rev. Mod. Phys. 84, 945 (2012).