Abstract
Using first-principles calculations and companion experimental validations, we demonstrate that the valence electron concentration (VEC) can be used to self-consistently parameterize the bonding characteristics of high-entropy diborides (HEBs) and in turn predict their mechanical properties. When VEC is 10.0 per formula unit (f.u.), HEBs enter the superhard category where Hv>40GPa because bonding states are optimally filled to resist shear deformation. Conversely, above or below a VEC of 10.0, the hardness decreases due to the filling of antibonding or the emptying of bonding states of the HEBs, respectively. This result is supported by analyses of the electronic structure, bonding, antibonding, and electronic orbitals' (metal d and B 2p) occupation as a function of VEC. To complement the first-principles calculations, four HEBs were synthesized using high power impulse magnetron sputtering to interrogate their crystalline structure and mechanical properties. All HEBs retain a single-phase AlB2-type hexagonal structure with highly dense nodular grain morphology. Hardness measurements reveal general agreement between theory and experiment. An HEB with VEC of 10.0/f.u. shows superhard characteristics, with micro- and nanoindentation hardness greater than 40 GPa. This combined entropy and VEC-based materials design formulation establishes a foundation for the discovery of high-entropy ceramics with enhanced thermomechanical properties, making them suitable for extreme engineering applications.
Recommended Citation
M. D. Hossain and N. S. McIlwaine and N. O. Marquez-Rios and A. C. Feltrin and V. Chawla and R. A. Mayanovic and W. G. Fahrenholtz and D. Penumadu and E. Zurek and D. W. Brenner and D. E. Wolfe and S. Divilov and H. Eckert and S. Curtarolo, "Superhard Refractory High-entropy Diborides," Physical Review Materials, vol. 10, no. 3, article no. 033604, American Physical Society, Mar 2026.
The definitive version is available at https://doi.org/10.1103/hqlp-dcvl
Department(s)
Materials Science and Engineering
International Standard Serial Number (ISSN)
2475-9953
Document Type
Article - Journal
Document Version
Final Version
File Type
text
Language(s)
English
Rights
© 2026 American Physical Society, All rights reserved.
Publication Date
01 Mar 2026
