Structural, mechanical, electronic properties of refractory Hf–Al intermetallics from SCAN meta-GGA density functional calculations

Hf–Al intermetallics are novel promising high-temperature structural materials, which exhibit excellent mechanical properties. In this work, the structural parameters, elastic constants, and mechanical anisotropies of Hf–Al intermetallics are investigated by applying the latest meta-GGA functional SCAN as well as several other widely used density functionals such as LDA, PBE and PBEsol. It is found that HfAl₂ is the most thermodynamically stable stoichiometric compound among all Hf–Al binary intermetallics. The elastic moduli like B, G, E, ductility index (B/G ratio) and Poisson's ratio (σ) of Hf–Al intermetallics are predicted based on Voigt–Reuss–Hill approximation, indicating most Hf–Al binary intermetallics are brittle except Hf₅Al₃ and Hf₂Al. Besides, the three-dimensional (3D) contour plots of mechanical moduli are provided to characterize the elastic anisotropy in Hf–Al intermetallics. HfAl shows obvious anisotropy in both Young's and bulk moduli along different crystallographic directions, while very weak anisotropy is revealed for both HfAl₂ and Hf₄Al₃ phases since the 3-D surface contours of mechanical moduli show little deviations from isotropic spherical shapes. The calculated electronic properties indicate that relatively high thermodynamic stability of HfAl₂ phase is mainly ascribed to the formation of a pseudo-gap in the electron density of states originating mainly from the Al-2p and Hf-5d states at the Fermi level.