Distinct electron density topologies and elastic properties of two similar omega phases: ω-Zr and Zr2Al

• Zr2Al and ω-Zr with similar structures show distinct mechanical properties.
• The origin of the strengthening effect of ordered Al substitution is revealed.
• Al substitution for Zr increases the bond directionality and reduces bond anisotropy.
• A criterion rationalizes the 3D plot of Young's modulus of hexagonal crystals.
• This study provides clues for tuning properties of ω phase in related alloys.

Omega (ω) phase plays a crucial role in determining performance of numerous Zr- or Ti-based alloys, which necessitates a sound knowledge of its fundamental properties. Through first-principles calculations, the present study gives a detailed comparison of structural, elastic and electronic properties of two closely related omega phases, ω-Zr and Zr2Al. Despite the structural similarity, their elastic properties turn out to be remarkably different. Zr2Al possesses considerably higher elastic stiffness constants (except C33), single crystal Young's modulus (except along directions near those in the xy-plane and near the z   axis), polycrystalline bulk and shear moduli, Vickers hardness and lower elastic anisotropy, demonstrating a pronounced strengthening effect of the ordered Al substitution for Zr. In addition, they have distinct 3D plots for crystal orientation dependence of Young's modulus, shear modulus and Poisson's ratio. We demonstrate that these 3D plots are not artificial results or technical mistakes and can be rationalized by simple mathematics. For example, whether the 3D plot of Young's modulus is ellipsoidal or not is determined by a proposed factor of (S11−S13−S44/2)/(S11+S33−2S13−S44)(S11−S13−S44/2)/(S11+S33−2S13−S44). Based on Bader's theory of atoms in molecules, subsequent electron density topological analysis uncovers a clear electron density origin for the different elastic properties. The ordered Al substitution for Zr is found to not only change the overall electron density topology but also increase the bond directionality and decrease the bond anisotropy. Additionally, intriguing “banana bonds” are found in both phases. The present study is of significant importance for design of advanced Zr-based alloys associated with ω phase.

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