Interatomic bonds and the tensile anisotropy of trialuminides in the elastic limit: a density functional study for Al₃(Sc, Ti, V, Cr)

Abstract

The tensile anisotropy in the elastic limit of Al₃(Sc, Ti, V, Cr) intermetallic compounds in both the L1₂ and D0₂₂ crystal structure has been investigated using first-principles density-functional calculations. In both crystal structures the main bonding character comes from the saturation of dominant d ³ (L1₂) and d ⁴ (D0₂₂) hybrid orbitals located on the TM atoms. The series Al₃Sc → Al₃V corresponds to gradual d-band filling and leads to a gradual increase of bond-strength and covalent bond formation. The magnetism of Cr breaks this trend in the Al₃Cr compound (for both ferromagnetic and antiferromagnetic configurations). In this series, a trend towards an increased anisotropy of the elastic constants, Young modulus Y and Poisson ratio ν is observed. The easy and hard directions of tension can be simply identified by the variation of Y, which corresponds to the presence or absence of covalently bonded–Al–TM–chains. A high anisotropy of the Poisson ratio arises also from an alternation of atoms in the lateral directions and can be understood in the same terms.

Acknowledgements

Work at the Vienna University has been supported by the VASP project. We acknowledge support also from the Grant Agency for Science in Slovakia (Grant No. 2/5096/25).

Notes

†Using the correlation table , , .

†Using the correlation table , , .

†We choose the 27×10⁻³ e/ų value due to the best viewing of the bonding charge in the Al³V compound. At this level the covalent contribution to the Al–V bonds can be seen easily.

†The irreducible representation for d ⁴ hybridization is . It can be decomposed into and , i.e. d ³ hybrids of d_xz , d_yz , d _{z ²} atomic orbitals and a separate contribution of d _{x ²−y ²} atomic orbital.