Response of fcc metals and L1₂ and D0₂₂ type trialuminides to uniaxial loading along [100] and [001]: ab initio DFT calculations

Abstract

Ab initio density-functional calculations have been used to investigate the response of the face-centred cubic (fcc) metals Al and Cu, and of the L1₂- and D0₂₂-type trialuminides Al₃(Sc,Ti,V) to uniaxial loading along the [100] and [001] directions. The results obtained under uniaxial strains are compared to the response to biaxial (epitaxial) strains. The ideal tensile and compressive strengths and their limitation by shear instabilities along these deformation paths have been calculated. Although the response of both pure fcc metals could be expected to be very similar, our results show a fundamental difference: whereas for Cu a special invariant state with C ₂₂ = C ₂₃, leading to a bifurcation from the tetragonal to an orthorhombic deformation path, is reached at a strain of 10%, for Al this state is reached only at a strain of 33% close to the critical strain defining the ideal tensile strength. The reaction of the L1₂-type trialuminides is comparable to the response of Al; no bifurcation to an orthorhombic deformation path is predicted. The response of the D0₂₂-type trialuminides is different from that of the L1₂-type phases because of the difference in the stacking of the atomic planes along the [001] direction. For D0₂₂-type trialuminides, the uniaxial compression along this direction or epitaxial tension in the (001) plane leads to the formation of a stress-free D0₃ structure, in complete analogy to the fcc ⇆ bcc transformations observed for the pure metals. Under uniaxial [100] loading the guiding symmetry along the deformation path is orthorhombic and leads to the formation of special structures under both tension and compression parts, which are related to the D0₃ structure in the same way as the parent D0₂₂-lattice is related to the L1₂ structure.

Keywords:

• transition-metal compounds
• mechanical properties
• stress–strain diagram
• strengthening mechanisms
• intermetallics
• computer simulation

Acknowledgements

Work at the University of Vienna has been supported by the VASP project and within the University Research Focus ‘Material Science’ and ‘Computational Science’. We thank T. Bučko for provision of the GADGET structural optimisation package.

Notes

Note

1. Note that the invariance condition has been formulated for uniaxial strain along [100] where C ₂₂ = C ₃₃ and C ₁₂ = C ₁₃. Under uniaxial [001] loading where C ₁₁ = C ₂₂ and C ₁₃ = C ₂₃ the ‘invariance condition’ reads C ₁₁ = C ₁₂. In this more conventional notation, it is evident that the invariance condition is equivalent to a vanishing tetragonal shear modulus C ^′ = (C ₁₁ − C ₁₂)/2 (for the tetragonal axis along [001]) or C ^′ = (C ₂₂ − C ₂₃)/2 (for the tetragonal axis along [100]), see also 17.