Fully resolved strain field of the β’’ precipitate calculated by density functional theory

The β′′ precipitate is the main hardening phase in age hardenable Al-Mg-Si alloys, and it is therefore of major scientific and industrial importance. A full model of the β′′ precipitate cross-section embedded in an aluminium host lattice is created for a range of precipitate sizes, and relaxed by first principle calculations. The influence of periodic images is avoided by applying a cluster based model with fixed boundary conditions, where the surface is corrected by a displacement field calculated by linear elasticity theory. The calculated misfit values between the precipitate and the host lattice vectors are consistent with experimental scanning transmission electron microscopy results. The misfit area increases proportionally with the cross sectional area, suggesting that the lattice parameters of β′′ do not change as the size increases. Both the displacement field and the strain field are in agreement with experimental results. The strain field calculated by density functional theory shows a local zone close to the precipitate where the chemical contribution to the strain field is dominant. The strong correspondence between the experimental and the modelling results supports the methodology to be used in general to study other phases