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.