A first-principles study of the β-phase in Al-Mg-Si alloys

Al-Mg-Si alloys gain an increase in strength due to small precipitates of Mg and Si formed from the solid-solution phase, where maximum hardness arises from a combination of a large number of fully coherent Guinier-Preston (GP) 1 zones and semi-coherent GP 2 zones (the beta-Mg5Si6 phase), both existing as needle-like structures. In the present work we investigate the nature of bonding within the equivalent bulk structure of the beta-phase, using the density functional theory technique. In particular we investigate the presence of covalent bonding between Si using the calculated charge-density/transfer distributions of the structure. In addition we find small residual Hellmann-Feynman forces on the atoms, and accordingly relax the structure and find a more symmetric structure in terms of geometry and charge density. We find also that the converged structure is stable against atomic position perturbations that break the inversion and mirror plane symmetries of the C2/m beta-phase. Finally we investigate a face-centred-cubic array of only Mg and Si atoms-a candidate model for the GP 1 phase, from which the beta-structure may be recovered by a simple transformation and subsequent atomic relaxation.