Interface configuration stability and interfacial energy for the β″ phase in Al-Mg-Si as examined with a first principles based hierarchical multi-scale scheme

We examine interface configuration stabilities and determine interfacial energies over the full precipitate cross-section for the needle-shaped main hardening phase β″ in the Al-Mg-Si alloy system. Our supercell based studies are performed within the framework of density functional theory, hence providing first principles accuracy for the electronic structure. In addition, each cell is distorted according to information from a hierarchical multi-scale model scheme, implying that also the local ionic structure is mimicked throughout. Making use of the larger structural freedom available compared to an isolated supercell based approach, we propose a modified expression for deriving the interfacial energy. When examined for an average sized β″-Mg5Al2Si4 precipitate, this expression provides non-negligible changes to the interfacial energies, exceeding 20% for one interface. We further argue that a full hybrid scheme would likely influence the energies non-negligibly, with a dependence on the precipitate dimensions appearing plausible. Additional modification of the interfacial energy expression for implementation in such a scheme is discussed. Our calculations suggest stability of the structural interface configuration, compatible with a stoichiometric precipitate for the chosen bulk phase composition, over the entire interface.