Interface energy determination for the fully coherent β″ phase in Al–Mg–Si: making a case for a first principles based hybrid atomistic modelling scheme

Abstract

We introduce a first principles based hierarchical multi-scale model scheme with application to a system comprising a fully coherent precipitate, immersed in a host lattice environment. As a test case, the needle-shaped main hardening phase β″ in the Al–Mg–Si alloy system has been examined. Calculations were confined to a cross-section slab, where the coherency of the interfaces is well established experimentally. The scheme couples a density functional theory (DFT) based description of the interface vicinity to a linear elasticity theory (LET) based description of the larger surroundings as well as the precipitate interior. The establishing link between these descriptions is purely structural, and LET based. At the boundary between the DFT and LET regions, subsystem distortion energies were compared using both formalisms, revealing only weak differences. On the basis of the modelling results, the need for a multi-scale model scheme over a full DFT analysis has been quantified through analysis of the β″ strain field decay. In the interface vicinity, and for a system comprising a β″–Mg5Al2Si4 precipitate with 4 × 8 unit cells along aP, cP, respectively, the calculated interface energy of 2.36 kJ per mol exceeds predictions as obtained with currently available alternative model schemes by ≈20%. Model system changes, required in order to approach a more reliable DFT–LET coupling and clarify the above described interface energy sensitivity, have been discussed. In comparison with alternative frameworks, our scheme offers additional flexibility when addressing interface configuration stabilities. This may allow for the study of more realistic configurations in the future.