Precipitate formation in aluminium alloys: Multi-scale modelling approach

Ternary Al–Mg–Si alloys have been modelled based on a multi-scale approach that spans across atomistic and mesoscale models and uses theoretically determined parameters. First, a cluster expansion model for total energy has been trained for atomistic configurations (FCC lattice) based on the data from density functional simulations of electronic structure. Free energy curves as a function of solute (Mg, Si) concentrations and disorder have been obtained by using this parameterisation together with meta-dynamics Monte Carlo sampling. In addition, free energy data, surface tensions as well as strain energy using the linear elasticity theory have been collected to be combined for a mesoscale phase-field model. The application of this approach shows that the formation of a layered MgSi phase, with (100) planes, is a particularly stable solute aggregation motif within the Al host matrix. Moreover, the phase-field model demonstrates that the preferred shape of the MgSi precipitates is needle-like (in FCC), and they can act as precursors for the important and well-known β″-type precipitates which are formed by translating one Mg column by a 1/2 lattice vector. The results provide theoretical evidence that the solute aggregation into needle-like MgSi domains (precipitates) is an inherent property of Al-Mg-Si alloys, and that it takes place even without the presence of vacancies which is a precondition for the eventual formation β″ precipitates.