A Theoretic Study of β'' Misfits and Strain in Al-Mg-Si Alloys - A Cluster-Based Approach Combining Density Functional Theory and Linear Elasticity
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Heat treatable aluminium alloys of the 6xxx series are important for many industrial applications in the modern world. They contain small amounts of the alloying elements magnesium and silicon, which cluster together to form precipitate phases in the aluminium matrix. In particular, the metastable beta'' precipitate strengthens the material significantly. This work calculates beta'' misfits and surrounding strain fields in the host Al matrix by density functional theory. A cluster-based model is employed, with periodic boundary conditions along the precipitate habit direction, and a static boundary condition obtained by linear elasticity in the cross-sectional plane. A detailed account of modeling parameters and assumptions is made. Convergence of displacement related properties is assessed with respect to the modeling parameters. Simulations are performed on a range of realistically sized beta'' precipitates, and atomic misfit values of the precipitates are calculated. The misfits, ma and mc, are larger by between 10%-30% relative to their experimentally reported counterparts, but fall below reported bulk values, as expected. ma and mc depend strongly on the precipitate aspect ratio, and decrease in response to an increased size in their respective lattice directions, consistent with previous experimental and theoretical reports. The misfit area decreases with precipitate size and is between 8.76%-9.75%, overestimating slightly compared to previously published results. Elastic strain around the precipitates is calculated and shown to be in good agreement with a previous pure DFT study of beta'' in an Al lattice.