A First-Principles Study of the Cu-Containing β″ Precipitates in Al-Mg-Si-Cu Alloy

The nanostructured β″ precipitates are critical for the strength of Al-Mg-Si-(Cu) aluminum alloys. However, there are still controversial reports about the composition of Cu-containing β″ phases. In this work, first-principles calculations based on density functional theory were used to investigate the composition, mechanical properties, and electronic structure of Cu-containing β″ phases. The results predict that the Cu-containing β″ precipitates with a stoichiometry of Mg_4+xAl_2−xCuSi₄ (x = 0, 1) are energetically favorable. As the concentration of Cu atoms increases, Cu-containing β″ phases with different compositions will appear, such as Mg₄AlCu₂Si₄ and Mg₄Cu₃Si₄. The replacement order of Cu atoms in β″ phases can be summarized as one Si3/Al site → two Si3/Al sites → two Si3/Al sites and one Mg1 site. The calculated elastic constants of the considered β″ phases suggest that they are all mechanically stable, and all β″ phases are ductile. When Cu atoms replace Al atoms at Si3/Al sites in β″ phases, the values of bulk modulus (B), shear modulus (G), and Young’s modulus (E) all increase. The calculation of the phonon spectrum shows that Mg_4+xAl_2−xCuSi₄ (x = 0, 1) are also dynamically stable. The electronic structure analysis shows that the bond between the Si atom and the Cu atom has a covalent like property. The incorporation of the Cu atom enhances the electron interaction between the Mg2 and the Si3 atom so that the Mg2 atom also joins the Si network, which may be one of the reasons why Cu atoms increase the structure stability of the β″ phases.