First-principles study of the thermodynamic stabilities and electronic structures of long-period stacking ordered phases in Mg-Y-Cu alloys

The long-period stacking ordered (LPSO) phases in magnesium alloys possess excellent mechanical performances, and have received considerable attention. The strengthening LPSO phases, such as 14H and 18R structures, are found experimentally in some Mg-Y-Cu alloys, which can significantly enhance the mechanical performances of the alloys. However, it is unknown which phase is more stable thermodynamically, and easier to form during the solidification. In this paper, thermodynamic stabilities and electronic characteristics of LPSO phases 14H and 18R (18R(m), 18R(t)) in Mg-Y-Cu alloys are investigated by the first-principles pseudopotential method based on the density functional theory. The present calculations are performed by using Vienna ab-initio simulation package (VASP) with projector-augmented plane wave pseudopotential, and the generalized gradient approximation is used to deal with and describe the exchange-correlation interaction. The plane wave cutoff energy is set to be 360 eV, the forces on all the atoms are less than 0.02 eV/angstrom. The k-point meshes of Brillouin zone sampling in a primitive cell are based on the Monkhorst-Pack scheme. The calculated enthalpies of formation indicate that the 14H and 18R phases coexist in Mg-Y-Cu alloys. The 18R phase has a larger absolute value of formation enthalpy, which means that it is easier to form than the 14H phase. The reaction energy is also computed for the transformation from the 18R phase to 14H phase, which shows that the 14H phase is more stable than the 18R phase. The results for density of states (DOS) reveal that the bondings of the 14H and 18R phases occur mainly among the valence electrons of Cu 3d, Y 4d, Mg 3s and Mg 2p orbits while those of Cu 4s, Y 4s and Y 4p orbits are very weak in the whole region. The bonding peaks of the 14H, 18R(m), and 18R(t) phases are localized, and the corresponding hybridization orbits, which are all or part of Mg 3s, Mg 2p, Cu 3d and Y 4d orbits, are determined. At the same time, there are sharp peaks on both sides of the Fermi level of the 14H, 18R(m) and 18R(t) phases, which shows that there exist pseudogaps in those phases. The presence of pseudogap indicates that the bonds in the 14H and 18R phases are noticeable covalent. In addition, the charge densities both on (0 0 0 1) plane of the 14H and 18R phases are analyzed in detail. The results show that the Cu-Y bond exhibits the covalent feature in the 14H and 18R phases, the covalent bonding of the 14H phase is stronger than that of the 18R phase, and it is the key reason that the 14H is more stable than the 18R. The calculated results for thermodynamic stabilities and electronic structures of LPSO phases will provide useful data for analyzing and designing Mg-Y-Cu alloys.