First-principles study of solid solution strengthening in Mg–X (X=Al, Er) alloys

Abstract

To study the solid solution strengthening effect on magnesium (Mg)–X (X = Al, Er) alloys, supercell models of Mg, $\hbox {Mg}_{35}\hbox {Er}$ and $\hbox {Mg}_{35}\hbox {Al}$ are established to perform the first-principles pseudopotential plane wave calculations based on density functional theory. The calculated cohesive energy of $\hbox {Mg}_{35}\hbox {Er}$ is lower than that of $\hbox {Mg}_{35}\hbox {Al}$. This indicates that $\hbox {Mg}_{35}\hbox {Er}$ has better structural stability than $\hbox {Mg}_{35}\hbox {Al}$. The bulk modulus, Young’s modulus and shear modulus of the solid solutions increases simultaneously when Al and Er are doped into the Mg matrix. Moreover, the solid solution strengthening of Er is much higher than the Al containing alloy. The order of toughness of the three solutions from the highest to the lowest is Mg, $\hbox {Mg}_{35}\hbox {Er}$ and $\hbox {Mg}_{35}\hbox {Al}$, while the order of increasing elastic anisotropy is in the reverse order. The number of bonding electrons of $\hbox {Mg}_{35}\hbox {Er}$ in the low-energy region of the Fermi level is much higher than that of $\hbox {Mg}_{35}\hbox {Al}$, and the density of states of $\hbox {Mg}_{35}\hbox {Er}$ at the Fermi level is higher than that of $\hbox {Mg}_{35}\hbox {Al}$. Compared with Al atoms, Er atoms share more electric charges with Mg atoms, which leads to an increasingly uniform charge distribution around Er atoms.