Solute–vacancy binding of the rare earths in magnesium from first principles

Abstract The thermodynamic and kinetic properties of Mg–rare earth (RE) alloys are not widely known, despite increased research in recent years into their mechanical strengthening mechanisms. To aid in the development of new alloys and strengthening models, the solute–vacancy binding energies for all 17 RE elements in hexagonal close-packed (hcp) Mg are calculated by density functional theory (DFT) in several solute/vacancy configurations. As the REs can be considerably larger than Mg, special care is taken to ensure convergence with respect to supercell size, and the binding of other large, non-RE solutes is calculated in the large supercells employed in the current work. It is found that the light and heavy lanthanides have favorable and unfavorable nearest-neighbor solute–vacancy binding, respectively. The binding energies exhibit a strong linear correlation to the magnitude of the solute’s displacement towards the vacancy, suggesting that local lattice relaxation is a significant contribution to the binding energy. There are four notable exceptions to this trend: Na, Sb, Pb and Bi. Explicit calculation of the lattice relaxation energy due to the presence of the solute–vacancy pair confirms that local relaxation is an important component of the binding energy, particularly for the larger solutes. Finally, empirical predictions of the dilute mixing energy disagree with those predicted by DFT. New experimental measurements are necessary to resolve the discrepancies, as there are no published thermodynamic data of the REs in hcp Mg.