From generalized stacking fault energies to dislocation properties: Five-energy-point approach and solid solution effects in magnesium

Abstract

Using ab initio calculations and symmetrized plane waves, we analyze the basal-plane generalized stacking fault energies in pure Mg and Mg-Y alloys and show that the knowledge of energies of only five specific points is sufficient to accurately predict the core structures and Peierls stresses of $\ensuremath{\langle}a\ensuremath{\rangle}$-type edge dislocations in these alloys. Our five-point approach substantially reduces the computational cost related to the Peierls-Nabarro (PN) model and allows for a high-throughput application of the PN model to study Peierls stress changes in Mg upon alloying. We employ our approach to study Mg binary alloys containing nine rare-earth (RE) and 11 other solutes. Based on the Peierls stresses of these 20 Mg alloys calculated from the Peierls-Nabarro model, the solutes are divided into three groups: (i) the first group, consisting of Be, Zn, Tl, Tc, Os, Ru, Re, and Co, when added as solutes into Mg, lead to more compact dislocation core structures and larger Peierls stresses than found for pure Mg. (ii) Elements in the second group, including Ti, Nd, Lu, Zr, Hf, La, and Pr change the core widths and Peierls stresses moderately. (iii) The solutes in the third group containing Y, Er, Tm, Ho, and Sc extend the stacking fault width, and the resulting Peierls stresses are generally very low. Based on an error analysis, we conclude that the first group has a clear solute strengthening effect and the third group has a clear solute softening effect, while the effects of the elements in the second group are too small to be resolved by the present approach.