Effects of calcium on planar fault energies in ternary magnesium alloys

Abstract

We are motivated by the need to design magnesium alloys that are free of rare-earth additions, but, nevertheless, forgeable and free of strong basal texture. It has become recently clear that calcium is a promising candidate to replace the economically strategic rare-earth elements. To this end, we focus on the planar faults that typically bound partial glide dislocations of the hcp lattice. We have made first-principles calculations to examine the generalized stacking fault energy (SFE) of the basal, first- and second-order pyramidal planes. We examine the changes in fault energy and anisotropy for increasing alloy concentrations and the effect of low concentrations of calcium. For the calculation of the SFEs from first principles, we use the non-self-consistent Harris-Foulkes approximation to the local density functional theory. We demonstrate that while this approximation leads to high computational efficiency, there is no significant loss of precision compared to the self-consistent Hohenberg-Kohn functional. We go beyond all previous work in which the alloying element is assumed to reside within the fault and instead address the more realistic situation in which the SFE is modified by the remote presence of the impurity. This allows us to determine whether segregation is expected and we find that while elements do segregate to the basal fault they do not to pyramidal faults. Nevertheless, in either case, the fault energy is strongly modified by alloying. This argues that either a long-ranged electronic structure effect is in play, or the fault energy modification is affected by the atomic size difference---particularly large in the case of Ca. We find that Mg-Li-Ca and Mg-Zn-Ca alloys show a remarkable decrease in anisotropy, which is consistent with their known high strength and formability. In favorable cases, this comes about by strengthening basal slip rather than weakening nonbasal slip. The Ca contribution increases inversely with the atomic size of the alloying element, allowing us to speculate that alloying effects are generally atomic size effects.