First-principles study of solute-vacancy binding in magnesium

Solute-vacancy binding is a key quantity in understanding diffusion kinetics, and may also have a considerable impact on the hardening response in Mg alloys. However, the binding energetics between solute impurities and vacancies in Mg are notoriously difficult to measure accurately and are largely unknown. Here, we present a large database of solute-vacancy binding energies in Mg from first-principles calculations based on density functional theory. Our vacancy formation energy and dilute mixing energy, which are byproducts of the solute-vacancy binding calculations, show good agreement with experiments, where available. We have investigated the simple physical effects controlling solute-vacancy binding in Mg and find that there is a modest correlation between binding energy and solute size, with larger solute atoms more favorably binding with neighboring vacancies to relax the strain induced by the solutes. Most early 3d transition metal solutes do not favorably bind with vacancies, indicating that a simple bond-counting argument is not sufficient to explain the trends in binding, in contrast to the case of binding in Al. We also predict positive vacancy binding energies for some commonly used microalloying elements in Mg which are known to improve age hardenability, i.e. Na, In, Zn, Ag and Ca. Even larger vacancy binding energies are found for some other solutes (e.g. Cu, Sn, Pb, Bi and Pt), which await experimental validation.