First-principles solubilities of alkali and alkaline-earth metals in Mg-B alloys

In this article, we present a comprehensive theoretical study of solubilities of alkali (Li, Na, K, Rb, Cs) and alkaline-earth (Be, Ca, Sr, Ba) metals in the boron-rich Mg-B system. The study is based on first-principles calculations of solutes formation energies in MgB2, MgB4, MgB7 alloys and subsequent statistical-thermodynamical evaluation of solubilities. The advantage of the approach consists in considering all the known phase boundaries in the ternary phase diagram. Substitutional Na, Ca, and Li demonstrate the largest solubilities, and Na has the highest (0.5%-1% in MgB7 at T=650-1000 K). All the considered interstitials have negligible solubilities. The solubility of Be in MgB7 cannot be determined because the corresponding low-solubility formation energy is negative indicating the existence of an unknown ternary ground state. We have performed a high-throughput search of ground states in binary Mg-B, Mg-A, and B-A systems, and we construct the ternary phase diagrams of Mg-B-A alloys based on the stable binary phases. Despite its high-temperature observations, we find that Sr9Mg38 is not a low-temperature equilibrium structure. We also determine two possible ground states CaB4 and RbB4, not yet observed experimentally.