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

摘要

By devising a novel framework, we present a comprehensive theoretical studyof solubilities of alkali (Li, Na, K, Rb, Cs) and alkaline earth (Be, Ca, Sr,Ba) metals in the he boron-rich Mg-B system. The study is based onfirst-principle calculations of solutes formation energies in MgB$_2$, MgB$_4$,MgB$_7$ alloys and subsequent statistical-thermodynamical evaluation ofsolubilities. The advantage of the approach consists in considering all theknown phase boundaries in the ternary phase diagram. Substitutional Na, Ca, andLi demonstrate the largest solubilities, and Na has the highest (0.5-1 % inMgB$_7$ at $T=650-1000$ K). All the considered interstitials have negligiblesolubilities. The solubility of Be in MgB$_7$ can not be determined because thecorresponding low-solubility formation energy is negative indicating theexistence of an unknown ternary ground state. We have performed ahigh-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 basedon the stable binary phases. Despite its high temperature observations, we findthat Sr$_{9}$Mg$_{38}$ is not a low-temperature equilibrium structure. We alsodetermine two new possible ground states CaB$_{4}$ and RbB$_{4}$, not yetobserved experimentally.