Phase Stability Analysis of Ternary Alkaline-Earth Hexaborides: Insights from DFT Calculations

We present a phase stability analysis of ternary mixtures of alkaline-earth hexaborides using insights from DFT calculations to determine the effect of homogeneity on properties including stability and domain formation. We find that linear mixing rules and Vegard's law type, describe very well octahedral volumes, inter and intra-octahedral bond lengths, lattice constants, bulk moduli, cation-facial distances for the mixtures of (MxM1-xB6)-M-1-B-2, where M-k can be Ca, Ba, or Sr, and composition (x) ranges from 0 to 1. In general, variations are less than 5% of the calculated mixture properties with positive deviations, except the interoctahedral boron bond lengths in systems with Ba. We find that doping with lighter cations may be an effective means of strengthening MB6 materials. Electronic structure calculations predict that the lattice constants and interoctahedral bond lengths with a mixture are identical, as the degree of homogeneity increases, indicative of formation of a single phase. However, bond lengths within the boron framework are found to be heavily dependent upon the local cation environment, and energies taken at absolute zero suggest phase splitting as a general tendency for certain stoichiometric ratios, in particular, for compositions at the 50% levels, which is in agreement with experimental evidence. The phase shifted regions are likely the product of the slight mismatch between interoctahedral bonds. These nanoregimes are interpreted as regions that have not yet fully mixed.