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

Abstract

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 intraoctahedral bond lengths, lattice constants, bulk moduli, cation–facial distances for the mixtures of M x 1M1–x 2B6, 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.

First principles study of electronic structure and thermoelectric transport in tin selenide and phase separated tin selenide–copper selenide alloy

“…Previous study by Cohen [51] revealed the power law dependence of bond length (d) with K for covalent crystal as K ∝ d −3.5 and for ionic crystal as K ∝ d −3 . In both cases it is evident that K will decrease with the increase in d [52,53]. In case of Cu 2 Se (Cu-Se bond length 2.56 Å), the size of Cu atom (140 pm) is much smaller than Sn atom (225 pm) in SnSe (Sn-Se bond length 2.83 and 2.79 Å) which eventually leads the formation of shorter bonds in Cu 2 Se and making K larger.…”

Morphology Control of Tantalum Carbide Nanoparticles through Dopant Additions

“…Strain effects have also been explored as parameters for morphological modification of copper and nickel particles, and doping has been applied for obtaining nanorods of magnesium . In addition, modeling − and experimental techniques − have been applied for exploring the behavior of borides of cubic and other morphologies. Moreover, experimental efforts have investigated shape change in cubic carbides as a function of carbon stoichiometry, which influences the relative growth rate of the dominant {111} and {100} facets. − …”