Electronic structure and bulk properties of $MB6$ and $MB12$ borides Available to Purchase

Ab initio band structure calculations are carried out for the higher borides $MB6$ and $MB12$⁠. High-precision measurements of the elastic constants are performed for the compounds $ZrB12$⁠, $HoB12$⁠, $ErB12$⁠, $TmB12$⁠, $LuB12$⁠, $YB6$ and $LaB6$ at low temperatures. The bulk properties of the borides are analyzed on the basis of the calculated equations of states and balanced crystal orbital overlap populations. Our calculations indicate that hexaborides with divalent metals, $CaB6$⁠, $SrB6$⁠, $BaB6$⁠, and $YbB6$⁠, are semiconductors with small energy gaps. The metallic $MB6$ hexaborides with trivalent M atoms are found to possess larger bulk moduli values. For dodecaborides the bulk moduli are found to be higher for $MB12$ with increased filling of the conduction band (⁠$ZrB12$⁠, $HfB12$⁠, $UB12$⁠) in comparison with $M3+B12$ compounds. The total energy calculations for different magnetic configurations in $YbB12$ point to the possibility of antiferromagnetic coupling between $Yb3+$ ions.