Boron oxides under pressure: Prediction of the hardest oxides

We search for stable compounds of boron and oxygen at pressures from 0 to 500 GPa using the ab initio evolutionary algorithm uspex. Only two stable stoichiometries of boron oxides, namely, ${\mathrm{B}}_{6}\mathrm{O}$ and ${\mathrm{B}}_{2}{\mathrm{O}}_{3}$, are found to be stable, in good agreement with experiment. A hitherto unknown phase of ${\mathrm{B}}_{6}\mathrm{O}$ at ambient pressure, $Cmcm\text{\ensuremath{-}}{\mathrm{B}}_{6}\mathrm{O}$, has recently been predicted by us and observed experimentally. For ${\mathrm{B}}_{2}{\mathrm{O}}_{3}$, we predict three previously unknown stable high-pressure phases---two of these ($Cmc{2}_{1}$ and $P{2}_{1}{2}_{1}{2}_{1}$) are dynamically and mechanically stable at ambient pressure, and should be quenchable to ambient conditions. Their predicted hardnesses, reaching 33--35 GPa, make them harder than $\mathrm{Si}{\mathrm{O}}_{2}$-stishovite. These are the hardest known oxides (if one disregards ${\mathrm{B}}_{6}\mathrm{O}$, which is essentially a boron-based insertion compound). Under pressure, the coordination number of boron atoms changes from 3 to 4 to 6, skipping fivefold coordination.