Design of three-dimensional solid-state boron oxide networks: Ab initio calculations using density functional theory

Most binary oxides are classic examples of densely packed systems; a given compound generally adopts only a small number of structures. Here for boron monoxide (BO) in contrast we demonstrate the existence of many low, equienergetic forms, consistent with the limited experimental NMR data. All are dominated by six-membered rings connected in various ways; there is considerable variation in B-O-B angles and torsion angles but not in bond lengths. The volume per formula unit of a less dense nanoporous phase is twice that of other denser forms.

Figure 1

(Color online) Calculated optimized chain and layer structures for solid boron monoxide (boron green/grey, oxygen red/dark grey) and their chemical formulas.

Figure 2

(Color online) Layered structure (local minimum) $\mathbf{E}$. The BOB angles are $129°$ and $141°$, and associated BBBB torsions $70°$ and $55°$, respectively.

Figure 3

(Color online) (a) Relative positions of six-membered rings in structure $\mathbf{F}$ (b) 3D structure $\left(V=53{\text{Å}}^3\right)$ viewed along the $b$ axis. BOB bond angles are $131°$ and $136°$, with associated BBBB torsion angles $120°$ and $63°$, respectively. (c) Higher density 3D structure $\mathbf{G}$ $\left(V=33{\text{Å}}^3\right)$ (with the same connectivity as $\mathbf{F}$) viewed along the $b$ axis, respectively. BOB bond angles are $143°$ and $146°$, with associated BBBB torsion angles $103°$ and $-117°$, respectively. Note (b) and (c) are viewed along the same direction.

Figure 4

(Color online) The structural transformation from structure $\mathbf{A}$ (assuming stacking of chains with $P2/m$ symmetry) to a high-pressure form structure $\mathbf{H}$ containing four-coordinate boron. The thermodynamic transition pressure for $\mathbf{A}\to \mathbf{H}$ is $\sim 10\text{GPa}$. (a) Energy (per formula unit) vs volume for $\mathbf{A}$ and $\mathbf{H}$. All energies relative to that of the lowest energy structure (a) at zero pressure. (b) High-pressure $\beta$-InS form $\mathbf{H}$ (c) Structure $\mathbf{A}$.