Thermodynamic stability of Borophene, ${\mathrm{B}}_2{\mathrm{O}}_3$ and other ${\mathrm{B}}_{1-\mathrm{x}}{\mathrm{O}}_{\mathrm{x}}$ sheets

Abstract

The recent discovery of borophene, a two-dimensional allotrope of boron, raises many questions about its structure and its chemical and physical properties. Boron has a high chemical affinity to oxygen but little is known about the oxidation behavior of borophene. Here we use first principles calculations to study the phase diagram of free-standing, two-dimensional ${\mathrm{B}}_{1-\mathrm{x}}{\mathrm{O}}_{\mathrm{x}}$ for compositions ranging from $x=0$ to $x=0.6$, which correspond to borophene and ${\mathrm{B}}_2{\mathrm{O}}_3$ sheets, respectively. Our results indicate that no stable compounds except borophene and ${\mathrm{B}}_2{\mathrm{O}}_3$ sheets exist. Intermediate compositions are heterogeneous mixtures of borophene and ${\mathrm{B}}_2{\mathrm{O}}_3$. Other hypothetical crystals such as ${\mathrm{B}}_2\mathrm{O}$ are unstable and some of them were found to undergo spontaneous disproportionation into borophene and ${\mathrm{B}}_2{\mathrm{O}}_3$. It is also shown that oxidizing borophene inside the flakes is thermodynamically unfavorable over forming ${\mathrm{B}}_2{\mathrm{O}}_3$ at the edges. All findings can be rationalized by oxygen's preference of two-fold coordination which is incompatible with higher in-plane coordination numbers preferred by boron. These results agree well with recent experiments and pave the way to understand the process of oxidation of borophene and other two-dimensional materials.

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