Stability and Strength of Atomically Thin Borophene from First Principles Calculations

A new two-dimensional (2D) material, borophene (2D boron sheet), has been grown successfully recently on single crystal Ag substrates by two parallel experiments [Mannix $\mathit{\text{et}}\mathit{\text{al.,}}\mathit{\text{Science}}$, 2015, $\mathbf{\text{350}}$, 1513] [Feng $\mathit{\text{et}}\mathit{\text{al.,}}\mathit{\text{Nature}}\mathit{\text{Chemistry}}$, 2016, $\mathbf{\text{advance}}\mathbf{\text{online}}\mathbf{\text{publication}}$]. Three main structures have been proposed (${\beta }_{12}$, ${\chi }_3$ and striped borophene). However, the stability of three structures is still in debate. Using first principles calculations, we examine the dynamical, thermodynamical and mechanical stability of ${\beta }_{12}$, ${\chi }_3$ and striped borophene. Free-standing ${\beta }_{12}$ and ${\chi }_3$ borophene is dynamically, thermodynamically, and mechanically stable, while striped borophene is dynamically and thermodynamically unstable due to high stiffness along $a$ direction. The origin of high stiffness and high instability in striped borophene along $a$ direction can both be attributed to strong directional bonding. This work provides a benchmark for examining the relative stability of different structures of borophene.