Fused borophenes: A new family of superhard light-weight materials

The search of new superhard materials has received a strong impulse by industrial demands for low-cost alternatives to diamond and $c$-BN, such as metal borides. In this Letter we introduce a new family of superhard materials, “fused borophenes” (FBs), containing 2D boron layers that are interlinked to form a 3D network. These materials, identified through a high-throughput scan of ${\mathrm{B}}_x{\mathrm{C}}_{1-x}$ structures, exhibit Vicker's hardness comparable to those of the best commercial metal borides. Due to their low formation enthalpies, FBs could be synthesized by high-temperature methods, starting from appropriate precursors, or through quenching of high-pressure phases.

Figure 1

The left panel shows the relative energy $\mathrm{\Delta }\mathrm{E}$(eV/atom) vs B fraction of all the $\sim 2700$ B-C structures at 0 GPa. The reference structures for C and B are C-graphite and $\alpha -{\mathrm{B}}_{12}$, respectively. The dashed black line represents the convex hull. The right panel shows the relative energy as a function of Vicker's hardness $V_H$ (GPa) of only the superhard B-C structures. The B fraction in these structures is indicated by the color bar at the top. The colored triangles, inverted triangles, and asterisks represent the 17 $cc$, 2 $cu$, and 8 $uu$ superhard FB, respectively. The green diamond and inverted pentagons represent diamond and IC structures, respectively. The remaining B-C structures are shown as gray circles.

Figure 2

Top and side views of BL in the three best superhard FB: $cc$* (a,b), $cu$* (c,d), and $uu$* (e,f), respectively. The orange- and blue-colored sticks indicate different BLs. Dark green sticks are centered on C atoms in one of the BL of $cu$*. The unit cell is shown as a black line.

Figure 3

Relative enthalpy $\mathrm{\Delta }\mathrm{H}$ (eV/atom) vs pressure P (GPa) of the most promising $uu$* FB (green dashed), $\gamma -{\mathrm{B}}_{28}$ (blue dashed), and $\alpha$-Ga (red dashed) phases of B. The $\mathrm{\Delta }\mathrm{H}$ is estimated with respect to $\alpha -{\mathrm{B}}_{12}$(black line).