Colossal Shear-Strength Enhancement of Low-Density Cubic ${\mathrm{BC}}_2\mathrm{N}$ by Nanoindentation

Recently synthesized low-density cubic ${\mathrm{BC}}_2\mathrm{N}$ exhibits surprisingly high shear strength inferred by nanoindentation in stark contrast to its relatively low elastic moduli. We show by first-principles calculation that this intriguing phenomenon can be ascribed to a novel structural hardening mechanism due to the compressive stress beneath the indenter. It significantly strengthens the weak bonds connecting the shear planes, yielding a colossal enhancement in shear strength. The resulting biaxial stress state produces atomistic fracture modes qualitatively different from those under pure shear stress. These results provide the first consistent explanation for a variety of experiments on the low-density cubic ${\mathrm{BC}}_2\mathrm{N}$ phase across a large range of strain.

Figure 1

(a) The calculated stress-strain relations of the low-density $c\mathrm{\text{−}}{\mathrm{BC}}_2\mathrm{N}$ under the $(111)[11\overline{2}]$ pure shear (${\sigma }_{zz}/{\sigma }_{xz}=0$) and biaxial (${\sigma }_{zz}/{\sigma }_{xz}=\tan 68°)$ stress. The inset shows the response of the normal compressive stress (${\sigma }_{zz}$) to the variation of the normal compressive strain ($\Delta {ϵ}_{zz}$) at the (fixed) critical shear strain ${ϵ}_{xz}=0.22$ (${\mathrm{S}}_3$). (b) The length variation of the [111] bonds that connect the $\{111\}$ shear planes and the $[11\overline{1}]$ bonds that are in the {111} shear planes under the biaxial stress. (c) The snapshots of the calculated structural unit cell at equilibrium (${ϵ}_{xz}=0$) and at four key points on the stress-strain curve under the biaxial stress shown in (a). The dashed lines indicate the weak (broken) bonds.

Figure 2

(a) The calculated stress-strain relations of cubic boron nitride ($c\mathrm{\text{−}}\mathrm{BN}$) under the $(111)[11\overline{2}]$ pure shear (${\sigma }_{zz}/{\sigma }_{xz}=0$) and biaxial (${\sigma }_{zz}/{\sigma }_{xz}=\tan 68°$) stress. The inset shows the response of the normal compressive stress (${\sigma }_{zz}$) to the variation of the normal compressive strain ($\Delta {ϵ}_{zz}$) at two fixed shear strains (${ϵ}_{xz}=0.38$ and 0.395) near the peak shear stress. (b) The snapshots of the calculated structural unit cell at equilibrium (${ϵ}_{xz}=0$) and at the critical shear strain ${ϵ}_{xz}=0.38$ under ${\sigma }_{zz}/{\sigma }_{xz}=\tan 68°$ right before the collapse of the [111] B-N bonds.