Anomalous bond softening mediated by strain-induced Friedel-like oscillations in a ${\mathrm{BC}}_2\mathrm{N}$ superlattice

The crystal structure of ${\mathrm{BC}}_2\mathrm{N}$ and the origin of its superhardness remain under constant debate, hindering its development. Herein, by evaluating the x-ray diffraction pattern, the thermodynamic stability at normal and high pressures of a series of ${\mathrm{BC}}_2\mathrm{N}$ candidates, the (111) $\mathrm{B}{\mathrm{C}}_2{\mathrm{N}}_{2\times 2}$ superlattice (labeled $\mathrm{R}2u-\mathrm{B}{\mathrm{C}}_2\mathrm{N}$) is identified as the realistic crystal structure of the experimentally synthesized ${\mathrm{BC}}_2\mathrm{N}$. We further reveal that the strain-induced Friedel-like oscillations dominates the preferable slip systems of $\mathrm{R}2u-\mathrm{B}{\mathrm{C}}_2\mathrm{N}$ by drastically weakening the heterogenous bonds across the slip plane and thus leads to its ultralow dislocation slip resistance, which originates from the metallization triggered by the reduction in energy separation between bonding and antibonding interactions of the softened bonds. Our results rule out $\mathrm{R}2u-\mathrm{B}{\mathrm{C}}_2\mathrm{N}$ as the intrinsic superhard material surpassing $c\text{−}\mathrm{BN}$, whereas the experimentally determined extreme hardness can be attributed to the nanocrystalline grains glued by interfacial amorphous carbon which provides a strong barrier for plastic deformation. These findings provide a view of the longstanding issue of the possible structure of experimentally observed ${\mathrm{BC}}_2\mathrm{N}$, and establish a mechanism underlying the strain-driven electronic instability of superlattice structures, providing guidance towards rational design of superhard materials.

Figure 1

(a) Relative enthalpy vs pressure for ${\mathrm{BC}}_2\mathrm{N}$. bc-${\mathrm{BC}}_2\mathrm{N}$ is taken as reference. (b) Simulated XRD patterns of $\mathrm{R}2u-\mathrm{B}{\mathrm{C}}_2\mathrm{N}$ and experimental pattern reproduced from Ref. [8]. (c) Crystal structure of $\mathrm{R}2u-\mathrm{B}{\mathrm{C}}_2\mathrm{N}$. (d) Enlarged diffraction peaks of simulated XRD patterns of $\mathrm{Rnu}-\mathrm{B}{\mathrm{C}}_2\mathrm{N}(n=1–4)$ and experimental pattern reproduced from Ref. [8].

Figure 2

(a) Tensile and shear stress-strain curves of $\mathrm{R}2u-\mathrm{B}{\mathrm{C}}_2\mathrm{N}$, and those of $c\text{−}\mathrm{BN}$ along its weakest tensile direction and shear path. Insets shows the key bond lengths (marked as “L1” to “L4”) variations in $\mathrm{R}2u-\mathrm{B}{\mathrm{C}}_2\mathrm{N}$ and $c\text{−}\mathrm{BN}$ under tensile and shear strains. Snapshots of deformed structures at equilibrium, peak and instability strains: (b)–(d) $\mathrm{R}2u-\mathrm{B}{\mathrm{C}}_2\mathrm{N}$ and (e)–(g) $c\text{−}\mathrm{BN}$ under tensile strains, (h)–(j) $\mathrm{R}2u-\mathrm{B}{\mathrm{C}}_2\mathrm{N}$ and (k)–(m) $c\text{−}\mathrm{BN}$ under shear strains. The structure transformation of B-N layers in $\mathrm{R}2u-\mathrm{B}{\mathrm{C}}_2\mathrm{N}$ under shear loading are highlighted as pale brown areas.

Figure 3

(a) Topological structure of $\mathrm{R}2u-\mathrm{B}{\mathrm{C}}_2\mathrm{N}$ with the possible weakest cleavage/slip planes marked as dotted lines. (b) GSFEs of different slip planes, (c) derived slide stress of shuffle-set planes, and (d) Peierls stress of different slip planes in $\mathrm{R}2u-\mathrm{B}{\mathrm{C}}_2\mathrm{N}$, together with those in $c\text{−}\mathrm{BN}$ shown for comparison. $\mathrm{R}2\mathrm{u}-\mathrm{n}\left(n=1–4\right)$ in (d) represents the corresponding Peierls stress of S/G1-4.

Figure 4

(a) Bond length variations in several layers around slip plane “S2” as a function of the displacement u in $\mathrm{R}2u-\mathrm{B}{\mathrm{C}}_2\mathrm{N}$, compared with those in $c\text{−}\mathrm{BN}$. VCDD of (b)–(d) $\mathrm{R}2u-\mathrm{B}{\mathrm{C}}_2\mathrm{N}$ and (e)–(g) $c\text{−}\mathrm{BN}$. DOS curves of (h) $\mathrm{R}2u-\mathrm{B}{\mathrm{C}}_2\mathrm{N}$ and (i) $c\text{−}\mathrm{BN}$ under various displacements u. The same isosurface level of $\pm 0.017\mathrm{electrons}/\mathrm{Boh}{\mathrm{r}}^3$ is used. Yellow and blue regions signify the states of charge accumulation (position) and depletion (negative), respectively. The Fermi level is set to zero. The electronic perturbations are highlighted as light purple areas in VCDDs.

Figure 5

COHP curves of several bonds around slip plane “S2” in $\mathrm{R}2u-\mathrm{B}{\mathrm{C}}_2\mathrm{N}$ under different slip displacements u: (a) $u=0.00$, and (b) $u=0.50$. The corresponding results for (c) $c\text{−}\mathrm{BN}$ are shown for comparison. The Fermi level is set to zero.