New ultrahard rhombohedral B₂N₂ and BC₂N – or hexagonal B₆N₆ and B₃C₆N₃ – are derived from 3R graphite based on crystal chemistry rationale schematizing a mechanism for 2D → 3D transformation. Full unconstrained geometry optimizations leading to ground state energy structures and energy derived quantities as energy-volume equation of states (EOS) and the elastic constants were based on computations within the density functional theory (DFT) with generalized gradient approximation (GGA) for exchange-correlation (XC) effects. The new binary and ternary phases are characterized by tetrahedral stacking alike diamond, visualized with charge density representations, and illustrating ion characters. Atom averaged total energies are similar between cubic BN and rh-B₂N₂ on one hand, and larger stabilization of rhombohedral BC₂N versus cubic and orthorhombic forms (in literature) assigned to favorable C–C and B–N bonding, on the other hand. The electronic band structures are characteristic of insulators with E_gap ~5 eV. Both phases are characterized by large bulk and shear moduli and high hardness values.

新的超硬菱形 B ₂ N ₂和 BC ₂ N – 或六边形 B ₆ N ₆和 B ₃ C ₆ N ₃– 源自基于晶体化学原理的 3R 石墨，对 2D → 3D 转换机制进行了示意图。完全不受约束的几何优化导致基态能量结构和能量导出量作为能量-体积状态方程 (EOS) 和弹性常数基于密度泛函理论 (DFT) 内的计算和广义梯度近似 (GGA) 交换-相关 (XC) 效应。新的二元和三元相的特征是四面体堆叠，类似于金刚石，通过电荷密度表示进行可视化，并说明离子特征。一方面，立方BN和rh-B ₂ N ₂之间的原子平均总能量相似，并且菱形BC _{2 的}稳定性更大另一方面，N 与立方和正交形式（在文献中）分配给有利的 C-C 和 B-N 键合。电子能带结构是具有 E_间隙~5 eV的绝缘体的特征。两相的特点是体积和剪切模量大，硬度值高。