Ultra-hard materials, characterized by a hardness exceeding 40 GPa, showcase remarkable mechanical properties such as superior wear resistance and compressive strength, outperforming traditional hard materials. The mid-20th-century breakthroughs in techniques like powder metallurgy and high-pressure synthesis have established ultra-hard materials as a distinct and advancing field within materials science. Among these materials, diamond and cubic boron nitride (cBN) stand out as prime examples, finding extensive application across various industries including resource extraction, precision processing, electronics, aerospace, and scientific research. Despite their exceptional properties, diamonds are limited by their low oxidation temperature and reactivity with iron, while cBN, although chemically stable and effective for processing ferrous metals, has a lower hardness compared to diamond. These limitations highlight the need for the development of new ultra-hard materials that can combine the strengths of both diamond and cBN. B-C-N compounds, composed of boron, carbon, and nitrogen, benefit from the strong covalent bonds formed due to their close proximity in the periodic table, endowing them with exceptional chemical stability and mechanical strength. Their robust lattice structures contribute to their durability and toughness, making them highly suitable for applications that demand high stability and strength. Recent research has delved into various B-C-N materials: Nakano et al. (1994) synthesized cubic BCN phases under high-pressure and high-temperature conditions, Komatsu et al. (1996) produced cBC_2.5N with notable nano-scale characteristics and a bulk modulus greater than that of cBN, and Solozhenko et al. (2001) synthesized cubic BC₂N blocks with a remarkable hardness of 76 GPa, surpassing cBN. The advent of advanced computer technology has seen first-principles calculations based on density functional theory play a significant role in materials design. Researchers have proposed various BCN structures, such as orthogonal BC₂N (Mattesini et al., 2001) and zinc blende BC₂N (Sun et al.), which have shown potential as ultra-hard materials. Gao et al. (2018) introduced BC₆N structures with mixed hybridization, demonstrating one-dimensional conductive properties.This study presents two novel BCN structures that are stable under ambient pressure and possess both ultra-hard properties and excellent conductivity. This represents a significant advancement in the research of metallic ultra-hard materials and provides essential theoretical foundations for their future practical applications in materials science.

The structural models were constructed in the Materials Visualizer module of Materials Studio. The property calculations for the two different structures were performed using the CASTEP software package on the basis of density functional theory. The calculations employed ultrasoft pseudopotentials, and the exchange-correlation functional (GGA) was chosen to be the Perdew-Burke-Ernzerhof (PBE) form of the generalized gradient approximation. After a series of convergence tests, the plane wave cutoff energy was set to 630 eV; the first Brillouin zones of all structures were meshed using the Monkhorst-Pack method, with the spacing of the K-point grid set to 2π × 0.04 Å⁻¹. The convergence criteria for the structural relaxation process were for the total energy of the structure, the maximum ionic displacement, the maximum internal stress, and the change in the Hellmann-Feynman force for the ions to be less than 5.0 × 10⁻⁶ eV/atom, 5.0 × 10⁻⁴ Å, 0.02 GPa, and 0.01 eV/Å, respectively. The elastic constants and electronic band structures of the structures were calculated using the primitive cell. The phonon spectra of the two structures were calculated using the finite displacement method.

The results show that both P2/m-BCN and Pm-BCN structures are elastic and dynamically stable. Their thermodynamic stability was assessed by calculating formation enthalpies at various pressures. Both structures have positive formation enthalpies, indicating higher energy than graphite and hBN, necessitating external forces like high pressure or catalysts for formation. Beyond a critical pressure, the enthalpy becomes negative, suggesting these BCN structures can be synthesized from graphite and hBN.

Using the HSE06 mixed functional method, we studied their electronic properties under atmospheric pressure, revealing a certain degree of conductivity. Projected density of states (PDOS) calculations indicate that the conductivity is primarily due to the 2p orbitals of carbon and boron atoms, highlighting the role of orbital hybridization.

Mechanical property analysis shows that P2/m-BCN and Pm-BCN have bulk and shear moduli slightly lower than cBN, indicating high incompressibility and shear resistance. Vickers hardness calculations yield 43.7 GPa and 49.9 GPa for P2/m-BCN and Pm-BCN, respectively, confirming their potential as superhard materials.

Stress-strain studies reveal a high tendency for cleavage on the (001) plane, suggesting brittle fracture along this direction. Notably, P2/m-BCN exhibits a unique bimodal stress-strain curve along the [100] direction, indicating a staged fracture process: initial selective bond breaking, partial stress release, and subsequent network failure under higher strain. This provides insights into the mechanical stability and fracture toughness of these structures.

This study successfully designs two novel BCN structures, P2/m-BCN and Pm-BCN, via first-principles calculations. These structures exhibit exceptional elastic and dynamical stability as metastable phases at ambient pressure, establishing a theoretical basis for potential applications. Structural analysis indicates that P2/m-BCN has sp²-hybridized carbon atoms, while Pm-BCN contains boron-nitrogen units, endowing them with unique electronic structures and metallic properties. Mechanical assessments reveal high strength and rigidity, with the lowest tensile strengths along the [001] direction (39.7 GPa for P2/m-BCN and 42.4 GPa for Pm-BCN), suggesting a strong cleavage tendency on the (001) plane. Notably, P2/m-BCN exhibits a distinctive double-peak stress-strain behavior along the [100] direction. Electron localization function (ELF) analysis reveals a stepwise fracture mechanism: initial B-N bond rupture leads to partial stress release, followed by load transfer to the C-C network, which fails at higher strain. This highlights the transient load-bearing capacity of heterogeneous bonding networks. Overall, these metastable metallic BCN phases enhance the structural diversity of superhard materials, combining high mechanical strength, metallicity, and tunable anisotropic fracture behavior. These findings offer new theoretical insights for designing superhard multifunctional materials, with promising applications in cutting, wear resistance, and extreme environments.