A first-principles study of orthorhombic CN as a potential superhard material

De Novo Inverse Design Superhard C-N Compounds via Global Machine Learning Interatomic Potentials and Multiobjective Optimization Algorithm

A major challenge in the field of superhard materials is the identification of compounds with a hardness exceeding that of diamond. In this study, we developed a variable-composition inverse material design (VC-IMD) approach for designing C-N superhard materials. In this approach, an improved multiobjective optimization algorithm is introduced, utilizing structure similarity constraint to prevent convergence toward local minima. Combined with active learning, it trains global machine learning interatomic potentials (g-MLIPs) while exploring target materials. By comparing several g-MLIPs and selecting the best, the resulting g-MLIPs achieved reasonable precision within three iterations. Through multiple searches, 38 novel and stable C-N superhard materials not present in major computational materials databases were identified. Notably, the material C3(P6422) with a hardness of 97.4 GPa was discovered, potentially exceeding that of diamond (94.0 GPa). This approach provided a new pathway for materials design with target properties.

Electron deficiency but semiconductive diamond-like B2CN originated from three-center bonds

B2CN was one of the synthesized light element compounds, which was expected to be superhard material with a metallic character due to its electron deficienct nature. However, in this work, we discovered two novel semiconducting superhard B2CN phases using particle swarm intelligence technique and first-principles calculations, which were reported to have three-dimensional and four coordinated covalent diamond-like structures. These two new phases were calculated to be dynamically stable at zero and high pressures, and can be deduced from the previously reported Pmma phase by pressure-induced structural phase transitions. More importantly, unlike the previously proposed metallic B2CN structures, these two new phases combine superhard (the calculated Vickers hardness reached ∼55 GPa) and semiconducting character. The semiconducting behavior of the newly predicted B2CN phases breaks the traditional view of the metallic character of the electron deficient diamond-like B-C-N ternary compounds. By a detail analyzation of the electron localization functions of these two new phases, three-center bonds were reported between some B, C and B atoms, which were suggested to be the primary mechanism that helps the compound overcome its electron-deficient nature and finally exhibit a semiconducting behavior.

New Spiral Form of Carbon Nitride with Ultrasoftness and Tunable Electronic Structures

The structural diversity and multifunctionality of carbon nitride materials distinct from pure carbon materials are drawing increasing interest. Using first-principles calculations, we proposed a stable spiral structure of carbon nitride, namely spiral-C3N, which is composed of sp2-hybridized carbon and pyridine nitrogen with a 60° helical symmetry along the z-direction. The stability was verified from the cohesive energy, phonon spectrum, and elastic constants. Despite the strong covalent bonds of the spiral framework, the spiral-C3N exhibits a hardness lower than 12.00 GPa, in sharp contrast to the superhardness of cubic carbon nitrides reported in previous literature, which can be attributed to the unique porous configuration. The softness of the spiral-C3N was also confirmed by the small ideal strengths, which are, respectively, 33.00 GPa at a tensile strain of 0.22 along the [1̅21̅0] direction and 18.00 GPa at a shear strain of 0.52 in the (0001)[1̅21̅0] direction. Electronic band structure of spiral-C3N exhibits metallic features. A metal-semiconductor transition can be triggered by hydrogenation of the pyridine nitrogen atoms of spiral-C3N. Such a new three-dimensional spiral framework of sp2-hyperdized carbon and nitrogen atoms not only enriches the family of carbon nitride materials but also finds application in energy conversion and storage.

Ground-state structures, physical properties and phase diagram of carbon-rich nitride C5N

Using the ab initio evolutionary algorithm, four thermodynamically stable C₅N phases ([Formula: see text], [Formula: see text]-1, [Formula: see text]-2 and C2/m) are uncovered. The structures of the [Formula: see text], [Formula: see text]-1 and [Formula: see text]-2 phases possess layered features. The dense C2/m phase with 3D strong covalent bond network is calculated to be superhard with hardness of 75.4 and 83.9 GPa by Chen and Gao models. The electronic properties of the C₅N is diverse including conductor ([Formula: see text]), indirect semiconductor ([Formula: see text]-1 and [Formula: see text]-2) and direct semiconductor (C2/m). Pressure-induced phase transition sequences and critical pressure points are calculated to be [Formula: see text]  →  [Formula: see text]-1  →  [Formula: see text]-2 at 2.7 and 34 GPa, respectively. Though the C2/m phase is metastable at zero temperature, our established pressure-temperature phase diagram of C₅N shows that the C2/m becomes stable under high temperatures and pressures. The pressure-temperature phase diagram will give theoretical guidance for further experimental synthesis of different C₅N phases.

First-principles study of the electronic and optical properties of a new metallic MoAlB

The structural, elastic, electronic and optical properties of MoAlB were investigated by first-principles calculations. The hardness of MoAlB is 12.71 GPa, which is relatively softer and easily machinable compared to the other borides. The analysis of the band structure and density (DOS) of states indicates that MoAlB has a metallic nature. The analysis of the electron localization function (ELF) shows that the Mo-B bond is a polar covalent bond with a short distance, which may increase the stability of the compound. The calculation of the phonon frequencies confirms the dynamical stability of MoAlB. Optical properties of MoAlB are investigated. In the energy range up to ~19 eV, MoAlB possesses high reflectivity and has the strongest absorption in the energy range of 0-23.0 eV. In addition, the plasma frequency of MoAlB is 20.4 eV and MoAlB can change from a metallic to a dielectric response if the incident light has a frequency greater than 20.4 eV.

First-principles investigation on elastic and thermodynamic properties of Pnnm-CN under high pressure

The elastic anisotropy and thermodynamic properties of the recently synthesized Pnnm-CN have been investigated using first-principles calculations under high temperature and high pressure. The calculated equilibrium crystal parameters and normalized volume dependence of the resulting pressure agree with available experimental and theoretical results. Within the considered pressure range of 0-90 GPa, the dependences of the bulk modulus, Young's modulus, and shear modulus on the crystal orientation for Pnnm-CN have been systematically studied. The results show that the Pnnm-CN exhibits a well-pronounced elastic anisotropy. The incompressibility is largest along the c-axis. For tension or compression loading, the Pnnm-CN is stiffest along [001] and the most obedient along [100] direction. On the basis of the quasi-harmonic Debye model, we have explored the Debye temperature, heat capacity, thermal expansion coefficient, and Grüneisen parameters within the pressure range of 0-90 GPa and temperature range of 0-1600K.

Cubic C₃N: A New Superhard Phase of Carbon-Rich Nitride

Using the particle swarm optimization technique, we proposed a cubic superhard phase of C₃N (c-C₃N) with an estimated Vicker’s hardness of 65 GPa, which is more energetically favorable than the recently proposed o-C₃N. The c-C₃N is the most stable phase in a pressure range of 6.5–15.4 GPa. Above 15.4 GPa, the most energetic favorable high pressure phase R3m-C₃N is uncovered. Phonon dispersion and elastic constant calculations confirm the dynamical and mechanical stability of c-C₃N and R3m-C₃N at ambient pressure. The electronic structure calculations indicate that both c-C₃N and R3m-C₃N are indirect semiconductor.

Two Novel C₃N₄ Phases: Structural, Mechanical and Electronic Properties

We systematically studied the physical properties of a novel superhard (t-C₃N₄) and a novel hard (m-C₃N₄) C₃N₄ allotrope. Detailed theoretical studies of the structural properties, elastic properties, density of states, and mechanical properties of these two C₃N₄ phases were carried out using first-principles calculations. The calculated elastic constants and the hardness revealed that t-C₃N₄ is ultra-incompressible and superhard, with a high bulk modulus of 375 GPa and a high hardness of 80 GPa. m-C₃N₄ and t-C₃N₄ both exhibit large anisotropy with respect to Poisson’s ratio, shear modulus, and Young’s modulus. Moreover, m-C₃N₄ is a quasi-direct-bandgap semiconductor, with a band gap of 4.522 eV, and t-C₃N₄ is also a quasi-direct-band-gap semiconductor, with a band gap of 4.210 eV, with the HSE06 functional.

Low-density superhard materials: computational study of Li-inserted B-substituted closo-carboranes LiBC11 and Li2B2C10

Insertion of Li atoms into a B-substituted carbon cage produces two superhard compounds with relatively low density: LiBC₁₁ and Li₂B₂C₁₀.