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Using first-principles calculations, we have investigated osmium carbides with various stoichiometries (i.e., OsC, Os2C3, and OsC2). It is found that the predicted cubic OsC is of about 0.29 eV/(formula unit) lower in energy than previously proposed NiAs–OsC at ambient conditions. The plot of the computed enthalpy as a function of pressure indicates that cubic OsC is more stable than NiAs–OsC up to about 33 GPa. Moreover, cubic OsC shows a semiconductor character with a narrow gap of about 0.5 eV. The hypothetical P-4c2 and Pbcn Os2C3 show large incompressibility with their bulk moduli being about 360 GPa. P-4c2 Os2C3 exhibits the semiconductor character, while Pbcn Os2C3 metallic. Among the considered osmium carbides, the two hexagonal OsC2 have larger shear moduli, which indicates that they are potential superhard materials, and the total density of states suggest they are metallic. We have also discussed the dependence of shear modulus on carbon content. It was found that the shear modulus increases with the increased carbon content, and that the strong C–C bond in OsC2 is helpful to its high shear modulus. It is also found that a sublinear relationship exists between the Debye temperature and shear modulus.

First-principles calculations were carried out on recently synthesized Re₂N and Re₃N as well as hypothetical Tc and Mn nitrides. It is found that structure and covalent bonds play an important role in determining mechanical properties. Under a large strain along (0001)<1010> direction, Re₂N undergoes a phase transformation with a slight increase in ideal shear strength. On the other hand, it is transformed into a phase with weaker mechanical properties, if the strain is along Re₂ <1210> direction. Mn₂N can be synthesized under moderate conditions due to its more negative formation energy. Re₂N, Re₃N, and Mn₂ N show structure-related mechanical property under larger strains to ReB₂ but exhibit much lower ideal strengths, which is attributed to the larger ionicity of cation-anion bond. Three-dimensional framework of strong covalent bonds is thus highly recommended to design superhard materials.

First-principles calculations were carried out to investigate the structural stability of synthesized orthorhombic Ta 2 N 3 . It is found that the stoichiometric orthorhombic Ta 2 N 3 is unstable below 20 GPa. However, it can be stabilized by a small amount of nitrogen vacancies or oxygen substitution into nitrogen sites. The calculated electron localization function indicates that both the formation of nitrogen vacancy and the substitution of oxygen atom can enhance the Ta-N bonding, which is essential for the structural stability. Furthermore, both oxygen substitution and nitrogen vacancy plays a similar role in stabilizing the orthorhombic lattice of Ta 2 N 3 . The results of our calculations show that nitrogen vacancies or oxygen substitution into nitrogen sites can alter the charge distribution over the unit cell, which leads to a new arrangement of atoms and enhanced Ta-N bonds.