Using first-principles calculations, the structural stability, elastic strength, and formation enthalpies of four diborides MB2 (M = Tc, W, Re, and Os) are investigated by means of the pseudopotential plane-waves method, as well as the roles of covalency and bond topology in the phase incompressibility. Three candidate structures of known transition-metal diborides are chosen to probe. The calculated lattice parameters, elastic properties, Poisson’s ratio, and B/G ratio are derived. It is observed that the ReB2-type structure containing well-defined zigzag covalent chains exhibits an unusual incompressibility along the c axis comparable to that of diamond. Formation enthalpy calculations demonstrate that the ground-state phase is synthesizable at low pressure, whereas the other phase can be achieved through the phase transformation. Moreover, according to Mulliken overlap population analysis, a semiempirical method to evaluate the hardness of multicomponent crystals with a partial metallic bond is presented. The predicted hardness of WB2–WB2, ReB2–ReB2, and OsB2–OsB2 is in reasonable agreement with experiment data. Both strong covalency and a zigzag topology of interconnected bonds underlie the ultraincompressibilities. In addition, the superior performance and largest hardness of ReB2–ReB2 indicate that it is a superhard material. This work provides a useful guide for designing novel borides materials having excellent mechanical performances.

Using the first-principles calculations, the structural features, mechanical properties, formation enthalpies, electronic properties and hardness of osmium carbides with various stoichometries have been investigated systematically. The structural stability, thermodynamic stability together with mechanical stability show that Re 2 N−Os 2 C, OsB 2 −OsC 2 , trigonal P3̅ m1 OsC 2 , trigonal P3̅ m1 OsC 3 , orthorhombic Cmmm OsC 4 and Ru 2 Ge 3 −Os 2 C 3 are the most stable structure for each kind of compounds. But, OsB 2 −OsC 2 and Ru 2 Ge 3 −Os 2 C 3 are dynamically unstable based on the calculation of phonon dispersion. The formation enthalpies under high pressure indicate that the Re 2 N−Os 2 C, P3̅ m1 OsC 3 , Cmmm OsC 4 and Os 2 Si 3 −Os 2 C 3 (P4c2) have structural stabilities in the entire range of pressure. While for OsC 2 , there is a high pressure phase transition exists above 40 GPa. In addition, all the studied osmium carbides exhibit metallic behavior and strong covalent bonding. According to the calculated Vicker hardness based on a semiempirical method, we found that the OsC 4 with Cmmm space group has the largest hardness value (28.4 GPa). Combined with its largest shear modulus and Yong's modulus, smallest Poission's ratio and low B/G ratio, we predict it is a potential superhard material. By the comparison between the crystal structure of OsC 2 and OsC 3 , it is found that the increased C−C bonds in a cell increase their hardness, whereas the ionicity Os−Os bonds are unfavorable.

Using first-principles calculations, the elastic constant, structural phase transition and effect of metallic bonding on the hardness of OsN2 under high pressure are investigated by means of the pseudopotential plane-waves method. Five candidate structures are chosen to investigate for OsN2, namely, the pyrite, CoSb2-type, marcasite, simple hexagonal and tetragonal structures. A comparison among the formation energies of OsN2 explains the synthesis of OsN2 marcasite under high pressure. On the basis of the third-order Birch-Murnaghan equation of states, the transition pressure Pt (Pt = 223 GPa) between the marcasite and simple tetragonal phase is determinated. Elastic constants, shear modulus, Young's modulus, Poisson's ratio and Debye temperature are derived. The calculated values are, generally speaking, in good agreement with experiments and other theoretical calculations. Our calculation indicates that the N-N bond length is one determinative factor for the ultrahigh bulk moduli of the heavy-transition-metal dinitrides. Moreover, based on Mulliken overlap population analysis in first-principles technique, a semiempirical method to evaluate the hardness of multicomponent crystals with partial metallic bonding is presented. The effect of metallic bonding on the hardness of OsN2 is investigated and the hardness shows a gradual decrease rather than increase under compression, which is different from diamond. This is a quantitative investigation on the structural properties of OsN2, and it still awaits experimental confirmation.

Using first-principles calculations, the elastic constants, thermodynamic properties and structural phase transition of NbN under high pressure are investigated by means of the pseudopotential plane-waves method, in addition to the effect of metallic bonding on its hardness. Three candidate structures are chosen to investigate NbN, namely, rocksalt (NaCl), NiAs and WC types. On the basis of the third-order Birch-Murnaghan equation of states, the transition pressure Pt (Pt = 200.64 GPa) between the WC phase and the NaCl phase of NbN is predicted for the first time. Elastic constants, formation enthalpies, shear modulus, Young's modulus, and Poisson's ratio of NbN are derived. The calculated results are found to be in good agreement with the available experimental data and theoretical values. According to the quasi-harmonic Debye model, the Debye temperature under high pressure is derived from the average sound velocity. Moreover, the effect of metallic bonding on the hardness of NbN is investigated and the hardness shows a gradual decrease rather than increase under compression. This is a quantitative investigation on the structural and thermodynamic properties of NbN, and it still awaits experimental confirmation.

In this work, we predicted three new two-dimensional (2D) Be 2 C structures, namely, α-Be 2 C, β-Be 2 C, and γ-Be 2 C, on the basis of density functional theory (DFT) computations and the particle-swarm optimization (PSO) method. In α-Be 2 C, a carbon atom binds to eight Be atoms, forming an octacoordinate carbon moiety. This is the first example of an octacoordinate carbon containing material. The other two structures, β-Be 2 C and γ-Be 2 C, are quasi planar hexacoordinate carbon (phC) containing 2D materials. Good stability with these three phases is revealed by their lower cohesive energy and positive phonon modes. More interestingly, these predicted new phases of Be 2 C are all semiconductors and have unusual negative Poisson's ratios (NPRs). If synthesized, 2D Be 2 C materials will have a broad range of applications in electronics and mechanics.

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