First-Principles Design Of Novel Superhard Be₃N₂

Superhard materials play an important role in a variety of industrial applications. Along with science and technology development, intense efforts have been focused on the design novel superhard materials in recent years. It is commonly accepted that superhard materials are those strongly three-dimensional covalent bonded compounds formed by light elements such as B, C, N and O, for example, diamond, c-BN, c-BC2N, B6O and B4C. However, one of the lightest elements, beryllium, has been often neglected to synthesize superhard materials. Earlier theoretical prediction indeed demonstrated that the beryllium compounds are promising hard materials. In particularly, the B12N2Be has been predicted to be superhard with the calculated hardness of 48.7 GPa and a metastable polymorph of beryllium nitride (γ-Be3N2) has been proposed to possess a high hardness of 51.5 GPa. It is therefore greatly desirable to explore the beryllium compounds in pursuing new superhard materials.Here, we mainly focus on Be3N2, which has been demonstrated to be synthesizable in experiment. In this paper, we ha ve extensively explored the stable and metastable structures of beryllium nitride by using the genetic algorithm,the large scale pressures in the range 0 ~ 150 GPa were also applied in search of the superhard polymorphs. First principles calculations were then performed to investigate the lattice parameters, bulk modulus, hardness, total energies, and density of states of the predicted structures. we uncovered two new crystal structures-R3m (15 atoms/cell, Struct1) and P-3m1 (5 atoms/cell, Struct2) reported here for the first time. For R3m structure, each N1 is bonded with five Be atoms, while N2 with six Be atoms. Interestingly, in P-3m1 phase N has a higher degree of Be neighbors, reaching seven. This illustrates nicely the new chemistry of nitrogen under high pressure. It shows that the ability to form chemical bonding for nitrogen can be tuned by pressure. The calculated enthalpy difference indicates that the R3m phase is a metastable structure, but the predicted P-3m1 structure becomes energetically preferable toβ-phase above 76 GPa and becomes most stable above 118 GPa among all the phases. What's more, we predicted R3m phase could be synthesized at a higher temperature about 2000-3000 K. However, the P-3m1 structure becomes most stable above 118 GPa. An application of temperature and pressure is thus greatly applicable to synthesize this compound. According the results of formation enthalpies, the two predicted structures are thermodynamic stability in the whole pressure range studied. The densities of states (DOS) of the two phases indicated that R3m and P-3m1 structures are wide gap dielectric materials characterized by large energy gaps of ~2.8 and ~4.3 eV. Both of them with strong Be-N covalent bonding characters which are signaled by the significant hybridization of Be 2p orbital with N 2p orbital. We calculated the zero-pressure elastic constants Cij of the predicted structures through strain-stress theory. The results suggested the Born criterion are clearly satisfied for rhombohedral and hexagonal stability, confirming that both the structural phases are mechanically stable. The large C33 (401 GPa for R3m and 416 GPa for P-3m1) in the two structures manifests that the c axial direction is extremely stiff. In addition, both phases exhibit high bulk modulus of 210 or 220 GPa, indicating ultra-incompressible structural nature. Therefore, the new structures are expected to be a possible superhard material.Remarkably, the calculated polycrystalline hardness using Gao's Mulliken model is 51 GPa for R3m and 54 GPa for P-3m1, which are greater than 40 GPa. This illustrates that the two phases belong to excellent superhard materials, and are harder than many known superhard materials, such as B6O (45 GPa) and B4C (49 GPa) . The origin of the high hardness of the two compounds can be traced to the very large Mulliken overlap population Pμof Be-N bonds (strong Be-N covalent bonding). Pμin R3m is in the range of 0.36-0.57, comparable to that (0.39) of B4C, while in P-3m1 the largest Pμvalue reaches 0.53 contributing mostly (42.9%) to the total bonds. Note that the smallest Pμin P-3m1 is only 0.07, but this type of bond only accounts for 14.3% of the total bonds. We are looking forward further studies of Be3N2 in experiment.