Physical Properties Of Ultra-incompressible B₃N₄ Under High Pressure Predicted From First Principles

Superhard materials are particularly useful in a variety of industrial applications because of their excellent physical and chemical properties.Superhard materials can be formed by light elements（B,C,N,O,and Si）with three-dimensional,directional and strong covalent bonds.Theoretical investigations indicate that five C3N4 polymorphs are potential superhard materials,and five B4C3 polymorphs with identical structures of the five C3N4 polymorphs also are potential superhard materials.Therefore,we speculate that five B₃N₄ polymorphs with the same structures of the five C3N4 polymorphs might be potential superhard materials.Density functional theory calculations for B₃N₄ polymorphs were performed,and the exchange correlation functional was treated within the Perdew-Burke-Ernzerhof（PBE）generalized gradient approximation（GGA）.The structural,mechanical,and electronic properties of the five hypothetical ultra-incompressible B₃N₄ polymorphs at zero pressure and high pressure were obtained.Through the quasiharmonic Debye model,we also investigated the thermodynamic properties of the B₃N₄ polymorphs under high temperature and high pressure.In this paper,chapter one introduces the current research situation and research significance of superhard materials and boron nitride compounds.Chapter two and chapter three introduce the theoretical knowledge for density functional theory,elasticity,and hardness,and the VASP and GIBBS software.Chapter four introduces the structural,mechanical,electronic,and thermodynamic properties of five B₃N₄ polymorphs,i.e.,α-B₃N₄（space group P31c）,β-B₃N₄（P63/m）,c-B₃N₄（I43d）,cs-B₃N₄（Fd3m）,and p-B₃N₄（P42m）,under zero pressure and high pressure.Chapter five is the summary and outlook for this paper.The main conclusion of this paper as follows:（1）Five B₃N₄ structures are established by substitution of C atoms with B atoms in the five hypothetical dense C3N4 phases,and their lattice parameters are consistent with available theoretical values.After geometry optimization,these B₃N₄ polymorphs（except cs-B₃N₄）are thermodynamically stable at 0 K and 0 GPa.（2）According to the calculated elastic constants at 0 GPa,the mechanical stability tests are satisfied for the five B₃N₄ polymorphs.It is predicted that the c-B₃N₄,cs-B₃N₄,and p-B₃N₄ are mechanically stable within 100 GPa,while the β-B₃N₄ and α-B₃N₄ become mechanically unstable when pressure increases to 30 and 80 GPa,respectively.（3）The ground state energy of c-B₃N₄ is the lowest among the five B₃N₄ polymorphs,and c-B₃N₄ possesses superior mechanical strength,such as high shear modulus（248 GPa）.Through empirical hardness formula,the calculated hardness value of c-B₃N₄ is 34.2 GPa,which indicates that it might be a potential ultra-incompressible and hard material.It is possible to experimentally fabricate the B₃N₄ phase with the lowest ground state energy and the metastable B₃N₄ phase.（4）The calculated B/G ratios indicated that c-B₃N₄ and α-B₃N₄ are brittle materials at zero pressure,while the two structures are prone to ductility at high pressure.The pB₃N₄,cs-B₃N₄,and β-B₃N₄ are ductile materials.（5）The calculated band structures and electronic density of states of the five B₃N₄ polymorphs show that all of them are insulators.With the increase of pressure from 0 to 100 GPa,the bandgaps of B₃N₄ polymorphs will be slightly widened.We expect that this work will provide certain reference for experimental synthesis and theoretical research in the quest for novel ultra-incompressible and hard materials,especially,in binary boron nitride compounds.