First-Principles Investigation on the Structural, Mechanical, and Bonding Properties of ZrB₂ Under Different Pressures

The crystal structures of zirconium diboride have been thoroughly explored up to 200 GPa by applying the particle-swarm optimization technique in company with first-principles calculations. The hexagonal ZrB2 with space group of P6/mmm is always stable in the pressure region of 0-200 GPa. Structurally, this structure consists of the intriguing regular ZrB1(2) hexagonal column and the planar hexagonal B ring unit. In addition, the stable AlB2-ZrB2 configuration is mechanically and dynamically stable as confirmed by the respective calculations of elastic constants and phonon dispersion curves. The hardness values exhibit a shrinking variation upon further compression, which mainly originates from the decreasing brittleness and degree of the directionality of the covalent bonds with the growing pressure. Interestingly, the analyses of the Poisson's ratio, density of states, electron location function and Bader charge substantiate that a combination of covalent and ionic characters exists in the AlB2-ZrB2 crystalline with the formidable covalent interaction in the B-B bonds, and partially covalent and partially ionic interactions in the Zr-B bonds. The hardness value for this phase unexpectedly reaches 45.41 GPa under ambient pressure, higher than the lower limit of superhard materials.