Correlation between hardness and pressure of CrB4

Abstract

The correlation between hardness and pressure for two different structures of CrB₄ is investigated by a first-principles approach. With increasing pressure, the hardness gradually decreases, in contrast to the bulk modulus, shear modulus, Young's modulus and B/G ratio, which monotonically increase. Pressure gives rise to a hardness transition from a superhard to a hard material, which is in good agreement with the experimental data. Moreover, the pressure leads to a brittle-to-ductile transition at 200 GPa based on the analysis of the B/G ratio, which is consistent with the hardness trend. The analysis of the density of states and chemical bonding implies that pressure induces electronic compression and collapse in localized regions, and the variation in hardness originates from the bond reversal between the B–B (3) and B–B (2) covalent bonds, which are located at the applied load plane. Finally, we conclude that the hardness of CrB₄ under pressure is related to the B/G ratio and bond characteristics.