Electronic structures and strengthening mechanisms of superhard high-entropy diborides

High-entropy diborides (HEBs) have attracted extensive research due to their potential ultra-high hardness. In the present work, the effects of transition metals (TM) on lattice parameters, electron work function (EWF), bonding charge density, and hardness of HEBs are comprehensively investigated by the first-principles calculations, including (TiZrHfNbTa)B-2, (TiZrHfNbMo)B-2, (TiZrfifTaMo)B-2, (TiZrNbTaMo)B-2, and (TiHfNbTaMo)B-2. It is revealed that the disordered TM atoms result in a severe local lattice distortion and the formation of weak spots. In view of bonding charge density, it is understood that the degree of electron contribution of TM atoms directly affects the bonding strength of the metallic layer, contributing to the optimized hardness of HEBs. Moreover, the proposed power-law-scaled relationship integrating the EWF and the grain size yields an excellent agreement between our predicted results and those reported experimental ones. It is found that the HEBs exhibit relatively high hardness which is higher than those of single transition metal diborides. In particular, the hardness of (TiZrNbTaMo)B-2 and (TiHfNbTaMo)B-2 can be as high as 29.15 and 28.02 GPa, respectively. This work provides a rapid strategy to discover/design advanced HEBs efficiently, supported by the coupling hardening mechanisms of solid solution and grain refinement based on the atomic and electronic interactions.