A new hard phase of ReB4 predicted from first principles

•A new stable trigonal R-3m structure is uncovered for ReB4 by first-principles.•Calculated phonon and formation enthalpy confirm its stability.•Calculated elastic properties show that R-3m ReB4 should be a new ultra-incompressible hard material.

Using newly developed particle swarm optimization algorithm on crystal structural prediction, we predicted a trigonal R-3m structure for ReB4. Its structure, elastic properties, electronic structure, phase stability, and chemical bonding have been investigated by first-principles calculations with density functional theory. The results show that R-3m ReB4 is thermodynamically and mechanically stable. Our calculations on the enthalpy-pressure relationship and convex hulls have demonstrated R-3m ReB4 can be synthesized at ambient condition. The large bulk modulus, large shear modulus, large Young’s modulus, and small Poisson’s ratio show that ReB4 should be a new ultra-incompressible hard material. Further analysis on density of states and electron localization function demonstrate that there are strong B–B and B–Re covalent bonds in R-3m ReB4.