Unexpectedly hard and highly stable WB₃ with a noncompact structure

Tungsten borides are currently a topic of promising superhard materials, but their structures are still not fully resolved. Here, we identify a highly stable WB₃ in hR24 symmetry (hR24-WB₃) by first-principles calculations. It can be derived from well-known hP3-WB₂ by removing one third of tungsten atoms systematically so that the remaining tungsten atoms form three cycled layers of open hexagons with each a layer displaced by one atom. Furthermore, such a noncompact and metallic system has an unexpectedly high hardness, which originates from its three-dimensional covalent framework consisting of hexagonal boron planes interconnected with strong zigzag W-B bonds.