Interstitial-Boron Solution Strengthened WB$_{3+x}$

By means of variable-composition evolutionary algorithm coupled with density functional theory and in combination with aberration-corrected high-resolution transmission electron microscopy experiments, we have studied and characterized the composition, structure and hardness properties of WB$_{3+x}$ ($x$ $<$ 0.5). We provide robust evidence for the occurrence of stoichiometric WB$_3$ and non-stoichiometric WB$_{3+x}$ both crystallizing in the metastable $hP$16 ($P6_3/mmc$) structure. No signs for the formation of the highly debated WB$_4$ (both $hP$20 and $hP$10) phases were found. Our results rationalize the seemingly contradictory high-pressure experimental findings and suggest that the interstitial boron atom is located in the tungsten layer and vertically interconnect with four boron atoms, thus forming a typical three-center boron net with the upper and lower boron layers in a three-dimensional covalent network, which thereby strengthen the hardness.