Crystal structures and formation mechanisms of boron-rich tungsten borides

Boron-rich tungsten borides tend to adopt mechanically unfavorable layered structures but experimentally exhibit excellent mechanical properties rivalling traditional superhard solids. Unravelling the contraindicated structure-property relationship, however, has been impeded by their structural ambiguities because of the difficulty in probing boron and atomic deficiency of these borides. Here, we study crystal structures of boron-rich tungsten borides WB3+x, and WB2+x, by neutron diffraction based on high-quality samples prepared by a high-pressure method, leading to definitive structural resolutions for both borides with unique compositions of WB5.14 and WB2.34. Combined with theoretical calculations, their structural stability is revealed to be closely related to atomic deficiency, which is governed by the valence-band filling with an optimal valence-electron concentration of similar to 10 per cell. The presence of interstitial boron trimers at the vacant W : 2b sites in WB5.14 alters the crystal symmetry, making the Wyckoff 2d site more favorably occupied by W, rather than the 2c site, as previously misassigned. The staggered planar boron layers and wrinkled boron bonding in WB2.34 are identified to be crucial for stabilizing its structure. These findings unveil the longstanding structural mysteries of boron-rich tungsten borides and offer powerful insights for rational design of borides by defect chemistry.