Crystal structures and formation mechanisms of boron-rich tungsten borides

Abstract

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 $\mathrm{W}{\mathrm{B}}_{3+x}$ and $\mathrm{W}{\mathrm{B}}_{2+x}$ 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 $\mathrm{W}{\mathrm{B}}_{5.14}$ and $\mathrm{W}{\mathrm{B}}_{2.34}$. 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 \ensuremath{\sim}10 per cell. The presence of interstitial boron trimers at the vacant $\mathrm{W}:2b$ sites in $\mathrm{W}{\mathrm{B}}_{5.14}$ 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 $\mathrm{W}{\mathrm{B}}_{2.34}$ 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.