Unravelling the structure and strength of the highest boride of tungsten ${\mathrm{WB}}_{4.2}$

Tungsten tetraboride is outstanding among transition-metal light-element compounds for its easy synthesis and superior mechanical properties. Its crystal structure, however, has eluded scientists for over half a century, impeding fundamental understanding and rational property optimization. Recent x-ray and neutron diffraction studies suggest rare boron trimers occupying vacant metal sites in the highest boride of tungsten ${\mathrm{WB}}_{4.2}$, but a viable crystal structure and key mechanical properties remain unresolved. Here we identify a ${\mathrm{WB}}_{4.2}$ phase in orthorhombic symmetry with a very large 104-atom unit cell using a tailored search algorithm treating boron trimer as a coherent unit. First-principles studies establish phase stability and unveil the mechanism for strength enhancement by newly identified bonding features. These findings solve a challenging crystal structure and elucidate its benchmark mechanical behaviors. This work offers powerful insights for exploring novel structures and properties of materials containing intricate multiatomic constituent structural units.

Figure 1

Crystal structure of $Cmcm{\mathrm{WB}}_{4.2}$. (a) The 104-atom unit cell comprising 20 tungsten and 84 boron atoms, represented by large and small balls, respectively. Boron trimers, shown in green, occupy vacant tungsten sites. The unit cell is divided into four layers, where layers $A$ and $B$ are related to $C$ and $D$ by proper symmetry operations. Balls in different colors indicate electron gain or loss by a Bader charge analysis listed in (b), which gives a planar view of atomic arrangements in layers $A$ and $B$. (c) Electron localization function in layers $A$ and $B$, and the boron trimer in (d), which shows a 15-atom boron tetradecagon, termed B15, comprising a boron trimer connected to two boron hexagons in adjacent layers.

Figure 2

Structural stability and characterization of $Cmcm{\mathrm{WB}}_{4.2}$. (a) Convex hull where filled (open) symbols represent stable (metastable) structures [29]. (b) Phonon dispersion curves. (c) Mean-squared displacements of atomic positions versus time at 300 K. (d),(e) Simulated XRD and neutron spectra of ${\mathrm{WB}}_{4.2}$ compared to the refined experimental XRD and neutron spectra [26]. X-ray and neutron wavelength are 1.540 56 Å and 1.08 Å, respectively.

Figure 3

Stress-strain relations of $Cmcm{\mathrm{WB}}_{4.2}$ along major crystallographic directions under (a) tensile, (b) pure shear, and (c) Vickers indentation shear loadings. Also shown are bond-breaking modes in each case along the loading path shortly past the lowest peak stress as indicated on pertinent stress curves. Only the boron atoms in the unit cell are shown for clarity.