The structure and hardness of the highest boride of tungsten, a borophene-based compound

Two-dimensional systems have strengthened their position as a key materials for novel applications. Very recently, boron joined the distinguished group of elements confirmed to possess 2D allotropes, named borophenes. In this work, we explore the stability and hardness of the highest borides of tungsten, which are built of borophenes separated by metal atoms. We show that the WB_3+x compounds have Vickers hardnesses approaching 40 GPa only for small values of x. The insertion of extra boron atoms is, in general, detrimental to the hardness of WB₃ because it leads to the formation of quasi-planar boron sheets that are less tightly connected with the adjacent tungsten layers. Very high concentrations of boron (x ≈ 1), give rise to a soft (Vickers hardness of ~8 GPa) and unstable hP20-WB₄ structure that can be considered to be built of quasi-planar boron α-sheets separated by graphitic tungsten layers. By contrast, we show that the formation of tungsten vacancies leads to structures, e.g. W_0.75B_3+x , with Vickers hardnesses that are not only similar in value to the experimentally reported load-independent hardnesses greater than 20 GPa, but are also less sensitive to variations in the boron content.