Recently, synthesized WB${}_4$ has attracted great interest because it exhibits the highest microindentation hardness among transition-metal light-element compounds. The latest theoretical studies [see, e.g., Zhang et al., Phys. Rev. Lett. 108, 255502 (2012)] show, however, that the previously assigned WB${}_4$ structure is unstable; a WB${}_3$ structure was proposed as an alternative structural model. Here we show by first-principles calculations that the pressure beneath the indenter drives a lateral bond and volume expansion in the proposed WB${}_3$ and related MoB${}_3$ structures, resulting in an unexpectedly low indentation strength to a level well below that of ReB${}_2$. This is in direct contradiction to experimental results that show WB${}_4$ has higher indentation hardness compared to ReB${}_2$. Moreover, the calculated normalized $c/a$ ratio of WB${}_3$ (and MoB${}_3$) exhibits a negative pressure dependence, which is inconsistent with the experimentally observed trend. We therefore conclude that the proposed WB${}_3$ structure is incompatible with experimental results and that the question of the crystal structure of the synthesized (nominal) WB${}_4$ must be reopened for further study.

• Received 29 September 2012

DOI:https://doi.org/10.1103/PhysRevB.86.180101