First-principles calculation of the indentation strength ofFeB4

Abstract

A recent experiment [H. Y. Gou et al., Phys. Rev. Lett. 111, 157002 (2013)] reported a measured Vickers hardness of over 60 GPa for ${\mathrm{FeB}}_{4}$, placing it as a superhard material far above all other similar ultrahard transition-metal borides, such as ${\mathrm{ReB}}_{2},{\mathrm{WB}}_{4}$, and especially ${\mathrm{CrB}}_{4}$, which has the same crystalline structure as that of ${\mathrm{FeB}}_{4}$ but a much lower measured Vickers hardness of around 23 GPa. This result, however, is contradicted by theoretical calculations that predict a smaller shear modulus for ${\mathrm{FeB}}_{4}$ than that of ${\mathrm{CrB}}_{4}$, indicating that ${\mathrm{FeB}}_{4}$ is softer than ${\mathrm{CrB}}_{4}$. Here we report first-principles calculations that aim to understand the stress response of ${\mathrm{FeB}}_{4}$ under indentation loadings and examine whether there exists a strain-stiffening effect that might enhance the indentation strength. Our results show that there is no strain stiffening in ${\mathrm{FeB}}_{4}$; instead, the normal pressure beneath the indenter drives a lateral structural expansion which further stretches and weakens the boron-boron and boron-iron bonds in addition to that caused by the shear deformation in Vickers indentation tests. This effect leads to a considerably reduced strength of ${\mathrm{FeB}}_{4}$, producing an ideal (i.e., an upper bound) indentation strength of 17 GPa that is lower than that (27 GPa) predicted for ${\mathrm{CrB}}_{4}$. The present results suggest that ${\mathrm{FeB}}_{4}$ is unlikely to be superhard and further experimental investigation is needed to clarify this issue.