Brittle failure of β- and τ-boron: Amorphization under high pressure

Element boron tends to form an icosahedral motif involving 26 electrons, leading to intriguing bonding conditions which complicate understating the structural variations under high pressure. Here we used density function theory (DFT) to examine the mechanical response of \ensuremath{\beta}- and recent discovered \ensuremath{\tau}-boron to shear along the most plausible slip system. We found that the failure mechanism of $\ensuremath{\beta}\ensuremath{-}{\mathrm{B}}₁₀₆$ is fracturing a ${\mathrm{B}}₂₈$ triply fused icosahedral cluster without destroying a regular ${\mathrm{B}}₁₂$ icosahedron, while the failure of $\ensuremath{\tau}\ensuremath{-}{\mathrm{B}}₁₀₆$ arises from the disintegration of a ${\mathrm{B}}₂₈$ cluster and one nearby icosahedron. The failure of $\ensuremath{\beta}\ensuremath{-}{\mathrm{B}}₁₀₆$ leads to a ${\mathrm{B}}₁₂$-embedded amorphous structure which transforms to the second amorphous phase with a fully deconstructed icosahedra at 81 GPa. The second amorphous phase retains the deconstructed icosahedra at ambient conditions which is different from the normal amorphous boron containing regular icosahedra which are bonded randomly to each other. The second amorphous phase is more stable than $\ensuremath{\beta}\ensuremath{-}{\mathrm{B}}₁₀₆$ above 90 GPa, which explains the previous experiments on pressure-induced amorphization. In addition, forming the second highest density amorphous phase likely causes the brittle failure of \ensuremath{\beta}-B and related materials.