Brittle failure of orthorhombic borides from first-principles simulations

The orthorhombic boride family $XM{\mathrm{B}}₁₄$, where $X$ and $M$ are metal atoms, have been of great interest in hard coating applications because of such novel properties as high thermal stability, low density, chemical stability, and a low friction coefficient. However, the brittle failure of orthorhombic borides limits their mechanical stability under working environments and prevents their extended engineering applications. To provide guidelines of improving their stability, we employed density functional theory (DFT) to examine the bonding character and mechanical response of $XM{\mathrm{B}}₁₄$ under pure shear, biaxial shear, and tensile loading conditions. Two typical $XM{\mathrm{B}}₁₄$ compounds, ${\mathrm{AlLiB}}₁₄$ and $\mathrm{A}{\mathrm{l}}_0.75\mathrm{M}{\mathrm{g}}_0.78{\mathrm{B}}₁₄$, were examined to illustrate the effects of intrinsic metal vacancies. We find that the ideal strength for ${\mathrm{AlLiB}}₁₄$ is higher than that for $\mathrm{A}{\mathrm{l}}_0.75\mathrm{M}{\mathrm{g}}_0.75{\mathrm{B}}₁₄$, suggesting that ${\mathrm{AlLiB}}₁₄$ is intrinsically stronger than $\mathrm{A}{\mathrm{l}}_0.75\mathrm{M}{\mathrm{g}}_0.75{\mathrm{B}}₁₄$. The failure mechanism of both ${\mathrm{AlLiB}}₁₄$ and $\mathrm{A}{\mathrm{l}}_0.75\mathrm{M}{\mathrm{g}}_0.78{\mathrm{B}}₁₄$ arises from deconstructing ${\mathrm{B}}₁₂$ icosahedra under pure shear and biaxial shear conditions, while the structural failure under tensile deformation arises from breaking interlayer bonds between icosahedral layers.