Stability and mechanical properties of W1−xMoxB4.2 ( x=0.0–1.0 ) from first principles

Abstract

Heavy transition-metal tetraborides (e.g., tungsten tetraboride, molybdenum tetraboride, and molybdenum-doped tungsten tetraboride) exhibit superior mechanical properties, but solving their complex crystal structures has been a long-standing challenge. Recent experimental x-ray and neutron diffraction measurements combined with first-principles structural searches have identified a complex structure model for tungsten tetraboride that contains a boron trimer as an unusual structural unit with a stoichiometry of 1:4.2. In this paper, we expand the study to binary ${\mathrm{MoB}}_{4.2}$ and ternary ${\mathrm{W}}_{1\ensuremath{-}x}{\mathrm{Mo}}_{x}{\mathrm{B}}_{4.2}$ ($x=0.0--1.0$) compounds to assess their thermodynamic stability and mechanical properties using a tailor-designed crystal structure search method in conjunction with first-principles energetic calculations. Our results reveal that an orthorhombic ${\mathrm{MoB}}_{4.2}$ structure in $Cmcm$ symmetry matches well the experimental x-ray diffraction patterns. For the synthesized ternary Mo-doped tungsten tetraborides, a series of ${\mathrm{W}}_{1\ensuremath{-}x}{\mathrm{Mo}}_{x}{\mathrm{B}}_{4.2}$ structures are theoretically designed using a random substitution approach by replacing the W to Mo atoms in the $Cmcm$ binary crystal structure. This approach leads to the discovery of several ${\mathrm{W}}_{1\ensuremath{-}x}{\mathrm{Mo}}_{x}{\mathrm{B}}_{4.2}$ structures that are energetically superior and stable against decomposition into binary ${\mathrm{WB}}_{4.2}$ and ${\mathrm{MoB}}_{4.2}$. The structural and mechanical properties of these low-energy ${\mathrm{W}}_{1\ensuremath{-}x}{\mathrm{Mo}}_{x}{\mathrm{B}}_{4.2}$ structures largely follow the Vegard's law. Under changing composition parameter $x=0.0--1.0$, the superior mechanical properties of ${\mathrm{W}}_{1\ensuremath{-}x}{\mathrm{Mo}}_{x}{\mathrm{B}}_{4.2}$ stay in a narrow range. This unusual phenomenon stems from the strong covalent network with directional bonding configurations formed by boron atoms to resist elastic deformation. The findings offer insights into the fundamental structural and physical properties of ternary ${\mathrm{W}}_{1\ensuremath{-}x}{\mathrm{Mo}}_{x}{\mathrm{B}}_{4.2}$ in relation to the binary ${\mathrm{WB}}_{4.2}/{\mathrm{MoB}}_{4.2}$ compounds, which open a promising avenue for further rational optimization of the functional performance of transition-metal borides that can be synthesized under favorable experimental conditions for wide applications.