Tungsten borides are among a distinct class of transition-metal light-element compounds with superior mechanical properties that rival those of traditional superhard materials. An in-depth understanding of these compounds, however, has been impeded by uncertainties regarding their complex crystal structures. Here, we examine a wide range of chemical compositions of tungsten borides using a recently developed global structural optimization approach. We establish thermodynamically stable structures and identify a large number of metastable phases. These results clarify and correct previous structural assignments and predict new structures for possible synthesis. Our findings provide crucial insights for understanding the rich and complex crystal structures of tungsten borides, which have broad implications for further exploration of this class of promising materials.

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A novel body-centered tetragonal CN(2) (4 units per cell), named as bct-CN(2), has been predicted here using our newly developed particle swarm optimization algorithm for crystal structure prediction. Bct-CN(2) is energetically much superior (3.022 eV per f.u.) to previously proposed pyrite structure and stable against decomposition into a mixture of diamond + N(2) or 1/3(C(3)N(4) + N(2)) above 45.4 GPa. No imaginary phonon frequencies in the whole Brillouin zone indicate bct-CN(2) is dynamically stable. The electronic calculations indicate that bct-CN(2) is a wide gap dielectric material with an indirect band gap of 3.6 eV. The ideal tensile, shear, and compressive strength at large strains of bct-CN(2) are examined to understand further the microscopic mechanism of the structural deformation. Strikingly, it is found that bct-CN(2) has high calculated ideal strength, bulk modulus, shear modulus, and simulated hardness, indicating its very incompressible and superhard nature. The results provide new thoughts for designing and synthesizing novel superhard carbon nitrides, and insights for understanding the mechanical properties.