Influence of uniaxial strains on the mechanical properties of transition metal borides X2B, XB and XB2 (X = Cr, Mo, W)

Borides of chromium, molybdenum, and tungsten are an attractive class of transition-metal light-element compounds with superior mechanical properties. Here, we explore in detail the binary X2B with I4∕m and I4∕mcm symmetry, XB with 141/amd and Cmcm symmetry as well as XB2 with P6∕mmm and P63∕mmc (X = Cr, Mo, W) systems by first principles calculations, especially their mechanical properties under uniaxial strains along the c axis. We report the calculated ideal tensile strength for each structure, which is the minimum stress required to break the material. The elastic constants, bulk modulus, shear modulus, and Young's modulus are calculated at equilibrium and uniaxial strains. For the same structure, WB compounds are more ductile than Cr-B and Mo-B because of their high B∕G ratio, while they fail to possess high hardness at the same time. The structures belong to space group P63∕mmc have the largest hardness, followed by 141-XB. Although with the highest boron content, hardness values for 191-XB2 are much lower than 194-XB2 phases with the same composition. The anisotropy of X-B systems has also been studied, which is rare in previous reports. The underlying mechanism for the high elastic modulus and hardness of XB systems is further discussed by the analysis of electronic density of states.