The elastic and mechanical properties of MB12 (M = Zr, Hf, Y, Lu) as a function of pressure

By means of plane-wave density functional first-principles calculations within the generalized gradient approximation (GGA), we report the structural, elastic and mechanical properties of MB12 (M = Zr, Hf, Y, Lu) with UB12-type structure. The lattice constants, bulk modulus, elastic constants and related quantities such as Young’s modulus, shear modulus, Zener anisotropy factor, Poisson’s ratio and Cauchy pressure are calculated and compared with the available experimental and other theoretical data. A deeper understanding, the pressure variations of the lattice constants, bulk modulus, elastic constants and other mechanical properties are also analyzed in a wide pressure range (0–50 GPa) and their trends are discussed. Additionally, Mulliken population analysis is used to clarify the bonding nature of all compounds. Combining the bonding nature and the structural information, microhardnesses of all compounds are calculated theoretically and then the detailed comparisons between hardness and other mechanical properties such as bulk modulus and shear modulus are made.

► MB12 (M = Zr, Hf, Y, Lu) with UB12–type structure dodecaboride compounds by first principles calculations have been given.
► All of MB12 compounds possess the high hardnesses comparable to superhardness limit (40 GPa) and the order of hardness is ZrB12 > HfB12 > YB12 > LuB12.
► The results are observed that total hardness of all compounds almost linearly increase with pressure.