Elastic anisotropies and thermodynamic properties of metal dodecborides under high pressure

Highlights: • The effects of pressure and temperature on elastic anisotropy and thermodynamic properties of MB₁₂ compounds areinvestigated. • The mechanical behaviors of MB₁₂ (M = Hf, Y, Zr and Sc) compounds are compared and discussed. • Two- dimensional and three-dimensionalfigures are used to analyze the elastic anisotropy and thermodynamic properties of MB₁₂ compounds. The elastic anisotropy and thermodynamic properties of MB₁₂ (M = Hf, Y, Zr and Sc) compounds have been investigated by combining the first principles with the quasi-harmonic Debye model. The negative values of cohesive energy indicate these compounds are thermodynamic stability. The results of elastic constants and elastic modulus explain that these compounds exhibit high hardness and strong anti-uniaxial stress ability. But the Vickers hardness values are all lower than that of the traditional threshold for superhard material (40 GPa). The B/G ratio and Poisson's ratio ν reveal that all MB₁₂ compounds are brittle at 0 GPa. ZrB₁₂ and HfB₁₂ possess similar fracture toughness, while ScB₁₂ possesses the lowest one. The 3D contours of the Young's modulus of four materials are very similar at both 0 GPa and 100 GPa. Also, pressure can increase the anisotropy for MB₁₂ compounds. The pressure and temperature dependence of the heat capacity, thermal expansion coefficient and Debye temperature of MB₁₂ compounds are also comprehensively discussed. These findings are of great value for the applications of these multifunctional materials in electromechanical and medical engineering.