Elastic anisotropies and thermodynamic properties of metal dodecborides under high pressure

Abstract The elastic anisotropy and thermodynamic properties of MB12 (M = Zr, Hf, Y and Sc) compounds with UB12-type structure have been investigated by combining the first principles with the quasi-harmonic Debye model. The results show that these structures exhibit strong resistance to the uniaxial stress. The Young’s modulus E is 50% higher than bulk modulus B and shear modulus G and the latter two are very close to each other. All MB12 compounds are brittle at 0 GPa. The Vickers hardness values are all lower than that of the traditional threshold for super hard material (40 GPa). Comparative studies reveal that ZrB12 and HfB12 show similar fracture toughness, while ScB12 shows the lowest one. Elastic anisotropy is evaluated by the universal anisotropy index AU, Emax/Emin, anisotropy shear Ashear, shear factor A1 and the 3D surface constructions of Young’s modulus. 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. The pressure and temperature dependence of the heat capacity, thermal expansion coefficient and Debye temperature of MB12 are also comprehensively discussed. These results will be able to meet the multifunctional requirements of these multifunctional materials in production.