Structural, elastic, mechanical and thermodynamic properties of HfB4 under high pressure

摘要

The present work aims to study the structural, elastic, mechanical and thermodynamic properties of the newly discovered orthorhombic Cmcm structure HfB₄ (denoted as Cmcm -HfB₄ hereafter) under pressure by the first-principles calculations. The obtained equilibrium structure parameters and ground-state mechanical properties were in excellent agreement with the other theoretical results. The calculated elastic constants and phonon dispersion spectra show that Cmcm -HfB₄ is mechanically and dynamically stable up to 100?GPa and no phase transition was observed. An analysis of the elastic modulus indicates that Cmcm -HfB₄ possesses a large bulk modulus, shear modulus and Young's modulus. The superior mechanical properties identify this compound as a possible candidate for a superhard material. Further hardness calculation confirmed that this compound is a superhard material with high hardness (45.5?GPa for GGA); and the relatively strong B–B covalent bonds’ interaction and the planar six-membered ring boron network in Cmcm -HfB₄ are crucial for the high hardness. Additionally, the pressure-induced elastic anisotropy behaviour has been analysed by several different anisotropic indexes. By calculating the B / G and Poisson's ratio, it is predicted that Cmcm -HfB₄ possesses brittle behaviour in the range of pressure from 0 to 100?GPa, and higher pressures can reduce its brittleness. Finally, the thermodynamic properties, including enthalpy (Δ H ), free energy (Δ G ), entropy (Δ S ), heat capacity ( C_V ) and Debye temperature ( Θ_D ) are obtained under pressure and temperature, and the results are also interpreted.