Structural, elastic, mechanical and thermodynamic properties of HfB 4 under high pressure

Abstract

The present work aims to study the structural, elastic, mechanical and thermodynamic properties of the newly discovered orthorhombic Cmcm structure HfB 4 (denoted as Cmcm -HfB 4 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 -HfB 4 is mechanically and dynamically stable up to 100 GPa and no phase transition was observed. An analysis of the elastic modulus indicates that Cmcm -HfB 4 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 -HfB 4 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 -HfB 4 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.