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. 2018 Jul 25;5(7):180701.
doi: 10.1098/rsos.180701. eCollection 2018 Jul.

Structural, Elastic, Mechanical and Thermodynamic Properties of HfB 4 Under High Pressure

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Free PMC article

Structural, Elastic, Mechanical and Thermodynamic Properties of HfB 4 Under High Pressure

Jing Chang et al. R Soc Open Sci. .
Free PMC article

Abstract

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 (ΔH), free energy (ΔG), entropy (ΔS), heat capacity (CV ) and Debye temperature (ΘD ) are obtained under pressure and temperature, and the results are also interpreted.

Keywords: HFB4; first-principles; mechanical properties; structural properties; thermodynamic properties.

Conflict of interest statement

We declare we have no competing interests.

Figures

Figure 1.
Figure 1.
(a) Optimized energetically most stable crystal structures of Cmcm-HfB4 at zero pressure; (b) HfB12 polyhedron and (c) B4 unit chain in the structure.
Figure 2.
Figure 2.
The normalized parameters X/X0(X = a, b, c and V), ρ/ρ0 of Cmcm-HfB4 as a function of pressure.
Figure 3.
Figure 3.
(a) Elastic constants, (b) elastic moduli, (c) Debye temperature ΘD—unit cell volume and (d) variation of the G/B—Poisson ratio (ν) of the Cmcm-HfB4 compounds under pressure. The inset in (c) shows the Debye temperature as a function of the unit cell.
Figure 4.
Figure 4.
Calculated DOS of the Cmcm-HfB4 at 0 and 100 GPa. The vertical dashed line shows the Fermi level EF.
Figure 5.
Figure 5.
(ad) Direction-dependent Young's modulus (GPa) and its plane projections for Cmcm-HfB4 at 0 (a,b) and 100 GPa (c,d).
Figure 6.
Figure 6.
(a) Calculated phonon dispersion curves along the high-symmetry directions; and (b) density of phonon states for Cmcm-HfB4 at P = 0 and 100 GPa.
Figure 7.
Figure 7.
(a) Temperature dependence of enthalpy, free energy and T*S; and (b) heat capacity dependence of temperature for Cmcm-HfB4 at P = 0 and 100 GPa.

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