“…The Vickers hardness is estimated by [ 56 ] where K represents the G / B ratio and G is the shear modulus. Using the model, the estimated Vickers hardness H v of Cmcm -HfB 4 is in good agreement with a previous study [ 38 ]. The high hardness of Cmcm -HfB 4 probably stems from the relatively strong B–B covalent bonding and the presence of a planar boron six-membered ring unit in Cmcm -HfB 4 structure.…”
Section: Resultssupporting
confidence: 89%
“…From figure 5 , one can discover that the (001) plane exhibits isotropic property but the (100) and (010) planes exhibit anisotropic behaviour at 0 GPa; these results are consistent with those obtained by Zhang et al . [ 38 ] In addition, from figure 5 c , d , it is not difficult to find that the anisotropy is significant with increase in pressure, which is in accordance with the above analysis from the anisotropy factor. Figure 5.…”
Section: Resultssupporting
confidence: 85%
“…The calculated bulk modulus, shear modulus, Young's modulus and Poisson's ratio of the Cmcm -HfB 4 together with the reference materials mentioned above are also listed in table 3 . From table 3 , one can find that the presented elastic moduli are consistent with that of [ 38 ] and the LDA results are larger than the GGA ones. Generally, a large elastic modulus means high hardness of materials.…”
Section: Resultssupporting
confidence: 85%
“…From table 2 , our results are in reasonable agreement with those obtained by Zhang et al . [ 38 ]. The good agreement between the current and previous results supports the accuracy and reliability of our elastic calculations.…”
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.
“…The Vickers hardness is estimated by [ 56 ] where K represents the G / B ratio and G is the shear modulus. Using the model, the estimated Vickers hardness H v of Cmcm -HfB 4 is in good agreement with a previous study [ 38 ]. The high hardness of Cmcm -HfB 4 probably stems from the relatively strong B–B covalent bonding and the presence of a planar boron six-membered ring unit in Cmcm -HfB 4 structure.…”
Section: Resultssupporting
confidence: 89%
“…From figure 5 , one can discover that the (001) plane exhibits isotropic property but the (100) and (010) planes exhibit anisotropic behaviour at 0 GPa; these results are consistent with those obtained by Zhang et al . [ 38 ] In addition, from figure 5 c , d , it is not difficult to find that the anisotropy is significant with increase in pressure, which is in accordance with the above analysis from the anisotropy factor. Figure 5.…”
Section: Resultssupporting
confidence: 85%
“…The calculated bulk modulus, shear modulus, Young's modulus and Poisson's ratio of the Cmcm -HfB 4 together with the reference materials mentioned above are also listed in table 3 . From table 3 , one can find that the presented elastic moduli are consistent with that of [ 38 ] and the LDA results are larger than the GGA ones. Generally, a large elastic modulus means high hardness of materials.…”
Section: Resultssupporting
confidence: 85%
“…From table 2 , our results are in reasonable agreement with those obtained by Zhang et al . [ 38 ]. The good agreement between the current and previous results supports the accuracy and reliability of our elastic calculations.…”
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.
“…Therefore, research has focused on the boron-rich borides such as TMB 3 , TMB 4 and TMB 12 in recent years. [17][18][19][20][21] However, the investigation of boron-rich boride faces two key problems: one is that the boron-rich boride has difficulty meeting stable conditions. For example, the published TMB 12 mainly focuses on the ZrB 12 and HfB 12 .…”
The crystal structures of zirconium diboride have been thoroughly explored up to 200 GPa by applying the particle‐swarm optimization technique in company with first‐principles calculations. The hexagonal ZrB2 with space group of P6/mmm is always stable in the pressure region of 0–200 GPa. Structurally, this structure consists of the intriguing regular ZrB12 hexagonal column and the planar hexagonal B ring unit. In addition, the stable AlB2–ZrB2 configuration is mechanically and dynamically stable as confirmed by the respective calculations of elastic constants and phonon dispersion curves. The hardness values exhibit a shrinking variation upon further compression, which mainly originates from the decreasing brittleness and degree of the directionality of the covalent bonds with the growing pressure. Interestingly, the analyses of the Poisson's ratio, density of states, electron location function and Bader charge substantiate that a combination of covalent and ionic characters exists in the AlB2–ZrB2 crystalline with the formidable covalent interaction in the BB bonds, and partially covalent and partially ionic interactions in the ZrB bonds. The hardness value for this phase unexpectedly reaches 45.41 GPa under ambient pressure, higher than the lower limit of superhard materials.
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