Intrinsic hardness of crystalline solids

Tse, John S.

doi:10.3103/s1063457610030044

Cited by 70 publications

(45 citation statements)

References 46 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…[40][41][42][43][44][45] The predicted hardness for FeB 4 is ~11-32 GPa (Table I), which is half that of the experimental value and much less than those found in diamond (~90 GPa) and c-BN (~65 GPa). Interestingly, these results indicate FeB 4 is not as superhard as suggested by experiment.…”

Section: Resultsmentioning

confidence: 72%

Hardness of FeB4: Density functional theory investigation

Zhang

et al. 2014

The Journal of Chemical Physics

View full text Add to dashboard Cite

A recent experimental study reported the successful synthesis of an orthorhombic FeB 4 with a high hardness of 62(5) GPa [Gou et al., Phys. Rev. Lett. 111,157002 (2013)], which has reignited extensive interests on whether transition-metal borides (TRBs) compounds will become superhard materials. However, it is contradicted with some theoretical studies suggesting transition-metal boron compounds are unlikely to become superhard materials. Here, we examined structural and electronic properties of FeB 4 using density functional theory. The electronic calculations show the good metallicity and covalent Fe-B bonding. Meanwhile, we extensively investigated stress-strain relations of FeB 4 under various tensile and shear loading directions. The calculated weakest tensile and shear stresses are 40 GPa and 25 GPa, respectively.Further simulations (e.g. electron localized function and bond length along the weakest loading direction) on FeB 4 show the weak Fe-B bonding is responsible for this low hardness. Moreover, these results are consistent with the value of Vickers hardness (11.7-32.3 GPa) by employing different empirical hardness models and below the superhardness threshold of 40 GPa. Our current results suggest FeB 4 is a hard material and unlikely to become superhard (> 40 GPa).2

show abstract

Section: Resultsmentioning

confidence: 72%

Hardness of FeB4: Density functional theory investigation

Zhang

et al. 2014

The Journal of Chemical Physics

View full text Add to dashboard Cite

show abstract

“…Thus, the computed bulk and shear moduli of I-42d (Pna2 1 -8fu) structures at 0 GPa are 130 GPa and 131 GPa (142 GPa and 124 GPa), respectively. Using the empirical hardness and shear modulus relationship (27), we estimate the hardness of Pna2 1 -8fu and I-42d structures to be 22 GPa and 21 GPa, respectively. These estimated values are verified from ab initio calculations of the ideal strengths of the I-42d and Pna2 1 -8fu structures.…”

Section: Metastability Of Co 2 -V At Ambient Pressurementioning

confidence: 99%

Crystal structures and dynamical properties of dense CO ₂

Yong

Liu

et al. 2016

Proc. Natl. Acad. Sci. U.S.A.

View full text Add to dashboard Cite

Structural polymorphism in dense carbon dioxide (CO 2 ) has attracted significant attention in high-pressure physics and chemistry for the past two decades. Here, we have performed high-pressure experiments and first-principles theoretical calculations to investigate the stability, structure, and dynamical properties of dense CO 2 . We found evidence that CO 2 -V with the 4-coordinated extended structure can be quenched to ambient pressure below 200 K-the melting temperature of CO 2 -I. CO 2 -V is a fully coordinated structure formed from a molecular solid at high pressure and recovered at ambient pressure. Apart from confirming the metastability of CO 2 -V (I-42d) at ambient pressure at low temperature, results of ab initio molecular dynamics and metadynamics (MD) simulations provided insights into the transformation processes and structural relationship from the molecular to the extended phases. In addition, the simulation also predicted a phase V′(Pna2 1 ) in the stability region of CO 2 -V with a diffraction pattern similar to that previously assigned to the CO 2 -V (P2 1 2 1 2 1 ) structure. Both CO 2 -V and -V′ are predicted to be recoverable and hard with a Vicker hardness of ∼20 GPa. Significantly, MD simulations found that the CO 2 in phase IV exhibits large-amplitude bending motions at finite temperatures and high pressures. This finding helps to explain the discrepancy between earlier predicted static structures and experiments. MD simulations clearly indicate temperature effects are critical to understanding the high-pressure behaviors of dense CO 2 structures-highlighting the significance of chemical kinetics associated with the transformations.carbon dioxide | molecular dynamics | high pressure | material science S olid carbon dioxide (CO 2 ) has a phase diagram rich in polymorphs, which exhibit great diversity in intermolecular interactions, chemical bonding, and crystal structures (1-7). Colloquially known as dry ice, solid CO 2 has a cubic Pa3 structure (phase I) under ambient pressure (8). At around 10 GPa, the cubic structure transforms to another molecular phase (Cmca, phase III) with different stacking pattern of CO 2 molecules. At sufficient compression, the molecular O = C = O bonds in solid CO 2 are replaced by an extended network of single C-O bonds, forming CO 4 tetrahedral units with sp 3 hybridized carbon atoms. The onset of such transformation occurs at 20 GPa, where the phase III transforms to a pseudotetragonal phase II (P4 2 /mnm or Pnnm) above ∼500 K and then to phase IV (P4 1 2 1 2 β-cristobalite structure) above ∼750 K (9-12). Continuing the compression to 40 GPa and then heating the product to 1,800 K, CO 2 further transforms to a nonmolecular polymeric strucutre V TD with the tridymite-like P2 1 2 1 2 1 structure (13, 14). Interestingly, following a different synthesis path, that is, heating the phase III first at 20 GPa and then compressing the product to 39 GPa and heating it again to ∼1,800 K, a different polymeric phase (CO 2 -V CR ) in a β-cristobalite-like I-42d structu...

show abstract

“…Therefore, we can conclude that the failure mode in T-carbon is dominated by the shear deformation type in the (100)<001> slip system. The calculated shear stress of 7.3 GPa basically sets the upper bound on its mechanical strength at zero pressure 44,45 , because the ideal strength is the stress where a defect-free crystal becomes unstable and undergoes spontaneous plastic deformation. It is well-known that the measurement of hardness has to first encounter the elastic deformation and then experience permanent plastic deformation.…”

Section: Fig 2: Vickers Hardnessmentioning

confidence: 99%

Hardness ofT-carbon: Density functional theory calculations

et al. 2011

View full text Add to dashboard Cite

We revisit and interpret the mechanical properties of the recently proposed allotrope of carbon, T-carbon [Sheng et al., Phys. Rev. Lett., 106, 155703 (2011)], using density functional theory in combination with different empirical hardness models. In contrast with the early estimation based on the Gao's model, which attributes to T-carbon an high Vickers hardness of 61 GPa comparable to that of superhard cubic boron nitride (c-BN), we find that T-carbon is not a superhard material, since its Vickers hardenss does not exceed 10 GPa. Besides providing clear evidence for the absence of superhardenss in T-carbon, we discuss the physical reasons behind the failure of Gao's andŠimůnek and Vackář's (SV) models in predicting the hardness of T-carbon, residing on their improper treatment of the highly anisotropic distribution of quasi-sp 3 -like C-C hybrids. A possible remedy to the Gao and SV models based on the concept of superatom is suggest, which indeed yields a Vickers hardness of about 8 GPa.

show abstract

Intrinsic hardness of crystalline solids

Abstract: Intrinsic hardness of crystalline solidsThe

Cited by 70 publications

References 46 publications

Hardness of FeB4: Density functional theory investigation

Hardness of FeB4: Density functional theory investigation

Crystal structures and dynamical properties of dense CO ₂

Hardness ofT-carbon: Density functional theory calculations

Contact Info

Product

Resources

About

Intrinsic hardness of crystalline solids

Abstract: Intrinsic hardness of crystalline solidsThe

Cited by 70 publications

References 46 publications

Hardness of FeB4: Density functional theory investigation

Hardness of FeB4: Density functional theory investigation

Crystal structures and dynamical properties of dense CO 2

Hardness ofT-carbon: Density functional theory calculations

Contact Info

Product

Resources

About

Crystal structures and dynamical properties of dense CO ₂