Potential Superhard Material Research Articles

First-principles study of influence of transition metal doping on the physical properties of TiB3

Superhard materials possess a multitude of advantageous properties and are utilized in a plethora of fields. The calculated hardness of TiB3 is 41.6 GPa and those of all TM-doped TiB3 are higher than 40 GPa, thereby indicating that TiB3 and TM-doped TiB3 are potential superhard materials. This paper presents a comprehensive study of the electronic, elastic and thermal properties, fracture toughness and damage tolerance of TiB3 and its doped transition metals (TMs, including Sc, V, Y, Zr, Nb, Hf and Ta) through the use of first-principles calculations. These materials are thermodynamically, kinetically and mechanically stable, as evidenced by the dispersion of phonon and Debye temperature. Furthermore, calculations were performed to determine the impact of doping on the brittleness and toughness of the materials, with specific attention paid to hardness, fracture toughness and elastic modulus. The anisotropy of the doped material is analysed through the projection of the 3D surface structure and the 2D Young's modulus. The metallic nature of these materials is revealed by energy band structure and density of states analyses. Finally, the effect of doping on the thermodynamic properties of the materials is explored by means of Debye temperature and sound velocity evaluations.

Predicting potential hard materials in Nb[sbnd]B ternary boride: First-principles calculations

To identify potential superhard materials, we conducted a comprehensive theoretical investigation of the thermodynamic and kinetic stability, mechanical properties, electronic structure, Debye temperatures and melting point of sixteen ternary transition metal borides NbTMBx (x = 1, 2, 4 and TM = Ti, V, Fe, Co, Ni, Zr, Ru, Hf, W, Os) using first-principles methods. Our findings indicate that, with the exception of NbFeB, NbRuB, and NbWB, all other borides exhibit both thermodynamic and kinetic stability. Notably, NbTiB4, NbVB4, NbZrB4 and NbHfB4 demonstrate superior hardness and enhanced resistance to deformation, with NbTiB4 showing an impressive hardness value of 40.84 GPa, positioning it as a promising candidate for superhard materials. Both NbVB4 and NbTiB4 have very high Debye temperatures and melting points and can be used in high temperature environments. We further explored the mechanical properties of NbTiB4 at elevated temperatures by employing a combination of first-principles and quasi-static methods. Our analysis reveals that the elastic constants and moduli of NbTiB4 decrease with increasing temperature. Additionally, bonding analysis indicates that all NbB ternary borides exhibit hybridization involving metallic, ionic, and covalent interactions, resulting in the formation of exceptionally strong covalent bonds between boron atoms.

Enhancing the Vickers hardness of Yttrium borides through bond optimization

The hard nature of transition metal boride reminds a conundrum. Compared to the diboride, we propose that the high hardness of transition metal boride strongly depends on the structural feature and bonding state (bond type, bond number and bond direction) in addition to the network B-B covalent bond. To demonstrate our idea, we symmetrically study the structural configuration, hardness, elastic properties and bonding state of the B-rich Y-B borides by using the first-principles method. The hexagonal YB2, tetragonal YB4, cubic YB6 and cubic YB12 are studied. The convex hull implies that YB4 has better thermodynamic stability in comparison to the YB2, YB6 and YB12. Importantly, it is found that the calculated Vickers hardness of the cubic YB12 is 41.4 GPa, indicating that YB12 is a potential superhard material. However, the Vickers hardness of YB2, YB4 and YB6 is lower than 40 GPa. Naturally, the high harness of YB12 is determined by the network B-B covalent bond. For non-superhard materials (YB2, YB4 and YB6), the hardness is related not only to the 3D network B-B covalent bond but also to the structural feature and bond state, particularly for TM-B bond. Compared to the strong B-B covalent bond, the Y-B bond plays an important role in harness because the Y-B bond is not surrounded by the 3D network B-B covalent bond. Therefore, we believe that the bond type and bond arrangement play an important role in hardness. This work can provide new design rule to adjust the structural feature and bond state to enhance the Vickers hardness of transition metal borides superhard materials.

A pressure-induced superhard SiCN4 compound uncovered by first-principles calculations.

Silicon-carbon-nitride (Si-C-N) compounds are a family of potential superhard materials with many excellent chemical and physical properties; however, only SiCN, Si2CN4 and SiC2N4 were synthesized. Here, we theoretically report a new SiCN4 compound with P41212, Fdd2 and R3̄ structures by first-principles structural predictions based on the particle swarm optimization algorithm. Pressure-induced structural phase transitions from P41212 to Fdd2, and then to the R3̄ phase were determined at 2 GPa and 249 GPa. By comparing enthalpy differences with 1/3Si3N4 + C + 4/3N2, it was found that these structures tend to decompose at ambient pressure. However, with the increase of pressure, the enthalpy differences of Fdd2 and R3̄ structures turn to be negative and they can be stabilized at a pressure of more than 41 GPa. They are also dynamically stable as no imaginary frequencies were found in their stabilized pressure ranges. The calculated band gap is 4.37 eV for P41212, 3.72 eV for Fdd2 and 3.81 eV for the R3̄ phase by using the Heyd-Scuseria-Ernzerhof (HSE06) method and the estimated Vickers hardness values are higher than 40 GPa by adopting the elastic modulus based hardness formula, which confirmed their superhard characteristics. These results provide significant insights into Si-C-N systems and will inevitably promote the future experimental works.

Hardness and superconductivity in tetragonal LiB4 and NaB4.

Boron-based compounds have triggered substantial attention due to their multifunctional properties, incorporating excellent hardness and superconductivity. While tetragonal metal borides LiB4 and NaB4 with BaAl4-type structure and striking clathrate boron motif have been induced under compression, there is still a lack of deep understanding of their potential properties at ambient pressure. We herein conduct a comprehensive study on I4/mmm-structured LiB4 and NaB4 under ambient pressure via first-principles calculations. Remarkably, both LiB4 and NaB4 are found to possess high Vickers hardness of 39GPa, which is ascribed to the robust boron framework with strong covalency. Furthermore, their high hardness values together with distinguished stability make them highly potential superhard materials. Meanwhile, electron-phonon coupling analysis reveals that both LiB4 and NaB4 are conventional phonon-mediated superconductors, with critical temperatures of 6 and 8K at 1 atmosphere pressure (atm), respectively, mainly arising from the coupling of B 2p electronic states and the low-frequency phonon modes associated with Li-, Na-, and B-derived vibrations. This work provides valuable insights into the mechanical and superconducting behaviors of metal borides and will boost further studies of emergent borides with multiple functionalities.

Design and investigated a novel BN polymorph in orthorhombic phase

In this work, a new BN polymorph with Pnma symmetry is proposed by RG2 and investigated by density functional theory. Pnma-II BN polymorph is shown to be dynamically and mechanically stable, and the relative enthalpy of Pnma-II BN is 0.187 eV per atom higher than that of c-BN, respectively. Mechanical properties calculations indicate that Pnma-II BN is also a potential superhard material with hardness of 49.7 GPa. The electronic band structures of Pnma-II BN show that the Pnma-II BN is a direct and ultrawide band gap semiconductor (band gap is 5.82 eV). The mechanical anisotropy of Young's modulus of Pnma-II BN and Pnma BN is greater than that of c-BN, while the mechanical anisotropy of shear modulus of Pnma-II BN in the (100), (001) plane is lower than that of c-BN. In addition, simulated X-ray diffraction patterns are provided for experimental confirmation of the predicted structures.

Density functional theory calculations of mechanical and electronic properties of W1−xTaxN6, W1−xMoxN6, and Mo1−xTaxN6 (0 ≤ x ≤ 1) alloys in a hexagonal structure

In this study, we report the structural, energetic, mechanical, electronic, thermal, and magnetic properties of W1−xTaxN6, W1−xMoxN6, and Mo1−xTaxN6 (0 ≤ x ≤ 1) alloys in a hexagonal structure (space group: R3¯m) determined using density functional theory–based first-principles calculations. These compounds are mechanically stable, whereas W0.33Ta0.66N6 is vibrationally unstable. Among both mechanically and vibrationally stable compounds, W0.66Ta0.33N6 and W0.66Mo0.33N6 have the highest hardness of 55 GPa, while the softest alloy (Mo0.33Ta0.66N6) exhibits 46 GPa, indicating new potential super hard materials. The high hardness in these materials is attributed to the combined effect of covalent N–N bonding of hexagonal rings and a metal to nitrogen charge transfer. Only two alloys, W0.33Mo0.66N6 and W0.66Mo0.33N6, are semiconducting alloys with electronic bandgaps of 1.82 and 1.92 eV, respectively. A significant magnetic moment of 0.82 μB per unit metal was calculated for W0.66Mo0.33N6.

Superhard and superconductive polycrystalline boron doped diamond synthesized with different concentration of B4C

Boron doped diamond are potential superhard materials with good electric conductivity. In this work, polycrystalline boron doped diamond (p-BDD) with different boron concentration were synthesized from the mixture of graphite and boron carbide under ultra-high pressure (15 GPa) and temperature (2500–2700 K). The results indicate that no more boron atoms can be inserted into diamond when the boron concentration is above 4 at%. The EELS spectra indicated that the boron atoms have been doped into the diamond grains, and surplus boron carbide locate at the grain boundary. The hardness measurements reveal that the p-BDD doped with 1 at% and 23 at% boron atoms exhibit high hardness of 78.5 GPa and 45 GPa, respectively, which is equivalent to the hardness of single crystal diamond and cubic boron nitride. The p-BDD is a semiconductor and transforms into superconductive state below 2.5 K. According to microstructure measurements, highly dense p-BDD and B4C bonded diamond exhibit superhard behavior because of the strong bonding of diamond grains by B4C additives. The oxidation temperature of these p-BDD specimens is around 1538 K in the air, which is far higher than diamond. B4C is demonstrated as a superior additive to sinter superhard and electric conductive p-BDD, which are extremely useful in areas where high hardness and electric conductive are highly desired.

The lattice vibration, mechanical anisotropy, stress-strain behavior and electronic properties of HfxSiy phases: A first-principles study

The lattice vibrations, elastic anisotropy, electronic properties and stress-strain behavior of HfxSiy phases were predicted using a first-principles calculations. The enthalpies of formation and lattice vibration frequencies of HfxSiy confirmed that they are phase-stable. The results of the elastic hardness show that they are elastically anisotropic. The order of anisotropy is Hf3Si2 > HfSi > Hf2Si > HfSi2 > Hf5Si3 > Hf5Si4. HfSi2 has a maximum hardness value of 19.7 GPa and is less than 20 GPa, indicating that it is not a potential superhard material. The results of stress-strain stretching increase with stretching and start a decreasing trend after the stress value reaches its highest point. Finally, we predicted sound velocity and Debye temperature.

First-principles study on stability, electronic and mechanical properties of 4^3T175 carbon allotrope

We present a systemical study on the stability, electronic and mechanical properties of a sp3-bonded carbon allotrope with 4^3T175 topology. This carbon allotrope is composed of a C-centered orthorhombic unit cell with 20 atoms and is mechanically and dynamically stable over a pressure range from ambient conditions to 50 GPa. According to the calculations, 4^3T175 is an indirect band gap semiconductor with band gap of 2.84 eV and also a potential superhard material with Vickers hardness of 73 GPa. The simulated X-ray diffraction pattern can be matched to some of the diffraction peaks of those unidentified carbon phases in detonation soot samples, indicating its possible presence in these specimens. These findings yield a deeper understanding of 4^3T175 and provide a guidance to elucidate the unidentified carbon phase in the high-pressure synthesis products.

Theoretical prediction of the structure and hardness of TiB4 tetraborides from first-principles calculations.

To search for a novel transition metal boride superhard material, the structural configuration, hardness and bonding state of the boron rich TiB4 tetraborides are studied using the first-principles method. Similar to the TMB4 tetraboride, four tetraborides, orthorhombic (Immm), orthorhombic (Cmcm), tetragonal (P4/mbm) and hexagonal (P63/mmc) phases, are predicted based on the phonon dispersion and thermodynamic model. The stable TiB4 with orthorhombic (Immm and Cmcm) is first predicted. In particular, the theoretical hardness of Cmcm and Immm TiB4 is 53.3 GPa and 35.6 GPa, respectively. We predict that orthorhombic (Cmcm) TiB4 is a potential superhard material. Here, the calculated lattice parameters of the Cmcm TiB4 are a = 5.2230 Å, b = 3.0627 Å and c = 9.8026 Å. The calculated lattice parameters of the Immm TiB4 are a = 5.0374 Å, b = 5.6542 Å and c = 3.0069 Å. Naturally, the high hardness of Cmcm TiB4 is related to the octagon B-B cage structure, which is composed of three different B-B covalent bonds. Although the B-B cage structure is formed in Immm TiB4, the hard discrepancy is that the bond strength of the B-B covalent bond in Immm TiB4 is weaker than the bond strength of the B-B covalent bond in Cmcm TiB4. In addition, the Debye temperature of the Cmcm TiB4 is higher than those of the other three TiB4 tetraborides. The high-temperature thermodynamic properties of TiB4 tetraboride are determined by the vibration in the B atom and B-B covalent bond. Therefore, our study indicates that a novel orthorhombic (Cmcm) TiB4 superhard material is found.

N2CO: A potential superhard material predicted by the first-principles calculations

Using the first-principles calculations, we have predicted the mechanical and thermal properties of N2CO, which belongs to the tetragonal structure (space group P43) with a = 5.18 Å, c = 3.99 Å and the c/a = 0.77. The tetragonal phase N2CO is thermodynamically, mechanically and dynamically stable, as verified by the cohesive energy, elastic constants and phonon dispersion. Further research show that N2CO has brittleness (B/G = 1.22), high Vickers hardness (47 GPa) and high Debye temperature (1383 K). The results show that the tetragonal N2CO can potentially be used as a superhard material.

Ordered structure and mechanical properties of ternary Sc0.5TM0.5B2 (TM = Ti, V, Zr) alloys under high pressure

The structural and mechanical properties of ScB2 and Sc0.5TM0.5B2 (TM = Ti, V, Zr) alloys are investigated in the pressure range of 0–150 GPa based on density functional theory. The ground state structures of ScB2 are screened out by structural substitution, and the P6/mmm is determined as the initial structure of alloying research according to structural stability. The structures of alloy generation and recognition (SAGAR) code combined with first-principles calculations selected the stable structures of Sc0.5TM0.5B2 (TM = Ti, V) and Sc0.5Zr0.5B2 alloys as ordered structure types Ⅰ and Ⅱ, respectively. The formation enthalpy, phonon dispersion and elastic constants demonstrate that Sc0.5TM0.5B2 (TM = Ti, V, Zr) alloys are thermodynamically, dynamically and mechanically stable. In the whole pressure range, the elastic moduli of Sc0.5TM0.5B2 (TM = Ti, V, Zr) increased significantly compared with ScB2. This indicates that the introduction of TM improves the mechanical properties of ScB2. The Vickers hardness (HV) of the ScB2 ground state is 42.4 GPa, and the HV of the Sc0.5TM0.5B2 (TM = Ti, V, Zr) alloys are increased to 47.8, 50.3 and 44.8 GPa, respectively. The electronic structures and chemical bonding reveal that the Sc0.5TM0.5B2 (TM = Ti, V, Zr) alloys have stronger B–B, B–TM covalent bonds, charge interaction, and higher valence electron density, which significantly improves the hardness. The results show that ScB2 and Sc0.5TM0.5B2 (TM = Ti, V, Zr) alloys are potential superhard multifunctional materials.

Pressure-induced structure, elasticity, intrinsic hardness and ideal strength of tetragonal C4N

A tetragonal C4N (t-C4N) structure was predicted via CALYPSO code, and the effects of pressure on its structural and mechanical properties were studied. The results show that t-C4N is different from various 2D CxNy compounds with a new type 3D crystal structure, which is similar to diamond. Bulk t-C4N is equipped with excellent elastic properties. When the pressure is increased from 0 GPa to 350 GPa, its bulk modulus B, shear modulus G and Young's modulus E are increased from 426.9 GPa to 1123.1 GPa, 371.4 GPa to 582.9 GPa and 863.7 GPa to 1490.9 GPa, respectively. The anisotropic Bmax, Gmax and Emax are increased from 582.38 GPa to 1751.41 GPa, 478.29 GPa to 1033.97 GPa and 1281.26 GPa to 2490.14 GPa, respectively. When the pressure is 0 GPa, the hardness calculated by Chen's and Tian's models are 51.15 GPa and 51.81 GPa, respectively. Its ideal tensile strength in [111] orientation is the smallest (63.46 GPa), which indicates that the (111) planes allow easy cleavage. The smallest ideal shear strength (67.98 GPa) can be obtained in the (111)[11̄0] orientation, which suggests its theoretical hardness is about 67.98 GPa. Due to its excellent mechanical properties, t-C4N can be used as an industrial superhard material.

BC2O in C2/m phase: Light element compound with direct band gaps

A novel ternary B–C–O compound, namely m-BC2O, is first proposed in this work. Based on density functional theory, the structural properties, electronic properties, mechanical anisotropy properties and stability of m-BC2O are investigated in this work. The m-BC2O is a potential superhard material due to the hardness of m-BC2O is 50.4 ​GPa utilizing the Lyakhov-Oganov model. The m-BC2O exhibits a larger mechanical anisotropy in Young's modulus. The ratio Emax/Emin of m-BC2O (Emax/Emin ​= ​3.24) is almost two times that of other B–C–O compounds, such as B2CO2 and B6C2O5. The Young's modulus for m-BC2O in (100) plane exhibits the largest anisotropy under ambient pressure than other (001) plane, (010) plane and (111) plane, while the (111) plane is the smallest one. The m-BC2O is a narrow and direct semiconductor materials with band gap of 0.48 ​eV, and the m-BC2O could be applied in optoelectronic devices.

Two orthorhombic superhard carbon allotropes: C16 and C24

In this work, two orthorhombic superhard carbon phases C16 and C24 are proposed theoretically based on first-principles calculations, and both their space group is Cmm2. Their structure, elastic properties (including stability, hardness, and anisotropy) and electronic properties are calculated and analyzed systematically. The mechanical stability and dynamic stability of C16 and C24 under ambient pressure and high pressure are proven by elastic constants and phonon spectrum. The bulk modulus and shear modulus of C16 are 365 GPa, 313 GPa, and those of C24 are 363 GPa, 308 GPa, which are larger than T-C9, oP8 carbon, C96 and tP40 carbon. By adopting Chen's model, the hardness of C16 and C24 are calculated to be 45.2 GPa and 44.1 GPa, suggesting that they are potential superhard carbon materials. Investigations of anisotropy factors, the ratio of maximum and minimum for elastic modulus and the 3D structure surface reveal that C16 and C24 exhibit anisotropy at different pressure and main planes. In addition, the band structures suggest that C16 and C24 both belong to indirect semiconductor with band gap of 4.078 eV and 2.941 eV respectively.

Four superhard sp3 hybrid cubic boron nitride polymorphs: A first principles calculations

In this study, four sp3 hybrid boron nitride polymorphs were proposed based on first principles calculations. The calculation results indicated that, at ambient conditions, four polymorphs are stable based on the criteria of dynamic and mechanical stability. At ambient conditions, they are thermodynamically metastable than h-BN, but more stable under high pressure conditions. In these four boron nitride phases, atoms are assembled in cubic symmetry, which are all sp3 hybrid cubic diamond-like structures, and the results showed that the Vickers hardness of them are as hard as c-BN, indicating they are potential superhard materials. Meanwhile, these four structures are considered as wide band gap semiconductor structures with direct band gap. Therefore, these four boron nitride structures have great potential as photovoltaic electronic devices and cutting tools.

Pressure-induced novel nitrogen-rich aluminum nitrides: AlN6, Al2N7 and AlN7 with polymeric nitrogen chains and rings.

Pressure-induced non-molecular phases of polymeric nitrogen have potential applications in the field of energetic materials. Here, through a structural search method combined with first-principles calculations, we have predicted four novel nitrogen-rich aluminum nitrides C2/m-AlN6, Cm-Al2N7, C2-Al2N7 and P1-AlN7. Nitrogen atoms polymerize into infinite chains in C2/m-AlN6, C2-Al2N7 and P1-AlN7 structures and form N3 chains and N4 rings in Cm-Al2N7. C2/m-AlN6 is stable in the pressure range from 30 to 80 GPa and Cm-Al2N7, C2-Al2N7 and P1-AlN7 are metastable in the pressure ranges of 35-65, 65-80 and 41-80 GPa, respectively. The present study predicts that C2/m-AlN6 has a superconducting transition temperature of 18.9 K at 0 GPa and can be quenched and recovered under ambient conditions. The energy densities of C2/m-AlN6, Cm-Al2N7, C2-Al2N7 and P1-AlN7 compounds are expected to be 4.80, 4.59, 5.46 and 5.59 kJ g-1, respectively, due to their high nitrogen content, indicating that they have potential to be high-energy density materials. The calculated Vickers hardness of C2/m-AlN6, Cm-Al2N7, Cm-Al2N7 and P1-AlN7 is 43.86, 39.32, 63.96 and 33.58 GPa, respectively, showing that the novel nitrogen-rich aluminum nitrides are potential superhard materials as well. This study may encourage further experimental exploration of high N content superhard or high-energy density nitrides.

High-throughput calculations screening for new direct band gap superhard carbon allotropes

High-throughput first principles calculations for 109 carbon allotropes were performed. The elastic constants and phonon calculations suggest that these new structures are mechanically and dynamically stable at ambient pressure. Seven direct band gap semiconductor carbon allotropes were uncovered. The Vickers hardness of all seven structures exceeds 40 GPa, indicating that these allotropes are potential superhard materials.

First-principles investigation of the structural, elastic, anisotropic and electronic properties of Pmma-carbon

An investigation of the structural, elastic, anisotropic and electronic properties of the recently reported Pmma-carbon was performed by means of first-principles calculations in this paper. The Pmma-carbon phase possesses an orthorhombic symmetry with space group Pmma (No. 51). It contains 10 carbon atoms per unit cell and adopts an all-sp 3 4+6+8-membered rings bonding network. The structural stability of Pmma-carbon is verified by analysis of the total energy, phonon spectra and elastic constants. The obtained bulk modulus and shear modulus indicate that Pmma-carbon is a brittle material and possesses elastically anisotropic. It is identified that Pmma-carbon is a potential superhard material with a Vickers hardness surpassing 70 GPa, which is lower than that of diamond but comparable with c-BN. The analysis of electronic band structure and density of states reveals that Pmma-carbon is an insulator with a quasi-direct band gap of 4.45 eV. The X-ray diffraction patterns of Pmma-carbon are also provided for future identifying the carbon phase in experiments. The present findings enrich the existing superhard carbon materials family and broaden our understanding of superhard carbon phases.