MATERIALS SCIENCE: Designing Superhard Materials

Prediction of superhard C1+xN1-x compounds with metal-free magnetism and narrow band gaps

The scarcity of superhard materials with magnetism or a narrow band gap, despite their potential applications in various fields, makes it desirable to design such materials. Here, a series of C1+xN1-x compounds are theoretically designed by replacing different numbers of nitrogen atoms with carbon atoms in the synthesized C1N1 compound. The results indicate that the compounds C5N3 and C7N1 possess both superhardness and antiferromagnetic ordering due to the introduction of low-coordinated carbon atoms. The hardness of the two compounds is about 40.3 and 54.5 GPa, respectively. The magnetism in both compounds is attributed to the unpaired electrons in low-coordinated carbon atoms, and the magnetic moments are 0.42 and 0.39 μB, respectively. Interestingly, the magnetism in C5N3 remains unaffected by the external pressure used in this study, whereas C7N1 becomes nonmagnetic when the pressure exceeds ∼80 GPa. Electronic calculations reveal that both compounds behave as indirect band gap semiconductors, with narrow energy gaps of about 0.30 and 0.20 eV, respectively. Additionally, the other two compounds, C6N2-I and C6N2-III, exhibit nonmagnetic ordering and possess hardness values of 52.6 and 35.0 GPa, respectively. C6N2-I behaves as a semiconductor with an energy gap of 0.79 eV, and C6N2-III shows metallic behavior. Notably, the energy gaps of C5N3 and C6N2-I remain nearly constant under arbitrary pressure due to their porous and superhard structure. These compounds fill the gap in magnetic or narrow band gap superhard materials, and they can be used in the spintronic or optoelectronic fields where conventional superhard materials are not suitable.

Computational and Experimental Investigations of Osmium-Rich Borides Hf2MOs5B2 (M = Mn, Fe, Co): From Spin Glass to Room-Temperature Magnetic Behaviors

The metal borides, Hf2MOs5B2 (M = Mn, Fe, Co), which are the first Os-rich quaternary variants of the prolific Ti3Co5B2 structure type, were investigated computationally and experimentally. In their crystal structures, osmium builds a network of prisms, in which the other elements are located. The magnetic M elements are found in face-connected Os8 square prisms leading to M-chains with intra- and interchain distances of about 3.0 and 6.5 Å, respectively. Density functional theory (DFT) showed that magnetic ordering is hugely favored for M = Mn and Fe but only slightly favored for M = Co. Experimental investigations then confirmed and extended the DFT predictions as a metamagnetic behavior was found for the M = Mn and Fe phases, whereby the antiferromagnetic interactions (TN = 19 and 90 K) found at low magnetic fields change to ferromagnetic at higher fields. A very broad transition (TN = 45 K) is found for M = Co, suggesting spin-glass behavior for this phase. For M = Fe, a hard-magnet hysteresis at 5 K is found with a 40 kA/m coercivity, and even at room temperature, a significant hysteresis is found. This study paves the way for the discovery of Os-based magnets in this structure type and other intermetallics.

First-principles study of multifunctional Mn2B3 materials with high hardness and ferromagnetism

Transition metal boride TM2B3 is widely studied in the field of physics and materials science. However, Mn2B3 has not been found in Mn-B systems so far. Mn2B3 undergoes phase transitions from Cmcm (0-28 GPa) to C2/m (28-80 GPa) and finally to C2/c (80-200 GPa) under pressure. Among these stable phases, Cmcm- and C2/m-Mn2B3s comprise six-membered boron rings and C2/c-Mn2B3 has wavy boron chains. They all have good mechanical properties and can become potential multifunctional materials. The strong B-B covalent bonding is mainly responsible for the structural stability and hardness. Comparison of the hardness of the five TM2B3s with different bonding strengths of TM-B and B-B bonds reveals a nonlinear change in the hardness. According to the Stoner model, these structures possess ferromagnetism, and the corresponding magnetic moments are almost the same as those of GGA and GGA + U (U = 3.9 eV, J = 1 eV).

High-pressure studies of size dependent yield strength in rhenium diboride nanocrystals

The superhard ReB2 system is the hardest pure phase diboride synthesized to date. Previously, we have demonstrated the synthesis of nano-ReB2 and the use of this nanostructured material for texture analysis using high-pressure radial diffraction. Here, we investigate the size dependence of hardness in the nano-ReB2 system using nanocrystalline ReB2 with a range of grain sizes (20-60 nm). Using high-pressure X-ray diffraction, we characterize the mechanical properties of these materials, including bulk modulus, lattice strain, yield strength, and texture. In agreement with the Hall-Petch effect, the yield strength increases with decreasing size, with the 20 nm ReB2 exhibiting a significantly higher yield strength than any of the larger grained materials or bulk ReB2. Texture analysis on the high pressure diffraction data shows a maximum along the [0001] direction, which indicates that plastic deformation is primarily controlled by the basal slip system. At the highest pressure (55 GPa), the 20 nm ReB2 shows suppression of other slip systems observed in larger ReB2 samples, in agreement with its high yield strength. This behavior, likely arises from an increased grain boundary concentration in the smaller nanoparticles. Overall, these results highlight that even superhard materials can be made more mechanically robust using nanoscale grain size effects.

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.

Centimeter-sized diamond composites with high electrical conductivity and hardness

Achieving high-performance materials with superior mechanical properties and electrical conductivity, especially in large-sized bulk forms, has always been the goal. However, it remains a grand challenge due to the inherent trade-off between these properties. Herein, by employing nanodiamonds as precursors, centimeter-sized diamond/graphene composites were synthesized under moderate pressure and temperature conditions (12 GPa and 1,300 to 1,500 °C), and the composites consisted of ultrafine diamond grains and few-layer graphene domains interconnected through covalently bonded interfaces. The composites exhibit a remarkable electrical conductivity of 2.0 × 104 S m-1 at room temperature, a Vickers hardness of up to ~55.8 GPa, and a toughness of 10.8 to 19.8 MPa m1/2. Theoretical calculations indicate that the transformation energy barrier for the graphitization of diamond surface is lower than that for diamond growth directly from conventional sp2 carbon materials, allowing the synthesis of such diamond composites under mild conditions. The above results pave the way for realizing large-sized diamond-based materials with ultrahigh electrical conductivity and superior mechanical properties simultaneously under moderate synthesis conditions, which will facilitate their large-scale applications in a variety of fields.

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 39 GPa, 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 8 K 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.

Discovery of Metastable W3P Single Crystals with High Hardness and Superconductivity

Hard and superconducting materials play significant roles in their respective application areas and are also crucial research fields in condensed matter physics. Materials with the key properties of both hard and superconducting properties could lead to technology development, but it is also full of challenges. Herein, we report the synthesis of high-quality metastable W3P single crystals with superconductivity and excellent mechanical properties. The synergistic effect of temperature and pressure was effective in suppressing further decomposition of metastable W3P as-synthesized by our synthesis technique (high-pressure and high-temperature method). The transport and magnetic measurements indicate that W3P is a typical type-II BCS superconductor, displaying a superconducting transition temperature of 5.9 K and an impressive critical magnetic field of 4.35 T. Theory calculations reveal a metallic property in W3P, and the phonon modes of the vibration of W atoms are important for electron-phonon interaction. Meanwhile, W3P shows excellent mechanical properties with a high fracture toughness of 8 MPa m1/2 and an impressive asymptotic hardness of 22 GPa, which is currently reported as being the hardest among transition metal phosphides. It opens up a new class of advanced materials that combine excellent mechanical properties with superconductivity.

Toward Three-Dimensional Printed Thermal Conductive Polymeric Composites Using a Binary-Composite Hybrid Based on Boron Nitride Nanoparticles and Micro-Diamonds

Thermally conductive polymeric composites are promising for heat management in microelectronic devices. This work presents a binary-hybrid composite of boron nitride (BN) nanoparticles and micro-diamond (D) fillers in an elastomeric polyurethane (PU) matrix which can be three- dimensionally printed to produce a highly flexible and self-supporting structure. The research shows that a combination of 16.7 wt% BN and 16.7 wt% D results in a robust network within the polymer matrix to improve the tensile modulus more than nine times with respect to neat PU. Significantly, the hybrid matrix enhances the thermal conductivity by more than two times when compared to neat PU. The enhancement in mechanical, and thermal features make this three-dimensional printable multiscale hybrid composite suitable for flexible and stretchable microelectronic applications.

Superhard bulk C4N3 compounds with metal-free magnetism assembled from two-dimensional C4N3: a first-principles study

Enriching the electronic properties of superhard materials is very important to extend their applications, and some superhard materials with metallic or superconducting characteristics have been designed via theoretical or experimental methods. However, their magnetic features have scarcely been studied, since most of them are limited to nonmagnetic ordering. Here, with the help of first-principles calculations, a series of C4N3 compounds are designed by stacking C4N3 sheets with different sequences. As expected, some of them exhibit both magnetic and superhard characteristics. Notably, all these compounds exhibit dynamic and mechanical stabilities, indicating that their dynamic and mechanical stabilities are independent of the stacking sequence. Among them, the ABC-stacked one is energetically favorable, and it exhibits antiferromagnetic ordering and has a hardness of ∼54.0 GPa, and the electronic calculations show that it is a semiconductor with a direct band gap of ∼1.20 eV. Besides, the magnetism of all magnetic C4N3 compounds is caused by the lower coordinated atoms, and the magnetic moments are located on three-fold C or two-fold coordinated N atoms. Additionally, the magnetic property is deeply dependent on the external pressure. This work opens a potential way to design magnetic superhard materials and can arouse their applications in the spintronic field.

Atomic stiffness for bulk modulus prediction and high-throughput screening of ultraincompressible crystals

Determining bulk moduli is central to high-throughput screening of ultraincompressible materials. However, existing approaches are either too inaccurate or too expensive for general applications, or they are limited to narrow chemistries. Here we define a microscopic quantity to measure the atomic stiffness for each element in the periodic table. Based on this quantity, we derive an analytic formula for bulk modulus prediction. By analyzing numerous crystals from first-principles calculations, this formula shows superior accuracy, efficiency, universality, and interpretability compared to previous empirical/semiempirical formulae and machine learning models. Directed by our formula predictions and verified by first-principles calculations, 47 ultraincompressible crystals rivaling diamond are identified from over one million material candidates, which extends the family of known ultraincompressible crystals. Finally, treasure maps of possible elemental combinations for ultraincompressible crystals are created from our theory. This theory and insights provide guidelines for designing and discovering ultraincompressible crystals of the future.

Green Diamond: A Superhard Boron Carbonitride with Bandgap in Green-Light Region and Anisotropic High Carrier Mobilities

The development of new multifunctional superhard materials beyond diamond is a great challenge for materials science and industry application. A new diamond-like boron carbonitride material (BC₆N) formed by covalently alternated stacking of two-dimensional BC₃ and C₃N monolayers is systemically investigated through first-principles method. The electronic structure calculations show that the new structure is a direct bandgap semiconductor with a bandgap of 2.404 eV (HSE06). It exhibits anisotropic high carrier mobility (μ_Lh = 1.88 × 10⁴ cm² V^-1 s^-1), varied absorbance in visible light and different regions of UV light, and theoretical Vickers hardness of 81.34 GPa, close to that of diamond. Furthermore, it is easily synthesizable due to its exothermic nature when reacted from the interlayer fusion of the BC₃ and C₃N monolayers in a bottom-up synthesis strategy. In addition, the properties of 3D-BC₆N-I can be tuned by applying strain, changing stacking patterns, and 2D-nanolization. The excellent mechanical, electronic, and optical properties and good synthesizability suggest that the new structure (named as "green diamond") may find broad applications as a superhard and high-temperature material as well as a semiconductor and optical devices beyond diamond.

The structure and multifunctionality of high-boron transition metal borides. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2023;35:173001. [PMID: 36758243 DOI: 10.1088/1361-648x/acbad6] [Citation(s) in RCA: 0] [Impact Index Per Article: 0]

High boron content transition metal (TM) borides (HB-TMBs) have recently been regarded as the promising candidate for superhard multifunctional materials. High hardness stems from the covalent bond skeleton formed by high content of boron (B) atoms to resist deformation. High valence electron density of TM and special electronic structure fromp-dhybridization of B and TM are the sources of multifunction. However, the reason of hardness variation in different HB-TMBs is still a puzzle because hardness is a complex property mainly associated with structures, chemical bonds, and mechanical anisotropy. Rich types of hybridization in B atoms (sp, sp², sp³) generate abundant structures in HB-TMBs. Studying the intrinsic interaction of structures and hardness or multifunction is significant to search new functional superhard materials. In this review, the stable structure, hardness, and multifunctionality of HB-TMBs are summarized. It is concluded that the structures of HB-TMBs are mainly composed by sandwiched stacking of B and TM layers. The hardness of HB-TMBs shows a increasing tendency with the decreasing atom radius. The polyhedron in strong B skeleton provides hardness support for HB-TMBs, among which C2/mis the most possible structure to meet the superhard standard. The shear modulus (G₀) generates a positive effect for hardness of HB-TMBs, but the effect from bulk modulus (G₀) is complex. Importantly, materials with a value ofB₀/G₀less than 1.1 are more possible to achieve the superhard standard. As for the electronic properties, almost all TMB₃and TMB₄structures exhibit metallic properties, and their density of states near the Fermi level are derived from the d electrons of TM. The excellent electrical property of HB-TMBs with higher B ratio such as ZrB₁₂comes from the channels between B-Bπ-bond and TM-d orbitals. Some HB-TMBs also indicate superconductivity from special structures, most of them have stronger hybridization of d electrons from TM atoms than p electrons from B atoms near the Fermi level. This work is meaningful to further understand and uncover new functional superhard materials in HB-TMBs.

Solving Strength–Toughness Dilemma in Superhard Transition-Metal Diborides via a Distinct Chemically Tuned Solid Solution Approach

Solid solution strengthening enhances hardness of metals by introducing solute atoms to create local distortions in base crystal lattice, which impedes dislocation motion and plastic deformation, leading to increased strength but reduced ductility and toughness. In sharp contrast, superhard materials comprising covalent bonds exhibit high strength but low toughness via a distinct mechanism dictated by brittle bond deformation, showcasing another prominent scenario of classic strength–toughness tradeoff dilemma. Solving this less explored and understood problem presents a formidable challenge that requires a viable strategy of tuning main load-bearing bonds in these strong but brittle materials to achieve concurrent enhancement of the peak stress and related strain range. Here, we demonstrate a chemically tuned solid solution approach that simultaneously enhances hardness and toughness of superhard transition-metal diboride Ta 1− x Zr x B 2 . This striking phenomenon is achieved by introducing solute atom Zr that has lower electronegativity than solvent atom Ta to reduce the charge depletion on the main load-bearing B–B bonds during indentation, leading to prolonged deformation that gives rise to notably higher strain range and the corresponding peak stress. This finding highlights the crucial role of properly matched contrasting relative electronegativity of solute and solvent atoms in creating concurrent strengthening and toughening and opens a promising avenue for rational design of enhanced mechanical properties in a large class of transition-metal borides. This strategy of concurrent strength–toughness optimization via solute-atom-induced chemical tuning of the main load-bearing bonding charge is expected to work in broader classes of materials, such as nitrides and carbides.

Vickers hardness prediction from machine learning methods

The search for new superhard materials is of great interest for extreme industrial applications. However, the theoretical prediction of hardness is still a challenge for the scientific community, given the difficulty of modeling plastic behavior of solids. Different hardness models have been proposed over the years. Still, they are either too complicated to use, inaccurate when extrapolating to a wide variety of solids or require coding knowledge. In this investigation, we built a successful machine learning model that implements Gradient Boosting Regressor (GBR) to predict hardness and uses the mechanical properties of a solid (bulk modulus, shear modulus, Young's modulus, and Poisson's ratio) as input variables. The model was trained with an experimental Vickers hardness database of 143 materials, assuring various kinds of compounds. The input properties were calculated from the theoretical elastic tensor. The Materials Project's database was explored to search for new superhard materials, and our results are in good agreement with the experimental data available. Other alternative models to compute hardness from mechanical properties are also discussed in this work. Our results are available in a free-access easy to use online application to be further used in future studies of new materials at www.hardnesscalculator.com .

Treating Superhard Materials as Anomalies

Superhard materials are among the most scarce functional inorganic solids in existence. Indeed, recent research suggested that less than 0.1% of all known materials are likely to have a Vickers hardness ≥40 GPa. Here, an anomaly detection framework is created to treat these materials as rare occurrences by encoding and reconstructing the input composition and crystal structure information without supervision. The resulting model can quantitatively identify outliers from "normal" behaving materials, leading to the discovery of materials with exceptional properties such as a superhard response. Moreover, examining the difference between the encoded and decoded crystal structure provides fundamental insights into the crystal-chemical origin of hardness. The presented methodology is ultimately generalizable, enabling the design of other outlier materials with rare and unexpected physical properties.

Structure stabilization effect of vacancies and entropy in hexagonal WN

The structural stability of hexagonal tungsten mononitride (WN) has been studied combining scanning transmission electron microscopy and first-principles calculations. The results show that the WC-type WN with vacancies of 6∼8 at% is more stable than the previously proposed MnP-type and NiAs-type structures. Due to the larger vibrational entropy of the WC-type WN, the vacancy concentration required to stabilize the WC-type structure is lower at high temperatures. The results demonstrate the importance of vacancies and configurational and vibrational entropies in the structural stability of compounds synthesized at high temperatures.

Electron-Hole Excitation Induced Softening in Boron Carbide-Based Superhard Materials

Photomechanical effect in semiconductors refers to a phenomenon that plastic deformation is influenced by light-induced electron-hole (e-h) excitation. To date, increasing amounts of theoretical and experimental studies have been performed to illustrate the physical origin of this phenomenon. In contrast, there has been little discussion about this effect in superhard materials. Here, we adopted constrained density functional theory simulations to assess how e-h excitation influences two boron-based superhard materials: boron carbide (B₄C) and boron subphosphide (B₁₂P₂). We found that the ideal shear strengths of both systems decrease under e-h excited states. Under e-h excitation, the redistribution of electrons and holes contributes to the decreased strength, weakening the bonds initially broken under the shear deformation. The simulation results provide a fundamental explanation for the softening effects of superhard materials under e-h excitation. This study also provides a basis to tune the mechanical properties of superhard materials via light irradiation.

Macroscale Robust Superlubricity on Metallic NbB2

Robust superlubricity (RSL), defined by concurrent superlow friction and wear, holds great promise for reducing material and energy loss in vast industrial and technological operations. Despite recent advances, challenges remain in finding materials that exhibit RSL on macrolength and time scales and possess vigorous electrical conduction ability. Here, the discovery of RSL is reported on hydrated NbB₂ films that exhibit vanishingly small coefficient of friction (0.001-0.006) and superlow wear rate (≈10^-17 m³ N^-1 m^-1 ) on large length scales reaching millimeter range and prolonged time scales lasting through extensive loading durations. Moreover, the measured low resistivity (≈10^-6 Ω m) of the synthesized NbB₂ film indicates ample capability for electrical conduction, extending macroscale RSL to hitherto largely untapped metallic materials. Pertinent microscopic mechanisms are elucidated by deciphering the intricate load-driven chemical reactions that generate and sustain the observed superlubricating state and assessing the strong stress responses under diverse strains that produce the superior durability.

Emerging interstitial/substitutional modification of Pd-based nanomaterials with nonmetallic elements for electrocatalytic applications

Palladium (Pd)-based nanomaterials have been identified as potential candidates for various types of electrocatalytic reaction, but most of them typically exhibit unsatisfactory performances. Recently, extensive theoretical and experimental studies have demonstrated that the interstitial/substitutional modification of Pd-based nanomaterials with nonmetallic atoms (H, B, C, N, P, S) has a significant impact on their electronic structure and thus leads to the rapid development of one kind of promising catalyst for various electrochemical reactions. Considering the remarkable progress in this area, we highlight the most recent progress regarding the innovative synthesis and advanced characterization methods of nonmetallic atom-doped Pd-based nanomaterials and provide insights into their electrochemical applications. What's more, the unique structure- and component-dependent electrochemical performance and the underlying mechanisms are also discussed. Furthermore, a brief conclusion about the recent progress achieved in this field as well as future perspectives and challenges are provided.

The crystal structures, phase stabilities, electronic structures and bonding features of iridium borides from first-principles calculations

We present results of an unbiased structure search for the lowest energy crystalline structures of various stoichiometric iridium borides, using first-principles calculations combined with particle swarm optimization algorithms. As a result, besides three stable phases of C2/m-Ir₃B₂, Fmm2-Ir₄B₃, and Cm-Ir₄B₅, three promising metastable phases, namely, P2₁/m-Ir₂B, P2₁/m-IrB, and Pnma-Ir₃B₄, whose energies are within 20 meV per atom above the convex hull curve, are also identified at ambient pressure. The high bulk modulus of 301 GPa, highest shear modulus of 148 GPa, and smallest Poisson's ratio of 0.29 for C2/m-Ir₃B₂ make it a promising low compressible material. C2/m-Ir₃B₂ is predicted to possess the highest Vickers hardnesses, with a Vickers hardness of 13.1 GPa and 19.4 GPa based on Chen's model and Mazhnik-Oganov's model respectively, and a high fracture toughness of 5.17 MPa m^0.5. The anisotropic indexes and the three-dimensional surface constructions of Young's modulus indicate that Ir–B compounds are anisotropic with the sequence of the elastic anisotropy of Ir₂B > IrB > Ir₄B₅ > Ir₃B₄ > Ir₄B₃ > Ir₃B₂. Remarkably, these iridium borides are all ductile. We further find that the four Ir–B phases of P2₁/m-Ir₂B, C2/m-Ir₃B₂, P2₁/m-IrB, and Fmm2-Ir₄B₃ possess dominant Ir–B covalent bonding character, while strong B–B and Ir–B covalent bonds are present in Cm-Ir₄B₅ and Pnma-Ir₃B₄, which are responsible for their excellent mechanical properties.

We mainly probe into phase stabilities, structural characters, elastic anisotropy and bonding features of the iridium borides under ambient pressure.

An electrically conductive and ferromagnetic nano-structure manganese mono-boride with high Vickers hardness

The combination of various desired physical properties greatly extends the applicability of materials. Magnetic materials are generally mechanically soft, yet the combination of high mechanical hardness and ferromagnetic properties is highly sought after. Here, we report the synthesis and characterization of nanocrystalline manganese boride, CrB-type MnB, using the high-pressure and high-temperature method in a large volume press. CrB-type MnB shares the specificity of large numbers of unpaired electrons of manganese ions and strong covalent boron zigzag chains. Thus, manganese mono-boride exhibits "strong" ferromagnetic, magnetocaloric behavior, and possesses high Vickers hardness. We demonstrate that zigzag boron chains in this structure not only play a pivotal role in strengthening mechanical properties but also tuning the exchange correlations between manganese atoms. Nontoxic and Earth-abundant CrB-type MnB is much more incompressible and tougher than traditional ferromagnetic materials. The unique combination of high mechanical hardness, magnetism, and electrical conductivity properties makes it a particularly promising candidate for a wide range of applications.

Super-hard "Tanghulu": cubic BP microwire covered with amorphous SiO2 balls

Superhard materials, which are widely used in metallurgy, petroleum drilling, and mechanical processing, have become the key to the development of processing and manufacturing industry. Boron phosphide is an excellent Superhard candidate material with excellent inert, high thermostability and heat conductivity. However, since synthesizing BP is a hard task, studies of its basic physical properties and applications are hindered to some extent. Here, we obtained a micron-scale “Tanghulu”, in the process of synthesizing boron phosphide single crystals using high-temperature flux method. Under a special appearance, "Tanghulu" is a superhard BP microwire covered by melted or amorphous SiO₂ and the hardness of the BP microwires is 40.16GPa. On the basis of a comprehensive material analysis, we established the formation mechanism of this Superhard “Tanghulu” as follows: during the heating process with continuous high temperature, SiO₂ molecules on the wall of quartz tube escape and diffuse freely and adhere to the boron phosphide rod-shaped single crystal, which will aggregate then under the effect of surface tension to form an isotropic spherical amorphous SiO₂ and form the “Tanghulu” finally. Our work can help to broaden the understanding of micro-scale materials.

Unusual suppression of tungsten 5delectron depletion in superhard tungsten tetraboride solid solution with chromium under compression

The lattice compressibility and deformation in superhard tungsten tetraboride (WB₄) solid solution with chromium (Cr) are investigated by high-pressure x-ray diffraction and x-ray absorption fine structure (XAFS) spectroscopy up to 54 GPa. In contrast to pure WB₄, thec-axis softening is effectively suppressed in W_0.9Cr_0.1B₄, and less compressibility is shown for thea- andc-axes in the entire pressure range. Meanwhile, the white-line peak of W L₃-edge XAFS in W_0.9Cr_0.1B₄shows an absence of the sudden intensity drop as previously observed in WB₄at ∼21 GPa, suggesting a strong inhibition of W 5delectron depletion. This phenomenon is followed by an initial increase and then decrease for the W-B bond disorder, with the magnitude greatly lower than that of WB₄. Besides the apparent atomic size mismatch effect, these results imply that addition of Cr, which has the same number of valence electrons as W, can introduce an unexpected electronic structure change to strengthen the W-B bond via a modification of W vacancies and B trimers distribution in WB₄lattice. Our findings point out the great significance to precise manipulation of the intrinsic W vacancies and B trimers through different solute atoms to rational optimization of WB₄hardness.

Nanostructured Metal Borides for Energy-Related Electrocatalysis: Recent Progress, Challenges, and Perspectives

The discovery of durable, active, and affordable electrocatalysts for energy-related catalytic applications plays a crucial role in the advancement of energy conversion and storage technologies to achieve a sustainable energy future. Transition metal borides (TMBs), with variable compositions and structures, present a number of interesting features including coordinated electronic structures, high conductivity, abundant natural reserves, and configurable physicochemical properties. Therefore, TMBs provide a wide range of opportunities for the development of multifunctional catalysts with high performance and long durability. This review first summarizes the typical structural and electronic features of TMBs. Subsequently, the various synthetic methods used thus far to prepare nanostructured TMBs are listed. Furthermore, advances in emerging TMB-catalyzed reactions (both theoretical and experimental) are highlighted, including the hydrogen evolution reaction, the oxygen evolution reaction, the oxygen reduction reaction, the carbon dioxide reduction reaction, the nitrogen reduction reaction, the methanol oxidation reaction, and the formic acid oxidation reaction. Finally, challenges facing the development of TMB electrocatalysts are discussed, with focus on synthesis and energy-related catalytic applications, and some potential strategies/perspectives are suggested as well, which will profit the design of more efficient TMB materials for application in future energy conversion and storage devices.

Toughening and Crack Healing Mechanisms in Nanotwinned Diamond Composites with Various Polytypes

As an emerging ceramic material, recently synthesized nanotwinned diamond composites with various polytypes embedded in nanoscale twins exhibit unprecedented fracture toughness without sacrificing hardness. However, the toughening and crack healing mechanisms at the atomic scale and the associated crack propagation process of nanotwinned diamond composites remain mysterious. Here, we perform large-scale atomistic simulations of crack propagation in nanotwinned diamond composites to explore the underlying toughening and crack healing mechanisms in nanotwinned diamond composites. Our simulation results show that nanotwinned diamond composites have a higher fracture energy than single-crystalline and nanotwinned diamonds, which originates from multiple toughening mechanisms, including twin boundary and phase boundary impeding crack propagation, crack deflection and zigzag paths in nanotwins and sinuous paths in polytypes, and the formation of disordered atom clusters. More remarkably, our simulations reproduce more detailed crack propagation processes at the atomic scale, which is inaccessible by experiments. Moreover, our simulations reveal that crack healing occurs due to the rebonding of atoms on fracture surfaces during unloading and that the extent of crack healing is associated with whether the crack surfaces are clean. Our current study provides mechanistic insights into a fundamental understanding of toughening and crack healing mechanisms in nanotwinned diamond composites.

Determining Temperature-Dependent Vickers Hardness with Machine Learning

Assessing the hardness of structural materials at elevated temperatures is experimentally and computationally challenging, yet crucial for their success. In this work, a machine-learning method was developed to determine a material's temperature-dependent hardness based on its chemical composition and crystal structure. A total of 593 Vickers hardness data collected at various temperatures were extracted from the literature and used to train an extreme gradient boosting (XGBoost) machine-learning model. Applying a combination of composition descriptors and smooth overlap of atomic positions (SOAP) structural descriptors to represent these materials resulted in outstanding accuracy (R² = 0.91; MAE = 2.52 GPa). The model's intrinsic variance was also measured by using a bootstrap aggregating (bagging) method, and the subsequent predictions showed strong agreement with the experimental data. The capability of the trained model was finally verified by demonstrating the model's ability to discriminate polymorphs, separate the properties of similar compositions, and reproduce the high-temperature hardness of several classic structural materials.

Zero Thermal Expansion and Strong Covalent Binding of VB2 Compound

Zero thermal expansion (ZTE) is an intriguing phenomenon by virtue of its peculiar lack of expansion and contraction with temperature. The achievement of ZTE in a metallic material is a desired but challenging task. Here we report the ZTE behavior of a single-phase metallic VB₂ compound, stacking with the V and B atomic layers along the c direction (α_V = 2.18 × 10^-6 K^-1, 5-150 K). Neutron powder diffraction demonstrates that the ZTE behavior is entangled in the direct blocking of the lattice expansion along all crystallographic directions with temperature. X-ray photoelectron spectroscopy and density functional theory calculations indicate that strong covalent binding adheres the nearest-neighbor B-B and V-B pairs, which is proposed to control the ZTE within both the basal plane and the c direction. An intimate correlation is revealed between the covalent binding and the lattice parameters. Our work indicates the opportunity to design metallic ZTE with strong chemical binding in the future.

Anisotropies in Elasticity, Sound Velocity, and Minimum Thermal Conductivity of Low Borides VxBy Compounds

Anisotropies in the elasticity, sound velocity, and minimum thermal conductivity of low borides VB, V5B6, V3B4, and V2B3 are discussed using the first-principles calculations. The various elastic anisotropic indexes (AU, Acomp, and Ashear), three-dimensional (3D) surface contours, and their planar projections among different crystallographic planes of bulk modulus, shear modulus, and Young’s modulus are used to characterize elastic anisotropy. The bulk, shear, and Young’s moduli all show relatively strong degrees of anisotropy. With increased B content, the degree of anisotropy of the bulk modulus increases while those of the shear modulus and Young’s modulus decrease. The anisotropies of the sound velocity in the different planes show obvious differences. Meanwhile, the minimum thermal conductivity shows little dependence on crystallographic direction.

Enhanced Hardness in Transition-Metal Monocarbides via Optimal Occupancy of Bonding Orbitals

An efficient strategy that can guide the synthesis of materials with superior mechanical properties is important for advanced material/device design. Here, we report a feasible way to enhance hardness in transition-metal monocarbides (TMCs) by optimally filling the bonding orbitals of valence electrons. We demonstrate that the intrinsic hardness of the NaCl- and WC-type TMCs maximizes at valence electron concentrations of about 9 and 10.25 electrons per cell, respectively; any deviation from such optimal values will reduce the hardness. Using the spark plasma sintering technique, a number of W_1-xRe_xC (x = 0-0.5) have been successfully synthesized, and powder X-ray diffractions show that they adopt the hexagonal WC-type structure. Subsequent nanoindentation and Vickers hardness measurements corroborate that the newly developed W_1-xRe_xC samples (x = 0.1-0.3) are much harder than their parent phase (i.e., WC), marking them as the hardest TMCs for practical applications. Furthermore, the hardness enhancement can be well rationalized by the balanced occupancy of bonding and antibonding states. Our findings not only elucidate the unique hardening mechanism in a large class of TMCs but also offer a guide for the design of other hard and superhard compounds such as borides and nitrides.

Crystal structures and mechanical properties of osmium diboride at high pressure

We have investigated the crystal structures and mechanical properties of osmium diboride (OsB2) based on the density functional theory. The structures of OsB2 from 0 to 400 GPa were predicted using the particle swarm optimization algorithm structure prediction technique. The orthorhombic Pmmn structure of OsB2 (oP6-OsB2) was found to be the most stable phase under zero pressure and it will transfer to the hexagonal P63/mmc structure (hP6-OsB2) around 12.4 GPa. Meanwhile, we have discovered a new stable orthorhombic Immm structure (oI12-OsB2) above 379.6 GPa. After that, a thorough and comprehensive investigation on mechanical properties of different OsB2 phases is performed in this work. Further studies showed that the hardness of oP6-OsB2 and hP6-OsB2 at zero pressure is 15.6 and 20.1 GPa, while that for oI12-OsB2 under 400 GPa is 15.4 GPa, indicating that these three phases should be potentially hard materials rather than superhard materials. Finally, the pressure-temperature phase diagram of OsB2 is constructed for the first time by using the quasi-harmonic approximation method. Our results showed that the transition pressures of oP6-OsB2 → hP6-OsB2 and hP6-OsB2 → oI12-OsB2 all decreases appreciably with the increase of temperature.

Electron deficiency but semiconductive diamond-like B2CN originated from three-center bonds

B2CN was one of the synthesized light element compounds, which was expected to be superhard material with a metallic character due to its electron deficienct nature. However, in this work, we discovered two novel semiconducting superhard B2CN phases using particle swarm intelligence technique and first-principles calculations, which were reported to have three-dimensional and four coordinated covalent diamond-like structures. These two new phases were calculated to be dynamically stable at zero and high pressures, and can be deduced from the previously reported Pmma phase by pressure-induced structural phase transitions. More importantly, unlike the previously proposed metallic B2CN structures, these two new phases combine superhard (the calculated Vickers hardness reached ∼55 GPa) and semiconducting character. The semiconducting behavior of the newly predicted B2CN phases breaks the traditional view of the metallic character of the electron deficient diamond-like B-C-N ternary compounds. By a detail analyzation of the electron localization functions of these two new phases, three-center bonds were reported between some B, C and B atoms, which were suggested to be the primary mechanism that helps the compound overcome its electron-deficient nature and finally exhibit a semiconducting behavior.

Finding the Next Superhard Material through Ensemble Learning

An ensemble machine-learning method is demonstrated to be capable of finding superhard materials by directly predicting the load-dependent Vickers hardness based only on the chemical composition. A total of 1062 experimentally measured load-dependent Vickers hardness data are extracted from the literature and used to train a supervised machine-learning algorithm utilizing boosting, achieving excellent accuracy (R²  = 0.97). This new model is then tested by synthesizing and measuring the load-dependent hardness of several unreported disilicides and analyzing the predicted hardness of several classic superhard materials. The trained ensemble method is then employed to screen for superhard materials by examining more than 66 000 compounds in crystal structure databases, which show that 68 known materials have a Vickers hardness ≥40 GPa at 0.5 N (applied force) and only 10 exceed this mark at 5 N. The hardness model is then combined with the data-driven phase diagram generation tool to expand the limited number of reported high hardness compounds. Eleven ternary borocarbide phase spaces are studied, and more than ten thermodynamically favorable compositions with a hardness above 40 GPa (at 0.5 N) are identified, proving this ensemble model's ability to find previously unknown materials with outstanding mechanical properties.

Dislocation-mediated shear amorphization in boron carbide

The failure of superhard materials is often associated with stress-induced amorphization. However, the underlying mechanisms of the structural evolution remain largely unknown. Here, we report the experimental measurements of the onset of shear amorphization in single-crystal boron carbide by nanoindentation and transmission electron microscopy. We verified that rate-dependent loading discontinuity, i.e., pop-in, in nanoindentation load-displacement curves results from the formation of nanosized amorphous bands via shear amorphization. Stochastic analysis of the pop-in events reveals an exceptionally small activation volume, slow nucleation rate, and lower activation energy of the shear amorphization, suggesting that the high-pressure structural transition is activated and initiated by dislocation nucleation. This dislocation-mediated amorphization has important implications in understanding the failure mechanisms of superhard materials at stresses far below their theoretical strengths.

Strain-Mediated High Conductivity in Ultrathin Antiferromagnetic Metallic Nitrides

Strain engineering provides the ability to control the ground states and associated phase transition in epitaxial films. However, the systematic study of the intrinsic character and strain dependency in transition-metal nitrides remains challenging due to the difficulty in fabricating stoichiometric and high-quality films. Here the observation of an electronic state transition in highly crystalline antiferromagnetic CrN films with strain and reduced dimensionality is reported. By shrinking the film thickness to a critical value of ≈30 unit cells, a profound conductivity reduction accompanied by unexpected volume expansion is observed in CrN films. The electrical conductivity is observed surprisingly when the CrN layer is as thin as a single unit cell thick, which is far below the critical thickness of most metallic films. It is found that the metallicity of an ultrathin CrN film recovers from insulating behavior upon the removal of the as-grown strain by the fabrication of freestanding nitride films. Both first-principles calculations and linear dichroism measurements reveal that the strain-mediated orbital splitting effectively customizes the relatively small bandgap at the Fermi level, leading to an exotic phase transition in CrN. The ability to achieve highly conductive nitride ultrathin films by harnessing strain-control over competing phases can be used for utilizing their exceptional characteristics.

An analysis of structural phase transition and allied properties of cubic ReN and MoN compounds

The present work aims at the study of structural, elastic, electronic, and thermodynamic properties of transition metal nitrides: ReN and MoN in the zinc-blende (B3) phase. The plane wave pseudopotential and norm-conserving pseudopotential have been applied in Quantum-Espresso code based on density-functional theory (DFT). The results show a first-order phase transition from B3 to B1 (rock-salt) structure at 42 GPa and 2.5 GPa for ReN and MoN respectively. The elastic behaviors of these compounds are also unfolded in this work. The brittleness of the ReN and ductility of MoN is identified with the help of Pugh's index and Poisson's ratio. The strong anisotropic behaviors of both compounds are detected under the influence of pressure. The electronic and bonding features of proposed compounds are evaluated by means of band structures, the density of states (DOS), Fermi surface, and charge density plots. The obtained results forecast the metallic behavior and ionic bonding of ReN and MoN in both phases: B3 and B1. Additionally, various thermodynamic properties are also investigated under high pressures and temperatures (from 0 to 2000 K). Conceivably, these properties are reported for the first time in the B3 structure of these compounds and will be useful for many applications in modern technologies as well.

Crystal Structure and Physical Properties of the Cage Compound Hf2B2-2δIr5+δ

Hf₂B_2–2δIr_5+δ crystallizes with a new type of structure: space group Pbam, a = 5.6300(3) Å, b = 11.2599(5) Å, and c = 3.8328(2) Å. Nearly 5% of the boron pairs are randomly replaced by single iridium atoms (Ir_5+δB_2–2δ). From an analysis of the chemical bonding, the crystal structure can be understood as a three-dimensional framework stabilized by covalent two-atom B–B and Ir–Ir as well as three-atom Ir–Ir–B and Ir–Ir–Ir interactions. The hafnium atoms center 14-atom cavities and transfer a significant amount of charge to the polyanionic boron–iridium framework. This refractory boride displays moderate hardness and is a Pauli paramagnet with metallic electrical resistivity, Seebeck coefficient, and thermal conductivity. The metallic character of this system is also confirmed by electronic structure calculations revealing 5.8 states eV^–1 fu^–1 at the Fermi level. Zr₂B_2–2δIr_5+δ is found to be isotypic with Hf₂B_2–2δIr_5+δ, and both form a continuous solid solution.

Hf₂Ir_5+δB_2−2δ is a cage compound with a three-dimensional anionic boron−iridium framework composed of [B₂Ir₈] units with cavities bearing the hafnium cations. Zr₂Ir_5+δB_2−2δ is found to be isotypic with Hf₂Ir_5+δB_2−2δ, and both form a continuous solid solution.

Electronic structure and anisotropic compression of Os2B3to 358 GPa

High pressure study on ultra-hard transition-metal boride Os2B3was carried out in a diamond anvil cell under isothermal and non-hydrostatic compression with platinum as an x-ray pressure standard. The ambient-pressure hexagonal phase of Os2B3is found to be stable with a volume compressionV/V0= 0.670 ± 0.009 at the maximum pressure of 358 ± 7 GPa. Anisotropic compression behavior is observed in Os2B3to the highest pressure, with thec-axis being the least compressible. The measured equation of state using the 3rd-order Birch-Murnaghan fit reveals a bulk modulusK0=397 GPa and its first pressure derivativeK0'=4.0. The experimental lattice parameters and bulk modulus at ambient conditions also agree well with our density-functional-theory (DFT) calculations within an error margin of ∼1%. DFT results indicate that Os2B3becomes more ductile under compression, with a strong anisotropy in the axial bulk modulus persisting to the highest pressure. DFT further enables the studies of charge distribution and electronic structure at high pressure. The pressure-enhanced electron density and repulsion along the Os and B bonds result in a high incompressibility along the crystalc-axis. Our work helps to elucidate the fundamental properties of Os2B3under ultrahigh pressure for potential applications in extreme environments.

Anomalous lattice stiffening in tungsten tetraboride solid solutions with manganese under compression

Tungsten tetraboride (WB₄)-based solid solutions represent one of the most promising superhard metal candidates; however, their underlying hardening mechanisms have not yet been fully understood. Here, we explore the lattice compressibility of WB₄ binary solid solutions with different manganese (Mn) concentrations using high-pressure x-ray diffraction (XRD) up to 52 GPa. Under initial compression, the lattices of low and high Mn-doped WB₄ alloys (i.e. W_0.96Mn_0.04B₄ and W_0.84Mn_0.16B₄) are shown to be more and less compressible than pure WB₄, respectively. Then, a c-axis softening is found to occur above 39 GPa in WB₄, consistent with previous results. However, an anomalous sudden a-axis stiffening is revealed at ~36 GPa in W_0.96Mn_0.04B₄, along with suppression of c-axis softening observed in WB₄. Furthermore, upon Mn addition, a simultaneous stiffening of a- and c-axes is demonstrated in W_0.84Mn_0.16B₄ at ~37 GPa. Speculation on the possible relationship between this anomalous stiffening and the combined effects of valence-electron concentration (VEC) and atomic size mismatch is also included to understand the origin of the nearly identical hardness enhancement in those two solid solutions compared to WB₄. Our findings emphasize the importance of accurate bonding and structure manipulation via solute atoms to best optimize the hardness of WB₄ solid solutions.

Structure, Stability, and Mechanical Properties of Boron-Rich Mo-B Phases: A Computational Study

Molybdenum borides were studied theoretically using first-principles calculations, parameterized lattice model, and global optimization techniques to determine stable crystal structures. Our calculations reveal the structures of known Mo-B phases, attaining close agreement with experiment. Following our developed lattice model, we describe in detail the crystal structure of boron-rich MoB_x phases with 3 ≤ x ≤ 9 as the hexagonal P6₃/mmc-MoB₃ structure with Mo atoms partially replaced by triangular boron units. The most energetically stable arrangement of these B₃ units corresponds to their uniform distribution in the bulk, which leads to the formation of a disordered nonstoichiometric phase, with ordering arising at compositions close to x = 5 because of a strong repulsive interaction between neighboring B₃ units. The most energetically favorable structures of MoB_x correspond to the compositions 4 ≲ x ≤ 5, with MoB₅ being the boron-richest stable phase. The estimated hardness of MoB₅ is 37-39 GPa, suggesting that the boron-rich phases are potentially superhard.

Effects of boron defects on mechanical strengths of TiB2 at high temperature: ab initio molecular dynamics studies

We report the determination of diffusion paths and potential barriers of boron point defects in TiB2 calculated using the climbing image nudged elastic band method at T = 0 K, and ab initio molecular dynamics studies on the structural stabilities, diffusion behavior of boron point defects and mechanical strengths of TiB2 at elevated temperatures. In contrast to the previous conjecture that TiB2 with boron vacancies are thermodynamically unstable based on the calculations at T = 0 K that boron vacancies have positive formation energies and shift electronic Fermi energies from the pseudogap valleys to the bonding states, our results show that boron vacancies in TiB2 are very robust and they have negligible effects on the structural stabilities and mechanical strengths of TiB2 at least up to 2000 K within the vacancy concentration we studied (<2.5 at%). On the other hand, our results reveal that the boron interstitials can diffuse easily in TiB2 at a moderately high temperature (1000 K) or under large shear and tensile deformations, which give rise to significant deteriorations (more than 50% reduction) in the mechanical strength of TiB2 at a high temperature (2000 K) with a boron interstitial density below 2.5 at%. Under all the shear and tensile deformations we applied, the boron interstitials in TiB2 eventually diffuse into the boron layers, causing deformations of these boron layers, which weakens their interactions with metal layers nearby and consequently reduces the mechanical strengths of the materials as temperature and boron interstitial density increase. The present findings expand our understandings on the material strength of TiB2 at high temperatures with boron point defects, and offer new insights for its applications as a high-strength ultra-high temperature ceramic.

Mechanical and Electrical Characteristics of WB2 Synthesized at High Pressure and High Temperature

Single-phase tungsten diboride (WB₂) was synthesized at high pressure and high temperature. The different grain sizes ranging from 300 nm to 3 µm were successfully obtained in WB₂ by controlling the experimental conditions. The effects of grain size on hardness and resistivity properties were investigated. The Vickers hardness of WB₂ was modulated with grain size. The maximum asymptotic Vickers hardness is 25.5 GPa for WB₂ with a grain size of 300 nm which is a 10% increase compared to WB₂ with a grain size of 3 µm. The optimal electrical resistivity of WB₂ was 10⁻⁷ Ωm with the biggest grain size of 3 µm, which is ascribed to low grain boundary density. The superior properties of hardness and electrical resistivity demonstrate that WB₂ should be a new functional hard material replacing WC which is widely used in industrial production.

Enhanced strength of nano-polycrystalline diamond by introducing boron carbide interlayers at the grain boundaries

Polycrystalline diamond with high mechanical properties and excellent thermal stability plays an important role in industry and materials science. However, the increased inherent brittle strength with the increase of hardness has severely limited its further widespread application. In this work, we produced well-sintered nano-polycrystalline (np) diamond by directly sintering fine diamond powders with the boron carbide (B₄C) additive at high pressure and high temperatures. The highest hardness value of up to ∼90 GPa was observed in the np-diamond (consisting of fine grains with a size of 16 nm) by adding 5 wt% B₄C at 18 GPa and 2237 K. Moreover, our results reveal that the produced samples have shown noticeably enhanced strength and toughness (18.37 MPa m^0.5) with the assistance of the soft phase at the grain boundaries, higher than that of the hardest known nano-twined diamond by ∼24% and a little greater than that of the toughest CVD diamond (18 MPa m^0.5). This study offers a novel functional approach in improving and controlling the hardness and stiffness of polycrystalline diamond.