Superhard Monoborides: Hardness Enhancement through Alloying in W1- x Tax B

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.

Core Electron Count as a Versatile and Accurate New Descriptor for Sorting Mechanical Properties of Diverse Transition Metal Compounds

Transition-metal light-element compounds show superb mechanical, chemical, and thermal properties, and accurate descriptors are important to sorting targeted properties among this vast class of materials. Valence electron concentration (VEC) can track broad trends of mechanical properties, but this widely used descriptor suffers low accuracy with sorted data strongly scattered along trendlines, necessitating an improved sorting strategy. Here, elastic parameters from first-principles calculations are examined for 81 ternary transition-metal nitrides (TMN) in cubic structure and 81 ternary transition-metal diborides (TMB2 ) in hexagonal structure and identify core electron count (CEC) of the solvent atoms as a new descriptor. Combined with VEC, the composite VEC-CEC descriptor exhibits greatly improved ability to sort elastic parameters of distinct TMN and TMB2 compounds. Unregulated property variations under the VEC description are well-captured by CEC, which tends to enhance ductility and reduce strength at fixed VEC and rising CEC. By invoking a full-electron consideration, the VEC-CEC descriptor accounts for the impact on bonding behaviors by both core and valence electrons with much-improved accuracy and versatility in sorting mechanical properties of diverse TM compounds compared to many other commonly used descriptors, opening a fresh path for rational design and optimization of TM compounds with tailored performance benchmarks.

Coexistence of Superhardness and Metal-Like Electrical Conductivity in High-Entropy Dodecaboride Composite with Atomic-Scale Interlocks

High electrical conductivity and super high hardness are two sought-after material properties, but both are contradictory because the effective suppression of dislocation movement generally increases the scattering of conducting electrons. Here we synthesized a high-entropy dodecaboride composite (HEDC) with a large number of atomic-scale interlocking layers. It shows a Vickers hardness of 51.2 ± 3.6 GPa under an applied load of 0.49 N and an electrical resistivity of 44.5 μΩ·cm at room temperature. Such HEDC achieves superhardness by inheriting the high intrinsic hardness of its constituent phases and restricting the dislocation motion to further enhance the extrinsic hardness through forming numerous atom-scale interlocks between different slip systems. Moreover, the HEDC maintains the excellent electrical conductivity of the constituent borides, and the competition between two correlating structures produces the special kind of coherent boundary that minimizes the scattering of conducting electrons and does not largely deteriorate the electrical conductivity.

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.

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.

The discovery of a superhard P-type transparent semiconductor: Al2.69B50

Superhard semiconductors have been long sought after for electronic device applications enduring extreme conditions, such as astronautics, due to their intrinsic toughness, high thermal and chemical stability. Here, we report the superhard p-type semiconductor Al_2.69B₅₀ single crystal with the determined Vickers hardness of ∼40.5 GPa under the load of 0.49 N, which is one of the hardest semiconductor compounds that have been ever found. With the direct band gap of 2.3 eV, Al_2.69B₅₀ exhibits excellent optical transmittance (>90%), covering the visible range from 459 nm to 760 nm and part of the infrared range, and also shows the high intensity of the photon emission in the visible light. Al_2.69B₅₀ is very stable, thermally and chemically, with an ultra-low density of ∼2.52 g cm^-3, allowing for further extension of its applications. Such an assembly of various excellent properties within one material has great implication for high power electronic design and applications.

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.

Two-Dimensional Covalent Organic Framework Solid Solutions

Covalent organic frameworks (COFs) generally leverage one or two monomers with specific sizes and shapes to access highly symmetric and periodic polymer networks. Almost all reported COFs employ the minimum sets of monomers needed for the polymerization (usually two, sometimes one) and crystallize in high-symmetry topologies. COFs synthesized from more than two monomers usually employ mixtures with different pendant functionalities to distribute these groups statistically throughout the structure, or monomers with different sizes in ratios targeting lower symmetry topologies. Here, we demonstrate that mixtures of monomers with different lengths generate single-phase, hexagonal two-dimensional covalent organic framework (2D COF) solid solutions at continuously variable feed ratios. X-ray diffraction measurements, Fourier-transform infrared spectroscopy, and Pawley refinement indicate that both monomers distribute randomly within the same lattice, and the lattice parameters continuously increase as more of the larger linker is incorporated. Furthermore, COF solid solutions are accessed directly by polymerizing a mixture of monomers but not via linker exchange from a preformed COF. As strain develops from the lattice accommodating monomers with different sizes, the nonlinear relationship between the monomer incorporation and the COF's lattice parameters suggests that bond-bending of the monomers plays a role in incorporating monomers of different lengths into the solid solutions. Solid solution formation represents a new strategy to design 2D COFs and increase their complexity. Specifically, varying the monomer composition of a given network enables many properties, such as the average pore size, to be continuously tuned between those of corresponding pure COFs.

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.

A Delicate Balance between Antiferromagnetism and Ferromagnetism: Theoretical and Experimental Studies of A2 MRu5 B2 (A=Zr, Hf; M=Fe, Mn) Metal Borides

Metal-rich borides with the Ti₃ Co₅ B₂ -type structure represent an ideal playground for tuning magnetic interactions through chemical substitutions. In this work, density functional theory (DFT) and experimental studies of Ru-rich quaternary borides with the general composition A₂ MRu₅ B₂ (A=Zr, Hf, M=Fe, Mn) are presented. Total energy calculations show that the phases Zr₂ FeRu₅ B₂ and Hf₂ FeRu₅ B₂ prefer ground states with strong antiferromagnetic (AFM) interactions between ferromagnetic (FM) M-chains. Manganese substitution for iron lowers these antiferromagnetic interchain interactions dramatically and creates a strong competition between FM and AFM states with a slight preference for AFM in Zr₂ MnRu₅ B₂ and for FM in Hf₂ MnRu₅ B₂ . Magnetic property measurements show a field dependence of the AFM transition (T_N ): T_N is found at 0.1 T for all phases with predicted AFM states whereas for the predicted FM phase it is found at a much lower magnetic field (0.005 T). Furthermore, T_N is lowest for a Hf-based phase (20 K) and highest for a Zr-based one (28 K), in accordance with DFT predictions of weaker AFM interactions in the Hf-based phases. Interestingly, the AFM transitions vanish in all compounds at higher fields (>1 T) in favor of FM transitions, indicating metamagnetic behaviors for these Ru-rich phases.

Role of TM-TM Connection Induced by Opposite d-Electron States on the Hardness of Transition-Metal (TM = Cr, W) Mononitrides

Recent reports exposed an astonishing factor of high hardness that the connection between transition-metal (TM) atoms could enhance hardness, which is in contrast to the usual understanding that TM-TM will weaken hardness as the source of metallicity. It is surprising that there are two opposite mechanical characteristics in the one TM-TM bond. To uncover the intrinsic reason, we studied two appropriate mononitrides, CrN and WN, with the same light-element (LE) content and valence electron concentration. The two high-quality compounds were synthesized by a new metathesis under high pressure, and the Vickers hardness is 13.0 GPa for CrN and 20.0 GPa for WN. Combined with theoretical calculations, we found that the strong correlation of d electrons in TM-TM could seriously affect hardness. Thus, we make the complementary suggestions of the previous hardness factors that the antibonding d-electron state in TM-TM near the Fermi level should be avoided and a strong d covalent coupling in TM-TM is very beneficial for high hardness. Our results are very important for the further design of high-hardness and multifunctional TM and LE compounds.

Synthesis and High-Pressure Mechanical Properties of Superhard Rhenium/Tungsten Diboride Nanocrystals

Rhenium diboride is an established superhard compound that can scratch diamond and can be readily synthesized under ambient pressure. Here, we demonstrate two synergistic ways to further enhance the already high yield strength of ReB₂. The first approach builds on previous reports where tungsten is doped into ReB₂ at concentrations up to 48 at. %, forming a rhenium/tungsten diboride solid solution (Re_0.52W_0.48B₂). In the second approach, the composition of both materials is maintained, but the particle size is reduced to the nanoscale (40-150 nm). Bulk samples were synthesized by arc melting above 2500 °C, and salt flux growth at ∼850 °C was used to create nanoscale materials. In situ radial X-ray diffraction was then performed under high pressures up to ∼60 GPa in a diamond anvil cell to study mechanical properties including bulk modulus, lattice strain, and strength anisotropy. The differential stress for both Re_0.52W_0.48B₂ and nano ReB₂ (n-ReB₂) was increased compared to bulk ReB₂. In addition, the lattice-preferred orientation of n-ReB₂ was experimentally measured. Under non-hydrostatic compression, n-ReB₂ exhibits texture characterized by a maximum along the [001] direction, confirming that plastic deformation is primarily controlled by the basal slip system. At higher pressures, a range of other slip systems become active. Finally, both size and solid-solution effects were combined in nanoscale Re_0.52W_0.48B₂. This material showed the highest differential stress and bulk modulus, combined with suppression of the new slip planes that opened at high pressure in n-ReB₂.

Revealing the Unusual Rigid Boron Chain Substructure in Hard and Superconductive Tantalum Monoboride

Poor electrical conductivity severely limits the diverse applications of high hardness materials in situations where electrical conductivities are highly desired. A "covalent metal" TaB with metallic electrical conductivity and high hardness has been fabricated by a high pressure and high temperature method. The bulk modulus, 302.0(4.9) GPa, and Vickers hardness, 21.3 GPa, approaches and even exceeds that of traditional insulating hard materials. Meanwhile, temperature-dependent electrical resistivity measurements show that TaB possesses metallic conductivity that rivals some widely-used conductors, and it will transform into a superconductor at T_c =7.8 K. Contrary to common understanding, the hardness of TaB is higher than that of TaB₂ , which indicates that low boron concentration borides could be mechanically better than the higher boron concentration counterparts. Compression behavior and first principles calculations denote that the high hardness is associated with the ultra-rigid covalent boron chain substructure. The hardness of TaB with different topologies of boron substructure shows that besides incorporating higher boron content, manipulating light element backbone configurations is also critical for higher hardness amongst transition metal borides with identical boron content.

Enhancing the Vickers hardness, melting point and thermodynamic properties of hafnium dodecaboride

Although HfB₁₂ is a promising surperhard material because of the boron cuboctahedron cage, the Vickers hardness of HfB₁₂ remains controversial. We apply first-principles calculations to investigate the influence of a transition metal on the structural stability, Vickers hardness and thermodynamic properties of HfB₁₂. The Vickers hardness of HfB₁₂ is 39.3 GPa. In particular, the Vickers hardness of TM-doped HfB₁₂, which are novel superhard materials, is larger than 40 GPa. The Vickers hardness of Re-doped HfB₁₂ is up to 47.6 GPa. The improvement of Vickers hardness is that the introduction of an alloying element improves the localized hybridization between B and Hf, and then enhances the bond strength of the B–B covalent bond and the Hf–B bond. In addition, these alloying elements enhance the melting-point and Debye temperature of the HfB₁₂. Therefore, we believe that alloying is an effective method to improve the Vickers hardness and thermodynamic properties of HfB₁₂ superhard material.

Although HfB₁₂ is a promising surperhard material because of the boron cuboctahedron cage, the Vickers hardness of HfB₁₂ remains controversial.

A Simple, General Synthetic Route toward Nanoscale Transition Metal Borides

Most nanomaterials, such as transition metal carbides, phosphides, nitrides, chalcogenides, etc., have been extensively studied for their various properties in recent years. The similarly attractive transition metal borides, on the contrary, have seen little interest from the materials science community, mainly because nanomaterials are notoriously difficult to synthesize. Herein, a simple, general synthetic method toward crystalline transition metal boride nanomaterials is proposed. This new method takes advantage of the redox chemistry of Sn/SnCl₂ , the volatility and recrystallization of SnCl₂ at the synthesis conditions, as well as the immiscibility of tin with boron, to produce crystalline phases of 3d, 4d, and 5d transition metal nanoborides with different morphologies (nanorods, nanosheets, nanoprisms, nanoplates, nanoparticles, etc.). Importantly, this method allows flexibility in the choice of the transition metal, as well as the ability to target several compositions within the same binary phase diagram (e.g., Mo₂ B, α-MoB, MoB₂ , Mo₂ B₄ ). The simplicity and wide applicability of the method should enable the fulfillment of the great potential of this understudied class of materials, which show a variety of excellent chemical, electrochemical, and physical properties at the microscale.

DFT prediction of a novel molybdenum tetraboride superhard material

Although transition metal borides (TMBs) are promising superhard materials, the research and development of new TMB superhard materials is still a great challenge. Naturally, the Vickers hardness of TMBs is related to the 3D-network chemical bonding, in addition to the valence electron density and covalent bonds. In this paper, we apply ab initio calculations to explore the structural stability, Vickers hardness and hardening mechanism of MoB₄ tetraboride. Four possible tetraborides are predicted based on the phonon dispersion model. We find that MoB₄ with monoclinic structure (C2/m) and orthorhombic structure (Immm) are dynamically stable at the ground state. The calculated Vickers hardness of MoB₄ with monoclinic and orthorhombic structures is 41.3 GPa and 40.0 GPa, respectively. We suggest that the high hardness is derived from the 3D-network B–B covalent bond owing to bond synergistic effects. On the other hand, the Vickers hardness of MoB₄ decreases gradually with increasing pressure. The calculated results show that the hardness of MoB₄ is attributed to the B/G ratio and c/a ratio. Finally, we predict that MoB₄ is a new superhard material.

In this work, we predict that MoB₄ with monoclinic structure (C2/m) and orthorhombic structure (Immm) are potential superhard materials because of the 3D-network B–B covalent bonds. In addition, the hardness of MoB₄ is attributed to the B/G ratio and c/a ratio.

Effects of Variable Boron Concentration on the Properties of Superhard Tungsten Tetraboride

Tungsten tetraboride is an inexpensive, superhard material easily prepared at ambient pressure. Unfortunately, there are relatively few compounds in existence that crystallize in the same structure as tungsten tetraboride. Furthermore, the lack of data in the tetraboride phase space limits the discovery of any new superhard compounds that also possess high incompressibility and a three-dimensional boron network that withstands shear. Thus, the focus of the work here is to chemically probe the range of thermodynamically stable tetraboride compounds with respect to both the transition metal and the boron content. Tungsten tetraboride alloys with a variable concentration of boron were prepared by arc-melting and investigated for their mechanical properties and thermal stability. The purity and phase composition were confirmed by energy dispersive X-ray spectroscopy and powder X-ray diffraction. For variable boron WB_x, it was found that samples prepared with a metal to boron ratio of 1:11.6 to 1:9 have similar hardness values (∼40 GPa at 0.49 N loading) as well as having a similar thermal oxidation temperature of ∼455 °C. A nearly single phase compound was successfully stabilized with tantalum and prepared with a nearly stoichiometric amount of boron (4.5) as W_0.668Ta_0.332B_4.5. Therefore, the cost of production of WB₄ can be decreased while maintaining its remarkable properties. Insights from this work will help design future compounds stable in the adaptable tungsten tetraboride structure.

Rediscovering the Crystal Chemistry of Borides

For decades, borides have been primarily studied as crystallographic oddities. With such a wide variety of structures (a quick survey of the Inorganic Crystal Structure Database counts 1253 entries for binary boron compounds!), it is surprising that the applications of borides have been quite limited despite a great deal of fundamental research. If anything, the rich crystal chemistry found in borides could well provide the right tool for almost any application. The interplay between metals and the boron results in even more varied material's properties, many of which can be tuned via chemistry. Thus, the aim of this review is to reintroduce to the scientific community the developments in boride crystal chemistry over the past 60 years. We tie structures to material properties, and furthermore, elaborate on convenient synthetic routes toward preparing borides.

Ultrastrong Boron Frameworks in ZrB12 : A Highway for Electron Conducting

ZrB₁₂ , with a high symmetrical cubic structure, possesses both high hardness ≈27.0 GPa and ultralow electrical resistivity ≈18 µΩ cm at room temperature. Both the superior conductivity and hardness of ZrB₁₂ are associated with the extended BB 3D covalent bonding network as it is not only favorable for achieving high hardness, but also provides conducting channels for transporting electrons.