Structure of superhard tungsten tetraboride: a missing link between MB2 and MB12 higher borides

Theoretical study of adsorption properties and CO oxidation reaction on surfaces of higher tungsten boride

Most modern catalysts are based on precious metals and rear-earth elements, making some of organic synthesis reactions economically insolvent. Density functional theory calculations are used here to describe several differently oriented surfaces of the higher tungsten boride WB5-x, together with their catalytic activity for the CO oxidation reaction. Based on our findings, WB5-x appears to be an efficient alternative catalyst for CO oxidation. Calculated surface energies allow the use of the Wulff construction to determine the equilibrium shape of WB5-x particles. It is found that the (010) and (101) facets terminated by boron and tungsten, respectively, are the most exposed surfaces for which the adsorption of different gaseous agents (CO, CO2, H2, N2, O2, NO, NO2, H2O, NH3, SO2) is evaluated to reveal promising prospects for applications. CO oxidation on B-rich (010) and W-rich (101) surfaces is further investigated by analyzing the charge redistribution during the adsorption of CO and O2 molecules. It is found that CO oxidation has relatively low energy barriers. The implications of the present results, the effects of WB5-x on CO oxidation and potential application in the automotive, chemical, and mining industries are discussed.

Recent Developments and Future Perspectives of Molybdenum Borides and MBenes

Metal borides have received a lot of attention recently as a potentially useful material for a wide range of applications. In particular, molybdenum-based borides and MBenes are of great significance, due to their remarkable properties like good electronic conductivity, considerable stability, high surface area, and environmental harmlessness. Therefore, in this article, the progress made in molybdenum-based borides and MBenes in recent years is reviewed. The first step in understanding these materials is to begin with an overview of their structural and electronic properties. Then synthetic technologies for the production of molybdenum borides, such as high-temperature/pressure methods, physical vapor deposition (PVD), chemical vapor deposition (CVD), element reaction route, molten salt-assisted, and selective etching methods are surveyed. Then, the critical performance of these materials in numerous applications like energy storage, catalysis, biosensors, biomedical devices, surface-enhanced Raman spectroscopy (SERS), and tribology and lubrication are summarized. The review concludes with an analysis of the current progress of these materials and provides perspectives for future research. Overall, this review will offer an insightful reference for the understanding molybdenum-based borides and their development in the future.

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.

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.

Rapid liquid phase-assisted ultrahigh-temperature sintering of high-entropy ceramic composites

High-entropy ceramics and their composites display high mechanical strength and attractive high-temperature stabilities. However, properties like strong covalent bond character and low self-diffusion coefficients make them difficult to get sintered, limiting their mass popularity. Here, we present a rapid liquid phase-assisted ultrahigh-temperature sintering strategy and use high-entropy metal diboride/boron carbide composite as a proof of concept. We use a carbon-based heater to fast-heat the composite to around 3000 K, and a small fraction of eutectic liquid was formed at the interface between high-entropy metal diborides and boron carbide. A crystalline dodecaboride intergranular phase was generated upon cooling to ameliorate the adhesion between the components. The as-sintered composite presents a high hardness of 36.4 GPa at a load of 0.49 N and 24.4 GPa at a load of 9.8 N. This liquid phase-assisted rapid ultrahigh-temperature strategy can be widely applicable for other ultrahigh-temperature ceramics as well.

Efficient Synthesis of WB5-x-WB2 Powders with Selectivity for WB5-x Content

We proposed an efficient method toward the synthesis of higher tungsten boride WB_5-x in the vacuumless direct current atmospheric arc discharge plasma. The crystal structure of the synthesized samples of boron-rich tungsten boride was determined using computational techniques, showing a two-phase system. The ab initio calculations of the energies of various structures with similar X-ray diffraction (XRD) patterns allowed us to determine the composition of the formed higher tungsten boride. We determined the optimal parameters of synthesis to obtain samples with 61.5% WB_5-x by volume. The transmission electron microscopy measurements showed that 90% of the particles have sizes of up to 100 nm, whereas the rest of them may have sizes from 125 to 225 nm. Our study shows the possibility of using the proposed vacuumless method as an efficient and inexpensive way to synthesize superhard WB_5-x without employing resource-consuming vacuum techniques.

Nanohardness from First Principles with Active Learning on Atomic Environments

We propose a methodology for the calculation of nanohardness by atomistic simulations of nanoindentation. The methodology is enabled by machine-learning interatomic potentials fitted on the fly to quantum-mechanical calculations of local fragments of the large nanoindentation simulation. We test our methodology by calculating nanohardness, as a function of load and crystallographic orientation of the surface, of diamond, AlN, SiC, BC₂N, and Si and comparing it to the calibrated values of the macro- and microhardness. The observed agreement between the computational and experimental results from the literature provides evidence that our method has sufficient predictive power to open up the possibility of designing materials with exceptional hardness directly from first principles. It will be especially valuable at the nanoscale where the experimental measurements are difficult, while empirical models fitted to macrohardness are, as a rule, inapplicable.

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.

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.

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.

First-principles calculation of 11B solid-state NMR parameters of boron-rich compounds I: the rhombohedral boron modifications and B12X2 (X = P, As, O)

In the present study, solid-state nuclear magnetic resonance (NMR) spectra under magic angle spinning conditions of the rhombohedral structures α-B and B12P2 are reported together with the corresponding parameter sets from first principles calculations on α-B B12X2 (X = P, As, O). With the combination of density functional theory (DFT) and the gauge-including projector-augmented wave (GIPAW) approach as the theoretical tools at hand the computed 11B parameters lead to unambiguous explanation of the measurements. Thereby, we overcome common obstacles of processing recorded NMR spectra of solid-state compounds with several crystallographic positions, in particular non-trivial signal assignments and parameter determination due to peak overlap or even unexpected intensity/area ratios. In fact, we find very good agreement between the theoretical results and measured spectra without applying fitting procedures. Using the Perdew-Burke-Ernzerhof (PBE) functional, the results of the common construction types for pseudopotentials and referencing methods for the chemical shift determination are compared. Suggestions and conclusions from experimental 11B NMR studies on parameters according to the icosahedral positions are critically discussed, for instance the early suspected correlation to chemical shifts is not confirmed. Regarding the electric field gradient (EFG) a detailed explanation for obtaining small deviations amongst all investigated structures of the icosahedral polar sites compared to the equatorial sites is given. Our results show an important link between the exohedral bonding situation of compounds with icosahedral structure elements and the main axis of the EFG and therefore, also measurable quadrupole coupling constants if certain geometrical conditions are fulfilled. Finally, this work also contributes to establishing the number of unique sites measured by solid-state NMR methods within the modification of β-B.

WB5- x : Synthesis, Properties, and Crystal Structure-New Insights into the Long-Debated Compound

The recent theoretical prediction of a new compound, WB5, has spurred the interest in tungsten borides and their possible implementation in industry. In this research, the experimental synthesis and structural description of a boron-rich tungsten boride and measurements of its mechanical properties are performed. The ab initio calculations of the structural energies corresponding to different local structures make it possible to formulate the rules determining the likely local motifs in the disordered versions of the WB5 structure, all of which involve boron deficit. The generated disordered WB4.18 and WB4.86 models both perfectly match the experimental data, but the former is the most energetically preferable. The precise crystal structure, elastic constants, hardness, and fracture toughness of this phase are calculated, and these results agree with the experimental findings. Because of the compositional and structural similarity with predicted WB5, this phase is denoted as WB5- x . Previously incorrectly referred to as "WB4," it is distinct from earlier theoretically suggested WB4, a phase with a different crystal structure that has not yet been synthesized and is predicted to be thermodynamically stable at pressures above 1 GPa. Mild synthesis conditions (enabling a scalable synthesis) and excellent mechanical properties make WB5- x a very promising material for drilling technology.

New theoretical insights into high-coordination-number complexes in actinides-centered borane

The coordination number of a given element affects its behavior, and consequently, there is great interest in understanding the related chemistry, which could greatly promote the extension and development of new materials, but remains challenging. Herein, we report a new record high coordination number (CN) for actinides established in the cage-like An(BH)24 (An = Th to Cm) via using relativistic quantum chemistry methods. Analysis of U(BH)n (n = 1 to 24) confirmed these series of systems as being geometric minima, with the BH acting as a ligand located in the first shell around the uranium. In contrast, global searches revealed a low CN half-cage structure for UB24, which could be extended to the series of AnB24 materials and which prevails over the competing structural isomers, such as cages. The intrinsic geometric difference for AnB24 and An(BH)24 mainly arise from the B sp3 hybridization in borane inducing strong interactions between An 5f6d7s hybrid orbitals and B 2pz orbitals in An(BH)24 compared to that of AnB24. This fundamental trend presents a valuable insight for future experimental endeavors searching for isolable complexes with high-coordination actinide and provides details of a new structural motif of boron clusters and nanostructures.

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.

Designing ultrastrong 5d transition metal diborides with excellent stability for harsh service environments

Much effort was devoted towards the rational design of ultrastrong transition metal borides (TMBs) with remarkable mechanical properties and excellent stabilities, owing to promising applications in machining, drilling tools and protective coatings for the aerospace industry. Although an enormous number of investigations have been performed on these TMBs under normal conditions, studies on the stability and mechanical strength in harsh high-pressure environments, which are critical for safe service behavior and a realistic understanding of stabilities and strengthening mechanisms, are yet nearly absent. In this work, taking 5d TMB2 (TM = Hf, Ta, W, Re, Os, Ir and Pt) as an illustration, we performed comprehensive high-throughput first-principles screening for thermodynamically stable and metastable structures under various pressures. Four experimentally observed structures are found to be thermodynamically feasible for most 5d TMB2 (TM = Hf, Ta, W, Re, Os and Ir) at 0 and 100 GPa. By exploiting orbital-decomposed electronic structures, we reveal that the pressure-induced stabilization and phase transitions of 5d TMB2 can be rationalized by the splitting of bonding and antibonding states around the Fermi level. Further investigations on the pressure-induced strengthening indicate that 5d TMB2 in the hP6[194] structure exhibit a profound strengthening effect under high pressure, which can be rationalized by the proposed strengthening factor η, but η fails in the oP6[59] structure due to the changed instability modes at different pressures. These findings suggest the necessity to explore the plasticity parameters for a realistic understanding of pressure-induced strengthening in TMBs, providing a strong argument for rules based on bond parameters at equilibrium in designing strong solids.

Double-zigzag boron chain-enhanced Vickers hardness and manganese bilayers-induced high d-electron mobility in Mn3B4

The D7b-type structure Mn3B4 was fabricated by high-temperature and high-pressure (HPHT) methods. Hardness examination yielded an asymptotic Vickers hardness of 16.3 GPa, which is much higher than that of Mn2B and MnB2. First principle calculations and XPS results demonstrated that double zigzag boron chains form a strong covalent skeletons, which enhances this structure's integrity with high hardness. Considering that the hardensses of MnB and Mn3B4 are higher than those of Mn2B and MnB2, zigzag and double zigzag boron backbones are superior to isolated boron and graphite-like boron layer backbones for achieving higher hardness. This situation also states that a higher boron content is not the sole factor for the higher hardness in the low boron content transition metal borides. Futhermore, the co-presence of metallic manganese bilayers contribute to the high d-electron mobility and generate electrical conductivity and antiferromagnetism in Mn3B4 which provide us with a new structure prototype to design general-purpose high hardness materials.

Effect of pressure on the structural, electronic and mechanical properties of ultraincompressible W2B

The crystal structures of W₂B have been extensively investigated by the swarm structure searching method at ambient and high-pressure conditions. Our calculated thermodynamic enthalpy data suggests that the tetragonal phase with I4/m symmetry is the most stable at 0–50 GPa. The theoretical elastic properties and phonon spectroscopy confirmed that I4/m W₂B is both mechanically and dynamically stable. The calculated band structure and density of states show that I4/m W₂B is metallic and the electronic properties are sensitive to changes in external pressure with the occurrence of an electronic topological transition. The simulated high elastic modulus, hardness and strain–stress relationships reveal that W₂B exhibits excellent ultraincompressible properties and high strength. The combination of superior conductivity and mechanical properties reveals that W₂B can be used for hard coatings and electrical measurements.

The combination of superior conductivity and mechanical properties reveals that W₂B can be used for hard coatings and electrical measurements.

Heterometallic boride clusters: synthesis and characterization of butterfly and square pyramidal boride clusters*

A number of heterometallic boride clusters have been synthesized and structurally characterized using various spectroscopic and crystallographic analyses. Thermolysis of [Ru3(CO)12] with [Cp*WH3(B4H8)] (1) yielded [{Cp*W(CO)2}2(μ 4-B){Ru(CO)3}2(μ-H)] (2), [{Cp*W(CO)2}2(μ 5-B){Ru(CO)3}2{Ru(CO)2}(μ-H)] (3), [{Cp*W(CO)2}(μ 5-B){Ru(CO)3}4] (4) and a ditungstaborane cluster [(Cp*W)2B4H8Ru(CO)3] (5) (Cp*=η 5-C5Me5). Compound 2 contains 62 cluster valence-electrons, in which the boron atom occupies the semi-interstitial position of a M4-butterfly core, composed of two tungsten and two ruthenium atoms. Compounds 3 and 4 can be described as hetero-metallic boride clusters that contain 74-cluster valence electrons (cve), in which the boron atom is at the basal position of the M5-square pyramidal geometry. Cluster 5 is analogous to known [(Cp*W)2B5H9] where one of the BH vertices has been replaced by isolobal {Ru(CO)3} fragment. Computational studies with density functional theory (DFT) methods at the B3LYP level have been used to analyze the bonding of the synthesized molecules. The optimized geometries and computed 11B NMR chemical shifts satisfactorily corroborate with the experimental data. All the compounds have been characterized by mass spectrometry, IR, 1H, 11B and 13C NMR spectroscopy, and the structural architectures were unequivocally established by crystallographic analyses of clusters 2–5.

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.

The structure and hardness of the highest boride of tungsten, a borophene-based compound

Two-dimensional systems have strengthened their position as a key materials for novel applications. Very recently, boron joined the distinguished group of elements confirmed to possess 2D allotropes, named borophenes. In this work, we explore the stability and hardness of the highest borides of tungsten, which are built of borophenes separated by metal atoms. We show that the WB_3+x compounds have Vickers hardnesses approaching 40 GPa only for small values of x. The insertion of extra boron atoms is, in general, detrimental to the hardness of WB₃ because it leads to the formation of quasi-planar boron sheets that are less tightly connected with the adjacent tungsten layers. Very high concentrations of boron (x ≈ 1), give rise to a soft (Vickers hardness of ~8 GPa) and unstable hP20-WB₄ structure that can be considered to be built of quasi-planar boron α-sheets separated by graphitic tungsten layers. By contrast, we show that the formation of tungsten vacancies leads to structures, e.g. W_0.75B_3+x, with Vickers hardnesses that are not only similar in value to the experimentally reported load-independent hardnesses greater than 20 GPa, but are also less sensitive to variations in the boron content.

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.

Exploring the Mechanical Anisotropy and Ideal Strengths of Tetragonal B₄CO₄

First-principles calculations were employed to study the mechanical properties for the recently proposed tetragonal B₄CO₄ (t-B₄CO₄). The calculated structural parameters and elastic constants of t-B₄CO₄ are in excellent agreement with the previous results, indicating the reliability of the present calculations. The directional dependences of the Young’s modulus and shear modulus for t-B₄CO₄ are deduced in detail, and the corresponding results suggest that the t-B₄CO₄ possesses a high degree of anisotropy. Based on the strain-stress method, the ideal tensile and shear strengths along the principal crystal directions are calculated, and the obtained results indicate that the shear mode along (001)[100] slip system dominates the plastic deformation of t-B₄CO₄, which can be ascribed to the breaking of the ionic B-O bonds. The weakest ideal shear strength of 27.5 GPa demonstrates that the t-B₄CO₄ compound is not a superhard material, but is indeed a hard material. Based on the atomic explanation that the ternary B-C-O compounds cannot acquire high ideal strength, we propose two possible routes to design superhard B-C-O compounds.

Crystal Field Splitting is Limiting the Stability and Strength of Ultra-incompressible Orthorhombic Transition Metal Tetraborides

The lattice stability and mechanical strengths of the supposedly superhard transition metal tetraborides (TmB4, Tm = Cr, Mn and Fe) evoked recently much attention from the scientific community due to the potential applications of these materials, as well as because of general scientific interests. In the present study, we show that the surprising stabilization of these compounds from a high symmetry to a low symmetry structure is accomplished by an in-plane rotation of the boron network, which maximizes the in-plane hybridization by crystal field splitting between d orbitals of Tm and p orbitals of B. Studies of mechanical and electronic properties of TmB4 suggest that these tetraborides cannot be intrinsically superhard. The mechanical instability is facilitated by a unique in-plane or out-of-plane weakening of the three-dimensional covalent bond network of boron along different shear deformation paths. These results shed a novel view on the origin of the stability and strength of orthorhombic TmB4, highlighting the importance of combinational analysis of a variety of parameters related to plastic deformation of the crystalline materials when attempting to design new ultra-incompressible, and potentially strong and hard solids.

Structural variety beyond appearance: high-pressure phases of CrB4 in comparison with FeB4

Employing particle swarm optimization (PSO) combined with first-principles calculations, we systemically studied high-pressure behaviors of hard CrB4. Our predictions reveal a distinct structural evolution under pressure for CrB4 despite having the same initial structure as FeB4. CrB4 is found to adopt a new P2/m structure above 196 GPa, another Pm structure at a pressure range of 261-294 GPa and then a Pmma structure beyond 294 GPa. Instead of puckering boron sheets in the initial structure, the high-pressure phases have planar boron sheets with different motifs upon compression. Comparatively, FeB4 prefers an I41/acd structure over 48 GPa with tetrahedron B4 units and a P213 structure above 231 GPa having equilateral triangle B3 units. Significantly, CrB4 exhibits persistent metallic behavior in contrast with the semiconducting features of FeB4 upon compression. The varied pressure response of hard tetraborides studied here is of importance for understanding boron-rich compounds and designing new materials with superlative properties.

Discovery of elusive structures of multifunctional transition-metal borides

A definitive determination of crystal structures is an important prerequisite for designing and exploiting new functional materials. Even though tungsten and molybdenum borides (TMBx) are the prototype for transition-metal light-element compounds with multiple functionalities, their elusive crystal structures have puzzled scientists for decades. Here, we discover that the long-assumed TMB2 phases with the simple hP3 structure (hP3-TMB2) are in fact a family of complex TMB3 polytypes with a nanoscale ordering along the axial direction. Compared with the energetically unfavorable and dynamically unstable hP3-TMB2 phase, the energetically more favorable and dynamically stable TMB3 polytypes explain the experimental structural parameters, mechanical properties, and X-ray diffraction (XRD) patterns better. We demonstrate that such a structural and compositional modification from the hP3-TMB2 phases to the TMB3 polytypes originates from the relief of the strong antibonding interaction between d electrons by removing one third of metal atoms systematically. These results resolve the longstanding structural mystery of this class of metal borides and uncover a hidden family of polytypic structures. Moreover, these polytypic structures provide an additional hardening mechanism by forming nanoscale interlocks that may strongly hinder the interlayer sliding movements, which promises to open a new avenue towards designing novel superhard nanocomposite materials by exploiting the coexistence of various polytypes.