Perspective: Superhard metal borides: A look forward Open Access

Metal borides possess many remarkable mechanical,^1–4 optical,⁵ magnetic,⁵ and thermal⁶ properties. Among the mechanical properties, hardness, and superhardness in particular, is a very important and appealing property as it has a host of potential applications, such as in materials for tools and abrasives. Superhardness is defined as a material exhibiting a Vickers hardness (H_v) above 40 GPa at a particular applied load, ideally at the asymptotic limit, i.e., the highest load, but more realistically at 0.49 N of applied load. The hardness at the lower load is important since most cutting operations are actually under low load. Among the hardest materials known are several elemental compounds (diamond^7,8 and γ-boron^9,10) as well as nitrides (e.g., cubic-BN¹¹), carbides (e.g., Ti_0.8Sc_0.2C and TiB₂—B₄C composite),^12–14 and borides (e.g., W_0.93Ta_0.02Cr_0.05B₄ and W_0.92Zr_0.08B₄),^15,16 all of which not only are superhard but also have a Vickers hardness greater than 50 GPa at 0.49 N of applied load or at the asymptotic limit as in the case of cubic-BN and diamond. However, cubic-BN and diamond are expensive since their bulk synthesis requires high temperature/high pressure conditions. Therefore, recent efforts to make new superhard materials have focused on compounds with short covalent bonds such as borides that can be made at ambient pressure. Binary metal borides can be further hardened through solid solution formation. To increase hardness even further, it is now important to consider ternary and higher metal borides as well as morphological control of the grain structure. Therefore, an understanding of the underlying principles of mechanical properties is needed to make additional advancements in the field of hard metal borides.

Hardness is a function of many variables but generally can be considered a weighted sum of intrinsic and extrinsic hardening effects and factors. Intrinsic effects depend on the composition of the metal boride as well as the underlying arrangement of atoms: metal atoms for sub-borides (M:B < 1:1) and boron atoms for other metal borides (M:B ≥ 1:1). The boron arrangement can range from lone metal and boron atoms to chains, networks, and backbones of boron atoms in higher borides. Generally, for a material to be intrinsically hard, it must possess both a high bulk modulus (resistance to volume change) and a high shear modulus (resistance to shape change, i.e., deformation). The bulk modulus directly correlates with the incompressibility (elastic stiffness) of a material, while the shear modulus correlates with the bending of bonds as well as with the direction and plane of shear.^17–19 

On the other hand, extrinsic effects depend strongly on the surface morphology and grain structure of the material, such as grain hardening, i.e., the Hall-Petch effect,^20–24 patterning and nanomorphology.¹⁶ Enhancing each of these factors leads to the increased hardness observed in metal borides. Intrinsic effects can be improved through the formation of solid solutions and alloys. Substitutional solid solution formation is predominantly governed by the Hume-Rothery rules requiring similarity of crystal structures, oxidation state (valency), electronegativity, and atomic size of the initial metal and the dopant (no greater than 15% difference in atomic radii).^25–28 Forming a solid solution can influence the hardness of a material through solid solution hardening effects, where due to the different atomic size of the doping metal, the crystal lattice is locally distorted and as a result dislocations can be pinned and hardness enhanced.^25–27,29 Intrinsic hardness is the result of the effects of two predominant factors: atomic size (radius) and electronic effects (valence electron density). Generally, the higher the electron density of the metal in a boride, the harder the resulting phase, for example, ReB₂ and WB₄. However, there are exceptions, such as OsB₂, where although Os metal has a higher valence electron density than Re, OsB₂ is about half as hard as ReB₂. The hardness of OsB₂ versus ReB₂ can be explained by the fact that in OsB₂, the boron nets are arranged in a “boat” conformation as opposed to the “chair” structure in ReB₂. The “boat” conformation is influenced by antibonding interactions of the osmium and boron dimers, resulting in longer boron-boron bonds, which as a result are weaker than in ReB₂, where all boron-boron bonding is enhanced.³⁰ On the other hand, the arrangement of boron can play an important role, as borides with a backbone of boron atoms forming B₁₂ icosahedra (e.g., boron itself, known as β-rhombohedral boron, MB₅₀ and MB₆₆) as well as true cage compounds [cubic-UB₁₂ (⁠$Fm3¯m$⁠) and tetragonal-ScB₁₂ (I4/mmm) structures] all form hard and superhard materials. For instance, although the bulk modulus of ZrB₁₂ is much lower than values for ReB₂ and WB₄, it still exhibits superhardness.^31,32 The high hardness of mechanically isotropic ZrB₁₂ originates from the 3-dimensional covalent network of highly symmetric B—B clusters similar to those observed in B₆O.³³ These examples illustrate that incompressibility does not necessarily lead to high hardness.

The other important factor is atomic size (in an appropriate metal coordination environment), as it usually governs what boride phases a particular metal can form. Here, Hägg’s ratio³⁴ (the ratio of boron to metal atom radii) can be applied for metals and phase formation can be predicted. According to this ratio, for most transition metals, the critical value is 0.59, above which metals form metastable structures instead of the normal cubic or hexagonal higher metal boride structures (e.g., MB₄, MB₆, and MB₁₂). For example, Hägg’s ratio for tungsten is 0.63, which correlates with W forming a defect WB_4(hex) structure, which is different from other metal tetraborides that exhibit a UB_4(tet) structure.^34,35

The atomic size is an extremely sensitive value, as the difference in size between Ti, W, and Re is enough to cause their diborides to have vastly different arrangements of boron atoms, and thus, affecting their hardness on going from flat hexagonal boron sheets for TiB₂ (r_Ti = 1.40 Å,³⁶ AlB₂-structure, P6/mmm), to alternating flat and corrugated sheets for WB₂ (r_W = 1.35 Å,³⁶ WB₂-structure, P6₃/mmc), to corrugated sheets for ReB₂ (r_Re = 1.35 Å,³⁶ ReB₂-structure, P6₃/mmm).^1,30 Furthermore, in the abovementioned example, OsB₂ has a totally different, orthorhombic structure (r_Os = 1.30 Å,³⁶ RuB₂-structure, Pmmn), yet the radius of Os is very close to that of Re. Furthermore, the relative atomic size of metals determines whether a phase is stable at ambient pressure or requires high pressure to form. For example, both Zr and Hf have similar atomic radii due to the lanthanide contraction (1.55 Å);³⁶ however, in a 12 coordinate environment, Hf has a slightly smaller atomic size than Zr (1.580 vs. 1.603 Å),³⁷ rendering ZrB₁₂ a phase that can be synthesized at ambient pressure, while HfB₁₂ requires 6.5 GPa to form,^37,38 although these high pressure dodecaborides can be stabilized in solid solutions.^39–41 

Furthermore, the relative atomic size in solid solutions can lead to limited solubility or the formation of a completely new ternary boride, with a structure different from the parent binary phases, such as in the system Re_1−xY_xB₂. In this example, the parent phases are hexagonal YB₂ (r_Y = 1.80 ų⁶) and ReB₂ and at 50/50 at. % metal substitution, a new orthorhombic (although nominally a diboride) phase forms with the stoichiometry YReB₄⁴² (YCrB₄-structure, Pbam) due to the relative size of the metals being outside of the range stipulated by the Hume-Rothery rules (<15% atomic radius difference) as illustrated in Fig. 1. Additionally, there exists a whole array of other pseudo-diboride structures, such as Y₂ReB₆^43–45 (Pbam), Y₃ReB₇^45,46 (Cmcm), and YMo₃B₇^47–49 (Pnma) as shown in Figs. 1 and 2. The first two structures (YReB₄ and Y₂ReB₆) resemble layered structures, similar to AlB₂ diborides. However, instead of having boron arranged in sheets of hexagons, these structures have boron atoms arranged in 5-, 6- and 7-membered rings. For example, Y₃ReB₇ has boron atoms arranged in corrugated cages. In the YMo₃B₇ structure, the boron atoms are arranged in stacked hexagonal bands, 6 hexagons wide, and infinite in length, while the metal atoms are arranged in chains. The last two structures in particular show how much of an effect metal atoms can have on the structure of the resulting boride, as the main difference is in the number of metals in the first or second position.

In order to enhance extrinsic effects, morphology, patterning, and grain size need to be controlled. This can be achieved through the addition of secondary metals which alter the cooling rate of the resultant boride sample.^50–54 For example, the addition of Zr to WB₄ causes not only a change in patterning but also a change to a nano-grain morphology at an 8 at. % doping level (Fig. 3).¹⁶ These methods can be further expanded to the synthesis of bulk nano-forms of known superhard materials, for example nanowires of W_0.5Ta_0.5B.^55,56 Patterning can be achieved through the use of doping metals which exhibit limited solubility and form phases with a vastly different melting temperature relative to the main phase, e.g., 3225 °C for TiB₂⁵⁷ vs. 2020 °C for WB₄.⁵⁸ For example, the addition of Ti to WB₄ causes the formation of TiB₂, which has a melting point over 1000 °C higher than WB₄, and as such forms before WB₄, thus providing a template for the growth of WB₄ grains (Fig. 4).¹⁶ 

Further investigation of WB₄ with other dodecaboride forming transition metals and lanthanides has led to additional fine-grained morphologies (Fig. 5).⁵⁹ These doping metals are completely soluble in the WB₄ defect cuboctahedral structure with increasing metal concentration until equilibrium is achieved with the doping metal’s highest boride or boron-rich boride phase. The observed phase equilibrium can be attributed to the reduction in total energy through the formation of the most thermodynamically favorable phase(s). Coexistence of the WB₄ parent phase with a boron-rich phase results in “dendritic” nanopatterning and consequently, smaller grains. This change in morphology and reduction in grain size pins dislocations in the bulk material, thus, enhancing the overall hardness.

Another factor affecting mechanical properties comes from the fact that some boride phases, e.g., WB₄ and ZrB₁₂, cannot be prepared in pure form using stoichiometric compositions. This necessitates either using excess boron or allowing lower boride phases to form, which can lead to inferior mechanical properties. WB₄ requires a minimum metal to boron ratio of 1:8.5 but is usually prepared from a melt at a ratio of 1:12, with lower ratios resulting in some WB₂ impurity.⁶⁰ However, it was found that WB₄ can be prepared almost stoichiometrically using ∼32 at. % Ta substitution, the resulting phase exhibited lower hardness.⁶⁰ Similarly, ZrB₁₂ has to be prepared at a metal to boron ratio of 1:20 in order to avoid the ZrB₂ phase.³² Although in a solid solution with YB₁₂ no lower phases exist at almost stoichiometric composition. Therefore, for many phases, it is still relevant to try to find compositions that result from using stoichiometric amounts of reactants yet possess similar mechanical properties.

All of the abovementioned factors: formation of solid solutions and changes in surface morphology and patterning are relevant not only to mechanical properties but also to oxidation resistance, magnetic, electronic, and optical properties as well as other potential applications, not usually attributed to borides, such as catalysis.⁶¹ Furthermore, going to the nanoscale^62,63 can potentially improve many of the properties listed above.^64–66 In addition, recent studies in the field have highlighted a simple synthesis of nanoscale transition metal borides with a wide range of different morphologies (nanorods, nanosheets, nanoprisms, nanoplates, and nanoparticles) using the redox chemistry of Sn/SnCl₂.⁶⁷ Moreover, metal borides are capable of forming layered structures with the addition of aluminum, which can be further etched to form 2D nanosheets.^68–70 

Although it is difficult if not impossible to devise simple rules (due to hardness being an aggregate of many factors) for what can be expected in terms of effects on hardness from using a particular metal dopant in each and every case, it is possible to describe general trends. In the case of intrinsic hardness effects, such as substitutional metal doping (Hume-Rothery rules),^25–27,29 the main effect on hardness is through solid solution hardening, which causes lattice distortions and consequently pins dislocations. In the case of extrinsic hardening, the main effect of the metals is through changes in morphology: through templating, due to the difference of phase melting points (e.g., the addition of group 4 or 5 metals), nanomorphology, due to rapid cooling resulting in a large number of nucleation sites and small grain size (e.g., the addition of scandium or zirconium), or patterning (e.g., the addition of yttrium or lanthanides).

The study of metal borides is a very old field, as such the limits of the binary boride world have all but been exhausted. Therefore, it is necessary to move to ternary and higher borides as starting materials. These compositions are all the more challenging due to factors such as phase stability relative to metal substitutions and simultaneous equilibrium of several phases in the product. The vast array of determined crystal structures to date offers the potential for targeted approaches toward structure and property predictions.⁷¹ Although there are almost no data for mechanical properties of ternary (e.g., YReB₄, Y₂ReB₆, Y₃ReB₇, and YMo₃B₇) and higher borides, a comprehensive understanding of the intrinsic and extrinsic factors discussed above can be utilized to approximate hardness on the basis of structure and chemical bonding.

We thank the National Science Foundation Division of Materials Research, Grant No. DMR-1506860 (R.B.K.) and Virginia Commonwealth University Startup Grant No. 137422 (R.M.) for financial support.