Progress in functional studies of transition metal borides^*

In monoborides, there are three main types of crystal structure, namely CrB-type, β-FeB-type, and α-MoB-type. The crystal structure of transition metal monoborides is shown in Fig. 1. The crystal structure of CrB, β-FeB, and α-MoB belong to the orthorhombic with space group Cmcm (No. 63),^[7] the orthorhombic with space group Pnma (No. 62),^[8] and the tetragonal with space group I41/amd (No. 141),^[9] respectively. The main difference between the three crystal structures is the position of the boron zigzag chain. In CrB, boron zigzag chains are parallel along the a axis. There are seven monoborides belonging to the CrB-type structure, which are respectively VB, CrB, α-FeB, NiB, β-MoB, TaB, and β-WB. The boron zigzag chains of β-FeB are similar to those of CrB in that they are parallel along the a axis, but the inclination of boron zigzag chain is different. The structure of TiB, MnB, β-FeB, CoB, and IrB is β-FeB-type. In contrast to CrB, α-MoB possesses the perpendicular boron zigzag chain skeleton. So far, only two monoborides with α-MoB-type structure have been found, namely α-MoB and α-WB.

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The structures of diborides can be roughly classified into five structural types: AlB₂-type, β-MoB₂-type, RuB₂-type, α -WB₂-type, and ReB₂-type. The crystal structure of transition metal diborides is shown in Fig. 2. Boron atoms form 2D boron layers or quasi-3D wrinkled boron layers in these structures. Among diborides, the number of TMB₂ with AlB₂-type structure is the largest.^[10] So far, twelve of TMB₂ with AlB₂-type structure have been prepared, namely, ScB₂, TiB₂, VB₂, CrB₂, MnB₂, YB₂, ZrB₂, NbB₂, α-MoB₂, HfB₂, TaB₂, and α -WB₂. In the AlB₂-type structure, boron atoms form graphite-like boron layers and transition metal atoms compose close-packed layers. Each transition metal atom sits at the center of a regular hexagon of boron atoms. Each boron atom has six nearest neighbor transition metal atoms which form a trigonal prism. The boron layer and the transition metal layer alternately arranged.

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Among the TMB₂ structures, other structures can be considered as modifications of the AlB₂-type structure. The alternating arrangement of boron and transition metal layers is the same, but the 2D structural units that boron atoms form are different. In these structures, boron atoms form a quasi-3D wrinkled boron layer, which is mainly caused by the amount of charge transfer and the directivity of the B–B covalent bond. In the structure of β-MoB₂, there are two kinds of structure units: graphene-like boron layer and wrinkled boron layer, which also arranged alternately.^[11] Different from the boron layer in the β-MoB₂ structure, the boron atom formation in the RuB₂ structure is pseudo-hexagonal corrugated boron layers.^[12] Only RuB₂, OsB₂, and IrB₂ have RuB₂-type structure.^[12,13] The boron layers of ReB₂ are all quasi-3D wrinkled boron layers, which is due to the special electron structure of rhenium formed a special electron transfer.^[12,14–19] This quasi-3D boron structure has an important effect on the properties of ReB₂, which makes it more difficult to compress in the c-axis direction.^[20]

There are some controversies about the structure of MnB₂, MoB₂, and WB₂. Manganese diboride has two crystal structures, AlB₂-type and ReB₂-type. Theoretical calculations showed that the ReB₂-type MnB₂ was more stable than the AlB₂-type MnB₂ and was predicted to be a superhard material,^[21,22] but only AlB₂-type MnB₂ was synthesized experimentally up to now.^[23] MoB₂ has two phases with α-MoB₂ and β-MoB₂. The theoretical calculations suggest the α-MoB₂, which has a hexagonal crystal structure with space group P6/mmm (No. 191), is thermodynamically unstable.^[24–27] But the α-MoB₂ was obtained in the experiment and is stable structures at ambient conditions. β-MoB₂ was originally considered to be the Mo₂B₅-type structure.^[28,29] Okata et al. firstly reported that the ratio of molybdenum atom and boron atom is 1:2 in Mo₂B₅, which is actually β-MoB₂.^[30] β-MoB₂ has a rhombohedral crystal structure with R-3m (No. 166) symmetry. As with the same group element molybdenum, the crystal structure of WB₂ also has the so-called W₂B₅ phase. So far, three crystal structures of WB₂ were reported in the experiment, Mo₂B₅-type (R-3m), AlB₂-type (P6/mmm), and W₂B₄-type (P63/mmc).^[31–41] However, the phonon calculations suggested the AlB₂-type WB₂ is dynamically unstable and was predicted to be a stable high-pressure phase above 65 GPa.^[33] Another controversy is the stoichiometric ratio of W₂B₅.^[42–44] Frotscher et al. reported that W₂B₅ is actually W₂B₄ (WB₂) with a space group of P63/mmc (No. 194),^[45] in which the crystal structures and composition were probed by x-ray diffraction (XRD), neutron diffraction, energy dispersive spectrometer (EDS), WDS, scanning electron microscope (SEM), and so on.

In the past few years, TMB₄ was paid attention extensively, because CrB₄, MnB₄, and FeB₄ were considered as potential superhard materials.^[21,46–54] The crystal structure of CrB₄, MnB₄, and FeB₄ has many similarities, they all have a 3D network structure. The crystal structure of CrB₄, MnB₄, and FeB₄ is shown in Figs. 3(a), 3(b), and 3(c). The crystal structure of CrB₄ belongs to the orthorhombic. Initially, CrB₄ was described in the space group of Immm (No. 71),^[46,55] but the theoretical calculation shown that the Pnnm (No. 58) phase of CrB₄ is more stable.^{[48,49,56,57]} According to the results of XRD and TEM, Niu et al. believed the space group of CrB₄ is Pnnm (No. 58).^[48] Wang et al. reported that the structural difference between Immm and Pnnm is the site of the boron atom.^[58] The powder x-ray and neutron diffraction patterns of Immm and Pnnm structures were simulated for CrB₄. The results showed that XRD of Immm and Pnnm structures are the same, the neutron diffraction peaks are the difference. The structural controversy of CrB₄ can be resolved by neutron diffraction. The structure of FeB₄ is similar to that of CrB₄. The symmetry of FeB₄ obtained by the experiment is Pnnm (No. 58),^[59] which is in agreement with the theoretical calculation results.^[60] MnB₄ was initially described in the space group of C2/m (No. 12).^[61] The theoretical calculation suggests that the structure of MnB₄ should be similar to that of CrB₄ and FeB₄, but the experimental results show that the structure of MnB₄ is monoclinic with the space group of P2₁/c (No. 11).^[52,62–64] This is mainly due to Peierls distortion, which causes the Mn–Mn atom dimers to appear in the MnB₄ structure and thus distort the MnB₄ crystal structure.

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The crystal structure of MoB₄ and WB₄ is also a controversial issue. Theoretically, the structure of WB₄ was considered to be thermodynamically unstable.^[65] Some studies suggested that the reported WB₄ is probably stoichiometric WB₃. Although they have the same hexagonal crystal structure with P63/mmc (No. 194) symmetry,^[66] the structure of WB₃ is more stable in theory.^[67,68] But Li et al. reported that the structure of WB₄ and WB₃ are thermodynamically stable and should be accessible to synthesis.^[69] Because the boron atom is small, it is difficult that the site of boron atoms is detected by x-ray diffraction. The symmetry of WB₄ and WB₃ is the same, thereby the x-ray diffraction diagram is similar except for diffraction peak strength. The difference in the crystal structure of WB₄ and WB₃ is the boron–boron dimer. There is the boron–boron dimer in WB₄. Cheng et al. reported that the results of Ac-HRTEM experiments suggested boron–boron dimer does not exist,^[70] so WB₃ was confirmed to exist. The crystal structure of WB₄ (WB₃) is shown in Fig. 3(d). Some other studies indicated that tungsten atom is the deficiency in WB₃, the chemical formula of WB₃ should be W_{1 – x} B₃.^[71] The crystal structure of reported WB₄ (WB₃) needs further investigations in theory and experiments. The crystal structure of MoB₄ is very similar to WB₄. The reported MoB₄ is not actually stoichiometric MoB₄.^[72,73] The general formula can be written as Mo_{1 – x} B₃, for example, Mo_0.8B₃ and Mo_0.91B₃. The crystal structure of Mo_{1 – x} B₃ is consistent with that of WB₄ in Fig. 3(d). In addition, the calculations suggested that the R-3m structure of ReB₄ is thermodynamically stable, but so far ReB₄ has not been prepared.^[74]

The crystal structure of transition metal dodecaborides (TMB₁₂) can be divided into two structural types: UB₁₂-type crystal structure,^[75] which is the majority of TMB₁₂ structure, and ScB₁₂-type crystal structure,^[76] to which only ScB₁₂ belongs. The crystal structure of UB₁₂-type and ScB₁₂-type are shown in Fig. 4. In both types of crystal structures, there are the same structural units in which TM atoms are surrounded by B₂₄ cages. In the UB₁₂-type structure, the structural unit of B₂₄ cages and TM atoms form the face-centered cubic structure, while in the ScB₁₂-type structure, the structural unit of B₂₄ cages and TM atoms form the body-centered tetragonal structure. In addition, B₁₂ clusters also exist in both structures. The crystal structure of UB₁₂-type is the same as that of NaCl, with B₁₂ clusters at the Na sites and TM atoms at the Cl sites. Interestingly, the structure of both B₂₄ cages and B₁₂ clusters is cuboctahedral networks.

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The ReB₂ is particularly noticeable. Base on the first-principle calculations, Hao et al. reported the mechanical properties of ReB₂.^[77] Chung et al. reported that ReB₂ was a superhard material experimentally.^[20] So ReB₂ was widely concerned. This is the beginning of the search for superhard materials in TMBs. The hardness of ReB₂ is mainly due to the existence of wrinkle boron layers in the crystal structure of ReB₂, which is a quasi-3D structure. However, asymptotic hardness is the true hardness of a material. ReB₂ only exhibited superhard property (H_V ≥ 40 GPa) under a load of 0.49 N.^[20,78] The Vickers hardness of ReB₂ is 31 GPa under a load of 4.9 N. The Vickers hardness of ReB₂ is shown in Fig. 5. Gu et al. reported that the hardness of ReB₂ is ∼ 27 GPa under a load of 4.9 N,^[79] but Qin et al. reported that the hardness of ReB₂ is only 18.4 GPa under a load of 4.9 N.^[80] This result is consistent with the theoretical calculation of Yang et al.^[81] The hardness difference of ReB₂ is ∼ 13 GPa under a load of 4.9 N. This is mainly influenced by some extrinsic factors, such as boron content. Because it is usually necessary to add excess boron to prepare the sample, this allows excess boron in the product. Levine et al. reported that the excess boron distributed through the compact drastically reduces the hardness of the materials.^[82] Because of the excess boron powder compact of ReB₂, the hardness is substantially reduced. Actually, the effect of amorphous boron on the hardness of polycrystalline TMBs is still needed to be further investigated because amorphous boron also has a high hardness. The hardness of the single crystal is the intrinsic hardness of the sample. So far, although the hardness of singlecrystal of ReB₂ has been reported, there are not the asymptotic hardness values under the high load.

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Although ReB₂ is not a superhard material, hardness greater than 25 GPa is rare in layered structures. According to previous reports, TMBs with 3D boron atomic structure are more likely to have high hardness. The high hardness of ReB₂ is mainly due to the wrinkled boron layer in its structure, which reflects the quasi-3D effect. This is also reflected in other TMB₂. MoB₂ has two phases with α-MoB₂ and β-MoB₂. The crystal structure of α-MoB₂ is AlB₂-type with space group P6/mmm (No. 191). The asymptotic Vickers hardness of α-MoB₂ is ∼ 15 GPa. β-MoB₂ has a rhombohedral crystal structure with R-3m (No. 166) symmetry, and its asymptotic Vickers hardness is ∼ 22 GPa. The graphite-like boron layers in α-MoB₂ can transfer to puckered boron layers in β-MoB₂ with enhanced the Vickers hardness of 7 GPa.^[11]

In the OsB₂ structure, boron atoms form another quasi-3D boron layer, a pseudo-hexagonal corrugated boron layer. The investigations suggest that the Vickers hardness of RuB₂-type OsB₂ reaches 37 GPa under a load of 0.245 N.^[83] The value is close to the standard of superhard materials (H_V ≥ 40 GPa). Hebbache et al.\ reported that RuB₂-type OsB₂ showed an asymptotic hardness of ∼ 29 GPa,^[84] but Gu et al. reported that RuB₂-type OsB₂ showed only an asymptotic hardness of ∼ 17 GPa.^[79] Although the hardness of RuB₂-type OsB₂ is a quite difference, both indicated that RuB₂-type OsB₂ is not a superhard material under high load. The investigations suggested that the hardness of RuB₂-type OsB₂ is highly dependent on the crystallographic orientation. The average hardness along the 〈 100 〉 direction is significantly higher than that in the orthogonal 〈 001 〉 direction. This is attributed to the stronger B–B bonds found along the 〈100〉 direction, which dominate the dislocation motion.^[85] There have been many studies on the compressibility of RuB₂-type OsB₂ in experiments and theories,^[33,86–91] and the results showed the bulk modulus of RuB₂-type OsB₂ was in the range of 365 GPa–395 GPa.^[85,92] The compressibility of RuB₂-type OsB₂ is also anisotropy. The c direction of the crystal is the most incompressible. It is interesting that the incompressibility of RuB₂-type OsB₂ along the c axis is even larger than the analogous linear incompressibility of diamond.^[84] This is because RuB₂-type OsB₂ belongs to the orthogonal crystal system with space group Pmmn (No. 59),^[12,93] under the external force, the Os atom and B atoms squeeze each other, so that the electrostatic repulsion between atoms reaches the maximum value, thereby increasing the incompressibility of the c axis. The RuB₂-type OsB₂ exhibits metallic property, but there is a covalent bond of B–B and Os–B that leads to a high hardness, which is generated by the superposition of the d-electron layer of the Os and the p-electron layer of B.

High boron phases tend to form quasi-3D or 3D structures and thus exhibit high hardness, but some low boron phases also exhibit good hardness. These results provide a deeper understanding of the hardness mechanism of materials. Han et al. report that the higher Vickers hardness of CrB (∼ 20 GPa)^[7] compared to CrB₂ (∼ 16 GPa)^[58] is mainly attributed to the strong 3D Cr–B and zigzag B–B bonding networks in CrB. The results indicate that the monoborides can have better mechanical behavior than the diborides counterparts. The boron content is hence not necessary criteria for the design of hard and superhard materials. The Vickers hardness of CrB and CrB₂ is shown in Fig. 5. The symmetrical electronic partition of the 3D Cr–B and zigzag B–B bonding networks is the reason why CrB can have higher bulk moduli than CrB₂ and CrB₄. The asymptotic Vickers hardness of MnB, Mn₃B₄, and MnB₂ are ∼ 16 GPa,^[94] ∼ 16 GPa,^[95] and ∼ 12 GPa,^[23] respectively. Similar to CrB, MnB and Mn₃B₄ have a higher hardness than that of MnB₂ due to the covalent zigzag or double zigzag B₁–B₂–B₁ backbone. The experimental results indicated the asymptotic Vickers hardness of α-MoB (18.4 GPa) is higher than that of β-MoB (12.2 GPa).^[9] Although the crystal structure of α-MoB and β-MoB has the boron zigzag chain (Bzc) skeletons (Bzcs), it is a different arrangement. The Bzcs of α-MoB has a higher shear modulus, and a higher grain boundary density, which resists the glide of dislocation. The results demonstrated modulating the covalent bond array and grain boundary density can also create high hardness in the low-boron content TMBs.

WB₄ is the first tetraboride to be synthesized, and its hardness exceeds 40 GPa under 0.49-N load,^[96] which has attracted a lot of attention. But the asymptotic Vickers hardness of WB₄ was in the range of 28 GPa–32 GPa.^[79,96,97] The crystal structure of WB₄ does not exist, it should actually be WB₃. The calculation indicated that the asymptotic hardness of WB₄ (WB₃) is lower than that of ReB₂ (∼ 27 GPa).^[79,98,99] Boron was excessive in reported experiments to prepare WB₄ (WB₃), and the hardness of amorphous boron is above 30 GPa,^[100] so the reported hardness of WB₄ (WB₃) could be influenced by excess amorphous boron. If the hardness of WB₄ (WB₃) is to be obtained, the effects of amorphous boron must be excluded. Tao et al. restudied the hardness of WB₃ and found that the hardness of WB₃ excluding the effect of amorphous boron is just 25.5 GPa,^[100] which is really lower than that of ReB₂. The asymptotic hardness of WB₃ is exhibited in Fig. 5.

Theoretical calculation showed that the Cr, Mn, Fe, and B in CrB₄, MnB₄, and FeB₄ are covalently bonded to form a strong 3D network like as diamond. So there could be superhard materials in these materials. However, the asymptotic Vickers hardness of CrB₄ is only ∼ 30 GPa.^[58] The Vickers hardness of CrB₄ is shown in Fig.5. Although it is the highest hardness of the Cr–B system, CrB₄ is not a superhard material. The reasons why CrB₄ with 3D crystal structure do not show superhard property are quantum-mechanical effect involving a transition between two-center and three-center bonding among the boron atoms that reduces the rigidity and directionality of the boron bonding and mechanistic effect caused by the pressure beneath the indenter that drives a lateral bond and volume expansion that further stretches and weakens the boron bonds in addition to the shear deformation in the CrB₄ structure under Vickers indentation hardness tests.^[50] Gou et al. reported that the Vickers hardness of MnB₄ is ∼ 37 GPa under a load of 9.8 N,^[64] but this value remains controversial. Knappschneider et al. also reported the nanoindentation hardness of MnB₄ with ∼ 25 GPa,^[63] which is well consistent with the reported by Ma et al., which the polycrystalline hardness of MnB₄ is about 20.1 GPa.^[101] FeB₄ was reported to be superhard materials with a hardness of 62 GPa.^[102] However, the other measurements of the hardness of FeB₄ indicate that FeB₄ is not a superhard material. Its asymptotic hardness is only 15.4 GPa, which is consistent with the calculated hardness (18.4 GPa).^[59] The Vickers hardness of FeB₄ is shown in Fig.5. Although this is still a contentious issue about its hardness, the point can be sure that FeB₄ is not a superhard material.

The higher boron content of transition metal dodecaborides also forms the 3D structures, and the presence of B₁₂ clusters in the structure suggests that TMB₁₂ are likely to exhibit superhard properties. The hardness of both ZrB₁₂ and ScB₁₂ exceeds 40 GPa at 0.49-N load,^[103,104] but unfortunately does not show superhard properties at high loads. The hardness of ZrB₁₂ and ScB₁₂ is 27 GPa^[103] and 28 GPa^[104] at 5 N, respectively. The Vickers hardness of ZrB₁₂ is shown in Fig. 5. The hardness of the single crystal of ZrB₁₂ is lower than that of polycrystalline samples. This may be caused by the effect of grain boundary in the polycrystalline samples.

So far, most of the TMBs prepared are conductors, some of which have excellent conductivity comparable to good metal conductors even in the high boron phase. ZrB₁₂ exhibits superior metallic behavior with ultralow electrical resistivity (∼ 18 μ Ω ⋅cm)^[103] at room temperature, which is comparable to that of Pt (∼ 20 μ Ω ⋅cm). The reason why zirconium dodecaboride shows metallic behavior is the extensive B–B covalent network in ZrB₁₂ can form delocalized π-bonds, which generate extensive conducting channels for valence electrons by contacting Zr 4d orbitals.

With the discovery of superconductivity of MgB₂,^[105] the electrical transport properties of TMBs have been paid more attention. So far, there are many TMBs with superconducting properties. The crystal structure of MgB₂ is AlB₂-type, but only ZrB₂ has been reported to have superconductivity with T_c = 5.5 K among the AlB₂-type TMB₂.^[106] However, these results were not observed in later studies. Stoichiometric NbB₂ does not show superconductivity, but NbB_{2 + x} with excess boron does show superconductivity with a critical temperature of 8.9 K–11 K.^[107,108] Like NbB_{2 + x} , adding excess boron to MoB₂ will make it exhibits superconductivity. MoB_{2 + x} also was reported to show superconductivity at T_c ≈ 7.5 K.^[108] Tang et al. reported that a boron-rich molybdenum boride, the large single-crystal of nonstoichiometry molybdenum triboride (Mo_0.757B₃), was prepared under high-pressure high-temperature conditions, it exhibits superconductivity with a T_C of 2.4 K.^[110] The analysis of theoretical calculations indicated that the occurrence of its superconductivity is derived from the partial occupancy of Mo atoms. MoB₄ is not a superconductor, but the Ti-doped and Nb-doped MoB₄ were found to be superconducting near 6 K to 8 K.^[111] Renosto et al. reported that the Zr_0.96V_0.04B₂ specimen exhibited bulk superconductivity at a critical temperature of 8.7 K and explained that the superconductivity of the Zr_0.96V_0.04B₂ specimen was related to multiple bands at the Fermi surface.^[112,113] Gou et al. reported the experiment results that FeB₄ shows the bulk superconductivity below 2.9 K.^[102] However, the later experimental investigation showed that FeB₄ did not exhibit the bulk superconductivity for temperature as low as 2.5 K.^[59] FeB₄ shows a metallic behavior from room temperature to 30 K. Further investigation is still needed for bulk superconductivity of FeB₄. TMB₁₂ with higher boron content has also been found to have superconductivity, such as ScB₁₂ (0.39 K),^[114] YB₁₂ (4.7 K),^[115,116] and ZrB₁₂ (5.8 K).^{[103,117–120]}

Energy and environment are the most important issues involved in the sustainable development of human society. Fossil fuels are a non-renewable resource, and their use will bring about environmental pollution, and the development of clean energy has become an urgent practical demand. Electrochemical water splitting is an important method for preparing clean fuel hydrogen with water, but the preparation of hydrogen is difficult and generally requires a catalyst. The most effective electrocatalysts are Pt-based materials for the hydrogen evolution reaction (HER), but the high cost and low earth abundance of noble metal based catalyst limit their wide use. It is very important to develop well-working nonprecious metal based electrocatalysts for HER.

α-MoB₂ is a superefficient electrocatalyst for the HER and has excellent catalytic stability during HER.^[121–124] It was demonstrated by Chen et al. that α-MoB₂ efficiently catalyzes the HER, even at large current densities.^[125] The theoretical and experimental results suggested the catalytic activity of α-MoB₂ is due to its excellent conductivity, a large density of efficient catalytic active sites, and good mass transport properties. β-MoB₂ is also the efficient electrocatalyst for HER, but the catalytic activities of β-MoB₂ is lower than that of α-MoB₂. In the Mo-B system, α-MoB₂ is the most efficient catalyst for the HER. All the tungsten borides have the catalytic activity for the HER. Like α-MoB₂, W₂B₄-type WB₂, which has the same crystal structure with α-MoB₂, is also the most efficient catalyst for the HER in the W–B system.^[126,127]

With the rapid development of micro-electromechanical systems devices, magnetic sensors, high-speed motors, and magnetic springs, new requirements are put forward for ferromagnetic materials. The low hardness of traditional magnetic materials, such as Fe (1.4 GPa),^[128] Fe₃O₄ (4 GPa),^[129] FeNi (4 GPa),^[130] etc., inevitably limits the application of traditional magnetic materials in harsh conditions. The demand for strong ferromagnetic materials with high hardness is constantly enhanced. Although the hardness of TMBs does not reach the hardness of superhard materials, most TMBs reach the hardness of cemented carbide. MnB exhibits high Curie temperature (546 K), high saturated magnetization (155.5 emu/g), and low coercive field (H_c = 15.9 Oe, 1 Oe = 79.5775 A⋅m⁻¹).^[94] The coercive field of MnB indicates that it is a soft magnetic material. The asymptotic Vickers hardness of MnB is ∼ 16 GPa, which is far higher than that of traditional ferromagnetic materials. Fe₂B also exhibits ferromagnetism and the Curie temperature (1017 K) is comparable to that of Fe (1043 K). The asymptotic Vickers hardness of Fe₂B (12.4 GPa) is far higher than that of traditional ferromagnetic materials.^[131] Fe₂B is a promising candidate for strong ferromagnetic and high hardness material.

Refractory materials are widely used in industrial fields, such as aerospace, geological exploration, machinery manufacturing, etc. The majority of TMBs are refractory. ZrB₂ has been widely paid attention to due to its excellent refractory properties. ZrB₂ has a hexagonal crystal structure with the space group of P6/mmm (No. 191). Because ZrB₂ has strong covalent B–B bonds, its melting point has a very high temperature of 3245 °C.^[132–134] ZrB₂ also shows outstanding oxidation resistance, surviving thermal cycling up to 2700 °C in air.^[135] The thermal conductivity (k) of ZrB₂ is its notable property. Kinoshita et al. reported that room-temperature k values for single crystals are 140 W⋅(m⋅K)⁻¹ along the c axis and 100 W⋅(m⋅K)⁻¹ along the a axis.^[136] Lonergan et al. reported the high temperature thermal conductivity of ZrB₂, which shows thermal conductivity of 127 W⋅(m⋅K)⁻¹ at 298 K and 80 W⋅(m⋅K)⁻¹ at 2273 K.^[137] Besides, the high temperature flexure strengths of ZrB₂ was measured by Neuman et al. The investigations indicated that strength between room temperature and 1200 °C was ∼ 390 MPa, decreasing to a minimum of ∼ 170 MPa between 1400 °C and 1500 °C and the strength increased to ∼ 220 MPa between 1600 °C and 2300 °C.^[138] The increase in strength was mainly attributed to stress relief through plastic flow. As a kind of high temperature resistant material, ZrB₂ has been used in the aerospace field.