*2.2.2 High-entropy borides (HEBs)*

The high-entropy borides are designed and fabricated from transition metal diborides, HfB2, ZrB2, TaB2, etc., aiming at developing a new class of ultrahigh temperature metal diboride materials with superior mechanical properties over conventional diborides.

Gild et al. [15] sintered HEBs from five-component equimolar metal diborides via SPS. The fabricated HEBs from compositions like (Hf0.2Zr0.2Ta0.2Mo0.2Ti0.2) B2 and (Mo0.2Zr0.2Ta0.2Nb0.2Ti0.2)B2 possess single-phase hexagonal AlB2 structure (**Figure 2**) as the parent metal diborides, with alternating hexagonal metal cations net and rigid boron net in the high-entropy structure. The authors reported that in case of using W2B5 in the starting precursors, single-phase solid solution was not successfully formed. Notably, W2B5 has a different crystal structure with other utilized metal borides, as well as limited solubility in other borides, which could

**Figure 2.**

*The hexagonal AlB2 structure of HEBs by Gild et al. [15] (licensed under CC BY 4.0, https://doi.org/10.1038/ srep37946).*

be potential factors of the formability of single-phase solid solution in the HEB system. The fabricated HEBs show improved hardness and oxidation resistance as compared to the average performances of the constituent borides.

The crystal structure, mechanical, and electronic properties of the HEB (Hf0.2 Zr0.2Ta0.2M0.2Ti0.2)B2 (M = Nb, Mo, Cr) were investigated by Sarkar et al. using ab initio calculations [16]. In the unique layered hexagonal lattice structure shown in **Figure 2**, the metal layer and 2D boron layer contain metallic bonds and covalent bonds, respectively, while both ionic and covalent bond were found between the two hexagonal layers. The high stability of the studied HEBs is contributed by strong boron-boron bond and metal-boron bond. Density-functional theory (DFT) calculations suggested negligible solid solution strengthening effect in elastic modulus, showing similar value with elastic modulus calculated by the mixing rule.

Tallarita et al. [17] synthesized bulk HEB (Hf0.2Mo0.2Ta0.2Nb0.2Ti0.2)B2 by selfpropagating high-temperature synthesis (SHS) from elemental metal and boron powders, followed by SPS at 2223 K. High fraction of high-entropy phase with hexagonal (space group P6/mmm) was obtained after the SHS process, along with minor amount of binary diborides and metal oxides. The SHS powders showed good sinterability with a relative density of 92.5% in the SPS product. The sintered HEB exhibits a single-phase hexagonal crystal structure which is similar to the hexagonal AlB2 structure reported by Gild et al. [15], with improved hardness (22.5 ± 1.7 GPa) and oxidation resistance. The authors mentioned that the single-phase structure could not be obtained when performing one-step reactive SPS process with the same reactants.

Based on the developed HEB system, Zhang et al. [18] adopted borothermal reduction process to synthesize high-entropy borides from metal oxides and amorphous boron powder, aiming at producing ultra-fine HEB powder with improved sinterability. The obtained HEB powders (Hf0.2Zr0.2Ta0.2Cr0.2Ti0.2)B2, (Hf0.2Mo0.2 Zr0.2Nb0.2Ti0.2)B2, and (Hf0.2Mo0.2Ta0.2Nb0.2Ti0.2)B2 showed an average particle size smaller than 1 μm and led to final relative densities greater than 95% in the SPS products. The sintered HEBs showed ultrahigh hardness values of 28.3, 26.3, and 25.9 GPa, respectively. Compared to the HEBs with same compositions sintered from −325 mesh diboride powders by Gild et al. [15] (about 22 GPa), these HEBs have improved hardness properties as a result of utilization of ultrafine starting particles in SPS.

#### *2.2.3 High-entropy carbides*

The first reported high-entropy carbides were synthesized from transition metal carbides HfC, TaC, ZrC, NbC, and TiC by Castle et al. [19]. Four-component metal

**161**

*High-Entropy Ceramics*

*DOI: http://dx.doi.org/10.5772/intechopen.89527*

carbides were mixed in equiatomic ratio using high-energy ball milling and sintered in SPS with a maximum sintering temperature of 2573 K to form high-entropy (Hf-Ta-Zr-Ti)C and (Hf-Ta-Zr-Nb)C ultra-high temperature carbides. A singlephase solid solution with a rocksalt crystal structure was formed. More complete inter-diffusion in the formation of single-phase solid solution was found in the (Hf-Ta-Zr-Nb)C than (Hf-Ta-Zr-Ti)C system. As the atomic radius of Ti, as well as the lattice parameter of TiC is the smallest among the five starting components, the effect of lattice mismatch among the starting metal carbides on formability of high-entropy solid solution was highlighted. By considering the metal atomic radii, melting points and vacancy formation energy of the carbides, it is believed that TaC, which has the lowest metal vacancy formation energy, acted as the host lattice during the diffusion, while other metal atoms migrate into TaC lattice and occupy the cation positions. The nanoindentation of the fabricated high-entropy (Hf-Ta-Zr-Nb) C shows a hardness of 36.1 ± 1.6 GPa, which is 30% higher than the theoretical value calculated from the rule of mixture. Low thermal conductivity was observed in the reported SPS high-entropy carbides. Further investigation on the microstructure, atomic structure, and localized chemical disorder of the fabricated four-component high-entropy (Hf-Ta-Zr-Nb)C was reported by Dusza et al. [20]. Homogeneity of the chemical composition in both micro- and nanoscale was proved by various experimental approaches including scanning electron microscopy (SEM), transmission electron microscopy (TEM), and electron backscattered diffraction (EBSD).

The low thermal conductivity and diffusivity behavior were observed by Yan et al. [21] in the five-component high-entropy (Hf0.2Zr0.2Ta0.2Nb0.2Ti0.2)C ceramic. The high-entropy carbide was synthesized in SPS at 2273 K and displayed rocksalt crystal structure with the metal atoms occupying the cation positions, while carbon occupied the anion positions in the lattice. The measured thermal diffusivity is reported to be lower than monocarbides and even some of the binary carbides. The increased number of principal elements in the structure led to lattice distortion, mainly through the carbon sublattice, which consequently caused severe phonon scattering. The same high-entropy carbide (Hf0.2Zr0.2Ta0.2Nb0.2Ti0.2)C in powder form was synthesized by Zhou et al. [22] via pressureless sintering in SPS.

Entropy-forming-ability (EFA), the first systematic criterion to determine relative propensity of a multicomponent (metal carbide) system to form a high-entropy single-phase crystal structure was introduced by Sarker et al. [23], published on Nature Communication in November 2018. A total of 56 five-component systems from 12 metal carbides (Hf, Nb, Mo, Ta, Ti, V, W, and Zr) were investigated in the work by evaluating the energy distribution spectra of the structures that were generated by the AFLOW-POCC (automatic FLOW partial occupation) [24] algorithm. A narrow spectrum suggests low energy barrier to introduce more configurational disorder, thereby displays high EFA value. The calculation results were verified by synthesizing nine from the 56 compositions in SPS at 2473 K and comparing the experimental and calculation results. The phase identification in **Figure 3** suggested that six compositions MoNbTaVWC5, HfNbTaTiZrC5, HfNbTaTiVC5, NbTaTiVWC5, HfNbTaTiWC5, and HfTaTiWZrC5 that have higher EFA values than the rest three compositions reveals single-phase rocksalt crystal structure after SPS, while secondary phases were observed in compositions HfMoTaWZrC5,

The *ab initio* entropy descriptor invented by Sarker et al. [23] provides a new understanding of the formation of single-phase high-entropy materials and offers a systematic guide for researchers to design high-entropy carbides. Group IV and V carbides are known to have nearly complete mutual solubility; therefore, the formation of single-phase solid solution is relatively probable, attributed to enthalpy stabilization. Meanwhile, the incorporation of carbides with different

HfMoTiWZrC5, and HfMoVWZrC5 with low EFA values.

#### *High-Entropy Ceramics DOI: http://dx.doi.org/10.5772/intechopen.89527*

*Engineering Steels and High Entropy-Alloys*

**Figure 2.**

*srep37946).*

be potential factors of the formability of single-phase solid solution in the HEB system. The fabricated HEBs show improved hardness and oxidation resistance as

*The hexagonal AlB2 structure of HEBs by Gild et al. [15] (licensed under CC BY 4.0, https://doi.org/10.1038/*

The crystal structure, mechanical, and electronic properties of the HEB (Hf0.2 Zr0.2Ta0.2M0.2Ti0.2)B2 (M = Nb, Mo, Cr) were investigated by Sarkar et al. using ab initio calculations [16]. In the unique layered hexagonal lattice structure shown in **Figure 2**, the metal layer and 2D boron layer contain metallic bonds and covalent bonds, respectively, while both ionic and covalent bond were found between the two hexagonal layers. The high stability of the studied HEBs is contributed by strong boron-boron bond and metal-boron bond. Density-functional theory (DFT) calculations suggested negligible solid solution strengthening effect in elastic modulus, showing similar value with elastic modulus calculated by the mixing rule. Tallarita et al. [17] synthesized bulk HEB (Hf0.2Mo0.2Ta0.2Nb0.2Ti0.2)B2 by selfpropagating high-temperature synthesis (SHS) from elemental metal and boron powders, followed by SPS at 2223 K. High fraction of high-entropy phase with hexagonal (space group P6/mmm) was obtained after the SHS process, along with minor amount of binary diborides and metal oxides. The SHS powders showed good sinterability with a relative density of 92.5% in the SPS product. The sintered HEB exhibits a single-phase hexagonal crystal structure which is similar to the hexagonal AlB2 structure reported by Gild et al. [15], with improved hardness (22.5 ± 1.7 GPa) and oxidation resistance. The authors mentioned that the single-phase structure could not be obtained when performing one-step reactive SPS process with the same reactants. Based on the developed HEB system, Zhang et al. [18] adopted borothermal reduction process to synthesize high-entropy borides from metal oxides and amorphous boron powder, aiming at producing ultra-fine HEB powder with improved sinterability. The obtained HEB powders (Hf0.2Zr0.2Ta0.2Cr0.2Ti0.2)B2, (Hf0.2Mo0.2 Zr0.2Nb0.2Ti0.2)B2, and (Hf0.2Mo0.2Ta0.2Nb0.2Ti0.2)B2 showed an average particle size smaller than 1 μm and led to final relative densities greater than 95% in the SPS products. The sintered HEBs showed ultrahigh hardness values of 28.3, 26.3, and 25.9 GPa, respectively. Compared to the HEBs with same compositions sintered from −325 mesh diboride powders by Gild et al. [15] (about 22 GPa), these HEBs have improved hardness properties as a result of utilization of ultrafine starting

The first reported high-entropy carbides were synthesized from transition metal carbides HfC, TaC, ZrC, NbC, and TiC by Castle et al. [19]. Four-component metal

compared to the average performances of the constituent borides.

**160**

particles in SPS.

*2.2.3 High-entropy carbides*

carbides were mixed in equiatomic ratio using high-energy ball milling and sintered in SPS with a maximum sintering temperature of 2573 K to form high-entropy (Hf-Ta-Zr-Ti)C and (Hf-Ta-Zr-Nb)C ultra-high temperature carbides. A singlephase solid solution with a rocksalt crystal structure was formed. More complete inter-diffusion in the formation of single-phase solid solution was found in the (Hf-Ta-Zr-Nb)C than (Hf-Ta-Zr-Ti)C system. As the atomic radius of Ti, as well as the lattice parameter of TiC is the smallest among the five starting components, the effect of lattice mismatch among the starting metal carbides on formability of high-entropy solid solution was highlighted. By considering the metal atomic radii, melting points and vacancy formation energy of the carbides, it is believed that TaC, which has the lowest metal vacancy formation energy, acted as the host lattice during the diffusion, while other metal atoms migrate into TaC lattice and occupy the cation positions. The nanoindentation of the fabricated high-entropy (Hf-Ta-Zr-Nb) C shows a hardness of 36.1 ± 1.6 GPa, which is 30% higher than the theoretical value calculated from the rule of mixture. Low thermal conductivity was observed in the reported SPS high-entropy carbides. Further investigation on the microstructure, atomic structure, and localized chemical disorder of the fabricated four-component high-entropy (Hf-Ta-Zr-Nb)C was reported by Dusza et al. [20]. Homogeneity of the chemical composition in both micro- and nanoscale was proved by various experimental approaches including scanning electron microscopy (SEM), transmission electron microscopy (TEM), and electron backscattered diffraction (EBSD).

The low thermal conductivity and diffusivity behavior were observed by Yan et al. [21] in the five-component high-entropy (Hf0.2Zr0.2Ta0.2Nb0.2Ti0.2)C ceramic. The high-entropy carbide was synthesized in SPS at 2273 K and displayed rocksalt crystal structure with the metal atoms occupying the cation positions, while carbon occupied the anion positions in the lattice. The measured thermal diffusivity is reported to be lower than monocarbides and even some of the binary carbides. The increased number of principal elements in the structure led to lattice distortion, mainly through the carbon sublattice, which consequently caused severe phonon scattering. The same high-entropy carbide (Hf0.2Zr0.2Ta0.2Nb0.2Ti0.2)C in powder form was synthesized by Zhou et al. [22] via pressureless sintering in SPS.

Entropy-forming-ability (EFA), the first systematic criterion to determine relative propensity of a multicomponent (metal carbide) system to form a high-entropy single-phase crystal structure was introduced by Sarker et al. [23], published on Nature Communication in November 2018. A total of 56 five-component systems from 12 metal carbides (Hf, Nb, Mo, Ta, Ti, V, W, and Zr) were investigated in the work by evaluating the energy distribution spectra of the structures that were generated by the AFLOW-POCC (automatic FLOW partial occupation) [24] algorithm. A narrow spectrum suggests low energy barrier to introduce more configurational disorder, thereby displays high EFA value. The calculation results were verified by synthesizing nine from the 56 compositions in SPS at 2473 K and comparing the experimental and calculation results. The phase identification in **Figure 3** suggested that six compositions MoNbTaVWC5, HfNbTaTiZrC5, HfNbTaTiVC5, NbTaTiVWC5, HfNbTaTiWC5, and HfTaTiWZrC5 that have higher EFA values than the rest three compositions reveals single-phase rocksalt crystal structure after SPS, while secondary phases were observed in compositions HfMoTaWZrC5, HfMoTiWZrC5, and HfMoVWZrC5 with low EFA values.

The *ab initio* entropy descriptor invented by Sarker et al. [23] provides a new understanding of the formation of single-phase high-entropy materials and offers a systematic guide for researchers to design high-entropy carbides. Group IV and V carbides are known to have nearly complete mutual solubility; therefore, the formation of single-phase solid solution is relatively probable, attributed to enthalpy stabilization. Meanwhile, the incorporation of carbides with different

#### **Figure 3.**

*(a) The energy distribution spectra of different configurations and the corresponding EFA value of the nine five-metal carbides. (b) The X-ray patterns of the sintered carbides with the same compositions, by Sarker et al. [23] (licensed under CC BY 4.0, https://doi.org/10.1038/s41467-018-07160-7).*

crystal structures was commonly understood to impede the formation of the highentropy phase because of the mismatch of lattice structure. It was observed that the addition of group VI elements (Cr, Mo, and W) is likely to reduce the chance of forming a single phase, as group VI metal monocarbides are generally demonstrated as non-cubic structure at room temperature. However, the MoNbTaVWC5 composition that simultaneously contains tungsten carbide (W2C) and molybdenum carbide (Mo2C), which exhibit orthorhombic and hexagonal structure, respectively, shows the highest EFA value among the 56 analyzed compositions and demonstrates single-phase FCC structure after SPS. The mechanical properties measured by experiments showed that the Vickers hardness and elastic modulus have significant enhancement compared to the predicted value from the rule of mixture, contributed by mass disorder in the structure and solid solution hardening. Following the work of the pioneers, a systematic study focused on the phase stability and mechanical properties of high-entropy carbides synthesized from group IV, V, and VI metal carbides [25] was carried out. It was verified that carbide system that was stated to have EFA value lower than 45 cannot form single-phase solid solution via SPS.
