Phase stability,mechanical and thermodynamic properties of (Hf,Zr, Ta,M)B2 (M= Nb,Ti, Cr,W) quaternary high-entropy diboride ceramics via first-principles calculations

As the high-entropy design concept applied to the diboride ceramic system, high-entropy diboride ceramics with a wide range of composition control, is expected to become a new high-performance material for extreme high-temperature environments. Herein, the effects of four transition metal elements (Nb, Ti, Cr, W) on the phase stability and properties of (Hf, Zr, Ta)B₂-based high-entropy diboride ceramics are systematically investigated via the first-principles calculations. All components were identified as thermodynamically, mechanically and dynamically stable from enthalpy of formation, elastic and phonon spectrum calculations. Among these, compared with the (Hf, Zr, Ta)B₂ ceramics, the addition of Nb and Ti on the metal sublattice is beneficial to improve the mechanical properties of ceramics, including Young's modulus, hardness and fracture toughness, while the introduction of Cr and W weakens the strength of covalently and ionic bonds inside the material, reducing its mechanical properties. The predicted thermophysical properties show that the high-entropy diboride ceramics containing Nb and Ti have better high-temperature comprehensive performance, including higher Debye temperature, thermal conductivity and lower thermal expansion characteristics, which is conducive to the application in extreme high-temperature environments. This research will provide important guidance for the design and development of new high-performance high-entropy diboride ceramics.     

Pressureless sintering of high-entropy boride ceramics

High-entropy boride ceramics were densified by pressureless sintering. Green densities of the ceramics varied by composition with the highest green density of 53.6 % for (Hf, Nb, Ta, Ti, Zr)B₂. After pressureless sintering, relative densities up to ∼100 % were obtained for (Cr, Hf, Ta, Ti, Zr)B₂ and (Hf, Ta, Ti, V, Zr)B₂. Two compositions, (Hf, Ta, Ti, W, Zr)B₂ and (Hf, Mo, Ti, W, Zr)B₂ contained secondary phases and did not reach full density. All compositions had average grain sizes less than 10 µm and less than 2 vol % of residual B₄C. This is the first report of conventional pressureless sintering of high-entropy boride ceramics powder compacts without evidence of liquid phase formation.     

Boro/carbothermal reduction co-synthesis of dual-phase high-entropy boride-carbide ceramics

Dense, dual-phase (Cr,Hf,Nb,Ta,Ti,Zr)B₂-(Cr,Hf,Nb,Ta,Ti,Zr)C ceramics were synthesized by boro/carbothermal reduction of oxides and densified by spark plasma sintering. The high-entropy carbide content was about 14.5 wt%. Grain growth was suppressed by the pinning effect of the two-phase ceramic, which resulted in average grain sizes of 2.7 ± 1.3 µm for the high-entropy boride phase and 1.6 ± 0.7 µm for the high-entropy carbide phase. Vickers hardness values increased from 25.2 ± 1.1 GPa for an indentation load of 9.81 N to 38.9 ± 2.5 GPa for an indentation load of 0.49 N due to the indentation size effect. Boro/carbothermal reduction is a facile process for the synthesis and densification of dual-phase high entropy boride-carbide ceramics with both different combinations of transition metals and different proportions of boride and carbide phases.     

Synthesis,mechanical, and thermophysical properties of high-entropy (Zr,Ti,Nb,Ta,Hf)C0.8 ceramic

Two high-entropy carbides, including stoichiometric (Zr,Ti,Nb,Ta,Hf)C and nonstoichiometric (Zr,Ti,Nb,Ta,Hf)C_0.8, were prepared from monocarbides and ZrH₂. Their sinterability, microstructures, mechanical properties, thermophysical properties, and oxidation behaviors were systematically compared. With the introduction of carbon vacancy, the sintering temperature was lowered up to 300°C, Vickers hardness was almost unaffected, whereas the strength decreased significantly generally due to the decrease of covalent bonds. The thermal conductivity shows a 50% decrease for nonstoichiometry high-entropy carbide, which is a major consequence of the lower electrical conductivity. The oxidation resistance in high temperature water vapor was not sensitive to carbon stoichiometry.     

Low-temperature sintering of single-phase,high-entropy carbide ceramics

Dense (Hf, Zr, Ti, Ta, Nb)C high-entropy ceramics were produced by hot pressing (HP) of carbide powders synthesized by carbothermal reduction (CTR). The relative density increased from 95% to 99.3% as the HP temperature increased from 1750°C to 1900°C. Nominally phase pure ceramics with the rock salt structure had grain sizes ranging from 0.6 µm to 1.2 µm. The mixed carbide powders were synthesized by high-energy ball milling (HEBM) followed by CTR at 1600°C, which resulted in an average particle size of ~100 nm and an oxygen content of 0.8 wt%. Low sintering temperature, high relative densities, and fine grain sizes were achieved through the use of synthesized powders. These are the first reported results for low-temperature densification and fine microstructure of high-entropy carbide ceramics.     

Hot-corrosion of refractory high-entropy ceramic matrix composites synthesized by alloy melt-infiltration

Carbon fiber-containing refractory high-entropy ceramic matrix composites (C/RHECs) were fabricated through a reaction with carbon powders, transition metal carbides, and Zr–Ti alloys as a novel heat resistant material used for components of hypersonic vehicles cruising at Mach 7–10. With the infiltration of alloys at 1750 °C into a composite preform containing carbon and carbide powders for 15 min, a high-entropy matrix was successfully formed in situ. Arc-jet tests were conducted in the temperature range of 1800–1900 °C. Results showed the formation of an oxidized region composed of complex oxides, such as (Zr, Hf)O₂, (Nb, Ta)₂(Zr, Hf)₆O₁₇, (Zr, Hf)TiO₄, and Ti(Nb, Ta)₂O₇, with an average thickness of ~600 μm, under which an unoxidized region remained. The porous oxidized region resulted from the evolution of CO_(g) during oxidation, while a dense oxide region formed as the outermost region. This indicates that the dense oxide region acted as a barrier to oxygen diffusion for the unoxidized region during oxidation.     

Room-temperature mechanical properties of a high-entropy diboride

The mechanical properties of a (Hf,Mo,Nb,Ta,W,Zr)B₂ high-entropy ceramic were measured at room temperature. A two-step synthesis process was utilized to produce the (Hf,Mo,Nb,Ta,W,Zr)B₂ ceramics. The process consisted of a boro/carbothermal reduction reaction followed by solid solution formation and densification through spark plasma sintering. Nominally, phase pure (Hf,Mo,Nb,Ta,W,Zr)B₂ was sintered to near full density (8.98 g/cm³) at 2000°C. The mean grain size was 6 ± 2 µm with a maximum grain size of 17 µm. Flexural strength was 528 ± 53 MPa, Young's modulus was 520 ± 12 GPa, fracture toughness was 3.9 ± 1.2 MPa·m^1/2, and hardness (HV_0.2) was 33.1 ± 1.1 GPa. A Griffith-type analysis determined the strength limiting flaw to be the largest grains in the microstructure. This is one of the first reports of a variety of mechanical properties of a six-component high-entropy diboride.     

Phase stability,mechanical properties and melting points of high-entropy quaternary metal carbides from first-principles

With a combination of first-principles calculations and thermodynamics formalism of configurational mixing entropy, we have constructed three-dimensional phase diagram in terms of thermodynamic and structural parameters including the configurational mixing entropy and enthalpy, the temperature of the melting point, and the lattice constant difference of the constitute carbides for fifteen equiatomic quaternary high-entropy metal carbide (HEMC) ceramics of group IVB and VB refractory metals (RM = Ti, Zr, Hf, V, Nb, and Ta). We further predicted nine new HEMCs and provided an explanation for the existence of six experimentally realized quaternary HEMCs. In addition, our calculations of the melting points and mechanical properties show that the HEMCs have the unique properties of high hardness, high fracture toughness, and ultrahigh melting points. The computational procedure involved in this work may be used to design new high-entropy ceramics for specific applications.     

Stability and mechanical properties of single-phase quinary high-entropy metal carbides: First-principles theory and thermodynamics

We have employed thermodynamics and first-principles density-functional calculations to investigate the structural stability and mechanical properties of fifty-six quinary high-entropy metal carbides composed of carbon and Groups IVB, VB, and VIB refractory transition metals, Ti, Zr, Hf, V, Nb, Ta, Mo, and W, thirty-eight of which have not yet been synthesized. To determine the stability of the quinary high-entropy metal carbides, we have constructed a three-dimensional phase diagram in terms of the average melting point, mixing enthalpy, mixing entropy, and lattice size difference, from which we predict that it is feasible to synthesize 38 new high-entropy metal carbides. We have further found that all the 56 metal carbides would have unique mechanical properties of high hardness and high fracture toughness. In addition, our study suggests that the brittleness of high-entropy metal carbides steadily decreases with the increase of the valence electron concentration.     

High-entropy boride–carbide ceramics by sequential boro/carbothermal synthesis

A dual-phase high-entropy boride (HEB)/carbide (HEC) ceramic with a fine grain size was synthesized by a sequential boro/carbothermal process. In the first step, an Hf–Nb–Ta–Ti–Zr-containing carbide was synthesized by a carbothermal reduction of oxides followed by the reaction of the carbide with B₄C and ZrH₂ to convert part of the carbide to boride. The resulting composition was ∼29 vol% HEB with an average grain size of ∼1.1 μm. Solid solution formation occurred at the densification temperature of 1900°C resulting in a relative density higher than 99%. The Vickers hardness was 26.5 ± 1.4 GPa. This is the first report of synthesizing dual-phase boride–carbide high-entropy ceramics from carbothermally synthesized, HEC powders.     

Interfacial reaction between ZrNbHfTa foil and graphite: Formation of high-entropy carbide and the effect of heating rate on its microstructure

The interfacial reaction between graphite and a ZrNbHfTa foil was investigated using a spark plasma sintering (SPS) machine. The interlayer was converted during the treatment into a high-entropy carbide by the reaction between the alloy and the graphite substrate. The degree of conversion depended on the processing time and temperature, but could be completed in only 16 s using the flash-spark plasma sintering process.The final microstructure was strongly influenced by the heating rate. Flash-SPS processing (heating rate about 120 °C/s) melted the alloy, which was then squeezed and deformed before its conversion to the high-entropy carbide (Zr,Nb,Hf,Ta)C. On the contrary, when conventional heating was used (i.e., 10 °C/min) the metal reacted with the graphite substrate before it melted. This concept appears to be generally applicable to different graphite/metal systems, with particular implications in the fields of graphite/metal joining.     

Oxyacetylene ablation of (Hf0.2Ti0.2Zr0.2Ta0.2Nb0.2)C at 1350 − 2050 °C

Ablation resistance of a multi-component carbide (Hf_0.2Ti_0.2Zr_0.2Ta_0.2Nb_0.2)C (HTZTNC) was investigated using an oxyacetylene flame apparatus. When the surface temperature of the HTZTNC was below 1800 °C, (Nb, Ta)₂O₅, (Hf, Zr)TiO₄, and (Hf, Zr)O₂ were found to be the main oxidation products, while at higher temperature, formation of (Hf, Zr, Ti, Ta, Nb)O_x was favored and its content gradually increased with the increase in ablation temperature. Based on the ablation results and thermodynamic simulation analysis, a possible ablation mechanism of HTZTNC was proposed. Active oxidation of TiC and outward diffusion of TiO were demonstrated to occur during the ablation process, which constitute the critical steps for the ablation of HTZTNC. These results can contribute to the design of ablation resistant ultra-high-temperature ceramics.     

Ti(C,N)基金属陶瓷抗弯强度的价电子判据研究

利用固体分子经验电子理论,计算了金属陶瓷中三元复合陶瓷相（Ｔｉ,Ｍｏ,Ｗ）Ｃ,四元复合陶瓷相（Ｔｉ,Ｍｏ,Ｗ,Ｎｂ）Ｃ和（Ｔｉ,Ｍｏ,Ｗ,Ｔａ）Ｃ五元复合陶瓷相（Ｔｉ,Ｎｏ,Ｗ,Ｎｂ,Ｔａ）Ｃ的价电子结构,探讨陶瓷相的价电子结构与金属陶瓷抗弯强度关系,提出判据关系式,此外,还进行了抗弯强度的实验验证。     

A facile route for the synthesis of high-entropy transition carbides/borides at low temperatures

As the main candidates in the field of ultra-high temperature ceramics, high entropy carbides/borides (HECs/HEBs) have good oxidation resistance properties, high hardness, as well as excellent thermal and electrical conductivities, which are the focused points of research nowadays. In the current study, (Hf,Ta,Zr,Nb,Mo,Ti)C powders were successfully synthesized by a three-step process, including the mixing process of raw oxides and carbon black with spaying Fe(NO₃)₃ solution, carbothermal reduction and subsequent calcium posttreatment. For the preparation of (Hf,Ta,Zr,Nb,Mo,Ti)B₂ powders, during the calcium posttreatment process, equal stoichiometric ratio of B₄C was added for the purpose of boriding reaction. The relevant X-ray diffraction and SEM characterizations indicate the successful preparations of face-centered cubic HECs and hexagonal HEBs. However, slight Mo local segregation was found in the prepared (Hf,Ta,Zr,Nb,Mo,Ti)B₂ powders. The iron generated from Fe(NO₃)₃ promotes the solid solution process between monocarbides during the carbothermal reduction process via the dissolution-diffusion-precipitation mechanism. In the calcium posttreatment process, the liquid calcium ensures the boriding reaction take place at a low temperature. In addition, the residual carbon could be combined with calcium to generate CaC₂ which is easy to be removed by acid leaching, and meanwhile, the added Fe could also be finally eliminated to produce pure HEC/HEB powders. The current method does not require the long-time high energy ball milling of raw materials, but only simple and mild mixing is enough. Therefore, such a facile route has a great potential application prospect for industrially preparing high entropy phase powders in a large scale.     

Effect of alloying elements on stacking fault energies and twinnabilities in high-entropy transition-metal carbides

Twinning is a fundamental mechanism behind the simultaneous increase in the strength and ductility of high-entropy alloys. Similar approaches may contribute to the remarkable improvements of the mechanical properties of high-entropy ceramics. In this study, the stacking fault energies (SFEs) and twinnabilities of a novel category of ZrNbTa-based high-entropy transition-metal carbides (HETMCs) are investigated in terms of their generalized stacking fault energy curves (γ-curves) via first-principle calculations. The γ-curves show that dislocation nucleation in ZrNbTa-based HETMCs occurs more easily than that of unary transition metal (TM, TM = Zr, Nb, Ta, Hf, Ti, V) carbides. When a pre-existing intrinsic stacking fault (ISF) is considered, C- vertices (TM- mirror) twinning fault (TF) more likely forms and TF may be more stable than ISF. The stable SFEs of C- vertices ISF and TF decrease with the addition of Hf, Ti, and V atoms to (ZrNbTa)C owing to the severe local lattice distortion. The calculated barrier energies and twinnabilities further indicate that twinning is possible for the selected ZrNbTa-based HETMCs. Theoretical twinnabilities (τ_a) decrease in the following sequence: (ZrNbTa)C > (ZrNbTaHfTi)C > (ZrNbTaHf)C > (ZrNbTaHfTiV)C. Thus, the addition of Hf, Ti, and V atoms to (ZrNbTa)C may decrease the twinning probability. This study may be used as a guide for the design of twinning-induced plasticity HETMCs with excellent mechanical properties.     

Ablation behavior of (Hf–Ta–Zr–Nb–Ti)C high-entropy carbide and (Hf–Ta–Zr–Nb–Ti)C–xSiC composites

The ablation behavior of (Hf–Ta–Zr–Nb–Ti)C high-entropy carbide (HEC-0) was investigated using a plasma flame in air for different times (60, 90, and 120 s) at about 2100°C. The effect of SiC content on the ablation resistance of HEC–xSiC composites (x = 10 and 20 vol%) was also studied. The linear ablation rate of HEC-0 decreases with increasing ablation time, showing the positive role of the oxide layer with a complex composition. The linear ablation rate of HEC–10 vol% SiC (0.3 µm s⁻¹) is only a 10th of that of HEC-0, showing a significant improvement in ablation resistance, probably due to the formation of a protective oxide layer containing melted SiO₂ and refractory Hf–Zr–Si–O oxides.     

High-strength medium-entropy (Ti,Zr,Hf)C ceramics up to 1800°C

Medium-entropy (Ti,Zr,Hf)C ceramics were prepared by hot pressing a dual-phase medium-entropy carbide powder with low oxygen content (0.45 wt%). The results demonstrate that the medium-entropy (Ti,Zr,Hf)C ceramics sintered at 2100°C had a relative density of 99.2% and an average grain size of 1.9 ± 0.6 μm. The flexural strength of (Ti,Zr,Hf)C carbide ceramics at room temperature was 579 ± 62 MPa. With an increase in temperature to 1600°C, the flexural strength showed an increase up to 619 ± 57 MPa, and had no significant degradation even up to 1800°C. The high-temperature flexural strengths of (Ti,Zr,Hf)C were obviously higher than those of the monocarbide ceramics (TiC, ZrC, and HfC). The primary strengthening mechanism in (Ti,Zr,Hf)C could be attributed to the high lattice parameter mismatch effects between TiC and ZrC, which not only inhibited the fast grain coarsening of (Ti,Zr,Hf)C ceramics, but also increased the grain-boundary strength of the obtained ceramics.     

Compositional pathways and anisotropic thermal expansion of high-entropy transition metal diborides

The recent discovery of high entropy transition metal diborides (HEBs) has sparked renewed interest in ultra-high temperature ceramics (UHTCs). Presently, transition metal (Me) oxides based boro-carbo/thermal reduction (BCTR) syntheses show great promise as relatively cheap production methods, but also may present limits to attain single phase pure HEBs. Herein, by selectively tuning the concentration of boron and carbon, the reducing agents of Me oxide mixture (Me = Ti, Ta, Nb, Zr and Hf), and exploiting high-resolution synchrotron X-ray powder diffraction, we first identified and quantified the formation of intermediate phases during the BCTR synthesis, with the ultimate intent to achieve a full dense (Ti,Ta,Nb,Zr,Hf)B₂ solid solution (SS). Additional insight was obtained by temperature dependent diffraction, which highlighted, for the first time in this class of materials, anisotropic thermal expansion, most likely at the origin of the SS micro-cracking, as was also observed by electron microscopy.     

Room-Temperature Mechanosynthesis of Carbides by Grinding of Elemental Powders

The direct room-temperature synthesis (mechanochemical synthesis or mechanosynthesis—MS) of most metal carbides by milling metal—carbon powders (size some tens of micrometers) mixtures is described. The particle size of the carbides obtained is of the order of 20 nm. Stable, metastable, mixed, and new carbides can be formed. Moreover, metal—carbon alloys can be obtained, such as in the Fe—C system. The synthesized compounds have been characterized by X-ray diffraction and Mössbauer spectroscopy for iron-containing systems. Carbides of the following elements were obtained: Ti, V, Cr, Mn, Fe, Co, Ni, Zr, Nb, Mo, Hf, Ta, W, Re, Al and Si.     

Effects of refractory metal additives on diboride-based ultra-high temperature ceramics: A review

Diboride-based ultra-high temperature ceramics (UHTCs) are a special class of ceramics with excellent comprehensive properties, which have extensive potential applications in extreme environments. However, their practical applications are limited, mainly due to the poor fracture toughness and thermal shock resistance. Refractory metals have high melting points, good ductility, and high toughness, which have huge potential to improve the properties of diboride-based ceramics. As a special class of additives, they have been adopted to promote densification, improve microstructure, and properties. However, diboride-based ceramics containing refractory metals have not received adequate attention due to relatively weak practical effects on property improvement. The present review highlights the progress and existing problems of transition metal diborides with refractory metal additives, including W, Ta, Mo, Nb, Hf, V, Cr, and Zr, focusing mainly on the microstructure change and property improvements, followed by challenges and possible future development strategies.