Phase stability,mechanical, and thermal properties of high-entropy transition and rare-earth metal diborides from first-principles calculations

The narrow composition design space of high-entropy transition metal diborides (HE TMB₂) limits their further development. In this study we designed six quaternary and quinary high-entropy transition metal and rare-earth diborides (HE TMREB₂) and investigated their phase stability using the energy distribution of the local mixing enthalpy of all possible configurations. The results show that both quaternary and quinary HE TMREB₂ have higher enthalpic driving forces, which facilitates the formation of single-phase AlB₂-type structures between TMB₂ and REB₂. Calculations of elastic constants show that the TMB₂ component has the greatest effect on the c₄₄ elastic constant and shear modulus G, while REB₂ significantly influences the bulk modulus B. Furthermore, LuB₂ and TmB₂ substantially affect the elastic modulus anisotropy of HE TMB₂. Rare-earth atoms in HE TMREB₂ can enhance the nonharmonic interactions between phonons, which results in a significant hindrance in the thermal transport of low-frequency phonons as well as an increase in the volume thermal expansion coefficients. Thus, the incorporation of REB₂ into HE TMB₂ has a significant impact on the phase stability and properties.     

First-principles study,fabrication, and characterization of (Hf0.2Zr0.2Ta0.2Nb0.2Ti0.2)C high-entropy ceramic

The formation possibility of (Hf_0.2Zr_0.2Ta_0.2Nb_0.2Ti_0.2)C high-entropy ceramic (HHC-1) was first analyzed by the first-principles calculations, and then, it was successfully fabricated by hot-pressing sintering technique at 2073 K under a pressure of 30 MPa. The first-principles calculation results showed that the mixing enthalpy and mixing entropy of HHC-1 were −0.869 ± 0.290 kJ/mol and 0.805R, respectively. The experimental results showed that the as-prepared HHC-1 not only had an interesting single rock-salt crystal structure of metal carbides but also possessed high compositional uniformity from nanoscale to microscale. By taking advantage of these unique features, it exhibited extremely high nanohardness of 40.6 ± 0.6 GPa and elastic modulus in the range from 514 ± 10 to 522 ± 10 GPa and relatively high electrical resistivity of 91 ± 1.3 μΩ·cm, which could be due to the presence of solid solution effects.     

Surface energies in high-entropy carbides with variable carbon stoichiometry

The carbon vacancy in high-entropy carbides (HECs) has a significant impact on their physical and chemical properties, yet relevant studies have still been relatively few. In this study, we investigate the surface energies of HECs with variable carbon vacancies through first-principles calculations. The results show that the surface energy of the (1 0 0) surface of the stoichiometric HECs is significantly lower than that of (1 1 1) surface. With the decrease in carbon stoichiometry, the surface energies of both (1 0 0) and (1 1 1) surfaces increase gradually, which is mainly due to the weakening of covalent bonding and the decrease of metal Hirshfeld-I (HI) charges. However, the surface energy of (1 0 0) surface increases more quickly than that of (1 1 1) surface and will exceed that of (1 1 1) surface when the carbon stoichiometry decreases to a certain extent, which is primarily attributed to the greater decrease rate of metal HI charges of (1 0 0) surface.     

Thermophysical and electrical properties of rare-earth-cerate high-entropy ceramics

A new series of rare-earth-cerate high-entropy ceramics with compositions of (La_0.2Nd_0.2Sm_0.2Gd_0.2Dy_0.2)₂Ce₂O₇ (HEC1), (La_0.2Nd_0.2Sm_0.2Gd_0.2Yb_0.2)₂Ce₂O₇ (HEC2), (La_0.2Nd_0.2Sm_0.2Yb_0.2Dy_0.2)₂Ce₂O₇ (HEC3), (La_0.2Nd_0.2Yb_0.2Gd_0.2Dy_0.2)₂Ce₂O₇ (HEC4), (La_0.2Yb_0.2Sm_0.2Gd_0.2Dy_0.2)₂Ce₂O₇ (HEC5) as well as a single component of Nd₂Ce₂O₇ are fabricated via sintering the corresponding sol–gel-derived powders at 1600°C for 10 h. HEC1–5 samples exhibit a single-cerate phase with fluorite structure and high configurational entropy. Compared with Nd₂Ce₂O₇, HEC1–5 samples have a lower grain growth rate owing to the sluggish diffusion effect. The chemical compositional uniformity of HEC1–5 as well as Nd₂Ce₂O₇ does not apparently change after annealing at 1500°C for different time intervals (1, 6, 12, and 18 h). Compared with 8YSZ, HEC1–5 samples display the decreased thermal conductivity and increased thermal expansion coefficient. The lattice size disorder parameter of HEC1–5 is negatively related to the thermal conductivity in 26–450°C. Furthermore, HEC1–5 and Nd₂Ce₂O₇ exhibit lower oxygen-ion conductivity, meaning an increased resistance to oxygen diffusion.     

The new complex high-entropy metal boron carbonitride: Microstructure and mechanical properties

In this contribution, the ternary BCN anion systems of high-entropy ceramics (HEC) are consolidated by hot-pressing sintering and the impacts of sintering temperature and the content of amorphous BCN addition on microstructural evolution and mechanical performance were evaluated. Results confirmed that high-entropy, oxide, and BN(C) phases were precipitated for (Ta_0.2Nb_0.2Zr_0.2Hf_0.2Ti_0.2)(B, C, N) ceramics after sintering at 1900°C. With the decrease of BCN addition, a new phase of MiB₂ (Mi representing the metal atoms) occurred. The Vickers hardness, bending strength, elastic modulus, and fracture toughness of the optimized bulk HECs were investigated, obtained at 24.5 ± 2.3 GPa, 522.0 ± 2.6 MPa, 478.9 ± 11.1 GPa, and 5.36 ± 0.56 MPa m^1/2, respectively.     

A novel approach to the rapid synthesis of high-entropy carbide nanoparticles

A novel strategy for the rapid synthesis of high-entropy carbide particles is proposed that involves the transformation of multicomponent intermetallic intermediates to multicomponent carbides (high-entropy carbide precursors). (Ti_0.25V_0.25Nb_0.25Ta_0.25)C nanoparticles with a uniform solute distribution were successfully synthesized in an Al matrix by heating Al-Ti-V-Nb-Ta-C powder mixtures at 1500°C for 10 minutes. The multicomponent aluminide intermediates led to the rapid formation of multicomponent carbides during heating to 1100°C, which transformed into a high-entropy solid solution during heating to 1500°C. We developed a new rapid approach for the synthesis of high-entropy ceramic particles.     

One-step synthesis of coral-like high-entropy metal carbide powders

The synthesis of high-entropy metal carbide powders is critical for implementing their extensive applications. However, the one-step synthesis of high-entropy metal carbide powders is rarely studied. Herein, the synthesis possibility of high-entropy metal carbide powders, namely (Zr_0.25Ta_0.25Nb_0.25Ti_0.25)C (ZTNTC), via one-step carbothermal reduction was first investigated theoretically by analyzing chemical thermodynamics and lattice size difference based on the first-principle calculations, and then the ZTNTC powders with particle size of 0.5-2 μm were successfully synthesized experimentally. The as-synthesized powders not only had a single rock-salt crystal structure of metal carbides, but also possessed high-compositional uniformity from nanoscale to microscale. More interestingly, they exhibited the distinguished coral-like morphology with the hexagonal step surface, whose growth was governed by a classical screw dislocation growth mechanism.     

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.     

In situ reaction synthesis of high-entropy carbide/diboride composite with high mechanical properties

A novel technique to simultaneously lower the synthesis temperature of high-entropy carbides and maintain their high mechanical properties was proposed. Certain amount of carbon vacancies was first introduced to significantly lower the temperature down to 2000°C for uniform elemental distributions in high-entropy carbides. Those carbon vacancies were then fully eliminated through the reaction between high-entropy carbides and certain amount of boron carbide. Concomitantly, the high-entropy boride phase was formed. The elimination of carbon vacancies and the formation of high-entropy boride phase significantly improved the mechanical properties of the high-entropy carbides. A high mechanical strength over 500 MPa can be obtained by phase optimization.     

Local orders,lattice distortions,and electronic structure dominated mechanical properties of (ZrHfTaM1M2)C (M = Nb,Ti, V)

High-entropy carbides (HECs) are regarded as potential candidate structural materials with attractive mechanical properties due to their ultra-high hardness. It is essential to reveal the atomic and electronic basis for strengthening mechanism in order to develop the advanced HECs. In the present work, C (M = Nb, Ti, V) are selected as case studies. The effects of transition metals (M) on the lattice parameters, bulk modulus, enthalpy of formation, electron work function (EWF), and bonding morphology/strength of HECs are comprehensively studied by first-principles calculations. It is found that the lattice parameters, equilibrium volumes, and bulk modulus of HECs are improved with the increase of M atomic volumes. The atomic-size differences among various groups of elements not only result in the lattice mismatch/distortion but also contribute to the formation of weak spots. In the view of bonding charge density, the electron redistributions caused by the coupling effect of the lattice distortion and valance electron differences can be revealed obviously, which identify the different bonding strength. Moreover, in terms of EWF, the proposed power-law-scaled hardness of HECs is validated and matches well with those reported theoretical and experimental results, providing a strategy to design advanced HECs with excellent mechanical properties.     

High-temperature oxidation behavior of (Hf0.2Zr0.2Ta0.2Nb0.2Ti0.2)C high-entropy ceramics in air

High-entropy metal carbides have recently been arousing considerable interest. Nevertheless, their high-temperature oxidation behavior is rarely studied. Herein the high-temperature oxidation behavior of (Hf_0.2Zr_0.2Ta_0.2Nb_0.2Ti_0.2)C high-entropy metal carbide (HEC-1) was investigated at 1573-1773 K in air for 120 minutes. The results showed that HEC-1 had good oxidation resistance and its oxidation obeyed a parabolic law at 1573-1673 K, while HEC-1 was completely oxidized after isothermal oxidation at 1773 K for 60 minutes and thereby its oxidation followed a parabolic-linear law at 1773 K. An interesting triple-layered structure was observed within the formed oxide layer at 1673 K, which was attributed to the inward diffusion of O₂ and the outward diffusion of Ti element and CO or CO₂ gaseous products.     

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.     

Low-temperature molten salt synthesis of high-entropy carbide nanopowders

Synthesis of the powders is critical for achieving the extensive applications of high-entropy carbides (HECs). Previously reported studies focus mainly on the high-temperature (>2000 K) synthesis of HEC micro/submicropowder, while the low-temperature synthesis of HEC nanopowders is rarely studied. Herein we reported the low-temperature synthesis of HEC nanopowders, namely (Ta_0.25Nb_0.25Ti_0.25V_0.25)C (HEC-1), via molten salt synthesis for the first time. The synthesis possibility of HEC-1 nanopowders was first theoretically demonstrated by analyzing lattice size difference and chemical reaction thermodynamics based on the first-principle calculations, and then the angular HEC-1 nanopowders were successfully synthesized via molten salt synthesis at 1573 K. The as-synthesized nanopowders possessed the single-crystal rock-salt structure of metal carbides and high compositional uniformity from nanoscale to microscale. In addition, their formation mechanism was well interpreted by a classical molten salt-assisted growth.     

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.     

Theoretical and experimental investigations of mechanical properties for polymorphous YTaO4 ceramics

In this work, the dense bulk polymorphous YTaO₄ ceramics with M or M' phase are synthesized by spark plasma sintering method accompanying with different tempering procedures. Combined with the nano-indentation and theoretical calculation, their mechanical properties are systematically investigated. The identification of crystal structure reveals that the YTaO₄ crystallizes into M phase (space group: I2/a) with higher tempering temperature, otherwise it crystallizes into M' phase (space group: P2/a). The results of mechanical properties indicate M-phase YTaO₄ possesses larger Young's modulus and hardness than that of M' phase. It is stemmed from the chemical bonding strength of M phase is stronger than that of M' phase, and the stronger bonding strength of M phase also results in its elastic resilience is superior to M' phase. Besides, on account of the low symmetry of monoclinic crystal system, the Young's modulus of polymorphous YTaO₄ ceramics exhibit strong anisotropy.     

The effect of submicron grain size on thermal stability and mechanical properties of high-entropy carbide ceramics

(Hf_0.2Zr_0.2Ta_0.2Nb_0.2Ti_0.2)C high-entropy ceramics (HEC) with a submicron grain size of 400 to 600 nm were fabricated by spark plasma sintering using a two-step sintering process. Both X-ray and neutron diffractions confirmed the formation of single-phase with rock salt structure in the as-fabricated (Hf_0.2Zr_0.2Ta_0.2Nb_0.2Ti_0.2)C samples. The effect of submicron grain size on the thermal stability and mechanical properties of HEC was investigated. The grain growth kinetics in the fine-grained HEC was small at 1300 and 1600°C, suggesting high thermal stability that was possibly related to the compositional complexity and sluggish diffusion in HEC. Compared to the coarse-grain HEC with a grain size of 16.5 µm, the bending strength and fracture toughness of fine-grained HEC were 25% and 20% higher respectively. The improvement of mechanical properties in fine-grained HEC may be attributed to micromechanistic mechanisms such as crack deflection.     

Microstructural evolution and mechanical properties of (Mg,Co,Ni,Cu,Zn)O high-entropy ceramics

The reaction sequence and mechanical properties were studied for (Mg,Co,Ni,Cu,Zn)O high-entropy ceramics that were synthesized using field-assisted sintering technology. The evolution from binary oxide starting powders to a single-phase rock salt structure exhibited a distinct incorporation sequence. For the rock salt oxides, MgO and CoO had the lowest vacancy formation energies and were the first to be incorporated into the high-entropy ceramic followed by NiO, which had a higher vacancy formation energy. Both CuO and ZnO had different crystal structures, and were incorporated into the single phase structure after the rock salt oxides due to the additional energy barrier associated with the transformations from their original structures to the rock salt structure. Distinctive morphological features including Cu-rich regions and lattice distortion were observed in the high entropy ceramic. In addition, a trade-off between densification and grain growth resulted in a maximum in strength (323 MPa) and elastic modulus (108 GPa) after densification at 900°C. This study has revealed new information that can be used to design other high-entropy ceramics including selection criteria for constituent compounds based on crystal structure and defect formation energy as well as the effects of grain size and porosity on control strength and elastic modulus.     

Fabrication and characterization of polymer-derived high-entropy carbide ceramic powders

Polymer-derived ceramic (PDC) route has been widely used to fabricate various ceramics or ceramic-matrix composites in recent years. However, the synthesis of high-entropy ceramics via PDC route has rarely been reported until now. Herein, we successfully synthesized a class of high-entropy carbides, namely (Hf_0.25Nb_0.25Zr_0.25Ti_0.25)C (HEC-1), via PDC route. The polymer-derived HEC-1 ceramics consisted of numerous superfine particles with the average particle size ~800 nm. Meanwhile, they possessed a rock-salt structure of metal carbides and high-compositional uniformity from nanoscale to microscale. In addition, the as-obtained HEC-1 ceramics had a low oxygen impurity content of 0.51% and a low free carbon impurity content of 2.56%. This work will open up a new research field on the fabrication of high-entropy ceramics or high-entropy ceramic-matrix composites via PDC route.     

Dual-phase high-entropy ultra-high temperature ceramics

A series of dual-phase high-entropy ultra-high temperature ceramics (DPHE-UHTCs) are fabricated starting from N binary borides and (5-N) binary carbides powders. > ∼99 % relative densities have been achieved with virtually no native oxides. These DPHE-UHTCs consist of a hexagonal high-entropy boride (HEB) phase and a cubic high-entropy carbide (HEC) phase. A thermodynamic relation that governs the compositions of the HEB and HEC phases in equilibrium is discovered and a thermodynamic model is proposed. These DPHE-UHTCs exhibit tunable grain size, Vickers microhardness, Young’s and shear moduli, and thermal conductivity. The DPHE-UHTCs have higher hardness than the weighted linear average of the two single-phase HEB and HEC, which are already harder than the rule-of-mixture averages of individual binary borides and carbides. This study extends the state of the art by introducing dual-phase high-entropy ceramics (DPHECs), which provide a new platform to tailor various properties via changing the phase fraction and microstructure.