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.     

Ultrafast high-temperature synthesis and densification of high-entropy carbides

Recently, high-entropy carbides have attracted great attention due to their remarkable component complexity and excellent properties. However, the high melting points and low self-diffusion coefficients of carbides lead to the difficulties in forming solid solution and sintering densification. In this work, six dense multicomponent carbides (containing 5–8 cations) were prepared by a novel ultrafast high-temperature sintering (UHS) technique within a full period of 6 min, and three of them formed a single-phase high-entropy solid solution. The solid solubility of the UHSed multicomponent carbides was highly sensitive to the compositional variation. The presence of Cr₃C₂ liquid had significant contributions to the formation of solid solution and the densification of multicomponent carbides. All UHSed multicomponent carbides exhibited high hardness, which, unexpectedly, did not simply increase with increasing number of the components. The highest nanohardness with a value of 36.6 ± 1.5 GPa was achieved in the (Ti_1/5Cr_1/5Nb_1/5Ta_1/5V_1/5)C_x high-entropy carbide. This work is expected to expedite the development of high-entropy carbides and broaden the application of UHS in the synthesis and densification of advanced ceramics.     

Pressure dependent mechanical properties of calcium carbides

The mechanical properties of newly synthesized Ca₂C₃ and Ca₂C under pressure have been studied by using the first-principles calculations with generalized gradient approximation. The equilibrium geometry, elastic stiffness constants, various moduli, and Pugh's ratio of the C2/m phase of Ca₂C₃ and the C2/m and Pnma phases of CaC₂ are systematically studied. The elastic stiffness constants of C2/m-Ca₂C₃ under 0–30GPa, C2/m-Ca₂C under 0–7.5 GPa, and Pnma-Ca₂C under 7.5–30 GPa satisfy the Born?Huang mechanical criteria. The three phases of calcium carbides exhibit ductile characteristics. The surface constructions of bulk and Young's moduli illustrate the mechanical anisotropy of Ca₂C₃ and Ca₂C. Our results are consistent with previously obtained experimental and theoretical data and have significant implications for the application of calcium carbides.     

Phase structure,mechanical properties and thermal properties of high-entropy diboride (Hf0.25Zr0.25Ta0.25Sc0.25)B2

A new high-entropy diboride (Hf_0.25Zr_0.25Ta_0.25Sc_0.25)B₂ was designed to investigate the effect of introducing rare-earth metal diboride ScB₂ into high-entropy diborides on its structure and properties. The local mixing enthalpy predicts that (Hf_0.25Zr_0.25Ta_0.25Sc_0.25)B₂ has high enthalpy driving force, which more easily allows the formation of single-phase AlB₂-type structures between components. The experiments further demonstrate that (Hf_0.25Zr_0.25Ta_0.25Sc_0.25)B₂ possesses excellent phase stability, lattice integrity and nanoscale chemical homogeneity. (Hf_0.25Zr_0.25Ta_0.25Sc_0.25)B₂ showed relatively high hardness (30.7 GPa), elastic modulus (E, G, and B of 522, 231 and 233 GPa, respectively), bending strength (454 MPa), and low thermal conductivity (13.9 W·m^?1·K^?1). The thermal expansion of (Hf_0.25Zr_0.25Ta_0.25Sc_0.25)B₂ is higher than that of ZrB₂ and HfB₂ due to weakened bonding (M d - B p and M dd bonding) and enhanced anharmonic effects. Thus, incorporating Sc into high-entropy diborides can tailor the properties associated with the bonding, which further expands the compositional space of high-entropy diborides.     

Single-phase formation and mechanical properties of (TiZrNbTaMo)C high-entropy ceramics: First-principles prediction and experimental study

The single-phase formation and related elastic properties of (TiZrNbTaMo)C with one equimolar and twenty non-equimolar systems have been investigated by first-principles calculation. Based on the calculation results, the “composition-structure-elastic properties” correlation heatmapping predicts that Ti element is favorable for increment of hardness and Young’s modulus, while Mo element shows contrary tendency. The (Ti_xZr₂Nb₂Ta₂Mo_4-x)C_10-y (x = 1, 2, 3) have been fabricated by carbothermal reduction assisted hot-pressing sintering. The obtained experimental results validate the prediction trend of first-principles calculation. The optimization hardness and Young’s modulus is achieved at (Ti₃Zr₂Nb₂Ta₂Mo₁)C_10-y, and the corresponding value is 27.1 ± 0.6 GPa at 9.8 N and 490 ± 5 GPa, respectively. Noteworthily, the single-phase formation mainly depends on configuration entropy. The equimolar (Ti₂Zr₂Nb₂Ta₂Mo₂)C_10-y exhibits a single-phase with homogeneous chemical composition, but some element segregation can be found in the other two non-equimolar samples sintered at 2100 ℃.     

First-principles prediction,fabrication and characterization of (Hf0.2Nb0.2Ta0.2Ti0.2Zr0.2)B2 high-entropy borides

The microstructure and mechanical properties of (Hf_0.2Nb_0.2Ta_0.2Ti_0.2Zr_0.2)B₂ high-entropy boride (HEB) were first predicted by first-principles calculations combined with virtual crystal approximation (VCA). The results verified the suitability of VCA scheme in HEB studying. Besides, single-phase (Hf_0.2Nb_0.2Ta_0.2Ti_0.2Zr_0.2)B₂ ceramics were successfully fabricated using boro/carbothermal reduction (BCTR) method and subsequent spark plasma sintering (SPS); furthermore, the effects of different amounts of B₄C on microstructure and mechanical properties were evaluated. Due to the addition of B₄C and C, all samples formed single-phase solid solutions after SPS. When the excess amount of B₄C increased to 5 wt%, the sample with fine grains exhibited superior comprehensive properties with the hardness of 18.1 ± 1.0 GPa, flexural strength of 376 ± 25 MPa, and fracture toughness of 4.70 ± 0.27 MPa m^1/2. Nonetheless, 10 wt% excess of B₄C coarsened the grains and decreased the strength of the ceramic. Moreover, the nanohardness (34.5–36.9 GPa) and Young's modulus (519–571 GPa) values with different B₄C contents just showed a slight difference and were within ranges commonly observed in high-entropy diboride ceramics.     

First-principles investigation of new structure,mechanical and electronic properties of Mo-based silicides

The adjustment of strength and ductility of high-temperature ceramics is still a big challenge. Although Mo-based silicides are promising high-temperature materials, the influence of Mo concentration on the mechanical and electronic properties of Mo-based silicides is unclear. In addition, it is necessary to explore the novel Mo-based silicides. In this paper, we present results of novel phases, mechanical and electronic properties of the stable Mo-based silicides within various stoichiometries. Two new Mo-based silicides: MoSi (Cmcm and Pnma) and Mo₂Si (I4/mcm) are predicted. The calculated results show that the volume deformation resistance of Mo-based silicides increases with increasing Mo concentration. MoSi₂ shows the strongest elastic stiffness and shear deformation resistance due to the strong Mo-Si bonds. The calculated intrinsic hardness of MoSi₂ (37.7 GPa) is much larger than that of other Mo-based silicides. In particular, MoSi₂ and MoSi show brittle behavior. However, other silicides exhibit ductility. We further find that high concentration of Mo can improve the electronic properties of Mo-based silicides because of the formation of Mo-Mo metallic bond. Finally, our works indicate that the adjustment of the Mo stoichiometric ratio to improve the mechanical and electronic properties of Mo-based silicides.     

Thermophysical and mechanical properties of novel high-entropy metal nitride-carbides

In this work, a novel (Hf_0.2Zr_0.2Ta_0.2Nb_0.2Ti_0.2)(N_0.5C_0.5) high-entropy nitride-carbide (HENC-1) with multi-cationic and -anionic sublattice structure was reported and their thermophysical and mechanical properties were studied for the first time. The results of the first-principles calculations showed that HENC-1 had the highest mixing entropy of 1.151R, which resulted in the lowest Gibbs free energy above 600 K among HENC-1, (Hf_0.2Zr_0.2Ta_0.2Nb_0.2Ti_0.2)N high-entropy nitrides (HEN-1), and (Hf_0.2Zr_0.2Ta_0.2Nb_0.2Ti_0.2)C high-entropy carbides (HEC-1). In this case, HENC-1 samples were successfully fabricated by hot-pressing sintering technique at the lowest temperature (1773 K) among HENC-1, HEN-1 and HEC-1 samples. The as-fabricated HENC-1 samples showed a single rock-salt structure of metal nitride-carbides and high compositional uniformity. Meanwhile, they exhibited high microhardness of 19.5 ± 0.3 GPa at an applied load of 9.8 N and nanohardness of 33.4 ± 0.5 GPa and simultaneously possessed a high bulk modulus of 258 GPa, Young's modulus of 429 GPa, shear modulus of 176 GPa, and elastic modulus of 572 ± 7 GPa. Their hardness and modulus are the highest among HENC-1, HEN-1 and HEC-1 samples, which could be attributed to the presence of mass disorder and lattice distortion from the multi-anionic sublattice structure and small grain in HENC-1 samples. In addition, the thermal conductivity of HENC-1 samples was significantly lower than the average value from the “rule of mixture” between HEC-1 and HEN-1 samples in the range of 300-800 K, which was due to the presence of lattice distortion from the multi-anionic sublattice structure in HENC-1 samples.     

Influence of vanadium content on the microstructural evolution and mechanical properties of (TiZrHfVNbTa)C high-entropy carbides processed by pressureless sintering

A series of (TiZrHfVNbTa)C high-entropy ceramics with different vanadium contents have been fabricated by pressureless sintering at 2300 °C–2500 °C for 1 h, utilizing self-synthesized carbide powders obtained by carbothermal reduction. The addition of vanadium is beneficial to promote densification process and refine grain, as well as facilitate the homogeneous distribution of metal elements. The distribution of pores is also modified, almost entirely existing at grain boundary, and the integral mechanical properties achieve optimization. However, excess adding vanadium does not favor forming a single-phase (TiZrHfVNbTa)C high-entropy ceramic. The optimal (TiZrHfVNbTa)C high-entropy ceramic sintered at 2300 °C possesses a high relative density of 97.5 % and homogeneous microstructure with small grain size of 1.2 μm. The flexural strength and Vickers hardness reach 473 MPa and 24.9 GPa, respectively. This work has established a cost-effective and convenient preparation of novel (TiZrHfVNbTa)C high-entropy carbide ceramics.     

Pressureless sintering and properties of (Hf0.2Zr0.2Ta0.2Nb0.2Ti0.2)C high-entropy ceramics: The effect of pyrolytic carbon

A novel (Hf_0.2Zr_0.2Ta_0.2Nb_0.2Ti_0.2)C high-entropy ceramic was successfully prepared by pressureless sintering at 2200 °C. With increasing content of resin-derived-carbon, the density, and mechanical and thermal properties increased up to a maximum content of 2～4 wt% resin addition, after which further addition was detrimental. All specimens showed high strength (≥347±36 MPa), with the highest value achieving 450±64 MPa, and fracture toughness significantly higher (>20 %) than those of the corresponding monocarbides and Ta_0.5Hf_0.5C, (Ta_1/3Zr_1/3Nb_1/3)C. The thermal conductivity was approximately equivalent to the lowest value of the corresponding mono-carbides, which was assumed to be due to the lattice distortion effect.     

Synthesis,microstructure and mechanical properties of high-entropy (VNbTaMoW)C5 ceramics

High-entropy ceramics (HEC) with a fixed composition of (VNbTaMoW)C₅ were prepared by spark plasma sintering (SPS) from 1500 °C to 2200 °C. XRD, TEM, HRTEM, SAED and EDX were used to investigate effects of the sintering temperatures on compositional homogeneity, constituent phases and microstructure of the HECs. The results showed that single-phase HEC formed at a temperature as low as 1600 °C while ultimate elemental distribution homogeneity could be obtained at 2200 °C. Elemental distribution homogenization was accompanied by microstructural coarsening and oxide impurities aggregating at grain boundaries as temperature increased. SPS at 1900 °C for 12 min could yield uniform HECs (VNbTaMoW)C₅ with Vickers hardness, nanohardness, fracture toughness and Young’s modulus reaching 19.6 GPa, 29.7 GPa, 5.4 MPa m^1/2 and 551 GPa, respectively. The resultant HECs showed excellent wear resistance when coupled with WC at room temperature.     

The role of Cr addition on the processing and mechanical properties of high entropy carbides

Group VI transition metals do not form room temperature stable carbides with a rock salt structure, however, they can be incorporated into a rock salt high entropy carbide lattice. Novel 5-metal high entropy carbides (Cr, Zr, Nb, Hf, Ta)C (HEC5-Cr) were produced using spark plasma sintering and compared with 4-metal carbide (Zr_0.25Nb_0.25Hf_0.25Ta_0.25)C (HEC4) and 8-metal carbide containing Cr (HEC8-Cr). The HEC5-Cr ceramics had higher density and smaller grain size (~14 µm) compared with HEC4 (~28 µm). The solubility limit of Cr on the metal site increased from ~2.5 at% for HEC5-Cr to ~6.0 at% for HEC8-Cr, implying that the high entropy effect increased the solubility of Cr. A significant Cr enrichment was observed at the grain boundaries of HEC5-Cr, and it showed a ~14% increase in nanohardness and a similar indentation modulus compared with HEC4. The nanohardness of HEC5-Cr was up to 41.2 GPa due to increased solid solution strengthening.     

Defect energetics and stacking fault formation in high-entropy carbide ceramics

Inspired by the concept of entropy stabilization, multicomponent transition metal carbide (MTMC) ceramics have received increasing attention due to their extraordinary performances. However, the role of partial disorder in the transition metal sublattice on the defect properties in MTMCs is still elusive. In this work, we study defect formation and generalized stacking fault energies (GSFEs) in MTMCs. In both cases, we compare the results in MTMCs to binary TMCs. Our results suggest that C-related defects generally exhibit lower formation energies in MTMCs, suggesting that MTMCs are prone to off-stoichiometry with C vacancies. We further show that lower formation energies of C interstitials and higher migration energies of C vacancies account for the experimentally-observed delayed defect evolution. Finally, our calculated GSFEs in different MTMCs are close to the averages from all the constituent binary TMCs, indicating that the rule of mixture (ROM) can be applied to estimate the stacking fault energies for stoichiometric MTMCs.     

Microstructure and mechanical properties of high-entropy borides derived from boro/carbothermal reduction

Starting from metal oxides, B₄C and graphite, a suite of high-entropy boride ceramics, formulated (Hf_0.2Zr_0.2Ta_0.2Nb_0.2Ti_0.2)B₂, (Hf_0.2Zr_0.2Mo_0.2Nb_0.2Ti_0.2)B₂ and (Hf_0.2Mo_0.2Ta_0.2Nb_0.2Ti_0.2)B₂ derived from boro/carbothermal reduction at 1600 °C were fabricated by spark plasma sintering at 2000 °C. It was found that the synthetic high-entropy boride crystalized in hexagonal structure and the yield of the targeting phase was calculated to be over 93.0 wt% in the sintered ceramics. Benefitting from the nearly full densification (96.3% ˜ 98.5% in relative density) and the refined microstructure, the products exhibited the relatively high Vickers hardness. The indentation fracture toughness was determined to be comparable with the single transition metal-diboride ceramics. It should be noted that the formation of high-entropy boride ceramics were featured with the relatively high hardness at no expense of the fracture toughness.     

High-temperature self-lubricating properties of single-phase high-entropy carbides under a vacuum environment

It is an enormous challenge to develop single-phase ceramics with satisfactory self-lubricity because of the strong chemical bonding and difficult to shearing. In this study, (Hf_0.2X_0.2Nb_0.2Ta_0.2Ti_0.2)C (X is Zr, W, and V, respectively) single-phase high-entropy ceramics can in situ formed tribo-film on the contact region during sliding process to achieve an excellent self-lubricating property. The friction coefficient is as low as 0.34 at 400°C. This originates from the carbon-rich tribo-films which are generated under the effect of high-temperature tribo-induced. With the test temperature increasing, the wear mechanism changes from abrasive wear to oxidative wear. For the 900°C, the tribo-oxidative film limits the direct contact between tribo-couple and enhances the tribological performances. Moreover, the compositions of the tribo-films also have an important effect on the tribological behaviors. This novel design concept—using own constituent elements to generate a lubricating tribo-film will provide a new strategy for the study of the single-phase self-lubricating ceramics.     

First-principle calculations of the bulk properties of 4d transition metal carbides and nitrides in the rocksalt, zincblende and wurtzite structures

Bulk properties and stability of the entire series of group 4d transition metal carbides and nitrides are reported in this work. The theoretical calculations were carried out within Local Density Approximation and Generalized Gradient Approximation using the Perdew, Burke and Ernzerhof exchange correlation functional. The generalized gradient approximation predictions were found to be closer to experimental values than the local density approximation predictions. In particular, LDA predictions were found to overestimate bulk moduli properties by as much as 5.6-11.5% while equilibrium lattice constants were found to be underestimated by as much as 0.2-5% compared to experimental values. On the other hand, GGA calculations were found to overestimate the lattice parameters by 0.2-6.9%, while underestimating the bulk moduli by as much as 0.07-5%. Out of the carbides considered, TcC and RuC were found to have the highest values of bulk moduli while YC and CdC had the lowest. Similarly, out of the nitrides, MoN and TcN were found to exhibit the largest bulk moduli, indicating that they were the hardest, while CdN had the lowest value and hence relatively softer. Overall, the nitrides presented higher values of bulk moduli than the carbides, an observation that is well supported by their correspondingly shorter bondlengths. The cohesive and structural properties of the 4d transition metal carbides and nitrides are also reported.     

Insight into the vacancy effects on mechanical and electronic properties of Tantalum Silicide

The effects of the vacancies on the structural stability, elastic constants, elastic moduli, brittle-to-ductile transition and electronic properties of Tantalum Silicide (TaSi₂) are investigated in detail by first-principles calculations. The values of vacancy formation energy confirm that the perfect TaSi₂ and TaSi₂ with different atomic vacancies can exhibit the structural stability at ground state. It is found that Ta atom vacancies are more stable than Si atom vacancies in TaSi₂ with vacancies. The elastic constants and elastic moduli describe the mechanical behavior for TaSi₂ and TaSi₂ with vacancies. The different atomic vacancies weaken the elastic stiffness for TaSi₂. But the values of B/G confirm that the brittle-to-ductile transition occurs with different atomic vacancies for TaSi₂. Although these vacancies make the shear and volume deformation resistance of TaSi₂ weaker, they obviously improve the brittle behavior of TaSi₂. The difference charge density and electronic structures are calculated to discuss and analyze the structural stability and mechanical properties for the perfect TaSi₂ and TaSi₂ with vacancies.     

Structure,mechanical, electronic and thermodynamic properties of Mo5Si3 from first-principles calculations

Transition metal silicides are promising advanced functional materials. However, the structure and relevant properties of Mo₅Si₃ are not well understood. In this work, we investigate the crystal structure, elastic properties, Vickers hardness, elastic anisotropy, electronic and thermodynamic properties of Mo₅Si₃ by using the first-principles calculations. Three structures: tetragonal, hexagonal and orthorhombic structures are considered. The calculated results show that those structures are thermodynamically stable. In particular, we firstly predict that Mo₅Si₃ with hexagonal (P63/mcm) structure is a stable phase. The calculated electronic structure shows that Mo₅Si₃ exhibits better electronic properties because of the charge overlap between Mo-4d state and Si-3p state near the Fermi level. Importantly, Mo₅Si₃ shows the strong deformation resistance and high elastic stiffness in comparison to other TM₅Si₃. Mo₅Si₃ with tetragonal structure has the smaller percentage anisotropy in compressibility and high percentage anisotropy in shear. We further find that the Debye temperature and heat capacity of tetragonal structure are larger than that of hexagonal structure. The high-temperature thermodynamic properties of Mo₅Si₃ are attributed to the vibration of Si atom.     

Effect of Nb content on the phase composition,densification, microstructure,and mechanical properties of high-entropy boride ceramics

Dense high-entropy (Hf,Zr,Ti,Ta,Nb)B₂ ceramics with Nb contents ranging from 0 to 20 at% were produced by a two-step spark plasma sintering process. X-ray diffraction indicated that a single-phase with hexagonal structure was detected in the composition without Nb. In contrast, two phases with the same hexagonal structure, but slightly different lattice parameters were present in compositions containing Nb. The addition of Nb resulted in the presence of a Nb-rich second phase and the amount of the second phase increased as the Nb content increased. The relative densities were all >99.5 %, but decreased from ～100 % to ～99.5 % as the Nb content increased from 0 to 20 at%. The average grain size decreased from 13.9 ± 5.5 μm for the composition without Nb additions to 5.2 ± 2.0 μm for the composition containing 20 at% Nb. The reduction of grain size with increasing Nb content was due to the suppression of grain growth by the Nb-rich second phase. The addition of Nb increased Young’s modulus and Vickers hardness, but decreased shear modulus. While some Nb dissolved into the main phase, a Nb-rich second phase was formed in all Nb-containing compositions.