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.     

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 ℃.     

Ultra-fast high-temperature synthesis and densification of high-entropy diborides and diboride-carbide ceramics

The strong covalent bonds and low self-diffusion coefficients of high-entropy diboride (HEBs) and diboride-carbide (HEB-HEC) ceramics render their densification difficult, which limits their applications. Here, we used an ultra-fast high-temperature sintering technique to synthesize and densify several HEBs and HEB-HEC (containing 5–8 cations) ceramics within an isothermal duration of 1 min and a total sintering period of 6 min. All ceramics formed a single-phase or dual-phase high-entropy solid solution, and showed high density, high hardness and good fracture toughness. The rapid densification mechanisms were determined, and the preferential occupancy of metal cations in HEB and HEC phases was explained using a simplified ideal solution model. A good fracture toughness in the range of 3.6–5.4 MPa·m^1/2 resulted from crack deflection or blunting and bridging of the rod-like diboride or boron-rich phase. This paper presents a simple, economical, and efficient method for the synthesis and densification of high-entropy ceramics and other advanced materials.     

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.     

Phase evolution and thermal stability of novel high-entropy (Mo0.2Nb0.2Ta0.2V0.2W0.2)Si2 ceramics

Owing to the high melting points and high-temperature stability, transition-metal disilicides are potential components for aerospace, automotive, and industrial engineering applications. However, unwanted oxidation known as PEST oxidation severely limits their application owing to the formation of volatile transition metal oxides, especially in the temperature range of 500–1000 °C. To overcome this problem, a new class of high-entropy disilicides, (Mo_0.2Nb_0.2Ta_0.2V_0.2W_0.2)Si₂, was selected by first-principles calculations and then successfully fabricated using a hot-pressing sintering technique. Furthermore, the phase evolution, thermal expansion behavior, thermal conductivity, and oxidation behavior were systematically investigated. Compared with MoSi₂, (Mo_0.2Nb_0.2Ta_0.2V_0.2W_0.2)Si₂ possessed a lower thermal conductivity (10.9–14.7 W·m^?1·K^?1) at 25–1000 °C, higher thermal expansion coefficients (8.6 ± 1.3^–6 K^–1) at 50–1200 °C, and especially an excellent thermal stability at 500–1000 °C owing to slow diffusion and selective oxidation. This work provides a strong foundation for the synthesis and application of high-entropy disilicides.     

Microstructure and dielectric properties of perovskite-structured high-entropy ceramics of Pb(Zr0.25Ti0.25Sn0.25Hf0.25)O3

A dielectric high-entropy ceramic with a composition of Pb(Zr_0.25Ti_0.25Sn_0.25Hf_0.25)O₃ was designed through B-site doping, and then prepared by solid phase reaction method combined with conventional sintering in air for 3 h at 1200 ^°C, 1250 ^°C and 1300 ^°C, respectively. All the high-entropy ceramics of Pb(Zr_0.25Ti_0.25Sn_0.25Hf_0.25)O₃ possess a perovskite structure with uniform elemental distribution and their average grain size falls within the range of 3.19–5.5 μm. For the sample sintered at 1250 ^°C, the dielectric loss is less than 0.07 in the testing frequency of 1 kHz∼1 MHz in 30–350 ^°C, and the dielectric constant reaches a peak of 14356 at about 270 ^°C at 1 kHz. At room temperature, the remnant polarization P_r reaches 28.8 μC/cm². The results demonstrate that the high-entropy ceramic of Pb(Zr_0.25Ti_0.25Sn_0.25Hf_0.25)O₃ has great potentials in the dielectric and ferroelectric field.     

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.     

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.     

Microstructural damage evolution of (WTiVNbTa)C5 high-entropy carbide ceramics induced by self-ions irradiation

High-entropy carbide ceramics (WTiVNbTa)C₅ were prepared by spark plasma sintering and irradiated with 1.0 MeV C-ions at room temperature (RT) and 650 ℃. Irradiation induced damage evolution and mechanical properties change were investigated. GIXRD and TEM results showed that the irradiation led to lattice expansion and micro-strain formation in the samples, which originated from the irradiation induced defects. The black-dot defects dominated in the damaged microstructure at fluence of 1E16 ions/cm² and transformed into dislocation loops and networks with the fluence increased at RT. Reduction of irradiation damage and formation of defect denuded zone were observed at 650 ℃. No amorphization or void formation were observed for all samples after irradiation. The irradiation hardening was most severe at fluence of 1E16 ions/cm² and recovered at higher fluence or temperature, while the elastic modulus monotonically decreased. The correlation between microstructural evolution and mechanical properties response was discussed.     

Gradient microstructure development and grain growth inhibition in high-entropy carbide ceramics prepared by reactive spark plasma sintering

High-entropy carbide ceramics (Ti_0.2Hf_0.2Nb_0.2Ta_0.2W_0.2)C is prepared from five transition metal oxides and graphite by reactive spark plasma sintering. X-ray diffraction indicates the synthesized ceramics with the single-phase face-centered cubic structure. The elemental distribution maps by energy dispersive spectroscopy demonstrate homogeneous distribution of the five metal elements in both central and circumferential regions of the sample. SEM and corresponding back scattered electron observations show the residual graphite particles locating at the grain boundaries of high-entropy carbide ceramics. Moreover, the content of the residual graphite decreases and the grain size of the high-entropy carbide phase increases from central to circumferential region of the sample. Thermodynamic calculation results indicate that gradient gas pressure inside the sample affects the carbothermal reduction reactions during sintering and consequently results in the existence of residual graphite with gradient distribution feature. This study points out an effective way to inhibit the grain growth of high-entropy carbide phase during sintering process by the incorporation of graphite as the second phase particles acting as grain growth inhibitor.     

Design and synthesis of high-entropy pyrochlore ceramics based on valence combination

In this paper, we report the design and synthesis of La³⁺ based high-entropy pyrochlore ceramics (HEPCs) with five different B-site cations using the valence combination strategy. The factors affecting the formation of pyrochlore phase have been investigated. The result reveals that both valence disorder and size disorder can significantly affect the formability of pyrochlore phase, and the formability increases as the two disorders decrease. Following this guideline, a set of new HEPCs with single phase have been successfully synthesized.     

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.     

Rare-earth-tantalate high-entropy ceramics with sluggish grain growth and low thermal conductivity

A series of rare-earth-tantalate high-entropy ceramics ((5RE_0.2)Ta₃O₉, where RE = five elements chosen from La, Ce, Nd, Sm, Eu and Gd) were prepared by conventional sintering in air at 1500 ^°C for 10 h. The (5RE_0.2)Ta₃O₉ high-entropy ceramics exhibit an orthogonal structure and sluggish grain growth. No phase transition occurs in the test temperature of 25–1200 ^°C. The thermal conductivities of all (5RE_0.2)Ta₃O₉ ceramics are in the range of 1.14–1.98 W m^?1 K^?1 at a test temperature of 25–500 ^°C, approximately half of that of YSZ. The sample of (Gd_0.2Ce_0.2Nd_0.2Sm_0.2Eu_0.2)Ta₃O₉ exhibits a low glass-like thermal conductivity with a value of 1.14 W m^?1 K^?1 at 25 ^°C. The thermal expansion coefficient of (5RE_0.2)Ta₃O₉ ceramics ranges from 5.6 × 10^?6 to 7.8 × 10^?6 K^?1 at 25–800 ^°C, and their fracture toughness is high (3.09–6.78 MPa·m^1/2). The results above show that (5RE_0.2)Ta₃O₉ ceramics could be a promising candidate for thermal barrier coatings.     

Novel high-entropy microwave dielectric ceramics Sr(La0.2Nd0.2Sm0.2Eu0.2Gd0.2)AlO4 with excellent temperature stability and mechanical properties

Novel high-entropy Sr(La_0.2Nd_0.2Sm_0.2Eu_0.2Gd_0.2)AlO₄ ceramics with a layered perovskite structure have been prepared via the standard solid-state reaction method. The design of high-entropy improves the bond valence and subsequently optimizes the large negative temperature coefficient of resonant frequency (τ_f = ?32 ppm/°C) of the simple SrLaAlO₄ ceramics. Excellent temperature stability (τ_f = ?6 ppm/°C) together with a relative permittivity (ε_r) of 18.6 and a quality factor (Qf = 14,509 GHz) are obtained in Sr(La_0.2Nd_0.2Sm_0.2Eu_0.2Gd_0.2)AlO₄ ceramics sintered at 1475 °C. It indicates that the present ceramics have great application prospects in passive microwave components such as resonators and filters. Meanwhile, significant improvements in compressive strength and strain are achieved, which are 1040 MPa and 15.7% for Sr(La_0.2Nd_0.2Sm_0.2Eu_0.2Gd_0.2)AlO₄ compared to 583 MPa and 12% in SrLaAlO₄. The enhanced mechanical properties originate from the dislocation strengthening mechanism as the intertwining of interlayer lattices is revealed from the high-resolution transmission electronic micrographs.     

New class of high-entropy defect fluorite oxides RE2(Ce0.2Zr0.2Hf0.2Sn0.2Ti0.2)2O7 (RE = Y,Ho, Er,or Yb) as promising thermal barrier coatings

High-entropy ceramics exhibit great application potential as thermal barrier coating (TBC) materials. Herein, a series of novel high-entropy ceramics with RE₂(Ce_0.2Zr_0.2Hf_0.2Sn_0.2Ti_0.2)₂O₇ (RE₂HE₂O₇, RE = Y, Ho, Er, or Yb) compositions were fabricated via a solid-state reaction. X-ray diffraction (XRD) and energy dispersive spectrometry (EDS) mapping analyses confirmed that RE₂HE₂O₇ formed a single defect fluorite structure with uniform elemental distribution. The thermophysical properties of the RE₂HE₂O₇ ceramics were investigated systematically. The results show that RE₂HE₂O₇ ceramics have excellent high-temperature phase stability, high thermal expansion coefficients (10.3–11.7 × 10^?6 K^-1, 1200 ℃), and low thermal conductivities (1.10-1.37 W m^-1 K^-1, 25 ℃). In addition, RE₂HE₂O₇ ceramics have a high Vickers hardness (13.7–15.0 GPa) and relatively low fracture toughness (1.14-1.27 MPa m^0.5). The outstanding properties of the RE₂HE₂O₇ ceramics indicate that they could be candidates for the next generation of TBC materials.