Carbon Stoichiometry Effects on the Structure, Mechanical Properties, and Ablation Resistance of (HfZrTiTaNb)Cx , (HfZrTiTaV)Cx , and (HfZrTiMoV)Cx High-Entropy Carbides

Carbon Stoichiometry Effects on the Structure, Mechanical Properties, and Ablation Resistance of (HfZrTiTaNb)Cx , (HfZrTiTaV)Cx , and (HfZrTiMoV)Cx High-Entropy Carbides | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article Carbon Stoichiometry Effects on the Structure, Mechanical Properties, and Ablation Resistance of (HfZrTiTaNb)C x , (HfZrTiTaV)C x , and (HfZrTiMoV)C x High-Entropy Carbides Artem Kim, Ekaterina Volokitina, Nikolay Razumov, Anatoliy Popovich This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8394818/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 15 You are reading this latest preprint version Abstract This study investigates the influence of carbon stoichiometry on the structure and properties of high-entropy carbides (HECs) (HfZrTiTaNb)C x , (HfZrTiTaV)C x , and (HfZrTiMoV)C x . Bulk samples with carbon content ranging from 30 to 65 at.% were synthesized via mechanical alloying and spark plasma sintering (SPS). X-ray diffraction analysis revealed a monotonic increase in the FCC lattice parameter with increasing carbon content until a plateau was reached, corresponding to the formation of a limiting stoichiometric phase. Experimentally, carbon concentrations of 40 at.% were found to provide maximum microhardness (28–32 GPa) and compressive strength (2500–2800 MPa), attributed to the minimization of vacancies in the carbon sublattice. Gas-dynamic testing in a high-enthalpy oxidative flow showed that optimal ablation resistance is achieved at 45–50 at.% C. This is associated with a compromise between the chemical stability of the carbide phase and enhanced radiative properties due to dispersed free carbon. Based on the optimized (HfZrTiTaNb)C x composition with 40 at.% C, a technology for depositing a single-phase carbide barrier coating (620 µm) on a carbon-carbon composite was developed. The coating demonstrated high microhardness (20.3 GPa) and thermochemical stability; however, its service life is limited by detachment due to the mismatch of coefficients of thermal expansion (CTE) with the substrate. The obtained results establish a quantitative relationship between carbon stoichiometry, lattice parameter, mechanical, and thermal properties of high-entropy carbides, which is critically important for their application as ultra-high-temperature ceramics and protective coatings. Physical sciences/Engineering Physical sciences/Materials science Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Introduction Initial research on high-entropy materials focused predominantly on metallic systems. However, recent years have seen a surge of interest in high-entropy ceramics (HECs), including carbides, borides, nitrides, oxides, silicides, and fluorides [ 1 – 19 ]. Similar to high-entropy alloys, they contain five or more principal elements but constitute a distinct family of materials with different properties and application areas. Their advantages include high thermal stability and enhanced mechanical characteristics, resulting from solid solution strengthening, fine-grained structure (and associated Hall-Petch strengthening), and sluggish diffusion. The first high-entropy nitrides based on Fe-Co-Ni-Cr-Cu-Al-Mn and Fe-Co-Ni-Cr-Cu-Al 0.5 systems were obtained in 2004 [ 20 ] by reactive sputtering. Studies assessed their hardness and initiated the exploration of nitrides as protective coatings. Subsequently, the range of potential applications expanded to include diffusion barriers and supercapacitors. The first high-entropy carbide was synthesized in 2010 by magnetron sputtering [ 3 ]. Subsequent research revealed a combination of exceptional properties: ultra-high hardness [ 4 ], increased wear resistance [ 5 ], and superior oxidation resistance at elevated temperatures [ 6 ]. These materials are promising for wear-resistant protective coatings, high-performance cutting tools, and components operating under extreme thermal and tribological loads. The structure of most multi-component carbides crystallizes in a NaCl-type (rock salt) lattice [ 21 ]. The key distinction from conventional carbides lies in the presence of five or more elements (e.g., Ti, Zr, Hf, Nb, Ta, V, Mo, etc.) in the cation sublattice, uniformly distributed forming a substitutional solid solution. Concentrations of metallic components are typically near-equiatomic, maximizing the configurational mixing entropy. This high entropy plays a crucial role in the thermodynamic stabilization of a single-phase structure at high temperatures, effectively suppressing the system's tendency to decompose into several binary or ternary carbide phases with lower entropy. Consequently, a homogeneous, thermally stable phase forms even with significant chemical diversity among constituent elements. An important feature of the transition metals used in such carbides (Ti, Zr, Hf, V, Nb, Ta, Mo, etc.) is their ability to form non-stoichiometric carbides of variable composition - MeC x , where x can vary widely. This homogeneity is due to vacancies in the carbon sublattice, which do not disrupt the fundamental crystal structure type but significantly influence the electronic structure and, consequently, the material's physical properties. This characteristic is directly inherited by multi-component carbides. Varying carbon stoichiometry in carbide systems opens avenues for tailoring properties such as hardness, strength, and thermal stability. However, the influence of carbon content on the structure and properties of HECs remains understudied. Due to high mixing entropy, covalent-ionic bonding, and lattice distortion effects, HECs demonstrate outstanding mechanical and thermal properties, driving interest in them for protective coatings and ultra-high-temperature ceramics [ 22 – 31 ]. Hardness is a primary parameter determining wear resistance and suitability for use as protective coatings or structural components. Compressive strength and fracture toughness are less studied due to brittleness and challenges in obtaining defect-free bulk samples. While the strength of HECs can reach 1500–2200 MPa, most exhibit brittle fracture without plasticity, limiting their application under dynamic loads. Recent work suggests the possibility of improving fracture toughness by introducing secondary phases (e.g., SiC), forming nanocomposite structures, or engineering compositional gradients. Oxidation Resistance. The oxidation mechanism of binary carbides typically follows two laws: linear (rapid oxidation) and parabolic (slow oxidation) [ 32 ]. The linear law is characteristic of initial stages or uncontrolled oxidation, while the parabolic law indicates the formation of a protective oxide layer and is governed by a diffusion-controlled process. Studies on the oxidation resistance of the (HfZrTiTaNb)C system showed its behavior follows parabolic kinetics in the 1073–1473 K range [ 33 ]. The oxidation rate initially increases from 1073 to 1273 K but decreases from 1273 to 1473 K. At 1573–1673 K, the material also exhibits parabolic oxidation kinetics, fully oxidizing only at 1773 K after 1 hour. Good resistance is attributed to the formation of mixed oxides in the surface layer [ 33 ]. At 1473 K and 90% humidity, the parabolic rate constant kp for this carbide was found to be half that of ZrC [ 34 ]. Adding SiC (10–30 vol.%) improves oxidation resistance at 1573–1773 K due to the formation of protective silicate layers (HfZrSiO 4 , HfZrTiO 4 ), with 20 vol.% being the most effective [ 35 ]. SiC does not change the oxidation mechanism but slows outward diffusion of elements. Ablation Resistance reflects a material's ability to retain mass and integrity under high-temperature, high-speed gas flow. Under such conditions, complex multi-component oxides form on the surface of HECs, effectively hindering oxygen penetration and protecting the carbide base [ 26 ]. Studies on the ablation resistance of multi-component carbides in an oxy-acetylene flame at 2000°C showed the formation of a dense inner layer of isolated (Zr,Hf) 6 (Nb,Ta) 2 O 17 grains uniformly distributed in a continuous Ti(Nb,Ta) 2 O 7 matrix, effectively suppressing oxygen diffusion. However, at 2600°C, a porous skeleton of (Hf,Zr)O 2 and (Hf,Zr,Ti,Ta)O x oxides bonded by a liquid phase is insufficiently strong, leading to spallation and failure of the oxide layer [ 36 ]. Materials and Methods For the synthesis of high-entropy alloy (HEA) powders, commercial elemental metal powders (Hf, Zr, Ti, Ta, Nb, V, Mo) with 99.6% purity were selected. Carbon black was added to the obtained HEA powders for HEC synthesis. Mechanical alloying (MA) was performed in a FRITSCH Pulverisette 4 planetary ball mill using steel jars and balls. MA was conducted under an argon atmosphere at a planetary disk speed of 200 rpm and jar speed of 400 rpm for 5–10 hours with a ball-to-powder weight ratio of 20:1. HEA powders were mixed with carbon black in a planetary ball mill to form a homogeneous mechanical mixture for 2.5 hours at a disk speed of 150 rpm and jar speed of 300 rpm. Stearic acid was added to the initial mixtures to prevent agglomeration. High-entropy carbides were synthesized via Spark Plasma Sintering (SPS) using an SPS HPD 25 FCT Systeme GmbH unit. Sintering was conducted in a graphite die at 2000°C under a pressure of 50 MPa. Phase and structural X-ray analysis was performed on a Rigaku SmartLab diffractometer using CuKα radiation (wavelength λ = 1.5418 Å). Data were collected in the 30–105° 2θ range with a step of 0.02° and a scanning speed of 0.8 °/min. Diffractogram interpretation was done using SmartLab Studio II software and the PDF-2 2021 database. Structural parameters were refined using the Rietveld method. Microstructure investigation and chemical composition analysis were conducted using a Mira 3 Tescan scanning electron microscope (SEM) with secondary electron (SE) and back-scattered electron (BSE) detectors. Chemical analysis was performed using an Oxford Instruments X-Max 80 energy-dispersive X-ray spectroscopy (EDX) detector. Differential scanning calorimetry (DSC) was carried out on a high-temperature Netzsch 404 F3 Pegasus calorimeter from 300 to 1500°C with a heating rate of 10°C/min. Compression tests were performed on cylindrical samples using a Zwick/Roell Z100 universal testing machine. Microhardness was measured on a Buehler microhardness tester under a 500-gram load. Measurements were taken on ground and polished samples on a cross-section parallel to the cylinder base. Diffusion heat treatment of the coating was performed in a universal SGL-1700 high-temperature furnace (STOMM) at 1600°C for 6 hours under an argon atmosphere. Heating rate was 10°C/min; the sample was furnace-cooled. Gas-dynamic experiments were conducted on an UPI-200 electric arc plasmatron. The temperature regime on the frontal sample surface was monitored using a Thermocont-TS5S6M pyrometer operating on a spectral ratio principle. A Tandem VS415 thermal imaging system was used to obtain surface temperature distribution fields and monitor geometry changes (linear ablation) during the experiment. Results Mechanical alloying The constituent elements were selected from those capable of forming refractory carbides and possessing high melting points of their oxides. The highest melting points for carbides and oxides are exhibited by: hafnium, zirconium, tungsten, tantalum, niobium, titanium, and molybdenum. To select systems including these elements, a calculation of thermodynamic and structural parameters for 26 systems was performed. Thermodynamic modeling of crystallization diagrams was then conducted, revealing that only 8 compositions could form BCC solid solutions: HfZrTiTaNb, HfZrTiTaV, HfZrTiTaMo, HfZrTiNbV, HfZrTiNbMo, HfZrTiMoV, HfZrTaNbMo, and HfZrTiTaNbMo. For further investigation of HECs, systems with a wide region of single-phase BCC solid solution existence were selected: HfZrTiTaNb, HfZrTiTaV, and HfZrTiMoV. These compositions, upon carbon addition, also possess sufficiently wide regions of single-phase FCC solid solution existence, which is preferable for studying the influence of carbon content on properties. Figure 1 shows the microstructure and elemental distribution in HfZrTiTaNb alloy powder depending on mechanical alloying time. Investigation of the MA process revealed a universal synthesis mechanism for all high-entropy systems. Initial MA stages involve plastic deformation and flattening of powder particles followed by cold welding, leading to the formation of lamellar-type composite particles. After 5 hours of processing, a distinct layered structure forms, which homogenizes by 7.5 hours with the formation of a chemically homogeneous solid solution, corresponding to a specific energy input of 11.1 Wh/g. Homogenization is accompanied by particle size reduction (d 10 = 21 µm, d 50 = 43 µm, d 90 = 68 µm after 5h; (d 10 = 17 µm, d 50 = 36 µm, d 90 = 60 µm after 7.5h). Further increase in processing time to 10 hours does not significantly improve homogeneity but leads to intense iron contamination from milling balls and jars. Particle size after 10h MA was: d 10 = 13 µm, d 50 = 30 µm, d 90 = 50 µm. X-ray phase analysis confirmed the formation of a single-phase BCC solid solution as a result of alloying. It was established that Nb and Ta dissolve first due to their smaller atomic radii. Diffractograms and elemental distribution maps indicate a small amount of undissolved Zr and Hf. Results of microstructure investigation of HfZrTiTaV and HfZrTiMoV alloys after 7.5h MA (Fig. 2 ) demonstrate high chemical homogeneity of the powders. However, both alloys exhibited localized areas of incomplete dissolution of zirconium and hafnium, appearing as small zones of elevated concentration on distribution maps. This confirms the lower diffusion rate of Zr and Hf in the studied high-entropy systems. Particle size distribution analysis showed both compositions are characterized by a narrow particle size distribution: d 10 = 17 µm, d 50 = 40 µm, d 90 = 68 µm (HfZrTiTaV) and d 10 = 13 µm, d 50 = 33 µm, d 90 = 53 µm (HfZrTiMoV). X-ray structural analysis confirmed the formation of a uniform BCC phase, corresponding to a solid solution of transition metals, in both systems after 7.5h MA. Weak signals corresponding to pure Zr and Hf metals were detected in both samples, consistent with electron microscopy data. Spark plasma sintering of HECs Carbide synthesis was performed using spark plasma sintering. A mechanical mixture of HEA powder and carbon black was used as feedstock. The process was conducted with constant monitoring of parameters: temperature, time, punch displacement, shrinkage rate, current, voltage, power, and pressing force. For all studied systems, sintering is characterized by a unified three-stage mechanism (Fig. 3 a). The first stage involves intensive chemical interaction between metals and carbon (Me + C → MeC). This process is accompanied by pronounced volumetric shrinkage due to powder consolidation and multi-component carbide formation. Chemical interaction is confirmed by XRD results (Fig. 3 b), showing FCC phase formation in the sample after heating to 1750°C. Differential scanning calorimetry additionally determined the reaction temperature to be 1367°C. The specific heat effect of the exothermic reaction was ΔH = − 67.4 J/g. The second sintering stage is associated with the carbothermal reduction of zirconia (ZrO₂) and hafnia (HfO 2 ), confirmed by X-ray diffractogram analysis. Notably, after heating the sample to 2000°C with a subsequent 2-minute hold, a noticeable decrease in the intensity of diffraction peaks corresponding to these oxides is observed, indicating their partial or complete conversion to metallic phases. The presence of oxides in the alloy is likely due to brief oxygen exposure during powder transfer to the SPS unit. The obtained experimental data agree with results presented in the scientific literature [ 37 ]. According to existing sources, intensive carbothermal reduction of ZrO 2 and HfO 2 by carbon in vacuum occurs in the 1800–2200°C range. The specific onset and completion temperatures depend on factors including residual pressure in the vacuum chamber, purity of initial components, and heating rate. The chemical basis of the process is described by the following carbothermal reduction equation: MeO 2 + 2C → Me + 2CO (gas) (1), where Me is Zr (zirconium) or Hf (hafnium). Vacuum plays a special role in ensuring the completeness and efficiency of this reaction. Creating reduced pressure in the reaction zone promotes continuous removal of generated gaseous CO from the system. According to Le Chatelier's principle, such removal shifts the chemical equilibrium towards the reaction products, i.e., towards the formation of metallic zirconium or hafnium. In the absence of vacuum, the partial pressure of CO rapidly increases, leading to slowing and eventual cessation of the reduction process due to equilibrium attainment. Thus, vacuum conditions are a crucial factor enabling the thermodynamic and kinetic feasibility of effective carbothermal reduction. The final sintering stage involves intensive plastic deformation of powder particles under applied external pressure. As a result, particles actively shift relative to each other, filling interparticle voids and micropores. This process is accompanied by significant reduction of intergranular porosity due to the combined action of diffusion mass transfer mechanisms and mechanical compaction. Plastic flow of the material promotes leveling of contact zones between grains, improves their bonding, and forms a dense, nearly monolithic structure. Elimination of residual porosity not only increases material strength and hardness but also improves its thermal conductivity and thermo-oxidative resistance. The phase composition of all samples after sintering completion is characterized predominantly by a single-phase FCC carbide structure. Small peaks corresponding to graphite are also observed on diffractograms. The structure of the sintered samples is characterized by a homogeneous phase with dispersed carbon inclusions up to 1 µm in size. Besides the main carbide phase, a small amount of free graphite was detected on sample surfaces. Graphite formation on the surface is associated with sintering technology specifics: the process was conducted in a graphite die, which at high temperatures can interact with powder mixture components and also serve as a carbon source. As noted earlier, despite the diversity of existing synthesis methods for multi-component carbides, the key problem of controlling stoichiometric composition remains unsolved. Within the chosen fabrication route, uncontrolled variation in carbon content is also observed: on one hand, the material reacts with the graphite die, leading to sample carburization; on the other hand, the introduced carbon is consumed for the reduction of zirconium and hafnium oxides. Carbon influence on lattice parametr To investigate the nature of carbon's influence, samples were synthesized from a mechanical mixture of HfZrTiTaNb powder with carbon black additions ranging from 30 to 65 at.% C. For HfZrTiTaV and HfZrTiMoV alloys, carbon black was added in amounts from 35 to 55 at.%. X-ray structural analysis was used to determine the lattice parameter on the surface and in the bulk of samples depending on the amount of carbon introduced; results are presented in Table 1 . Table 1 Lattice parameter values versus introduced carbon amount on the surface and in the bulk of samples. Alloy (HfZrTiTaNb)С x (HfZrTiTaV)С x (HfZrTiMoV)С x C (at.%) Bulk Surface Bulk Surface Bulk Surface 30 4.476 4.481 - - - - 35 4.491 4.507 4.437 4.445 4.391 4.402 40 4.496 4.515 4.439 4.449 4.399 4.416 45 4.499 4.513 4.445 4.456 4.403 4.418 50 4.508 4.514 4.447 4.457 4.407 4.417 55 4.51 4.514 4.452 4.457 4.408 4.417 60 4.514 4.513 - - - - 65 4.514 4.514 - - - - It was established that with increasing carbon content, the lattice parameter in the (HfZrTiTaNb)C x alloy on the sample surface increases to 4.514 Å, thereafter remaining constant. This indicates attainment of the limiting carbon content in the variable-composition carbide and the formation of a stoichiometric phase. The lattice parameter in the sample bulk increases monotonically, reaching a limiting value at an introduced carbon amount of 60 at.%. To verify the obtained data, the theoretical lattice parameter for (HfZrTiTaNb)C was calculated using the additivity rule, resulting “a” = 4.516 Å, demonstrating good agreement with experimental data. To determine the minimum lattice parameter value, the initial HfZrTiTaNb HEA was sintered without carbon addition. X-ray phase analysis results indicated the presence of a metallic BCC phase and a carbide FCC phase in the material. The minimum lattice parameter value was 4.462 Å. The content of unreduced zirconium and hafnium oxides was 4.6 wt.%. Similarly to the (HfZrTiTaNb)C x alloy, a monotonic increase in parameter “a” with increasing carbon content in the sample bulk is observed for (HfZrTiTaV)C x and (HfZrTiMoV)C x alloys. At an introduced carbon amount of 45 at.%, the lattice parameter of (HfZrTiTaV)C x reaches a limiting value of 4.457 Å. The maximum lattice parameter value is smaller compared to (HfZrTiTaV)C, explained by the shorter covalent bond length in binary VC compared to NbC. The calculated “a” parameter for (HfZrTiTaV)C was 4.454 Å. In the (HfZrTiMoV)C x system, the lattice parameter on the surface reaches a plateau already at 0.45 at.% C and stabilizes at 4.417 Å. The limiting lattice parameter value in this system is the smallest among all studied carbide systems. The calculated lattice parameter is “a” = 4.419 Å. X-ray phase analysis of HfZrTiTaV and HfZrTiMoV alloy samples sintered without carbon addition showed the formation of a two-phase structure consisting of BCC and FCC phases. Based on the obtained data, minimum FCC phase lattice parameters were determined: 4.423 Å and 4.388 Å for HfZrTiTaV and HfZrTiMoV systems, respectively. Quantitative phase composition assessment revealed the presence of impurity oxides: zirconia content was 3.4%, and hafnia content was 2.3%. Carbon influence on HECs properties Results of mechanical tests on samples (Fig. 4 ) with varying carbon content demonstrate that the maximum hardness and material strength in all samples are achieved at an introduced carbon amount of 40 at.%. Maximum strength, hardness, and lack of plasticity are indicative of a metal-to-carbon stoichiometric ratio close to 1:1. At such a ratio, the carbide sublattice is fully ordered, vacancies are absent or minimal, and the structure possesses high cohesive energy. With carbon deficiency (less than 40 at.%), vacancies form in the anionic sublattice. These defects disrupt the covalent network continuity, weaken interatomic bonds, and reduce overall crystal binding energy, leading to decreased hardness and strength. Conversely, with carbon excess, the system cannot incorporate additional carbon into the carbide lattice due to structural constraints. Excess carbon precipitates as a secondary phase - free graphite - detrimentally affecting structural homogeneity and mechanical properties. The presented thermograms (Fig. 5 ) show the distribution of thermal fields on the surface of (HfZrTiTaNb)C x system samples with different carbon content (35 to 65 at.% C) during gas-dynamic testing (GDT) conducted under high-temperature oxidative gas flow conditions. Analysis of GDT results (Table 2 ) showed that among the studied samples of (HfZrTiTaNb)C x , (HfZrTiTaV)C x , and (HfZrTiMoV)C x systems, compositions with carbon content of 45–50 at.% possess the greatest resistance to ablation in a high-enthalpy gas flow. Table 2 Gas-dynamic test results. Carbon amount, at.% Temperature, °C (HfZrTiTaNb)C x (HfZrTiTaV)C x (HfZrTiMoV)C x 35 1735 1999 2042 40 1837 2026 2066 45 1925 2053 2118 50 1953 2146 2098 55 1828 2081 2099 60 1731 - - Under non-equilibrium, intensive thermal exposure characteristic of GDT, determining factors for material resistance become not only chemical oxidation stability but also the ability to effectively dissipate absorbed thermal energy. Thermal energy dissipation occurs via various mechanisms, the main ones being: thermal radiation from the surface, surface evaporation (sublimation), and thermal conductivity into the material bulk. Free dispersed graphite likely darkens the surface and enhances radiative heat transfer, allowing the material to more effectively dissipate thermal energy into the environment as infrared radiation, and also increases material thermal conductivity. Furthermore, combustion of graphite particles may generate CO, which acts as a reducing agent. Thus, a slight carbon excess in high-entropy systems (HfZrTiTaNb)C x , (HfZrTiTaV)C x , and (HfZrTiMoV)C x provides an optimal compromise between chemical resistance, radiative, and thermal conductive properties. Microstructural investigation of the (HfZrTiTaNb)C sample surface after GDT established that under intensive heat flux with temperatures exceeding 2000°C, active oxidation begins on the material surface, accompanied not only by protective oxide film formation but also selective removal of individual elements. Elements Ti, Ta, Nb, whose oxides have lower melting points (below 3000°C) and higher volatility, are first subjected to erosion and evaporation. Oxides TiO 2 , Ta 2 O 5 , Nb 2 O 5 partially transition to molten or vapor states at high temperatures, leading to their gradual washing from the surface by the gas flow. Molten compounds react with more stable zirconium and hafnium oxides, forming complex structures like Zr 6 Nb 2 O 17 in the near-surface layer. The lower, denser layer (approx. 10 µm thick) adjacent to the main carbide material is significantly enriched with zirconium and hafnium and protects the sample interior from further oxidation. Coating To demonstrate the feasibility of forming a barrier coating based on multi-component carbide (HfZrTiTaNb)C x on a carbon-carbon composite (CCC) surface, three schemes were applied. The schemes and corresponding microstructures of the obtained coatings are presented in Fig. 6 . First Scheme A mechanical mixture of carbon black and HfZrTiTaNb powder was poured onto the CCC placed on the lower punch of the graphite die. After sintering, the obtained coating lacked adhesion to the substrate and easily detached even under minimal mechanical impact. Carbide formation occurred within the powder bed volume without affecting the interface with the substrate, preventing chemical bonding. Second Scheme HfZrTiTaNb powder without carbon black was poured onto the composite material. In this case, the graphite die and the substrate material itself served as carbon sources. Implementing this scheme resulted in significant improvement in coating adhesion strength after sintering. The microstructure of the obtained coating and the interface are shown in Fig. 6 . It is noted that the coating contains a significant fraction of residual metallic phase from the initial HfZrTiTaNb. XRD confirmed the presence of metallic BCC phase and hafnium/zirconium oxides. Attempts to increase the sintering hold time to 15 minutes and perform additional heat treatment (1600°C, 6 hours) did not achieve substantial reduction of the metallic phase or obtain a single-phase carbide structure. Third scheme. To eliminate this drawback and obtain a single-phase coating, a three-layer powder pouring scheme was developed and tested. The composition consisted of a bottom layer of pure HEA in contact with the substrate, an intermediate layer of HEA mixed with 40 at.% carbon black, and again a top layer of pure HEA. Analysis of the obtained coating microstructure (Fig. 6 ) confirmed the formation of a homogeneous carbide structure. Coating thickness was about 620 µm, with no signs of secondary phases, free graphite, or residual metallic alloy. The coating-substrate interface is characterized by continuous contact without gaps or delamination; large pores, cracks, and oxide inclusions are absent. X-ray phase analysis confirmed the formation of a single-phase carbide coating with FCC structure. The lattice parameter of the synthesized coating was 4.492 Å, corresponding to 35 to 40 at.% introduced carbon (Fig. 7 a). Microhardness test results (Fig. 7 b) showed the carbide coating (HfZrTiTaNb)C x on CCC had a hardness of 2069 HV (20.3 GPa). This value corresponds to the microhardness of material with 35–40 at.% introduced carbon, consistent with results from lattice parameter X-ray analysis. During GDT of a CCC sample with applied carbide coating (HfZrTiTaNb)C x , the average surface temperature until failure was 2003°C. Failure occurred 39 seconds after the start of high-enthalpy gas flow exposure and manifested as coating delamination from the substrate along the interface. Analysis of the failure mechanism indicates that the primary cause of degradation is the incompatibility of coefficients of thermal expansion (CTE) between the layers. The CTE of the CCC substrate is significantly lower (0.5-2 ×10 − 6 K − 1 ) than that of the binary compounds constituting the multi-component carbide (6.7–7.8 ×10 − 6 K − 1 ). Under intensive heating, temperature gradients reach several hundred degrees per millimeter, and significant thermomechanical stresses arise in the bonding zone, exceeding the interfacial bonding strength, leading to coating spallation. It is important to note that the carbide layer surface itself and the CCC substrate showed no signs of intensive ablation, such as component evaporation, porous oxide layer formation, or erosive destruction. This attests to the high thermochemical stability and ablation resistance of the coating material itself under extreme gas-dynamic exposure. The enhanced stability compared to bulk samples of similar composition is likely due to the high thermal conductivity of the substrate, which promotes effective heat removal from the surface and reduces local overheating, slowing oxidation and destruction processes. Nevertheless, despite the high properties of the carbide itself, the adhesion problem remains a key limiting factor for the practical application of carbide coatings. To solve it, the introduction of an intermediate (bonding) layer with a gradient or compensating composition, capable of smoothing the CTE mismatch between substrate and functional coating, appears promising. Candidates may include: composite layers with silicon carbide addition, thin-film systems with gradual composition change from C to (HfZrTiTaNb)C x . Conclusions Single-phase high-entropy carbides (HfZrTiTaNb)C x , (HfZrTiTaV)C x , and (HfZrTiMoV)C x with variable carbon content (30 to 65 at.%) were successfully synthesized via mechanical alloying followed by spark plasma sintering. The sintering process is characterized by a three-stage mechanism involving carbide formation, carbothermal reduction of oxides, and plastic compaction. The dependence of the FCC lattice parameter on carbon content was established. For all systems, a monotonic increase in parameter “a” is observed until reaching a limiting value (4.514 Å for (HfZrTiTaNb)C, 4.457 Å for (HfZrTiTaV)C, 4.417 Å for (HfZrTiMoV)C), after which it stabilizes, indicating the formation of a limiting stoichiometric phase. Experimental values show good agreement with calculations based on the additivity rule. It was determined that maxima in microhardness (28–32 GPa) and compressive strength (2500–2800 MPa) are achieved at a carbon content of 40 at.%. This optimum corresponds to the most complete filling of the anionic sublattice, vacancy minimization, and cohesive energy maximization. Deviation from this stoichiometry in either direction leads to degradation of mechanical properties. Gas-dynamic testing in a high-enthalpy oxidative flow showed that maximum ablation resistance (surface temperature 1950–2150°C) is exhibited by compositions with 45–50 at.% C. The enhanced resistance with a slight carbon excess is explained by a synergistic effect: the chemical stability of the carbide matrix combines with improved radiative heat dissipation and thermal conductivity due to the presence of dispersed free carbon. A three-layer deposition scheme was developed, enabling the fabrication of a single-phase carbide coating (HfZrTiTaNb)C x (40 at.% C) with a thickness of 620 µm on a carbon-carbon composite substrate. The coating possesses high microhardness (20.3 GPa) and structural homogeneity. The key limitation for coating application is its delamination under gas-dynamic exposure after 39 seconds due to critical thermomechanical stresses at the interface. These stresses are caused by a significant mismatch in the coefficients of thermal expansion between the coating and the carbon-carbon substrate. Notably, the carbide phase itself and the substrate material showed no signs of intensive ablation, confirming the high thermochemical stability of the coating. For the practical implementation of high-entropy carbide coatings, the development and integration of an intermediate gradient or compensating layer capable of reducing thermal stresses at the interface with the substrate is necessary (e.g., based on composites with SiC or systems with gradually varying composition). Declarations Author Contribution A.K.: Conceptualization, Methodology, Investigation, Formal analysis, Data curation, Writing – original draft, Visualization. Conducted the main experimental research, including material synthesis, mechanical alloying, spark plasma sintering, X-ray structural and microstructural analysis, mechanical and gas-dynamic testing. Performed processing and interpretation of experimental data, prepared the draft manuscript, figures, and illustrations.E.V.: Investigation, Validation, Writing – original draft, Writing – review & editing, Visualization. Actively participated in experimental work, including sample preparation, measurements, and data collection. Performed independent validation of key results. Made a major contribution to the preparation and formatting of the manuscript: participated in writing and structuring the initial text, significantly revised and edited the draft, prepared and organized graphical materials (figures, tables). Conducted literature review and reference formatting.N.R.: Resources, Validation, Writing – review & editing. Provided material, technical, and resource support for the research. Participated in discussion and critical evaluation of the results, reviewing, and revising the manuscript text.A.P.: Supervision, Funding acquisition, Writing – review & editing. Provided overall scientific supervision of the project, formulated general research objectives. Responsible for securing and administering funding. Participated in the final review and approval of the manuscript.All authors have read and approved the final version of the manuscript for submission. Acknowledgement The study was supported by the Ministry of Science and Higher Education of the Russian Federation (State Assignment No. 075-03-2025-256). Data Availability The datasets used and/or analysed during the current study are available from the corresponding author upon reasonable request. References Lewin, E. Multi-component and high-entropy nitride coatings—A promising field in need of a novel approach. J. Appl. Phys. 127 , 160901 (2020). Kirnbauer, A. et al. Mechanical properties and thermal stability of reactively sputtered multi-principal-metal Hf-Ta-Ti-V-Zr nitrides. Surf. Coat. Technol. 389 , 125674 (2020). Braic, M. et al. Characteristics of (TiAlCrNbY)C films deposited by reactive magnetron sputtering. Surf. Coat. Technol. 204 , 2010–2014 (2010). Wang, Y. et al. Enhanced Hardness in High-Entropy Carbides through Atomic Randomness. Adv. Theory Simul. 3 , 2000029 (2020). Zhang, H. et al. A high-entropy B4(HfMo2TaTi)C and SiC ceramic composite. Dalton Trans. 48 , 5161–5167 (2019). Razumov, N., Makhmutov, T., Kim, A. & Popovich, A. Synthesis of high-entropy carbides (TiTaNb)xHfyZrzC with strong thermal-oxidative resistant properties by mechanical alloying and spark plasma sintering. J. Mater. Res. Technol. 27 , 7184–7194 (2023). Wang, S. et al. MgCoNiCuZn)O high-entropy ceramic membrane with high oil-in-water emulsion flux and rejection ratio. Ceram. Int. 51 , 37230–37241 (2025). Mnasri, W. et al. Synthesis of (MgCoNiCuZn)O entropy-stabilized oxides using solution-based routes: influence of composition on phase stability and functional properties. J. Mater. Chem. C . 9 , 15121–15131 (2021). Wang, Q. et al. Multi-anionic and -cationic compounds: new high entropy materials for advanced Li-ion batteries. Energy Environ. Sci. 12 , 2433–2442 (2019). Amoretti, M. et al. Production and detection of cold antihydrogen atoms. Nature 419 , 456–459 (2002). Dąbrowa, J. et al. Stabilizing fluorite structure in ceria-based high-entropy oxides: Influence of Mo addition on crystal structure and transport properties. J. Eur. Ceram. Soc. 40 , 5870–5881 (2020). Gild, J. et al. High-entropy fluorite oxides. J. Eur. Ceram. Soc. 38 , 3578–3584 (2018). Yang, Y. et al. Structural, mechanical and electronic properties of (TaNbHfTiZr)C high entropy carbide under pressure: Ab initio investigation. Phys. B . 550 , 163–170 (2018). Gild, J. et al. High-Entropy Metal Diborides: A New Class of High-Entropy Materials and a New Type of Ultrahigh Temperature Ceramics. Sci. Rep. 6 , 37946 (2016). Gild, J. et al. Thermal conductivity and hardness of three single-phase high-entropy metal diborides fabricated by borocarbothermal reduction and spark plasma sintering. Ceram. Int. 46 , 6906–6913 (2020). Tallarita, G. et al. Novel processing route for the fabrication of bulk high-entropy metal diborides. Scr. Mater. 158 , 100–104 (2019). Qin, Y. et al. A high entropy silicide by reactive spark plasma sintering. J. Adv. Ceram. 8 , 148–152 (2019). Liu, D., Huang, Y., Liu, L. & Zhang, L. A novel of MSi2 high-entropy silicide: Be expected to improve mechanical properties of MoSi2. Mater. Lett. 268 , 127629 (2020). Gild, J. et al. A high-entropy silicide: (Mo0.2Nb0.2Ta0.2Ti0.2W0.2)Si2. J. Materiomics . 5 , 337–343 (2019). Chen, T. K., Shun, T. T., Yeh, J. W. & Wong, M. S. Nanostructured nitride films of multi-element high-entropy alloys by reactive DC sputtering. Surf. Coat. Technol. 188–189 , 193–200 (2004). Dusza, J. et al. Microstructure of (Hf-Ta-Zr-Nb)C high-entropy carbide at micro and nano/atomic level. J. Eur. Ceram. Soc. 38 , 4303–4307 (2018). Ye, B. et al. First-principles study, fabrication and characterization of (Zr0.25Nb0.25Ti0.25V0.25)C high-entropy ceramics. Acta Mater. 170 , 15–23 (2019). Jiang, S. et al. Mechanical behavior of high entropy carbide (HfTaZrTi)C and (HfTaZrNb)C under high pressure: Ab initio study. Int. J. Quantum Chem. 121 , e26584 (2021). Sarker, P. et al. High-entropy high-hardness metal carbides discovered by entropy descriptors. Nat. Commun. 9 , 4980 (2018). Moskovskikh, D. O. et al. High-entropy (HfTaTiNbZr)C and (HfTaTiNbMo)C carbides fabricated through reactive high-energy ball milling and spark plasma sintering. Ceram. Int. 46 , 19008–19014 (2020). Yan, X. et al. Hf0.2Zr0.2Ta0.2Nb0.2Ti0.2)C high-entropy ceramics with low thermal conductivity. J. Am. Ceram. Soc. 101 , 4486–4491 (2018). Feng, L., Fahrenholtz, W. G. & Hilmas, G. E. Low-temperature sintering of single‐phase, high‐entropy carbide ceramics. J. Am. Ceram. Soc. 102 , 7217–7224 (2019). Castle, E. et al. Processing and Properties of High-Entropy Ultra-High Temperature Carbides. Sci. Rep. 8 , 8609 (2018). Demirskyi, D. et al. High-temperature flexural strength performance of ternary high-entropy carbide consolidated via spark plasma sintering of TaC, ZrC and NbC. Scr. Mater. 164 , 12–16 (2019). Lu, K. et al. Microstructures and mechanical properties of high-entropy (Ti0.2Zr0.2Hf0.2Nb0.2Ta0.2)C ceramics with the addition of SiC secondary phase. J. Eur. Ceram. Soc. 40 , 1839–1847 (2020). Wang, F. et al. The effect of submicron grain size on thermal stability and mechanical properties of high-entropy carbide ceramics. J. Am. Ceram. Soc. 103 , 4463–4472 (2020). Ye, B., Wen, T. & Chu, Y. High-temperature oxidation behavior of (Hf0.2Zr0.2Ta0.2Nb0.2Ti0.2)C high‐entropy ceramics in air. J. Am. Ceram. Soc. 103 , 500–507 (2020). Ye, B., Wen, T., Liu, D. & Chu, Y. Oxidation behavior of (Hf0.2Zr0.2Ta0.2Nb0.2Ti0.2)C high-entropy ceramics at 1073–1473 K in air. Corros. Sci. 153 , 327–332 (2019). Tan, Y. et al. Oxidation behaviours of high-entropy transition metal carbides in 1200°C water vapor. J. Alloys Compd. 816 , 152523 (2020). Wang, H., Cao, Y., Liu, W. & Wang, Y. Oxidation behavior of (Hf0.2Ta0.2Zr0.2Ti0.2Nb0.2)C-xSiC ceramics at high temperature. Ceram. Int. 46 , 11160–11168 (2020). Mirovaya, E. et al. Structure and Oxidation Behavior of Multicomponent (Hf,Zr,Ti,Nb,Mo)C Carbide Ceramics. Materials 16 , 3163 (2023). Sevastyanov, V. G. et al. Low-temperature synthesis of nanodispersed titanium, zirconium, and hafnium carbides. Russ J. Inorg. Chem. 56 , 661–672 (2011). Additional Declarations No competing interests reported. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-8394818","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":592117958,"identity":"119be460-2d66-4d40-a309-b751f5de4310","order_by":0,"name":"Artem Kim","email":"","orcid":"","institution":"Peter the Great St. Petersburg Polytechnic University","correspondingAuthor":false,"prefix":"","firstName":"Artem","middleName":"","lastName":"Kim","suffix":""},{"id":592117959,"identity":"96fb9c1e-8f8c-4fa3-82d2-293100851f8a","order_by":1,"name":"Ekaterina Volokitina","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA/0lEQVRIiWNgGAWjYFAC5gbGBgMGHgYGxsYHCRU2DCDGAfxaGEFaDIBamJsNPpxJA4sQoYXBAMhgbxOc2XIYLIZXi8HxxsaHMwr+yJizH2xj5m04b7e2/TDQlhqbaJxazhxsNtwAdJhlT2LbY94dt5O3nUkEajmWltuAQ4vkjMQ2yQdALQYHEtuNec/cTjY7ANTC2HCYCC3nH7ZJ87adSzY7/xC/Fn4JoBaQwwxuABkz2w7Ymd0gYAs/D9AvMwyMgVoeggI5OcHsBtCWBDx+YWNvPviw54+cvcH59IfAqLSzNwMxPtTY4NSCARLBKhOIVQ4C9qQoHgWjYBSMgpEBAK2baajHx0DdAAAAAElFTkSuQmCC","orcid":"","institution":"Peter the Great St. Petersburg Polytechnic University","correspondingAuthor":true,"prefix":"","firstName":"Ekaterina","middleName":"","lastName":"Volokitina","suffix":""},{"id":592117960,"identity":"73dd365a-9cb5-4686-9adc-f71824c91559","order_by":2,"name":"Nikolay Razumov","email":"","orcid":"","institution":"Peter the Great St. Petersburg Polytechnic University","correspondingAuthor":false,"prefix":"","firstName":"Nikolay","middleName":"","lastName":"Razumov","suffix":""},{"id":592117961,"identity":"e478a4bb-e5fa-4710-ab0b-8b90a8d2a3ee","order_by":3,"name":"Anatoliy Popovich","email":"","orcid":"","institution":"Peter the Great St. Petersburg Polytechnic University","correspondingAuthor":false,"prefix":"","firstName":"Anatoliy","middleName":"","lastName":"Popovich","suffix":""}],"badges":[],"createdAt":"2025-12-18 11:23:39","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-8394818/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8394818/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":102964217,"identity":"824fc813-c921-4578-bcab-4168dbd56457","added_by":"auto","created_at":"2026-02-19 04:21:46","extension":"jpeg","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":548716,"visible":true,"origin":"","legend":"\u003cp\u003eMicrostructure and elemental distribution in HfZrTiTaNb alloy powder after MA for: 5 hours (a), 7.5 hours (b), 10 hours (c).\u003c/p\u003e","description":"","filename":"floatimage1.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-8394818/v1/531354071a0709045fd8f5ad.jpeg"},{"id":102964415,"identity":"23fafd27-a502-4135-a927-75f7243edeba","added_by":"auto","created_at":"2026-02-19 04:22:14","extension":"jpeg","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":909688,"visible":true,"origin":"","legend":"\u003cp\u003eMicrostructure and elemental distribution in powder after 7.5h MA for alloys HfZrTiTaV (a) and HfZrTiMoV (b).\u003c/p\u003e","description":"","filename":"floatimage2.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-8394818/v1/614cca97420abb8e3e7cd196.jpeg"},{"id":102926643,"identity":"7aae7f0a-7d78-42b7-94e9-70853620c7f6","added_by":"auto","created_at":"2026-02-18 14:02:52","extension":"jpeg","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":170277,"visible":true,"origin":"","legend":"\u003cp\u003eChange in punch displacement rate versus temperature and holding time (a) and phase analysis results (b).\u003c/p\u003e","description":"","filename":"floatimage3.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-8394818/v1/a79e617a00c84c3eb2c2a5a1.jpeg"},{"id":102926640,"identity":"d9b03576-1ff1-4f37-8b61-de7a49f1d5b2","added_by":"auto","created_at":"2026-02-18 14:02:52","extension":"jpeg","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":321274,"visible":true,"origin":"","legend":"\u003cp\u003eMechanical properties of HfZrTiTaNb-C, HfZrTiTaV-C, HfZrTiMoV-C systems: hardness (a), compressive strength (b).\u003c/p\u003e","description":"","filename":"floatimage4.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-8394818/v1/67ce7c677532c8d721c46a95.jpeg"},{"id":102926645,"identity":"5aeaa68d-a472-4b4b-be54-5543624c79eb","added_by":"auto","created_at":"2026-02-18 14:02:52","extension":"jpeg","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":1194177,"visible":true,"origin":"","legend":"\u003cp\u003eThermograms of tests for (HfZrTiTaNb)C\u003csub\u003ex\u003c/sub\u003e samples.\u003c/p\u003e","description":"","filename":"floatimage5.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-8394818/v1/d597dee8ad6e93a2cfddb0e6.jpeg"},{"id":102963707,"identity":"ebddbb09-5487-4b34-9776-62f01549a360","added_by":"auto","created_at":"2026-02-19 04:20:10","extension":"jpeg","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":629292,"visible":true,"origin":"","legend":"\u003cp\u003eScheme for obtaining carbide coating on CCC and microstructures of the obtained coatings.\u003c/p\u003e","description":"","filename":"floatimage6.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-8394818/v1/308f55837a2bc28507a33b86.jpeg"},{"id":102926646,"identity":"16f33452-10b8-4a0b-9a98-02375661f862","added_by":"auto","created_at":"2026-02-18 14:02:52","extension":"jpeg","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":184924,"visible":true,"origin":"","legend":"\u003cp\u003eLattice parameter (a) and hardness (b).\u003c/p\u003e","description":"","filename":"floatimage7.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-8394818/v1/d70c19eb4a28af5b2d838586.jpeg"},{"id":102965484,"identity":"f1d6932e-0f86-4690-b4b9-38de42290671","added_by":"auto","created_at":"2026-02-19 04:31:41","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":4682838,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8394818/v1/fe03d5ce-4f14-4f0e-85e3-c9f2e7d54de0.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"\u003cp\u003eCarbon Stoichiometry Effects on the Structure, Mechanical Properties, and Ablation Resistance of (HfZrTiTaNb)C\u003csub\u003ex\u003c/sub\u003e , (HfZrTiTaV)C\u003csub\u003ex\u003c/sub\u003e , and (HfZrTiMoV)C\u003csub\u003ex\u003c/sub\u003e High-Entropy Carbides\u003c/p\u003e","fulltext":[{"header":"Introduction","content":"\u003cp\u003eInitial research on high-entropy materials focused predominantly on metallic systems. However, recent years have seen a surge of interest in high-entropy ceramics (HECs), including carbides, borides, nitrides, oxides, silicides, and fluorides [\u003cspan additionalcitationids=\"CR2 CR3 CR4 CR5 CR6 CR7 CR8 CR9 CR10 CR11 CR12 CR13 CR14 CR15 CR16 CR17 CR18\" citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e]. Similar to high-entropy alloys, they contain five or more principal elements but constitute a distinct family of materials with different properties and application areas. Their advantages include high thermal stability and enhanced mechanical characteristics, resulting from solid solution strengthening, fine-grained structure (and associated Hall-Petch strengthening), and sluggish diffusion.\u003c/p\u003e \u003cp\u003eThe first high-entropy nitrides based on Fe-Co-Ni-Cr-Cu-Al-Mn and Fe-Co-Ni-Cr-Cu-Al\u003csub\u003e0.5\u003c/sub\u003e systems were obtained in 2004 [\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e] by reactive sputtering. Studies assessed their hardness and initiated the exploration of nitrides as protective coatings. Subsequently, the range of potential applications expanded to include diffusion barriers and supercapacitors.\u003c/p\u003e \u003cp\u003eThe first high-entropy carbide was synthesized in 2010 by magnetron sputtering [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e]. Subsequent research revealed a combination of exceptional properties: ultra-high hardness [\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e], increased wear resistance [\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e], and superior oxidation resistance at elevated temperatures [\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e]. These materials are promising for wear-resistant protective coatings, high-performance cutting tools, and components operating under extreme thermal and tribological loads.\u003c/p\u003e \u003cp\u003eThe structure of most multi-component carbides crystallizes in a NaCl-type (rock salt) lattice [\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e]. The key distinction from conventional carbides lies in the presence of five or more elements (e.g., Ti, Zr, Hf, Nb, Ta, V, Mo, etc.) in the cation sublattice, uniformly distributed forming a substitutional solid solution. Concentrations of metallic components are typically near-equiatomic, maximizing the configurational mixing entropy. This high entropy plays a crucial role in the thermodynamic stabilization of a single-phase structure at high temperatures, effectively suppressing the system's tendency to decompose into several binary or ternary carbide phases with lower entropy. Consequently, a homogeneous, thermally stable phase forms even with significant chemical diversity among constituent elements.\u003c/p\u003e \u003cp\u003eAn important feature of the transition metals used in such carbides (Ti, Zr, Hf, V, Nb, Ta, Mo, etc.) is their ability to form non-stoichiometric carbides of variable composition - MeC\u003csub\u003ex\u003c/sub\u003e, where x can vary widely. This homogeneity is due to vacancies in the carbon sublattice, which do not disrupt the fundamental crystal structure type but significantly influence the electronic structure and, consequently, the material's physical properties. This characteristic is directly inherited by multi-component carbides.\u003c/p\u003e \u003cp\u003eVarying carbon stoichiometry in carbide systems opens avenues for tailoring properties such as hardness, strength, and thermal stability. However, the influence of carbon content on the structure and properties of HECs remains understudied.\u003c/p\u003e \u003cp\u003eDue to high mixing entropy, covalent-ionic bonding, and lattice distortion effects, HECs demonstrate outstanding mechanical and thermal properties, driving interest in them for protective coatings and ultra-high-temperature ceramics [\u003cspan additionalcitationids=\"CR23 CR24 CR25 CR26 CR27 CR28 CR29 CR30\" citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e]. Hardness is a primary parameter determining wear resistance and suitability for use as protective coatings or structural components.\u003c/p\u003e \u003cp\u003eCompressive strength and fracture toughness are less studied due to brittleness and challenges in obtaining defect-free bulk samples. While the strength of HECs can reach 1500\u0026ndash;2200 MPa, most exhibit brittle fracture without plasticity, limiting their application under dynamic loads. Recent work suggests the possibility of improving fracture toughness by introducing secondary phases (e.g., SiC), forming nanocomposite structures, or engineering compositional gradients.\u003c/p\u003e \u003cp\u003e \u003cb\u003eOxidation Resistance.\u003c/b\u003e The oxidation mechanism of binary carbides typically follows two laws: linear (rapid oxidation) and parabolic (slow oxidation) [\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e]. The linear law is characteristic of initial stages or uncontrolled oxidation, while the parabolic law indicates the formation of a protective oxide layer and is governed by a diffusion-controlled process.\u003c/p\u003e \u003cp\u003eStudies on the oxidation resistance of the (HfZrTiTaNb)C system showed its behavior follows parabolic kinetics in the 1073\u0026ndash;1473 K range [\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e]. The oxidation rate initially increases from 1073 to 1273 K but decreases from 1273 to 1473 K. At 1573\u0026ndash;1673 K, the material also exhibits parabolic oxidation kinetics, fully oxidizing only at 1773 K after 1 hour. Good resistance is attributed to the formation of mixed oxides in the surface layer [\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e]. At 1473 K and 90% humidity, the parabolic rate constant kp for this carbide was found to be half that of ZrC [\u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e]. Adding SiC (10\u0026ndash;30 vol.%) improves oxidation resistance at 1573\u0026ndash;1773 K due to the formation of protective silicate layers (HfZrSiO\u003csub\u003e4\u003c/sub\u003e, HfZrTiO\u003csub\u003e4\u003c/sub\u003e), with 20 vol.% being the most effective [\u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e35\u003c/span\u003e]. SiC does not change the oxidation mechanism but slows outward diffusion of elements.\u003c/p\u003e \u003cp\u003e \u003cb\u003eAblation Resistance\u003c/b\u003e reflects a material's ability to retain mass and integrity under high-temperature, high-speed gas flow. Under such conditions, complex multi-component oxides form on the surface of HECs, effectively hindering oxygen penetration and protecting the carbide base [\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e]. Studies on the ablation resistance of multi-component carbides in an oxy-acetylene flame at 2000\u0026deg;C showed the formation of a dense inner layer of isolated (Zr,Hf)\u003csub\u003e6\u003c/sub\u003e (Nb,Ta)\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e17\u003c/sub\u003e grains uniformly distributed in a continuous Ti(Nb,Ta)\u003csub\u003e2\u003c/sub\u003e O\u003csub\u003e7\u003c/sub\u003e matrix, effectively suppressing oxygen diffusion. However, at 2600\u0026deg;C, a porous skeleton of (Hf,Zr)O\u003csub\u003e2\u003c/sub\u003e and (Hf,Zr,Ti,Ta)O\u003csub\u003ex\u003c/sub\u003e oxides bonded by a liquid phase is insufficiently strong, leading to spallation and failure of the oxide layer [\u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e36\u003c/span\u003e].\u003c/p\u003e"},{"header":"Materials and Methods","content":"\u003cp\u003eFor the synthesis of high-entropy alloy (HEA) powders, commercial elemental metal powders (Hf, Zr, Ti, Ta, Nb, V, Mo) with 99.6% purity were selected. Carbon black was added to the obtained HEA powders for HEC synthesis. Mechanical alloying (MA) was performed in a FRITSCH Pulverisette 4 planetary ball mill using steel jars and balls. MA was conducted under an argon atmosphere at a planetary disk speed of 200 rpm and jar speed of 400 rpm for 5\u0026ndash;10 hours with a ball-to-powder weight ratio of 20:1. HEA powders were mixed with carbon black in a planetary ball mill to form a homogeneous mechanical mixture for 2.5 hours at a disk speed of 150 rpm and jar speed of 300 rpm. Stearic acid was added to the initial mixtures to prevent agglomeration.\u003c/p\u003e \u003cp\u003eHigh-entropy carbides were synthesized via Spark Plasma Sintering (SPS) using an SPS HPD 25 FCT Systeme GmbH unit. Sintering was conducted in a graphite die at 2000\u0026deg;C under a pressure of 50 MPa.\u003c/p\u003e \u003cp\u003ePhase and structural X-ray analysis was performed on a Rigaku SmartLab diffractometer using CuKα radiation (wavelength λ\u0026thinsp;=\u0026thinsp;1.5418 \u0026Aring;). Data were collected in the 30\u0026ndash;105\u0026deg; 2θ range with a step of 0.02\u0026deg; and a scanning speed of 0.8 \u0026deg;/min. Diffractogram interpretation was done using SmartLab Studio II software and the PDF-2 2021 database. Structural parameters were refined using the Rietveld method.\u003c/p\u003e \u003cp\u003eMicrostructure investigation and chemical composition analysis were conducted using a Mira 3 Tescan scanning electron microscope (SEM) with secondary electron (SE) and back-scattered electron (BSE) detectors. Chemical analysis was performed using an Oxford Instruments X-Max 80 energy-dispersive X-ray spectroscopy (EDX) detector.\u003c/p\u003e \u003cp\u003eDifferential scanning calorimetry (DSC) was carried out on a high-temperature Netzsch 404 F3 Pegasus calorimeter from 300 to 1500\u0026deg;C with a heating rate of 10\u0026deg;C/min.\u003c/p\u003e \u003cp\u003eCompression tests were performed on cylindrical samples using a Zwick/Roell Z100 universal testing machine. Microhardness was measured on a Buehler microhardness tester under a 500-gram load. Measurements were taken on ground and polished samples on a cross-section parallel to the cylinder base.\u003c/p\u003e \u003cp\u003eDiffusion heat treatment of the coating was performed in a universal SGL-1700 high-temperature furnace (STOMM) at 1600\u0026deg;C for 6 hours under an argon atmosphere. Heating rate was 10\u0026deg;C/min; the sample was furnace-cooled.\u003c/p\u003e \u003cp\u003eGas-dynamic experiments were conducted on an UPI-200 electric arc plasmatron. The temperature regime on the frontal sample surface was monitored using a Thermocont-TS5S6M pyrometer operating on a spectral ratio principle. A Tandem VS415 thermal imaging system was used to obtain surface temperature distribution fields and monitor geometry changes (linear ablation) during the experiment.\u003c/p\u003e"},{"header":"Results","content":"\u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003eMechanical alloying\u003c/h2\u003e \u003cp\u003eThe constituent elements were selected from those capable of forming refractory carbides and possessing high melting points of their oxides. The highest melting points for carbides and oxides are exhibited by: hafnium, zirconium, tungsten, tantalum, niobium, titanium, and molybdenum. To select systems including these elements, a calculation of thermodynamic and structural parameters for 26 systems was performed. Thermodynamic modeling of crystallization diagrams was then conducted, revealing that only 8 compositions could form BCC solid solutions: HfZrTiTaNb, HfZrTiTaV, HfZrTiTaMo, HfZrTiNbV, HfZrTiNbMo, HfZrTiMoV, HfZrTaNbMo, and HfZrTiTaNbMo. For further investigation of HECs, systems with a wide region of single-phase BCC solid solution existence were selected: HfZrTiTaNb, HfZrTiTaV, and HfZrTiMoV. These compositions, upon carbon addition, also possess sufficiently wide regions of single-phase FCC solid solution existence, which is preferable for studying the influence of carbon content on properties.\u003c/p\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e shows the microstructure and elemental distribution in HfZrTiTaNb alloy powder depending on mechanical alloying time. Investigation of the MA process revealed a universal synthesis mechanism for all high-entropy systems. Initial MA stages involve plastic deformation and flattening of powder particles followed by cold welding, leading to the formation of lamellar-type composite particles.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eAfter 5 hours of processing, a distinct layered structure forms, which homogenizes by 7.5 hours with the formation of a chemically homogeneous solid solution, corresponding to a specific energy input of 11.1 Wh/g. Homogenization is accompanied by particle size reduction (d\u003csub\u003e10\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;21 \u0026micro;m, d\u003csub\u003e50\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;43 \u0026micro;m, d\u003csub\u003e90\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;68 \u0026micro;m after 5h; (d\u003csub\u003e10\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;17 \u0026micro;m, d\u003csub\u003e50\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;36 \u0026micro;m, d\u003csub\u003e90\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;60 \u0026micro;m after 7.5h). Further increase in processing time to 10 hours does not significantly improve homogeneity but leads to intense iron contamination from milling balls and jars. Particle size after 10h MA was: d\u003csub\u003e10\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;13 \u0026micro;m, d\u003csub\u003e50\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;30 \u0026micro;m, d\u003csub\u003e90\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;50 \u0026micro;m. X-ray phase analysis confirmed the formation of a single-phase BCC solid solution as a result of alloying. It was established that Nb and Ta dissolve first due to their smaller atomic radii. Diffractograms and elemental distribution maps indicate a small amount of undissolved Zr and Hf.\u003c/p\u003e \u003cp\u003eResults of microstructure investigation of HfZrTiTaV and HfZrTiMoV alloys after 7.5h MA (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e) demonstrate high chemical homogeneity of the powders. However, both alloys exhibited localized areas of incomplete dissolution of zirconium and hafnium, appearing as small zones of elevated concentration on distribution maps. This confirms the lower diffusion rate of Zr and Hf in the studied high-entropy systems.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eParticle size distribution analysis showed both compositions are characterized by a narrow particle size distribution: d\u003csub\u003e10\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;17 \u0026micro;m, d\u003csub\u003e50\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;40 \u0026micro;m, d\u003csub\u003e90\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;68 \u0026micro;m (HfZrTiTaV) and d\u003csub\u003e10\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;13 \u0026micro;m, d\u003csub\u003e50\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;33 \u0026micro;m, d\u003csub\u003e90\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;53 \u0026micro;m (HfZrTiMoV). X-ray structural analysis confirmed the formation of a uniform BCC phase, corresponding to a solid solution of transition metals, in both systems after 7.5h MA. Weak signals corresponding to pure Zr and Hf metals were detected in both samples, consistent with electron microscopy data.\u003c/p\u003e \u003c/div\u003e\n\u003ch3\u003eSpark plasma sintering of HECs\u003c/h3\u003e\n\u003cp\u003eCarbide synthesis was performed using spark plasma sintering. A mechanical mixture of HEA powder and carbon black was used as feedstock. The process was conducted with constant monitoring of parameters: temperature, time, punch displacement, shrinkage rate, current, voltage, power, and pressing force. For all studied systems, sintering is characterized by a unified three-stage mechanism (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ea).\u003c/p\u003e \u003cp\u003eThe first stage involves intensive chemical interaction between metals and carbon (Me\u0026thinsp;+\u0026thinsp;C \u0026rarr; MeC). This process is accompanied by pronounced volumetric shrinkage due to powder consolidation and multi-component carbide formation. Chemical interaction is confirmed by XRD results (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003eb), showing FCC phase formation in the sample after heating to 1750\u0026deg;C.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eDifferential scanning calorimetry additionally determined the reaction temperature to be 1367\u0026deg;C. The specific heat effect of the exothermic reaction was ΔH\u0026thinsp;=\u0026thinsp;\u0026minus;\u0026thinsp;67.4 J/g.\u003c/p\u003e \u003cp\u003eThe second sintering stage is associated with the carbothermal reduction of zirconia (ZrO₂) and hafnia (HfO\u003csub\u003e2\u003c/sub\u003e), confirmed by X-ray diffractogram analysis. Notably, after heating the sample to 2000\u0026deg;C with a subsequent 2-minute hold, a noticeable decrease in the intensity of diffraction peaks corresponding to these oxides is observed, indicating their partial or complete conversion to metallic phases. The presence of oxides in the alloy is likely due to brief oxygen exposure during powder transfer to the SPS unit.\u003c/p\u003e \u003cp\u003eThe obtained experimental data agree with results presented in the scientific literature [\u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e37\u003c/span\u003e]. According to existing sources, intensive carbothermal reduction of ZrO\u003csub\u003e2\u003c/sub\u003e and HfO\u003csub\u003e2\u003c/sub\u003e by carbon in vacuum occurs in the 1800\u0026ndash;2200\u0026deg;C range. The specific onset and completion temperatures depend on factors including residual pressure in the vacuum chamber, purity of initial components, and heating rate. The chemical basis of the process is described by the following carbothermal reduction equation:\u003c/p\u003e \u003cp\u003eMeO\u003csub\u003e2\u003c/sub\u003e\u0026thinsp;+\u0026thinsp;2C \u0026rarr; Me\u0026thinsp;+\u0026thinsp;2CO (gas) (1),\u003c/p\u003e \u003cp\u003ewhere Me is Zr (zirconium) or Hf (hafnium).\u003c/p\u003e \u003cp\u003eVacuum plays a special role in ensuring the completeness and efficiency of this reaction. Creating reduced pressure in the reaction zone promotes continuous removal of generated gaseous CO from the system. According to Le Chatelier's principle, such removal shifts the chemical equilibrium towards the reaction products, i.e., towards the formation of metallic zirconium or hafnium. In the absence of vacuum, the partial pressure of CO rapidly increases, leading to slowing and eventual cessation of the reduction process due to equilibrium attainment. Thus, vacuum conditions are a crucial factor enabling the thermodynamic and kinetic feasibility of effective carbothermal reduction.\u003c/p\u003e \u003cp\u003eThe final sintering stage involves intensive plastic deformation of powder particles under applied external pressure. As a result, particles actively shift relative to each other, filling interparticle voids and micropores. This process is accompanied by significant reduction of intergranular porosity due to the combined action of diffusion mass transfer mechanisms and mechanical compaction. Plastic flow of the material promotes leveling of contact zones between grains, improves their bonding, and forms a dense, nearly monolithic structure. Elimination of residual porosity not only increases material strength and hardness but also improves its thermal conductivity and thermo-oxidative resistance.\u003c/p\u003e \u003cp\u003eThe phase composition of all samples after sintering completion is characterized predominantly by a single-phase FCC carbide structure. Small peaks corresponding to graphite are also observed on diffractograms.\u003c/p\u003e \u003cp\u003eThe structure of the sintered samples is characterized by a homogeneous phase with dispersed carbon inclusions up to 1 \u0026micro;m in size. Besides the main carbide phase, a small amount of free graphite was detected on sample surfaces. Graphite formation on the surface is associated with sintering technology specifics: the process was conducted in a graphite die, which at high temperatures can interact with powder mixture components and also serve as a carbon source.\u003c/p\u003e \u003cp\u003eAs noted earlier, despite the diversity of existing synthesis methods for multi-component carbides, the key problem of controlling stoichiometric composition remains unsolved. Within the chosen fabrication route, uncontrolled variation in carbon content is also observed: on one hand, the material reacts with the graphite die, leading to sample carburization; on the other hand, the introduced carbon is consumed for the reduction of zirconium and hafnium oxides.\u003c/p\u003e\n\u003ch3\u003eCarbon influence on lattice parametr\u003c/h3\u003e\n\u003cp\u003eTo investigate the nature of carbon's influence, samples were synthesized from a mechanical mixture of HfZrTiTaNb powder with carbon black additions ranging from 30 to 65 at.% C. For HfZrTiTaV and HfZrTiMoV alloys, carbon black was added in amounts from 35 to 55 at.%. X-ray structural analysis was used to determine the lattice parameter on the surface and in the bulk of samples depending on the amount of carbon introduced; results are presented in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eLattice parameter values versus introduced carbon amount on the surface and in the bulk of samples.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"7\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAlloy\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c3\" namest=\"c2\"\u003e \u003cp\u003e(HfZrTiTaNb)С\u003csub\u003ex\u003c/sub\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c5\" namest=\"c4\"\u003e \u003cp\u003e(HfZrTiTaV)С\u003csub\u003ex\u003c/sub\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c7\" namest=\"c6\"\u003e 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colname=\"c5\"\u003e \u003cp\u003e4.457\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e4.407\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e4.417\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e55\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e4.51\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e4.514\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e4.452\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e4.457\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e4.408\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e4.417\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e60\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e4.514\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e4.513\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e65\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e4.514\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e4.514\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eIt was established that with increasing carbon content, the lattice parameter in the (HfZrTiTaNb)C\u003csub\u003ex\u003c/sub\u003e alloy on the sample surface increases to 4.514 \u0026Aring;, thereafter remaining constant. This indicates attainment of the limiting carbon content in the variable-composition carbide and the formation of a stoichiometric phase. The lattice parameter in the sample bulk increases monotonically, reaching a limiting value at an introduced carbon amount of 60 at.%.\u003c/p\u003e \u003cp\u003eTo verify the obtained data, the theoretical lattice parameter for (HfZrTiTaNb)C was calculated using the additivity rule, resulting \u0026ldquo;a\u0026rdquo; = 4.516 \u0026Aring;, demonstrating good agreement with experimental data.\u003c/p\u003e \u003cp\u003eTo determine the minimum lattice parameter value, the initial HfZrTiTaNb HEA was sintered without carbon addition. X-ray phase analysis results indicated the presence of a metallic BCC phase and a carbide FCC phase in the material. The minimum lattice parameter value was 4.462 \u0026Aring;. The content of unreduced zirconium and hafnium oxides was 4.6 wt.%.\u003c/p\u003e \u003cp\u003eSimilarly to the (HfZrTiTaNb)C\u003csub\u003ex\u003c/sub\u003e alloy, a monotonic increase in parameter \u0026ldquo;a\u0026rdquo; with increasing carbon content in the sample bulk is observed for (HfZrTiTaV)C\u003csub\u003ex\u003c/sub\u003e and (HfZrTiMoV)C\u003csub\u003ex\u003c/sub\u003e alloys. At an introduced carbon amount of 45 at.%, the lattice parameter of (HfZrTiTaV)C\u003csub\u003ex\u003c/sub\u003e reaches a limiting value of 4.457 \u0026Aring;. The maximum lattice parameter value is smaller compared to (HfZrTiTaV)C, explained by the shorter covalent bond length in binary VC compared to NbC. The calculated \u0026ldquo;a\u0026rdquo; parameter for (HfZrTiTaV)C was 4.454 \u0026Aring;. In the (HfZrTiMoV)C\u003csub\u003ex\u003c/sub\u003e system, the lattice parameter on the surface reaches a plateau already at 0.45 at.% C and stabilizes at 4.417 \u0026Aring;. The limiting lattice parameter value in this system is the smallest among all studied carbide systems. The calculated lattice parameter is \u0026ldquo;a\u0026rdquo; = 4.419 \u0026Aring;.\u003c/p\u003e \u003cp\u003eX-ray phase analysis of HfZrTiTaV and HfZrTiMoV alloy samples sintered without carbon addition showed the formation of a two-phase structure consisting of BCC and FCC phases. Based on the obtained data, minimum FCC phase lattice parameters were determined: 4.423 \u0026Aring; and 4.388 \u0026Aring; for HfZrTiTaV and HfZrTiMoV systems, respectively. Quantitative phase composition assessment revealed the presence of impurity oxides: zirconia content was 3.4%, and hafnia content was 2.3%.\u003c/p\u003e\n\u003ch3\u003eCarbon influence on HECs properties\u003c/h3\u003e\n\u003cp\u003eResults of mechanical tests on samples (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e) with varying carbon content demonstrate that the maximum hardness and material strength in all samples are achieved at an introduced carbon amount of 40 at.%.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eMaximum strength, hardness, and lack of plasticity are indicative of a metal-to-carbon stoichiometric ratio close to 1:1. At such a ratio, the carbide sublattice is fully ordered, vacancies are absent or minimal, and the structure possesses high cohesive energy.\u003c/p\u003e \u003cp\u003eWith carbon deficiency (less than 40 at.%), vacancies form in the anionic sublattice. These defects disrupt the covalent network continuity, weaken interatomic bonds, and reduce overall crystal binding energy, leading to decreased hardness and strength.\u003c/p\u003e \u003cp\u003eConversely, with carbon excess, the system cannot incorporate additional carbon into the carbide lattice due to structural constraints. Excess carbon precipitates as a secondary phase - free graphite - detrimentally affecting structural homogeneity and mechanical properties.\u003c/p\u003e \u003cp\u003eThe presented thermograms (Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e) show the distribution of thermal fields on the surface of (HfZrTiTaNb)C\u003csub\u003ex\u003c/sub\u003e system samples with different carbon content (35 to 65 at.% C) during gas-dynamic testing (GDT) conducted under high-temperature oxidative gas flow conditions.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eAnalysis of GDT results (Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e) showed that among the studied samples of (HfZrTiTaNb)C\u003csub\u003ex\u003c/sub\u003e, (HfZrTiTaV)C\u003csub\u003ex\u003c/sub\u003e, and (HfZrTiMoV)C\u003csub\u003ex\u003c/sub\u003e systems, compositions with carbon content of 45\u0026ndash;50 at.% possess the greatest resistance to ablation in a high-enthalpy gas flow.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eGas-dynamic test results.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"4\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eCarbon amount, at.%\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"3\" nameend=\"c4\" namest=\"c2\"\u003e \u003cp\u003eTemperature, \u0026deg;C\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003e(HfZrTiTaNb)C\u003csub\u003ex\u003c/sub\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003e(HfZrTiTaV)C\u003csub\u003ex\u003c/sub\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003e(HfZrTiMoV)C\u003csub\u003ex\u003c/sub\u003e\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e35\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e1735\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1999\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e2042\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e40\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e1837\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e2026\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e2066\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e45\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e1925\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e2053\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e2118\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e50\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e1953\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e2146\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e2098\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e55\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e1828\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e2081\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e2099\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e60\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e1731\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eUnder non-equilibrium, intensive thermal exposure characteristic of GDT, determining factors for material resistance become not only chemical oxidation stability but also the ability to effectively dissipate absorbed thermal energy. Thermal energy dissipation occurs via various mechanisms, the main ones being: thermal radiation from the surface, surface evaporation (sublimation), and thermal conductivity into the material bulk.\u003c/p\u003e \u003cp\u003eFree dispersed graphite likely darkens the surface and enhances radiative heat transfer, allowing the material to more effectively dissipate thermal energy into the environment as infrared radiation, and also increases material thermal conductivity. Furthermore, combustion of graphite particles may generate CO, which acts as a reducing agent. Thus, a slight carbon excess in high-entropy systems (HfZrTiTaNb)C\u003csub\u003ex\u003c/sub\u003e, (HfZrTiTaV)C\u003csub\u003ex\u003c/sub\u003e, and (HfZrTiMoV)C\u003csub\u003ex\u003c/sub\u003e provides an optimal compromise between chemical resistance, radiative, and thermal conductive properties.\u003c/p\u003e \u003cp\u003eMicrostructural investigation of the (HfZrTiTaNb)C sample surface after GDT established that under intensive heat flux with temperatures exceeding 2000\u0026deg;C, active oxidation begins on the material surface, accompanied not only by protective oxide film formation but also selective removal of individual elements.\u003c/p\u003e \u003cp\u003eElements Ti, Ta, Nb, whose oxides have lower melting points (below 3000\u0026deg;C) and higher volatility, are first subjected to erosion and evaporation. Oxides TiO\u003csub\u003e2\u003c/sub\u003e, Ta\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e5\u003c/sub\u003e, Nb\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e5\u003c/sub\u003e partially transition to molten or vapor states at high temperatures, leading to their gradual washing from the surface by the gas flow. Molten compounds react with more stable zirconium and hafnium oxides, forming complex structures like Zr\u003csub\u003e6\u003c/sub\u003eNb\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e17\u003c/sub\u003e in the near-surface layer.\u003c/p\u003e \u003cp\u003eThe lower, denser layer (approx. 10 \u0026micro;m thick) adjacent to the main carbide material is significantly enriched with zirconium and hafnium and protects the sample interior from further oxidation.\u003c/p\u003e \u003cdiv id=\"Sec8\" class=\"Section2\"\u003e \u003ch2\u003eCoating\u003c/h2\u003e \u003cp\u003eTo demonstrate the feasibility of forming a barrier coating based on multi-component carbide (HfZrTiTaNb)C\u003csub\u003ex\u003c/sub\u003e on a carbon-carbon composite (CCC) surface, three schemes were applied. The schemes and corresponding microstructures of the obtained coatings are presented in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003cstrong\u003eFirst Scheme\u003c/strong\u003e \u003cp\u003eA mechanical mixture of carbon black and HfZrTiTaNb powder was poured onto the CCC placed on the lower punch of the graphite die. After sintering, the obtained coating lacked adhesion to the substrate and easily detached even under minimal mechanical impact. Carbide formation occurred within the powder bed volume without affecting the interface with the substrate, preventing chemical bonding.\u003c/p\u003e \u003c/p\u003e \u003cp\u003e \u003cstrong\u003eSecond Scheme\u003c/strong\u003e \u003cp\u003eHfZrTiTaNb powder without carbon black was poured onto the composite material. In this case, the graphite die and the substrate material itself served as carbon sources. Implementing this scheme resulted in significant improvement in coating adhesion strength after sintering.\u003c/p\u003e \u003c/p\u003e \u003cp\u003eThe microstructure of the obtained coating and the interface are shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e. It is noted that the coating contains a significant fraction of residual metallic phase from the initial HfZrTiTaNb. XRD confirmed the presence of metallic BCC phase and hafnium/zirconium oxides.\u003c/p\u003e \u003cp\u003eAttempts to increase the sintering hold time to 15 minutes and perform additional heat treatment (1600\u0026deg;C, 6 hours) did not achieve substantial reduction of the metallic phase or obtain a single-phase carbide structure.\u003c/p\u003e \u003cp\u003e \u003cem\u003eThird scheme.\u003c/em\u003e To eliminate this drawback and obtain a single-phase coating, a three-layer powder pouring scheme was developed and tested. The composition consisted of a bottom layer of pure HEA in contact with the substrate, an intermediate layer of HEA mixed with 40 at.% carbon black, and again a top layer of pure HEA.\u003c/p\u003e \u003cp\u003eAnalysis of the obtained coating microstructure (Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e) confirmed the formation of a homogeneous carbide structure. Coating thickness was about 620 \u0026micro;m, with no signs of secondary phases, free graphite, or residual metallic alloy. The coating-substrate interface is characterized by continuous contact without gaps or delamination; large pores, cracks, and oxide inclusions are absent.\u003c/p\u003e \u003cp\u003eX-ray phase analysis confirmed the formation of a single-phase carbide coating with FCC structure. The lattice parameter of the synthesized coating was 4.492 \u0026Aring;, corresponding to 35 to 40 at.% introduced carbon (Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003ea).\u003c/p\u003e \u003cp\u003eMicrohardness test results (Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003eb) showed the carbide coating (HfZrTiTaNb)C\u003csub\u003ex\u003c/sub\u003e on CCC had a hardness of 2069 HV (20.3 GPa). This value corresponds to the microhardness of material with 35\u0026ndash;40 at.% introduced carbon, consistent with results from lattice parameter X-ray analysis.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eDuring GDT of a CCC sample with applied carbide coating (HfZrTiTaNb)C\u003csub\u003ex\u003c/sub\u003e, the average surface temperature until failure was 2003\u0026deg;C. Failure occurred 39 seconds after the start of high-enthalpy gas flow exposure and manifested as coating delamination from the substrate along the interface.\u003c/p\u003e \u003cp\u003eAnalysis of the failure mechanism indicates that the primary cause of degradation is the incompatibility of coefficients of thermal expansion (CTE) between the layers. The CTE of the CCC substrate is significantly lower (0.5-2 \u0026times;10\u003csup\u003e\u0026minus;\u0026thinsp;6\u003c/sup\u003e K\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e) than that of the binary compounds constituting the multi-component carbide (6.7\u0026ndash;7.8 \u0026times;10\u003csup\u003e\u0026minus;\u0026thinsp;6\u003c/sup\u003e K\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e).\u003c/p\u003e \u003cp\u003eUnder intensive heating, temperature gradients reach several hundred degrees per millimeter, and significant thermomechanical stresses arise in the bonding zone, exceeding the interfacial bonding strength, leading to coating spallation.\u003c/p\u003e \u003cp\u003eIt is important to note that the carbide layer surface itself and the CCC substrate showed no signs of intensive ablation, such as component evaporation, porous oxide layer formation, or erosive destruction. This attests to the high thermochemical stability and ablation resistance of the coating material itself under extreme gas-dynamic exposure.\u003c/p\u003e \u003cp\u003eThe enhanced stability compared to bulk samples of similar composition is likely due to the high thermal conductivity of the substrate, which promotes effective heat removal from the surface and reduces local overheating, slowing oxidation and destruction processes.\u003c/p\u003e \u003cp\u003eNevertheless, despite the high properties of the carbide itself, the adhesion problem remains a key limiting factor for the practical application of carbide coatings. To solve it, the introduction of an intermediate (bonding) layer with a gradient or compensating composition, capable of smoothing the CTE mismatch between substrate and functional coating, appears promising. Candidates may include: composite layers with silicon carbide addition, thin-film systems with gradual composition change from C to (HfZrTiTaNb)C\u003csub\u003ex\u003c/sub\u003e.\u003c/p\u003e \u003c/div\u003e"},{"header":"Conclusions","content":"\u003cp\u003eSingle-phase high-entropy carbides (HfZrTiTaNb)C\u003csub\u003ex\u003c/sub\u003e, (HfZrTiTaV)C\u003csub\u003ex\u003c/sub\u003e, and (HfZrTiMoV)C\u003csub\u003ex\u003c/sub\u003e with variable carbon content (30 to 65 at.%) were successfully synthesized via mechanical alloying followed by spark plasma sintering. The sintering process is characterized by a three-stage mechanism involving carbide formation, carbothermal reduction of oxides, and plastic compaction.\u003c/p\u003e \u003cp\u003eThe dependence of the FCC lattice parameter on carbon content was established. For all systems, a monotonic increase in parameter \u0026ldquo;a\u0026rdquo; is observed until reaching a limiting value (4.514 \u0026Aring; for (HfZrTiTaNb)C, 4.457 \u0026Aring; for (HfZrTiTaV)C, 4.417 \u0026Aring; for (HfZrTiMoV)C), after which it stabilizes, indicating the formation of a limiting stoichiometric phase. Experimental values show good agreement with calculations based on the additivity rule.\u003c/p\u003e \u003cp\u003eIt was determined that maxima in microhardness (28\u0026ndash;32 GPa) and compressive strength (2500\u0026ndash;2800 MPa) are achieved at a carbon content of 40 at.%. This optimum corresponds to the most complete filling of the anionic sublattice, vacancy minimization, and cohesive energy maximization. Deviation from this stoichiometry in either direction leads to degradation of mechanical properties.\u003c/p\u003e \u003cp\u003eGas-dynamic testing in a high-enthalpy oxidative flow showed that maximum ablation resistance (surface temperature 1950\u0026ndash;2150\u0026deg;C) is exhibited by compositions with 45\u0026ndash;50 at.% C. The enhanced resistance with a slight carbon excess is explained by a synergistic effect: the chemical stability of the carbide matrix combines with improved radiative heat dissipation and thermal conductivity due to the presence of dispersed free carbon.\u003c/p\u003e \u003cp\u003eA three-layer deposition scheme was developed, enabling the fabrication of a single-phase carbide coating (HfZrTiTaNb)C\u003csub\u003ex\u003c/sub\u003e (40 at.% C) with a thickness of 620 \u0026micro;m on a carbon-carbon composite substrate. The coating possesses high microhardness (20.3 GPa) and structural homogeneity.\u003c/p\u003e \u003cp\u003eThe key limitation for coating application is its delamination under gas-dynamic exposure after 39 seconds due to critical thermomechanical stresses at the interface. These stresses are caused by a significant mismatch in the coefficients of thermal expansion between the coating and the carbon-carbon substrate. Notably, the carbide phase itself and the substrate material showed no signs of intensive ablation, confirming the high thermochemical stability of the coating.\u003c/p\u003e \u003cp\u003eFor the practical implementation of high-entropy carbide coatings, the development and integration of an intermediate gradient or compensating layer capable of reducing thermal stresses at the interface with the substrate is necessary (e.g., based on composites with SiC or systems with gradually varying composition).\u003c/p\u003e"},{"header":"Declarations","content":"\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003eA.K.: Conceptualization, Methodology, Investigation, Formal analysis, Data curation, Writing \u0026ndash; original draft, Visualization. Conducted the main experimental research, including material synthesis, mechanical alloying, spark plasma sintering, X-ray structural and microstructural analysis, mechanical and gas-dynamic testing. Performed processing and interpretation of experimental data, prepared the draft manuscript, figures, and illustrations.E.V.: Investigation, Validation, Writing \u0026ndash; original draft, Writing \u0026ndash; review \u0026amp; editing, Visualization. Actively participated in experimental work, including sample preparation, measurements, and data collection. Performed independent validation of key results. Made a major contribution to the preparation and formatting of the manuscript: participated in writing and structuring the initial text, significantly revised and edited the draft, prepared and organized graphical materials (figures, tables). Conducted literature review and reference formatting.N.R.: Resources, Validation, Writing \u0026ndash; review \u0026amp; editing. Provided material, technical, and resource support for the research. Participated in discussion and critical evaluation of the results, reviewing, and revising the manuscript text.A.P.: Supervision, Funding acquisition, Writing \u0026ndash; review \u0026amp; editing. Provided overall scientific supervision of the project, formulated general research objectives. Responsible for securing and administering funding. Participated in the final review and approval of the manuscript.All authors have read and approved the final version of the manuscript for submission.\u003c/p\u003e\u003ch2\u003eAcknowledgement\u003c/h2\u003e\u003cp\u003eThe study was supported by the Ministry of Science and Higher Education of the Russian Federation (State Assignment No. 075-03-2025-256).\u003c/p\u003e\u003ch2\u003eData Availability\u003c/h2\u003e\u003cp\u003eThe datasets used and/or analysed during the current study are available from the corresponding author upon reasonable request.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eLewin, E. Multi-component and high-entropy nitride coatings\u0026mdash;A promising field in need of a novel approach. \u003cem\u003eJ. Appl. Phys.\u003c/em\u003e \u003cb\u003e127\u003c/b\u003e, 160901 (2020).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eKirnbauer, A. et al. 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Low-temperature synthesis of nanodispersed titanium, zirconium, and hafnium carbides. \u003cem\u003eRuss J. Inorg. Chem.\u003c/em\u003e \u003cb\u003e56\u003c/b\u003e, 661\u0026ndash;672 (2011).\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"scientific-reports","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"scirep","sideBox":"Learn more about [Scientific Reports](http://www.nature.com/srep/)","snPcode":"","submissionUrl":"","title":"Scientific Reports","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Scientific Reports","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"","lastPublishedDoi":"10.21203/rs.3.rs-8394818/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8394818/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThis study investigates the influence of carbon stoichiometry on the structure and properties of high-entropy carbides (HECs) (HfZrTiTaNb)C\u003csub\u003ex\u003c/sub\u003e, (HfZrTiTaV)C\u003csub\u003ex\u003c/sub\u003e, and (HfZrTiMoV)C\u003csub\u003ex\u003c/sub\u003e. Bulk samples with carbon content ranging from 30 to 65 at.% were synthesized via mechanical alloying and spark plasma sintering (SPS). X-ray diffraction analysis revealed a monotonic increase in the FCC lattice parameter with increasing carbon content until a plateau was reached, corresponding to the formation of a limiting stoichiometric phase. Experimentally, carbon concentrations of 40 at.% were found to provide maximum microhardness (28\u0026ndash;32 GPa) and compressive strength (2500\u0026ndash;2800 MPa), attributed to the minimization of vacancies in the carbon sublattice. Gas-dynamic testing in a high-enthalpy oxidative flow showed that optimal ablation resistance is achieved at 45\u0026ndash;50 at.% C. This is associated with a compromise between the chemical stability of the carbide phase and enhanced radiative properties due to dispersed free carbon. Based on the optimized (HfZrTiTaNb)C\u003csub\u003ex\u003c/sub\u003e composition with 40 at.% C, a technology for depositing a single-phase carbide barrier coating (620 \u0026micro;m) on a carbon-carbon composite was developed. The coating demonstrated high microhardness (20.3 GPa) and thermochemical stability; however, its service life is limited by detachment due to the mismatch of coefficients of thermal expansion (CTE) with the substrate. The obtained results establish a quantitative relationship between carbon stoichiometry, lattice parameter, mechanical, and thermal properties of high-entropy carbides, which is critically important for their application as ultra-high-temperature ceramics and protective coatings.\u003c/p\u003e","manuscriptTitle":"Carbon Stoichiometry Effects on the Structure, Mechanical Properties, and Ablation Resistance of (HfZrTiTaNb)Cx , (HfZrTiTaV)Cx , and (HfZrTiMoV)Cx High-Entropy Carbides","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-02-18 14:02:31","doi":"10.21203/rs.3.rs-8394818/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2026-03-03T11:03:44+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2026-02-22T04:43:13+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"136430270763357000744345475666682058048","date":"2026-02-20T17:31:08+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2026-02-19T09:45:04+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2026-02-16T11:48:29+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2026-02-15T19:10:30+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"251216436732343017351744552240418610321","date":"2026-02-14T04:00:02+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"157460482724447685264116900375271684352","date":"2026-02-14T03:44:50+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"234664563591897045401044801181139815927","date":"2026-02-13T16:15:42+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"337287601872568015806282982561620321716","date":"2026-02-13T11:17:54+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2026-02-13T09:43:09+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2026-02-13T09:38:23+00:00","index":"","fulltext":""},{"type":"editorInvited","content":"","date":"2026-02-13T09:31:33+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2026-01-29T13:56:18+00:00","index":"","fulltext":""},{"type":"submitted","content":"Scientific Reports","date":"2026-01-27T07:40:08+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"scientific-reports","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"scirep","sideBox":"Learn more about [Scientific Reports](http://www.nature.com/srep/)","snPcode":"","submissionUrl":"","title":"Scientific Reports","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Scientific Reports","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"1f4a9680-d38f-44ec-9b15-6e8f916bed35","owner":[],"postedDate":"February 18th, 2026","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[{"id":63140654,"name":"Physical sciences/Engineering"},{"id":63140655,"name":"Physical sciences/Materials science"}],"tags":[],"updatedAt":"2026-04-18T16:23:22+00:00","versionOfRecord":[],"versionCreatedAt":"2026-02-18 14:02:31","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-8394818","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-8394818","identity":"rs-8394818","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}