Extremely hard and tough high entropy nitride ceramics

Simultaneously hard and tough nitride ceramics open new venues for a variety of advanced applications. To produce such materials, attention is focused on the development of high-entropy ceramics, containing four or more metallic components distributed homogeneously in the metallic sublattice. While the fabrication of bulk high-entropy carbides and borides is well established, high-entropy nitrides have only been produced as thin films. Herein, we report on a newel three-step process to fabricate bulk high-entropy nitrides. The high-entropy nitride phase was obtained by exothermic combustion of mechanically-activated nanostructured metallic precursors in nitrogen and consolidated by spark plasma sintering. The fabricated bulk high-entropy nitride (Hf0.2Nb0.2Ta0.2Ti0.2Zr0.2)N demonstrates outstanding hardness (up to 33 GPa) and fracture toughness (up to 5.2 MPa∙m1/2), significantly surpassing expected values from mixture rules, as well as all other reported binary and high-entropy ceramics and can be used for super-hard coatings, structural materials, optics, and others. The obtained results illustrate the scalable method to produce bulk high-entropy nitrides with the new benchmark properties.

High-entropy (HE) ceramics are solid solutions based on interstitial phases (carbides, borides, silicides, etc.) and contain 4 or more metallic species, which endow them with unique physical and mechanical properties as a result of entropy stabilization [1][2][3] . HE ceramics have attracted increasing interest, as they surpass binary ceramics (such as TiC, TiN, SiC, Si 3 N 4 , ZrO 2 , Al 2 O 3 ) in terms of hardness, fracture toughness, corrosion resistance, and high-temperature stability [4][5][6] . Among conventional ceramics, transition-metal nitrides (TMN) have historically been used as cutting tools and wear-resistant coatings because of their high hardness and strength, high melting points, excellent thermal conductivity, coupled with thermal and chemical stability [7][8][9][10] . The hardness and toughness of TMN and related solid solutions with FCC structure are interrelated functions of electron valence. As the valence electron concentration (VEC) is minimized, the hardness is maximized (usually at VEC = 8.4); oppositely, when the valence is maximized, the toughness is minimized (at VEC ≥ 10) 7,11,12 as the result of antibonding state occupation-induced lattice softening 13,14 . For example, in δ-TiN 1−x , the microhardness maximum occurs at δ-TiN 0.67 , which corresponds to 7.3 valence electrons 14 . An increased valence electron concentration resulting from higher nitrogen content leads to a decrease in hardness. This is the reason why zirconium and titanium carbonitrides have lower hardness when carbon atoms are replaced with nitrogen 15 . However, for δ-HfN 1−x , a smooth increase in microhardness with nitrogen content is observed, due to the difference in 5f electron bonding states 15 . Thus, hardness and fracture toughness are inversely related in nitride ceramics, and bypassing this effect would lead to extraordinary properties and more widespread use.
Ternary nitride (TN) systems are predicted to be supertough-harder and more ductile than binary systemsdue to the increased valence electron concentration 12,16,17 . Various research groups have studied the effect of valence electron concentration on mechanical properties for the design of advanced TMNs 17 . According to Balasubramanian et al. 12 the optimized hardness and toughness in TMNs are expected at VEC of 9.0-9.5. A brittleto-ductile transition is expected at a critical VEC = 10 and a transition to mechanical instability at VEC = 10.6. However, the calculated phonon dispersion curves indicate a dynamical stability-to-instability transition between VEC = 9 and 10, which is smaller than the critical VEC = 10.6 for the mechanical stability-instability transition. Overall, a narrow region between VEC = 9 and 10 is outlined for the search of phases with the highest toughness. Considering this, Ti 0.5 Ta 0.5 N (VEC = 9.5) possesses one of the highest among TNs theoretical and experimentally To date, HENs are predominantly produced as thin films [19][20][21][22][23][24][25] , due to their enhanced solubility and phase stability 26 compared to bulk ceramics. Jin et al. 27 reported the synthesis of powdered metal HEN V 0.2 Cr 0.2 Nb 0.2 Mo 0.2 Zr 0.2 N 1−x by planetary ball milling a mixture of five transition-metal chlorides with urea and subsequent annealing of the reactive mixture under N 2 flow. The resulting powders were tested as supercapacitors, but neither the sintering nor mechanical testing was reported. Therefore, the goal of our work was the development of fabrication technology and studying the structure, and mechanical properties of a bulk HEN ceramic (Hf 0.2 Nb 0.2 Ta 0.2 Ti 0.2 Zr 0.2 )N.
The fabricated composition was based on the ternary Ti 0.5 Ta 0.5 N ceramic with the highest reported hardness 17,18,28,29 . Three additional metallic constituents were added to produce the entropy stabilization effect 3 . The additional metals were chosen to retain VEC close to 9.5. The article shows the results of the successful application of the complex technology of CS-SPS consolidation of mechanically activated powders for bulk HEN ceramics production and can be used for mass production of high-quality bulk HE ceramics of different types.

Results and discussion
The convex hulls for the Hf-Nb-Ta-Ti-Zr-N system were constructed at various chemical nitrogen potentials (μ N ) to estimate the range where all constituent metals could form mono-nitrides (Supplementary Table S-I in Supplementary Information). The decrease of μ N corresponds to an increase in temperature or decrease of nitrogen partial pressure in the system. The stability range of mono-nitrides decreases in the following order: TiN (space group Fm 3 m) was found to be stable in the investigated system (stability range − 9.333 < μ N < − 11.492). Although its energy of formation from HfN and ZrN is relatively low (− 5 kJ/mol at 0 °C), the relatively broad stability range increases the probability of formation of Hf 0.5 Zr 0.5 N as an intermediate phase during the employed threestep processing. This finding is consistent with the predictions of Sun et.al. 30 , who indicated HfZrN as the only stable TN in the TM1-TM2-N systems (TM = Ta, Hf, Ti, Zr, Nb, V).
Most of the binary nitrides in TM1-TM2-N systems (TM = Ti, Zr, Hf, Ta, Nb, V) are predicted to be thermodynamically unstable yet meta-stabilizable 30 . In a narrow μ N interval of − 9.333 < μ N < − 9.033, the Hf 0.5 Zr 0.5 N phase undergoes decomposition while all 5 mono-nitrides retain stability (Supplementary Table S-I). The co-existence of mono-nitride phases might be instrumental for the formation of a HEN solid solution.
The first preparation stage allowed us to make composite particles involving all five metals mixed on submicron sized layers of metallic constituents (Fig. 1a,g). Due to the cold-welding phenomenon during milling, thin layers of metals with a thickness of 10-100 nm formed in the bulk of each particle, providing high homogeneity for their mixing. The EDS analysis indicated that the ratio between the metals remained to be equimolar. Also, milling at relatively low speed (200 rpm) and under high pressure of pure argon allowed to produce powders with low concentrations of impurities. The XRD patterns (Fig. 1d) of thus prepared powders showed that all metals retained their crystallinity even after 10 h of mechanical treatment.
The goal of the second preparation stage is to introduce nitrogen into the system in the form of metal nitrides, as well as nitrogen solid solutions. This task was accomplished by using energy-saving combustion synthesis method 31 . Supplementary Table S-II demonstrates that the reactions between considered metals and nitrogen are highly exothermic with adiabatic combustion temperature well above 3000 K. The reaction between the metal composite particles and nitrogen was initiated locally by hot tungsten wire, followed by the rapid combustion front propagation along with the media. The total nitridation process duration was ~ 5 s. It can be seen that the combustion of such reactive metal particles in a nitrogen atmosphere leads to the formation of multiple nitride phases (Fig. 1b,e), among which there was detected the predicted Hf 0.5 Zr 0.5 N 1-x TN phase. The microstructure of the inner part of the composite particles became coarser (Fig. 1b) with the grain size in the range 0.5-1 μm. A mixed hafnium-zirconium-based oxide phase was also present in the combustion products (Fig. 1h), which presumably originated due to the oxygen impurities in the initial powders and exposure of mechanically activated mixture to air during the pressing of green pellets for combustion synthesis.
In the third stage, the SPS of the synthesized complex metal nitride particles were used to produce bulk ceramics. After the SPS at the experimentally optimized conditions, the measured relative density of the ceramics was 96.6% of the theoretical maximum. The obtained HEN phase is characterized by narrow grain size distribution (10-16 μm) and crystals of polyhedric, mostly hexagonal, shape (Fig. 1c). Moreover, the Hf 0.5 Zr 0.5 N 1−x TN phase was not found in the sintered specimens (Fig. 1f,i), indicating its successful conversion into the HEN. The lattice constant a = 0.4443 was calculated based on the XRD pattern of the HEN (Fig. 1f). According to the results of XRD and EDS analysis ~ 4.2 mol% of the (Hf,Zr)O x phase, formed during the combustion synthesis, retained in the sintered ceramics (Fig. 1f,i). The amount of oxides is relatively small and, we suppose, could be removed by applying additional technological steps or by adjusting the technological process.
Detailed TEM investigations (Fig. 2) were performed to confirm the presence of a HEN in the sintered specimens and to define the composition of the HEN phase. HRTEM (Fig. 2a) and selected area diffraction pattern (SAED) (Fig. 2b) (Fig. 1f and Supplementary Fig. S1). The hardness and Vickers fracture toughness of this high entropy nitride were measured at 4.9-98 N loads and compared to mono-nitrides and nitride solid solutions reported in the literature (Supplementary Table S-IV). The measured hardness HV 0.5 and elastic modulus of HEN are 32.8 ± 1.6 GPa and 352 ± 17 GPa, respectively. The elastic modulus value is comparable with the value of 360 GPa, obtained in coatings 32 . An increase in the indentation load leads to a gradual decrease of the hardness to HV 10 = 22.5 ± 1.4 GPa (Fig. 3). However, the experimentally measured values of hardness and fracture toughness of the HEN ceramic surpasses the values calculated based on the rule of the mixture on 130% and 82%, respectively (HV 1 = 31.2 ± 3.6 GPa and K 1C = 5.2 ± 0.18 MPa are the experimental data, and m 1/2 ROM HV 1 = 13.6 GPa, K 1C = 2.85 MPa•m 1/2 are the calculated). It should be noticed, the measured results for our HEN are significantly higher the previously reported values for carbide, nitride, and silicide ceramics, including the HE compositions (Fig. 3). Moreover, the hardness values of   Fig. 3 can be found in Supplementary Information (Supplementary Table S-IV). Earlier, Sarker et al. 3 described an explicit strengthening effect in HE carbides. The hardness of sintered Hf 0.2 Nb 0.2 Ta 0.2 Ti 0.2 Zr 0.2 C ceramic of 32 GPa is 40% above the value calculated by the rule of mixture (23 GPa). A similar entropy-induced strengthening effect might be responsible for the increased hardness of the HEN, obtained in this work. Previously, enhancement of the mechanical performance of TMN was achieved by engineering alternating layers of TMNs and more ductile body-centered cubic metals 33 . Similarly, nanocomposite structures developed by Voevodin and Zabinski 34 demonstrates high hardness at stresses below the elastic strength limit, while at extreme loading their mechanical behavior switches to ductile, thus preventing brittle failure. A related effect might be responsible for the increase of the fracture hardness of the HENs due to possible nanoscale precipitates of ductile elements (i.e. Ta) on the boundaries of HEN grains during the sintering.
Moreover, as the valence electron concentration of the HENs is close to the optimal value of 9.5, derived by Guo 35 and Sangiovanni 17 , the "lattice softening" effect could also contribute to the increased fracture toughness of the HEN phase. The effect of a simultaneous considerable increase of hardness and fracture toughness in HEN warrants closer investigation and theoretical modeling. However, these results indicate that HENs have the potential to become the new benchmark ceramic for structural and machining applications since the mechanical performance of the (HfNbTaTiZr)N ceramic developed in this work is considerably superior to conventional SiC, TiC, TiN, and TiB 2 .

Conclusions
1. Grand potential phase diagram modeling revealed that mono-nitrides of Hf, Zr, Ta, Nb, and Ti are stable at relatively narrow nitrogen potential range − 9.033 < μ N < − 9.98 and that trigonal Hf 0.5 Zr 0.5 N is the only stable at − 9.333 < μ N < − 11.492 TN in the system. A nitrogen potential range was indicated (− 9.033 < μ N < − 9.333) where this trigonal phase will decompose into FCC ZrN and HfN to facilitate the formation of FCC HEN solid solution. 2. Based on the proposed model, a three-stage synthesis protocol was developed to produce bulk HEN ceramics, including mechanical treatment of the metallic constituents in an argon atmosphere, combustion of mechanically-induced nanostructured particles in nitrogen, and spark plasma sintering of the combustion products.

Methods
Calculation of grand potential phase equilibria. To analyze the phase equilibria in this system, the formation enthalpies for nitride phases were calculated using mixed GGA and GGA + U (semiempirically-tuned generalized gradient approximations) frameworks, which is known for its ability to correctly predict the phase stability 36 . Grand potential phase diagrams at varied nitrogen potentials were calculated using PDApp software, which is integrated into Materials API 37,38 and employs a database of DFT computed bulk material energies with crystal structures obtained from the Inorganic Crystal Structure Database (ICSD) 39 and those generated by applying data-mined chemical substitutions 40,41 .
Fabrication of high-entropy ceramics. Figure 4 provides the schematic for the three-stage process employed for the synthesis of bulk high-entropy nitride ceramics. The overall processing method includes three stages: (i) preparation of the reactive nanocomposite powders by high energy ball milling (HEBM); (ii) combustion synthesis (CS) of TNs; and (iii) spark plasma sintering (SPS) of the bulk HEN ceramics.
Preparation of reactive composite powders. The metallic powders of Hf, Nb, Ta, Ti and Zr (RusRed-Met, Russia, > 99% purity) with a particle size distribution of 40-60 µm were used for preparation of a precursor mixtures. HEBM of reactive mixtures was conducted in an argon atmosphere (4 atm, 99.998%) using a doublestation planetary ball mill (Activator-2s, Russia) equipped with steel mill and steel grinding medium (balls). Batches consisted of 20 g powders and were mixed in an equimolar ratio Hf:Nb:Ta:Ti:Zr = 1:1:1:1:1 using 250 ml steel jars and 6 mm steel balls. The ball to powder mixture weight ratio was 20:1, The milling speed was 200 rpm at a rotational coefficient of K = 1. The total duration of the mechanical treatment was 10 h. The goal is to produce nanostructured composite particles, which involve all five components. www.nature.com/scientificreports/ up to 8 atm. Powder mixtures were locally preheated using a hot tungsten wire to initiate a chemical reaction with the subsequent propagation of a self-sustaining combustion front. At this stage, the metal nitrides were synthesized. The combustion products were then ball-milled for 2 h at 60 rpm using WiseMixSBML mill (DAIHAN Scientific, South Korea) equipped with 250 ml steel jars and 6 mm steel balls. The ball to powder mixture weight ratio was 6:1. Material characterization. X-ray diffraction (XRD) was applied for the study of phase composition of the fabricated materials using DRON-4-07 (Russia) monochromatic Co-Kα radiation. The structure of the experimental materials was analyzed via scanning electron microscopy (SEM) on a Vega 3 (TESCAN, Czech Republic) and JSM-7600F (JEOL, Japan) with a microanalysis system (EDX, Oxford Instruments) and a high-resolution transmission electron microscopy (TEM) on TITAN 800-300 (Thermo Fisher Scientific, USA) equipped with an Ultim Max EDS system (Oxford Instruments). Vickers hardness tests were used for the study of the microhardness of the synthesized materials [Emco-Test DuraScan 70 (Austria)]. The applied loads varied from 0.5 to 10 N. The fracture toughness was measured using the Vickers indentation-induced cracks corresponding to the Anstis method 42 . The elastic modulus was measured by Anton Paar CSM Micro Indentation Tester (Austria) under applied loads of 100 mN.