High-pressure synthesis of ultraincompressible hard rhenium nitride pernitride Re2(N2)(N)2 stable at ambient conditions

High-pressure synthesis in diamond anvil cells can yield unique compounds with advanced properties, but often they are either unrecoverable at ambient conditions or produced in quantity insufficient for properties characterization. Here we report the synthesis of metallic, ultraincompressible (K0 = 428(10) GPa), and very hard (nanoindentation hardness 36.7(8) GPa) rhenium nitride pernitride Re2(N2)(N)2. Unlike known transition metals pernitrides Re2(N2)(N)2 contains both pernitride N24− and discrete N3− anions, which explains its exceptional properties. Re2(N2)(N)2 can be obtained via a reaction between rhenium and nitrogen in a diamond anvil cell at pressures from 40 to 90 GPa and is recoverable at ambient conditions. We develop a route to scale up its synthesis through a reaction between rhenium and ammonium azide, NH4N3, in a large-volume press at 33 GPa. Although metallic bonding is typically seen incompatible with intrinsic hardness, Re2(N2)(N)2 turned to be at a threshold for superhard materials.

A ccording to the approach formulated by Yeung et al. 1 , the design of novel superhard materials should be based on the combination of a metal with high valence electron density with the first-row main-group elements, which form short covalent bonds to prevent dislocations. This conclusion was based on the synthesis of hard borides, such as OsB 2 2 , ReB 2 3-5 , FeB 4 6 , or WB 4 7 , whose crystal structures possess covalently bonded boron networks. Similar to boron, nitrogen as well can form covalent nitrogen-nitrogen bonds, but there are several factors, which make it difficult to synthesize nitrogen-rich nitrides. The large bond enthalpy of the triply bound N 2 molecule (941 kJ·mol −1 ) 8 makes this element generally unreactive. In many reactions the activation barrier for N 2 bond breaking requires temperatures, which are higher than the decomposition temperatures of the target phases. MN x compounds with x > 1 are rarely available via direct nitridation reactions or ammonothermal syntheses 9,10 . Therefore, binary M-N systems are often limited to interstitial metal-rich nitrides. Usually, they are less compressible and have higher bulk moduli in comparison with pure metals due to the increasing repulsion between metal and nitrogen atoms, whereas their shear moduli are not always much different from those of metals.
Application of pressure is one way to increase the chemical potential of nitrogen and to stabilize nitrogen-rich phases 11 . Several transition metal dinitrides, PtN 2 12 , PdN 2 13 , IrN 2 14 , OsN 2 14 , TiN 2 15 , RhN 2 16 , RuN 2 17 , CoN 2 18 , and FeN 2 19 , containing covalently bound dinitrogen units were recently synthesized in laser-heated diamond anvil cells (LHDACs) via reactions between elemental metal and nitrogen in a pressure range of 40-80 GPa. Although LHDAC is an efficient method to study high-pressure chemical reactions, it is challenging to scale up the synthesis. The search for suitable synthetic strategies, which would enable an appropriate reaction to be realized in a large volume press (LVP) instead of a LHDAC, is an important challenge for high-pressure chemistry and materials sciences. In this study, focusing on the high-pressure synthesis of nitrogen-rich phases in the Re-N system and the development of new synthetic strategies, we resolved this problem for a rhenium nitride ReN 2 with unusual crystal chemistry and unique properties.
Direct reactions between rhenium and nitrogen were studied by Friedrich et al. 20 , who synthesized two interstitial rhenium nitrides Re 3 N at 13 GPa and 1700 K, and Re 2 N at 20 GPa and 2000 K. Both compounds have exceptionally large bulk moduli exceeding 400 GPa (as measured upon compression in a nonhydrostatic medium 21 ), but only moderate shear moduli as expected for interstitial compounds 22 . Kawamura et al. 23 reported synthesis of ReN 2 with MoS 2 structure type (m-ReN 2 ) in a metathesis reaction between Li 3 N and ReCl 5 at 7.7 GPa. Subsequently, Wang et al. 21 suggested, based on the first-principle calculations, that m-ReN 2 is unstable and 'real stoichiometric' ReN 2 should have monoclinic C2/m symmetry and transform to the tetragonal P4/mbm phase above 130 GPa. However, this suggestion has not been proven experimentally as yet. Recently Bykov et al. reported a novel inclusion polynitrogen compound ReN 8 ·xN 2 synthesized from elements at 106 GPa 24 , but the region of~35-100 GPa still remains completely unexplored for the Re-N system.
Here, we report the high-pressure synthesis of an ultraincompressible metallic hard compound ReN 2 via reactions between rhenium and nitrogen or ammonium azide at pressures of 33-86 GPa. The usage of a solid nitrogen precursor NH 4 N 3 allows to scale up the synthesis of ReN 2 in the large volume press.

Results
Synthesis of Re 2 (N 2 )(N) 2 in a laser-heated diamond anvil cell. We have studied chemical reactions between Re and nitrogen and other reagents, such as sodium azide NaN 3 and ammonium azide NH 4 N 3 , in LHDACs in a range of 29-86 GPa at temperatures of 2000-2500 K ( Table 1, Experiments #1 through #6). The reactions products typically contained numerous single-crystalline grains of several rhenium nitride phases (Table 1), which were identified using synchrotron single-crystal X-ray diffraction (Supplementary Note 1, Supplementary Fig. 1, Supplementary Tables 1-3).
A direct reaction between Re and N 2 ( Table 1) resulted in the synthesis of three rhenium nitrides ReN 2 , Re 2 N, and ReN 0.6 , two of which (ReN 2 and ReN 0.6 ) have never been observed before. The third phase identified in these experiments, Re 2 N (P6 3 /mmc), has previously been reported 20 . After a stepwise decompression of the sample obtained in Experiment #1 down to the ambient pressure, all of the three phases (ReN 2 , ReN 0.6 , Re 2 N) were found to remain intact even after being exposed to atmospheric oxygen and moisture for several months. Crystal structure analysis of ReN 0.6 showed that it has a defect WC structure type (space group P 6m2) (for details on ReN 0.6 see Supplementary Note 2, Supplementary Figs. 2 and 3, Supplementary Table 4).
Analysis of the crystal structure of ReN 2 revealed its unusual crystal-chemistry. Figure 1 shows the crystal structure of ReN 2 , which is built of distorted ReN 7 capped trigonal prisms (Fig. 1d) and contains both N-N units (dumbbells) (Fig. 1f) and discrete N atoms (N2) (Fig. 1e) in an atomic ratio 1:1. The N1-N1 dumbbells are located in a trigonal antiprism formed by Re atoms (Fig. 1f), while discrete N2 atoms have a tetrahedral coordination by Re (Fig. 1e). The N1-N1 bond length (d N1-N1 = 1.412(16) Å at ambient conditions) suggests that the N 2 unit should be considered as a pernitride anion N 2 4− . Therefore, ReN 2 is a rhenium nitride pernitride and its crystal-chemical formula is In the following discussion we interchangeably use both empirical formula ReN 2 and crystalchemical formula for this compound.
Compressibility of Re 2 (N 2 )(N) 2 . The compressibility of ReN 2 was measured on the sample #2 (Table 1), which was synthesized at 49 GPa, then decompressed down to ambient conditions, and re-loaded into another DAC with a neon pressure-transmitting medium, which provides much better hydrostaticity of the sample environment than nitrogen 25 . The sample was first characterized using single-crystal XRD at ambient conditions. On compression,  Table 5). The pressure-volume dependence was described using the third-order Birch-Murnaghan equation of state 26 with the following fit parameters: V 0 = 107.21(4) Å 3 , K 0 = 428(10) GPa, K' = 1.6(5). Figure 2c shows a plot of correlated values of K 0 and K' to different confidence levels. The bulk modulus K 0 lies within the range of 410-447 GPa at the 99.73% confidence level. Thus, K 0 of ReN 2 is larger than that of any compound in the Re-N system and is comparable to that of diamond (K 0 = 440 GPa) and IrN 2 (K 0 = 428(12) GPa) 14 . Among very incompressible pernitrides of transition metals, ReN 2 is the only compound, in which the metal atom has oxidation state (+V) higher than (+IV). The enhancement of the bulk modulus of ReN 2 in comparison to OsN 2 , PtN 2 , and TiN 2 is therefore in agreement with the general trend, that the bulk modulus of a compound increases with an increase of the product of formal charges of anions and cations 19,27 .
Search for solid nitrogen precursor. More detail characterization of physical properties of ReN 2 , such as hardness, electrical conductivity, etc. require a sample to be at least a few tens of microns in size that is much larger than can be synthesized in a LHDAC.
The large volume press technique enables the synthesis of such a sample, but precludes from using N 2 as a reagent. First, the amount of nitrogen, which can be sealed in a capsule along with Re, is insufficient for the desired reaction yield; second, unavoidable deformation of the capsule upon compression may potentially lead to the loss of nitrogen. Therefore, a solid source of nitrogen had to be found and we tested sodium and ammonium azides, NaN 3 and NH 4 N 3 , as potential precursors in LHDACs (Experiments #5, #6, Table 1) (for a discussion regarding the choice of the solid reagents see Supplementary Note 4). The experiment with NaN 3 (Experiment #5) did not result in the synthesis of ReN 2 . The major product of the reaction was NaReN 2 (Supplementary Fig. 7), whose lattice parameters turned out to be very close to those reported for m-ReN 2 by Kawamura et al. 23 , that might suggest that the material described in ref. 23 as rhenium nitride indeed could be a different compound (for a related discussion see Supplementary Note 4). The experiment in LHDAC with NH 4 N 3 as a source of nitrogen resulted in the synthesis of ReN 2 among other products (Experiment #6, Table 1).
Synthesis of Re 2 (N 2 )(N) 2 in a large volume press. Based on results of this experiment in DAC, we explored a possibility to scale up the synthesis of ReN 2 in a multianvil LVP at 33 GPa and 2273 K via a reaction between rhenium and ammonium azide (Experiment #7, Supplementary Note 5, Supplementary Fig. 8).
The product of the reaction was a mixture of Re 2 N and ReN 2 . Each phase was separated ( Supplementary Fig. 9) and characterized using single-crystal X-ray diffraction. A phase-pure polycrystalline sample of ReN 2 (70 × 60 × 50 μm 3 ), which was synthesized in the LVP, was used for nanoindentation hardness and electrical resistance measurements ( Supplementary Fig. 10). Nanoindentation was performed using a nanoindenter equipped with Berkovich diamond tip and featuring continuous stiffness measurement capabilities. The average hardness and Young's modulus measured between 200 and 400 nm depths are 36.7 (8) GPa and 493 (14) GPa, respectively (Fig. 2e, Table 2). The hardness approaching 40 GPa, a threshold for superhard materials, and extreme stiffness comparable with diamond makes    Fig. 2f. Electrical resistivity of metals increases with temperature and this is the case for ReN 2 . The shape of the resistance-temperature curve (Fig. 2f) is reproducible as confirmed in a number of independent measurements on the same sample with re-glued electrical contacts.
Theoretical calculations. To confirm the experimentally observed peculiarities of ReN 2 and to gain deeper insights into the mechanical and electronic properties of this compound, we performed theoretical calculations based on the density functional theory. First, we considered the crystal structure of ReN 2 . We carried out the full structure optimization for the compound at ambient pressure and found that calculations and experiment are in very close agreement (Supplementary Table 2). Calculated elastic constants for ReN 2 (Table 3) fulfill the mechanical stability conditions 31 , and calculated phonon dispersion relations (Fig. 3a) show only real frequencies confirming its dynamic stability. Theoretically calculated N1-N1 vibrational frequency form a localized band giving rise to a peak of the phonon density of states at~1031 cm −1 . This vibrational behavior is similar to other pernitrides 12,15,32 . The metallic nature of the material confirmed by our calculations of the electronic density of states (DOS) (Fig. 3c). Calculated vibrational and electronic properties of N1-N1 unit confirm that it is a pernitride anion N 2 4− . On the contrary, electronic and vibrational properties of N2 atoms (Fig. 3a, c) are quite distinct from those of N1, providing strong support to the experimental observation of the crystal chemistry of ReN 2 , which is unique for transition metals pernitrides.

Discussion
The unique chemistry of the compound is essential for understanding its superior mechanical properties. The bulk modulus, calculated theoretically using Voigt-Reuss-Hill approximation (413.5 GPa) 33 is in a good agreement with the experiment (428 (10) GPa), confirming that ReN 2 can be characterized as highly incompressible material. At the same time, the value of the Poisson coefficient is close to 0.25, and relatively high ratio between share and bulk elastic moduli indicates substantial degree of covalence in ReN 2 chemical bonding. A direct calculation of the charge density map (Fig. 3b) confirms the expectation. One sees a formation of covalent bonds between two N1 atoms. It is of single bond character with very high degree of electron localization (Fig. 3d) typical for a pernitride anion N 2 4− in other transition metal pernitrides, 34 and incompressible N 2 4− is supposed to contribute to very low compressibility of the materials. The covalent bond between Re and N2 atoms is formed by substantially less localized electrons (compare Fig. 3b and Fig. 3d). Indeed, measured temperature dependence of the electrical resistance (Fig. 2f) and the estimated resistivity (~4 × 10 −6 Ω·m-16 × 10 −6 Ω·m in a temperature range 150-400 K) are in agreement with the theoretical conclusion and the description of ReN 2 as a metal. The formation of the covalent bonds between Re and N2 atoms indicates strong hybridization between the electronic states of the atoms. The calculated electronic DOS (Fig. 3c) shows the presence of the pseudogap between occupied, predominantly bonding states of Re and unoccupied non-bonding and anti-bonding states. According to Jhi et al. 35 , such features optimize electronic contribution to hardness enhancement in transition-metal carbonitrides, which can also explain very high hardness of ReN 2 . Thus, the formation of strong covalent bond between Re and N2 atoms, a unique feature of the material synthesized in this work in comparison with known transition metal pernitrides, appears to be essential for its spectacular mechanical and electronic properties. To summarize, in the present work we have synthesized a transition metal nitride ReN 2 (Re +V 2 (N −II 2 )(N −III ) 2 ) with the unique crystal structure and outstanding properties. The structure with Re atoms in the high oxidation state +V features both discrete nitride and pernitride ions. A combination of the high electron density of the transition metal with interstitial nitride anions and covalently bound pernitride units makes this compound ultraincompressible and extremely hard at the same time. The developed method for scaling up the synthesis of ReN 2 in a LVP using ammonium azide as a nitrogen precursor may be applied for producing nitrides of other transition metals. We demonstrated the complete route for materials development from screening experiments in diamond anvil cells to the synthesis of samples large enough for physical property measurements. It is not only our results per se that are important, but the fact that the development and synthesis of the new material was realized contrary to the established concepts and should encourage further theoretical and experimental works in the field.

Methods
Synthesis of Re-N phases in laser-heated diamond anvil cells. In all synthesis experiments a rhenium powder (Sigma Aldrich, 99.995%) was loaded into the sample chamber of a BX90 diamond anvil cell (Boehler-Almax anvils, 250-μm size). In four experiments the chamber was filled with nitrogen at 1.5 kbar that served as a pressure-transmitting medium and as a reagent. In two experiments, the chamber was filled either with ammonium azide NH 4 N 3 or with sodium azide NaN 3 . Pressure was determined using the equation of state of rhenium [36][37][38] . The compressed sample was heated using the double-sided laser-heating system installed at the Bayerisches Geoinstitut (BGI), University of Bayreuth, Germany. Successful syntheses were performed at 40, 42, 49, 71, and 86 GPa at temperatures of 2200-2500 K ( Table 1).
Synthesis of Re-N phases in the large-volume press. High-pressure synthesis was performed using a Kawai-type multi-anvil apparatus IRIS15, installed at the BGI 39 . The NH 4 N 3 sample (0.5 mm thickness, 0.8 mm in diameter) was sandwiched between two layers of Re powder (0.1 mm thick, 0.8 mm in diameter) and between two tubes of dense alumina in a Re capsule, which also acted as a heater. The capsule was placed in a 5 wt% Cr 2 O 3 -doped MgO octahedron with a 5.7 mm edge that was used as the pressure medium. The assembly scheme is given in the Supplementary Fig. 8. Eight tungsten carbide cubes with 1.5 mm truncation edge lengths were used to generate high pressures. The assembly was pressurized at ambient temperature to 33 GPa, following the calibration given by Ishii et al. 39 and then heated to~2273(100) K within 5 min and immediately quenched after the target temperature was reached. The assembly was then decompressed during 16 h. Synthesis of NH 4 N 3 . Ammonium azide, NH 4 N 3 was obtained by the metathesis reaction between NH 4 NO 3 (2.666 g, 33 mmol, Sigma-Aldrich, 99.0%) and NaN 3 (2.165 g, 33 mmol, Acros Organics, Geel, Belgium, 99%) in a Schlenk tube. By heating from room temperature to 170°C in a glass oven and annealing for 7.5 h at 170°C and then for 12 h at 185°C, NH 4 N 3 precipitated at the cold end of the tube separated from NaNO 3 , which remained at the hot end during the reaction 40 .
Compressibility measurements. For the compressibility measurements the sample synthesized at 49 GPa and 2200 K (Experiment #2) was quenched down to ambient pressure and re-loaded into another diamond anvil cell. The sample chamber was then filled with Ne that served as a pressure-transmitting medium. A powder of gold (Sigma Aldrich, 99.99%) was placed into the sample chamber along with the sample and used as a pressure standard 41 . The sample was then compressed up to~45 GPa in 13 steps. At each pressure point we have collected powder X-ray diffraction data. Synchrotron X-ray diffraction. High-pressure single-crystal and powder synchrotron X-ray diffraction studies of the reaction products were performed at the beamlines P02.2 (DESY, Hamburg, Germany) 42  Powder diffraction measurements were performed either without sample rotation (still images) or upon continuous rotation in the range ±20°ω. The images were integrated to powder patterns with Dioptas software 43 . Le-Bail fits of the diffraction patterns were performed with the TOPAS6 software.
In-house X-ray diffraction. Ambient-pressure single-crystal XRD datasets were collected with a high-brilliance Rigaku diffractometer (Ag Kα radiation) equipped with Osmic focusing X-ray optics and Bruker Apex CCD detector in the BGI.
Structure solution and refinement. The structure was solved with the ShelXT structure solution program 44 using intrinsic phasing and refined with the Jana 2006 program 45 . CSD-1897795 contains the supplementary crystallographic data for this paper. These data can be obtained free of charge from FIZ Karlsruhe via www.ccdc. cam.ac.uk/structures. Nanoindentation. Nanoindentation was performed using a Nanoindenter G200 platform (KLA-Tencor, Milpitas, CA, USA), equipped with a Berkovich diamond tip (Synton MDP, Nidau, Switzerland) and featuring the continuous stiffness based method (CSM) 46 . Each sample was indented at 16 different locations separated by a distance of at least 10 µm, so that their plastic zones did not overlap. For each measurement, loading was performed at a constant strain-rate of 0.025 s −1 up to a maximal indentation depth of at least 400 nm. A 2 nm large oscillation superimposed on the loading signal allowed continuously measuring the contact stiffness. The acquired data were evaluated using the Oliver-Pharr method 47,48 . To this purpose, the diamond punch geometry was calibrated from 1000 nm deep references measurements in fused silica and the machine frame stiffness value was refined so as to obtain a constant ratio between stiffness squared and load during indentation of the samples. The conversion of the reduced moduli to a uniaxial Young's moduli was performed assuming a Poisson's ratios of 0.24 and 0.29, respectively for ReN 2 and Re 49 .
Temperature-dependent resistance measurements. The resistance of the sample was measured by four-probe method passing a constant DC 90 mA current through the sample and measuring both current and voltage drop across the sample. Temperature was measured using the S-type thermocouple.  Theoretical calculations. The ab initio electronic structure calculations of ReN 2 (12 atoms), ReN (2 atoms), and ReN x (2 × 3 × 2 supercell) were performed using the all electron projector-augmented-wave (PAW) method 50 as implemented in the VASP code [51][52][53] . Among the tested exchange-correlation potentials (PBE 54 , PBEsol 55 , AM05 56 ) the PBEsol approximation has resulted into the best agreement between the derived experimental and theoretical equation of state. Convergence has been obtained with 700 eV energy cutoff for the plane wave basis and a (18 × 10 × 14) Monkhorst-Pack k-points 57 type sampling of the Brillouin zone for ReN 2 . Gaussian smearing technique was chosen with smearing of 0.05 eV. The convergence criterion for the electronic subsystem has been chosen to be equal to 10 −4 eV for two subsequent iterations, and the ionic relaxation loop within the conjugated gradient method was stopped when forces became of the order of 10 −3 eV/Å. The elastic tensor C ij has been calculated from the total energy applying (+/−) 1% and 2% lattice distortions. The Born mechanical stability conditions have been verified using the elastic constants. The phonon calculations have been performed within quasiharmonic approximation at temperature T = 0 K using the finite displacement approach implemented into PHONOPY software 58 . Converged phonon dispersion relations have been achieved using a (3 × 3 × 3) supercell with 324 atoms and (5 × 5 × 5) Monkhorst-Pack k-point sampling.

Data availability
The data that support the findings of this study are available from the corresponding author upon reasonable request. CSD-1897795 contains the supplementary crystallographic data for this paper. These data can be obtained free of charge from FIZ Karlsruhe via www.ccdc.cam.ac.uk/structures. The source data underlying Fig. 2a