# High-Pressure Synthesis of Ultra-Incompressible, Hard and Superconducting Tungsten Nitrides

Akun Liang, Israel Osmond, Georg Krach, Lan-Ting Shi, Lukas Brüning, Umbertoluca Ranieri, James Spender, Ferenc Tasnadi, Bernhard Massani, Callum R. Stevens, et al.

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Akun Liang, Israel Osmond, Georg Krach, Lan-Ting Shi, Lukas Brüning, et al., High-Pressure Synthesis of Ultra-Incompressible, Hard and Superconducting Tungsten Nitrides. Advanced Functional Materials, 2024, 34 (32), pp.2313819. 10.1002/adfm.202313819. hal-05098772

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# High-Pressure Synthesis of Ultra-Incompressible, Hard and Superconducting Tungsten Nitrides

Akun Liang,* Israel Osmond, Georg Krach, Lan-Ting Shi, Lukas Brüning, Umbertoluca Ranieri, James Spender, Ferenc Tasnadi, Bernhard Massani, Callum R. Stevens, Ryan Stewart McWilliams, Eleanor Lawrence Bright, Nico Giordano, Samuel Gallego-Parra, Yuqing Yin, Andrey Aslandukov, Fariia Iasmin Akbar, Eugene Gregoryanz, Andrew Huxley, Miriam Peña-Alvarez, Jian-Guo Si, Wolfgang Schnick, Maxim Bykov, Florian Trybel, and Dominique Laniel*

Transition metal nitrides, particularly those of 5d metals, are known for their outstanding properties, often relevant for industrial applications. Among these metal elements, tungsten is especially attractive given its low cost. In this high-pressure investigation of the W–N system, two novel ultra-incompressible tungsten nitride superconductors, namely $W_2N_3$ and $W_3N_5$, are successfully synthesized at 35 and 56 GPa, respectively, through a direct reaction between $N_2$ and W in laser-heated diamond anvil cells. Their crystal structure is determined using synchrotron single-crystal X-ray diffraction. While the $W_2N_3$ solid’s sole constituting nitrogen species are $N^{3-}$ units, $W_3N_5$ features both discrete $N^{3-}$ as well as $N_2^{4-}$ pernitride anions. The bulk modulus of $W_2N_3$ and $W_3N_5$ is experimentally determined to be 380(3) and 406(7) GPa, and their ultra-incompressible behavior is rationalized by their constituting $W_7$ polyhedra and their linkages. Importantly, both $W_2N_3$ and $W_3N_5$ are recoverable to ambient conditions and stable in air. Density functional theory calculations reveal $W_2N_3$ and $W_3N_5$ to have a Vickers hardness of 30 and 34 GPa, and superconducting transition temperatures at ambient pressure (50 GPa) of 11.6 K (9.8 K) and 9.4 K (7.2 K), respectively. Additionally, transport measurements performed at 50 GPa on $W_2N_3$ corroborate with the calculations.

## 1. Introduction

Recently, the high-pressure synthesis of transition metal nitrides has drawn significant attention and research efforts due to their excellent mechanical and electronic properties, such as high bulk modulus,[1] high hardness,[2] high electronic conductivity, and high superconducting transition temperature ($T_c$).[3] In particular, some of the newly synthesized metal nitrides can be stabilized and recovered to ambient conditions, making them potential candidates for industrial applications.[2a,4]

The synthesis strategy for these hard and incompressible metal nitrides involves around two key aspects. First, it involves utilizing 5d transition metals—that is, elements with a high electronic density—as starting materials. As illustrated in Figure 1a, these elements feature high incompressibility, with tungsten,[5] rhenium,[6] osmium,[7] and iridium[1] exhibiting a bulk modulus equal to or

A. Liang, I. Osmond, U. Ranieri, J. Spender, B. Massani, C. R. Stevens, R. S. McWilliams, E. Gregoryanz, A. Huxley, M. Peña-Alvarez, D. Laniel Centre for Science at Extreme Conditions and School of Physics and Astronomy
University of Edinburgh
Edinburgh EH8 9YL, UK
E-mail: aliang@ed.ac.uk; dominique.laniel@ed.ac.uk

<figure><img src="image_3.png" /></figure>

The ORCID identification number(s) for the author(s) of this article can be found under https://doi.org/10.1002/adfm.202313819

© 2024 The Authors. Advanced Functional Materials published by Wiley-VCH GmbH. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

DOI: 10.1002/adfm.202313819

G. Krach, W. Schnick
Department of Chemistry
University of Munich (LMU)
81377 Munich, Germany

L.-T. Shi, J.-G. Si
Spallation Neutron Source Science Center
Dongguan 523000, P. R. China

L. Brüning, M. Bykov
Institute for Inorganic Chemistry
University of Cologne
50923 Cologne, Germany

F. Tasnadi, F. Trybel
Department of Physics, Chemistry and Biology (IFM)
Linköping University
Linköping 58183, Sweden
exceeding 300 GPa. Osmium, in particular, has been reported as the most incompressible elemental metal,[⁸] with literature values ranging from 397 to 462 GPa for its bulk modulus.[⁹] Second, the addition of nitrogen enables the formation of short covalent bonds between nitrogen and the transition metal, which not only significantly enhances the bulk modulus (as shown in Figure 1a) but also improves the material's shear modulus due to the directional nature of these bonds. Given that a material's hardness is dominantly controlled by both the bulk modulus and the shear modulus, 5d transition metal nitrides generally exhibit superior hardness when compared to their parent metals, as summarized in Figure 1b. Another driving force behind the synthesis of transition metal nitrides is that they typically retain their metallic nature and exhibit relatively higher values of T<sub>c</sub> compared to their parent transition metals at ambient conditions (as shown in Table S1, Figure S1, Supporting Information). For instance, HfN has a T<sub>c</sub> of 8.8 K at ambient conditions,[¹⁰] representing a significant increase in T<sub>c</sub> when compared to Hf (0.17 to 0.35 K).[¹¹] The higher T<sub>c</sub> observed in binary transition metal nitrides can be attributed to the strengthening of electron-longitudinal-acoustic phonon coupling at a short wavelength.[¹²] The emergence of the superconducting state in transition metal nitrides is closely linked to the presence of anomalies in the phonon dispersion curve.[¹³] Materials exhibiting both super hardness and good electronic conductivity are of particular interest for a broad range of applications, such as coatings, electronic connectors, and other components working in extreme environments.

An additional criterion for transition metal nitrides regard-
ing industrial relevance is their extraction cost. In that regard,
tungsten outshines other 5d transition metals, being significantly
cheaper—and, in particular, ≈50 times cheaper than rhenium.[16]
Therefore, it does not come as a surprise that many studies
have been focused on tungsten nitrides (Figure 1). Most of
these nitrides have been synthesized using a large-volume press
with a synthesis pressure lower than 10 GPa, such as WC-type
WN,[14h] cubic-W<sub>3</sub>N<sub>4</sub>,[14h] W<sub>2.25</sub>N<sub>3</sub>,[14e] r-W<sub>2</sub>N<sub>3</sub>,[14h] h-W<sub>2</sub>N<sub>3</sub>,[14h]

E. L. Bright, S. Gallego-Parra
European Synchrotron Radiation Facility
Grenoble 38000, France

N. Giordano
Photon Science
Deutsches Elektronen-Synchrotron
22607 Hamburg, Germany

Y. Yin, A. Aslandukov, F. I. Akbar
Material Physics and Technology at Extreme Conditions
Laboratory of Crystallography
University of Bayreuth
95447 Bayreuth, Germany

E. Gregoryanz
Center for High-Pressure Science and Technology Advanced Research
Shanghai 201203, P. R. China

E. Gregoryanz
Key Laboratory of Materials Physics
Institute of Solid State Physics
Chinese Academy of Sciences (CAS)
Hefei, Anhui 230031, P. R. China

M. Bykov
Institute of Inorganic and Analytical Chemistry
Johann Wolfgang Goethe Universität
60438 Frankfurt, Germany

cF8-W<sub>0.92</sub>N<sub>0.61</sub>, cP6-WN<sub>0.94</sub>,<sup>[14a]</sup> and MoC-type WN<sub>0.6</sub>.<sup>[14d]</sup> Their bulk modulus varies from 226(12) GPa for r-W<sub>2</sub>N<sub>3</sub>.<sup>[14h]</sup> to 383(5) GPa for WC-type WN.<sup>[14d]</sup> With the exception of r-W<sub>2</sub>N<sub>3</sub>,<sup>[14h]</sup> all tungsten nitrides have a higher or equal bulk modulus than pure tungsten. Similarly, WN, cP6-WN<sub>0.94</sub>, and cF8-W<sub>0.92</sub>N<sub>0.61</sub> all exhibit a hardness higher than W, having experimentally measured values of 13.8, 18, and 18 GPa, respectively.<sup>[14a,17]</sup> It can be noted that tungsten atoms in all of the aforementioned tungsten nitrides are sixfold coordinated by nitrogen atoms, forming WN<sub>6</sub> octahedra. Other tungsten nitrides were discovered at significantly higher pressures (i.e., >70 GPa) in laser-heated diamond anvil cell (DAC), that is, U<sub>7</sub>Te<sub>12</sub>-type W<sub>7</sub>N<sub>12</sub> (70 GPa),<sup>[4]</sup> WN<sub>8</sub>-N<sub>2</sub> (105 GPa)<sup>[18]</sup> and WN<sub>6</sub> (126–165 GPa).<sup>[14b]</sup> While W<sub>7</sub>N<sub>12</sub> and WN<sub>8</sub>-N<sub>2</sub> are comprised of WN<sub>7</sub> and WN<sub>8</sub> polyhedra, respectively, WN<sub>6</sub> contains armchair-like hexazine N<sub>6</sub> rings featuring N–N single bonds. Moreover, the coordination change of tungsten, from sixfold at low pressure to seven and eightfold at high pressure fits the trend of the coordination number increasing concomitantly with pressure.<sup>[19]</sup> One can also note that superconductivity studies on tungsten nitrides are scarce (Figure S1, Supporting Information), with the only demonstrated case being W<sub>2</sub>N<sub>2</sub>,<sup>[20]</sup> which shows a T<sub>c</sub> of 1.3 K at ambient conditions, representing only marginal improvement compared to pure tungsten (0.011 K).<sup>[21]</sup>

From this literature survey, it is clear that the W–N system
has yet to be investigated in the mild to moderate pressure
regime, namely from ≈20 to 70 GPa. According to theoretical
calculations,[²²] this pressure domain is promising for the discov-
ery of novel solids with attractive mechanical properties. In the
current work, the W–N system was investigated between 35 and
56 GPa and two new tungsten nitrides, W<sub>2</sub>N<sub>3</sub> and W<sub>3</sub>N<sub>5</sub>, were
synthesized, along with the known MoC-type WN<sub>0.6</sub> and WC-type
WN.[¹⁴d] Their structures, solved and refined by single-crystal X-
ray diffraction (SCXRD), are analyzed, and their bulk moduli are
determined. The two new solids are also found to be recoverable
to ambient conditions and stable in air. The Vickers hardness of
W<sub>2</sub>N<sub>3</sub> and W<sub>3</sub>N<sub>5</sub> is calculated by ab initio methods, as well as
their phonon dispersion and electron band structure, supercon-
ducting transition temperature, and electron localization func-
tion. Signs of the superconducting transition for W<sub>2</sub>N<sub>3</sub> at low
temperatures have been observed experimentally. The relation-
ship between the crystal structures of these tungsten nitrides and
their mechanical and electronic properties is discussed.

## 2. Results and Discussion

2.1. Synthesis and Data Analysis Procedure

For the performed experiments, three independent experiments with BX90-type DACs equipped with 250 or 200 µm culet anvils were prepared. In two of the experiments, tungsten metal pieces were loaded in the experimental chamber along with high-pressure molecular nitrogen (≈2000 bars), which served as both a reagent and a pressure-transmitting medium (PTM). In the third experiment, Be<sub>4</sub>W<sub>2</sub>N<sub>5</sub>, synthesized in a large-volume press, was loaded with neon in the sample chamber. The equation of state (EOS) of tungsten or neon was used to estimate the pressure in the sample chamber.<sup>[5,23]</sup> The full experimental and calculation details can be found in the Experimental Section. In the
<figure><img src="image_4.png" /><figcaption>**Figure 1.** Bulk modulus and hardness of pure 5d transition metals and their corresponding nitrides, as reported in the literature[1,2,4–7,14] and this study. The data used to produce these graphs can be found in Table S1 (Supporting Information). a) The experimentally determined bulk modulus of the pure metals and their nitrides is represented by solid red and black dots, respectively. The three synthesized tungsten nitrides reported in this study are indicated by green dots. The horizontal dashed blue line represents the bulk modulus of the diamond.[15] b) The experimentally measured hardness value (exp.) of pure 5d transition metals and their nitrides is illustrated by solid red and black dots, respectively. The theoretically calculated hardness (calc.) of metal nitrides found in the literature is shown as purple dots. The predicted Vickers hardness of the two newly synthesized tungsten nitrides and the previously reported ReN<sub>2</sub>[2a] are represented by green dots. Only the 5d transition metal nitrides stable at ambient conditions are plotted in Figure 1b.</figcaption></figure>

first experiment (exp #1), a sample was initially compressed to 35.0 GPa and laser-heated to 3000(200) K. After laser-heating, an X-ray diffraction map (Figure 2c) of the sample revealed the presence of previously absent diffraction spots (Figures S2–S5, Supporting Information), suggesting the formation of a compound. SCXRD measurements performed on the polycrystalline sample resulted in high-quality data from which the structure of the novel W<sub>2</sub>N<sub>3</sub> compound was solved and refined (Figures S2,S4, Supporting Information). The presence of MoC-type WN<sub>0.6</sub> was also found (Table S2, Figure S4, Supporting Information).[4,14d] The sample was then further compressed to 56.0 GPa and laser-heated to 3100(200) K. While the diffraction signal of W<sub>2</sub>N<sub>3</sub> was seen, new diffraction spots were also observed (Figures S3,S5, Supporting Information). From the collected single-crystal data, the unidentified diffraction spots could be assigned to the previously unknown W<sub>3</sub>N<sub>5</sub> compound, for which a full structure model was obtained (Figure 2). In another independent experiment (exp #2), the pressure was increased to 45 GPa and the sample was laser-heated to 2400(200) K, W<sub>2</sub>N<sub>3</sub> and the previously reported WC-type WN was found. In the third experiment (exp #3), with the starting materials Be<sub>4</sub>W<sub>2</sub>N<sub>5</sub> and Ne, the pressure was increased to 40.2 GPa and the sample was laser-heated to a temperature higher than 2000 K. In exp #3, only W<sub>2</sub>N<sub>3</sub> was found. The outcome of each experiment is summarized in Table S2 (Supporting Information). The presence of other phases was ruled out through the detailed analysis of the powder X-ray diffraction data (Figures S4,S5, Supporting Information). The synthesized compounds were then decompressed to ambient conditions—under which they were found to persist and to be stable in air. SCXRD data were collected at several pressure points during decompression.

## 2.2. Crystal Structure at Ambient Conditions

The determined crystal system of WN<sub>0.6</sub> is hexagonal (space group P6<sub>3</sub>/mmc, no. 194), and the ambient conditions lattice parameters are *a*<sub>0</sub> = *b*<sub>0</sub> = 2.909(5) Å and *c*<sub>0</sub> = 10.167(4) Å, (V<sub>0</sub> = 74.52(4) Å<sup>3</sup>), in excellent agreement with previously reported values.[14d] The lattice parameters at different pressures can be found in Table S3 (Supporting Information).

W<sub>2</sub>N<sub>3</sub> crystallizes in the orthorhombic crystal system (Figure 2a) with space group *Pnma* (no. 62). The lattice parameters of W<sub>2</sub>N<sub>3</sub> at ambient and high pressure can be found in Table S4 (Supporting Information), while the refinement results, quality factors and crystal structure at ambient condition and 35.0 GPa can be found in Tables S6–S8 (Supporting Information). The CIF (Crystallographic Information File) files at ambient condition and 35.0 GPa are deposited in the Cambridge Crystallographic Data Center (CCDC) with the deposition numbers 2305422 and 2305423, respectively. W<sub>2</sub>N<sub>3</sub> is isostructural to the previously reported transition metal nitrides η-Ta<sub>2</sub>N<sub>3</sub>[14] and Nb<sub>2</sub>N<sub>3</sub>[24] and has the U<sub>2</sub>S<sub>3</sub>-type structure. Furthermore, the existence of W<sub>2</sub>N<sub>3</sub> was predicted by previous theoretical calculations.[22a] The crystal structure of W<sub>2</sub>N<sub>3</sub> (Figure 2a) is composed of two crystallographically distinct tungsten atoms (W1 and W2) as well as the three unique nitrogen atoms (N1, N2 and N3), all located on the 4c Wyckoff position. Each tungsten atom is surrounded by seven nitrogen atoms, forming WN<sub>7</sub> polyhedra. For the W1N<sub>7</sub> polyhedron, it is edge-sharing with five W2N<sub>7</sub> and two W1N<sub>7</sub> polyhedra, as well as face-sharing with two W1N<sub>7</sub> polyhedra along the *b*-axis (Figure 2b). For the W2N<sub>7</sub> polyhedron, it is edge-sharing with five W1N<sub>7</sub> and four W2N<sub>7</sub> polyhedra. At ambient conditions, the W–N bond distance in
<figure><img src="image_5.png" /><figcaption>**Figure 2.** Crystal structure of the two new tungsten nitrides at ambient conditions. a) Crystal structure of W₂N₃. b) Edge-sharing WN₇ polyhedra found in the crystal structure of W₂N₃. c) X-ray diffraction map of the sample cavity in exp#1 at 56 GPa, showing the position of tungsten (sky blue), W₂N₃ (red), W₃N₅ (pink), and WN₀.₆ (green). The green and black circles indicate the laser-heated position at 35 and 56 GPa, respectively. The intensity of the peak at the 2θ angle provided for each compound was utilized to construct the map. d) Crystal structure of W₃N₅; the discrete N³⁻ anions are shown in blue while the (N₂)⁴⁻ dimers are shown in red. e) The immediate chemical environment of the single bonded nitrogen dimer. f) Edge- and g) face-sharing WN₇ polyhedra found in the crystal structure of W₃N₅. In all cases, the W1 and W2 atoms, crystallographically distinct in both structures, are shown as white and green balls. The bond distances indicated next to the bonds are in Å. Unit cells are drawn with continuous black lines.</figcaption></figure>
both distinct WN₇ polyhedra varies from 2.044(3) to 2.233(4) Å, consistent with the W–N bond distance reported in the literature for tungsten nitrides.[4,14a,d,e,h] The W–W distance is 2.9245(3) Å, larger than that of pure tungsten (2.74 Å).[14r] The discrete nitrogen atoms are four (N3) or fivefold (N1, N2) coordinated by tungsten.

W₃N₅ contains both discrete N atoms and N₂ dimers—and can thereby also be written as W₃(N₂)(N₃)—and crystallizes in the orthorhombic crystal system (Figure 2d), adopting space group Cmcm (no. 63). The lattice parameters of W₃N₅ at ambient and at high pressure can be found in Table S5 (Supporting Information), while the refinement results, quality factors and crystal structure at ambient conditions and 56.0 GPa can be found in Tables S9–S11 (Supporting Information). The deposition number of the CIF files in CCDC at ambient conditions and 56.0 GPa are 2305424 and 2305425, respectively. W₃N₅ has two crystallographically distinct tungsten atoms on the 4c (W1) and 8f (W2) Wyckoff positions. The discrete N atoms (N1 and N3), which usually exhibit an -III oxidation state, can thus be written as N³⁻ anions, and are located on 4c and 8f Wyckoff sites, and the N₂ atoms (8f Wyckoff site) form N₂ dimers. The bond length of the N₂ dimer is found to be 1.47(3) Å at ambient conditions, suggesting a single bond and thus a N₂⁻ pernitride,[25] consistent with that found in Mo₃N₅ (1.412 Å),[26] PtN₂ (1.42 Å),[27] OsN₂ (1.40 Å),[27] IrN₂ (1.42 Å),[27] and ReN₂ (1.412 Å).[2a] The nitrogen atoms constituting the N₂ dimers are bonded to three tungsten atoms at a distance of 2.095(8) or 2.157(12) Å (Figure 2e). The discrete N³⁻ anions have five tungsten atoms in their first coordination shell, each W1 atom is surrounded exclusively by seven discrete N³⁻ anions while each W2 atom is surrounded by four discrete N³⁻ anions plus three pernitride N₂⁻ anions, producing WN₇ polyhedra. Each W1N₇ polyhedra is face-sharing with two W2N₇ polyhedra plus two W1N₇ polyhedra, and edge-sharing with four W2N₇ polyhedra (Figure 2f,g). In sum, the crystal structure could be described as columns of W1N₇ polyhedra running along the *b*-axis, separated by columns of pairs of edge-sharing W2N₇ polyhedra, interconnected through N₂ dimers (Figure 2d). The W–N bond distance ranges from 2.043(15) to 2.176(8) Å, very similar to those found in W₂N₃. W₃N₅ is isostructural to the recently discovered Mo₃N₅,[26] a fact that is easily rationalized given that molybdenum is the lighter homolog of tungsten in the periodic table.

## 2.3. Atomic Charge and Bond Type

Based on the chemical formula of W₂N₃ and under a fully ionic approximation, where all nitrogen atoms are considered as forming nitrides (N³⁻), it is reasonable to assume that the W atoms share a combined charge of +9. Under this assumption, one tungsten would be in the oxidation state of +V and the other in +IV. This assignment is supported by smaller volumes of W1N₇ polyhedra compared to W2N₇ (Figure 4e). In the case of W₃N₅, given the W₃(N₂)⁴⁻(N³⁻)₃ chemical formula, the three discrete N³⁻ anions and one N₂⁻ collectively carry a charge of -13. Consequently, a plausible charge distribution across the two distinct tungsten atoms would entail W2 (8f Wyckoff site) to have a +4 charge and W1 (4c Wyckoff site) a +5 charge. To better understand the bond character and charge distribution in these W–N

solids, Löwdin charge, Mulliken charge, and integrated crystal orbital bond index (ICOBI) were calculated (Tables S12–S14, Supporting Information). The calculated Mulliken charge for tungsten in those two new compounds fall within the range of +1.33 e to +1.43 e. For the discrete N³⁻ anion, the calculated charge varies from -0.89 e to -0.97 e, and for the N₂⁻ pernitride, the charge is -1.2 e. The significantly lower charges for all the cations and anions compared to the oxidation states suggest that the bonds are far from being purely ionic. The bond covalency was assessed through the ICOBI. The ICOBI value for the W–N bonds fall within the range of 0.53 to 0.72 in the case of W₃N₅, indicating a substantial electron contribution from covalent bonding. This suggests that the bond between these atoms is a mixture of ionic and covalent. This observation aligns with the ICOBI versus absolute electronegativities difference relationship established for some compounds.[28] In that relationship, the ICOBI for the classical ionic compound NaCl is 0.09, indicating a negligible contribution from the covalent bond. Conversely, the calculated ICOBI for the classical covalent bond compound diamond is 0.95. The ICOBI calculated for the N₂ pernitride is 0.98, implying a single-bond, in agreement with the deduction made from the N–N bond length. This analysis is further supported by the calculated electron localization function (ELF) values obtained for different W–N bonds and the N–N dimer (Figures S6,S7, Supporting Information). The ELF value at the bond critical point of the W–N bond hovers ≈0.5; an ELF of 0.5 corresponds to electron-gas-like pair probability,[29] and the value at the bond critical point for the N–N dimer is as high as 0.8, a value commonly observed for classical covalent bonds.[30]

## 2.4. Superconductivity, Phonons, and Electronic Properties

The vibrational and electronic properties of the newly synthesized tungsten nitrides have been explored through theoretical calculations employing density functional theory (DFT). This investigation included phonon and electronic band structures (Figure 3; Figures S8,S9, Supporting Information) as well as elastic constants (Table S15, Supporting Information) at ambient pressure. The phonon band structure of both compounds exhibited no negative frequencies, thereby confirming their dynamical stability. The phonon band structure of W₂N₃ (Figure 3a) can be divided into two regions. The low-frequency region, below 10 THz, features contributions from tungsten atoms. The middle-frequency region between 10 to 25 THz displays the contribution from the discrete N³⁻ nitrogen alone. The phonon band structure of W₃N₅ (Figure 3b) can be divided into three regions and, besides two regions analogous to those in W₂N₃, it has a high-frequency region (>25 THz) with the sole contributor being the single-bonded N–N dimer. The peak of the latter vibration band is at a frequency of 27 THz (≈934 cm⁻¹), which closely mirrors the calculated peaks in other pernitrides, such as PtN₂ (752 cm⁻¹),[31] IrN₂ (836 cm⁻¹),[31] OsN₂ (778 cm⁻¹),[31] and ReN₂ (1031 cm⁻¹),[2a] yet notably differs from the vibrational frequency of the N=N double bond as seen in N₂H₂ (1550 cm⁻¹).[32]

The electronic band structures of W₂N₃ and W₃N₅, as depicted in Figures S8 and S9 (Supporting Information) respectively, reveal their closed band gap and therefore their metallic nature. The *T*<sub>c</sub> of those two compounds has been estimated using the
<figure><img src="image_6.png" /><figcaption>**Figure 3.** Density functional theory calculated phonon dispersion weighted by the magnitude of the phonon linewidth (red dots), projected phonon density of states and Eliashberg spectral function $\alpha^2 F(\omega)$ (grey), as well as the integrated strength of electron-phonon coupling of $\lambda(\omega)$ (yellow lines) for a) $W_2N_3$ and b) $W_3N_5$ at ambient pressure. The density of the red dots gives rise to the appearance of lines with varying broadness.</figcaption></figure>

Allen-Dynes-modified McMillan formula, as shown in the Section Density Functional Theory Calculations.[33] The $T_c$ values for $W_2N_3$ and $W_3N_5$ at ambient pressure are found to be 11.6 and 9.4 K, respectively. In this formula, the $T_c$ is directly correlated with the electron-phonon coupling (EPC) parameter $\lambda(\omega)$ (0.67 and 0.60 calculated for $W_2N_3$ and $W_3N_5$, respectively) and the logarithmic average frequency $\omega_{log}$ (369.2 and 397.2, calculated for $W_2N_3$ and $W_3N_5$, respectively). $\lambda(\omega)$ is obtained by integrating the

Eliashberg spectral function $\alpha^2 F(\omega)/\omega$ over the entire frequency range, and $\omega_{log}$ is calculated by integrating the $\alpha^2 F(\omega) \cdot \ln(\omega/\omega_0)$, where the Eliashberg spectral function $\alpha^2 F(\omega)$ in different frequency regions is represented by the grey area in Figure 3. In the low-frequency region of the phonon dispersion, the tungsten atoms contribute 56.6% and 52.4% to the total integration of $\lambda$ in $W_2N_3$ and $W_3N_5$, respectively. Another significant contribution to $\lambda$ comes from the middle-frequency region, indicating the
<figure><img src="image_7.png" /><figcaption>**Figure 4.** Transport measurements for a laser-heated W–N₂ sample at 50 GPa. a) An optical image of the sample after laser heating at 50 GPa. The aqua-colored square surrounding the initially pure tungsten sample shows the boundary of the X-ray diffraction map shown in (b). b) The X-ray diffraction intensity map obtained at 50 GPa displays the positions of tungsten (sky blue), W₂N₃ (red), W₃N₅ (green), and Pt (aqua). The intensity of the peak at the 2θ angle provided for each compound was utilized to construct the map. For clarity, nitrogen, present in both the t- and ε-phases, was omitted from the map, as it was found essentially everywhere in the sample chamber. c) Electrical resistance as a function of temperature measured after laser heating tungsten. d) Electrical resistance as a function of the temperature of the synthesized sample under an applied magnetic field up to 0.6 T. The insert displays the superconducting upper critical field (Hc2) versus the critical temperature (Tc), fitted with Ginzburg–Landau (GL) formalisms.[37]</figcaption></figure>

vibration of the discrete N³⁻ anions, contributing 43.4% and 45.6% of the total integration of λ in W₂N₃ and W₃N₅, respectively. The presence of nitrogen is hence responsible for the increased T_c compared to that of pure tungsten. The N–N dimer in W₃N₅ contributes only 2% to λ and thus has a negligible impact on the T_c of W₃N₅. The T_c predicted for W₂N₃ and W₃N₅ at ambient conditions also significantly exceeds that of pure tungsten (0.011 K), as well as those of other 5d-transition metal nitrides, such as HfN (8.83 K),[34] and cubic-TaN (6.5 or 8.15 K)[35] (Figure S1, Supporting Information). Notably, W₂N₃ exhibits the highest T_c among all reported 5d-transition metal nitrides to date (Figure S1, Supporting Information) and is comparable to the highest T_c, 16 K of δ-NbN,[36] found among all the transition metal nitrides. Following the same methodology, the T_c of W₂N₃ and W₃N₅ was calculated at 50 GPa (Figure S10, Supporting Information). The estimated T_c values for W₂N₃ and W₃N₅ are 9.8 and 7.2 K, respectively.

An independent cell (exp #4) has been prepared to measure the transport properties of the synthesized sample at 50 GPa (Figure 4a). An X-ray diffraction mapping (Figure 4b) was conducted on the same sample at 50 GPa. An example of the Le Bail refinement of the powder X-ray diffraction data obtained from the center position in the map is shown in Figure S11 (Supporting Information). The map reveals the synthesized sample to be predominantly composed of W₂N₃ (in red) with a small proportion of W₃N₅ (in green), along with t- and ε-nitrogen, and pure tungsten (in blue). The resistance measurements of the synthesized sample (Figure 4c) exhibit an abrupt drop at a temperature of 11.2 K. This can be interpreted as the signature of a superconducting

transition in W₂N₃ since it is the primary compound in the sample chamber and because the T_c for pure tungsten is known to be significantly below 11 K,[21] while both t- and ε-nitrogen are insulators. The resistance does not decrease to zero due to the sample's inhomogeneity and the lack of a full W₂N₃ conduction path between the electrodes. Further evidence pointing to a superconducting behavior is observed in the decrease of T_c under an applied magnetic field (Figure 4d). Fitting and extrapolation of the upper critical field (Hc2) versus temperature suggest that the T_c will be completely suppressed at an Hc2 higher than 3.7 T. The experimentally measured T_c of 11.2 K matches very well with the value expected from DFT calculations at 50 GPa, that is, 9.8 K.

## 2.5. Compressibility and Hardness

The structures of W₂N₃ and W₃N₅ were refined at each pressure step during the decompression, and the obtained unit cell volumes were plotted in Figure 5a,b. The data was fitted using a second-order Birch–Murnaghan (BM) EOS,[38] and the quality of the fitting was evaluated through the Eulerian strain (f) versus the normalized pressure (F) plot (Figures S12,S13, Supporting Information). The bulk modulus of W₂N₃ and W₃N₅ was determined to be 380(3) and 406(7) GPa, respectively. As both values are above the 300 GPa threshold, they qualify as ultra-incompressible.[39] As depicted in Figure 1a, their bulk modulus is higher than those of any previously reported tungsten nitrides. Figure 5d illustrates the pressure dependence of the normalized lattice parameters of W₃N₅. The crystal exhibits an isotropic
<figure><img src="image_8.png" /><figcaption>**Figure 5.** Physical properties of W₂N₃ and W₃N₅ extracted from the SCXRD data solution and refinement. Dots are experimental data and solid lines are second-order BM equations of state fits. a) Unit cell volume of W₂N₃ as a function of pressure (Exp.). b) Unit cell volume of W₃N₅ as a function of pressure (Exp.). The dashed lines are the theoretically calculated equation of state (DFT). c) Normalized unit cell volume of WN₀.₆ (blue triangles), W₂N₃ (black squares), and W₃N₅ (red circles) as a function of pressure. d) Normalized lattice parameters for W₃N₅ at different pressures. e) The green/blue and red/black dots are the volume of the WN₇ polyhedra extracted from W₃N₅ and W₂N₃, respectively. The same color system was also applied to the WN₇ bulk modulus values written in the figure. The inset of this graph is a representative WN₇ polyhedra (W1N₇ in W₃N₅ at ambient conditions), in which the tungsten and nitrogen atoms are shown by grey and blue balls. f) Pressure dependence of the bond distance of the N—N dimer.</figcaption></figure>

compressibility at lower pressures and minor anisotropic behavior at higher pressures, with the *b*-axis becoming the most incompressible axis. This anisotropy is attributed to the orientation of the N—N dimer, which is almost fully parallel to the *b*-axis. The bond length of this N—N dimer remains nearly unchanged under compression, as shown in Figure 5f. The observed anisotropic behavior is unrelated to the arrangement of the WN₇ polyhedra, as the mixture of edge- and face-sharing connected WN₇ polyhedra are observed along all three crystallographic directions. The bulk modulus of WN₀.₆ was also determined (356(2) GPa, see Figure 5c; Figure S14, Supporting Information) and found to be slightly larger than the literature value (338(3) GPa).[¹⁴d]

To shed some light on the underlying mechanism behind the incompressibility of W₂N₃ and W₃N₅, the pressure versus volume relationship of their WN₇ polyhedra was plotted (Figure 5e). A second-order BM EOS was employed to fit the volume of the polyhedra. The bulk moduli of all four distinct WN₇ are found to be closely related, with values of 424(7) GPa (392(6) GPa) for the W1N₇ (W2N₇) polyhedra in W₂N₃ and 417(9) GPa (428(8) GPa) for the W1N₇ (W2N₇) polyhedra in W₃N₅. It appears clear the bulk moduli value of the W₂N₃ and W₃N₅ compounds are similar to that of their constituting WN₇ unit. As such, it can be inferred that the compounds' bulk moduli mainly originate from the compressibility of the WN₇ polyhedra themselves. Indeed,

the polyhedra linkages are not thought to significantly affect the solids' compressibility, as face- and edge-sharing—both exclusively present in W₂N₃ and W₃N₅ and along all three crystallographic directions—are the most rigid.[⁴⁰] The mild difference in compressibility between W₂N₃ and W₃N₅ is likely due to the existence of the ultra-incompressible N—N dimer in W₃N₅ (Figure 5f). This dimer strengthens the gaps between pairs of W2N₇ polyhedra through the substantial Coulomb interaction between the paired nitrogen atoms,[⁴¹] as also found in IrN₂,[¹,³¹] PtN₂,[¹⁴p,³¹] and ReN₂.[²a]

The theoretical calculations of the mechanical properties, including elastic constant, bulk modulus, shear modulus, Young's modulus, and Vickers hardness, of the two new tungsten nitrides as well as for ReN₂, can be found in Table S15 (Supporting Information). In comparison to the hardness of 5d transition metal nitrides (and the pure metals) summarized in Figure 1b, both of the reported tungsten nitrides exhibit significantly higher hardness values compared to the tungsten nitrides reported in the literature, with their calculated Vickers hardness being of 30 and 34 GPa for W₂N₃ and W₃N₅, respectively. It is noteworthy that the calculated Vickers hardness for both W₂N₃ and W₃N₅ is comparable to the reported nanoindentation hardness (36.7 GPa) of ReN₂,[²a] which is well reproduced by our calculations (39 GPa, see Table S15, Supporting Information). The agreement
observed between the calculated Vickers hardness and the experimental hardness for ReN₂ underlines the reliability of this hardness model for the two new tungsten nitrides presented in this study. According to the assumptions made by Gao et al.,[42] the hardness of a covalent crystal can be described by the resistance of the bond against the external forces per unit area.[43] Therefore, the high Vickers hardness found in W₂N₃ and W₃N₅ could be attributed to the higher covalency of the W–N bonds within the WN₇ polyhedra. Additionally, the existence of the N–N dimer and the strong covalent bond between them contribute to the even greater hardness found in W₃N₅ and ReN₂.

### 3. Conclusion

By employing a combination of single-crystal X-ray diffraction techniques and theoretical calculations, we have successfully characterized two novel tungsten nitrides, synthesized at high pressure and temperature and recovered to ambient conditions, namely W₂N₃ and W₃N₅. Both compounds' mechanical stability at ambient pressure has been confirmed theoretically. W₂N₃, for which the lowest synthesis conditions found in this work are 35 GPa and 3000(200) K, exhibits a bulk modulus of 380(3) GPa, a calculated Vickers hardness of 30 GPa and is calculated to be superconducting below 11.6 K at ambient pressure and 9.8 K at a pressure of 50 GPa. Transport measurements suggest W₂N₃ to feature, at 50 GPa, a superconducting transition at 11.2 K. Notably, its critical temperature ($T_c$) predicted at ambient pressure is the highest among 5d-transition metal nitrides reported to date.

W₃N₅, comprised of both isolated N³⁻ as well as N₂⁴⁻ anions, is formed at a pressure of 56 GPa and a temperature of 3100(200) K, and has a bulk modulus of 406(7) GPa, a calculated Vickers hardness of 34 GPa and a superconducting transition temperature of 9.4 K at ambient pressure and 7.2 K at 50 GPa. Remarkably, its bulk modulus stands as the highest within the tungsten–nitrogen system, comparable to the most incompressible 5d transition metal nitrides.

The exceptionally incompressible behavior exhibited by both compounds can be attributed to the interconnected face- and edge-sharing WN₇ polyhedra. Additionally, the presence of the N₂ dimer in W₃N₅ contributes to its exceptional mechanical properties. Electronic band structure calculations indicate a closed band gap for both compounds, indicative of their metallic nature. The competitive hardness of these two compounds, coupled with the significantly lower cost of tungsten compared to other 5d transition metals, positions them as excellent candidates for industrial applications requiring toughness, good electronic conductivity, and cost-effective materials.

### 4. Experimental Section

**High-Pressure Experiments:** Three independent series of experiments were performed for the synthesis of tungsten nitrides by using BX90-type DACs with Boehmer–Almax type diamonds. The synthesis conditions and the outcomes are summarized in Table S2 (Supporting Information). Experiment #1 (exp #1) was conducted in a DAC equipped with a pair of 250 µm-culet diamonds, while exp #2 and #3 were conducted in DACs equipped with a pair of 200 µm-culet diamonds. A rhenium foil was used as the gasket and pre-indented to a thickness of 25 µm. A 120-µm hole was drilled in the center of the indentation and served as the sample chamber.

In exp #1 and #2, several pieces of high-purity tungsten (Alfa Aesar, purity 99.9%) were loaded in the sample chamber with molecular nitrogen, the latter serving as both a reagent and a PTM. In exp #3, the ternary precursor Be₄W₂N₅, synthesized in a large volume press was used. The crystal structure and synthesis details of the precursor would be reported elsewhere. This sample was loaded with neon. The samples were compressed to the target pressure of 35 and 56 GPa in exp #1, 45 GPa in exp #2, and 40 GPa in exp #3, respectively. Then the starting materials were laser heated with a home-built double-sided YAG laser-heating system. The temperature was measured by using the sample's thermal radiation. The pressure in the sample chamber was determined either from the EOS of tungsten (exp #1 and #2)[5] or Ne (exp #3).[23] Transport measurements (exp #4) were performed using a symmetric-type steel DAC suitable for electrical measurements in low-applied magnetic fields. This cell employed an insulating Al₂O₃-epoxy composite gasket in order to electrically insulate the electrodes from the metallic gasket. To provide the electrical connection to the sample, four Pt wires were placed in the sample chamber and fixed in place with silver epoxy before loading the W foil (99.999%, Goodfellow) and the research-grade nitrogen (99.9995%) at 2 kbar, the latter which acted as both the reactant and a hydrostatic PTM. After compression to 50 GPa (determined using the Raman shift of the diamond peak) the W foil was laser heated to a temperature of ≈2300 K.

**X-Ray Diffraction Experiments:** SCXRD experiments were performed at the ID11 beamline of the European Synchrotron Radiation Facility[44] (ESRF, in Grenoble, France), the P02.2 beamline of PETRAIII[45] (in Hamburg, Germany) synchrotron and 13IDD beamline of the APS (in Chicago, United States). At the ID11 beamline of the ESRF, the wavelength of the monochromatic X-ray beam was 0.2846 Å, the beam spot size was ≈1 × 1 µm² (full width at half maximum), and a Dectris Eiger2 X CdTe 4M detector was used to collect the signal. At the P02.2 beamline of PETRAIII, the wavelength of the monochromatic X-ray beam was 0.2905 Å, the beam spot size was ≈2 × 2 µm², and a Perkin Elmer XRD 1621 detector was used to collect the signal. At the 13IDD beamline of APS, the wavelength of the monochromatic X-ray beam was 0.2952 Å, and a Pilatus CdTe 1M detector was used to collect the signal. In all the cases, an X-ray mapping was performed in the sample chamber around the heated area to find the position of interest for SCXRD data collection, then obtained by rotating the cell around the vertical ω-axis in steps of 0.5 degrees from -36° to +36° (exp #1), or -30° to +30° (exp #2 and #3) for DACs with a smaller opening. The X-ray diffraction map of the sample in exp #4 was collected at the ID15B beamline of the ESRF. The wavelength of the monochromatic X-ray beam was 0.4094 Å, the beam spot size was ≈1 × 1 µm² (full width at half maximum), and a Dectris Eiger2 X CdTe 9M detector was used to collect the signal.

The CrysAlisPro software[46] package was used for the SCXRD data analysis, including peak search, removing the parasitic peak from the diamond anvils, unit cell determination, and data integration. An orthoenstatite single crystal (Mg₁.93 Fe₀.06) (Si₁.93, Al₀.06)O₆, space group: *Pbca*, lattice parameter: *a* = 8.8117(2) Å, *b* = 5.1832(1) Å, *c* = 18.2391(3) Å was used to calibrate the instrumental model used in CrysAlisPro, which included the sample-to-detector distance, the detector's origin, offsets of goniometer angles, and the rotation of both the X-ray beam and the detector with respect to the instrument axis. The DAFi program[47] was employed to search for the reflections that belonged to an individual single crystal. The crystal structures were solved with the SHELXT structure solution program[48] and refined in the Olex2 software.[49] Powder X-ray diffraction (PXRD) patterns were collected without the rotation of the cell, and integrated to a 2D X-ray diffraction pattern in the DIOPTAS software.[50] The Le Bail refinement of the integrated PXRD spectra was performed in the FULLPROF suite.[51]

**Density Functional Theory Calculations:** Kohn–Sham DFT-based electronic structure calculations were performed with the QUANTUM ESPRESSO (QE) package[52] using the projector augmented wave method.[53] The generalized gradient approximation by Perdew–Burke–Ernzerhof (PBE) was used for exchange and correlation,[54] the corresponding potential files for W 4f electrons and N 1s electrons were treated as scalar-relativistic core states. D3 van der Waals (vdW) corrections were included following the approach by Grimme et al.[55] as implemented in
QE for all calculations, except for the estimation of the critical superconducting temperature (see below). Convergence tests with a threshold of 1 meV per atom in energy and 0.1 meV Å⁻¹ per atom for forces led to a Monkhorst-Pack[56] k-point grid of 6 × 16 × 5 for W₂N₃ and 22 × 22 × 6 for W₃N₅ with a cutoff for the wave-function expansion of 100 Ry for both phases, with a mild Gaussian smearing of 0.005 Ry. The influence of spin-orbit coupling on the band structure and electronic density of states (Figures S8, S9, Supporting Information), which is in agreement with previous calculations in the W–N system was investigated.[57] Therefore, spin-orbit interactions were not included in further calculations.

Variable cell relaxations (lattice parameters and atomic positions) were performed on all experimental structures to optimize the atomic coordinates and the cell vectors until the total forces were smaller than 0.1 meV Å⁻¹ per atom and the deviation from the experimental pressure was below 0.1 GPa. EOS calculations were performed via variable-cell structural relaxations in 5 GPa steps up to 60 GPa. A second-order BM EOS was fitted to the energy-volume points, P(V) calculated, and benchmarked versus the target pressure of the relaxations to ensure convergence. Values of V₀ = 189.81 Å³, B₀ = 364 GPa for W₂N₃, and V₀ = 296.59 Å³ and B₀ = 387 GPa for W₃N₅ were found, close to the respective values for the bulk modulus of 365 and 385 GPa from elastic constants calculations (see Table S15, Supporting Information). Overall the best agreement with the experiment was found using the PBE functional with vdW corrections.

Löwding and Mulliken charges, as well as the ICOBI, were calculated with the LOBSTER package.[58]

To estimate the “polycrystalline” or Vickers hardness[59] of W₂N₃ and W₃N₅, the single-crystal elastic stiffness constants Cᵢⱼ was calculated and derived the polycrystalline bulk (B₀) and shear (G) moduli. The energy-strain relationships and a finite difference method with (+/-) 1 and 2% strain were utilized and the total energies were calculated using QE with the same numerical parameters as listed above. The values for the elastic constants and moduli can be found in Table S15 (Supporting Information).

Phonon dispersion relations were calculated with Phonopy[60] in a 2 × 4 × 2 and 3 × 3 × 2 supercells for W₂N₃ and W₃N₅, respectively, with k-points adjusted according to the supercell size. Calculations were performed with and without vdW corrections (structures without vdW corrections were re-relaxed to 0 GPa within this level of approximation) to ensure that the T_c calculations in using QE, where vdW corrections cannot be included, adequately represent the phonon dispersion relation. A very small influence was seen and concluded that vdW interactions should not have any significant influence on the calculated transition temperatures.

To estimate T_c, additional phonon and EPC calculations were carried out using density functional perturbation theory[61] as implemented in the QE, the same projected augmented wave pseudopotentials for N and W with a reduced kinetic energy cutoff of 100 Ry were employed. 3 × 5 × 3 and 4 × 4 × 3 q-point grids were employed to calculate the EPC of W₂N₃ and W₃N₅, respectively. Commensurate Monkhorst-Pack grids of 12 × 20 × 12 and 16 × 16 × 12 were used to ensure k-point sampling convergence and Gaussian smearing with a width of 0.01 Ry improving convergence. The superconducting critical temperature T_c was estimated based on the Allen-Dynes modified McMillan formula:[35]

$$T_c = \frac{\omega_{log}}{1.2} \exp \left[ - \frac{1.04 (1 + \lambda)}{\lambda - \mu^* - 0.32 \lambda \mu^*} \right] \quad (1)$$

where μ* is the effective Coulomb pseudopotential which was set to a typical value of 0.1. The integrated EPC constant can be evaluated by

$$\lambda (\omega) = \int_{0}^{\omega} \frac{\alpha^2 F (\omega')}{\omega'} d\omega' \quad (2)$$

The EPC constant λ used in Equation (1) is λ (ωmax), where ωmax is the maximum of the phonon frequency.

Here, ωlog is the logarithmically averaged characteristic phonon frequency, which is defined as

$$\omega_{log} = \exp\left[\frac{2}{\lambda} \int \frac{d\omega}{\omega} \frac{\alpha^2 F(\omega)}{\omega} \ln \omega\right] \quad (3)$$

**Transport Measurements:** Four-probe electrical measurements were performed using a Keithley 6221 current source combined with a Stanford SR830 Lock-In amplifier for voltage measurements, with a 141 µA excitation current at 84 Hz. Due to the large mass of the cell, data was taken at an approximate rate of 0.1–0.2 K min⁻¹ to ensure good thermalization. For the electrical measurements in an applied magnetic field, resistance offsets were applied to normalize the data above the superconducting transition to remove the effects of any observed magnetoresistance. T_c was extracted as the temperature at 80% of the observed resistance drop.

## Supporting Information

Supporting Information is available from the Wiley Online Library or from the author.

## Acknowledgements

The authors acknowledge the European Synchrotron Radiation Facility (ESRF), the Deutsches Elektronen-Synchrotron (DESY), and Advanced Photon Source (APS), Argonne National Laboratory for the provision of beamtime at the ID11, ID15B, P02.2, and 13IDD beamlines, respectively. D.L. thanks the UKRI Future Leaders Fellowship (MR/V025724/1) for financial support. M.B. acknowledges the support of Deutsche Forschungsgemeinschaft (DFG Emmy-Noether project BY112/2-1). G.K. thanks the Friedrich Naumann Foundation for Freedom for a Ph.D. scholarship with Funds from the Federal Ministry of Education and Research (BMBF). B.M. and R.S.M. acknowledge the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation program (Grant Agreement No. 101002868). Portions of this work were performed at GeoSoilEnviroCARS (University of Chicago, Sector 13), GeoSoilEnviroCARS was supported by the National Science Foundation – Earth Sciences (EAR-1634415). This research used resources from the Advanced Photon Source, a U.S. Department of Energy (DOE) Office of Science User Facility operated for the DOE Office of Science by Argonne National Laboratory under Contract No. DE-AC02-06CH11357. F.T. acknowledge support from the Knut and Alice Wallenberg Foundation (Wallenberg Scholar grant no. KAW-2018.0194). I.O. and M.P.A. thank UKRI Future Leaders fellowship Mrc-Mr/T043733/1 for the financial support. L.-T.S. acknowledges the Guangdong Basic and Applied Basic Research Foundation (Grant No. 2022a1515110404). Computations were enabled by resources provided by the National Academic Infrastructure for Supercomputing in Sweden (NAISS) and the Swedish National Infrastructure for Computing (SNIC) using Dardel at the PDC Center for High-Performance Computing, KTH Royal Institute of Technology and LUMI at the IT Center for Science (CSC), Finland partially funded by the Swedish Research Council through grant agreements no. 2022–06725 and no. 2018–05973. For the purpose of open access, the author had applied a Creative Commons Attribution (CC BY) license to any Author Accepted Manuscript version arising from this submission.

## Conflict of Interest

The authors declare no conflict of interest.

## Data Availability Statement

The data that support the findings of this study are available from the corresponding author upon reasonable request.

## Keywords

high hardness, high-pressure synthesis, single-crystal X-ray diffraction, tungsten nitrides, ultra-incompressible
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