Pressure-Driven Ne-Bearing Polynitrides with Ultrahigh Energy Density

Exploring the behavior of inert elements including He, Ne, Ar, Kr, and Xe is the key to understanding the formation and evolution of planets.^[1,2] These inert elements generally exist in gaseous form since they have typical closed-shell structures and can hardly react with other elements or compounds under ambient conditions. However, Dong et al. have successfully synthesized a stable Na₂He compound under high pressure.^[3] Recently, many theoretical works reported that the inert gas may react with other elements or compounds under high-pressure conditions (such as iron,^[4] iron peroxide,^[5] alkali metal oxide, sulfide compound,^[6] alkaline earth metal fluoride,^[7] or H₂O^[8–11]), which indicate that inert-element-stored compounds may exist in the planet's interior. Moreover, these compounds exhibit interesting properties, such as plastic and superionic states, which lead to potential applications in materials science.^[8–11] Thus, an increasing number of theoretical and experimental studies have been committed to investigating the compounds with inert elements.^[12–15]

Nitrogen is the most abundant element in the Earth's atmosphere and exists as the stable gaseous form of N₂ molecules with the strong triple N bond (N≡N) under ambient conditions. Because of the energy difference between a single bond (∼160 kJ/mol) and a triple bond (∼1 MJ/mol),^[16] it is difficult to convert N₂ molecules into polymeric nitrogen. On the other hand, polynitrogens with N–N single bonds can produce a large amount of energy and N₂ when they are thermally decomposed. Meanwhile, the rapid release of N₂ causes high pressure. Therefore, polynitrogens with N–N single bonds as high-energy-density materials may have important potential applications for military, industry, and engineering,^[17,18] and have become a hot spot in the field of new green energy sources.

Numerous efforts have been made to obtain polymeric nitrogen. The single-bonded cubic gauche phase (cg-N) of nitrogen was first predicted,^[19] and then was confirmed by experiments using laser-heated diamond anvil cells at a temperature above 2000 K and under the pressure above 110 GPa.^[20] Subsequent works also reported various polynitrogens under high-pressure conditions, such as layered Pba2,^[21] cage-like diamond N₁₀,^[22] metallic P4/nbm nitrogen,^[23] single-bonded nitrogen,^[24] and black-phosphorus-structure polynitrogen.^[25,26] However, synthesizing these polynitrogens require extremely high pressure and some are thermally metastable under ambient conditions. So far, much attention has been focused on the lower-pressure limits of thermodynamic stability of metal nitrides.^[27–32] Unfortunately, these metal nitrides do not contain pure nitrogen covalent bonds, but a mixture of ionic bonds and nitrogen covalent bonds. The result is that the energy density is not enough high for industrial applications. A remarkable observation is that inserting noble elements into the nitrogen system can significantly change the long-range Coulomb interactions and reduce the synthesis pressure of polynitrogen compounds.^[7] For instance, solid van der Waals (vdW) compound He(N₂)₁₁ was synthesized under a low pressure (9 GPa) at room temperature.^[33] Thereafter, many inert elements-nitrogen compounds with high-energy densities have been predicted, including HeN₄,^[34] HeN₁₀,^[35] and XeN₆.^[15] As an important member of inert elements, Ne atoms not only can trace the internal evolution of stars and the formation of solar nebulae,^[2] but also have an electronic structure similar to nitrogen, which allows Ne atoms to possibly occupy vacancies in the nitrogen polymer network. The solid vdW compound (N₂)₆Ne₇ with guest-host structure was successfully synthesized at the room temperature and at pressure of 8 GPa,^[36] but not found to contain polymeric nitrogen. It is still uncertain whether Ne and N can form new compounds with polymeric nitrogen under pressure.

In this work, to search for Ne-containing polynitrides, we systematically explored the Ne–N system under pressure via swarm-intelligence structure search. Three new Ne–N compounds with polymeric nitrogen are found: $R\bar{3}m$ NeN₆, P6₃/m NeN₁₀, and I4/m NeN₂₂. The ab initio molecular dynamics (AIMD) simulations and phonon spectra indicate that P6₃/m NeN₁₀ and I4/m NeN₂₂ are mechanically and dynamically stable above 500 K under the ambient pressure. In particular, after removal of Ne or Ne and N₂ dimers from NeN₂₂, the unique pure tetragonal polymeric nitrogen structures, t-N₂₂ and t-N₂₀ are obtained, and they are dynamically and thermally stable upon decompression to the ambient pressure. Remarkably, the energy densities of P6₃/m NeN₁₀, I4/m NeN₂₂, t-N₂₂, and t-N₂₀ are found to be 11.1, 11.5, 11.6, and 12.0 kJ/g, respectively, indicating that they are promising high-energy-density materials.

Calculation Details. For the crystal structure search, we employed the unbiased swarm intelligence structure prediction method as implemented in the CALYPSO code.^[37,38] Its validity has been widely confirmed by a variety of systems, from element solids to binary and ternary compounds.^[39–42] Structural optimizations and electronic property calculations were performed in the framework of the density functional theory within the Perdew–Burke–Ernzerhof (PBE)^[43] of generalized gradient approximation^[43] as implemented in the VASP package.^[44] The PBE functional was applied to all the calculations, and we have optimized the NeN₂₂ at 1 atm with the local-density-approximation functional. The resulting lattice parameters of NeN₂₂ are a = b = c = 6.0054 Å, which are smaller than those (a = b = c = 6.0869 Å) calculated using the PBE exchange-correlation functional. The electron-ion interaction was described by means of the all-electron projector augmented wave (PAW)^[45] with 2s²² p⁶ and 2s²² p³ valence electrons for Ne and N atoms, respectively. A kinetic-energy cutoff of 750 eV and a Monkhorst–Pack scheme^[46] with a k-point grid of 2π × 0.03 Å⁻¹ were adopted to ensure that total energy calculations converged to less than 1 meV per atom. To verify the dynamical stability of predicted structures, we carried out the phonon calculations via the finite displacement approach^[47] as performed in the Phonopy code.^[48] The vdW interactions are also taken into consideration by using DFT-D3 functional^[49,50] in VASP. Using AIMD within the NPT ensemble with a Langevin thermostat.^[51] The AIMD simulations were carried out within the 2 × 2 × 2 (176 atoms), 2 × 2 × 1 (184 atoms), 2 × 2 × 1 (176 atoms), and 2 × 2 × 1 (160 atoms) supercells for NeN₁₀, NeN₂₂, t-N₂₂, and t-N₂₀, respectively. AIMD simulation lasted for 7 ps with a time step of 1.0 fs, and the equilibrium structures were obtained from the last step of AIMD simulations. The electron localization function (ELF) was utilized to measure the degree of electron localization.^[52] Crystal orbital Hamilton populations (COHPs)^[53] as implemented in the LOBSTER program^[54] was used to quantitatively characterize the chemical bonding properties. The noncovalent interactions (NCIs) in molecular structures were analyzed by the CRITIC2 code.^[55,56] The steric NCIs are visualized through the Visual Molecular Dynamics software.^[57]

Results and Discussion. To determine the stable Ne–N phases, we focus on nitrogen-rich NeN_x (x = 1–10, 22) compounds and perform structure search at 1 atm, 50 GPa, and 100 GPa. It has been shown that nitrides containing noble elements can be stabilized under high pressure mainly due to the participation of the vdW effects.^[34,35] Therefore, the vdW interactions are also considered to calculate the formation enthalpies of each NeN_x structure with the lowest enthalpy at the corresponding pressure, where the formation enthalpy ΔH is defined as

$$\begin{eqnarray}&&\Delta H({{\rm{NeN}}}_{x})=[H({{\rm{NeN}}}_{x})-H({\rm{Ne}})-xH({\rm{N}})]/(1+x).\end{eqnarray} \tag{ 1 }$$

Here, H = U + PV is the enthalpy of each composition with U, P, and V being internal energy, pressure, and volume, respectively; H(NeN_x ) is the enthalpy per formula unit of NeN_x ; H(Ne) and H(N) represent the enthalpy per atom of elemental Ne and N, respectively; α-nitrogen and P4₁2₁2 structures are used for pure nitrogen.^[58,59] Meanwhile, $Fm\bar{3}m$ Ne as a reference phase is taken for the computation of formation enthalpy.^[60] Then, the resulting ΔH of each NeN_x at selected pressure is used to build the convex hull as shown in Fig. 1(a). The thermodynamically stable compounds are located on the convex hull (solid lines), whereas compounds lying on the dotted lines are energetically unstable. According to the convex hulls shown in Fig. 1(a) and the pressure-composition phase diagram illustrated in Fig. 1(b), we found three new stable phases: $R\bar{3}m$ NeN₆, P6₃/m NeN₁₀, and I4/m NeN₂₂. At 1 atm, there are no compounds showing negative formation enthalpies with respect to the mixture of Ne and N₂. With an increase in pressure, NeN₆ is found to be stable at 69 GPa. As pressure further increases, NeN₁₀ becomes energetically more favorable than NeN₆ or Ne and N₂ mixtures above 70 GPa, as shown in Fig. S1 in the Supporting Information. For the stoichiometry NeN₂₂ with the highest N content, it becomes thermodynamic stable at a higher pressure of 76 GPa, as shown in the inset of Fig. 1(b). In addition, it should be mentioned that (N₂)₆Ne₇ was successfully synthesized under high pressure,^[36] which offers the possibility of synthesizing our predicted Ne–N phases.

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NeN₆ is predicted to stabilize into a hexagonal structure with $R\bar{3}m$ symmetry [Fig. 2(a)]. In this structure, all nitrogen atoms have the equivalent 18h Wyckoff position. More interestingly, a planar N₆ ring with a bond length of 1.32 Å at 100 GPa appears in the structure. These nitrogen hexagons are connected through six N–N bonds with a distance of 1.43 Å and further makeup of the nitrogen network. In contrast, Ne atoms reside in the center of the hexagonal nitrogen unit. Further electron localization function calculation of NeN₆ shows that each nitrogen has a pair of lone electrons, and the electron localization around each N atom is stronger than that of the N–N covalent bond [Fig. S2(a)].

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More N-rich NeN₁₀ has a hexagonal structure with space group P6₃/m [Fig. 2(b)], in which N atoms have three inequivalent Wyckoff positions (2d, 6h, and 12i). Each nitrogen atom is located in a tetrahedron formed by three N atoms. Two kinds of nitrogen-nitrogen distances of 1.30 and 1.34 Å are found in the NeN₁₀ structure at 100 GPa, which are between the N–N single bond (1.45 Å) and N=N double bond (1.25 Å). Due to the different bond lengths, the N atoms constitute the highly distorted N₁₀ rings. Notably, each of the six N₁₀ rings contributes one bond with a bond length of 1.30 Å to form a regular hexagon (N₆) in the plane. Furthermore, the bonding feature of the N₆ is further supported by the ELF within the (001) plane (Fig. S2). It is noted that each N in N₆ hexagons have one lone pair of electrons, which reveals that the N₆ has six σ bonds in the sp² hybridization state. In addition, some of the N atoms in NeN₁₀ show the sp³ hybridizations or lone pair distribution [Fig. S3(a)]. Moreover, the Ne atoms are interspersed in the framework of N atoms. Such a structural character effectively increases the stability of the NeN₁₀ structure.

NeN₂₂, having the highest N content among the predicted Ne–N phases, is a tetragonal host-guest structure with space group I4/m [Fig. 2(c)]. I4/m NeN₂₂ consists of I4/mmm Ne and I4/m N sublattices, in which guest atoms (Ne) occupy the 2a position of the sublattice with I4/mmm symmetry, whereas N atoms constituting guest N₂ and host N₂₀ occupy four inequivalent Wyckoff positions (8h, 8e, 16i, and 16i) of N sublattice with space group I4/m N₂₂ named t-N₂₂, Interestingly, the obtained host N₂₀ structure from NeN₂₂, termed t-N₂₀, still maintains the symmetry of I4/m by removing both Ne and N₂. Notably, t-N₂₀ has a channel parallel to the c crystallographic axis [Fig. 2(d)]. In the NeN₂₂, N₂ dimers are symmetrically equivalent. In addition, the bond length in the N₂ is about 1.10 Å, which is similar to that of a triple bond in -N₂.^[58,59] Each atom of N₂₀ bonded to the other three N atoms with the distance of 1.33–1.35 Å in the polyatomic network structure. The nearest neighboring Ne and N atoms have distance of approximately 2.08 Å, while the shortest distance between the N₂ dimer and the t-N₂₀ is about 2.20 Å. The exotic t-N₂₀ framework connects with the surface of irregular N₁₂ and N₁₀ rings. N₁₂ rings with channels parallel to the c-axis, while the bond of the N₂ dimers is also parallel to the c-axis. Such a structural character is conducive to the separation of Ne atoms and N₂ from the channel without destroying the N₂₂ frame structure. Because the experiments show that guests may be sufficiently removed to leave behind metastable empty clathrates,^[14,61] guest-free Si,Ge-clathrates, and H₂O have indeed been obtained.^[9,62,63] Based on the work reported previously, we can not only obtain t-N₂₂ by removing guest Ne, but also acquire t-N₂₀ via the removal of guest Ne and the N₂ dimer from the natural pores of NeN₂₂. We have optimized the pure tetragonal polymeric nitrogen structures t-N₂₂ and t-N₂₀ at 1 atm. The final lattice constants of t-N₂₂ and t-N₂₀ are a = b = c = 6.0183 Å and a = b = c = 5.9487 Å, respectively, which are smaller than the lattice constants (a = b = c = 6.0869 Å) of the NeN₂₂ at 1 atm. The lattice constants of t-N₂₂ and t-N₂₀ are only about 1% and 2% smaller than that of Ne₂₂, respectively. Therefore, the removal of the guest atom from NeN₂₂ results in a slight change in the lattice constant. We also observed the effect of pressure on the lattice by calculating the pressure-dependent lattice constants of NeN₂₂, t-N₂₂, and t-N₂₀ (Fig. S4). The results show that the lattice constants of NeN₂₂, t-N₂₂, and t-N₂₀ gradually decrease with increasing pressure. The lattice constants of t-N₂₂ and t-N₂₀ are smaller than that of NeN₂₂ at high pressure. The ELF shows that NeN₂₂ also has lone pairs [Fig. S3(b)]. Overall, they show increased polymerization characteristics with increasing N content. More structural details are listed in Table S1.

These nitrogen-rich P6₃/m NeN₁₀ and I4/m NeN₂₂ with peculiar structures further motivate us to explore their mechanical properties. Based on the Born stability criteria,^[64] the calculated elastic constants via the stress-strain approach^[65] of hexagonal P6₃/m NeN₁₀ and tetragonal I4/m NeN₂₂ verify that they are mechanically stable at ambient pressure (Table S2). Furthermore, their bulk modulus B, shear modulus G, Young's modulus E, and Poisson's ratio ν are calculated using the Voigt–Reuss–Hill approximation.^[66] As shown in Table S2, both P6₃/m NeN₁₀ and I4/m NeN₂₂ have large bulk modulus, shear modulus, Young's modulus, and low Poisson's ratio, indicating that they are stiff materials. Interestingly, based on Gao's model.^[67] the Vickers hardness of P6₃/m NeN₁₀ is estimated to be 31.3 GPa, which is larger than the high-hardness standard (30 GPa).^[68] This result implies that NeN₁₀ is also a promising candidate of high-hardness materials. In contrast, the hardness of I4/m NeN₂₂ (26.4 GPa) is slightly lower than that of P6₃/m NeN₁₀.

We analyzed the dynamic stabilities of NeN₁₀ and NeN₂₂ by calculating their phonon spectra at 1 atm [Figs. 3(a) and 3(b)]. Interestingly, there are no negative phonon frequencies below 0 THz in the respective Brillouin zones of NeN₁₀ and NeN₂₂, which confirms that they are dynamically stable under ambient pressure. Based on the analysis of the phonon density of states (PHDOS) of NeN₁₀ [Fig. S5(a)], we found that the phonon dispersion curve can be split into three groups: low-frequency acoustic modes (below 8 THz), low-frequency optic modes (8–24 THz), and high-frequency optic modes (24–42 THz). The acoustic modes primarily come from the contribution of vibrations of Ne atoms. The low-frequency optic vibrational modes are mainly contributed by the coupled vibrations between Ne and N atoms, while the high-frequency vibrational modes are dominated by N atoms. In contrast, the phonon modes corresponding to N atoms in NeN₂₂ dominate the whole frequency region compared to those of Ne atoms, which is closely related to the nitrogen framework. Notably, NeN₂₂ has an independent optical branch offered by N atoms at about 75 THz [Fig. S5(b)]. In addition, the absence of imaginary frequencies in the Brillouin zone indicates that P6₃/m NeN₁₀ and I4/m NeN₂₂ also exhibit good dynamic stability at 100 GPa (Fig. S6). NeN₆ becomes dynamically stable at 100 GPa [Fig. S7(a)]. However, it becomes unstable at 1 atm, so we will not discuss its property further. Meanwhile, we further remove the Ne atoms from the framework of P6₃/m NeN₁₀ and I4/m NeN₂₂ and explore the naked nitrogen properties. Moreover, the phonon dispersion curves show that the obtained nitrogen structures P6₃/m N₁₀, t-N₂₂, and t-N₂₀ remain dynamically stable under ambient pressure [Fig. S6 in the Supporting Information, and Figs. 3(c) and 3(d)]. Surprisingly, they remain dynamically stable under ambient pressure, in which t-N₂₂ and t-N₂₀ with peculiar nitrogen structures are our focus.

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To confirm the thermal stability of NeN₁₀, NeN₂₂, t-N₂₂, and t-N₂₀, we performed molecular dynamics simulations at 1 atm and at different temperatures. As shown in Fig. S8, the total energies of these structures have no significant fluctuations with the evolution of time, indicating that they are in equilibrium at considered temperatures. To clearly reveal the efficiency of molecular dynamics simulations, the equilibrium structures were obtained from the last step of AIMD simulations. The radial distribution functions (RDFs) examine the thermal stability of NeN₁₀, NeN₂₂, t-N₂₂, and t-N₂₀ under ambient pressure and at 300 K, where the sharp peaks on the far left of each line represent the nearest N–N, Ne–N, and Ne–Ne distances, respectively [Figs. 3(e)–3(h)]. Generally, the closest distances between atoms of equilibrium structure have little change compared to the original structure, proving that this structure is thermally stable. For NeN₂₂, the first sharp peak of RDF is at approximately 1.09 Å, which matches well with the shortest N–N bond length of the N₂ dimer of the original structure (vertical dashed line). The second sharp peak representing the second shortest bond between nitrogen atoms is at 1.39 Å, which is consistent with the second shortest N–N bond length of the original structure. The first sharp peak of Ne–N is at approximately 2.31 Å, which agrees well with the shortest distance between Ne and N atoms of the original structure. Remarkably, the nearest N–N, Ne–N, and Ne–Ne distances have little change compared to those in the initial structures of NeN₁₀, NeN₂₂, t-N₂₂, and t-N₂₀, which implies that they remain solid and keep thermal stability. As also can be seen from the insets in Figs. 3(e)–3(h), the terminal structures (NeN₁₀, NeN₂₂, t-N₂₂, and t-N₂₀) from the last step of the AIMD simulations still retain their structural integrity. Furthermore, we performed the AIMD simulations at higher temperatures by adopting the initial structure. The AIMD simulations for NeN₁₀ at 1000 K and NeN₂₂ at 500 K [Figs. S9(a) and S9(b)] prove that they are still stable at higher temperatures. The above dynamic and thermal stability analyses of NeN₁₀ and NeN₂₂ indicate that they can be quenched to ambient conditions once synthesized at high pressure. In addition, we performed AIMD simulations of NeN₂₂ at a pressure of 76 GPa and a temperature of 300 K. As shown in Fig. S10(a), there is only a tiny difference in the simulated interatomic distance for the terminal structure compared to the original structure. The result shows that NeN₂₂ remains thermally stable at high pressure. In view of the above analysis, we prove that the ambient pressure polymerized nitrogen phases can be synthesized by removing the guest atoms from I4/m NeN₂₂.

The unique crystal structures in NeN₁₀ with N₆ and N₁₀ rings and NeN₂₂ with the N₂ dimers and N₂₀ framework further stimulate us to study their electronic properties. Strikingly, the calculated electronic bands and projected density of states (PDOS) of NeN₁₀ and NeN₂₂ at 1 atm reveal that they are semiconductors with large direct bandgaps of 2.8 and 3.0 eV, respectively (Fig. S11). As pressure increases up to 100 GPa, the increased band gaps of NeN₁₀ and NeN₂₂ become 3.8 and 4.6 eV, respectively [Figs. S12(a) and 4(a)]. In addition, NeN₂₂ was found to have a bandgap of 4.3 eV at an initial thermodynamically stable pressure of 76 GPa [Fig. S10(b)]. As illustrated in PDOS of Fig. S11, the obvious overlap between N s and N p orbitals exists in the valence band region, proving the strong coupling between N atoms and supporting the structural stability. Further, Bader charge analysis shows that the charge transfer from each Ne atom to N atoms in these two structures is less than 0.05|e| in NeN₁₀ and NeN₂₂ at 1 atm (Tables S3 and S4), which indicates that adding Ne has almost no effect on the electronic distribution of the N framework. Additionally, charge transfer could hardly be observed between the Ne and N atoms of NeN₁₀ and NeN₂₂ with further increasing pressures. However, for NeN₂₂, there are slightly large charge transfers from N₂₀ cages to N₂ dimers as pressure increases (Table S4), which indicates that the N atoms in NeN₂₂ can act as both cations and anions.

To investigate the reasons for the bonding characteristics of NeN₁₀ and NeN₂₂, we calculated their minus projected COHP (–pCOHP) at 100 GPa, as shown in Figs. 4(b) and S12(b). In general, the positive and negative –pCOHPs characterize the bonding and antibonding states, respectively. The –pCOHP for averaged nitrogen-nitrogen pair (N–N) [Fig. 4(b)] demonstrates that there is a bonding state between nitrogen atoms in the N₂ dimers, while the antibonding interactions between the shortest N–N of N₂₀ cage or N₂ dimers and N₂₀ cages are both negative in the energy range from −6 to 0 eV below the top of the valence bands. For NeN₁₀, the integrated COHP (ICOHP) values of Ne–N and N–N pairs are 0.01 and −12.90 eV/pair up to the Fermi level, respectively. For NeN₂₂, the ICOHP values of the N–N bond in N₂ dimer and the nearest N–N bond in N₂₀ up to the Fermi level are −8.86 and −24.54 eV/pair (Table S5), respectively, which shows that the triple bond in N₂ dimer is stronger than both the single and the double bond in N₂₀. The ICOHP values among N₂₀, Ne, and N₂ dimers are close to 0 eV/pair, further indicating that Ne and N₂ can be removed.

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Although the vdW interactions in nitrides bearing noble elements have been studied, there are no quantitative studies on the weak interactions in nitrides bearing noble elements. At the same time, due to the low electron density, the intricate weak noncovalent interactions (NCIs) cannot be identified via some analysis algorithms such as Bader charge transfer and ELF. Therefore, we introduce the reduced density gradient (RDG) to gain additional insight into the stable mechanism of the P6₃/m NeN₁₀ and host-guest structure I4/m NeN₂₂ at 100 GPa [Figs. S12(c) and 4(c)]. RDG is defined as

$$\begin{eqnarray}&&s={[2(3{\pi }^{2})]}^{2}|\Delta \rho {|}^{-4/3},\end{eqnarray} \tag{ 2 }$$

where ρ represents the electron density. To distinguish the different types of interactions, we multiplied RDG by the sign of the second Hessian eigenvalue [sign(λ₂)] of Δ2ρ. The low-density [sign(λ₂)ρ (arb. units)] and low-gradient [s (arb. units)] spikes indicate the existence of weak interactions. The two-dimensional (2D) and related three-dimensional (3D) graphs of RDG can clearly show the NCI regions [Figs. 4(c), 4(d), S12(c), and S12(d)]. The areas surrounded by solid red lines in 2D graphs of RDG represent the vdW interactions in NeN₁₀ and NeN₂₂, corresponding to green contours plotted in 3D graphs of RDG. The cyan and red counters in 3D graphs of RDG display attractive and repulsive interactions, respectively. As seen in Fig. S12(d), the attractive interaction is stronger than the repulsive one around the Ne atoms in NeN₁₀. For NeN₂₂, button-like red contours are located around the Ne atoms and the N₂ dimers, indicating that the repulsive interaction is stronger than the attractive interaction. The results are consistent with the –pCOHP, also indicating that guest atoms can be removed in NeN₂₂.

The decomposition enthalpies of P6₃/m NeN₁₀ and I4/m NeN₂₂ relative to Ne and nitrogen at ambient pressure are 1.61 and 1.64 eV/atom, respectively, indicating that they are potential high-energy-density materials. Thus, the energy density and explosive performance of NeN₁₀ and NeN₂₂ are further studied, in which the energy of nitrogen molecule is adopted.^[58,59] NeN₁₀ and NeN₂₂ can be detonated in the following ways: NeN₁₀ (solid) → Ne (gaseous) + 5N₂ (gaseous), NeN₂₂ (solid) → Ne (gaseous) + 11N₂ (gaseous). Further calculations show that the energy densities (E_d) of NeN₁₀ with density of 3.24 g/cm³ and NeN₂₂ with a density of 3.17 g/cm³ are estimated to be approximately 11.1 and 11.5 kJ/g, respectively, which are significantly larger than trinitrotoluene (TNT, 4.3 kJ/g) and 1, 3, 5, 7-tetrazoctane (HMX, 5.7 kJ/g).^[69] More interestingly, t-N₂₂ and t-N₂₀ exhibit high-energy densities of 11.6 and 12.0 kJ/g, respectively, which are higher than those of all reported polynitrogen materials. Additionally, as shown in Table 1, we also estimate the explosive performance including detonation velocity (V_d) and pressure (P_d) of P6₃/m NeN₁₀, I4/m NeN₂₂, t-N₂₂, and t-N₂₀ through the Kamlet–Jacobs empirical equation.^[70] Its validity has been widely confirmed.^[71–75] Using these equations, we also calculated detonation velocity and pressure for TNT and HMX, where the monoclinic P2₁/c TNT and P2₁/c HMX are adopted.^[76,77] The differences between the calculated and experimental values for TNT and HMX are within acceptable limits (Table 1), indicating that our calculation methods are applicable. The Kamlet–Jacobs empirical equations are as follows:

$$\begin{eqnarray}&&{V}_{{\rm{d}}}=1.01{(N{M}^{0.5}{E}_{{\rm{d}}}^{0.5})}^{0.5}(1+1.30\rho),\end{eqnarray} \tag{ 3 }$$

$$\begin{eqnarray}&&{P}_{{\rm{d}}}=15.58{\rho }^{2}N{M}^{0.5}{E}_{{\rm{d}}}^{0.5}.\,\end{eqnarray} \tag{ 4 }$$

Here, N, M, and ρ represent moles of N₂ per gram of explosives (mol/g), the molar mass for N₂ gas (28 g/mol), and the density (g/cm³), respectively. A large amount of N₂ is released when NeN₁₀ and NeN₂₂ explode, resulting in a huge P_d and detonation velocity. We found that NeN₁₀ and NeN₂₂ release a huge detonation velocity of about 3 times higher than that of TNT and an explosion pressure of about 14 times than that of TNT. Notably, the calculated V_d of t-N₂₂ and t-N₂₀ (22.82 and 22.09 km/s) are approximately 2 times higher than that of TNT (6.90 km/s) and twice the value of HMX (9.10 km/s).^[69,70] P6₃/m NeN₁₀, I4/m NeN₂₂, t-N₂₂, and t-N₂₀ can be considered as candidates for high-energy-density materials.

In summary, to obtain high-energy-density Ne-containing nitrides, we have systematically studied Ne–N systems under high pressure by exploiting the first-principles swarm-intelligence structure search and calculated the convex hull of the Ne–N systems at 1 atm, 50 GPa, and 100 GPa. Strikingly, three previously unknown thermodynamically stable Ne–N phases are determined: $R\bar{3}m$ NeN₆, P6₃/m NeN₁₀, and I4/m NeN₂₂. Introducing Ne atoms into a pure nitrogen system can greatly reduce the synthesis pressure to form single and double N bonds compared to the synthesis with pure nitrogen. The predicted structures exhibit various forms of nitrogen: molecular N₂, N₆ ring, N₁₀ ring, and N₂₀. Interestingly, the reduced density gradient exhibits the weak non-covalent interactions between the Ne and N atoms, which stabilize the guest atoms within the host framework. In particular, NeN₁₀ and NeN₂₂ are dynamically and mechanically stable under ambient pressure. Based on the unique structure of I4/m NeN₂₂ and weak interactions between host and guest, we propose to remove Ne or Ne and N₂ dimers in NeN₂₂ from the natural channels of the structure, and the unique pure tetragonal polymeric nitrogen structures t-N₂₂ and t-N₂₀ are obtained. Furthermore, the nitrogen framework in NeN₂₂ remains dynamically stable under ambient pressure after the removal of the Ne atom or Ne and N₂. The AIMD calculations suggest that NeN₁₀ and NeN₂₂ are thermally stable up to 1000 and 500 K under ambient pressure, respectively. More importantly, these results indicate that they are potentially quenchable to ambient conditions. The estimated energy density of NeN₁₀, NeN₂₂, t-N₂₂, or t-N₂₀ is more than 2 times larger than that of TNT. In addition, the detonation velocity and the detonation pressures of NeN₁₀, NeN₂₂, t-N₂₂, and t-N₂₀ are significantly larger than those of TNT and HMX. The results demonstrate that P6₃/m NeN₁₀, I4/m NeN₂₂, t-N₂₂, and t-N₂₀ are promising high-energy-density materials. Our work provides insights into the formation and properties of Ne–N compounds and deepens the understanding of the evolution of planets.

Acknowledgments