The properties of cg-N with point defects and an interface are investigated based on the first-principles method. Our results show that at 0 GPa, the stability of cavities depends on their size. A smaller cavity has higher stability than the larger case. The decomposition of N_{2} molecules mainly occurs on the (110) surface of the cavity. However, the decomposition process will be suppressed by applying high-pressure. For the interface constructed by (110) surfaces, N_{2} molecules will be released at low pressure, and polymerization of N_{2} molecules with surfaces is triggered by loading pressures of 80–100 Gpa, giving rise to a stable polymerized interface, which is also stable after decreasing the pressure to 0 GPa. The results indicate that the existence of polymeric nitrogen networks can enhance the polymerization of N_{2} molecules at low-temperature.

## I. INTRODUCTION

Nitrogen in nature mainly forms nitrogen gas with N≡N triple bonds. The bond energy of the N≡N triple bond is 954 kJ/mol, which is one of the strongest chemical bonds. The bond energy of the N=N double bond and the N–N single bond is 418 and 160 kJ/mol, respectively. Polymeric nitrogen formed by N–N single or N=N double bonds will release a huge energy when it decomposes into triple-bonded nitrogen, and the energy density is about 5 times higher than that of the traditional energy material TNT. Therefore, polymeric nitrogen can be used as a potential high energy density material (HEDM). Over the years, polymeric nitrogen has drawn considerable attention and has been extensively studied by theoretical and experimental approaches.^{1–18} High-pressure is a popular way to enhance the interaction between N_{2} molecules and to synthesize polymeric nitrogen with N–N single or N=N double bond.

Nitrogen is gaseous under ambient conditions, and it solidifies into a molecular crystal with increasing pressure. As early as 1985, McMahan and LeSar predicted the formation of non-molecular phases of nitrogen under 100 GPa.^{18} Nellis *et al.* first observed the dissociation of nitrogen molecules experimentally.^{19} Based on the first-principles method, researchers had found that polymeric nitrogen structures consisting of multiple atoms are more energetically stable than the known molecular structures under high-pressure.^{1–8} Later, Mailhiot *et al.* predicted that cubic gauche polymeric nitrogen (cg-N) has the lowest enthalpy and becomes the most stable structure at about 50 GPa.^{20} Besides, other forms of polymeric nitrogen were also predicted by theoretical simulations.^{21} Until 2004, cg-N was experimentally synthesized by compressing nitrogen gas at a high-temperature of 2000 K and high-pressure of 110 GPa based on the diamond anvil cell.^{22} Since the successful synthesis of cg-N, several other polymeric nitrogen compounds, such as LP-N, HLP-N, and BP-N, were obtained experimentally under high-pressure conditions.^{23–28} However, these polymeric nitrogen compounds cannot be stabilized at ambient pressures, which impedes their practical application as an HEDM.

In order to realize the application of polymeric nitrogen, researchers have tried several ways to improve the stability of polymeric nitrogen. In the process of material synthesis, defects are formed inevitably, which may affect the properties of materials significantly. The cg-N structure exhibits a N–N single bond and a threefold coordination, which is dynamically stable at 0 GPa in the absence of imaginary frequency.^{8} It is implied that cg-N could be metastable at ambient pressure. However, polymeric cg-N is decomposed into nitrogen gas when the pressure is down to 42 GPa.^{22} Investigating the effects of point defects and the interface on the stability of the cg-N structure can help us understand the reasons for the decomposition of cg-N, which will be of great significance for finding ways to enhance its stability. Therefore, the properties of cg-N with point defects and an interface are studied by first-principles calculations.

## II. METHODS

All calculations are carried out based on the Car–Parrinello second kind molecular dynamics program (CP2K)^{29} adopting the DZVP-MOLOPT-SR-GTH basis set. The structures are relaxed based on the first-principles method combined with the Generalized Gradient Approximation (GGA) exchange correlation functional in Perdew–Burke–Ernzerhof (PBE) form.^{30} The energy cutoff is set to be 400 Ry, and rel_cutoff is set to be 80 Ry. The Brillouin zone only at the Γ point is used since the supercell is large. The convergence threshold of the density matrix in the self-consistent field algorithm is set to be 3.0 × 10^{−6} eV. The structure is optimized by using a cell optimization method that keeps the crystal angle unchanged. The Broyden–Fletcher–Goldfarb–Shanno (BFGS) algorithm is employed for structural relaxation, and all atomic positions are fully relaxed. The trust radius in the BFGS algorithm is set at 0.2 Å, and the maximum force and RMS force are set to 4.5 × 10^{−4} and 3 × 10^{−4} eV/Å, respectively.

## III. RESULTS AND DISCUSSIONS

The cg-N crystal with a cubic symmetry has eight nitrogen atoms in the unit cell. A 5 × 5 × 5 supercell containing 1000 atoms is used for studying the properties of point defects, which are constructed at the center of the supercell. The same crystal plane of cg-N can have several different surfaces with different atomic arrangements. Previous work had demonstrated that at 0 GPa, the desorption barrier of the (110) plane is lower among the three low-index surfaces of cg-N,^{8} implying that the (110) plane is easier to dissociate. Therefore, we construct cavities with more (110) planes. For this purpose, the cuboid cavity is relatively rotated in the initial unit cell. The structures with defects after rotation and the crystal planes selected are shown in Fig. 1. For the (110) crystal plane, four different kinds of surfaces are constructed and named as 110a, 110b, 110c, and 110d. For the (100) crystal plane, two surfaces 110a and 110b are constructed, as shown in Figs. 1(b) and 1(c), where two types of cuboid cavities (smaller and larger one) are constructed at the center of the supercell. The size of the smaller (larger) cuboid cavity is 3.57 Å (6.25 Å), 3.57 Å (5.05 Å), and 3.15 Å (6.25 Å) along the *x*, *y*, and *z* axes, respectively. The number of atoms in the supercell with the smaller (larger) cavity is 994 (968). To minimize the interaction between defects, the large supercell with a lattice of 19.01 Å is used. Furthermore, the center position of the supercell was selected to construct defects, which expand almost evenly in six directions. Therefore, the distance between defects is large enough, and the interaction between defects is marginal.

After full structural relaxation at 0 GPa, as shown in Fig. 2(a), we find that the surfaces around the smaller cavity is stable and do not release N_{2} molecules since the size of the cavity is small. In contrast, for the supercell with a larger cavity, six N_{2} molecules escape form the surfaces at 0 GPa. The results indicate that small free surfaces in cg-N at 0 GPa are stable. However, the free surfaces will start to decompose into N_{2} molecules when the size of the free surface becomes larger. It is interesting to answer the following question: how about the stability of the large cavity at high-pressure? To clarify this, a perfect cg-N crystal is relaxed to a pressure of 100 GPa, and then the 32-atom defect cluster is removed to reoptimize the structure. The structure before and after structural relaxation is shown in Figs. 2(c) and 2(d), respectively, where we can find that only one N_{2} molecule is decomposed from the free surface. This result shows that high-pressure can suppress the decomposition of free surfaces in cg-N. In the following paragraph, we will discuss the origin of decomposed N_{2} molecules.

Based on above-mentioned results, we analyzed the decomposition process of the surface at 0 and 100 GPa. At 0 GPa, as shown in Fig. 3, the surface where the N_{2} molecules decomposed first is the 110d surface, followed by the 110b surface, and then the 100a surface. For the case of 100 GPa, as shown in Fig. 2, the molecules in the red box are the decomposed N_{2} molecules during the structure optimization process, and they decompose from the 110d surface. It can be concluded that nitrogen atoms on the (110) surface can decompose to N_{2} molecules more easily than those on the (100) surface, which indicates that the (110) surface is less stable than the (100) surface.

The decomposition of N_{2} molecules is sensitive to the surface; therefore, it is interesting to explore the stability of cg-N with an interface, especially the interface formed by the (100) surfaces, which can decompose into N_{2} molecules easily. As shown in Fig. 4, 110b and 110d surfaces are used to construct the 110b–110d interface with unit cell parameters of *a* = 11.40 Å, *b* = 10.75 Å, *c* = 27.01 Å, *α* = *β* = *γ* = 90°, and *V* = 3314.13 Å^{3}. To construct the 110b–110d interface, we alternately delete atoms on both sides of the 110b surface (Fig. 4). At 0 GPa, the 110b–110d interface become unstable, and decomposed N_{2} molecules are found between the boundaries, as shown in Fig. 4. The structure is separated into two (left and right) parts by decomposed N_{2} molecules.

In order to investigate the effects of pressure on the stability of the 110b–110d interface, we optimized its structure by gradually increasing the pressure to 100 GPa, and the relaxed structures at high-pressure are shown in Fig. 4. With increasing pressure, the unit cell parameters and bond lengths of the 110b–110d interface are gradually decreased, and at the same time, the arrangement of the decomposed N_{2} molecules is gradually becoming more orderly (Fig. 5). The evolution of the bond length of N_{2} molecules is shown in Fig. 6, where we can find that at pressures ranging from 0 to 80 GPa, the bond length of N_{2} molecules is around 1.11–1.13 Å, which is comparable to the bond length of the N≡N triple bond. The results indicate that up to pressures as high as 80 GPa, decomposed N_{2} molecules maintains the N≡N triple bond and do not bond with surfaces. As shown in Fig. 5, the two separated parts are not connected to each other at a pressure of 80 GPa.

With pressure increasing to 100 GPa, the decomposed N_{2} molecules form bonds with the surfaces, giving rise to a polymerized interface. The bond length of N_{2} molecules increases suddenly to 1.22–1.23 Å, similar to the bond length of the N=N double bond. Furthermore, the bond lengths of N between N_{2} molecules and surfaces range from 1.32 to 1.43 Å, which are comparable to the bond length of the N–N single bond, indicating that polymerization between the N_{2} molecules and surfaces occurs. A stable interface with both N=N double and N–N single bonds is obtained. We can preliminarily conclude that with the networks of the polymeric nitrogen bond as the seed, the polymerization of N_{2} molecules can be triggered by applying 80–100 GPa pressure at low-temperature.

In order to further analyze the stability of the polymerized interface under low-pressure conditions, we gradually decrease the pressure from 100 to 0 GPa with full structural optimization. The results show that as the pressure gradually decreases, the length of the N–N bond at the polymerized interface gradually increases (Fig. 6) and there is no atomic desorption at the polymerized interface (Fig. 5). The bonds of N_{2} molecules (between N_{2} molecules and surfaces) have the bond lengths comparable to those of the N=N double bond (N–N single bond) with pressure decreasing to 0 GPa. The polymerized interface is stable at ambient pressure. For the established stable 110b–110d polymerized interface, we calculate its partial density of states at 0 GPa, and the result is shown in Fig. 7, together with the partial density of states of perfect cg-N. The perfect cg-N is a semiconductor, and by introducing an interface, its bandgap is significantly reduced to 0.695 eV. The density of states in the bandgap primarily contributes to the *p*-orbitals of nitrogen atoms at the interface.

## IV. CONCLUSION

Based on the first-principles calculations, the properties of cg-N with cavities and an interface are investigated with a supercell containing ∼1000 nitrogen atoms. At 0 GPa, the smaller cavity is stable; however, the larger one will release N_{2} molecules. By analyzing the decomposition process, we find that the released N_{2} molecules come mainly from the (110) surface. The decomposition will be suppressed by pressure, indicating that the stability of cavities in cg-N will be increased by pressure. The interface constructed by two (110) surfaces will release N_{2} molecules as well, and the N_{2} molecules still exist after increasing the pressure to 80 GPa. Furthermore, the polymerization between N_{2} molecules and surfaces is triggered by applying 100 GPa pressure, and the polymerization is still stable after decreasing the pressure to 0 GPa.

## ACKNOWLEDGMENTS

This work was supported by the National Natural Science Foundation of China (NSFC), under Grant Nos. U2030114, and the CASHIPS Director’s Fund. The calculations were partly performed at the Center for Computational Science of CASHIPS, the ScGrid of the Supercomputing Center and Computer Network Information Center of the Chinese Academy of Sciences, and the Hefei Advanced Computing Center.

## AUTHOR DECLARATIONS

### Conflict of Interest

The authors have no conflicts to disclose.

### Author Contributions

**Zhenyang Zhai**: Data curation (equal); Investigation (equal); Writing – original draft (equal). **Guo Chen**: Data curation (equal); Software (equal). **Jie Zhang**: Writing – review & editing (equal). **Xianlong Wang**: Conceptualization (equal); Supervision (equal). **Zhi Zeng**: Conceptualization (equal).

## DATA AVAILABILITY

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

## REFERENCES

*ab initio*study

_{2}N

_{2}at high pressures