The New High-Pressure Phases of Nitrogen-Rich Ag–N Compounds

The high-pressure phase diagram of Ag–N compounds is enriched by proposing three stable high-pressure phases (P4/mmm-AgN2, P1-AgN7 and P-1-AgN7) and two metastable high-pressure phases (P-1-AgN4 and P-1-AgN8). The novel N7 rings and N20 rings are firstly found in the folded layer structure of P-1-AgN7. The electronic structure properties of predicted five structures are studied by the calculations of the band structure and DOS. The analyses of ELF and Bader charge show that the strong N–N covalent bond interaction and the weak Ag–N ionic bond interaction constitute the stable mechanism of Ag–N compounds. The charge transfer between the Ag and N atoms plays an important role for the structural stability. Moreover, the P-1-AgN7 and P-1-AgN8 with the high-energy density and excellent detonation properties are potential candidates for new high-energy density species.

Silver nitrides have received much attention for their outstanding chemical and physical properties, such as the energetic explosive, propulsion application, gas generators, photographic materials, etc. [62][63][64]. Recently, the armchair-antiarmchair N-chain and N 5 ring structures are severally reported for AgN 3 and AgN 5 /AgN 6 compounds [65,66]. Beyond that, no other new silver nitrides with the high-pressure polymeric structures have been reported. Thus, a detailed high-pressure study that considers the different stoichiometry in silver nitrides is necessary for exploring new polynitrogen polymeric structures.

Computation Details
The structural research has been performed by the particle swarm optimization methodology implemented in the CALYPSO structure prediction method [67]. The structure optimizations and property calculations have been carried out by the Vienna ab initio simulation package (VASP) code [68]. The generalized gradient approximation (GGA) with the Perdew-Burke-Ernzerhof (PBE) exchange-correlation function has been employed for the first-principles calculations [69][70][71]. The 4d 10 5s 1 and 2s 2 2p 3 are treated as the valence electrons of Ag and N atoms, respectively. In order to ensure that the enthalpy is converged to less than 1 meV/atom, the cutoff energy of Projector Augmented Wave (PAW) pseudopotential and the Monkhorst-Pack k-mesh density are severally set to 520 eV and 2π × 0.03 Å −1 in the calculation. The ∆H f of each Ag-N structure is calculated by using the following equation: have been calculated by using the finite displacement approach through the PHONOPY code [72]. The 2 × 2 × 2 supercell with the lattice size of about 10 Å is constructed in the calculation of phonon. The dissociation energies are calculated by considering the following decomposition paths: AgN x → Ag + x/2N 2 . The P6 3 /mmc phase of Ag and Pa 3 phase of N 2 are the decomposition productions, respectively. The detonation velocity and detonation pressure have been calculated by using the Kamlet-Jacobs simi-empirical equation: V d = 1.01(NM 0.5 E d 0.5 ) 0.5 (1 + 1.30ρ) and P d = 15.58ρ 2 NM 0.5 E d 0.5 . N represents the moles of gas per gram of AgNx, M represents the average molar mass of gas products, E d is the detonation chemical energy, and ρ is the mass density.

Results and Discussion
Eight stoichiometries of AgN x (x = 2, 3,4,5,6,7,8,10) are considered in the structural research with the simulation cells containing 1, 2 and 4 formula units (f.u.). The prediction for each stoichiometry is carried out at three pressures (50, 100 and 150 GPa). As shown in Figure 1a-c, the formation enthalpies (∆H f ) of Ag-N compounds are presented in the thermodynamic convex hull. The solid squares on the convex hull are the thermodynamically stable phases, while the ones that deviate from the convex hull are the metastable/unstable phases. For the AgN 2 stoichiometry, we found the thermodynamically stable P4/mmm phase at 100 and 150 GPa. At 50 and 100 GPa, the reported P-1-AgN 3 in Ref. [65] is also found in this work. For the AgN 7 stoichiometry, the thermodynamically stable P1 and P-1 phases are found at 50 GPa and 100/150 GPa, respectively. No thermodynamically stable phases are found for the rest of the stoichiometries (AgN 4 , AgN 5 , AgN 6 , AgN 8 and AgN 10 ). For the presented high-pressure phase diagrams of AgN 2 and AgN 7 in Figure 1d, we can see that the P4/mmm-AgN 2 is thermodynamically stable in the pressure region of (75-150 GPa). The P1-AgN 7 and P-1-AgN 7 are thermodynamically stable in the pressure ranges of (25-75 GPa) and (125-150 GPa), respectively. The dynamical stability of AgN 2 and AgN 7 are further evaluated by the phonon dispersion. As shown in Figure 2, no imaginary frequency is found throughout the Brillouin zone, indicating that the P4/mmm-AgN 2 , P1-AgN 7 and P-1-AgN 7 are dynamically stable at 100, 50 and 150 GPa, respectively. Interestingly, the presented phonon dispersion curves in Figure 3 show that the P-1-AgN 4 and P-1-AgN 8 are dynamically stable at 150 GPa, indicating that they are the metastable phases. Moreover, the mechanical stabilities of P4/mmm-AgN 2 , P1-AgN 7 , P-1-AgN 7 , P-1-AgN 4 and P-1-AgN 8 are evaluated by the calculation of elastic constants (Table 1). According to the mechanical stability criteria of tetragonal structure of (C 11 > |C 12 |, 2C 13 2 < C 33 (C 11 + C 12 ), C 44 > 0), we know that the tetragonal P4/mmm-AgN 2 is mechanically stable. The mechanical stability criteria of monoclinic structure are shown as follows [73]: C 11 > 0, C 22 > 0, C 33 > 0, C 44 > 0, C 55 > 0, C 66 > 0, [C 11 + C 22 + C 33 + 2 (C 12 + C 13 + C 23 )] > 0, C 33 C 55 -C 35 2 > 0, C 44 C 66 -C 46 2 > 0, C 22 + C 33 -2C 23 > 0, We can see that the elastic tensors Cij of P1-AgN 7 , P-1-AgN 7 , P-1-AgN 4 and P-1-AgN 8 satisfy the criteria, indicating that they possess the mechanical stability. Thus, we proposed three stable high-pressure phases (P4/mmm-AgN 2 , P1-AgN 7 and P-1-AgN 7 ) and two metastable high-pressure phases (P-1-AgN 4 and P-1-AgN 8 ) by the structural prediction method.           The crystal structures of P4/mmm-AgN 2 , P1-AgN 7 , P-1-AgN 7 , P-1-AgN 4 and P-1-AgN 8 are presented in Figure 4. In P4/mmm-AgN 2 , the polymeric N-structure unit is the dumbbell-shaped N 2 structure, which is composed of two equivalent nitrogen atoms. At 100 GPa, the bond length of N 1 -N 1 is 1.165 Å. For the P1-AgN 7 presented in Figure 4b, one unit cell contains one dumbbell-shaped N 2 structure and one N 5 ring structure. The N 5 ring structure is composed of five inequitable nitrogen atoms (N 1 ->N 5 ), while the dumbbell-shaped N 2 structure is composed of two inequitable nitrogen atoms (N 6 -N 7 ). At 50 GPa, the bond lengths of N 1 -N 5 , N 2 -N 3 , N 3 -N 4 , N 4 -N 5 , N 5 -N 1 and N 6 -N 7 are 1.296 Å, 1.309 Å, 1.296 Å, 1.301 Å, 1.307 Å and 1.114 Å, respectively. The P-1-AgN 7 is the folded layer structure, which is constituted by the N 20 ring and two fused N 7 rings. At 150 GPa, the bond lengths of ten N-N bonds (N 1 -N 4 , N 4 -N 3 , N 3 -N 2 , N 2 -N 2 , N 2 -N 5 , N 5 -N 6 , The electronic structural properties including the band structure, the density of states (DOS), the electronic local function (ELF) and the Bader charge transfer are calculated for analyzing the electronic structure property and stable mechanism of structures. As shown in Figure 5, the P4/mmm-AgN 2 at 100 GPa and P1-AgN 7 at 50 GPa are the semiconductor phases with the band gaps of 1.0 eV and 2.4 eV, respectively. For the P4/mmm-AgN 2 , the electronic states of valence bands near the Fermi level are mainly contributed by the Ag_d and N_p orbitals, while the conduction bands near the Fermi level are mainly contributed by the Ag_s and N_p orbitals. For the P1-AgN 7 , the electronic states of valence bands near the Fermi level are mainly contributed by the Ag_d and N_p orbitals, while the conduction bands near the Fermi level are mainly contributed by the N_p orbitals. The P-1-AgN 7 at 150 GPa is the metal phase, for which the electronic states near the Fermi level are mainly contributed by the N_p orbitals. For the presented band structure and DOS in Figure 6, the P-1-AgN 4 and P-1-AgN 8 at 150 GPa are both the metal phases, for which the electronic states of valence bands near the Fermi level are mainly contributed by the Ag_d and N_p orbitals, while the conduction bands near the Fermi level are mainly contributed by the N_p orbitals. novel N7 rings and N20 rings are firstly reported for this work. The P-1-AgN4 is the 1-D chain structure, which is constructed by the alternate N2 and N6 ring. At 150 GPa, the bond lengths of five N-N bonds (N1-N1, N1-N2, N2-N3, N3-N4 and N4-N2) that are constructed by four inequitable nitrogen atoms (N1->N4) are 1.266 Å, 1.282 Å, 1.300 Å, 1.281 Å and 1.306 Å, respectively. The P-1-AgN8 is the layer structure, which is constructed by the fused N18 ring structure. At 150 GPa, the bond lengths of five N-N bonds (N1-N4, N4-N4, N1-N2, N2-N2 and N1-N3,) that are constructed by four inequitable nitrogen atoms (N1->N4) are 1.271 Å, 1.257 Å, 1.272 Å, 1.269 Å and 1.280 Å, respectively.  The electronic structural properties including the band structure, the density of states (DOS), the electronic local function (ELF) and the Bader charge transfer are calculated for analyzing the electronic structure property and stable mechanism of structures. As shown in Figure    In Figure 7, as the fixed value of isovalue (0.8) in ELF, the high localization electronic states between the nitrogen atoms indicate the strong N-N covalent bond interaction. The lone electron pairs distribute at the outside corner of N atoms for reducing the repulsive interaction. In combination with the analysis of Figure 4, we know that the N atom in the dumbbell-shaped N2 structure of P4/mmm-AgN2 and P1-AgN7 hybridizes in the sp state, which is formed by one N-N σ bond and one lone pair electron. The N atom in the N5 ring hybridizes in the sp 2 state, which is formed by two N-N σ bonds and one lone electron pair. In the P-1-AgN7, the N1, N3, N5 and N7 atoms hybridize in sp 2 states, which are formed by two N-N σ bonds and one lone electron pair, while the N2, N4, and N6 atoms hybridize The electronic structural properties including the band structure, the density of states (DOS), the electronic local function (ELF) and the Bader charge transfer are calculated for analyzing the electronic structure property and stable mechanism of structures. As shown in Figure    In Figure 7, as the fixed value of isovalue (0.8) in ELF, the high localization electronic states between the nitrogen atoms indicate the strong N-N covalent bond interaction. The lone electron pairs distribute at the outside corner of N atoms for reducing the repulsive interaction. In combination with the analysis of Figure 4, we know that the N atom in the dumbbell-shaped N2 structure of P4/mmm-AgN2 and P1-AgN7 hybridizes in the sp state, which is formed by one N-N σ bond and one lone pair electron. The N atom in the N5 ring hybridizes in the sp 2 state, which is formed by two N-N σ bonds and one lone electron pair. In the P-1-AgN7, the N1, N3, N5 and N7 atoms hybridize in sp 2 states, which are formed by two N-N σ bonds and one lone electron pair, while the N2, N4, and N6 atoms hybridize In Figure 7, as the fixed value of isovalue (0.8) in ELF, the high localization electronic states between the nitrogen atoms indicate the strong N-N covalent bond interaction. The lone electron pairs distribute at the outside corner of N atoms for reducing the repulsive interaction. In combination with the analysis of Figure 4, we know that the N atom in the dumbbell-shaped N 2 structure of P4/mmm-AgN 2 and P1-AgN 7 hybridizes in the sp state, which is formed by one N-N σ bond and one lone pair electron. The N atom in the N 5 ring hybridizes in the sp 2 state, which is formed by two N-N σ bonds and one lone electron pair. In the P-1-AgN 7 , the N 1 , N 3 , N 5 and N 7 atoms hybridize in sp 2 states, which are formed by two N-N σ bonds and one lone electron pair, while the N 2 , N 4 , and N 6 atoms hybridize in sp 3 states, which are formed by three N-N σ bonds and one lone electron pair. In the P 1-AgN 4 , the N 1 , N 3 , and N 4 atoms hybridize in sp 2 states, which are formed by two N-N σ bonds and one lone electron pair, while the N 2 atom hybridizes in the sp 3 state, which is formed by three N-N σ bonds and one lone electron pair. In the P 1-AgN 8 , the N 2 , N 3 , and N 4 atoms hybridize in sp 2 states, which are formed by two N-N σ bonds and one lone electron pair, while the N 1 atom hybridizes in the sp 3 state, which is formed by three N-N σ bonds and one lone electron pair. No localization electron is distributed around the Ag atom and between the Ag and N atoms due to the weak Ag-N electronic overlap interaction. As the presented charge transfer in Table 2, we can see that the Ag and N atoms are severally the electron donor and receptor, which means the weak Ag-N ionic bond interaction. Clearly, this charge transfer enhances the N-N covalent bond and Ag-N ionic bond interaction, which improves the structural stability. According to the above discussion, we know that the stable mechanism of our predicted Ag-N compounds originates from the strong N-N covalent bond interaction and the weak Ag-N ionic bond interaction. Moreover, the charge transfer between the Ag and N atoms plays an important part in their structural stability. in sp 3 states, which are formed by three N-N σ bonds and one lone electron pair. In the P⎯1-AgN4, the N1, N3, and N4 atoms hybridize in sp 2 states, which are formed by two N-N σ bonds and one lone electron pair, while the N2 atom hybridizes in the sp 3 state, which is formed by three N-N σ bonds and one lone electron pair. In the P⎯1-AgN8, the N2, N3, and N4 atoms hybridize in sp 2 states, which are formed by two N-N σ bonds and one lone electron pair, while the N1 atom hybridizes in the sp 3 state, which is formed by three N-N σ bonds and one lone electron pair. No localization electron is distributed around the Ag atom and between the Ag and N atoms due to the weak Ag-N electronic overlap interaction. As the presented charge transfer in Table 2, we can see that the Ag and N atoms are severally the electron donor and receptor, which means the weak Ag-N ionic bond interaction. Clearly, this charge transfer enhances the N-N covalent bond and Ag-N ionic bond interaction, which improves the structural stability. According to the above discussion, we know that the stable mechanism of our predicted Ag-N compounds originates from the strong N-N covalent bond interaction and the weak Ag-N ionic bond interaction. Moreover, the charge transfer between the Ag and N atoms plays an important part in their structural stability. The energy densities and detonation properties of P-1-AgN7 and P-1-AgN8 are presented in Table 3. It can be seen that the energy density of P-1-AgN7 and P-1-AgN8 is 3.9 kJ/g, which is close to that of the TNT (4.3 kJ/g). The detonation velocities of P-1-AgN7 (13.58 km/s) and P-1-AgN8 (17.59 km/s) are 2.0 and 2.5 times the value (6.90 km/s) of TNT, respectively. The detonation pressures of P-1-AgN7 (115.5 GPa) and P-1-AgN8 (210.7 GPa) are 6 and 11 times the value (19.00 GPa) of TNT. Thus, the P-1-AgN7 and P-1-AgN8 are potential candidates for new high-energy density species.   The energy densities and detonation properties of P-1-AgN 7 and P-1-AgN 8 are presented in Table 3. It can be seen that the energy density of P-1-AgN 7 and P-1-AgN 8 is 3.9 kJ/g, which is close to that of the TNT (4.3 kJ/g). The detonation velocities of P-1-AgN 7 (13.58 km/s) and P-1-AgN 8 (17.59 km/s) are 2.0 and 2.5 times the value (6.90 km/s) of TNT, respectively. The detonation pressures of P-1-AgN 7 (115.5 GPa) and P-1-AgN 8 (210.7 GPa) are 6 and 11 times the value (19.00 GPa) of TNT. Thus, the P-1-AgN 7 and P-1-AgN 8 are potential candidates for new high-energy density species.

Conclusions
The crystal structure, electronic structure and energy property of silver nitrides in nitrogen-rich aspects are studied by using the first-principles calculations combining the particle-swarm structural searching. In addition to the reported P-1-AgN 3 , three stable high-pressure phases (P4/mmm-AgN 2 , P1-AgN 7 and P-1-AgN 7 ) and two metastable high-pressure phases (P-1-AgN 4 and P-1-AgN 8 ) are proposed by the structural prediction method. The stable pressure range of P4/mmm-AgN 2 , P1-AgN 7 and P-1-AgN 7 are proposed by the enthalpy difference analysis. Interestingly, the novel N 7 rings and N 20 rings are firstly found in the folded layer structure of P-1-AgN 7 . In electronic structure analysis, the P4/mmm-AgN 2 and P1-AgN 7 are the semiconductor phases, while the P-1-AgN 7 , P-1-AgN 4 and P-1-AgN 8 are the metal phases. The analysis of ELF and Bader charge shows that the stable mechanism of predicted Ag-N compounds originates from the strong N-N covalent bond interaction and the weak Ag-N ionic bond interaction. Moreover, the charge transfer between the Ag and N atoms plays an important role for their structural stability. The P-1-AgN 7 and P-1-AgN 8 with the high energy densities and excellent detonation properties are potential candidates for new high-energy density species. This work not only enriched the high-pressure phase diagram of Ag-N compounds but also proposed two new high-energy density structures.

Data Availability Statement:
The data presented in this study are available on request from the corresponding author.

Conflicts of Interest:
The authors declare no conflict of interest.