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.

1. Introduction

Due to the significant energy differences between the N–N bond, N=N bond and N≡N bond, polymeric nitrogen with the single/double bond structure is the potential high-energy-density materials (HEDMs). Moreover, the decomposition product of polymeric nitrogen is the clean diatomic nitrogen gas (N2). Thus, the polymeric nitrogen can be used as the environmentally friendly HEDM. Many efforts have been performed for exploring the novel polymeric nitrogen structures, such as the chain-shaped structures (ch, Cmcm, PP) [1,2], the layered structures (A7, BP-N, LP-N, LB-N) [1,3,4,5], the caged structures (N10) [6], the networked structures (cg-N, rcg-N, P-421m, P212121, P21/m, C2/c, P212121-500, Pnnm, P21, CW) [1,7,8,9] and the molecular crystal structures (N2-N6, N6, N8, 2N5) [10,11,12,13]. Up to now, the cg-N, BP-N, LP-N and HLP-N have been successfully synthesized at (110 GPa, 2000 K), (146 GPa, 2200 K), (150 GPa, 3000 K) and (244 GPa, 3300 K), respectively. The study of decomposition shows that the cg-N, BP-N, LP-N and HLP-N can be quenched down to 42 GPa, 48 GPa, 52 GPa and 66 GPa, respectively [14,15,16,17,18]. Clearly, the harsh synthesis conditions (P > 100 GPa, T > 2000 K) and the low stability of polymeric nitrogen limit its application.

Recent studies show that introducing an impurity element (M) into the pure nitrogen structure can induce the novel polynitrogen structures, which may exhibit the excellent properties, such as the mild synthesis conditions, high stability, etc. A series of polynitrogen structures has been reported in theoretical studies. Typically, the novel N4 ring is reported for P4/mmm-MnN4, Cm-Al2N7, P-1-Na2N8, P21/c-Li2N4, C2/m-MgN4 and Immm-AlN4 compounds [19,20,21,22]. Especially, the regular N4 rings results in a superhard property of P4/mmm-MnN4 and Cm-Al2N7. The N5 ring structures are found in the M2N5 (M = Na) and MN5 (M = Li, Na, Rb, Cs, Ca, Sr, Ba, Cu) compounds [23,24,25,26,27,28,29]. More interestingly, the double-, triple- and quadruple-N5 ring structures are found in MN10 (M = Be, Mg, Ba), MN15 (M = Al, Ga, Sc, Y) and HfN20 compounds, respectively [30,31,32,33]. Among these reported structures, the P21-LiN5, Cm-NaN5, Pc-RbN5 and P-1-BaN10 are stable with the pressure larger than 9.9 GPa, 20 GPa, 30 GPa and 12 GPa, respectively. The Fdd2-BeN10 and Fdd2-MgN10 compounds are possibly synthesized at relatively low pressures (around 28 GPa for BeN10 and 12 GPa for MgN10) and can be preserved under ambient pressure. The good gravimetric energy density of Fdd2-BeN10 (5.39 kJ/g), Fdd2-MgN10 (3.48 kJ/g) and Cc-AlN15 (5.31 kJ/g) makes them the potential (HEDMs). The novel N6 ring structures are found in MN3 (M = Cs, Ca, Sr, K, Mg) [26,27,28,34,35,36,37,38] and MN6 (M = W) compounds [39,40]. Among them, the P-1-MgN3 phase with the N6 ring structure is recoverable at ambient pressure [36]. The superhard R-3m-WN6 remains dynamically stable at ambient conditions [40]. The N-chain structures are found in MN4 (M = Be, Cd, Fe, Gd, Re, Os, W, Ru, Zn) [41,42,43,44,45,46,47,48], GdN6 [45], ReN8 [49] and HfN10 compounds [50]. Among them, P-1-BeN4, γ-P-1-BeN4 and δ-P-1-BeN4 with the N-chain structures can be synthesized under pressures of 25.4, 20.8 and 27.4 GPa, respectively, which is greatly lower than 110 GPa for synthesizing the cg-N. The analysis of dynamical and thermal stability shows that the P-1-GdN6 can be recovered to ambient conditions upon synthesis under compression. The Immm-HfN10 is discovered to be stable at moderate pressure above 23 GPa and can be preserved as a metastable phase at ambient pressure. The novel N18-ring, N6 + N10-ring, N10-ring and N18-ring layered structures are found in P6/mcc-K2N16, C2/m-BaN6, P21/c-BeN4 and P-31c-CoN8 compounds, respectively [31,51,52,53]. Moreover, the N14-ring band-shape structure is the first reported for P-1-CoN10 [53]. The P-31c-CoN8 (6.14 kJ/g) and P-1-CoN10 (5.18 kJ/g) with high-energy density can be quenched down to ambient conditions. The three-dimensional network structures are found in the C2/m-CdN6, I41/a-HeN4, R-3m-HeN6, P63/m-HeN10 and C2/m-HeN22 [43,54,55]. The C2/m-CdN6 and C2/m-HeN22 with respectively high-energy-density values of 3.82 kJ/g and 10.44 kJ/g may be quenchable to ambient pressure. In the experiment, the cyclo-N5 ring in LiN5, NaN5 and CsN5 compounds are synthesized at 45, 52 and 65 GPa, respectively [56,57,58]. The CsN5 and LiN5 can be quenched down to 18 GPa and ambient pressure, respectively. The armchair-like hexazine N6 ring in R-3m-WN6 is synthesized with pressure larger than 126 GPa [59]. The N-chain structure in Ibam-MgN4 and FeN4 are synthesized at 50 and 180 GPa, respectively [60,61]. As the review above, we know that the introduced impurity element can induce the novel polymeric nitrogen structures, which may exhibit more prominent properties than the pure polymeric nitrogen structures, such as the milder synthesis pressure and the higher stability.

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 N5 ring structures are severally reported for AgN3 and AgN5/AgN6 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.

2. 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 4d105s1 and 2s22p3 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 ΔHf of each Ag–N structure is calculated by using the following equation: ΔHf (AgNx) = [H(AgNx) − H(AgN) − (x − 1) H(N)]/(1 + x). The most stable structures of AgN (Abma-phase) and N (P2/c- and cg-phases) are chosen as the reference structures in their corresponding stable pressure range. The phonon frequencies 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: AgNx → Ag + x/2N2. The P63/mmc phase of Ag and Pa phase of N2 are the decomposition productions, respectively. The detonation velocity and detonation pressure have been calculated by using the Kamlet–Jacobs simi-empirical equation: Vd = 1.01(NM0.5Ed0.5)0.5(1 + 1.30ρ) and Pd = 15.58ρ2NM0.5Ed0.5. N represents the moles of gas per gram of AgNx, M represents the average molar mass of gas products, Ed is the detonation chemical energy, and ρ is the mass density.

3. Results and Discussion

Eight stoichiometries of AgNx (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 (ΔHf) 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 AgN2 stoichiometry, we found the thermodynamically stable P4/mmm phase at 100 and 150 GPa. At 50 and 100 GPa, the reported P-1-AgN3 in Ref. [65] is also found in this work. For the AgN7 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 (AgN4, AgN5, AgN6, AgN8 and AgN10). For the presented high-pressure phase diagrams of AgN2 and AgN7 in Figure 1d, we can see that the P4/mmm-AgN2 is thermodynamically stable in the pressure region of (75–150 GPa). The P1-AgN7 and P-1-AgN7 are thermodynamically stable in the pressure ranges of (25–75 GPa) and (125–150 GPa), respectively. The dynamical stability of AgN2 and AgN7 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-AgN2, P1-AgN7 and P-1-AgN7 are dynamically stable at 100, 50 and 150 GPa, respectively. Interestingly, the presented phonon dispersion curves in Figure 3 show that the P-1-AgN4 and P-1-AgN8 are dynamically stable at 150 GPa, indicating that they are the metastable phases. Moreover, the mechanical stabilities of P4/mmm-AgN2, P1-AgN7, P-1-AgN7, P-1-AgN4 and P-1-AgN8 are evaluated by the calculation of elastic constants (Table 1). According to the mechanical stability criteria of tetragonal structure of (C11 > |C12|, 2C132 < C33 (C11 + C12), C44 > 0), we know that the tetragonal P4/mmm-AgN2 is mechanically stable. The mechanical stability criteria of monoclinic structure are shown as follows [73]:C

Figure 1

The formation enthalpies of Ag-N phases with respect to the Abma-AgN phase and nitrogen solids at different pressures (a–c). (d) shows the phase diagram of AgN2 and AgN7.

Figure 2

The phonon dispersion of P4/mmm-AgN2 at 100 GPa (a), the P1-AgN7 at 50 GPa (b) and P-1-AgN7 at 150 GPa (c).

Figure 3

The phonon dispersion of P-1-AgN4 at 150 GPa (a) and P-1-AgN8 at 150 GPa (b).

Table 1

The elastic constants Cij (GPa) of the Ag–N compounds at high pressure.

AgNx	(GPa)	C11	C22	C33	C44	C55	C66	C12	C13	C15	C23	C25	C35	C46
P4/mmm-AgN2	100	563	-	648	85	-	22	313	310	-	-	-	-	-
P1-AgN7	50	215	294	231	70	68	42	160	154	−3	173	−5	8	24
P-1-AgN7	150	943	942	800	221	207	279	513	396	−85	377	−113	−19	−85
P-1-AgN4	150	910	912	710	127	148	270	593	354	−42	338	−39	49	27
P-1-AgN8	150	1163	1114	861	193	56	250	604	152	−17	228	−24	12	0.24

We can see that the elastic tensors Cij of P1-AgN7, P-1-AgN7, P-1-AgN4 and P-1-AgN8 satisfy the criteria, indicating that they possess the mechanical stability. Thus, we proposed 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) by the structural prediction method.

The crystal structures of P4/mmm-AgN2, P1-AgN7, P-1-AgN7, P-1-AgN4 and P-1-AgN8 are presented in Figure 4. In P4/mmm-AgN2, the polymeric N-structure unit is the dumbbell-shaped N2 structure, which is composed of two equivalent nitrogen atoms. At 100 GPa, the bond length of N1-N1 is 1.165 Å. For the P1-AgN7 presented in Figure 4b, one unit cell contains one dumbbell-shaped N2 structure and one N5 ring structure. The N5 ring structure is composed of five inequitable nitrogen atoms (N1->N5), while the dumbbell-shaped N2 structure is composed of two inequitable nitrogen atoms (N6-N7). At 50 GPa, the bond lengths of N1-N5, N2-N3, N3-N4, N4-N5, N5-N1 and N6-N7 are 1.296 Å, 1.309 Å, 1.296 Å, 1.301 Å, 1.307 Å and 1.114 Å, respectively. The P-1-AgN7 is the folded layer structure, which is constituted by the N20 ring and two fused N7 rings. At 150 GPa, the bond lengths of ten N–N bonds (N1-N4, N4-N3, N3-N2, N2-N2, N2-N5, N5-N6, N6-N1, N6-N6, N4-N7 and N7-N7) that are constructed by seven inequitable nitrogen atoms (N1->N7) are 1.286 Å, 1.315 Å, 1.270 Å, 1.286 Å, 1.274 Å, 1.282 Å, 1.254 Å, 1.318 Å, 1.277 Å and 1.261 Å, respectively. Up to now, the reported N-rings in the polynitrogen structures are the N5, N6, N10, N12, N14 and N18 rings [51,52,53,54]. As the construction unit of the layer structure, the 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.

Figure 4

The 2 × 2 × 2 supercell structures of Ag-N compounds: P4/mmm-AgN2 (a), P1-AgN7 (b), P-1-AgN7 (c), P-1-AgN4 (d) and P-1-AgN8 (e).

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-AgN2 at 100 GPa and P1-AgN7 at 50 GPa are the semiconductor phases with the band gaps of 1.0 eV and 2.4 eV, respectively. For the P4/mmm-AgN2, 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-AgN7, 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-AgN7 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-AgN4 and P-1-AgN8 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.

Figure 5

Band structures and projected density of states of P4/mmm-AgN2 at 100 GPa (a), P1-AgN7 at 50 GPa (b), P-1-AgN7 at 150 GPa (c).

Figure 6

Band structures and projected density of states of P-1-AgN4 (a) and P-1-AgN8 (b) at 150 GPa.

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 sp2 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 sp2 states, which are formed by two N–N σ bonds and one lone electron pair, while the N2, N4, and N6 atoms hybridize in sp3 states, which are formed by three N–N σ bonds and one lone electron pair. In the P -AgN4, the N1, N3, and N4 atoms hybridize in sp2 states, which are formed by two N–N σ bonds and one lone electron pair, while the N2 atom hybridizes in the sp3 state, which is formed by three N–N σ bonds and one lone electron pair. In the P -AgN8, the N2, N3, and N4 atoms hybridize in sp2 states, which are formed by two N–N σ bonds and one lone electron pair, while the N1 atom hybridizes in the sp3 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.

Figure 7

The ELFs of P4/mmm-AgN2 (a), P1-AgN7 (b), P-1-AgN7 (c), P-1-AgN4 (d) and P-1-AgN8 (e) (isovalue = 0.8).

Table 2

The Bader charge analysis of P4/mmm-AgN2, P1-AgN7, P-1-AgN7, P-1-AgN4 and P-1-AgN8 at different pressures. The negative and positive values mean the donor and the receptor of charge, respectively.

Structures	Pressure	Element	σ(e)/Atom
P4/mmm-AgN2	100	Ag	−0.70
		N	+0.35
P1-AgN7	50	Ag	−0.82
		N	+0.117
P-1-AgN7	150	Ag	−0.623
		N	+0.089
P-1-AgN4	150	Ag	−0.64
		N	+0.16
P-1-AgN8	150	Ag	−0.76
		N	0.095

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.

Table 3

The energy density and detonation properties of P-1-AgN7 and P-1-AgN8 compounds in comparison to TNT.

Compounds	Energy Densities (kJ/g)	Detonation Velocity (km/s)	Detonation Pressure (GPa)
P-1-AgN7	3.90	13.58	115.5
P-1-AgN8	3.90	17.59	210.7
TNT	4.30	6.90	19.00

4. 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-AgN3, 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) are proposed by the structural prediction method. The stable pressure range of P4/mmm-AgN2, P1-AgN7 and P-1-AgN7 are proposed by the enthalpy difference analysis. Interestingly, the novel N7 rings and N20 rings are firstly found in the folded layer structure of P-1-AgN7. In electronic structure analysis, the P4/mmm-AgN2 and P1-AgN7 are the semiconductor phases, while the P-1-AgN7, P-1-AgN4 and P-1-AgN8 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-AgN7 and P-1-AgN8 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.