⇦Chinese Physics Letters, 2021, Vol. 38, No. 6, Article code 066201 New Members of High-Energy-Density Compounds: YN$_{5}$ and YN$_{8}$ Jun-Yi Miao (苗俊一)1,2, Zhan-Sheng Lu (路战胜)1, Feng Peng (彭枫)2,1*, and Cheng Lu (卢成)3* Affiliations 1School of Physics, Henan Normal University, Xinxiang 453007, China 2College of Physics and Electronic Information, Luoyang Normal University, Luoyang 471022, China 3School of Mathematics and Physics, China University of Geosciences (Wuhan), Wuhan 430074, China Received 11 March 2021; accepted 6 April 2021; published online 25 May 2021 Supported by the National Natural Science Foundation of China (Grant Nos. 11774140, U1804121, and 11304167), and China Postdoctoral Science Foundation (Grant No. 2016M590033).
*Corresponding authors. Email: fpeng@calypso.cn; lucheng@calypso.cn Citation Text: Miao J Y, Lu Z S, Peng F, and Lu C 2021 Chin. Phys. Lett. 38 066201    Abstract Polymeric nitrogen is a promising candidate for a high-energy-density material. Synthesis of energetic compounds with high chemical stability under ambient conditions is still a challenging problem. Here we report a theoretical study on yttrium nitrides by first principles calculations combined with an effective crystal structure search method. It is found that many yttrium nitrides with high nitrogen content can be formed under relatively moderate pressures. The results indicate that the nitrogen-rich YN$_{5}$ and YN$_{8}$ compounds are recoverable as metastable high-energy materials under ambient conditions, and can release enormous energies (2.51 kJ$\cdot$g$^{-1}$ and 3.18 kJ$\cdot$g$^{-1}$) while decomposing to molecular nitrogen and YN. Our findings enrich the family of transition metal nitrides, and open avenues for design and synthesis of novel high-energy-density materials. DOI:10.1088/0256-307X/38/6/066201 © 2021 Chinese Physics Society Article Text Exploration of novel high-energy-density materials (HEDMs) in polynitrogen form has attracted significant attention for decades due to its important applications, such as energy storage, rocket propellants and explosives. Polynitrogen materials become ideal HEDM candidates because they are “green” energetic materials and exhibit a uniquely large difference in energies between different phases consisting of single bonds and triple bonds.[1] Generally, nitrogen is a diatomic N$_{2}$ molecule with a strong triple N$\equiv$N bond under ambient conditions.[2] An effective method to break the extremely strong triple N$\equiv$N bond and to obtain polymeric nitrogen is using high pressure.[3] In this direction, the predicted single-bonded frameworks of cubic gauche (cg-N) has been synthesized successfully at high pressure (110 GPa) and high temperature (2000 K).[3,4] Very recently, the layered $Pba_{2}$ (LP-N) structure has been observed.[5,6] However, both cg-N and LP-N are just metastable at pressures above 42 GPa at room temperature[3] and the ultrahigh pressure required to stabilize them has precluded their practical applications. To reduce the synthesis pressure of single-bonded polymeric nitrogen, many works have focused on searching the novel polymeric nitrogen materials by introducing other elements into “precompressing” N$_{2}$. A reliable research tool for screening HEDM candidates is pressing, and thereby will avoid expensive and dangerous experimental tests. Many metal nitrides,[7–14] and nonmetal nitrides[15–18] are predicted. Recently, Raza et al.[19] have found that N$_{2}$ can react with carbon monoxide at pressures above 52 GPa. While relieving the pressure to the ambient pressure, the corresponding compound maintains its three-dimensional (3D) covalent frame-work and is dynamically stable.[19] The underlying mechanism of the reduced stabilization pressure might be attributed to the chemical precompression resulting from other elements,[20] the existence of more types of N–N bonds than the N$_{2}$ molecule,[21] or the assistance of additional chemical bonds between N and other elements. Synthesis of polynitrogen materials requires elimination of N$_{2}$-like molecular units. One feasible method is to introduce electrons which are favored by N$_{2}$ molecules and which occupy the empty antibonding $\sigma ^*$ orbitals of N$_{2}$ molecules, thus weakening the intramolecular N–N bonds and dissociation of the N$_{2}$ isomer. Recent work reported that the MgN$_{10}$ compound can be stable at high pressure since two N$_{5}$ anions accept 2$e$ from the magnesium atom,[22] while LiN$_{5}$ can be stable due to 1$e$ charge transfer of Li$\to$N$_{5}$.[7] The more the electrons are obtained, the higher the nitrogen content in the compound can be achieved. Therefore, rare earth (RE) nitrides have entered our research perspectives. Normally, RE elements, such as Y metal, can easily lose electrons because of their small electronegativities in the range of 1.0–1.36 on the Pauli scale,[23] which is comparable to that of Mg metal with a value of 1.0. Moreover, the RE elements accommodate higher oxidation states more easily (e.g., in 3$^+$ or 4$^+$) than that of Mg (2$^+$) in MgN$_{10}$, which enables donation of more electrons to the nitrogen molecules. In this work, we carry out an extensively structural search of yttrium nitrides in a large pressure range from 0 to 100 GPa using the swarm-structure searching algorithm in conjunction with first-principles calculations.[24,25] Our results show that nitrogen can react with Y at a relatively low pressure (about 10 GPa) and form high-energy-density compounds with various compositions. The structures are diverse, including one-dimensional polymeric crystals such as YN$_{4}$/YN$_{5}$ and three-dimensional extended solid such as YN$_{8}$. Most importantly, the three-dimensional YN$_{8}$ shows a surprisingly high energy density of about 3.18 kJ$\cdot$g$^{-1}$, which is the highest nitride among all the known polynitrogen compounds, making YN$_{8}$ a promising candidate for HEDM. Our structural searches are carried out using the particle swarm optimization (PSO) method as implemented in the CALYPSO code,[24–26] which is based on a global minimization of free energy surfaces obtained from ab initio total-energy calculations. It is specially designed for global structural minimization unbiased by any known structural information. This method has been benchmarked on various known systems, ranging from elements to binary and ternary compounds.[27–35] Total energy calculations are calculated by density functional theory (DFT) within the generalized gradient approximation[36] as implemented in the Vienna ab initio simulation package (VASP).[37] The Perdew–Burke–Ernzerhof (PBE)[38] functionals and the projector-augmented wave (PAW) method[39] are adopted in the structural optimizations. The $4s^{2}4p^{6}5s^{2}4d^{1}$ and $2s^{2}2p^{3}$ are treated as valence electrons for Y and N atoms, respectively. The energy cutoff of 900 eV and the adequate $k$-point sampling are chosen to ensure the excellent convergence of total energies. To obtain the stable pressure range for Y–N compounds, we calculated the formational enthalpies of all the chemical reaction channels for stable stoichiometries and the pure solid Y and N$_{2}$. Phonon calculations are calculated by the Phonopy code.[40] The thermodynamic stability of Y–N systems with different stoichiometries of YN$_{x}$ [$x = 1/4, 2/7, 1/3, 2/5, 1/2, 1, 3/2, 2, 5/2$, and 3–12] are thoroughly examined by comparing the formation enthalpies[29] at pressures of 0, 25, 50, 75 and 100 GPa, relative to the dissociation into solid Y and N$_{2}$, as shown by the convex hull [Fig. 1(a)]. The results show that YN is the most stable system at both high pressure and ambient pressure. This is consistent with the experiment, where only YN compounds with cubic structure can form at ambient pressure.[41] Figure 1(a) also indicates that the N content of the thermodynamically stable stoichiometries tends to rise with increasing pressure. In the low-pressure range ($ < 25$ GPa), Y$_{5}$N$_{2}$, YN$_{3}$, YN$_{4}$ and YN$_{10}$ are all stable besides the most stable YN. Unexpectedly, besides YN, YN$_{3}$, YN$_{4}$ and YN$_{10}$, YN$_{5}$ and YN$_{8}$ are also stable stoichiometries in the moderate pressure range about 75 GPa. Up to high pressure ranges ($> 100$ GPa), the stable stoichiometries are Y$_{3}$N$_{2}$, YN, YN$_{2}$, YN$_{3}$, YN$_{5}$, and YN$_{8}$. To explore the dynamic stability of these nine newly uncovered Y-N compounds, we calculate their phonon dispersions (see Figs. S1–S9 in the Supplementary Material). The calculated phonon dispersions show no imaginary vibrational modes over the Brillouin zone, confirming the dynamic stabilities of these compounds. Thus, they are thermodynamically stable under the corresponding pressure range. The shift of the phase stability towards N-rich compositions with increasing pressure is accompanied by a series of structural changes promoted by variations in N–N bonding patterns. With increasing N content, the bonding patterns of N evolve from isolated N anion (Y$_{5}$N$_{2}$, Y$_{3}$N$_{2}$ and YN) to anionized N$_{4}$ (YN$_{2}$) and N$_{6}$ (YN$_{3}$), one-dimensional (1D) polynitrogens (YN$_{4}$ and YN$_{5}$), two-dimensional (2D) polynitrogens (YN$_{8}$) and eventually N$_{5}$ rings (YN$_{10}$).
cpl-38-6-066201-fig1.png
Fig. 1. (a) The convex hull of yttrium nitrides under different pressures. (b) The predicted stable pressure ranges of yttrium nitrides.
Y$_{5}$N$_{2}$, the Y rich nitride, is a layered structure with tetragonal $P4/nmm$ symmetry [see Fig. S10(a) in the Supplementary Material] at 25 GPa. The structure parameters are listed in Tables S1–S2 in the Supplementary Material. Y$_{5}$N$_{2}$ contains two YN layers, one Y double layer and one quadruple layer of Y. The nitrogen in Y$_{5}$N$_{2}$ is absolutely reduced to isolated N anions in YN layers. The isolated N anion is a common configuration in alkali metal and alkali earth metal nitrides, such as Li$_{3}$N or Ca$_{2}$N.[23,24] Bader charge analysis[42] [see Fig. S11 in the Supplementary Material] reveals only a part of the charge ($1.47e$) of the Y atom transfer to the N atom in YN layers and a few charge transfers of Y$\to$ N in the layers of Y. In addition, a part of the valence charges of the Y atom are located in the interstices in the Y layers, which is confirmed by the electron localization function (ELF)[43] [see Fig. S12(a) in the Supplementary Material], and the other valence charges of the Y atom are looked upon as free electrons confirmed by the metallic characters from the electronic band structure and electronic density of states (DOS) calculations (see the Supplementary Material, Fig. S13). Y$_{3}$N$_{2}$ is a monoclinic structure with $C2/m$ symmetry at 100 GPa [see Fig. S10(b) in the Supplementary Material] and the structure parameters are listed in Tables S1 and S2 in the Supplementary Material. It consists of Y cations and isolated N anions, which is verified by ELF [see Fig. S12(b) in the Supplementary Material]. Bader charge analysis, as shown in Fig. S11 in the Supplementary Material, reveals that some charge, about 1.14$e$, of the Y atom transfers to the N atom, and the other valence charges are free electrons, leading to its metallic character. YN is a typical cubic $Fm\bar{3}m$ structure in the considered pressure range. The crystal structure parameters are present in Fig. S10(c) and Tables S1 and S2 in the Supplementary Material. Bader charge analysis (see the Supplementary Material, Fig. S11) reveals that 1.71$e$ of the Y atom transfer to the N atom. The electronic band structure and DOS calculations (see the Supplementary Material, Fig. S14) show that YN is a weak metal. Generally, the chemical bonds of RE metal nitrides are a mixture of ionicity and covalent characters due to their $d$ orbitals. However, the average distance between Y and N atoms in most Y–N compounds is about 2.51 Å, which is much larger than the sum of the covalent radii of Y (1.61 Å) and N (0.71 Å) atoms. It leads to the weak covalent character of Y–N bonds. YN$_{2}$ adopts the monoclinic $P21/c$ structure [see the Supplementary Material, Fig.  S10(d) and Tables S1 and S2] at 100 GPa, which contains N$_{4}$ anions and Y cations due to the charge transfer (1.81$e$) of Y$\to$N. Previous reports show similar N$_{4}$ anions in the high pressure phases of CsN[8] and CaN.[9] The calculated electronic band structure and DOS, as shown in Fig. S15 in the Supplementary Material, visibly display the metallic character of YN$_{2}$. The N–N distances in YN$_{2}$ under 100 GPa are about 1.39 Å and 1.40 Å, which are close to the typical N–N bond lengths of single bond (1.45 Å) and double bond (1.25 Å). YN$_{3}$ is a triclinic $P\bar{1}$ structure [see the Supplementary Material, Fig. S10(e)]. It is thermodynamically stable above 20.21 GPa [Fig. 1(b)]. It consists of N$_{6}$ anions and Y cations. The neutral N$_{6}$ molecule is a chained diazide geometry. However, the N$_{6}$ anion in YN$_{3}$ is a double U geometry with opposite direction and edge-sharing [see the Supplementary Material, Fig. S10(e)–S10(b)]. The calculated N–N distance of YN$_{3}$ under 50 GPa is 1.32 Å.
cpl-38-6-066201-fig2.png
Fig. 2. Crystal structures of polynitrogens in yttrium nitrides. (a) The $P\bar{1}$ phase of YN$_{4}$ at 50 GPa. (b) The $C/2m$ structure of YN$_{5}$ at 100 GPa. (c) The polymeric $P\bar{1}$ phase at 75 GPa for YN$_{8}$. (d) Puckered plane N$_{5}$ ring $Ibam$ phase of YN$_{10}$ at 75 GPa.
cpl-38-6-066201-fig3.png
Fig. 3. ELFs and units of polynitrogens of yttrium nitrides. (a) The $P\bar{1}$ phase of YN$_{4}$ at 50 GPa. ELF plots in (0.34,0,1) sections for N$_{4}$ unit. (b) The $C/2m$ structure of YN$_{5}$ at 100 GPa. ELF plots in (0.65,0,$-$1) sections for N$_{10}$ unit. (c) The polymeric $P\bar{1}$ phase of YN$_{8}$ at 75 GPa. ELF plots in ($-$1,$-$1,1) sections for N$_{18}$ unit. (d) The puckered plane N$_{5}$ ring in $Ibam$ phase of YN$_{10}$ at 75 GPa. ELF plots in (0.48,1,0.3) sections for N$_{5}$ unit.
YN$_{4}$ is stable at pressures above 20.62 GPa [see Fig. 1(b)], with $P\bar{1}$ symmetry. The N atoms in YN$_{4}$ form 1D infinite chains, as shown in Fig. 2(a). The smallest unit contains four N atoms with a zigzag shape, which contains 1 single bond and 3 double bonds, i.e., [–N=N–N=N=]. The calculated N–N distances are 1.30, 1.36, 1.30, and 1.29 Å, respectively. The equal bonding nature of N$_{4}$ is confirmed by the ELF map [see Fig. 3(a)]. Interestingly, the similar repeated N$_{4}$ units are reported in our recent study[9] of CaN$_{4}$ under high pressure. Moreover, the electronic band structure calculations of the $P\bar{1}$ phase (see the Supplementary Material, Fig. S17) show that YN$_{4}$ is metallic with nonzero DOS near the Fermi level. YN$_{5}$ is a $C2/m$ structure [see Fig. 2(b)], and it is stable above 53.65 GPa. The N atoms are flocked together with [–N$_{2}$–N$_{6}$–N$_{2}$–] anions [Fig. 3(b)]. Y atoms are the electron donors. N atoms are bonded by six $\sigma$ bonds with six lone pairs in the N$_{6}$ anion puckered plane [Fig. 3(b)]. Outside the N$_{6}$ anion plane, there are more than six $\pi$ electrons that form a series of $\pi$ bonds, which are uniformly distributed in the six N atoms. The ELF reveals that the N$_{2}$ anions are bonded by a single bond, and the rest of the electrons are lone pairs. The N–N distances in the N$_{6}$ ring of YN$_{5}$ phase are 1.36 Å and 1.38 Å at 100 GPa, which are between the single bond length of 1.45 Å and the double bond length of 1.20 Å.[3] The ground state of YN$_{5}$ reveals that it is a semiconductor with a small energy gap of about 0.2 eV [Fig. 4(a)].
cpl-38-6-066201-fig4.png
Fig. 4. Electronic band structure, DOS and phonon dispersion curves of yttrium nitrides. Band structures and DOS of $C2/m$ phase for YN$_{5}$ at 100 GPa (a) and $P\bar{1}$ phase of YN$_{8}$ at 75 GPa (b). Phonon dispersion curves of $C2/m$-YN$_{5}$ (c) and $P\bar{1}$-YN$_{8}$ (d) at ambient pressure.
YN$_{8}$ adopts a triclinic $P\bar{1}$ structure as shown in Fig. 2(c). It becomes thermodynamically stable above 57.95 GPa [see Fig. 1(b)]. The N atoms in YN$_{8}$ form 2D and puckered N$_{18}$ rings with edge sharing, which are bonded by 18 $\sigma$ bonds with 18 lone pairs outside the N atoms [Fig. 3(c)]. Meanwhile, there are more than 18 $\pi$ electrons which constitute a number of $\pi$ bonds that are unequally distributed in the 18 N atoms above and below the N$_{18}$ rings. The layer nitrene is metallic due to the connection of $\pi$ bonds confirmed by the ELF [Fig. 3(c)] and band structure [Fig. 4(b)] calculations. The DOSs [Fig. 4(b)] are primary N $p$ states mixing with Y $d$ states near the fermi level. The N–N distances in the N$_{18}$ ring range from 1.29 Å to 1.37 Å at 75 GPa. Interestingly, the calculated $T_{\rm c}$ value is 3.3 K using Coulomb pseudopotential parameters ($\mu ^*$) with 0.1 for YN$_{8}$ at 75 GPa, which is the same behavior of TaN at high pressure.[44] YN$_{10}$ is an Ibam structure, as shown in Fig. 2(d). It is stable under pressure of at least 21.79 GPa. The N atoms inside are stacked as the N$_{5}$ anions [see Fig. 3(d)], and Y atoms are the electron donors. The N atoms, in the puckered plane N$_{5}$ anions, are bonded by five $\sigma$ bonds concomitant with five lone pairs. More than five $\pi$ electrons constitute a number of $\pi$ bonds and are equally distributed between the five N atoms. The N–N distances in the N$_{5}$ anion are 1.28 Å, 1.33 Å and 1.29 Å at 75 GPa. It is noteworthy to mention that more than five $\pi$-electron N$_{5}$ rings disobey Hückel's rule, and the N$_{5}$ anion is unstable. Since the N$_{5}$ anion has additional electrons compared to its aromatic counterpart,[7,8] the ground state of YN$_{10}$ is metallic (see Fig. S18 in the Supplementary Material). The calculated elastic constants of $P2_{1}/c$-YN$_{4}$, $C2/m$-YN$_{5}$, $P\bar{1}$-YN$_{8}$, and Ibam-YN$_{10}$ at ambient pressure are listed in Table S3 in the Supplementary Material.[45] It can be seen that the elastic constants of $P2_{1}/c$-YN4, $C2/m$-YN$_{5}$, and $P\bar{1}$-YN$_{8}$ obey the mechanical stability criteria of monoclinic and orthorhombic phases. However, the calculated elastic constants of Ibam-YN$_{10}$ reveal that YN$_{10}$ is unstable. The phonon dispersion curves at ambient pressure suggest that the YN$_{4}$ (see the Supplementary Material, Fig. S6)/YN$_{5}$ [Fig. 4(c)] with 1D nitrogen array and the YN$_{8}$ [Fig. 4(d)] with 2D nitrogen array are stable. Compared the structures of YN$_{4}$, YN$_{5}$ and YN$_{8}$ with other compounds, it can be seen that the N atoms in YN$_{4}$, YN$_{5}$ and YN$_{8}$ are polymerized into N chains or N rings, which enhances the adhesion between the adjacent N atoms and improves their stability due to the strong covalent interactions. The above three metastable yttrium nitrides are expected to decompose exothermically to the products as solid YN and N, and we consider the decomposition reactions as follows: $$\begin{alignat}{1} &{\rm YN} _{4} \to {\rm YN} + 1.5{\rm N} _{2} + 1.97\,{\rm eV},~~ \tag {1} \end{alignat} $$ $$\begin{alignat}{1} &{\rm YN} _{5} \to {\rm YN} + 2{\rm N} _{2} + 4.13\,{\rm eV},~~ \tag {2} \end{alignat} $$ $$\begin{alignat}{1} &{\rm YN} _{8} \to {\rm YN} + 3.5{\rm N} _{2} + 6.63\,{\rm eV}.~~ \tag {3} \end{alignat} $$ The chemical energies released during these reactions are estimated to be 1.97, 4.13, and 6.63 eV per YN$_{4}$, YN$_{5}$ and YN$_{8}$ unit at the GGA-PBE level, and the corresponding energy densities are approximately 1.31 kJ$\cdot$g$^{-1}$, 2.51 kJ$\cdot$g$^{-1}$, and 3.18 kJ$\cdot $g$^{-1}$. The highest energy density is YN$_{8}$, which is a good HEDM compared with conventional explosives, such as 1,3,5-triamino-2,4,6-trinitrobenzene (TATB), hexahydro-1,3,5-trinitro-1,3,5-triazine (RDX), and cyclotetramethylene tetranitramine (HMX) with the energy densities ranging from 1 to 5 kJ$\cdot $g$^{-1}$. [46] In summary, we have predicted seven new stable yttrium nitrides under high pressure, including Y$_{5}$N$_{2}$/Y$_{3}$N$_{2}$ and YN phases with isolated N anions, YN$_{2}$ phase with anionic N$_{4}$, YN$_{3}$ phase with anionic N$_{6}$, YN$_{4}$/YN$_{5}$ phases with 1D polynitrogen array, YN$_{8}$ phase with 2D poly-nitrogen array and YN$_{10}$ with N$_{5}$ rings array, by swarm-intelligence structure searches and first principles calculations. Phonon dispersion curve and formation enthalpy calculations suggest that the YN$_{4}$, YN$_{5}$ and YN$_{8}$ are metastable at ambient pressure. Most strikingly, YN$_{5}$ and YN$_{8}$, potentially recoverable at ambient pressure, can release enormous amounts of energy (about 2.51 kJ$\cdot$g$^{-1}$ and 3.18 kJ$\cdot$g$^{-1}$) while decomposing to solid YN and molecular nitrogen, making it a promising new HEDM compared to conventional explosives. These findings offer fundamental understanding of yttrium nitrides under high pressure, which provide powerful guidance for further design and synthesis of novel HEDMs. One can see the Supplementary Material for details on the structural and electronic properties, phonon dispersion curves, and ELF curves of various yttrium nitrides under different pressures. 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