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Pressure-induced stable BeN4 as a high-energy density material
Journal of Power Sources 365 (2017) 155e161
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Pressure-induced stable BeN4 as a high-energy density material Shoutao Zhang, Ziyuan Zhao, Lulu Liu, Guochun Yang* Centre for Advanced Optoelectronic Functional Materials Research and Key Laboratory for UV Light-Emitting Materials and Technology of Ministry of Education, Northeast Normal University, Changchun 130024, China
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The P1-BeN4 can be synthesized by the reaction of Be3N2 and N2 at 25.4 GPa. BeN4 with P1symmetry has the high energy density of 3.60 kJ g1. N∞ chains in P1-BeN4 transform to N10 rings network in P21/c phase at 115.1 GPa. P1-BeN4 is metallic, whereas P21/cBeN4 is an insulator.
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Article history: Received 4 June 2017 Received in revised form 9 August 2017 Accepted 22 August 2017 Available online 30 August 2017
Polynitrogens are the ideal rocket fuels or propellants. Due to strong triple N≡N bond in N2, the direct polymerization of nitrogen is rather difficult (i.e. extreme high temperature and high pressure). However, the use of nitrides as precursors or the reaction of N2 with other elements has been proved to be an effective way to obtain polynitrogens. Here, with assistance of the advanced first-principles swarm-intelligence structure searches, we found that P1-BeN4, containing infinite zigzag-like polymeric nitrogen chains, can be synthesized by compressing the mixture of Be3N2 and N2 at 25.4 GPa, which is greatly lower than 110 GPa for synthesizing cubic gauche nitrogen and other polynitrogen compounds (e.g. bulk CNO at 52 GPa and SN4 at 49 GPa). Its structural stability can be attributed to the coexistence of ionic BeN and covalent N-N bonds. Intriguingly, this phase has high kinetic stability and remains metastable at ambient pressure. The exceptional properties, including high energy density (3.60 kJ g1), high nitrogen content (86.1%), high dynamical stability, and low polymerization pressure, make P1-structured BeN4 a promising high energy material. Infinite nitrogen chains in P1-BeN4 transform to N10 rings network in P21/c phase at 115.1 GPa. P1-BeN4 is metallic, while P21/c-BeN4 is an insulator. © 2017 Elsevier B.V. All rights reserved.
Keywords: High-energy density material Polynitrogen compound Beryllium nitride Electronic property High pressure First-principles
1. Introduction In some special application areas (e.g. propellants, explosives, and rocket fuel), materials are required to have extremely high energy density [1]. Polynitrogens are considered as the most
* Corresponding author. E-mail address: [email protected] (G. Yang). http://dx.doi.org/10.1016/j.jpowsour.2017.08.086 0378-7753/© 2017 Elsevier B.V. All rights reserved.
suitable candidates for these applications [2e6]. This is attributed to extraordinarily large energy release upon the decomposition of singly or doubly bonded polynitrogens to solid nitrogen molecule (N2) [7]. Notably, polynitrogens are harmless to environment because the final product of the transformation is nitrogen. However, direct synthesis of polynitrogens from solid nitrogen is extremely difficult because of its strong triple N≡N bond with a bonding energy of 954 kJ/mol [8]. For instance, cubic gauche phase
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(cg-N), connected through single N-N bond, was synthesized from solid nitrogen at temperatures above 2000 K and pressures above 110 GPa [9]. Although it has high energy density of 9.7 kJ g1, its synthetic conditions greatly limit its practical application. As a consequence, great efforts have been made to obtain polynitrogens at relatively low temperature and low pressure conditions [10e14]. The mixture of nitrogen-containing compound and N2 as precursor has been proved to be an effective way to reduce the synthesis pressure of polynitrogens. By compressing NaN3 with N2, the cg-N can be synthesized at a pressure of 50 GPa [15], which is remarkably lower than 110 GPa in pure N2. On the other hand, lots of metal azides have been used as starting materials to synthesize polynitrogen compounds (e.g. LiN3 [16], LiN5 [12,17], NaN3 [18,19], KN3 [20,21], and CsN5 [22,23]) at relatively low pressure. Interestingly, the transfer charge from metal to polynitrogen plays an important role in reducing the synthesis pressure and enhancing structural stabilities. Notably, the resultant charged polynitrogen species have significantly improved kinetic stabilities over pure polynitrogens [24e28]. Other nonmetal polynitrogen compounds were also reported in S-N [29], B-N [30], N-H [31], Xe-N [32], and CNO (CO/N2 mixture) [33] systems. Overall, these polynitrogen compounds can be used as the potential high energy density materials (HEDMs). Alkaline earth metals and alkali metals usually have similar properties. Much attention has been paid to alkaline earth metal polynitrides in view of excellent properties and low synthesis pressures of alkali metal polynitrides. Specifically, MgN3 and MgN4, containing the polynitrogens, become stable above 10 GPa, and have the energy density of 2.83 and 2.01 kJ g1, respectively [34]. Four N-rich chemical stoichiometries of calcium polynitrides (Ca2N3, CaN3, CaN4, and CaN5) were found to be stable at the pressure above 8 GPa [35]. As the sister element of the heavy alkaline earth metal elements (e.g. Mg and Ca), beryllium (Be) has smaller atomic radius and stronger electronegativity. It is noted that some properties are different among them. For example, MgO2 and CaO2 are stable at ambient pressure, however BeO2 becomes stable at high pressure (~89.6 GPa) [36]. Their pressure-dependent electronic properties are also different [36]. Very recently, Cui et al. studied phase diagram of Be-N system at high pressures [37]. However, their reported phases are different from ones predicted in this work. Based on our tested calculations, the real synthetic pressure of reported P21/c phase is 115.1 GPa, not less than 40 GPa. Its synthetic pressure is comparable to that of cg-N, and is not for practical application. Notably, for the same chemistry stoichiometry of polynitrogen compounds, the smaller atomic mass is one of favorable factors to enhance the energy density. As a consequence, the study of beryllium polynitrides would help to not only fully understand alkaline earth metals polynitrides but also find more promising high-energy materials. In the present study, the structures and stabilities of beryllium nitrides for various BexNy (x ¼ 1 and y ¼ 1e6; x ¼ 2e3 and y ¼ 1e3) compositions were extensively studied by using unbiased CALYPSO structural search method. For Be3N2, the reported structures and phase transition pressure were perfectly reproduced. As expected, a N-rich P1-structured BeN4, consisting of infinitely polymeric nitrogen chains (N∞), becomes energetically stable above 25.4 GPa. This phase can release a large amount of energy (3.60 kJ g1) upon decompression down to ambient pressure, which is much higher than that of MgN4 (2.01 kJ g1), and slightly lower than well-known HEDM TNT (4.3 kJ g1). BeN4 undergoes a structural phase transition from P1 to P21/c structure at pressure of 115.1 GPa. The two phases exhibit different electronic properties (i.e. metal and insulator).
2. Computational methods The structure search, for the potential BexNy compounds in the pressure range of 0e200 GPa, was carried out by Particle Swarm Optimization structure prediction method as implemented in CALYPSO code [38,39]. This methodology is effectively capable of finding stable or metastable structures only depending on the given chemical composition. Its power has been successfully illustrated by a number of applications, from element solid to binary and ternary compounds [40e46]. Detail structural predictions can be described in the Supplementary Materials. The Vienna Ab initio Simulation Package (VASP) code [47] within the framework of densityefunctional theory (DFT) was adopted to perform structural relaxations and electronic properties calculations. The PerdeweBurkeeErnzerhof (PBE) [48] functional in the generalized gradient approximation [49] was used. The electron-ion interactions were represented by means of the allelectron projector augmented-wave (PAW) method [50] with 2s2 and 2s22p3 treated as the valence electrons of Be and N atoms, respectively. The validity of the adopted pseudopotentials was examined with the full-potential linearized augmented plane-wave method as implemented in the WIEN2k package [51]. A plane-wave kinetic energy cutoff of 800 eV and Monkhorst-Pack scheme [52] with a high-quality k-point grid of 2p 0.025 Å1 in the Brillouin zone were found to give converged energy less than 1 meV/ atom. To determine the dynamical stability, the phonon calculations were performed by using a supercell approach with the finite displacement method [53] as done in the Phonopy code [54]. Electron localization function (ELF) was used to measure the degree of electron localization [55]. Bader's Quantum Theory of Atoms in Molecules (QTAIM) analysis was adopted for the charge transfer analysis [56].
3. Results and discussion 3.1. Thermodynamic stability In general, the higher nitrogen content in polynitrides, the higher is the energy density. Thus, extensive structure searches were concentrated on N-rich BexNy (x ¼ 1 and y ¼ 1e6; x ¼ 2e3 and y ¼ 1e3) compositions at 0 K and the selected pressures of 0, 50, 100, and 200 GPa. Then, their relatively energetic stabilities are determined by calculating the formation enthalpy (DHf) with respect to elementary Be and N solids using the following formula: DHf ¼ [H(BexNy) e xH(Be) e yH(N)]/(x þ y). Here, H(BexNy) is the enthalpy of the considered compound, H(Be) and H(N) are the enthalpy of elemental Be and N, respectively. The elemental Be solid with P63/mmc symmetry was used to calculate formation enthalpies over the explored pressures [57]. The Pa3 [58], P41212 [59], I213 [9], and Pba2 [60] phases of elemental N were used. The resultant DHf is used to construct convex hull (Fig. 1). Based on convex data, the thermodynamically stable structures are located on convex hull, whereas the metastable ones are located above convex hull. As illustrated in Fig. 1, Be3N2 is the only stable composition at ambient pressure, which is consistent with previous study [61]. It should be noted that Be3N2 is still stable in the high-pressure region. The two known Be3N2 phases are readily reproduced. In addition, our calculated phase transition pressure (117.5 GPa) from Ia3 to P3m1 phase is also in good agreement with the reported value (Fig. 1) [62]. These results indicate that our adopted method is suitable to Be-N system. At elevated pressures, it is exciting to note
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in Fig. 2. It obviously indicates that the DPV term makes the major contributions to DH in contrast to DU, mainly originating from the larger volume reduction of P21/c relative to P1 phase. Thus, the P21/ c phase is much denser than P1 under further compression, and the phase transition belongs to the first-order transformation. Based on the quasi-harmonic approximation calculations, the effect of temperature on the phase stability of Be-N compounds were also considered. It is found that all of stable Be-N compounds at 0 K remain thermodynamically stable at the elevated temperatures of 300 and 1000 K, respectively (Fig. S4). 3.2. Crystal structure and chemical bonding
Fig. 1. Chemical stability of Be-N binary compounds. Calculated formation enthalpies (DH) per atom of the considered Be-N compounds with respect to elemental Be and N solids. The thermodynamically stable phases at each pressure are represented by solid symbols, which are linked by the convex hull (solid lines). Data points corresponding to the metastable phases are directly linked by dotted lines. Schematic illustration of the phase diagram of Be-N system in the pressure range from 0 to 200 GPa is shown in the inset.
that only stable N-rich composition is BeN4, which is in sharp contrast with Mg-N [34,63] (MgN3 and MgN4) and Ca-N [35] (Ca2N3, CaN3, CaN4, and CaN5) systems. After detailed analysis, there are two stable BeN4 phases in the considered pressure range. P1-structured BeN4 becomes stable at 25.4 GPa, and then transforms to P21/c phase at 115.1 GPa (Fig. 2). Very recently, Cui et al. also investigated Be-N system, and just found one stable BeN4 phase at less than 40 GPa [37], which is the same as our P21/c phase. Notably, without considering the P1 phase greatly underestimates the synthesis pressure of P21/c-structured BeN4 (Fig. S2). Based on above analysis, the predicted P1-structured BeN4 can be synthesized at 25.4 GPa by using a mixture of Be3N2 and N2 as precursor (Fig. S3). This is rather lower than 50 GPa of cg-N by compressing NaN3 with N2 [15]. In fact, occurrence of this reaction needs to overcome energy barrier. Thus, the real synthesized pressure becomes larger than 25.4 GPa. To illustrate this transition mechanism, the change of enthalpy (DH), internal energy (DU), and DPV term with increasing pressure of P21/c phase with respect to P1 phase were calculated and shown
Fig. 2. (a) Calculated change of enthalpy (DH), internal energy (DU), and DPV per formula unit of P21/c-structured BeN4 with respect to P1-structured BeN4. The horizontal dashed line represents the P1 phase. (b) Pressure dependence of volume per formula unit for P1 and P21/c phases of BeN4. The vertical dashed line indicates the transition pressure.
The predicted low-pressure BeN4 stabilizes into a triclinic structure (space group P1, 2 formula units per cell, Fig. 3a). It contains one equivalent Be atom occupying the Wyckoff 2i (0.1095, 0.7935, 0.2669) site, and four inequivalent N atoms sitting at the Wyckoff 2i (0.0201, 0.0844, 0.0866), 2i (0.5511, 0.5702, 0.5845), 2i (0.9986, 0.4556, 0.0884), and 2i (0.5047, 0.9548, 0.5943) positions. Each Be atom is coordinated with five N atoms, forming a Be-N pentahedron (Fig. 3a). These pentahedrons are interlinked by sharing vertex-N atoms. Interestingly, polymerization of nitrogen is achieved in this structure. Nitrogen atoms form infinite zizag-like nitrogen chains (N∞) (Fig. 3c). According to the average N-N bond length, there are two types of nitrogen chains with different N-N distances of 1.32 and 1.35 Å, respectively. These N-N distances are larger than double N¼N bond length of 1.25 Å [64], and much shorter than single N-N bond length of 1.45 Å [65]. In addition, they are comparable to 1.35 Å in cg-N at 115 GPa) [9], indicating that it also has high energy capacity. The resultant energy density reaches 3.60 kJ g1, which is much higher than CNO (2.2 kJ g1) [33] and LiN5 (2.72 kJ g1) [12], and slightly lower than the well-known HEDM TNT (4.3 kJ g1) [66]. With further compression, P21/c phase, containing N10 rings network, is more stable than P1 above 115.1 GPa. To further describe the bonding feature of polymeric nitrogen chains in P1 phase, the electron localization function (ELF) was calculated, as performed in the VASP code. As a rule, the large ELF values (>0.5) usually correspond to the lone electron pairs, core electrons, or covalent bonds, whereas the ionic bonds are represented by smaller ELF values (<0.5). An ELF value of 0.5 is the typical metallic bond. As shown in Fig. 3d, the large ELF values locating at near N atoms indicate the lone electron pairs. The ELF values between the neighboring N atoms are large, showing that each N atom forms two strong covalent bonds with two adjacent N atoms. As illustrated in Fig. S5, the bond between Be and N atom is ionic, which is further supported by the Bader charge analysis (Table S2). 3.3. Lattice dynamical stability To examine the dynamical stabilities of P1-structured and P21/cstructured BeN4, their phonon spectra were calculated with the supercell method, as illustrated in Fig. 4a and Fig. 4c. No imaginary vibrational modes over the Brillouin zone confirm their dynamical stabilities. On the basis of the analysis of phonon density of states (PHDOS) of P1-structured BeN4 (Fig. 4b), the low-frequency vibrational modes below 33.7 THz arise mainly from the strongly coupled vibrations between Be and N atoms, whereas the highfrequency vibrational modes at ~34.5 THz are predominantly attributed to the N-N stretching mode. The similar case is also observed in the phonon density of states of P21/c-structured BeN4 (Fig. 4d). Notably, the P1 phase is dynamic stable even at ambient pressure, indicating it is mechanically stable and might be quench recoverable (Fig. S6). It is also beneficial for HEDMs [16,19,20,27,67e70].
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Fig. 3. Stable structures of the predicted BeN4 compounds. (a) Low-pressure phase of BeN4 with P1 symmetry. (b) View of buckled tenfold rings of polymeric nitrogen in P21/cstructured BeN4. (c) View of infinite polymeric nitrogen chains in BeN4 phase with P1 symmetry along the b-axis direction. (d) Two dimensional electron function localization (ELF) map shown on the N∞ plane included inequivalent N sites for the P1 structure.
Fig. 4. Lattice dynamic stability of BeN4 compounds. Phonon dispersion curves (a, c) and PHDOS (b, d) projected on Be and N atoms for P1-structured BeN4 at 30 GPa and P21/cstructured BeN4 at 120 GPa, where the red, green, and blue lines indicate the PHDOS of unit cell, Be, and N atoms, respectively. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
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3.4. Electronic properties of polymeric P1 and P21/c phases To probe the potential application and the formation mechanism of the P1 and P21/c phases, we have calculated their electronic band structures and the corresponding projected density of states (PDOS). Intriguingly, P1-structured BeN4 is metallic (Fig. 5a), while P21/c-BeN4 is an insulator (Fig. 5b). The metallicity of P1-BeN4 is kept in its stable pressure region, and mainly comes from the contribution of N 2p and Be 2p (Fig. 5c). Moreover, there is a large overlap between N 2p and Be 2p in the valence band region, indicating the strong coupling between Be 2p and N 2p (Fig. 5d). Based on the Bader charge analysis, each N atom obtains 0.43 electrons from Be atom, and the resultant Be-N bond is ionic (Table S2). This kind of charge transfer plays certain role in stabilizing polymeric nitrogen chain [12,23,35]. Pressure usually has great effect on electronic band gap. Thus, pressure dependence of electronic band gap of P21/c structure was investigated. As illustrated in Fig. 5e, its electronic band gap gradually becomes smaller with the further compression, and still keeps non-metallic feature with band gap of
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~2.36 eV at 200 GPa. Its PDOS (Fig. 5f) and charge transfer (Table S2) are nearly similar to those of P1 phase.
4. Conclusions With the aim of finding potential high-energy density materials, we have explored the energy landscape of the Be-N system at high pressures by employing first-principles swarm-intelligence structure searches. The N-rich P1-BeN4 phase, with infinite zigzag-like nitrogen chains, becomes stable above 25.4 GPa, and transforms to P21/c phase at 115.1 GPa. The P1 phase exhibits metallic feature in its stable pressure region, whereas the P21/c phase keeps the nonmetallic feature until 200 GPa. The P1-BeN4 has a much possibility to be excellent high-energy density material from the standpoint of high energy density (~3.60 kJ g1), high nitrogen content (86.1%), high dynamical stability, and relatively low stabilization pressure. Our study is also important for fully understanding structures and electron properties of beryllium nitrides.
Fig. 5. Electronic properties of stable BeN4 phases at selected pressures. Electronic band structure (a) and PDOS (c) of the P1 structure at 30 GPa, where the horizontal dashed line represents the Fermi level. (d) PDOS of the P1-structured BeN4 at 110 GPa. The vertical dashed line shows the Fermi level. (e) Pressure dependence of electronic band gap of P21/ c phase. Electronic band structure (b) and PDOS (f) of the P21/c phase at 120 GPa.
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Acknowledgements This research was supported by Natural Science Foundation of China under Nos. 21573037 and 11504007, the Postdoctoral Science Foundation of China under grant 2013M541283, the Natural Science Foundation of Jilin Province (20150101042JC), and the Fundamental Research Funds for the Central Universities (2412017QD006). Appendix A. Supplementary data Supplementary data related to this article can be found at http:// dx.doi.org/10.1016/j.jpowsour.2017.08.086. References [1] C. Zhang, C. Sun, B. Hu, C. Yu, M. Lu, Synthesis and characterization of the pentazolate anion Cyclo-N-5 in (N5)6(H3O)3(NH4)4Cl, Science 355 (2017) 374e376. [2] R.P. Singh, R.D. Verma, D.T. Meshri, J.M. Shreeve, Energetic nitrogen-rich salts and ionic liquids, Angew. Chem. Int. Ed. 45 (2006) 3584e3601. [3] G. Steinhauser, T.M. Klapotke, “Green” pyrotechnics: a chemists' challenge, Angew. Chem. Int. Ed. 47 (2008) 3330e3347. [4] H. Gao, J.M. Shreeve, Azole-based energetic salts, Chem. Rev. 111 (2011) 7377e7436. [5] Q. Zhang, J.M. Shreeve, Energetic ionic liquids as explosives and propellant fuels: a new journey of ionic liquid chemistry, Chem. Rev. 114 (2014) 10527e10574. [6] Q. Wang, Q. Wang, F. Pang, G. Wang, J. Huang, F. Nie, F.-X. Chen, Pentazadiene: a high-nitrogen linkage in energetic materials, Chem. Commun. 53 (2017) 2327e2330. [7] K.O. Christe, Polynitrogen chemistry enters the ring, Science 355 (2017) 351. [8] H. Yu, D. Duan, F. Tian, H. Liu, D. Li, X. Huang, Y. Liu, B. Liu, T. Cui, Polymerization of nitrogen in ammonium azide at high pressures, J. Phys. Chem. C 119 (2015) 25268e25272. [9] M.I. Eremets, A.G. Gavriliuk, I.A. Trojan, D.A. Dzivenko, R. Boehler, Singlebonded cubic form of nitrogen, Nat. Mater 3 (2004) 558e563. [10] B. Hirshberg, R.B. Gerber, A.I. Krylov, Calculations predict a stable molecular crystal of N8, Nat. Chem. 6 (2014) 52e56. [11] M.J. Greschner, M. Zhang, A. Majumdar, H. Liu, F. Peng, J.S. Tse, Y. Yao, A new allotrope of nitrogen as high-energy density material, J. Phys. Chem. A 120 (2016) 2920e2925. [12] F. Peng, Y. Yao, H. Liu, Y. Ma, Crystalline LiN5 predicted from first-principles as a possible high-energy material, J. Phys. Chem. Lett. 6 (2015) 2363e2366. [13] H. Wang, M.I. Eremets, I. Troyan, H. Liu, Y. Ma, L. Vereecken, Nitrogen backbone oligomers, Sci. Rep. 5 (2015) 13239. [14] A.F. Goncharov, N. Holtgrewe, G. Qian, C. Hu, A.R. Oganov, M. Somayazulu, E. Stavrou, C.J. Pickard, A. Berlie, F. Yen, Backbone NxH compounds at high pressures, J. Chem. Phys. 142 (2015) 214308. [15] M. Popov, Raman and IR study of high-pressure atomic phase of nitrogen, Phys. Lett. A 334 (2005) 317e325. €tke, J. Evers, Phase [16] S. Medvedev, I. Trojan, M. Eremets, T. Palasyuk, T. Klapo stability of lithium azide at pressures up to 60 GPa, J. Phys. Condens. Matter 21 (2009) 195404. [17] Y. Shen, A.R. Oganov, G. Qian, J. Zhang, H. Dong, Q. Zhu, Z. Zhou, Novel lithiumnitrogen compounds at ambient and high pressures, Sci. Rep. 5 (2015) 14204. [18] M. Zhang, K. Yin, X. Zhang, H. Wang, Q. Li, Z. Wu, Structural and electronic properties of sodium azide at high pressure: a first principles study, Solid State Commun. 161 (2013) 13e18. [19] H. Zhu, F. Zhang, C. Ji, D. Hou, J. Wu, T. Hannon, Y. Ma, Pressure-induced series of phase transitions in sodium azide, J. Appl. Phys. 113 (2013) 33511. [20] C. Ji, F. Zhang, D. Hou, H. Zhu, J. Wu, M.-C. Chyu, V.I. Levitas, Y. Ma, High pressure X-Ray diffraction study of potassium azide, J. Phys. Chem. Solids 72 (2011) 736e739. [21] G. Vaitheeswaran, K.R. Babu, Metal azides under pressure: an emerging class of high energy density materials, J. Chem. Sci. 124 (2012) 1391e1398. [22] F. Peng, Y. Han, H. Liu, Y. Yao, Exotic stable cesium polynitrides at high pressure, Sci. Rep. 5 (2015) 16902. [23] B.A. Steele, E. Stavrou, J.C. Crowhurst, J.M. Zaug, V.B. Prakapenka, I.I. Oleynik, High-pressure synthesis of a pentazolate salt, Chem. Mater 29 (2017) 735e741. €, Scandium cycloheptanitride, ScN7: a predicted high[24] L. Gagliardi, P. Pyykko energy molecule containing an [h7-N7]3- ligand, J. Am. Chem. Soc. 123 (2001) 9700e9701. [25] S. Fau, K.J. Wilson, R.J. Bartlett, On the stability of Nþ 5 N5, J. Phys. Chem. A 106 (2002) 4639e4644. [26] M. Zhang, H. Yan, Q. Wei, H. Wang, Z. Wu, Novel high-pressure phase with pseudo-benzene “N6” molecule of LiN3, EPL Europhys. Lett. 101 (2013) 26004. [27] X. Wang, J. Li, J. Botana, M. Zhang, H. Zhu, L. Chen, H. Liu, T. Cui, M. Miao, Polymerization of nitrogen in lithium azide, J. Chem. Phys. 139 (2013) 164710.
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Pressure-induced stable BeN4 as a high-energy density material Shoutao Zhang, Ziyuan Zhao, Lulu Liu, Guochun Yang* Centre for Advanced Optoelectronic Functional Materials Research and Key Laboratory for UV Light-Emitting Materials and Technology of Ministry of Education, Northeast Normal University, Changchun 130024, China
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The P1-BeN4 can be synthesized by the reaction of Be3N2 and N2 at 25.4 GPa. BeN4 with P1symmetry has the high energy density of 3.60 kJ g1. N∞ chains in P1-BeN4 transform to N10 rings network in P21/c phase at 115.1 GPa. P1-BeN4 is metallic, whereas P21/cBeN4 is an insulator.
a r t i c l e i n f o
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Article history: Received 4 June 2017 Received in revised form 9 August 2017 Accepted 22 August 2017 Available online 30 August 2017
Polynitrogens are the ideal rocket fuels or propellants. Due to strong triple N≡N bond in N2, the direct polymerization of nitrogen is rather difficult (i.e. extreme high temperature and high pressure). However, the use of nitrides as precursors or the reaction of N2 with other elements has been proved to be an effective way to obtain polynitrogens. Here, with assistance of the advanced first-principles swarm-intelligence structure searches, we found that P1-BeN4, containing infinite zigzag-like polymeric nitrogen chains, can be synthesized by compressing the mixture of Be3N2 and N2 at 25.4 GPa, which is greatly lower than 110 GPa for synthesizing cubic gauche nitrogen and other polynitrogen compounds (e.g. bulk CNO at 52 GPa and SN4 at 49 GPa). Its structural stability can be attributed to the coexistence of ionic BeN and covalent N-N bonds. Intriguingly, this phase has high kinetic stability and remains metastable at ambient pressure. The exceptional properties, including high energy density (3.60 kJ g1), high nitrogen content (86.1%), high dynamical stability, and low polymerization pressure, make P1-structured BeN4 a promising high energy material. Infinite nitrogen chains in P1-BeN4 transform to N10 rings network in P21/c phase at 115.1 GPa. P1-BeN4 is metallic, while P21/c-BeN4 is an insulator. © 2017 Elsevier B.V. All rights reserved.
Keywords: High-energy density material Polynitrogen compound Beryllium nitride Electronic property High pressure First-principles
1. Introduction In some special application areas (e.g. propellants, explosives, and rocket fuel), materials are required to have extremely high energy density [1]. Polynitrogens are considered as the most
* Corresponding author. E-mail address: [email protected] (G. Yang). http://dx.doi.org/10.1016/j.jpowsour.2017.08.086 0378-7753/© 2017 Elsevier B.V. All rights reserved.
suitable candidates for these applications [2e6]. This is attributed to extraordinarily large energy release upon the decomposition of singly or doubly bonded polynitrogens to solid nitrogen molecule (N2) [7]. Notably, polynitrogens are harmless to environment because the final product of the transformation is nitrogen. However, direct synthesis of polynitrogens from solid nitrogen is extremely difficult because of its strong triple N≡N bond with a bonding energy of 954 kJ/mol [8]. For instance, cubic gauche phase
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(cg-N), connected through single N-N bond, was synthesized from solid nitrogen at temperatures above 2000 K and pressures above 110 GPa [9]. Although it has high energy density of 9.7 kJ g1, its synthetic conditions greatly limit its practical application. As a consequence, great efforts have been made to obtain polynitrogens at relatively low temperature and low pressure conditions [10e14]. The mixture of nitrogen-containing compound and N2 as precursor has been proved to be an effective way to reduce the synthesis pressure of polynitrogens. By compressing NaN3 with N2, the cg-N can be synthesized at a pressure of 50 GPa [15], which is remarkably lower than 110 GPa in pure N2. On the other hand, lots of metal azides have been used as starting materials to synthesize polynitrogen compounds (e.g. LiN3 [16], LiN5 [12,17], NaN3 [18,19], KN3 [20,21], and CsN5 [22,23]) at relatively low pressure. Interestingly, the transfer charge from metal to polynitrogen plays an important role in reducing the synthesis pressure and enhancing structural stabilities. Notably, the resultant charged polynitrogen species have significantly improved kinetic stabilities over pure polynitrogens [24e28]. Other nonmetal polynitrogen compounds were also reported in S-N [29], B-N [30], N-H [31], Xe-N [32], and CNO (CO/N2 mixture) [33] systems. Overall, these polynitrogen compounds can be used as the potential high energy density materials (HEDMs). Alkaline earth metals and alkali metals usually have similar properties. Much attention has been paid to alkaline earth metal polynitrides in view of excellent properties and low synthesis pressures of alkali metal polynitrides. Specifically, MgN3 and MgN4, containing the polynitrogens, become stable above 10 GPa, and have the energy density of 2.83 and 2.01 kJ g1, respectively [34]. Four N-rich chemical stoichiometries of calcium polynitrides (Ca2N3, CaN3, CaN4, and CaN5) were found to be stable at the pressure above 8 GPa [35]. As the sister element of the heavy alkaline earth metal elements (e.g. Mg and Ca), beryllium (Be) has smaller atomic radius and stronger electronegativity. It is noted that some properties are different among them. For example, MgO2 and CaO2 are stable at ambient pressure, however BeO2 becomes stable at high pressure (~89.6 GPa) [36]. Their pressure-dependent electronic properties are also different [36]. Very recently, Cui et al. studied phase diagram of Be-N system at high pressures [37]. However, their reported phases are different from ones predicted in this work. Based on our tested calculations, the real synthetic pressure of reported P21/c phase is 115.1 GPa, not less than 40 GPa. Its synthetic pressure is comparable to that of cg-N, and is not for practical application. Notably, for the same chemistry stoichiometry of polynitrogen compounds, the smaller atomic mass is one of favorable factors to enhance the energy density. As a consequence, the study of beryllium polynitrides would help to not only fully understand alkaline earth metals polynitrides but also find more promising high-energy materials. In the present study, the structures and stabilities of beryllium nitrides for various BexNy (x ¼ 1 and y ¼ 1e6; x ¼ 2e3 and y ¼ 1e3) compositions were extensively studied by using unbiased CALYPSO structural search method. For Be3N2, the reported structures and phase transition pressure were perfectly reproduced. As expected, a N-rich P1-structured BeN4, consisting of infinitely polymeric nitrogen chains (N∞), becomes energetically stable above 25.4 GPa. This phase can release a large amount of energy (3.60 kJ g1) upon decompression down to ambient pressure, which is much higher than that of MgN4 (2.01 kJ g1), and slightly lower than well-known HEDM TNT (4.3 kJ g1). BeN4 undergoes a structural phase transition from P1 to P21/c structure at pressure of 115.1 GPa. The two phases exhibit different electronic properties (i.e. metal and insulator).
2. Computational methods The structure search, for the potential BexNy compounds in the pressure range of 0e200 GPa, was carried out by Particle Swarm Optimization structure prediction method as implemented in CALYPSO code [38,39]. This methodology is effectively capable of finding stable or metastable structures only depending on the given chemical composition. Its power has been successfully illustrated by a number of applications, from element solid to binary and ternary compounds [40e46]. Detail structural predictions can be described in the Supplementary Materials. The Vienna Ab initio Simulation Package (VASP) code [47] within the framework of densityefunctional theory (DFT) was adopted to perform structural relaxations and electronic properties calculations. The PerdeweBurkeeErnzerhof (PBE) [48] functional in the generalized gradient approximation [49] was used. The electron-ion interactions were represented by means of the allelectron projector augmented-wave (PAW) method [50] with 2s2 and 2s22p3 treated as the valence electrons of Be and N atoms, respectively. The validity of the adopted pseudopotentials was examined with the full-potential linearized augmented plane-wave method as implemented in the WIEN2k package [51]. A plane-wave kinetic energy cutoff of 800 eV and Monkhorst-Pack scheme [52] with a high-quality k-point grid of 2p 0.025 Å1 in the Brillouin zone were found to give converged energy less than 1 meV/ atom. To determine the dynamical stability, the phonon calculations were performed by using a supercell approach with the finite displacement method [53] as done in the Phonopy code [54]. Electron localization function (ELF) was used to measure the degree of electron localization [55]. Bader's Quantum Theory of Atoms in Molecules (QTAIM) analysis was adopted for the charge transfer analysis [56].
3. Results and discussion 3.1. Thermodynamic stability In general, the higher nitrogen content in polynitrides, the higher is the energy density. Thus, extensive structure searches were concentrated on N-rich BexNy (x ¼ 1 and y ¼ 1e6; x ¼ 2e3 and y ¼ 1e3) compositions at 0 K and the selected pressures of 0, 50, 100, and 200 GPa. Then, their relatively energetic stabilities are determined by calculating the formation enthalpy (DHf) with respect to elementary Be and N solids using the following formula: DHf ¼ [H(BexNy) e xH(Be) e yH(N)]/(x þ y). Here, H(BexNy) is the enthalpy of the considered compound, H(Be) and H(N) are the enthalpy of elemental Be and N, respectively. The elemental Be solid with P63/mmc symmetry was used to calculate formation enthalpies over the explored pressures [57]. The Pa3 [58], P41212 [59], I213 [9], and Pba2 [60] phases of elemental N were used. The resultant DHf is used to construct convex hull (Fig. 1). Based on convex data, the thermodynamically stable structures are located on convex hull, whereas the metastable ones are located above convex hull. As illustrated in Fig. 1, Be3N2 is the only stable composition at ambient pressure, which is consistent with previous study [61]. It should be noted that Be3N2 is still stable in the high-pressure region. The two known Be3N2 phases are readily reproduced. In addition, our calculated phase transition pressure (117.5 GPa) from Ia3 to P3m1 phase is also in good agreement with the reported value (Fig. 1) [62]. These results indicate that our adopted method is suitable to Be-N system. At elevated pressures, it is exciting to note
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in Fig. 2. It obviously indicates that the DPV term makes the major contributions to DH in contrast to DU, mainly originating from the larger volume reduction of P21/c relative to P1 phase. Thus, the P21/ c phase is much denser than P1 under further compression, and the phase transition belongs to the first-order transformation. Based on the quasi-harmonic approximation calculations, the effect of temperature on the phase stability of Be-N compounds were also considered. It is found that all of stable Be-N compounds at 0 K remain thermodynamically stable at the elevated temperatures of 300 and 1000 K, respectively (Fig. S4). 3.2. Crystal structure and chemical bonding
Fig. 1. Chemical stability of Be-N binary compounds. Calculated formation enthalpies (DH) per atom of the considered Be-N compounds with respect to elemental Be and N solids. The thermodynamically stable phases at each pressure are represented by solid symbols, which are linked by the convex hull (solid lines). Data points corresponding to the metastable phases are directly linked by dotted lines. Schematic illustration of the phase diagram of Be-N system in the pressure range from 0 to 200 GPa is shown in the inset.
that only stable N-rich composition is BeN4, which is in sharp contrast with Mg-N [34,63] (MgN3 and MgN4) and Ca-N [35] (Ca2N3, CaN3, CaN4, and CaN5) systems. After detailed analysis, there are two stable BeN4 phases in the considered pressure range. P1-structured BeN4 becomes stable at 25.4 GPa, and then transforms to P21/c phase at 115.1 GPa (Fig. 2). Very recently, Cui et al. also investigated Be-N system, and just found one stable BeN4 phase at less than 40 GPa [37], which is the same as our P21/c phase. Notably, without considering the P1 phase greatly underestimates the synthesis pressure of P21/c-structured BeN4 (Fig. S2). Based on above analysis, the predicted P1-structured BeN4 can be synthesized at 25.4 GPa by using a mixture of Be3N2 and N2 as precursor (Fig. S3). This is rather lower than 50 GPa of cg-N by compressing NaN3 with N2 [15]. In fact, occurrence of this reaction needs to overcome energy barrier. Thus, the real synthesized pressure becomes larger than 25.4 GPa. To illustrate this transition mechanism, the change of enthalpy (DH), internal energy (DU), and DPV term with increasing pressure of P21/c phase with respect to P1 phase were calculated and shown
Fig. 2. (a) Calculated change of enthalpy (DH), internal energy (DU), and DPV per formula unit of P21/c-structured BeN4 with respect to P1-structured BeN4. The horizontal dashed line represents the P1 phase. (b) Pressure dependence of volume per formula unit for P1 and P21/c phases of BeN4. The vertical dashed line indicates the transition pressure.
The predicted low-pressure BeN4 stabilizes into a triclinic structure (space group P1, 2 formula units per cell, Fig. 3a). It contains one equivalent Be atom occupying the Wyckoff 2i (0.1095, 0.7935, 0.2669) site, and four inequivalent N atoms sitting at the Wyckoff 2i (0.0201, 0.0844, 0.0866), 2i (0.5511, 0.5702, 0.5845), 2i (0.9986, 0.4556, 0.0884), and 2i (0.5047, 0.9548, 0.5943) positions. Each Be atom is coordinated with five N atoms, forming a Be-N pentahedron (Fig. 3a). These pentahedrons are interlinked by sharing vertex-N atoms. Interestingly, polymerization of nitrogen is achieved in this structure. Nitrogen atoms form infinite zizag-like nitrogen chains (N∞) (Fig. 3c). According to the average N-N bond length, there are two types of nitrogen chains with different N-N distances of 1.32 and 1.35 Å, respectively. These N-N distances are larger than double N¼N bond length of 1.25 Å [64], and much shorter than single N-N bond length of 1.45 Å [65]. In addition, they are comparable to 1.35 Å in cg-N at 115 GPa) [9], indicating that it also has high energy capacity. The resultant energy density reaches 3.60 kJ g1, which is much higher than CNO (2.2 kJ g1) [33] and LiN5 (2.72 kJ g1) [12], and slightly lower than the well-known HEDM TNT (4.3 kJ g1) [66]. With further compression, P21/c phase, containing N10 rings network, is more stable than P1 above 115.1 GPa. To further describe the bonding feature of polymeric nitrogen chains in P1 phase, the electron localization function (ELF) was calculated, as performed in the VASP code. As a rule, the large ELF values (>0.5) usually correspond to the lone electron pairs, core electrons, or covalent bonds, whereas the ionic bonds are represented by smaller ELF values (<0.5). An ELF value of 0.5 is the typical metallic bond. As shown in Fig. 3d, the large ELF values locating at near N atoms indicate the lone electron pairs. The ELF values between the neighboring N atoms are large, showing that each N atom forms two strong covalent bonds with two adjacent N atoms. As illustrated in Fig. S5, the bond between Be and N atom is ionic, which is further supported by the Bader charge analysis (Table S2). 3.3. Lattice dynamical stability To examine the dynamical stabilities of P1-structured and P21/cstructured BeN4, their phonon spectra were calculated with the supercell method, as illustrated in Fig. 4a and Fig. 4c. No imaginary vibrational modes over the Brillouin zone confirm their dynamical stabilities. On the basis of the analysis of phonon density of states (PHDOS) of P1-structured BeN4 (Fig. 4b), the low-frequency vibrational modes below 33.7 THz arise mainly from the strongly coupled vibrations between Be and N atoms, whereas the highfrequency vibrational modes at ~34.5 THz are predominantly attributed to the N-N stretching mode. The similar case is also observed in the phonon density of states of P21/c-structured BeN4 (Fig. 4d). Notably, the P1 phase is dynamic stable even at ambient pressure, indicating it is mechanically stable and might be quench recoverable (Fig. S6). It is also beneficial for HEDMs [16,19,20,27,67e70].
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Fig. 3. Stable structures of the predicted BeN4 compounds. (a) Low-pressure phase of BeN4 with P1 symmetry. (b) View of buckled tenfold rings of polymeric nitrogen in P21/cstructured BeN4. (c) View of infinite polymeric nitrogen chains in BeN4 phase with P1 symmetry along the b-axis direction. (d) Two dimensional electron function localization (ELF) map shown on the N∞ plane included inequivalent N sites for the P1 structure.
Fig. 4. Lattice dynamic stability of BeN4 compounds. Phonon dispersion curves (a, c) and PHDOS (b, d) projected on Be and N atoms for P1-structured BeN4 at 30 GPa and P21/cstructured BeN4 at 120 GPa, where the red, green, and blue lines indicate the PHDOS of unit cell, Be, and N atoms, respectively. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
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3.4. Electronic properties of polymeric P1 and P21/c phases To probe the potential application and the formation mechanism of the P1 and P21/c phases, we have calculated their electronic band structures and the corresponding projected density of states (PDOS). Intriguingly, P1-structured BeN4 is metallic (Fig. 5a), while P21/c-BeN4 is an insulator (Fig. 5b). The metallicity of P1-BeN4 is kept in its stable pressure region, and mainly comes from the contribution of N 2p and Be 2p (Fig. 5c). Moreover, there is a large overlap between N 2p and Be 2p in the valence band region, indicating the strong coupling between Be 2p and N 2p (Fig. 5d). Based on the Bader charge analysis, each N atom obtains 0.43 electrons from Be atom, and the resultant Be-N bond is ionic (Table S2). This kind of charge transfer plays certain role in stabilizing polymeric nitrogen chain [12,23,35]. Pressure usually has great effect on electronic band gap. Thus, pressure dependence of electronic band gap of P21/c structure was investigated. As illustrated in Fig. 5e, its electronic band gap gradually becomes smaller with the further compression, and still keeps non-metallic feature with band gap of
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~2.36 eV at 200 GPa. Its PDOS (Fig. 5f) and charge transfer (Table S2) are nearly similar to those of P1 phase.
4. Conclusions With the aim of finding potential high-energy density materials, we have explored the energy landscape of the Be-N system at high pressures by employing first-principles swarm-intelligence structure searches. The N-rich P1-BeN4 phase, with infinite zigzag-like nitrogen chains, becomes stable above 25.4 GPa, and transforms to P21/c phase at 115.1 GPa. The P1 phase exhibits metallic feature in its stable pressure region, whereas the P21/c phase keeps the nonmetallic feature until 200 GPa. The P1-BeN4 has a much possibility to be excellent high-energy density material from the standpoint of high energy density (~3.60 kJ g1), high nitrogen content (86.1%), high dynamical stability, and relatively low stabilization pressure. Our study is also important for fully understanding structures and electron properties of beryllium nitrides.
Fig. 5. Electronic properties of stable BeN4 phases at selected pressures. Electronic band structure (a) and PDOS (c) of the P1 structure at 30 GPa, where the horizontal dashed line represents the Fermi level. (d) PDOS of the P1-structured BeN4 at 110 GPa. The vertical dashed line shows the Fermi level. (e) Pressure dependence of electronic band gap of P21/ c phase. Electronic band structure (b) and PDOS (f) of the P21/c phase at 120 GPa.
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