Experimental realization and ambient-condition stability of the predicted cage-like N$_{10}^{6-}$ salt Be$_3$N$_{10}$

The crystalline salt Be$_3$N$_{10}$, predicted from first-principles structure search (Li et al., EPL 124, 67004 (2018)), would be the first bulk material containing the cage-like N$_{10}^{6-}$ anion: the diamondoid ten-nitrogen cage of a high-pressure phase of pure nitrogen, retained at ambient pressure through charge transfer from six Be$^{2+}$ cations per unit cell, with exclusively N-N single bonds, a computed 3.06 eV band gap, and a predicted energy density of 5.75 kJ/g. Whether this phase is a real, persistent material is unknown: no synthetic route has been demonstrated, no binary beryllium polynitride has ever been synthesized, the thermodynamic standing of Be$_3$N$_{10}$ relative to competing Be-N phases and pentazolate alternatives at ambient pressure is unpublished, and the decomposition barriers that would let a metastable sample survive decompression and ambient storage have never been computed. The open problem is to establish - by synthesis and recovery, structural and electronic verification, and quantitative metastability and decomposition-kinetics analysis - whether Be$_3$N$_{10}$ exists as an ambient-condition material (or cannot), thereby deciding the untested cage-anion branch of the metal-stabilized polynitrogen strategy that has already succeeded for pentazolate rings.

Background

High-energy-density materials (HEDMs) store chemical energy in metastable bonding arrangements and release it on decomposition. Because the N$\equiv$N triple bond of molecular nitrogen is among the strongest in chemistry, an extended nitrogen framework held together by N-N single bonds stores a large amount of energy per atom relative to its only stable decomposition product, N$_2$ gas, so realizing single-bonded polynitrogen at ambient conditions is a long-standing goal. Pure nitrogen forms such polymeric phases only under high pressure: cubic gauche nitrogen (cg-N, the polymeric phase in which every nitrogen atom is single-bonded to three neighbours), synthesized above roughly 110 GPa (Eremets, Gavriliuk, Trojan, Dzivenko and Boehler, Nature Materials 2004), and, among later predictions, a cage-like 'diamondoid' N$_{10}$ phase found by crystal-structure search (Wang, Wang, Miao, Zhong, Lv, Cui, Li, Chen, Pickard and Ma, Physical Review Letters 109, 175502 (2012)). These pure phases collapse back to molecular N$_2$ when the pressure is released. A route around this limitation is to stabilize polynitrogen species as anions in salts with metal cations, which donate charge, saturate dangling bonds, and add ionic and covalent stabilization. The strategy is validated by the pentazolate anion cyclo-N$_5^-$ (a five-membered all-nitrogen ring): LiN$_5$ was predicted from first principles (Peng, Yao, Liu and Ma, Journal of Physical Chemistry Letters 2015), and bulk pentazolate salts followed - ambient-metastable metal pentazolate hydrates made by wet chemistry (Xu, Wang, Shen, Lin, Wang and Lu, Nature 2017) and high-pressure syntheses with recovery to ambient conditions, namely CuN$_5$ (Li, Sun, Wang, Zhu and Miao, Journal of Physical Chemistry C 2018) and LiN$_5$ made at about 45 GPa from laser-heated lithium in N$_2$ (Laniel, Weck, Gaiffe, Garbarino and Loubeyre, Journal of Physical Chemistry Letters 2018). In parallel, structure searches targeted nitrogen-rich beryllium compounds, since Be$^{2+}$ is small, strongly polarizing, and an effective electron donor; an early example is a Be$_2$N$_6$ monolayer containing benzene-like N$_6$ rings (F. Li et al., Journal of Materials Chemistry C 2017). The source work (Jianfu Li, Qiwen Jiang, Zuoqin Zhu, Hongyang Zhu and Xiaoli Wang, EPL 124, 67004 (2018)) extends this logic from rings and chains to a cage: density-functional theory (DFT) calculations using the semilocal GGA-PBE exchange-correlation functional (the Perdew-Burke-Ernzerhof form of the generalized gradient approximation), combined with structure search, predict the crystalline salt Be$_3$N$_{10}$, in which the diamondoid N$_{10}$ cage of the high-pressure nitrogen phase survives at ambient pressure as a discrete N$_{10}^{6-}$ anion with exclusively N-N single bonds, charge-balanced by six Be$^{2+}$ cations per unit cell (two N$_{10}^{6-}$ cages) in the cubic space group $I\bar{4}3m$. Reported computed properties include a 3.06 eV band gap, an energy density of 5.75 kJ/g relative to decomposition into N$_2$, a nitrogen mass fraction of 83.8%, dynamical stability (no imaginary phonon modes - no destabilizing lattice vibrations - at 0 GPa), and finite-temperature stability from picosecond-scale ab initio molecular dynamics at 300 K, all as reported in the source. The work is purely computational: no synthetic route is proposed or demonstrated. Although the published abstract calls the phase kinetically and thermodynamically stable, the source record indicates its total energy lies above at least some reference combinations (for example BeN$_3$ + N$_2$), so the phase is at best metastable and its persistence hinges on decomposition barriers that were not computed. Whether this first proposed bulk, ambient-pressure N$_{10}^{6-}$ cage salt can actually be made and kept is the unresolved question.

Problem Statement

Determine whether the predicted cage-anion salt Be$_3$N$_{10}$ is a real, persistent material at ambient conditions, by establishing jointly: (1) Experimental realization - a demonstrated synthetic route (natural candidates, by analogy with the demonstrated high-pressure synthesis and ambient recovery of LiN$_5$ and CuN$_5$, are high-pressure, high-temperature reactions of beryllium with nitrogen followed by quench and recovery) that produces crystalline Be$_3$N$_{10}$; (2) Structural and electronic verification - confirmation or correction of the predicted $I\bar{4}3m$ structure, the integrity of the discrete N$_{10}^{6-}$ cage with exclusively N-N single bonds, and the computed electronic structure (including the reported 3.06 eV gap) for the recovered material, by diffraction, spectroscopy, and/or higher-level calculations; and (3) Metastability and decomposition kinetics - the thermodynamic standing of Be$_3$N$_{10}$ at ambient pressure relative to competing channels (Be-N phases plus N$_2$, and pentazolate alternatives such as BeN$_{10}$), together with the activation barriers, dominant decomposition pathways, and kinetic lifetimes that decide whether a recovered sample survives beyond the picosecond molecular-dynamics timescale at ambient conditions and as a function of temperature. These components jointly answer one question: does the N$_{10}^{6-}$ cage exist in a bulk salt recoverable to ambient conditions? A rigorous negative resolution also counts as an answer - for example, an unbiased structure search at the Be$_3$N$_{10}$ stoichiometry showing the predicted phase is unstable, or demonstrated decomposition barriers so low that recovery to ambient conditions is impossible.

References

1. Jianfu Li, Qiwen Jiang, Zuoqin Zhu, Hongyang Zhu, Xiaoli Wang, 'Cage-like N$_{10}^{6-}$ salt with N-N single bonds', EPL (Europhysics Letters) 124, 67004 (2018). DOI: 10.1209/0295-5075/124/67004, https://doi.org/10.1209/0295-5075/124/67004
2. Mikhail I. Eremets, Alexander G. Gavriliuk, Ivan A. Trojan, Dymitro A. Dzivenko, Reinhard Boehler, 'Single-bonded cubic form of nitrogen', Nature Materials 3, 558-563 (2004). DOI: 10.1038/nmat1146, https://doi.org/10.1038/nmat1146
3. Xiaoli Wang, Yanchao Wang, Maosheng Miao, Xin Zhong, Jian Lv, Tian Cui, Jianfu Li, Li Chen, Chris J. Pickard, Yanming Ma, 'Cagelike Diamondoid Nitrogen at High Pressures', Physical Review Letters 109, 175502 (2012). DOI: 10.1103/PhysRevLett.109.175502, https://doi.org/10.1103/PhysRevLett.109.175502
4. Feng Peng, Yansun Yao, Hanyu Liu, Yanming Ma, 'Crystalline LiN$_5$ Predicted from First-Principles as a Possible High-Energy Material', Journal of Physical Chemistry Letters 6, 2363-2366 (2015). DOI: 10.1021/acs.jpclett.5b00995, https://doi.org/10.1021/acs.jpclett.5b00995
5. Yuangang Xu, Qian Wang, Cheng Shen, Qiuhan Lin, Pengcheng Wang, Ming Lu, 'A series of energetic metal pentazolate hydrates', Nature 549, 78-81 (2017). DOI: 10.1038/nature23662, https://doi.org/10.1038/nature23662
6. Feng Li, Yu Wang, Hong Wu, Zhifa Liu, Urs Aeberhard, Yafei Li, 'Benzene-like N$_6$ rings in a Be$_2$N$_6$ monolayer: a stable 2D semiconductor with high carrier mobility', Journal of Materials Chemistry C 5, 11515-11521 (2017). DOI: 10.1039/C7TC03363J, https://doi.org/10.1039/C7TC03363J
7. Jianfu Li, Lei Sun, Xiaoli Wang, Hongyang Zhu, Maosheng Miao, 'Simple Route to Metal cyclo-N$_5^-$ Salt: High-Pressure Synthesis of CuN$_5$', The Journal of Physical Chemistry C 122, 22339-22344 (2018). DOI: 10.1021/acs.jpcc.8b08924, https://doi.org/10.1021/acs.jpcc.8b08924
8. D. Laniel, G. Weck, G. Gaiffe, G. Garbarino, P. Loubeyre, 'High-Pressure Synthesized Lithium Pentazolate Compound Metastable under Ambient Conditions', Journal of Physical Chemistry Letters 9, 1600-1604 (2018). DOI: 10.1021/acs.jpclett.8b00540, https://doi.org/10.1021/acs.jpclett.8b00540
9. Jiani Lin, Zuoqin Zhu, Qiwen Jiang, Shitai Guo, Jianfu Li, Hongyang Zhu, Xiaoli Wang, 'Stable zigzag and tripodal all-nitrogen anion N$_4^{4-}$ in BeN$_2$', AIP Advances 9, 055116 (2019). DOI: 10.1063/1.5098867, https://doi.org/10.1063/1.5098867
10. Kang Xia, Xianxu Zheng, Jianan Yuan, Cong Liu, Hao Gao, Qiang Wu, Jian Sun, 'Pressure-Stabilized High-Energy-Density Alkaline-Earth-Metal Pentazolate Salts', The Journal of Physical Chemistry C 123, 10205-10211 (2019). DOI: 10.1021/acs.jpcc.8b12527, https://doi.org/10.1021/acs.jpcc.8b12527
11. Zhixiu Wang, Tao Yang, Bingchao Yang, Wencai Yi, 'Prediction of stable energetic beryllium pentazolate salt under ambient conditions', CrystEngComm 22, 6057-6062 (2020). DOI: 10.1039/d0ce00780c, https://doi.org/10.1039/d0ce00780c
12. Xunjiang Zhang, Xing Xie, Huafeng Dong, Xin Zhang, Fugen Wu, Zhongfei Mu, Minru Wen, 'Pressure-Induced High-Energy-Density BeN$_4$ Materials with Nitrogen Chains: First-Principles Study', The Journal of Physical Chemistry C 125, 25376-25382 (2021). DOI: 10.1021/acs.jpcc.1c07500, https://doi.org/10.1021/acs.jpcc.1c07500
13. Shuang Liu, Hai-yan Li, Zhen Yao, Shuangchen Lu, 'Study of cage-like diamondoid polymeric nitrogen N$_{10}$ confined inside single-wall carbon-nanotube', Materials Today Communications 26, 101670 (2021). DOI: 10.1016/j.mtcomm.2020.101670, https://doi.org/10.1016/j.mtcomm.2020.101670
14. Zhi-Xin Bai, Cheng-Lu Jiang, Sheng-Hai Zhu, Mi Zhong, Ming-Jian Zhang, Fu-Sheng Liu, Bin Tang, Qi-Jun Liu, Xiang-Hui Chang, 'First-principles study of the structural phase transition process of solid nitrogen under pressure', Journal of Molecular Modeling 27, 307 (2021). DOI: 10.1007/s00894-021-04919-6, https://doi.org/10.1007/s00894-021-04919-6
15. Qinglin Wang, Xiaofeng Wang, Jianfu Li, Tianru Qin, Dandan Sang, Jiaoli Liu, Feng Ke, Xiaoli Wang, Yinwei Li, Cailong Liu, 'Conduction transition and electronic conductivity enhancement of cesium azide by pressure-directed grain boundary engineering', Journal of Materials Chemistry C 9, 4764-4770 (2021). DOI: 10.1039/D1TC00382H, https://doi.org/10.1039/D1TC00382H
16. Shuyi Lin, Meiling Xu, Yiwei Liang, Xuanhao Yuan, Yiming Zhang, Feilong Wang, Jian Hao, Yinwei Li, 'Ambient-Pressure Recoverable Polynitrogen Solids Assembled by Pentazolate Rings with High Energy Density', Inorganic Chemistry 61, 15532-15539 (2022). DOI: 10.1021/acs.inorgchem.2c02240, https://doi.org/10.1021/acs.inorgchem.2c02240
17. Ran Liu, Miao Yu, Haodi Zhang, Peng Wang, Shuang Liu, Zhen Yao, Bingbing Liu, Shuangchen Lu, 'Capturing High-Energy Polymeric Nitrogen Structures Stabilized by Lutetium at Ambient Conditions', Inorganic Chemistry 64, 2748-2757 (2025). DOI: 10.1021/acs.inorgchem.4c04710, https://doi.org/10.1021/acs.inorgchem.4c04710
18. Georg Krach, Lukas Brüning, Sebastian Ambach, Elena Bykova, Nico Giordano, Björn Winkler, Maxim Bykov, Wolfgang Schnick, 'High-Pressure Synthesis of Ultra-Incompressible Beryllium Tungsten Nitride Pernitride BeW$_{10}$N$_{14}$(N$_{2}$)', Angewandte Chemie International Edition 64, e202505778 (2025). DOI: 10.1002/anie.202505778, https://doi.org/10.1002/anie.202505778