Ambient-condition realization of the predicted zig-zag polymeric nitrogen chain phases C2/m-PN$_x$ ($x=6$–$14$) and the covalently bonded N$_6$-ring phase R-PN$_6$

First-principles structure searches predict a family of nitrogen-rich phosphorus nitrides — C2/m-PN$_x$ ($x=6,8,10,12,14$), hosting one-dimensional zig-zag nitrogen chains between PN$_6$ octahedra, and the metastable R-PN$_6$, hosting the first N$_6$ ring stabilized by covalent bonds to phosphorus — that are dynamically and mechanically stable at ambient pressure and are computed to have detonation performance exceeding TNT and HMX. Whether these phases can be synthesized under high pressure, recovered (quenched) to ambient conditions, kept stable there against decomposition, and have their predicted energetic and hardness properties validated is entirely open: no experiment has produced any phosphorus nitride richer in nitrogen than PN$_2$, no decomposition or formation barriers have been computed for these phases.

Background

Single-bonded (polymeric) nitrogen is a long-sought class of high-energy-density materials (HEDMs): the N–N single bond stores far less energy than the triple bond of the N$_2$ molecule, so a solid made of polymerized nitrogen can in principle release large amounts of energy while yielding only N$_2$ as the exhaust product. The first polymeric nitrogen, the cubic gauche phase (cg-N), was synthesized in a laser-heated diamond anvil cell at about 110 GPa and 2000 K (Eremets et al., 2004); layered polymeric phases (LP-N, Tomasino et al. 2014; black-phosphorus-type BP-N, Laniel et al. 2020) followed at 100–150 GPa. A persistent obstacle is that most high-pressure polymeric nitrogen motifs decompose when the pressure is released, so recent work explores chemical routes (free-standing cg-N stable at 760 K under ambient pressure, Xu et al. 2024) and nitrogen-rich compounds in which a second element stabilizes polynitrogen motifs at lower pressures — e.g. pentazolate salts (materials containing the five-membered cyclic N$_5^-$ ring anion) and metal polynitrides with N$_6$ and N$_8$ anionic units (Aslandukov et al. 2024; Zhang et al. 2026).

Within this program, the one-dimensional zig-zag nitrogen chain — the motif of the hypothetical pure-nitrogen chain phase Ch-N, built from N$_2$ dimers joined in a buckled chain — had never been realized inside a compound, and all pure-nitrogen chain phases previously predicted to adopt it show imaginary phonon frequencies (i.e. lattice vibrations with negative frequency, signalling dynamical instability) at ambient pressure. Zhang, Chen, Zhang, Zhang and Wang (arXiv:2502.19729; published as Chinese Physics Letters 43, 030801, 2026) addressed this with CALYPSO particle-swarm crystal-structure prediction (a method that searches for low-enthalpy crystal structures at fixed composition and pressure) combined with density-functional theory calculations (using the PBE exchange-correlation functional, a standard approximation for electron–electron exchange and correlation in density-functional theory, with van der Waals dispersion corrections). They predicted a structurally homologous series, C2/m-PN$_x$ with $x=6,8,10,12,14$ (C2/m is the monoclinic space group of the crystal structure), in which zig-zag N chains of growing length are terminated and stabilized by corner-sharing PN$_6$ octahedra: C2/m-PN$_6$ lies on the convex hull (the tie-line of lowest formation enthalpy versus composition, below which no phase is thermodynamically stable) between 43 and 100 GPa, and the other members become stable near 53–58 GPa. Phonon dispersion and elastic-constant calculations show all five phases, plus the metastable rhombohedral R-PN$_6$ (space group R3m, 66 meV/atom above the convex hull at 100 GPa, with a non-coplanar N$_6$ ring held by six covalent P–N bonds — the first N$_6$ ring reported to be stabilized covalently rather than ionically), remain dynamically and mechanically stable when decompressed to 0 GPa, suggesting they could be quenched to ambient conditions. The longest chain sustainable is 14 nitrogen atoms (C2/m-PN$_{14}$): beyond it, an inter-chain vibrational mode at the Brillouin-zone point A (a high-symmetry wavevector of the crystal's reciprocal lattice) softens to negative frequency. Using the empirical Kamlet–Jacobs detonation relations (empirical formulas estimating detonation velocity and pressure from an explosive's composition and heats of formation; Kamlet and Jacobs, 1968) the authors estimate detonation velocities and pressures exceeding TNT and HMX (for R-PN$_6$: energy density 5.915 kJ/g, detonation velocity 11.447 km/s, detonation pressure 81.415 GPa), and a first-principles hardness proxy gives R-PN$_6$ a Vickers hardness of 47.59 GPa (Vickers hardness is a standard indentation-hardness scale).

The calculations establish thermodynamic plausibility and lattice-level (phonon and elastic) stability only. They provide no synthesis pathway or reaction-barrier information, no activation barriers against decomposition at ambient conditions, no atmospheric or thermal-stability data, and the energetic and hardness figures rest on empirical detonation relations calibrated on conventional C/H/N/O explosives and on idealized hardness models. For comparison, the only high-pressure experimental study of the phosphorus–nitrogen system (Laniel et al. 2022, laser-heated diamond anvil cells up to 137 GPa) reached no composition richer in nitrogen than PN$_2$; no N/P ratio above 2 has ever been synthesized in this binary system.

Problem Statement

Can the predicted ambient-pressure-stable polymeric-nitrogen phosphorus nitrides — the zig-zag-chain phases C2/m-PN$_x$ ($x=6,8,10,12,14$) and the covalently bonded N$_6$-ring phase R-PN$_6$ — be realized as actual materials at ambient conditions, and do their predicted properties hold? The single scientific objective is to convert these in-silico candidates into synthesized, recovered, and validated materials, and it decomposes into linked, jointly necessary parts: (1) identify viable synthesis routes — high-pressure/high-temperature conditions, precursors, and reaction pathways (including kinetic barriers to formation) under which the phases can be made, noting that no phosphorus nitride with N/P ratio above 2 has ever been synthesized; (2) demonstrate recovery, i.e. quenching of the synthesized phases from their stabilization pressures (roughly 43–100 GPa) to ambient pressure without decomposition or transformation, as the phonon and elastic stability at 0 GPa suggest but do not prove; (3) establish kinetic stability at ambient conditions — activation barriers to decomposition into P3N5-rich phases plus N$_2$, chemical stability in atmosphere, and thermal stability at elevated temperatures, none of which have been computed or measured; and (4) validate the predicted performance metrics: the detonation velocity, detonation pressure, and energy density estimated via the empirical Kamlet–Jacobs relations and the Vickers hardness of 47.59 GPa for R-PN$_6$, against experiment or higher-accuracy calculations (including the effect of the exchange-correlation functional, zero-point and finite-temperature contributions). Each of the four parts may be resolved by the strongest available mode — measurement or a first-principles or analytical demonstration (computed formation and decomposition barriers, candidate synthesis routes and quench conditions, and higher-accuracy property calculations) — and a complete answer states which mode was used for each part and either (i) demonstrates, for each of the six phases, whether a synthesis route exists and, for those that can be made, reports the recovered structure, how long and under what conditions it survives at ambient pressure, and its energetic and hardness properties, or (ii) demonstrates with explicit evidence that none can be formed.

References

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