Nitrogen oxides under pressure: stability, ionization, polymerization and superconductivity

Abstract

Nitrogen oxides are textbook class of molecular compounds, with extensive industrial applications. Nitrogen and oxygen are also among the most abundant elements in the universe. We explore the N-O system at 0 K and up to 500 GPa though ab initio evolutionary simulations. Results show that two phase transformations of stable molecular NO₂ occur at 7 and 64 GPa and followed by decomposition of NO₂ at 91 GPa. All of the NO⁺NO₃⁻ structures are found to be metastable at T = 0 K, so experimentally reported ionic NO⁺NO₃⁻ is either metastable or stabilized by temperature. N₂O₅ becomes stable at 9 GPa and transforms from P-1 to C2/c structure at 51 GPa. NO becomes thermodynamically stable at 198 GPa. This polymeric phase is superconducting (T_c = 2.0 K) and contains a -N-N- backbone.

Introduction

Both nitrogen and oxygen have been extensively investigated in experiments and theoretical simulations. Generally, nitrogen is an insulator or a semiconductor. Cubic gauche phase of nitrogen¹ is stable in a wide range of pressure². Other nitrogen structures, such as chain and rings^3,4,5, have also been reported. All known phases of oxygen are molecular^6,7. Experiments and first-principles calculations for oxygen under high pressure revealed the complex evolution of insulator->semiconductor->metal->semiconductor⁸. The superconductivity of solid oxygen (T_c = 0.6 K) was observed at pressure above 96 GPa in experiment⁹. The known nitrogen oxides are semiconducting (for example, the band gap of Im-3 NO₂ calculated is approximately 2.8 eV).

At ambient pressure, nitrogen oxides exist as molecular crystals with many applications in chemical industry and important biological roles. The volumetric behavior of nitrous oxide under pressure has been investigated since 1961¹⁰. The synthesis and phase transformations of N₂O have been analyzed in experimental and theoretical studies^{11,12,13,14,15,16}. Different from normal phases containing N₂O₄ molecules, the ionic NO⁺NO₃⁻ was reported in the range of 1.5 to 3.0 GPa¹⁷. The typical N-O stretching frequency of NO⁺ was characterized at 2234 cm⁻¹, consistent with previous reports^17,18. In 2001, Somayazulu et al.¹⁹ synthesized the ionic NO⁺NO₃⁻ (nitrosonium nitrate) phase from N₂O at above 20 GPa and 1000 K and performed first structural characterization of NO⁺NO₃⁻. Somayazulu et al.¹⁹ proposed an ionic NO⁺NO₃⁻ model based on aragonite with space group of P2₁cn. Other P2₁/m²⁰ and Pna2₁¹⁶ models of NO⁺NO₃⁻ were also suggested and the later one is more stable. However, the simulated XRD data of the Pna2₁ structure is quite different from that in experiments, indicating that other undiscovered stable NO⁺NO₃⁻ structures might exist.

Results and Discussions

We employed the evolutionary algorithm USPEX^21,22,23,24 to predict stable N-O compounds and structures under high pressures. Up to 500 GPa, only three stable N-O compounds were found (NO₂, N₂O₅ and NO), as seen in Fig. 1. Most of them retain their molecular structures even under high pressure. Experimentally known “laughing gas” N₂O is metastable. The stable phases are discussed as follows.

• 1 NO₂: Besides the known cubic (Im-3) and monoclinic (P2₁/c) NO₂ structures are stable in pressure ranges of 0–7 and 7–64 GPa respectively, another P2₁/c structure was found to be stable from 64 to 91 GPa (Fig. 2a). Similar to the known phases, this novel NO₂ structure also contains N₂O₄ molecules. Different from known P2₁/c NO₂, the proposed P2₁/c NO₂ is denser and has 8 formula units in the unit cell. NO₂ decomposes at 91 GPa.

  Figure 2

  

  Structures of (a) P2₁/c NO₂, (b) P-1 and (c) C2/c N₂O₅, (d) P2₁/m NO.

• 2 N₂O₅: Molecular N₂O₅ phases are stable in a wide pressure range (9–446 GPa). At 51 GPa, N₂O₅ transforms from P-1 (Fig. 2b) to C2/c (Fig. 2c) structure. The N₂O₅ molecules remain planar. At 446 GPa, N₂O₅ becomes unstable and decomposes into NO and O. At 0 GPa, the P-1 N₂O₅ is 0.04 eV/atom more stable than known hexagonal NO₂NO₃, however, both of them are calculated to be above the convex hull and therefore metastable.

• 3 NO: NO is a metastable compound at low pressures. A polymeric NO structure (Fig. 2d, P2₁/m) becomes stable at 198 GPa. Nitrogen atoms form a strong covalent backbone (N-N = 1.34 Å) in the shape of a zigzag chain. Indeed, that is right between the typical values of single (1.45 Å) and double (1.25 Å) nitrogen-nitrogen bonds. Each nitrogen atom is also bonded to one oxygen atom (N-O bond length is 1.20 Å). A similar backbone has also been reported for the N-H system²⁵. Distance between neighboring quasi-one-dimensional structures is 1.86 Å. Phonon dispersion curves of this remarkable polymeric phase were calculated (shown in Fig. S6). No imaginary frequencies were observed, implying its dynamical stability.

Figure 1

Phase diagram of the N–O system.

While most of the stable N-O phases are semiconducting, polymeric NO is metallic. The band structure of NO is shown in Fig. 3. Using the Allen-Dynes modified McMillan equation^26,27 with value of the Coulomb pseudopotential μ* = 0.13, polymeric NO is superconducting with T_c = 2.0 K at 200 GPa, which is close to that of oxygen^8,9.

Figure 3

Band structure of P2₁/m NO at 198 GPa. Z(0,0,0.5), A(0.5,0.5,0.5), M(0.5,0.5,0), G(0,0,0), R(0,0.5,0.5) and X(0,0.5,0).

As mentioned above, ionic NO⁺NO₃^- has been observed in several high-pressure experiments^19,20,28. However, no stable NO⁺NO₃⁻ structure was found in our variable-composition searches. To find the lowest-enthalpy ionic NO⁺NO₃⁻ structure, we performed (NO)_n(NO₃)_n (n = 6 or 8) calculations at 0–50 GPa, assembling structures from ready-made NO and NO₃ units in variable proportion. A novel metastable monoclinic NO⁺NO₃⁻ (P2₁, Fig. 4) was found to be more stable than orthorhombic phase¹⁶ and monoclinic P2₁/m NO⁺NO₃^− 20 at pressures above 1.7 GPa. The main difference between novel P2₁ and P2₁/m NO⁺NO₃⁻ models²⁰ is the orientation of the NO⁺ molecules. Importantly, at all pressures structures made of N₂O₄ molecules are more stable than ionic NO⁺NO₃⁻ structures (Fig. 4)

Figure 4

Enthalpies of NO₂ phases as a function of pressures.

In experiments, the typical Raman frequencies of NO⁺NO₃⁻ are 2234 cm⁻¹ for the N-O stretch in NO⁺, together with 1345, 1056 and 721 cm⁻¹ for anti-symmetric stretch, symmetric stretch and in-plane deformation for NO₃⁻ respectively^{17,19,28,29,30}. The Raman frequencies and intensities of NO⁺NO₃⁻ and NO₂ structures were calculated at 20 GPa. Here, Raman frequencies of NO⁺ and NO₃⁻ were used for comparison. As shown in Fig. 5, the computed Raman spectra of P2₁/c NO₂ and Pna2₁ NO⁺NO₃⁻ are significantly different from experimental ones.¹⁷. The typical Raman frequencies of N-O stretch are 2071 cm⁻¹ of P2₁ and 2151 cm⁻¹ of P2₁/m structures. Both of them basically match the experimental data¹⁹, but that of P2₁ NO⁺NO₃⁻ obtains better match in terms of relative intensity. Similar comparison for Raman and XRD data could also be observed under other pressures^20,31.

Figure 5

Simulated Raman spectra of P2₁/c NO₂ and P2₁, P2₁/m²⁰ and Pna2₁¹⁶ NO⁺NO₃⁻ at 20 GPa.

Typical Raman frequencies of NO⁺ and NO₃⁻ in experiment¹⁷ were drawn by dotted lines.

In summary, stable NO₂, N₂O₅ and NO phases were found in N-O system up to 500 GPa. The P2₁/c NO₂ becomes stable at 64 GPa and decomposes at 91 GPa. N₂O₅ with P-1 becomes stable at 9 GPa, transforms to C2/c at 51 GPa and decomposes at 446 GPa. The only metallic structure (P2₁/m NO) has -N-N- zigzag backbone and possesses superconductivity with T_c = 2.0 K. Our results show that ionic NO⁺NO₃⁻ is metastable and we identify a novel P2₁ structure that matches experimental data better and has lower enthalpy than previously proposed structures.

Methods

An evolutionary algorithm, as implemented in the USPEX code^21,22,23,24, were utilized to search for the stable compounds and structures. This method has already been successfully applied to study numerous systems, including nitrogen and oxygen under pressure^5,7. Structure relaxations were done using density functional theory (DFT)^32,33 within the generalized gradient approximation (GGA)³⁴ using the all-electron projector augmented wave (PAW)^35,36 method as implemented in the VASP code³⁷. The plane-wave kinetic energy cutoff was set to 600 eV and Brillouin zone was sampled at a resolution of 2π×0.06 Å⁻¹. At first, variable-composition were carried out at 0, 10, 20, 30, 50, 100, 150, 200, 250, 300, 350, 400, 450 and 500 GPa. Stability of compounds was judged using the convex hull construction: those compounds which are on the convex hull (i.e. which are more favorable than any isochemical mixture of other phases) are thermodynamically stable at given conditions. The PHONOPY code³⁸ was employed to calculate phonon dispersions for all promising structures and all the discussed structures were found to be dynamically stable. All Raman frequencies and intensities were calculated according to the method of Porezag and Pederson³⁹. The electron–phonon coupling calculations in Quantum Espresso⁴⁰ with 180 Ry plane-wave cutoff energy were used to calculate the critical temperature of superconductivity (T_c).