A novel class of oxynitrides stabilized by nitrogen dimer formation

Despite the wide applicability of oxynitrides from photocatalysis to refractory coatings, our understanding of the materials has been limited in terms of their thermodynamics. The configurational entropy via randomly mixed O/N or via cation vacancies are known to stabilize oxynitrides, despite the positive formation enthalpies. Here, using tin oxynitrides as a model system, we show by ab initio computations that oxynitrides in seemingly charge-unbalanced composition stabilize by forming pernitrides among metal-(O,N)6 octahedra. The nitrogen pernitride dimer, =(N-N)=, results in the effective charge of −4, facilitating the formation of nitrogen-rich oxynitrides. We report that the dimer forms only in structures with corner-sharing octahedra, since the N-N bond formation requires sufficient rotational degrees of freedom among the octahedra. X-ray photoemission spectra of the synthesized tin oxynitride films reveal two distinct nitrogen bonding environments, confirming the computation results. This work opens the search space for a novel kind of oxynitrides stabilized by N dimer formation, with specific structural selection rules.

Doping or mixing different species of anions in ceramics' lattice may extend the known horizon of materials properties. Oxynitrides (or equivalently oxide nitrides) are one example where oxygen and nitrogen compose the anion sublattice 1 . The discovered oxynitrides have proven to be useful engineering materials in various applications including photocatalysts 2 , passivation layers 3 , refractory materials 4 or LED phosphors 5 . Compared to cation mixed ceramics, however, understanding on oxynitrides has been limited in terms of their crystal structures, compositions and elements comprising oxynitrides. The number of synthesized crystalline oxynitrides falls far below those of oxides or nitrides, with some well-known oxynitrides including perovskite-based oxynitrides 6,7 , SiO x N y 5 , AlO x N y 8 , GaO x N y 9 , TaO x N y 10 , or more complex ones with several cations such as SiAl z O x N y 3 . A significant portion of vacancies and the following configurational entropy have been argued to stabilize the structure despite the positive enthalpy of formation 9,11,12 .
Recently discovered crystalline tin oxynitrides, however, calls for further understanding on the thermodynamics of oxynitride formation 13 . Sputtering rutile SnO 2 under ammonia/nitrogen environment results in nitrogen-rich tin oxynitrides in fluorite-type (Spacegroup: Pa3) structure. The compound forms only in this specific phase, suggesting that the thermodynamics of phase selection in oxynitrides may differ significantly from those in its oxide counterparts; fluorite SnO 2 is a high-pressure phase that forms at above 10 GPa. In addition, the nitrogen-rich composition calls for questions in the charge balancing problem. Since tin does not form 5+ oxidation state, each nitrogen incorporation into fluorite SnO 2 requires oxygen vacancy formation to meet the charge neutrality:  15 . The formation of nitrogen-rich tin oxynitrides, therefore, suggests that additional stabilization mechanism to configurational entropy may exist for the ceramics.
Here, we use density functional theory (DFT) computations to study the energetics of phase selection among tin oxynitride polymorph phases. For 7 different O-N substitution ratios, the formation energies are compared in four well-known SnO 2 polymorph structures, namely the rutile (P4 2 /mnm), CaCl 2 -type (Pnnm), α-PbO 2 type (Pbcn) and the fluorite-type (Pa3) structures (Fig. 1). To study whether specific O-N ordering affects the thermodynamics of oxynitrides, we study 30 symmetrically distinct O-N configurations for each structure and composition. We find that specific O-N configuration leads to the nitrogen-nitrogen covalent bond formation and significantly stabilizes the fluorite phase as opposed to the other phases unaffected by O-N configurations. Experimental characterization efforts reveal nitrogen-nitrogen bonding in the synthesized thin films, confirming the results of the computation.   been verified by both experimental and computational work 11,16 . The lowest energy O-N ordering that is also consistent with the experimentally observed case differs only by 74 meV per two anions from the highest energy ordering 11 . This is much less than the 603 meV observed among O-N orderings in fluorite SnO 0.5 N 1.5 (Pa3) phase. The other structures do not get affected by the different O-N orderings, with the energies between ordering varied by only 8 meV. The large energy difference in fluorite also exceeds the formation energy difference of 100 meV/f.u. between the ground state (rutile) and high-pressure phase (fluorite) SnO 2 ( Supplementary Fig. S2). This large enthalpy difference, on the order of bond breaking, signals that specific O-N ordering may lead to additional covalent bond formation. The lowest-energy configuration yields reduced unit cell volume (34.4 Å 3 /f.u.) compared to that (37.35 Å 3 /f.u.) of the high-energy configuration (Supporting Table S1). The 8% volume difference shows that nitrogen dimer formation leads to the more tightly packed material in the same composition. The density for the lowest-energy configuration is 7.23 g/cm 3 , notably higher than that of rutile SnO 2 (6.61 g/cm 3 ) or that of the highest-energy configuration (6.66 g/cm 3 ). The increased density of tin oxynitrides despite the inclusion of larger-sized nitrogen atoms is in good agreement with the experimental observations that the synthesized tin oxynitride thin films possess higher density (7.49 g/cm 3 ) than the rutile SnO 2 (6.99 g/cm 3 ) 13 .

Results
The pernitride formation is observed consistently in fluorite SnO 2−x N x in all seven compositions we considered. At each composition, the lowest-energy configuration in fluorite phase always involves the nitrogen dimer formation, even when fluorite is not the ground state at SnO 1.67 N 0.33 composition. While such anion-anion bonding has rarely been observed in oxide ceramics 18 , it has been observed in some classes of transition metal nitrides. For instance, PtN 2 has been reported to form N-N bonding among PtN 6 octahedra, with the nitrogen dimers exhibiting valences of −4 ( Supplementary Fig. S3) 19,20 . Since the nitrogen atoms participate in forming a covalent single bond with each other, the effective valences of the pernitrides [=N-N=] are −4, with each nitrogen being effectively −2 valence. This unique feature to nitrogen-containing compounds effectively solves the charge neutrality problem, eliminating the need for excessive vacancy formation mentioned in the Introduction.
The density of states (DOS) and crystal orbital Hamilton population 21,22 (COHP) shown in Fig. 3 reveal the electronic structure of the lowest-energy SnO 0.5 N 1.5 configuration and the nature of its N-N bonding. The atomic orbital-projected DOS in Fig. 3a reveal that N 2p orbitals are responsible for the reduced band gap of the oxynitride compared to the oxide counterpart. The COHP diagrams in Fig. 3b show bonding orbitals to the right of the neutral axis and antibonding orbitals to the left. We notice filled antibonding orbitals among N-N interaction, with the antibonding states reaching down to −3.35 eV from the Fermi level. The qualitative molecular orbital diagrams in Supplementary Fig. S4 show that a nitrogen dimer fills the antibonding states, only when the dimer accepts additional electrons from its neutral state. Similar, yet more comprehensive diagrams have been reported in the literature 20   Interestingly, the Sn-N interaction in SnN 6 octahedra shows only the bonding states, with unfilled antibonding states above the Fermi level. This contrasts the Sn-N interaction in Sn 3 N 4 where we clearly observe low-density yet filled antibonding states ( Supplementary Fig. S5). Sn-O interaction, on the other hand, shows consistently filled antibonding states in both SnO 0.5 N 1.5 and rutile SnO 2 , indicating that Sn-O interaction does not get affected by N-N dimer formation as much as the Sn-N interaction. In the charge density difference plot (Fig. 3c), the electron density between the two neighboring N atoms increases at the center and decreases between the center point and the atoms. This indicates that the formation of N-N bond is covalent, with electron cloud shifting towards the center compared to their atomic states. We also notice that the electron density isosurface around each N atom has three large blobs towards the Sn atoms that the N bonds to. This shows that Sn's electron cloud shifts towards N from Sn, reflecting partially ionic character of the Sn-N bonds. At the same electron density isosurface, however, we do not observe as much electron cloud shift towards oxygen, although the electronegativity difference is greater between Sn and O than that between Sn and N. This suggests that the formation of N-N dimer adds some ionic character of the Sn-N interaction.
Performing similar analyses on the lowest-energy SnO 1.67 N 0.33 further confirm that N-N bond formation affects the Sn-N interaction. The unit cell for the lowest-energy SnO 1.67 N 0.33 configuration contains 4 nitrogen atoms, with two forming N-N bonds while the other two not participating in N-N bond formation (Fig. 4a). The cell thus provides the model system to examine the difference in Sn-N interaction via COHP between the dimer-forming N atoms and regular N atoms that do not participate in pernitride formation. Figure 4b shows that the DOS has strongly localized states near the band gap, contributed largely by the N 2p orbitals. The COHP in Fig. 4c shows that the dimered N-N interaction results in strongly localized antibonding states just below the band gap. The Sn-N interaction of the dimered N atom shows strongly localized bonding states and no antibonding orbitals occupied, similar to those observed in SnO 0.5 N 1.5 . The Sn-N interaction of the non-dimered N in the same unit cell, however, shows COHP similar to that of Sn 3 N 4 , with glimpse of antibonding states near the band gap. This contrast clearly shows that N-N bond formation changes the nature of the Sn-N interaction, affecting the overall electronic structure and ionic character to the material.
The existence of N-N bonding is confirmed experimentally by observing the X-ray photoemission spectra (XPS). Figure 5 plots the XPS obtained from the synthesized tin oxynitride thin films with the reported composition of SnO 0.39 N 1.26 13 . The XPS spectra reveal two distinct bonding environment for nitrogen, one corresponding to Sn-N bonds at 396.6 eV and the other to N-N bonds at 404.2 eV. The two bonding environments consistently occur in both polycrystalline films grown on glass substrates and epitaxial films grown on MgO substrates. The grown films are reported to be in fluorite phase via X-ray diffraction, without any sign of secondary phases 13 . These results, in accordance with the computation results, confirm the existence of nitrogen dimers.
While the pernitride formation stabilize tin oxynitrides in fluorite structure, the 0 K phase diagram analysis shows that the configuration is metastable (Fig. 6a). The constructed phase diagram shows that there exists no stable tin oxynitride at 0 K, except for one nitrate phase (Sn(NO 3 ) 4 ). This instability owes in large part to the exceptional stability of N 2 gas and Sn 3 N 4 , which are included in the decomposition products of the metastable oxynitrides. The energy hull construction in Fig. 6b reveals that the computed oxynitrides are metastable by at least 193 meV/atom for all composition, with the computed SnO 0.5 N 1.5 structure metastable by 240 meV/atom. At this specific composition, the energy above hull for the other three structures reach up to ~805 meV/atom, showing that the nitrogen dimer stabilizes the fluorite structure by a significant amount.

Discussion
Interestingly in our computation, the nitrogen-nitrogen bonding only occurs in fluorite tin oxynitrides; no O-N configuration in the other three polymorph structures results in the dimer formation. Considering that fluorite SnO 2 is not the ground state, we question whether specific structural features favor the formation of pernitrides. Comparing the original fluorite structure with the DFT relaxed structure in Fig. 2b, we notice that the pernitride formation involves a significant amount of octahedral rotation (Supplementary Fig. S6). For some specific O-N  ordering, the corner-sharing octahedra rotate collectively to form nitrogen dimers for all nitrogen atoms. It comes naturally from this observation that rigid structures that constrain polyhedra's rotational degrees of freedom have difficulty nucleating the nitrogen dimer-stabilized oxynitrides. Among the four SnO 2 polymorphs considered in this study, we notice that fluorite structure consists of only corner-sharing SnO 6 octahedra, with each anion corner shared between three octahedra. In the other three structures, most octahedra share two edges among each other. The spinel Sn 3 N 4 phase also consists of edge-sharing SnN 6 octahedra and SnN 4 tetrahedra 23 . The polyhedral network connected by edge-sharing polyhedra limits the rotational degree of freedom, possibly suppressing the formation of nitrogen dimers.
The nitrogen dimer stabilization does not yield fluorite as the ground state in oxygen-rich SnO 1.67 N 0.33 composition, with the rutile phase being the ground state ( Supplementary Fig. S1). The energetics at this composition remains more or less similar to SnO 2 , with the stability order of rutile, CaCl 2 -type, α-PbO 2 -type and fluorite-type structures. The lowest-energy O-N ordering in fluorite is 42 meV/f.u. higher in energy compared to the rutile phase, and involves two N atoms forming a dimer. The other two N atoms remain bonded only to three Sn atoms like the oxygen atoms. The presence of nitrogen atoms not participating in dimer may be caused by the incomplete sampling of the O-N ordering; 30 distinct configurations ranked by electrostatic summation may not provide the configuration with nitrogen atoms in neighboring pairs. However, we do observe that the stability of fluorite tin oxynitrides against the rutile phase linearly increases with the nitrogen substitution content (Supplementary Fig. S7). The more nitrogen gets substituted into SnO 2 , the more stable the fluorite structure becomes compared to the other polymorphs. These suggest that nitrogen dimer-stabilized oxynitrides favor nitrogen-rich composition, as opposed to the oxygen-rich oxynitrides stabilized via vacancies and their configurational entropy contribution.
Regarding the oxynitrides' stability, the metasability of 200 meV/atom is considered large. However, Sun et al. recently showed that the thermodynamic scale of nitrides' metastability reaches 192 meV/atom at 90 th percentile 24 . The large metastability of the computed oxynitride phases along with the reported synthesis of tin oxynitrides, therefore, suggest that the energetic barrier to decompose the oxynitrides may be large. This is likely due to the extra pernitride bond formation. The analyses in this work suggests that there may be a group of novel oxynitrides stabilized by nitrogen dimer formation yet to be discovered.

Conclusion
In summary, we show by density functional theory computations that nitrogen-rich tin oxynitrides stabilize in fluorite phase by forming nitrogen dimers as opposed to the other polymorph structures of SnO 2 . The electronic structure confirms the covalent N-N bonding, and X-ray photoelectron spectra of synthesized tin oxynitride films reveal two distinct nitrogen bonding environment, consistent with the computation results. The formation of pernitrides requires sufficient nitrogen concentration in the anion sublattice and specific O-N configuration with nitrogen in neighboring pairs. For sufficient rotational degrees of freedom, structures with corner-sharing polyhedra network are favored over the edge-sharing or face-sharing polyhedra. This specific structural feature stabilizes the tin oxynitrides in the high-pressure polymorph form under ambient conditions. The mechanisms revealed in this work opens up the avenues for the discovery of other nitrogen-rich oxynitrides, particularly in metastable phases in their oxide counterpart.

Methods
Computation Details. Vienna ab initio simulations package was used to perform the density functional theory (DFT) calculations 25 . Generalized-gradient approximation (GGA) was used to treat the exchange-correlation functional and Perdew-Burke-Erzenhof functional with projector-augmented wave method was used 26,27 . All structural elements including cell parameters and ionic positions were relaxed with the energy cutoff of 520 eV. The K-point density of at least 1000/atom was used, and all calculations were spin-polarized. No Hubbard-like U correction was employed, and symmetry in the wavefunction was explicitly broken during calculation.
The formation energies of computed structures were evaluated according to the scheme by MaterialsProject 30 . The gas phase energies required for formation energy calculations were corrected according to the previous works by Wang et al. 31 . The decomposition products were assessed via phase diagram construction, implemented in the MaterialsProject API 32 . The COHP was obtained using Lobster 21,22,33,34 . The charge density difference plot was generated using the atomic states as the reference. The computed structures were visualized with VESTA 35 .

Experimental Details
The tin oxynitride films are synthesized as reported in our previous publication 13 . XPS measurements are obtained for thin films grown at 75 W on glass and MgO substrates using PHI 5000 VersaProbe(Ulvac-PHI). The surface few layers of the films were etched before XPS measurement, to minimize the effect of surface oxidation and adsorbents. The background pressure was 6.7 × 10 −8 Pa, and the XPS peaks were calibrated using C1s peak at 284.6 eV. The X-ray spot size was 100 μm × 100 μm.