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Zhujun Zhang, Kazuki Miyashita, Tong Wu, Jun Kujirai, Kiya Ogasawara, Jiang Li, Yihao Jiang, Masayoshi Miyazaki, [Satoru Matsuishi](https://orcid.org/0000-0001-8905-0255), Masato Sasase, Tomofumi Tada, [Hideo Hosono](https://orcid.org/0000-0001-9260-6728), Masaaki Kitano

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[Anion vacancies activate N2 to ammonia on Ba–Si orthosilicate oxynitride-hydride](https://mdr.nims.go.jp/datasets/25e41d2f-bc06-495a-8435-7c864b9339af)

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nature chemistryhttps://doi.org/10.1038/s41557-025-01737-8ArticleAnion vacancies activate N2 to ammonia on Ba–Si orthosilicate oxynitride-hydrideIn the format provided by the authors and uneditedSupplementary informationhttps://doi.org/10.1038/s41557-025-01737-81   Table of contents    1. Supplementary Figs. 1-45                             2-46        2. Supplementary Table 1-7                             47-53     2     Supplementary Fig. 1. XRD patterns of Ba3SiO5−xNyHz synthesized at various temperatures. The pure tetragonal Ba3SiO5 phase can be obtained at 400-700°C.    3        Supplementary Fig. 2. Experimental XRD patterns of (a) as-synthesized Ba3SiO5 and (b) Ba3SiO5−xNyHz (prepared at 600°C) with Rietveld fitting. Both Ba3SiO5 and Ba3SiO5−xNyHz have the same crystal structure (tetragonal symmetry, I4/mcm).    4       Supplementary Fig. 3. (a) Diffuse reflectance spectra for Ba3SiO5−xNyHz and Ba3SiO5. Inset: photograph of the Ba3SiO5−xNyHz and Ba3SiO5 powder. (b) Projected DOSs of calculated Ba3SiO2.5NH2. Inset: band structure of calculated Ba3SiO2.5NH2. The white colored Ba3SiO5 powder, which was obtained by heating a mixture of BaCO3 and SiO2 at 1250 oC in a gasses flow of Ar (95%) and H2 (5%) for 20 h, has a wide band gap of ca. 3.7 eV as determined by the Tauc plot analysis of the diffuse reflectance spectrum (DRS) (Supplementary Fig. 3a). On the other hand, the yellow colored Ba3SiO5−xNyHz powder has a much narrower band gap of ca. 3.4 eV. In Ba3SiO5−xNyHz, broad shoulder absorption was observed below the band gap energies, which is attributed to the presence of Va. Based on a projected density of states (DOSs) analysis (Supplementary Fig. 3b), the conduction band minimum (CBM) is dominated by Ba_vacant 5d orbitals, and strong hybridization of the N_2p and H_1s orbitals with O_2p orbitals upshifts the valance band maximum (VBM). In particular, the N_2p band occupies above the H_1s and O_2p bands, and thus contributes mostly to the observed band gap narrowing.    5            Supplementary Fig. 4. (a) FT-IR spectra of as-prepared Ba3SiO5-xNyHz and barium amide (Ba(NH2)2). (b) TPD of NH3 from as-prepared Ba3SiO5-xNyHz. The NHx species would be formed on the sample surface during the synthesis of Ba3SiO5-xNyHz.  Both the broad N-Hx (x=1,2) stretching band at around 3200 cm-1 and week N-H bending vibration at 1543 cm-1 can be observed for as-prepared Ba3SiO5-xNyHz. This IR result agrees well with the results of solid state NMR (Fig. 1b). The amount of NHx species was estimated to be 0.04 mmol g-1 based on TPD of NH3 (Supplementary Fig. 4b), which is only around 2.5% that of total lattice N3-. These results indicate that most hydrogen species are present as hydridic H in the lattice, but a small amount of NH species is also formed on the Ba3SiO5−xNyHz surface.      4000 3500 3000 2500 2000 1500 10000.00.51.01.52.02.5Absorbance (a. u.)Wavelength (cm−1) Ba(NH2)2 Ba3SiO5-xNyHz (as-prepared)NHx (x=1,2)NH2N-H stretchingN-H bendingNΞN200 400 600 800Intensity (a.u.)Temperature (oC) m/z=17a b6          Supplementary Fig. 5. (a) Crystal structure of Ba3SiO5 (left). Local structure of SiO4 and Ba6O block (right). (b) Antiperovskite-like unit of Ba3SiO5  Ba3SiO5 can be regarded as A3BX-type antiperovskite. The oxygen occupies the center of the octahedral site (X) and is coordinated by 6 Ba (A). The large complex anions, (SiO4)4-, occupy the B sites. The tetragonal Ba3SiO5 crystal has two types of oxygen sites, i.e., four OI sites bonded with one silicon (SiO4) and one OII site surrounded by six barium atoms (Ba6O). a b7    Supplementary Fig. 6. The Ba-H, Si-N, Si-H bond distances of Ba3SiO2.5N1.0H2.0, as well as the charge of each element determined by DFT calculations.   8         Supplementary Fig. 7. (a) XRD patterns of Ba3SiO5−xNyHz heated in Ar flow at various temperatures. (b) TPD profiles of Ba3SiO5−xNyHz before and after heating in Ar at various temperatures. The tetragonal structure of Ba3SiO5−xNyHz was preserved up to 650°C; however, the diffraction peaks shifted to higher angles compared to those of the as-prepared sample as a result of lattice shrinkage induced by the removal of lattice H− and N3− ions.    9      Supplementary Fig. 8. TEM image (a) and HAADF-STEM image with corresponding EDS-mapping (b) of a typical particle of Ba3SiO5-xNyHz collected after ammonia synthesis. (c) High resolution TEM images and fast Fourier transform (FFT) pattern of Ba3SiO5-xNyHz focused in each area of Supplementary Fig. 8a. The lattice fringes can be clearly seen in all regions in Supplementary Fig. 8a. The corresponding FFT pattern along the (110) and (100) axis gives bright spots, indicating that the Ba3SiO5-xNyHz is well crystallized without any amorphous phase. The FFT pattern agrees well with the diffraction from Ba3SiO5 phase (tetragonal symmetry, I4/mcm).     10     Supplementary Fig. 9. AES depth profile of as-prepared Ba3SiO5-xNyHz (a,b) and Ba3SiO5-xNyHz collected after ammonia synthesis (c,d). Ba, Si, O, and N elements are uniformly distributed from the surface to bulk region and the elemental ratio is well consistent with Ba3SiO2.87N0.80H1.86 determined by other elemental analyses. The contribution of impurity phase to the catalytic performance of Ba3SiO5-xNyHz can be ruled out.      11        Supplementary Fig. 10. TEM image (a) and HAADF-STEM image with corresponding EDS-mapping (b) of a typical particle of Ba3SiO5-xNyHz collected after heated in Ar flow at 650oC for 2 h. (c) High resolution TEM images and FFT pattern of the same sample focused in each area of Supplementary Fig. 10a. The lattice fringes and FFT spot pattern can be clearly seen in all regions in Supplementary Fig. 10c, indicating that the crystal structure of Ba3SiO5-xNyHz is maintained after Ar heat treatment without formation of any impurity phase.    12       Supplementary Fig. 11. (a) Solid-state 1H MAS NMR of Ba3SiO5-xNyHz  Ar/650oC and Ba3SiO5-xNyHz  Ar/650oC-used. (b) Solid-state 29Si MAS NMR of Ba3SiO5-xNyHz  Ar/650oC. After heat treatment at 650oC in Ar, 1H-NMR signals almost disappeared, but the signal of hydrides can be regenerated when the sample is exposed in the ammonia synthesis conditions. These results indicate the heat treatment (Ar/650oC) removes most of H− from the lattice. After heat treatment at 650oC in Ar, the 29Si-NMR signals at around -30 and -40 ppm almost disappeared, but the 29Si-NMR signals at around -66 and -51.6 ppm remained. Therefore, SiO2NH and SiONH2 are converted into SiOxN species.   As a conclusion, we can confirm that the heat treatment in Ar at 650oC would remove a large amount of lattice H− and surface N3− from Ba3SiO5−xNyHz without decomposition of the crystal structure.     13        Supplementary Fig. 12. EPR spectra of as-prepared Ba3SiO5−xNyHz shown in Fig. 1f.     14        Supplementary Fig. 13. Electron concentration of Ba3SiO5−xNyHz heated at various temperatures. The electron concentration was determined by the EPR signal using standard CuSO4·5H2O crystals.   15       Supplementary Fig. 14. Diffuse reflectance spectra of Ba3SiO5−xNyHz before and after heating in Ar at various temperatures. In addition to the band gap absorption of Ba3SiO5−xNyHz at ca. 3.6 eV, new isolated absorption peaks below 3.6 eV emerged with the increased temperature. In particular, two optical absorption bands centered at around 1.7 and 0.9 eV were observed for the samples heated at above 600°C, which gave rise to a persistent color change from light yellow to dark green (Fig. 1e). These new absorption bands are attributed to the formation of anionic electrons confined at Va sites, which is analogous to the C12A7 electride11, which was further investigated by EPR analysis (Fig. 1f).   16         Supplementary Fig. 15. Ammonia formation over Ba3SiO5−xNyHz under different gas flow at 400oC and 0.9 MPa. The amounts of ammonia produced under Ar and H2/Ar are 0.004 and 0.011 mmol, respectively, which are lower than the amount of lattice N (0.16 mmol) in Ba3SiO5−xNyHz. The ammonia formation induced by thermal decomposition of Ba3SiO5−xNyHz is negligibly low as compared with the catalytic ammonia production.   17         Supplementary Fig. 16. XRD patterns of (a) Ba3Si6O9N4 and (b) BaSi2O2N2 powder prepared by reported procedures. Inset shows the photograph of each sample. (c) TPD of N2 (m/z=28) under Ar atmosphere and (d) NH3 desorption (m/z=17) profiles during H2-TPR from Ba3Si6O9N4 (black line), BaSi2O2N2 (red line), and Ba3SiO5−xNyHz (blue line) in a flow of H2(5%)/Ar.    10 20 30 40 50 60 70 80Ba3Si6O9N4 as-preparedIntensity (a.u.)2 Theta (degree)Ba3Si6O9N4 ICSD:415918 10 20 30 40 50 60 70 80BaSi2O2N2 as-preparedIntensity (a.u.)2 Theta (degree)BaSi2O2N2 ICSD:419450200 400 600 800Intensity (a.u.)Temperature (oC) Ba3Si6O9N4 BaSi2O2N2 Ba3SiO5−xNyHzN2 desorption200 400 600 800 Ba3Si6O9N4 BaSi2O2N2 Ba3SiO5−xNyHzIntensity (a.u.)Temperature (oC)H2-TPRa bc d18         Supplementary Fig. 17. Temperature-programmed NH3 formation (m/z=17) from Ba3SiO5-xNyHz in a flow of pure N2 and H2(5%)/Ar (the same result shown in Supplementary Fig. 16d, but the temperature region is below 500 oC).    19     Supplementary Fig. 18. Ammonia synthesis activity of Ru/Ba3SiO5−xNyHz prepared with different amounts of Ru precursors. (Reaction conditions: 0.1 g catalyst, N2/H2 = 15:45 mL min−1, 0.9 MPa, 400°C). The inset table shows the actual loading amount of Ru was determined by XRF analysis of the used samples.            20       Supplementary Fig. 19. (a) Time courses for ammonia synthesis over Ru(1.5wt.%)/Ba3SiO5−xNyHz at 400°C and 0.9 MPa. (b) XRD patterns of as-prepared Ru(1.5wt.%)/Ba3SiO5−xNyHz and after ammonia synthesis test. (c) TPD analysis of H2 and N2 release from Ba3SiO5−xNyHz and Ru(1.5wt.%)/Ba3SiO5−xNyHz (these samples were collected after ammonia synthesis test) under Ar atmosphere. (d) X-band EPR spectra of Ba3SiO5−xNyHz and Ru(1.5wt.%)/Ba3SiO5−xNyHz (these samples were collected after ammonia synthesis test).      21      Supplementary Fig. 20. Nitrogen gas adsorption–desorption isotherm of as-prepared Ba3SiO5−xNyHz (orange curve) and Ba3SiO5−xNyHz_HS (green curve) powders.    22      Supplementary Fig. 21. a, Ammonia synthesis rates of Ru/Ba3SiO5−xNyHz_HS tested at 300°C and 0.9 MPa under various WHSV (Catalyst: 0.1 g; Temperature: 300oC). b, Ammonia synthesis rates of Ru(1.5wt%)/Ba3SiO5−xNyHz_HS tested at 300°C, 0.9 MPa and WHSV of 60000 mL g−1 h−1 with various ratios of N2 and H2 (Catalyst: 0.1 g). c, Temperature dependence of the ammonia synthesis rate over Ru(5.0wt%)/Ba3SiO5−xNyHz_HS tested at 300°C and 1.0 MPa under a WHSV of 60000 mL g−1 h−1 with H2:N2 ratio of 3 (Catalyst: 0.03 g). d, Ammonia synthesis rates of Ru(5.0wt%)/Ba3SiO5−xNyHz_HS tested at 300°C, 0.9 MPa and WHSV of 60000 mL g−1 h−1 with various ratios of N2 and H2 (Catalyst: 0.03 g). The error range defined as the standard deviation for a set of experimental runs (n = 3) was ±4%.    23         Supplementary Fig. 22. Temperature dependence of the ammonia synthesis rate over (a) Ru/Ba3SiO5−xNyHz and (b) of Ru/Ba3SiO5−xNyHz_HS under a pressure of 0.9 MPa before and after exposed in air for 2 h.     24        Supplementary Fig. 23. HAADF-STEM image of (a) Ru/ Ba3SiO5−xNyHz and (b) Ru/Ba3SiO5 collected after the ammonia synthesis test. Inset: particle size distribution of Ru nanoparticles.    25        Supplementary Fig. 24. a, HAADF-STEM image and corresponding energy dispersive X-ray spectroscopy (EDX)-mapping of Ru/Ba3SiO5−xNyHz_HS collected after the ammonia synthesis test. b, Coverage mapping images of Si K, Ba L, and Ru L in panel a. c, HAADF-STEM image Ru/Ba3SiO5−xNyHz_HS collected after the ammonia synthesis. Inset: particle size distribution of Ru nanoparticles.    26         Supplementary Fig. 25. a, Ru K-edge X-ray absorption near edge structure (XANES) spectra of the used Ru/Ba3SiO5−xNyHz, along with RuO2 and Ru_foil. b, Corresponding Ru K-edge FT-EXAFS spectra of the samples.             27          Supplementary Fig. 26.  XPS Ru 3p spectra of used Ru/Ba3SiO5−xNyHz and Ru/Ba3SiO5.   28      Supplementary Fig. 27. Dependence of NH3 synthesis rate on the partial pressures of N2, H2 and NH3 over Ru/Ba3SiO5−xNyHz at 340°C and 0.9 MPa (a, b) and Ba3SiO5−xNyHz at 400°C and 0.9 MPa (c, d).  For the TM-free sample, the reaction order of N2 is similar to that of Ru-loaded sample. However, its reaction orders of H2 and NH3 are more positive and more negative, respectively, than those for the Ru-loaded sample. This result suggests that NHx species are more densely populated on Ba3SiO5-xNyHz surface than hydrogen species, i.e., the hydrogenation processes are much difficult in the absence of Ru. On the other hand, the hydrogenation of surface nitrogen species is enhanced by the supported Ru particles, resulting in the high ammonia synthesis activity.   29         Supplementary Fig. 28. a, b, Mass spectra for ammonia synthesis from 15N2 and H2 over Ba3SiO5−xNyHz at 400°C.    30      Supplementary Fig. 29. a, b, Mass spectra for ammonia synthesis from 14N2 and H2 over Ba3SiO5−xNyHz. c, Reaction time profiles for the ratio changes of 16/17 according to (b). The m/z=18 (water) signal is due to the gas sampling system of closed glass circulation reactor. The gas in the sampling loop (pressure < 0.1 MPa) was flushed out with He gas (0.1 MPa) and injected into the GC and Q-mass. According to the pressure difference between the sampling loop and flushed gas, small amount of water from air atmosphere may be introduced to the injection line. However, the m/z=18 (water) signal does not increase with reaction time, which is contrast to the m/z=17 and 16 signals. In addition, the contribution of water to the mass signal intensity of m/z=17 is negligibly small compared with the theoretical mass signal ratio of (m/z=17)/(m/z=18) = 0.21 for H2O. The observed mass signal ratio of (m/z=16)/(m/z=17) is close to 0.8 corresponding to the theoretical ratio for NH3.        31          Supplementary Fig. 30. a, b, Mass spectra for ammonia synthesis from 15N2 and H2 over Ru/MgO at 400°C. c, Time courses for the intensity ratio of mass signal of (m/z=16)/(m/z=18) and (m/z=17)/(m/z=18) calculated based on panel b.   32        Supplementary Fig. 31. a, b, Mass spectra for ammonia synthesis from 15N2 and H2 over Ru/Ba3SiO5−xNyHz at 400°C.   33        Supplementary Fig. 32. Ammonia formation over used Ru/Ba3SiO5−xNyHz (0.1g) under pure flow of pure H2 (45 mL min−1) and pure N2 (15 mL min−1) at 0.1 MPa (The orange line indicates the heating program).  The Ru/Ba3SiO5−xNyHz sample was heated under pure H2 flow from 30 to 400oC and kept at 400oC for several hours. Then, the reaction gas was switched to pure N2 and naturally cooling to 30oC. This reaction cycle was repeated several times.  The ammonia formation during the catalytic cycle is monitored by ion-chromatography. From this experiment, it was found that N2 molecule can be captured at Va site at room temperature, and then hydrogenated to form NH3 at elevated temperature. Furthermore, the amount of the adsorbed N2 molecules at Va sites can be quantitatively monitored by the ammonia production via hydrogenation by H2.     34       Supplementary Fig. 33. a, b, Mass spectra for ammonia synthesis from 15N2 and H2 over Ni/Ba3SiO5−xNyHz at 400°C c, Time courses for the intensity ratio of mass signals of (m/z=16)/(m/z=18) and (m/z=17)/(m/z=18). d, TPD analysis of the sample collected after the isotope labeled ammonia synthesis.    35       Supplementary Fig. 34. (a) NH3 desorption (m/z=17) profiles during H2-TPR from Ba3SiO5-xNyHz, Ba3SiO5-xNyHz (Ni-loading), and Ba3SiO5-xNyHz (Ru-loading). All the above samples are collected after ammonia synthesis test. The TMs loading amount are both 1.5 wt.%.  Ammonia was formed upon heating the as-prepared Ba3SiO5-xNyHz under a flow of H2(5%)/Ar(95%) (H2-TPR), which means that N3- on the surface of Ba3SiO5-xNyHz is hydrogenated to ammonia. Upon Ru-loading, the amount of ammonia production was 24 times higher than that of bare Ba3SiO5-xNyHz. The resultant VN density is, thus, estimated to be 0.80, 0.15, and 0.03 mmol g-1 for Ru-loaded, Ni-loaded, and TM-free Ba3SiO5-xNyHz samples, respectively. While the estimated VN density is not necessarily the same as that under ammonia synthesis conditions, the above results clearly indicate that TM-loading significantly promotes nitrogen vacancy formation on the Ba3SiO5-xNyHz under the ammonia synthesis conditions. And the strong Ru-N interaction facilitates the VN formation rather than Ni-N interaction.        100 200 300 400 500Normalized intensity (a. u.)Temperature (oC) Ba3SiO5-xNyHz Ni-loading Ru-loading0.00.20.40.60.8Amount of VN site (mmol g−1)Ba3SiO5-xNyHz Ni-loading Ru-loadinga b36       Supplementary Fig. 35. DRIFTS N2 adsorption on Ba3SiO5−xNyHz at −170°C under various pressures of 14N2 or 15N2. The N2 peak intensity increased with the N2 pressure and the peak position showed a red-shift of 60–70 cm−1 when 14N2 was replaced by 15N2. This isotope effect is clear evidence that the observed peaks are attributed to chemisorbed N2 on Ba3SiO5−xNyHz with end-on geometry.    37         Supplementary Fig. 36. (a) Time courses for mass signal of m/z=29 during isotope N2 exchange measurement for Ru/Ba3SiO5−xHyNz and Ru/MgO from 15N2 (4 kPa) and 14N2 (16 kPa) at 400 oC. (b) Schematic illustration of the dissociative ammonia synthesis processes over conventional Ru/MgO catalyst.       38      Supplementary Fig. 37. a, DRIFTS of Ba3SiO5−xNyHz (Ru-free) and Ru/Ba3SiO5−xNyHz (Ru-loaded) under a flow of N2 (3 mL min−1) and H2 (9 mL min−1) at 30°C. b, In situ DRIFTS observation of intermediates formation on Ba3SiO5−xNyHz (Ru-free) and Ru/Ba3SiO5−xNyHz (Ru-loaded) under a flow of N2 (3 mL min−1) and H2 (9 mL min−1) at different temperatures range from 30 to 300°C. The spectra measured at 30°C in panel a were used as background for In situ DRIFTS measurements in Fig. 4d and Supplementary Fig. 37b. N2 adsorption is observed for each sample at 30°C. The Ba3SiO5-xNyHz sample was pretreated at 650oC/Ar for 2h before in situ DRIFTS measurement. The Ru/Ba3SiO5-xNyHz sample was pretreated at 400oC under ammonia synthesis condition.   39            Supplementary Fig. 38. The structures of the transition states (TS I – TS VI) of Fig. 5. The energy barrier for each step is represented in parentheses.     TS I (0.74 eV) TS II (1.15 eV) TS III (1.08 eV)TS IV (0.79 eV) TS V (1.18 eV) TS VI (0.84 eV)40         Supplementary Fig. 39. Schematic illustration of (a) N2 dissociation and (b) NNH formation on Ru/MgO and (c) corresponding energy diagrams.   The energy barrier for N2 dissociation (1.06 eV) is lower than that for NNH formation (1.31 eV). The latter reaction is endothermic and the NNH* species is energetically unstable. Therefore, it makes sense that direct N2 dissociation proceeds on Ru/MgO, and this is in good agreement with the conventional reaction mechanism on Ru surface.   41      Supplementary Fig. 40. The formation energy of N vacancies (ENV) on the Ba3SiO5−xNyHz surface with and without Ru.   During ammonia synthesis reaction, N vacancy sites will be formed via the following reaction: [Ba3SiO5−xNyHz + 3/2 H2 (gas) → Ba3SiO5−xNyHz-with N-vacancy   +   NH3 (gas)]. Therefore, ENV was defined as: ENV = {Etot(VN/surface) + Etot(NH3)} − {Etot(surface) + 1.5Etot(H2)} where Etot(VN/surface) and Etot(surface) are the total energy for the optimized surface with and without N vacancies, respectively, and Etot(NH3) and Etot(H2) are the total energy of an NH3 and H2 molecule, respectively.   -1.0-0.50.0ENVRu-free Ru-loadingVNVN42           Supplementary Fig. 41.  a, N2 adsorption on the VN site and Ru surface of Ru/Ba3SiO5-xNyHz. b, N2 dissociation on Ru surface of Ru/Ba3SiO5-xNyHz.   N2 adsorption on Ru/Ba3SiO5-xNyHz was simulated without any adsorption from gas-phase H2. The hydrogen species on Ru was migrated from the lattice of Ba3SiO5-xNyHz just after Ru cluster is loaded on Ba3SiO5-xNyHz surface.     43        Supplementary Fig. 42. CO chemisorption on the used Ru/MgO (a) and Ru/Ba3SiO5-xNyHz catalyst (b) by the pulse method.   The amounts of CO adsorbed on Ru/MgO and Ru/Ba3SiO5-xNyHz were 125.2 μmol g-1 and 0.60 μmol g-1, respectively. Assuming that the CO/Ru adsorption ratio is 1, the mean Ru particle size of each catalyst was determined to be 4.8 nm and 436.1 nm, respectively. This result clearly indicates that Ru metal surface is barely exposed on Ru/Ba3SiO5-xNyHz since it is covered by the support components.      44    Supplementary Fig. 43. N2 activation via the dissociative pathway (blue) and the associative pathway (red).  The energy barrier for N2 dissociation at VN site is extremely large, and therefore, the simulation for this step does not converge.      IX XVIIIN2 dissociation at VN+∞-0.15 eV0.00 eV0.64 eVN2 hydrogenation at VNVN45         Supplementary Fig. 44. Hydrogen transfer during H2 adsorption on the VN site of Ru/Ba3SiO5-xNyHz.                 46       Supplementary Fig. 45. Determination of the concentration of lattice N3− in Ba3SiO5−xNyHz by an acid dissolution method accompanied with ion chromatography (IC).   47  Supplementary Table 1. Lattice parameters and band gap of Ba3SiO5, Ba3SiO2.87N0.8H1.86, and calculated Ba3SiO2.5NH2. Sample a (Å) c (Å) V (Å3) ∆ V/V0* Eg (eV) Ba3SiO5 (Exp.) 7.308(1) 11.222(2) 599.4(2) +0% 3.7 Ba3SiO2.87N0.8H1.86 (Exp.) 7.463(3)  11.724(5)  653.0 (6)  +8.9% 3.4 Ba3SiO5 (Cal.) 7.406 11.373 624.3 +0% 3.5 Ba3SiO2.5NH2 (Cal.) 7.559 11.981 682.9  +9.4% 2.8 *∆V/V0 means the cell volume expansion from Ba3SiO5 (Exp.) to Ba3SiO2.87N0.8H1.86 (Exp.), or Ba3SiO5 (Cal.) to Ba3SiO2.5NH2 (Cal.).   48  Supplementary Table 2. DFT calculation of N-H pair at O-O pair (Ba3SiO5−2xNxHx). x substituted sites ∆Hf (eV) V (Å3) Eg (eV) 2.50 16 O1 + 4 O2  654.65 +4.9% 0.24 2.00 16 O1 -196.0 648.96 +4.0% 1.62 2.00 14 O1 + 2 O2 -195.9 655.54 +5.0% 1.76 2.00 12 O1 + 4 O2 -195.8 652.91 +4.6% 0.37 1.50 12 O1 -208.5 649.52 +4.0% 1.54 1.50 10 O1 + 2 O2 -208.4 658.11 +5.4% 1.19 1.50 8 O1 + 4 O2 -208.2 645.12 +3.3% 0.98 1.00 8 O1 -221.0 640.91 +2.7% 2.61 1.00 6 O1 + 2 O2 -220.9 654.70 +4.9% 2.20 1.00 4 O1 + 4 O2 -220.6 643.02 +3.0% 0.32 0.50 4 O1 -233.6 632.13 +1.3% 2.86 0.50 4 O2 -233.7 636.22 +1.9% 2.19 0.00   624.28  3.49  For the computation models of Ba3SiO5−2xNxHx (N-H pairs that substitute two O sites (2O2− ⇒ N3− + H−)), the energy is decreased with the decrease of amount of N-H pairs that substitute different oxygen sites. Although the energy of the model Ba3SiO5−2xNxHx with x=0.5 (Ba3SiO4N0.5H0.5) and with N-H pairs substitute the O2 sites is the smallest one. The lattice parameters and compositions is far from the experimental results.    49   Supplementary Table 3. DFT calculation of H-H pair at O (Ba3SiO5−yH2y). y Substituted sites ∆Hf (eV) V (Å3) Eg (eV) 1.00 4 O1 -233.6 672.25 +7.7% 3.11  4 O2 -231.0 643.59 +3.1% metal 0.50 2 O2  639.92 +2.5% metal 0.00   624.28  3.49  Although the computation models of Ba3SiO5−yH2y (H-H pair replace oxygen, O2− ⇒ 2H−) shows a smaller energy, their compositions is far from the experimental results.   50   Supplementary Table 4. DFT calculation of N-H pair & H-H pair (Ba3SiO5−2x−y NxHx+2y). x Substituted sites y Substituted sites ∆Hf (eV) V (Å3) Eg (eV) 1.00 4 O1 0.25 1 O1 -218.0 654.18 +4.9% 2.95 1.00 4 O1 0.25 1 O2 -218.6 669.72 +7.3% 2.97 1.00 2 O1 + 2O2 0.25 1 O1 - - - - 1.00 2 O1 + 2O2 0.25 1 O2 -218.5 666.15 +6.7% 2.21 1.00 4 O2 0.25 1 O1 -217.5 666.02 +6.7% 1.48 1.00 2 O1 0.50 2 O1 -215.3 653.86 +4.7% 3.01 1.00 2 O1 0.50 1 O1 + 1 O2 -216.1 683.18 +9.4% 3.06 1.00 2 O1 0.50 2 O2 -217.0 682.89 +9.4% 2.78 1.00 1 O1 + 1 O2 0.50 2 O1 -215.2 678.48 +8.7% 1.89 1.00 1 O1 + 1 O2 0.50 1 O1 + 1 O2 -215.7 695.91 +11.5% 2.11 1.00 1 O1 + 1 O2 0.50 2 O2 -216.6 670.86 +7.5% 2.23 1.00 2 O2 0.50 2 O1 -214.9 690.58 +10.6% 1.38 0.00  0.00   624.28  3.49  For the computation models of Ba3SiO5−2x−yNxHx+2y (N-H pair replace O-O pair and with an extra H-H pair). An x value or 1.00 and y value of 0.50 could give a formula of Ba3SiO2.5NH2 is mostly close to the experimental result. When fixed this compositions, the lowest energy of the computation model was fund to be the case with 2O1 sites substituted by N-H pair (2O12− ⇒ N3− + H−) and one O2 site was substituted by additional H-H pair ( O22− ⇒ 2H−). In addition, the lattice expansion value (∆V/V0 = +9.4%) is very close to the experimental result (Supplementary Table 1). We therefore select this structure as the bench marking computation model of Ba3SiO5−xNyHz.   51  Supplementary Table 5. Concentration of H− and N3− of Ba3SiO5−xNyHz pretreated in different conditions. Sample N3− contents (mmol g−1) H− contents (mmol g−1) As-prepared Ba3SiO5−xNyHz 1.60 (±0.03) 3.74 (±0.19) Ba3SiO5−xNyHz Ar/650oC 1.48 (±0.02) 0.60 (±0.05) Ba3SiO5−xNyHz Ar/650oC-used 1.54 (±0.03) 3.62 (±0.20) Ru/Ba3SiO5−xNyHz-used 1.56 (±0.05) 3.12 (±0.22) N3− and H− content was determined by an acid dissolution method (Supplementary Fig. 41) and TPD, respectively.    52  Supplementary Table 6. ICP-AES analysis result of Ba3SiO5-xNyHz collected after ammonia synthesis test. Sample Concentration (ppm) Fe Co Ni Mo Ru Ba Blank <0.01 <0.01 0.01 0.01 0.01 <0.01 Ba3SiO5−xNyHz after reaction <0.01 <0.01 0.01 0.01 0.01 90  Inductively coupled plasma atomic emission spectroscopy (ICP-AES) analysis of the Ba3SiO5−xNyHz after the ammonia synthesis test show that possible impurities such as Fe, Co, Ni, Mo, and Ru are negligible low (below 0.01 ppm), which are almost identical to the blank level.    53  Supplementary Table 7. Summary of the catalytic ammonia synthesis performance at around 0.9 MPa and 300 oC for the most active Ru-based heterogeneous catalysts. Catalyst Ru content (wt.%) r                      (mmol gcat-1 h-1)  r                    (mmol gRu-1 h-1)  WHSV     (mL g-1 h-1)  Ratio of H2/N2 Ref. Ru/Ba3SiO5-xNyHz 1.5 6.0  398 36000 3/1 This work Ru/Ba3SiO5-xNyHz_HS 1.5 15.7 1047 36000 3/1 This work Ru/Ba3SiO5-xNyHz_HS 1.5 25.1 1673 60000 3/2 This work Ru/Ba3SiO5-xNyHz_HS 5.0 40.1 (1.0 MPa) 802 60000 3/2 This work Ru/Ba-Ca(NH2)2 10 23.3 233 36000 3/1 23 Ba2RuH6/MgO 5 34.0 (1.0 MPa)  680 (1.0 MPa) 60000 2/3 15 Li4RuH6/MgO 8 22.0 (1.0 MPa) 275 (1.0 MPa) 60000 2/3 15 Ru/BaO-CaH2 10 16.5 165 36000 3/1 27 Ru/Ba/LaCeOx 5 ~15 (1.0 MPa) ~300 72000 3/1 28 Ru/Ca2N:e– 1.8 4.1 (320 oC) 228 (320 oC) 36000 3/1 29 Ru/C12A7:e– 1.8 1.7 (320 oC) 94 (320 oC) 36000 3/1 12 Ru/BaCeO3–xNyHz 4.5 5.0 111 36000 3/1 26