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Strain-induced creation and switching of anion vacancy layers in perovskite oxynitrides

Perovskite oxides can host various anion-vacancy orders, which greatly change their properties, but the order pattern is still difficult to manipulate. Separately, lattice strain between thin film oxides and a substrate induces improved functions and novel states of matter, while little attention has been paid to changes in chemical composition. Here we combine these two aspects to achieve strain-induced creation and switching of anion-vacancy patterns in perovskite films. Epitaxial SrVO3 films are topochemically converted to anion-deficient oxynitrides by ammonia treatment, where the direction or periodicity of defect planes is altered depending on the substrate employed, unlike the known change in crystal orientation. First-principles calculations verified its biaxial strain effect. Like oxide heterostructures, the oxynitride has a superlattice of insulating and metallic blocks. Given the abundance of perovskite families, this study provides new opportunities to design superlattices by chemically modifying simple perovskite oxides with tunable anion-vacancy patterns through epitaxial lattice strain.

In order to examine the oxygen/nitrogen distribution, we performed Rietveld analysis of neutron diffraction pattern (Supplementary Fig. 2f). We imposed a constraint of gOi + gNi = 1 for each site (i = 1, 2, 3). The z coordinates and atomic displacement parameters Uiso for the vanadium sites were fixed to the value obtained from the X-ray refinement since the scattering length of V is close to zero. The refined occupancy factor of nitrogen atom at the O2 and O3 sites gN2 and gN3 was ~1/3 and ~1/8, respectively, while no appreciable nitrogen was detected at the O1 site (gN1 = -0.04(4)), hence gN1 was  (3)), thus giving the composition of SrVO2.22(5)N0.58 (5). Taking into account the VN impurity (16 wt%), the total nitrogen amounts to 7.20 wt%, in a good agreement with the value obtained from the combustion analysis (7.0(3) wt%).
When SrVO3 was ammonized at 500 °C, we obtained a cubic perovskite phase ( Supplementary Fig.   1b). The lattice constant, a = 3.850 Å, is slightly larger than a = 3.843 Å for the oxide precursor SrVO3.
Combustion analysis resulted in the nitrogen content of 0.64 wt%, corresponding to SrVO2.85N0.1. The vanadium valence remains +4. The same valence is seen in SrV 4+ O2.7N0.2 obtained from SrVO2H ammonolized at 300 °C. The XRD pattern at the reaction temperature of 600 °C could be indexed by a rhombohedral unit cell with a = 5.51 Å and c = 34.3 Å. It contains an Sr3V2O8 impurity phase. 5 The hexagonal pattern obtained also resembles with the SrVO2H sample after the same ammonolysis treatment. Combustion analysis gave the nitrogen content of 3.3(3) wt%.
We also carried out Rietveld refinement of X-ray and neutron data for the SrVO3 sample nitridized at 600 °C by using the same structural model (see the main text, Supplementary Fig. 2c , 2d and   Supplementary Table 2), and obtained in principle the same structure with a composition of SrVO2.203(8)N0.597 (8). Taking into account the Sr3V2O8 impurity with 16 wt%, the total nitrogen amount in the sample is 3.8 wt%, which is consistent with the value obtained from the combustion analysis We calculated the total energies of all the possible 11 configurations of nitrogen for the supercell consisting of Sr5V5O11N3 (SrVO2.2N0.6) as a calculation model, where two nitrogen atoms are placed at the O2 site and one nitrogen atom at the O3 site ( Supplementary Fig. 3a). This situation (33% and 17% for O2 and O3 sites) approximately corresponds to the experimental ratio of the nitrogen substitution (34% and 15% for O2 and O3 sites). The unit cell vectors were set to be a1 = (a/2, -(Ö3/2)a, c/3), a2 =(a/2, (Ö3/2)a, c/3), and a3 = (-a, 0, c/3). We optimized both the lattice constants (the a and c axes) and atomic coordinates, while the cell shape was kept fixed. The plane-wave cutoff energy of 600 eV and a 6 × 6 × 6 k-mesh were used. We found that the most stable structure includes the cis-VO4N2 octahedra ( Supplementary Fig. 3a). The total energy of structure with trans-VO4N2 octahedra is at least 0.2 eV/f.u. higher than the most stable one. The possible preference of the cisconfiguration was also suggested in NdVO2N. 6 By using the most stable configuration of Sr5V5O11N3, first-principles band-structure calculation and the subsequent Wannier construction for the V-d orbitals were performed to investigate electronic structure. The unit cell vectors were changed in the band-structure calculation by the WIEN2k code as shown in Supplementary Fig. 3a. The partial density of states (pDOS) is presented in Supplementary   Fig. 3b. The RKmax parameter used in the WIEN2k code was set to be 7.0. The octahedral coordinate V2 and V3 sites have significant DOS between -1 to 0 eV while the tetrahedral V1 site has almost no DOS at the same energy region. The electron occupancies are evaluated as 0.2, 1.1, and 1.4 electrons for V1, V2 and V3, respectively. This suggests that the V2 and V3 sites are nearly tetravalent while the V1 site is pentavalent, in consistency with the BVS calculation (Supplementary Table 4) and NMR ( Fig. 2). The first-principles band structure and the band structure calculated with the tight-binding model consisting of the Wannier orbitals are shown in Supplementary Fig. 3c. The Fermi surface was calculated with the tight-binding model derived here using a 100 × 100 × 100 k-mesh, and depicted using the FermiSurfer 7 as shown in Fig. 3a.

Supplementary Note 3. Characterization of the oxynitride thin films deposited on LSAT (111).
The oxynitride film on LSAT (111) was obtained by ammonolysis reaction of the epitaxially grown SrVO3 (600 °C, 12 hours). EDS spectra implied the formation of oxynitride after ammonolysis since a nitrogen Kα was clearly observed (Supplementary Fig. 4g). The retention of epitaxy in the oxynitride film was confirmed by reciprocal space mapping ( Supplementary Fig. 4d, 4e). The 111 peak of the thin film shifts to lower angle by the ammonolysis treatment, which is the same tendency with the ammonolysis of the bulk sample ( Supplementary Fig. 4b, 4c). However, no superlattice peak could be detected in out of plane XRD at the low angle, suggesting the vacancy formation of the thin film and bulk are rather different. Figure  is obtained for the tetrahedral site. It is thus expected that, similarly to 15R-SrVO2.2N0.6, the tetrahedral vanadium is V 5+ and the octahedral and pyramidal vanadium are V 3~4+ .
EDS spectra implied the formation of oxynitride after ammonolysis since the N Kα peak was observed ( Supplementary Fig. 5b). The 111 peak of the thin film shifts to lower angle by the ammonolysis.
While no superlattice peak could be detected in out of plane XRD at the low angle ( Supplementary   Fig. 5a) Fig. 5c-5e), suggesting that the structure is identical to that of the film on LSAT.
The oxynitride film on SrTiO3 (111) was obtained by ammonolysis reaction (620 °C, 12 hours). EDS spectra the N Kα peak, implying the formation of oxynitride after ammonolysis ( Supplementary   Fig. 6c). The 111 peak of the thin film shifts to lower angle by the ammonolysis, the same tendency as the bulk sample ( Supplementary Fig. 6a). If one assumes the 15R-structure where the LSAT [111] direction corresponds to the c direction of 15R structure, superlattice refractions, such as (1/5 1/5 1/5)p (2q ~ 7.7°), are expected to be observed by out of plane XRD. However, we observed a superlattice peak at 6.5° (Supplementary Fig. 6b) which corresponds to (1/6 1/6/ 1/6)p reflection, indicating a sixfold superstructure with (111)p planar vacancy. The six-fold superstructure along [111]p, was also observed in Fourier transform (FT) pattern (inset in Fig. 4b). To compute the thermodynamic competition for the two orientations of SVOxNy, we therefore need to calculate and .
Katsura previously conducted a thorough thermodynamic analysis of μN(lattice) and μH2(g) in the nitridation of a metal using ammonia gas. 10 It was found that both μH and μN is significantly higher in flowing ammonia gas than would be expected from the direct equilibrium of NH3(g) à 1/2 N2(g) + 3/2 H2(g). This is due to the fact that NH3 dissociation does not proceed to completion. The activity of nitrogen and hydrogen was found to depend on the NH3 dissociation constant, which varies with ammonia gas flow rate; as well as with temperature. In a following paper, Katsura benchmarked on a ( ) U2N3+x system that NH3(g) has a dissociation constant of 0.3 at 600 °C for a flow rate of 50 mL/min. 11 However, a higher NH3(g) flow rate was discussed to have a lower dissociation constant, with corresponding higher nitrogen activity. 12 The experiments here are carried out at 600 °C and a flow rate of 200 mL/min, with the corresponding nitrogen activity and dissociation constant shown on Supplementary Fig. 9 below (as reproduced from Ref. 8 ). We do not have the data to specify the exact NH3 dissociation constant, but we know that the dissociation constant should be < 0.3, so we estimate the activity of nitrogen and hydrogen as aN = 10 4 , aH = 10 1.3 .
Because the oxygen and nitrogen stoichiometries between SVON-111 and SVON-112 are slightly different, errors in the nitrogen and hydrogen chemical potential could plausibly influence the equilibrium relationships between these two anion-vacancy orderings as a function of strain. In Supplementary Fig. 9, we also include error bars on the free-energy diagram corresponding to a range of nitrogen activities between log(aN) = 4.8 and log(aN) = 3.3. The figure shows that the equilibrium relationships between the two SVON anion-vacancy orderings as a function of strain are not very sensitive to potential errors in the nitrogen activity. The influence of hydrogen activity varying between log(aH) =1 -1.5 has negligible influence and the error bars are convolved with the nitrogen activity (since the relevant molecular specie is ammonia).
Next we assume that the activity of water has a negligible contribution to the chemical potential of water (in other words, that the water chemical potential is dominated by the TS term), so that . The chemical potentials for oxygen and nitrogen in the SVON grand potential can therefore specified as: This results in Figure 4g and Supplementary Figure 10 in the manuscript.

Supplementary Tables
Supplementary Table 1