Conversion of La2Ti2O7 to LaTiO2N via ammonolysis: a first-principles investigation

Perovskite oxynitrides are, due to their reduced band gap compared to oxides, promising materials for photocatalytic applications. They are most commonly synthesized from {110} layered Carpy-Galy (A2B2O7) perovskites via thermal ammonolysis, i.e. the exposure to a flow of ammonia at elevated temperature. The conversion of the layered oxide to the non-layered oxynitride must involve a complex combination of nitrogen incorporation, oxygen removal and ultimately structural transition by elimination of the interlayer shear plane. Despite the process being commonly used, little is known about the microscopic mechanisms and hence factors that could ease the conversion. Here we aim to derive such insights via density functional theory calculations of the defect chemistry of the oxide and the oxynitride as well as the oxide's surface chemistry. Our results point to the crucial role of surface oxygen vacancies in forming clusters of NH3 decomposition products and in incorporating N, most favorably substitutionally at the anion site. N then spontaneously diffuses away from the surface, more easily parallel to the surface and in interlayer regions, while diffusion perpendicular to the interlayer plane is somewhat slower. Once incorporation and diffusion lead to a local N concentration of about 70% of the stoichiometric oxynitride composition, the nitridated oxide spontaneously transforms to a nitrogen-deficient oxynitride. Since anion vacancies are crucial for the nitrogen incorporation and diffusion as well as the transformation process, their concentration in the precursor oxide is a relevant tuning parameter to optimize the oxynitride's synthesis and properties.

The lattice parameters of LTO computed at the PBE+U level of theory are a=7.774Å, b=5.537Å, c=13.165Å, β=81.5 • , in good agreement with experimental values 1 (relative error of about 1%). The electronic density of states of pristine LTO is reported in Fig. S1: the valence band (VB) is dominated by O-2p states with smaller contributions of the Ti-3d and La orbitals, reflecting the partially covalent character of the Ti -O bonds, while the bottom of the conduction band (CB) has mainly Ti-3d character. The computed band gap of 3.05 eV slightly underestimates experiment (3.29-3.82 eV) 2-4 , due to the limited effect of the Hubbard correction of the empty Ti-3d states for a material with nominal d 0 transition-metal configuration.
FIG. S1: Total and atom-projected density of states (PDOS) for LTO.
For LTON we considered a model with cis order of the N atoms on the anion sublattice. In Fig. S2 we confirm the previously reported small N-2p shoulder at the top of the valence band, with Ti-3d orbitals forming the bottom of the conduction band 5 . The computed band-gap of 1.43 eV, is inevitably smaller than the experimental value of 2.10 eV ? within our GGA+U framework. The LTO phase diagram in Fig. S3 was derived considering that, at equilibrium, the chemical potentials should satisfy where ∆H f (LTO) is the heat of formation of bulk LTO. Since the O chemical potential is controlled during the transformation of LTO to LTON by the ammonia flow removing oxygen, different synthesis conditions are considered by adjusting the oxygen chemical potential (µ O = µ 0 O + ∆µ O ). We assume equilibrium with O 2 gas to determine µ 0 O = 1 2 µ O2 , where µ O2 is the computed total energy of the O 2 molecule. ∆µ O can then vary within a range limited by the formation of competing phases like La 2 O 3 (2µ La + 3µ O ≤ ∆H f (La 2 O 3 )) and TiO 2 (µ Ti + 2µ O ≤ ∆H f (TiO 2 )) and by the decomposition of LTO into metallic La (µ La < µ La,metal ) and Ti (µ Ti < µ Ti,metal ). The DFT+U computed formation energies, derived according to Ref. 6, are in good agreement with those from experiment (Table S1). We will report defect formation energies in LTO for O-poor conditions (∆µ O = −4.54 eV) relevant for ammonolysis. FIG. S3: Computed phase diagram for LTO. LTO is stable in the purple region, while in the green and blue shaded areas TiO 2 and La 2 O 3 respectively form. Also indicated is the O-poor compositional limit as well as the O-rich limit.

B. LTON
The LTON phase diagram in Fig. S4 was derived considering that, at equilibrium, the chemical potentials should satisfy where ∆H f (LTON) is the heat of formation of bulk LTON. Only N-rich conditions (∆µ N = 0 eV) were considered because the environment is saturated with NH 3 during thermal ammonolysis. The O chemical potential was limited by the same competing phases considered above for LTO and in addition also the formation of LTO as a competing phase (2µ La + 2µ Ti + 7µ O = ∆H f (LTO)). We will report defect formation energies in LTON for O-poor conditions (∆µ O = −6.72 eV) relevant for ammonolysis. To ease comparison with experiment, the chemical potentials (∆µ O ) were converted to oxygen partial pressure via where p 0 is the standard pressure of 21% · 1 bar, k the Boltzmann constant and we chose a typically ammonolysis temperature of T = 1223 K.

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S3. INTERACTION OF LTO (001) WITH NH3 Table S2 reports the relative energies of the different oxygen vacancy sites at the LTO (001) surface. Figure S5 shows top views of the stoichiometric surface as well as the two most stable oxygen vacancy sites, both of which are located at the very surface on top of a Ti atom. In the remaining calculations we considered V O -41 only. We considered doubly and singly positively charged as well as neutral oxygen vacancies in LTO. Neutral V O 0 are associated with the two extra electrons in a shallow defect state dominated by Ti-3d orbitals and centered on the vacancy site ( Fig. S8a and d). For a singly charged V O +1 , a singly occupied defect state much deeper in the band gap leads to reduction of one of the Ti atoms adjacent to the defect ( Fig. S8b and e). Finally, an empty defect appears at the bottom of the CB for doubly charged V O +2 ( Fig. S8c and f). Due to the low symmetry of monoclinic LTO, there are 14 different sites for V O as shown in Fig. S7. Figure S9 reports the formation energy computed in the O-poor limit for the different configurations and charge states. Increasing the defect charge stabilizes configurations lying in the interlayer and destabilizes those in the middle and bulk layer (Table S3). The large difference in formation energy for V O within the same layer is due to the symmetry lowering octahedral rotations, as revealed by comparing Fig. S9a with data obtained for neutral defects in a cell without rotations (Fig. S11).
The change in V O formation energy as a function of the Fermi energy (E Fermi ) indicates a transition of the most stable charge state from V O +2 to V O +1 at a Fermi energy of about 2.2 eV, and finally to V O 0 for E Fermi close to the CBM (Fig. S10a). Under experimentally relevant conditions, we expect to find neutral V O 0 in sites further than 1.9Å from the interlayer interface. The formation energy for this defect increases from about 1 eV in O-poor to 6 eV in O-rich conditions as shown in Fig. S10b), suggesting that the oxygen-vacancy concentration may not be very high. This is in line with the experimental evidence that V O are important to trigger the zipper mechanism and that the nitridation gas-diffusion path can be quite long before a defect able to start the chain reaction is encountered.    is formed and both filled and empty defect states appear below and above the Fermi level, which are respectively dominated by N-2p and O-2p orbitals (Fig. S12c). These impurity states were previously associated with the band gap reduction in N-doped LTO 8-10 , but they could also act as recombination centers. More importantly, this type of doping would result in p-type conductivity, which is very unusual for a wide band gap metal oxide semiconductor, since acceptor states above the Fermi level are generally thermodynamically unstable. However, the change in formation energy of N O as a function of the Fermi energy reported in Fig. S14a clearly indicates that N O 0 is not a stable charge state. N O +1 is the most stable charge for E Fermi lower than about 1 eV. The formation of the electron-deficient N O +1 is accompanied either by the appearance of an empty defect state at the top of the VB (Fig. S12a) or with the formation of a N -O bond when N substitutes for an O atoms close to the interlayer where the neighboring O atoms have enough flexibility to relax toward the substitutional N and stabilize it (Fig. S12e). For higher Fermi energies, i.e. under experimentally relevant conditions, N O -1 is the most stable charge state and is associated with fully occupied defect states merged with the VB, resulting in a band-gap reduction of about 0.6 eV, in good agreement with experimental observations for N-doped LTO 11 . In the experimentally relevant -1 charge state, N O prefer sites in the middle layer (Fig. S13c). Formation energies for the different configurations are reported in Table S4.   Fig. S7 for site labels). S11 C. Interstitial nitrogen (Ni ) The most stable charge state for an interstitial N is N i 0 for Fermi energies below 2 eV, N i -1 between 2 and 2.7 eV, and finally N i -3 for Fermi energies close to the experimental band gap (Fig. S17a). Interestingly, regardless the charge state, strong structural relaxations are observed with N i migrating towards one of the neighboring O atoms and finally resulting in a substitutional nitrogen at an O site and an interstitial O bonded to N. This results in N-2p and O-2p states appearing at the top and bottom of the VB (Fig. S15). This result is line with XPS spectra of N-doped LTO that show the environment of La not to be affected by the doping while N is bonded to Ti atoms as part of the Ti octahedra 11,12 . N i show a slight preference for sites in the middle layer (Fig. S16) and a -3 charge state (Fig. S17). Details on the configurations can be found in Fig. S16 and Table S5,   To further investigate the role of N O -O i , we studied this defect complex more in detail by fixing one N O in the most stable position and by positioning the interstitial O atom at different sites in the LTO slab. The most stable charge state for Fermi energies close to the LTO band gap is (N O -O i ) -3 (Fig. S20a). In this charge state the two defects can be spatially separated, while for all other charge states, configurations with formation of a N O -O i bond are favored, larger N O -O i distances corresponding to higher formation energies (Fig. S19). Details on the configurations can be found in Fig. S21 and Table S5. FIG. S19: Formation energy of the different configurations for a)  We also considered the defect complex of a substitutional nitrogen and an oxygen vacancy (N O -V O ) created by fixing the V O close to the interlayer interface while positioning N O at different distances from V O . Results indicated that there is no general correlation between the N O -V O distance and the relative stability of the configuration, but they rather point towards the already known preference of N O to lie in the middle layer (Fig. S23). Details on configurations can be found in Fig. S25 and Table S7. This defect in its experimentally most relevant -3 charge state (Fig. S24) induces defect states below the CB (Fig. S22).
FIG. S22: Total and atom-projected density of states For each defect, the origin of the energy scale was set to the respective Fermi energy.
FIG. S23: Formation energy of the different configurations for a)    During the transformation of LTO to LTON N may be incorporated in the vicinity of already incorporated N atoms. One possibility is a combination of an interstitial N and a substitutional N, which we model by fixing the N O at its most stable site and sampling different positions for the N i as shown in Fig. S29. The formation energy decreases with increasing N i -N O distance ( Fig. S27 and Table S8), which, especially for lower charge states, can be rationalized with N -N bond formation with a bond length close to the N -N single bond in hydrazine. This suggests that anion-anion coupling takes place and stabilizes the relevant configurations, which is also supported by peaks with large N character at the bottom of the VB for (N i -N O ) 0 in Fig. S26a. Unsurprisingly, the length of the N -N bonds increases with increasing charge of the defect complex from 1.2Å for (N i -N O ) 0 to 1.4Å for (N i -N O ) -4 , which is the most stable charge state for E Fermi = E expt g (Fig. S28a). Interestingly for this charge state, relevant under experimental conditions, defect configurations with N i lying in the middle layer at larger distances from N O can be as stable as configurations stabilized by the formation of N -N bonds (Fig. S27d). The formation energy of N i -N O decreases with decreasing ∆µ O , N i -N O defects becoming more stable than single N-related defects in LTO for ∆µ O < 2 eV when N 2 is used as reference state for the N chemical potential.     Another possibility to incorporate N in presence of already incorporated N is as two substitutional N. We also fix one N O in either of three of the most favorable positions (see Table S9 for details) and sample other positions for the second N O . For the electron deficient (N O -N O ) 0 charge state, configurations in which N -N bonds can be formed are the most stable (Fig. S31a). These are characterized by two occupied N-dominated states in the band gap (Fig. S30a). For the (N O -N O ) -2 charge state most relevant under experimental conditions (Fig. S32a) configurations with larger N -N distances and the second N O defect lying either in the middle or bulk layer are most favorable (Fig. S31b). For these configurations the N-dominated states lie just above the valence band (Fig. S30b).
Comparing the formation energies of N i -N O and N O -N O , the latter becomes more favorable under ∆µ O smaller than -3 eV. These results suggest that even when N is already substituted in the lattice, further N insertion in LTO can favorably happen, in particular under O-poor conditions, with N entering as interstitial in the interlayer and eventually substituting for O, especially in the middle layer.  Table S9 for details).    Table S10 reports the largest migration barriers for the paths shown in Fig. S34.     (Fig. S36a). In this case the two configurations show very similar formation energies (Fig. S37), while larger differences are observed for charged defects with the IP configuration being lower by 0.23 and 0.47 eV for V O +1 and V O +2 respectively (Table S11). This can be rationalized by the different electrostatic taking place in the two cases. Interestingly, when computed for the same synthesis conditions, the formation energy of an oxygen vacancy in LTON is about 1 eV higher compared to LTO. This suggests that in coexistence of the two materials, during the transformation of LTO to LTON, oxygen vacancies will preferentially be formed in the oxide where they can be annihilated by N, favoring further conversion to LTON. Furthermore, in the N-rich environment of the thermal ammonolysis, formation of oxygen vacancies is much more favorable than the formation of nitrogen vacancies (V N ), compare Figs. S37 and S39 as well as Tables S11 and S12) by as much as 1-2 eV for E Fermi = E expt  Substitutional nitrogen (N O ) are among the most stable defects in LTON under the considered N-rich conditions ( Fig. S41 and Table S13). The formation of N O does not lead to in-gap states which could be detrimental to the photocatalytic performance of LTON (Fig. S40). N prefers to be inserted in IP positions in Fig. S35 supporting that, when nitrogen is already present, further N introduction is favored in a cis arrangement due to the bonding optimization between N/O and the Ti atoms compared to the trans order resulting from substitution at OP sites.

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Substitutional O at a nitrogen site prefers the -1 charge state and is possible only under O-richer conditions, in particular for ∆µ O > −4.1 eV, where it becomes the most stable O-related defect in LTON (Fig. S43 and Table S14). These defects do not lead to in-gap states and do not negatively affect the photocatalytic performance of LTON (Fig. S42).  These results on substitutional atoms again underline the importance of the synthesis environment, a N-rich environment from which O is continuously removed being pivotal to favor LTON formation.

S27
C. Interstitial nitrogen (Ni ) and oxygen (Oi ) For nitrogen and oxygen interstitials we sampled the positions shown in Fig. S44. The interstitials generally prefer to be located at distances of more than 2.5Å from the nearest anion ( Fig. S46 and in the experimentally most relevant -3 charge state (Fig. S47a and Table S15) lead to defect states in the band gap (Fig. S45c).   In both cases, the colored area indicates the variation of E f (N i ) for different configurations.

S29
Neutral oxygen interstitials (Fig. S49a) prefer to form close to a nitrogen, forming O -N bonds. This is not the case in the doubly negatively charged oxygen interstitial (Fig. S49b), where configurations with large O -N distances are more stable. It is visible from Figs. S49c and d, though, that in the doubly charged case O -O bonds are preferred, which is not the case for the neutral interstitial. Oxygen intersititials do, in the experimentally relevant -2 charge state ( Fig. S50a and Table S16) not induce any gap states (Fig. S48).  In addition to isolated interstitial N and O, we also considered complexes with oxygen vacancies (V O ). The N i -V O complex prefers a -3 charge state under experimentally relevant conditions ( Fig. S51a and Table S17) and becomes more stable than an isolated N i only under very O-poor conditions (Fig. S51b).  The O i -V O Frenkel pair leads to doping into the conduction band (Fig. S52) in the experimentally relevant -2 charge state ( Fig. S54a and Table S18)  La and Ti-related defects are not directly involved in the transformation of LTO to LTON, but they could form during the process, affecting it or influencing the properties of the resulting oxynitride. We considered both antisite defects (La Ti and Ti La ) and neutral defect pairs (La Ti -O N and Ti La -N O ).
For La Ti , the most relevant charge state under experimental conditions is La Ti -2 , for which we observe filling of the states at the bottom of the CB (Fig. S55d). La Ti -2 could be easily formed under Ti-poor and La-rich conditions independently of µ O/N (Fig. S56b and Table S19). In Ti-poor, La-rich and O-rich environments, the formation of La Ti -O N could also take place (Fig. S58), defect pair configurations in which La Ti and O N are close to each other being most favored (Fig. S57 and Table S20).   Under Ti-rich and La-poor conditions, the formation of Ti La is also possible ( Fig. S60b and Table S21). Ti La 0 is the most relevant charge state under experimental conditions (Fig. S60a) and is associated with the appearance of a filled Ti-3d state at the top of the VB (Fig. S59a). Under O-poor conditions (µ O < −5.7 eV, Fig. S62 and Table S21), which are relevant for the transformation of LTO to LTON, the Ti La -N O defect pair becomes favorable, especially for configurations in which the two defects are close to each other and N O is in IP position (Fig. S61), similarly to what was already observed for a single N O .     Figures S63 and S64 summarize the formation energies of all considered defects in LTO and LTON respectively, considering either N 2 or NH 3 as reference for the N chemical potential. For LTON, we additionally consider Tirich/La-poor and Ti-poor/La-rich conditions. In our calculations, µ 0 N (NH 3 ) is found to be 1.01 eV higher than µ 0 N (N 2 ) and consequently when NH 3 is used as a reference, N-related defects are slightly destabilized. In LTO, the relative stability of N-related defects with the same N content is not affected, but defects with a larger N content (N i -N O and N O -N O ) are more strongly affected and become more stable than single N-based defects for lower values of the O chemical potential compared to using N 2 as reference. Similarly in LTON, the relative stability of N-based defects is not affected, but these defects are destabilized with respect to O-based defects, especially for O-rich conditions. In panels a) and c) the formation energy is computed using N 2 as a reference for the N chemical potential, while for panels b) and d) NH 3 was used.