Probing Oxide-Ion Mobility in the Mixed Ionic–Electronic Conductor La2NiO4+δ by Solid-State 17O MAS NMR Spectroscopy

While solid-state NMR spectroscopic techniques have helped clarify the local structure and dynamics of ionic conductors, similar studies of mixed ionic–electronic conductors (MIECs) have been hampered by the paramagnetic behavior of these systems. Here we report high-resolution 17O (I = 5/2) solid-state NMR spectra of the mixed-conducting solid oxide fuel cell (SOFC) cathode material La2NiO4+δ, a paramagnetic transition-metal oxide. Three distinct oxygen environments (equatorial, axial, and interstitial) can be assigned on the basis of hyperfine (Fermi contact) shifts and quadrupolar nutation behavior, aided by results from periodic DFT calculations. Distinct structural distortions among the axial sites, arising from the nonstoichiometric incorporation of interstitial oxygen, can be resolved by advanced magic angle turning and phase-adjusted sideband separation (MATPASS) NMR experiments. Finally, variable-temperature spectra reveal the onset of rapid interstitial oxide motion and exchange with axial sites at ∼130 °C, associated with the reported orthorhombic-to-tetragonal phase transition of La2NiO4+δ. From the variable-temperature spectra, we develop a model of oxide-ion dynamics on the spectral time scale that accounts for motional differences of all distinct oxygen sites. Though we treat La2NiO4+δ as a model system for a combined paramagnetic 17O NMR and DFT methodology, the approach presented herein should prove applicable to MIECs and other functionally important paramagnetic oxides.

Two classes of supercells, denoted NOI and LNO, were constructed and optimized. NOI ("no interstitials") was derived from the experimental high-temperature tetragonal 1 (I4/mmm) structure of stoichiometric La2NiO4 and converted to a primitive triclinic 7-atom cell with isotropic lattice parameters of ~6.96 Å. For LNO, the experimental room-temperature orthorhombic (Fmmm) structure of La2NiO4+δ (δ = 0.17) 1 was used to construct a 57-atom supercell La16Ni8O33 corresponding to δ = 0.125. The LNO supercell was tetragonal due to expansion of the orthorhombic structure by √2 along new axes defined to be [110]Fmmm and [11 0]Fmmm. The supercells are depicted in Figure S4.
As stated in the Experimental section, calculations made use of two all-electron basis sets (BS-I and BS-II). The minimal basis set BS-I was derived from the CRYSTAL online basis set repository and used for structural optimizations, band structure calculations and density of states plots. Atomic species were represented in BS-I as (30s21p10d)/[1s6sp3d] for La, (20s12p5d)/[1s4sp2d] for Ni, and (14s6p1d)/ [1s3sp1d] for O, with the number of Gaussian primitives given in parentheses and the contraction scheme in square brackets. Hyperfine properties and quadrupolar coupling constants were computed from single-point energy calculations with the larger basis set BS-II, wherein (13s9p5d)/[7s5p3d] and (10s6p2d)/[6s5p2d] sets were adopted for Ni and O, respectively; the La basis set was the same as for BS-I. Initial exponents and coefficients were derived from IGLO-III (O) and DZP (Ni) basis sets as used previously. 2 Prior to use of BS-II, the most diffuse exponents in the basis set for each atomic species were first energy-optimized in the simpler NOI system using a numerical conjugate method implemented through the LoptCG script included with the CRYSTAL code.
The displacement of axial oxygen into split sites has implications for the calculation and assignment of our NMR spectra; we briefly discuss its origin. The phenomenon is associated with, but distinct from, rotation of the NiO6 octahedra. As Perrichon et al. note in the case of Nd2NiO4+δ, octahedral rotation may occur with minor changes in the Ni-Oax distance, and conversely a large contraction may not necessarily accompany a large tilt. 3 Disregarding octahedral rotation, therefore, one can rationalize the displacement of axial sites via steric or electronic arguments. According to the former, axial oxygen initially positioned "between" Oi and Ni sites, if repelled along a path directly away from a nearby interstitial, will move to an environment with a shorter Ni-Oax distance. Alternatively, in the latter argument, charge compensation of O 2interstitials occurs via oxidation of some Ni 2+ sites to Ni 3+ , with a more nuanced and longer-range effect on axial sites. The smaller ionic radius of Ni 3+ favors shorter overall Ni-O bonds; this effect competes with the axial elongation arising from the Jahn-Teller distortion of Ni 3+ . Regardless of the net change in bond length, charge ordering on Ni may contribute to a range of Ni-Oax distances. We note that in our calculations the Ni sites not adjacent to Oi have marginally more Ni 3+ character, with slightly shorter equatorial bonds and longer axial bonds, and this represents the source of the variation in Ni-Oax distances we observe within a rocksalt layer.
The exact nature of the Oax distortion is expected to be highly dependent on the specific superstructural arrangement of interstitials. In our calculations, this three-dimensional superstructure is artificially constrained by the periodicity of the relatively small supercell. Nonetheless, experimental evidence for a more complex model of long-distance interstitial ordering, as in the neutron diffraction study by Demourgues et al. of "La8Ni4O17" (δ = 0.25), is associated with a similar splitting of Oax sites into five (or possibly six) types based on proximity to Ni. 4,5 However, diffraction-based approaches (with patterns indexed on unit cells of high symmetry) generally resolve one "normal" and one distorted Oax site with averaged, and thus comparable, Ni bond lengths. Only for materials with significant stacking-axis contraction (e.g. Nd2NiO4+δ 3 ), or containing transition metal cations that undergo large changes in Jahn-Teller distortion upon oxidation (e.g. La1.2Sr0.8MnO4+δ 6 ), do diffraction data evidence a clear reduction of the average Ni-Oax bond length. The sensitivity of paramagnetic 17 O NMR to subtle forms of local disorder, even in the absence of any long-range superstructure (as required for diffraction), is a distinct advantage of this methodology, and ultimately derives from the exceptional strength of the hyperfine interaction and its dependence on small changes in distance to nearby paramagnetic centers.
We first assume that the dominant source of T2 relaxation arises from low-frequency motion, i.e. oxygen dynamics, and not high-frequency processes such as electron relaxation (T1e) or electron hopping. (This assumption is justified by measurements at room temperature of a much longer T1 (~60 ms) for Oi compared to T2 (~1.5 ms); high-frequency processes contribute to both T1 and T2, but low-frequency processes only influence T2.) Then, in the slow motion regime, it is known 7-9 that the exchange rate kex is inversely proportional to T2 : for some positive proportionality constant c. Technically, the slow motion regime is influenced by the temperature dependence of the paramagnetic shifts, but this effect is expected to be small and at all temperatures we can assume we are at or below the coalescence temperature as argued in the main text.
Secondly, we assume the integrated intensity of the interstitial feature, I, exhibits a mono-exponential T2 decay, such that where is the rotor period, experimentally fixed to a constant value of 80 μs for all Hahn echo experiments. We justify the exclusion of T1 effects on the measured intensity as the recycle delay in these experiments is already quantitative (>5T1), and we find that theT1 of this site only decreases further with an increase in temperature. Thus, other than changes in the Boltzmann distribution of spin states considered later, we assume the signal loss is entirely due to T2 relaxation prior to acquisition. Explicitly, a faster exchange rate at higher temperature leads to a shorter T2 and thus a greater attenuation of signal. By contrast, in an ideal "one-pulse" experiment in which acquisition immediately follows application of the rf pulse, we would not expect any loss of signal, regardless of exchange rate; dynamics induces significant broadening, but no change in the overall integrated intensity. (As a conclusive test of the origin of the signal loss, one could measure T2 at each temperature and S3 compare the ideal T2-induced and experimental decreases in intensity. In this study, however, we have not performed thorough T2 measurements due to the prohibitive time cost of acquiring signal at high temperature in even a single Hahn echo experiment.) Combining equations [1] and [2], we obtain where we have also assumed a simple Arrhenius relationship between kex and the sample temperature T, with corresponding pre-exponential factor A0 and activation energy Ea. This gives -, [4] which is a power-law dependence of log I on the quantity exp(-1/T), with exponent Ea/R. To obtain experimental values of I at each temperature T, we integrate the centerband of the interstitial feature over a 12.5 kHz window (i.e. with boundaries equidistant from the centerband and nearest spinning sidebands). As the spinning sideband pattern is essentially temperature-independent, the centerband intensity accurately approximates a fixed fraction of the total intensity across the entire temperature range. We correct these values by the expected loss in intensity due to a reduction in the population difference of the central transition spin states, i.e., ----, [5] such that the intensity is referenced to the lowest temperature (T0 = 308 K) measurement. Here the Boltzmann-distributed population ratio of spin states is well-approximated linearly as a consequence of the small energy of the transition (ω0 = 5.966 • 10 8 rad s -1 ).
Finally, to extract Ea, we plot log I' against exp(-Ea/RT) for a range of Ea values, fit the data to a linear function, and compare r 2 values (coefficients of determination). From Figure S10a, we see that a value of Ea = 0.48 eV maximizes the goodness of fit to Equation [4] (with r 2 = 0.988). Figure S10b shows the reasonable linearity of the log I' vs. exp(-Ea/RT) data when Ea = 0.48 ± 0.06 eV, with the notable exception of the highest temperature data at 134°C (red cross). This point remains a persistent outlier regardless of the choice of Ea. The outsize intensity at this temperature arises from immobile oxide ions in similar but chemically distinct environments, possibly distorted La2O3-like environments near the surface. We have therefore excluded this data point when initially determining Ea. However, this additional intensity clearly contributes to the signal at all temperatures and leads to an underestimated value of Ea. Therefore, as a final correction, we repeat the analysis after subtracting the intensity measured at 134°C (I' high-T) from the other data points. We then obtain a value of Ea = 0.59 ± 0.07 eV ( Figure S11a) with an improved r 2 = 0.996, suggesting that removing the excess intensity does enhance the fit of Equation [4] to the data. Figure S11b depicts the best-fit line with Ea = 0.59 eV.
Assuming the immobile La2O3-like site at 565 ppm ( Figure 4, 134°C) possesses a similar T2 to the interstitial feature at room temperature, the relative intensity ratio gives one such OLa4 site in surface La2O3 to ~10 interstitial oxides in the bulk sample. Given a sample composition of δ = [Oi''] = 0.17, and assuming that two-thirds of the oxygen sites in the La2O3 phase are tetrahedrally-coordinated (as in the bulk compound), the molar phase fraction of surface La2O3 is calculated to be 2-3%. (For comparison, assuming roughly 1 μm spherical particles, this corresponds to a surface depth of 7-10 nm.) We have established that the feature at 2400 ppm seen above 110°C ( Figure 5) arises from the La4Ni3O10 impurity phase (previously resolved by XRD), as well as other higher-order Ruddlesden-Popper phases such as La3Ni2O7 that form during high-temperature 17 Oenrichment. Although synthesis and 17 O-enrichment of the pure higher-order phases has not yet proven possible, 17 O-enrichment of a mixture of La2NiO4+δ and NiO at 1000°С yields a 17 O-enriched sample of 55 wt % La2NiO4+δ, ~25 wt % La4Ni3O10 and ~20 wt % La3Ni2O7 as determined by XRD, with the latter two phases difficult to distinguish due to significant overlap of reflections ( Figure S13). The room-temperature 17 O NMR spectrum of this mixed sample contains the typical features of La2NiO4+δ but with the familiar additional peak at 2400 ppm ( Figure  S14). This resonance, clearly associated with the impurity phase(s), is tentatively assigned to an axial oxygen site with two nearby Ni cations, i.e. the oxygen environment present in La3Ni2O7 and La4Ni3O10 but not in La2NiO4+δ. Its smaller hyperfine shift compared to Oax in La2NiO4+δ, despite the proximity of the site to an additional paramagnetic center, is attributed to the higher concentration of Ni 3+ (S = ½), as well as to the onset of metallic behavior and Pauli paramagnetism in the higher-order phases. 10 The latter property in particular gives rise to a smaller Knight shift rather than a pure Fermi (Curie-Weiss) contact shift, as previously shown for 17 O NMR spectra of metallic oxides. 11 As with the shoulder assigned to the distorted La2O3 phase, the higher-order impurity feature is apparent for the La2NiO4+δ sample only in high temperature spectra, such that signal from the main phase is greatly diminished. Based on the above assignment and the integrated NMR signal, we estimate a molar phase fraction of La3Ni2O7 / La4Ni3O10 equal to 2-4%, in good agreement with earlier refined XRD results (~3 wt % of La4Ni3O10). (The uncertainty in the molar phase fraction arises from the lack of knowledge of the exact contribution of each of the very similar higher-order phases to the signal at 2400 ppm.) The extensive spinning sideband manifold associated with this feature suggests a highly anisotropic environment with significant local structural disorder, possibly caused by oxygen vacancies, or otherwise ascribed to the situation of the higher-order phases in the disordered subsurface region of La2NiO4+δ, as predicted by Wu et al. 12 Our results indicate that the oxidation mechanism of La2NiO4+δ to La3Ni2O7 and La4Ni3O10, which is of relevance to SOFC cathode operation and degradation, involves the preferential incorporation of O2 (here as 17 O2) into the axial sites bridging the perovskite layers (as seen at 2400 ppm).

S4
We recently became aware of a 17 13 Given the proximity of this shift to the feature we observe at ~170 ppm, as well as the possibility of forming lanthanum silicate during 17 O-enrichment of La2NiO4+δ at 1000°C within a quartz (SiO2) tube, one could reasonably propose an alternative assignment of this feature to La9.6Si6O26.4. As seen from Figure S7, the calculated mole fraction of this impurity (<1 mol%) is well below detection by powder XRD, and cannot be definitively assigned to either the aluminate or silicate phase.   (2) La2NiO4 + H2 --> La2O3 + Ni + H2O. The differential thermogravimetry (DTG) trace (inset), the numerical first derivative of the TGA data, was used to determine the flattest region of each plateau from which each mass loss was determined. Here the mass losses for the two reduction steps were 0.67% and 4.59%, yielding a calculated oxygen excess of δ = 0.15. Figure S3. Correlation between oxygen excess (δ) and refined lattice parameters. As-synthesized samples (red) show smaller c lattice parameters and larger a and b lattice parameters as determined from refinements of XRD patterns, correlating with a smaller oxygen excess (δ = 0.12 to 0.14) as determined by TGA. After 17 Figure S4. Empirical fit to broadband room-temperature spectrum of La2NiO4+δ for quantitation. Lorentzian functions centered at ~6650 ppm and ~3272 ppm, with additional intensity arising from satellite transitions, are fit to the Oeq and Oax sites, while a simple spinning sideband manifold (CSA only) is fit to Oi at 532 ppm. The model has been computed and optimized using the dmfit software. 16 Though the fit does not capture the Oeq and Oax lineshapes perfectly, and moreover does not resolve accurate CQ values for these sites, we nonetheless obtain a relative integrated intensity ratio of Oeq : Oax : Oi = 47.7 : 47.5 : 4.8 that is in very good agreement with that expected from stochastic 17 Figure 4 are shown centered about the 170 ppm feature assigned to LaAlO3. The small reduction in signal (~20-30%) with increase in temperature is consistent with that expected from the temperature-dependent Boltzmann distribution of spin states. However, the signal does not vanish completely as does Oi (with sidebands at ~138 and ~240 ppm), implying the loss of Oi signal is due to other effects, i.e. a decrease in T2 consistent with oxide-ion motion in La2NiO4+δ. The LaAlO3 feature is weak and difficult to phase due to a sloping baseline, accounting for the unusual lineshape seen at 35°C. Spectra were acquired at 16.4 T under a MAS rate of 12.5 kHz. Spectra have been normalized to the number of scans acquired. Asterisks denote spinning sidebands of Oi (centerband at 532 ppm, not shown).  Figure 5). The feature at 2400 ppm assigned to the La3Ni2O7/La4Ni3O10 impurity phase is indicated by #, with asterisks denoting spinning sidebands of this feature. The weakly resolved peaks in the diamagnetic region are assigned to "surface" La2O3 (~565 ppm), the ZrO2 sample container (~380 ppm), and the LaAlO3 impurity phase (~170 ppm). The spectrum was acquired at 7.05 T at a MAS rate of 12.5 kHz. Figure S10. Initial determination of Ea for interstitial motion. a) For each Ea, the corrected intensity data (log I ') are plotted against the quantity exp(-Ea/RT), as depicted in b), and a linear fit to the data is performed, excluding the point corresponding to 134°C. The coefficient of determination r 2 is extracted for each linear fit as a measure of the goodness of fit. A value of Ea = 0.48 ± 0.06 eV (grey dotted line with red error bars) is found to give the best fit to Equation [4] (r 2 = 0.988). The error in Ea follows from considering the maximum variation in r 2 (≈ 0.0025) upon re-fitting the intensity data subject to their errors, which are inversely related to the signal-to-noise ratio of each spectrum. b) The corrected intensity data (log I ') are plotted against the quantity exp(-Ea/RT), where the optimized value of Ea = 0.48 eV maximizes the collinearity of the data. The best fit line (grey dotted line) gives an r 2 coefficient of 0.988. The intensity at 134°C (red cross) is a persistent outlier and has been excluded from the fit. c) Plot of the corrected intensity data (log I ') against 1/T, showing the best fit of Equation [4] assuming Ea = 0.48 eV (again, excluding the outlier at 134°C). The observation that the signal at 134 °C is an outlier is consistent with its assignment to an environment that is not in the main phase. S11 Figure S11. Revised determination of Ea for interstitial motion. a) For each Ea, the corrected intensity data, after subtracting the excess intensity of the feature at 134°C (log (I ' -I 'high-T)), are plotted against the quantity exp(-Ea/RT), as depicted in b). As before, a linear fit to the data is performed. The coefficient of determination r 2 is extracted for each linear fit as a measure of the goodness of fit. A value of Ea = 0.59 ± 0.07 eV (grey dotted line with red error bars) is found to give the best fit with r 2 = 0.996, indicating a better agreement with Equation [4] than that obtained in the initial analysis ( Figure S10). The error in Ea follows from considering the maximum variation in r 2 (≈ 0.0024) upon re-fitting the intensity data subject to their errors, which are inversely related to the signal-to-noise ratio of each spectrum. b) The corrected and subtracted intensity data (log (I ' -I 'high-T ')) are plotted against the quantity exp(-Ea/RT), where the optimized value of Ea = 0.59 eV maximizes the collinearity of the data. The best fit line (grey dotted line) gives an r 2 coefficient of 0.996. The 134°C data point is not depicted; we cannot resolve any intensity at this temperature other than the overlapping feature at 565 ppm subtracted from the other data. c) Plot of the corrected and subtracted intensity data against 1/T, showing the best fit of Equation [4] assuming Ea = 0.59 eV. Figure S12. Asymmetric two-site simulations of axial-interstitial exchange. Simulated 17 O NMR spectra of the interstitial and axial oxygen environments (fixed at 532 ppm and 3400 ppm, respectively) are shown as a function of the axial-interstitial exchange rate kex. A shift of 3400 ppm for Oax is chosen in agreement with the apparent peak position of Oax at a MAS rate of 12.5 kHz (as in Figure 1) at 35 °C. The population ratio of axial to interstitial oxygen sites is fixed at 16:1. The Larmor frequency of 17 O has been set at ~95.0 MHz (corresponding to a magnetic field of 16.4 T), matching the experimental conditions of the VT-NMR spectra depicted in Figure 4. The inset shows the region around the Oi feature; no distinguishable intensity from Oi sites is observed above log10(kex) ≈ 5.5, i.e. kex ≈ 320 kHz. The shift of the Oax resonance reflects coalescence with the Oi resonance: we have not included the Curie-Weiss temperature-dependence of this resonance. Simulations have been performed using the MEXICO code. 18   Figure S13), is 55 wt % La2NiO4+δ , ~25 wt % La3Ni2O7 and ~20 wt % La4Ni3O10. The appearance of an additional feature in the spectrum at 2400 ppm (indicated by #), with associated spinning sideband manifold, is assigned to the higher-order Ruddlesden-Popper phases La3Ni2O7 and La4Ni3O10, and specifically to the unique Oax-like sites bridging adjacent perovskite layers in these phases. Intensity of the sites is not quantitative; the pulse carrier frequency is centered at 3000 ppm and so the Oeq resonance is not efficiently excited. Dashed blue lines indicate positions of spinning sidebands of the 2400 ppm feature; dashed red lines indicate positions of spinning sidebands of the feature assigned to interstitial oxygen (Oi) in La2NiO4+δ . The room-temperature Hahn echo spectrum was acquired at 7.05 T with a MAS rate of 14 kHz, using a π/6 rf pulse centered at 3000 ppm. The shifts change only slightly (<2 ppm) across the studied temperature range; at 135°C, the OLa4 and OLa6 sites are located at approximately 583.6 ppm and 469.2 ppm, respectively. In particular, the OLa4 feature does not change significantly with increase in temperature to 140°C, supporting our claim that the 565 ppm feature observed in high temperature (130-140°C) spectra of La2NiO4+δ does not arise from a bulk La2O3 impurity, but rather a distorted La2O3-like layer at the surface of La2NiO4+δ. Spectra were acquired at 16.4 T with a recycle delay of 5 s at a spinning speed of 12.5 kHz, on a sample of La2O3 previously enriched in 17 O under 1 atm of 70% 17 O2 at 1000°C for 24 h. All spectra have been normalized to the number of scans. Asterisks denote spinning sidebands.