Oxygen Vacancy Distribution in Yttrium-Doped Ceria from 89Y–89Y Correlations via Dynamic Nuclear Polarization Solid-State NMR

Comprehending the oxygen vacancy distribution in oxide ion conductors requires structural insights over various length scales: from the local coordination preferences to the possible formation of agglomerates comprising a large number of vacancies. In Y-doped ceria, 89Y NMR enables differentiation of yttrium sites by quantification of the oxygen vacancies in their first coordination sphere. Because of the extremely low sensitivity of 89Y, longer-range information was so far not available from NMR. Herein, we utilize metal ion-based dynamic nuclear polarization, where polarization from Gd(III) dopants provides large sensitivity enhancements homogeneously throughout the bulk of the sample. This enables following 89Y–89Y homonuclear dipolar correlations and probing the local distribution of yttrium sites, which show no evidence of the formation of oxygen vacancy rich regions. The presented approach can provide valuable structural insights for designing oxide ion conductors.


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List of Contents

Sample Preparation
Samples were prepared following the co-precipitation route described in ref. 1

X-Ray Powder Diffraction
Formation of the desired structure was confirmed with X-ray powder diffraction ( Figure S1). Measurements were performed on a TTRAX-III Rigaku diffractometer equipped with a rotating Cu anode operating at 50 kV and 200 mA. Phase analysis was S3 done with the software JADE 2010. All prepared samples were high purity materials with less than 1 % impurities. Incorporation of yttrium cations in the lattice was confirmed by a decrease in the unit cell parameter of the cubic fluorite structure (space group Fm-3m). The obtained unit cell lattice parameters, accounting only for the peaks for the fluorite structure (vide infra) are 5.4095 ± 0.0001 Å, for 10Y05GdC, 5.4100 ± 0.0001 Å, for 10Y01GdC, 5.4016 ± 0.0001 Å, for 25Y01GC and 5.3918 ± 0.0001 Å for 40Y01GC.
In the sample with largest yttrium content additional peaks were observed (see inset in Figure S1). This behavior has already been reported within this concentration range and is attributed to superstructure peaks indicating an ordering of the OV positions creating a repetition unit larger than the fluorite unit cell 2,3 . This can be understood as a consequence of a phase transition from fluorite to C-type. The peak positions are in good agreement with the space group Ia-3, the relative intensity of the superstructure peaks and the pure fluorite peaks depend on the yttrium content. The position of the superstructure peaks are in agreement with the reported values for 43.75 % yttrium by by Coduri et al. 3 Figure S1. X-ray powder diffraction pattern of 10Y05GdC, 10Y01GdC, 25Y01GC and 40Y01GC, from bottom to top.

EM and EDX
High-resolution scanning transmission electron microscopy (STEM) images and energy dispersive X-ray spectroscopy (EDS) maps were recorded in a double aberration-corrected
The obtained X-band results are shown in Figure S4. The Q-band results are shown in Figure S5. Increasing the gadolinium content to 0.5% causes significant broadening of the EPR line. Figure S4. X-Band EPR spectra of (a) 10Y05GdC and (b) 10Y01GdC obtained at 50 K. Figure S5. Q-Band EPR spectra of (a) 10Y05GdC, (b) 10Y01GdC, (c) 25Y01GC and (d) 40Y01GC obtained at 50 K

NMR Measurements
All NMR measurements were performed on a Bruker 9.4 T Avance-Neo spectrometer equipped with a sweep coil and a 263 GHz gyrotron system. All measurements were done using a 3.2 mm double resonance LT-DNP probe at around 100 K. MAS rates were stable within ±3 Hz, the rates used in the rotational resonance experiments are given in the corresponding figure captions, all other measurements were performed at 8 kHz, unless otherwise specified. Spectra were obtained with the Hahn echo sequence using an echo delay of one rotor period. The rf-amplitudes used were 71.4 and 23.8 kHz, for 17 O and 89 Y, S8 respectively. 89 Y chemical shift was referenced to Y(NO3)3·6H2O at room temperature at -53.2 ppm 4 . Build-up times, TBU, under microwaves (μW) irradiation were determined using the saturation recovery sequence 5 and the measured data was fitted to a stretched exponential function: Transverse magnetization decay times, T2, were determined using the Hahn echo sequence with variable echo delay and the measured data was fitted to a stretched exponential function: Processing of the NMR spectra was done with RMN 1.8.6 6 , spectral deconvolution and CSA analysis were done with DMFIT 7 .

a. DNP field sweep profiles
The DNP field sweep profiles obtained for Y10Gd01C and Y10Gd05C are shown in Figure   S6. The profile of Y10Gd01C shows maximum positive and negative enhancements separated by twice the Larmor frequency, indicating that the solid effect is the dominating DNP mechanism. The broadening of the EPR lines caused by higher gadolinium content results in broader features of the DNP field sweep profile and a reduced enhancement factor of approximately 40, compared to 176 obtained with 0.1 % Gd. Since spin diffusion is not expected to be efficient for any of the present nuclei and nuclear spin relaxation in these samples is governed by paramagnetic relaxation enhancement 8 from the introduced gadolinium, the DNP enhancements arise from direct polarization from the gadolinium center. We have shown in previous work that the steady state enhancement for this scenario is independent of the distance between polarizing agent and nucleus 9 .
The magnetic field which gave the maximum enhancement for sample Y10Gd01C was used for 25Y01GC and 40Y01GC without furhter optimization. Note that the enhancements are negative and a 180° phase correction on the μW ON spectra was applied for esthetic purposes in Figure 1 of the main document.

b. Spectral deconvolution
Isotropic chemical shift (δiso), area and full width at half maximum (FWHM) obtained for the different yttrium sites after deconvolution of the 89 Y MAS NMR spectra are summarized in Table S1. The line broadenings increase with higher yttrium concentration and lower coordination number, indicating larger lattice distortions. Interestingly, the additional peak ( [7b] Y) observed in 10Y01GC, which has been attributed to a second 7coordinated yttrium environment with differences in the second coordination sphere 10 , was not present in the analogue sample with larger gadolinium content, 10Y05GC. At this point, parameters leading to its presence or absence are not understood. We also note that all peaks are strongly broadened compared to pristine Y2O3 11 (same is true for 17 O compared to CeO2 12 ). 89 Y chemical shift anisotropies were estimated from the spectrum of 40Y01GC obtained at a spinning speed of 3.6 kHz ( Figure S7). S10 Y (mol %) [ Table S1. Summary of the parametes obtained from deconvolution of the 89 Y spectra shown in Figure 1 and the spectrum obtained for 10Y05GC (spectrum not shown and indicated with an asterisk in table) assuming mixed Gaussian/Lorentzian line shapes. Figure S7. Thick gray line is the 89 Y MAS DNP NMR spectrum of 40Y01GC obtained at a spinning speed of 3.6 kHz. Best fit simulated spectrum (dashed blue line) was obtained by fitting the experimental spectrum with three sites [6] Y (dotted green line), [7] Y (dotted red line) and [8] Y (dotted purple line) for estimating the chemical shift anisotropy. Good fit was obtained with an anisotropy of δaniso = δzz-δiso = 2.0 kHz for all three sites, while the asymmetry parameter was held constant at η = 0. While the uncertainty for [7] Y is within 0.2 kHz, for [6] Y and [8] Y it is much larger, as only one spinning sideband can be distinguished at this spinning speed. These values are similar to the reported CSA in Y2O3. 13 S11

c. Relaxation
Longitudinal magnetization build-up times were obtained from fittings of the saturation recovery curves ( Figure S8). The transverse magnetization decay of 25Y01GC was obtained from a Hahn echo experiment of variable echo delay ( Figure S9). Due to the rigidity of the structure at 100 K, the weakness of the homonuclear couplings and the absence of heteronuclei, the main source of both longitudinal and transverse relaxation is paramagnetic relaxation enhancement caused by the gadolinium ions.
We note some variations in both the TBU relaxation times and the 89 Y enhancements (Table   S2) of samples with nominally the same dopant concentration. These deviations could be due to a reduced symmetry around the gadolinium center, following the increment in oxygen vacancies with increasing yttrium concentration 14 . Such scenario would lead to shorter T1e and consequently smaller enhancement factors. Larger enhancements have been observed in the absence of yttrium, probably due to the conservation of high symmetry 15 .
This reduced T1e would also cause a shortening of nuclear T1 according to PRE theory 16 .
An alternative possible source of the observed variations could simply be related to small variations in the gadolinium concentration, which could result in a broadening of the EPR line. S12 Figure S8. DNP buildup curves from integrated intensities of the 89 Y NMR signal obtained for the individual sites from a Hahn echo saturation recovery experiment. Solid curves are best fits obtained from fitting to equation S1. Intensities are normalized with respect to Mz(∞).
It should be highlighted that we do not observe differential T1 relaxation times for different sites within a sample ( Figure S8). Following the same rationale as for yttrium, one could also expect OV to preferentially coordinate on gadollinium 14 . Thus, the lack of differential relaxation can be understood as an additional indication of the absence of clustering   [6] Y, [7] Y amd [8] Y, respectively, were obtained. Intensities are normalized with respect to Mxy(0). No significant variations of the transverse decay curves were observed as a funtion of the spinning speed (not shown here). b) Fourier transform of a stretched exponential function with T2 = 2 ms and β = 0.5. S14

d. Rotational resonance
Figure S10 (a) shows an 89 Y 2D MAS DNP NMR correlation spectrum of 10Y01GC with a mixing time of 18 s. Additionally, 2D spectra with mixing times of 0.05, 1, 4 and 9 s were acquired and two selected cross sections are shown in Figure S10 (b). Distinction between spinning sidebands, constant in intensity, and dipolar cross peaks is evident.
Cross-peaks between the [8] Y and [7b] Y sites could also be observed by choosing an appropriate spinning speed (not shown here). Evolution of the exchange of Zeeman order was mapped by inverting the magnetization of the [6] Y and [8] Y signals relative to the [7] Y signal, and storing it along the longitudinal axis for a variable time τmix while at the rotational resonance condition. Selective inversion of both signals was achieved by exploiting the fact that both peaks have approximately the same difference in isotropic chemical shift relative to [7] Y, using the three pulse sequence, shown in Figure 2 of the main document, with a fixed t1 time ensuring a ninety degree phase shift between signals. The small relative intensity of the overlapping spinning sidebands ( Figure S7) does not impede good selectivity 18 . Spectra were acquired for 12 S15 different logarithmically spaced mixing times between 0.1 and 512 s and the results are shown in Figure S11. In addition to the dipolar coupling induced modulation of the signal the intensity decays due to longitudinal relaxation. Note that in sample 25Y01GC the [6] Y and [8] Y peaks have a zero-crossing at clearly distinct times. This is not due to a distinct mean dipolar coupling strength to the [7] Y site, but rather an artifact of the presence of noninverted spinning sidebands. The intensity of the [6] Y site in 25Y01GC is very low, and only slightly larger than the overlapping spinning sideband of the [7] Y peak. After accounting for the overlapping spinning sidebands, the intensities of the [6] Y and [8] Y sites cross zero after the same mixing time, within the experimental error (compare Figure 3 in main document). Figure S11. 89 Y MAS DNP NMR spectra obtained using the sequence shown in Figure 2a of the main document, with fixed values of t1, to invert the magnetization of the [6] Y and [8] Y signals relative to the [7] Y signal. Figures (a)

Rotational Resonance Simulations
In order to justify our interpretation of the experimental findings a series of simulations were performed using the SPINEVOLUTION program 19 . In these simulations we analyzed The obtained results are divided into two parts, summarized in the following paragraphs and corresponding figures. First, we focused on the effects of mismatch of the rotational resonance (R 2 ) condition and second, the effect of T2ZQ was analyzed.
Under the R 2 condition, the longitudinal magnetization of two coupled spins will oscillate about their mean value with a frequency determined by the strength of the dipolar coupling due to the effect of the flip-flop operator I+I-( Figure S13b). Due to the angular dependence S18 of the dipolar coupling with respect to the external magnetic field, in a polycrystalline sample the distribution of coupling strengths leads to a dampening of the oscillation ( Figure   S13c). Deviations from the R 2 condition lead to an incomplete exchange of Zeeman order ( Figure S14). The strictness of the condition becomes more severe as the coupling strength becomes weaker ( Figure S15). Of course, it should be noted that homogeneous broadenings were not considered in these simulations, which will alleviate the strictness of the matching condition (vide infra).
The efficiency of the exchange of Zeeman order between two spins (A and B) is truncated in the presence of a third spin (C), if it has a stronger dipolar coupling to one of the spins (B) and is, at the same time, as well at the R 2 condition ( Figure S16b). The effect of truncation is, however, diminished in case of deviation from the rotational resonance condition between C and B ( Figure S16c and (d)), or the number of equivalent spins B is increased ( Figure S17).
The number of spins to exchange magnetization does not have a strong effect on the buildup rates (compare Figure S17 (a) and (c) with (b) and (d), respectively). Instead, the buildup rate of the longitudinal magnetization of the inverted spins depends mainly on the distance to the source of exchanging magnetization, this is shown in Figure S18 (the effect of T2ZQ will be discussed later).
A series of simulations were done to examine whether discrimination between spins within a cluster from spins outside this cluster is in principle feasible with this approach ( Figure   S18). The used distances were chosen to roughly reproduce the experimental curves, these values, however, are not intended to have any real physical meaning, as relaxation was not considered. The simulations reproduce three groups of spins with the same isotropic chemical shifts which are at the rotational resonance condition among each other. All spins are dipolar coupled according to their geometrical properties. As the initial condition the two smaller spin groups are inverted. Due to exchange of Zeeman order, the magnetization of the inverted spins grow, while of the magnetization of the main group decreases. Clearly distinct behavior is observed as a function of the mean distance among groups.

S19
The effect of T2ZQ on the exchange of magnetization for a pair of spins at the rotational resonance condition is shown in Figure S19. The simulated curves are in perfect agreement with the analytical expression given by Levitt 20 . When the rate of decoherence, (T2ZQ) -1 , is larger than the dipolar coupling, the magnetization exchange becomes slower with shorter T2ZQ. As already pointed out, in this system single quantum 89 Y transverse relaxation times (T2) are dominated by the paramagnetic relaxation enhancement due to gadolinium ions.
Gadolinium is known to have relative (compared to other paramagnetic metal ions) long electronic relaxation times 21 , which in turn results in a significant shortening of the T2 of the surrounding nuclei. Estimation of T2ZQ from addition of the individual single quantum decay rates is only a valid approximation if the source of relaxation is uncorrelated 22 . In these samples with only minor gadolinium doping, the differences in the local field fluctuations affecting two close yttrium nuclei will be minimal. Therefore, we can expect much longer T2ZQ for close pairs and in the following simulations we will use a T2ZQ of 1 ms as the lowest limit. In Figure S20 and S21Figure S21 (and Figure 4 of the main document) we explore different scenarios of distance, relaxation and R 2 offsets. As expected, shorter relaxation times alleviate the strictness of the R 2 matching condition. The curves evidence how different combinations of conditions can lead to similar behavior of magnetization exchange and that attributing the experimental results to a specific R 2 condition would likely be meaningless. At the same time, it becomes clear that the polarization buildup curves are very sensitive to changes in the mean conditions and therefore, should carry valuable conformational information. For instance, formation of oxygen vacancies cluster will cause a change in the mean dipolar coupling strength among [6] Y and [7] Y sites, which would lead to faster polarization transfer.   Figure S16. MAS NMR simulations of 89 Y-89 Y rotational resonance correlation for the three-spin system shown in (a) after averaging over 233 orientations. As the initial condition the magnetization of the green and orange spins was inverted with respect to the blue spin. The spinning speed νR was set to 2470 Hz. The blue and orange spins were held at the rotational resonance condition, the isotropic chemical shift of the green spin was varied as given in the figure legend.