Polar surface structure of oxide nanocrystals revealed with solid-state NMR spectroscopy

Compared to nanomaterials exposing nonpolar facets, polar-faceted nanocrystals often exhibit unexpected and interesting properties. The electrostatic instability arising from the intrinsic dipole moments of polar facets, however, leads to different surface configurations in many cases, making it challenging to extract detailed structural information and develop structure-property relations. The widely used electron microscopy techniques are limited because the volumes sampled may not be representative, and they provide little chemical bonding information with low contrast of light elements. With ceria nanocubes exposing (100) facets as an example, here we show that the polar surface structure of oxide nanocrystals can be investigated by applying 17O and 1H solid-state NMR spectroscopy and dynamic nuclear polarization, combined with DFT calculations. Both CeO4-termination reconstructions and hydroxyls are present for surface polarity compensation and their concentrations can be quantified. These results open up new possibilities for investigating the structure and properties of oxide nanostructures with polar facets.

P olar surfaces, which have a permanent dipole moment perpendicular to the surface, are of great importance in both physical and chemical applications [1][2][3][4] . Due to the very large energies of uncompensated surfaces, polarity compensation is required, generating different and complex surface configurations for these facets. Therefore, it is extremely difficult to understand the atomic-scale structure of polar surfaces, which is essential in order to design related nanomaterials for a targeted property [5][6][7][8] . By applying electron microscopy and computational modelling, a variety of polarity compensation mechanisms have been proposed, including ordered surface reconstructions 9 , surface disorder 10 , adsorption of environmental gas molecules 11 , surface metal layers deposition 12 , and subsurface oxygen vacancies 13 . Despite the many advantages of microscopy techniques, they are limited to the visualization of a small fraction of the sample which may not yield reliable quantitative information about the whole sample, and are typically performed at high vacuum conditions that may alter the surface environment 14 . Furthermore, light elements, such as hydrogen and oxygen which are of key importance for many materials, are difficult to probe with such techniques 15 . Although significant developments have been made in environmental electron microscopy, which allows materials to be investigated under adjustable pressure conditions and in variable gaseous environments [16][17][18] , the other disadvantages remain and complementary methods are required.
Solid-state NMR spectroscopy is a powerful method which can provide rich local structural information for solids [19][20][21][22][23][24][25][26] , complementary to the information obtainable from diffraction 27 and microscopy techniques. Recently, 17 O solid-state NMR spectroscopy has been developed as a new approach for determining the surface structure of oxide nanomaterials, with help from surfaceselective labeling and DFT calculations. Oxygen ions in different layers of ceria nanostructures 28 and at different facets of anatase titania nanocrystals 29 can be distinguished according to the NMR shifts. However, only non-polar facets were studied previously and no attempt was made to investigate the more challenging oxide nanostructures with polar facets. Furthermore, quantification of different surface species was not possible using exclusively 17 O NMR, due to the quadrupolar nature of 17 O and the potentially non-uniform isotopic labeling procedure.
Ceria nanocubes expose (100) facets, which show exceptional properties as both the catalytically active plane and the support facet; this is a relatively simple polar surface, making ceria nanocubes an ideal model [30][31][32][33] . Using the example of ceria nanocubes, we introduce a strategy of qualitative 17 O and quantitative 1 H solid-state NMR spectroscopy combined with DFT calculations to characterize oxide nanocrystals with polar facets. We thereby quantitatively determine detailed polar surface structural information, specifically the presence and concentration of reconstructed Ce terminated structures (CeO 4 -t) and hydroxyl groups.

Results
Morphology of the ceria nanocubes. Ceria nanocubes were hydrothermally synthesized with Ce(NO 3 ) 3 ·6H 2 O and NaOH (see methods). The X-ray diffraction (XRD) data (Supplementary Fig. 1) confirms the formation of ceria with a fluorite structure (JCPDS No. 34-0394). High-resolution transmission electron microscopy (HRTEM) images show that the samples adopt a cubic morphology with sizes of 18 to 40 nm, dominated by (100) polar surfaces before and after 17 O enrichment ( Supplementary  Fig. 2). Inductively coupled plasma mass spectrometry (ICP-MS), elemental analysis and X-ray photoelectron spectroscopy (XPS) data show that there are no detectable Na + or NO 3 − impurities (Supplementary Fig. 3 5) due to the OCe 4 environment in the bulk of the ceria nanocubes, but other signals can also be observed at 970, 935, and 825 ppm. 17 O NMR signals for ceria samples with (111) facets have previously been observed at 1040, 920, and 825 ppm due to oxygen ions in the first, second, and third (sub-)surface layers respectively 28 ; the shoulder resonance at 825 ppm in the NCs-17 O 2 spectrum is therefore most likely due to a deeper sub-surface layer while the signals at 970 and 935 ppm, which have not previously been observed, may be tentatively assigned to the oxygen ions at the (100) surface.
For the spectrum of NCs-H 2 17 O, in addition to the bulk signal with a maximum at 877 ppm, two broad peaks centered at approximately 250 and 1012 ppm can be observed. The former is most likely to be related to surface hydroxyl groups (Ce-OH) 29,34 , and on closer inspection can also just be distinguished for NCs-17 O 2. The latter can again, based on its high frequency compared to the bulk resonance, be attributed to under-coordinated surface oxygen species. Surface-selective isotopic labeling is achieved by exposing the samples to 17 O 2 gas or to H 2 17 O vapor at relatively low temperatures, although there are differences between the spectra that will be discussed later.
A possible explanation for the higher frequency signal in the spectrum of NCs-H 2 17 O is the formation of some degree of the thermodynamic (111) surface, given that the first surface layer in this case has been observed at 1040 ppm. However, the HRTEM images show little evidence for (111) facets ( Supplementary  Fig. 2), and after re-enriching NCs-H 2 35,36 and the lineshapes can be affected by the distribution of hydrogen bond distances; in particular, stronger hydrogen bonding results in higher frequency 1 H NMR signals 37 . The spectrum of NCs-17 O 2 in Fig. 2a shows a broad resonance between 2-16 ppm (the sum of the green deconvoluted Lorentzian functions), along with a shoulder at 5.4 ppm (blue signal), and a relatively sharp peak at 2.5 ppm (brown signal); a summary of these deconvoluted signals is presented in Supplementary Table 2. The signal at 5.4 ppm is most likely due to molecularly adsorbed water molecules and the 2.5 ppm signal can be assigned to terminal hydroxyl species (-OH T ) 38 ; the remaining intensity is then assigned to bridging hydroxyl groups (-OH B ) with a distribution of environments and degrees of hydrogen bonding. A similar 1 H NMR spectrum was observed for NCs-H 2 17 O (Fig. 2b), but with a broader signal centered around 8 ppm, corresponding to bridging hydroxyl groups with an even greater distribution of environments and hydrogen bonding. Quantitative analysis of the integrated 1 H intensities, combined with the specific surface areas as measured from the BET isotherms, yields adsorbed water contents for NCs- 17 (Fig. 2c) shows correlations between the 17 O signals at around 250 ppm with the 1 H signals due to hydroxyl groups, confirming the assignment of the 17 O NMR spectra. Furthermore, hydroxyl sites with higher 17 O shifts are associated with higher 1 H shifts, and thus a stronger acidity (although stronger hydrogen bonding can also result in larger shifts) 39 . The conclusion that bridging hydroxyl groups are more acidic than terminal hydroxyls is in agreement with previous reports in zeolites 39 . Since the 17 O NMR shift range is much wider than for 1 H NMR shifts, 17 O NMR spectroscopy may provide an alternative and more sensitive probe of the acidity and acid-catalysis reactivity for oxide nanomaterials. However, 17 O NMR experiments often require spectra acquired at multiple magnetic fields, preferably higher fields, or with high resolution techniques (e.g., MQMAS 40 ), in order to decrease the linewidths arising from quadrupolar interactions.
Spectral Assignments from DFT Calculations. DFT calculations have previously proved successful in aiding spectral assignment for surface oxygen ions in oxide nanostructures 28,29 . The differences between the calculated and experimental results are generally around or less than 10 ppm 28 , allowing reliable spectral assignment. An oxygen terminated (O-t) model of ceria (100) surface was previously investigated for DFT calculations 28 (Fig. 3a), however, the calculated 17 O NMR parameters (Supplementary Figs. 8-10 and Supplementary Table 4) are not in agreement with our NMR observations, i.e., no surface species in the calculations are associated with resonant frequencies at 970, 935 or~1012 ppm and the calculated signal for the 1 st layer twocoordinate oxygen ion (O 2C ), with a high frequency chemical shift (1117 ppm), is not observed in the experimental spectrum.
As seen from the 1 H and 17 O NMR spectra, a significant number of hydroxyl groups are present at the surface, which must be considered. A previous computational study reported that dissociative adsorption of water is much more favorable than the molecular adsorption of water on the (100) O-t surface 41  suggests that the structure of polar (100) facets in ceria nanocubes is more complicated than the simple O-t model. Two recent studies suggested that a fraction of ceria (100) facets may form CeO 4 terminated (CeO 4 -t) reconstructions, which yield a lower surface energy than cerium terminated (Ce-t) or O-t surfaces 10,42 . Therefore, DFT calculations were performed on a model comprising CeO 4 -t reconstructions linked by O 2C sites (CeO 4 -t surface, Fig. 3b)-a pure CeO 4 -t reconstruction has previously been shown to have a high surface energy and is thus unstable 10 .
First, the relative energies of dissociative and molecular adsorption were calculated for a single H 2 O molecule per CeO 4 -t surface unit . A comparison of the adsorption energies shows that H 2 O molecules also prefer to adsorb dissociatively on clean CeO 4 -t ceria (100) surfaces (Supplementary Table 9 Supplementary Fig. 39).
The O 2C ions in the first layer of models M 0 and M 1 are associated with very high chemical shifts of 1162 and 1168 ppm respectively; such high frequency signals are not present in the experimental 17 17 O have resonant frequencies closer to the bulk shift of 877 ppm, which is consistent with the relatively broad component observed experimentally for the peak centered at 877 ppm. The predicted peak in the 2 nd layer at 756 ppm for M 2 is not experimentally observed; this environment, although fully coordinated, is highly distorted (see Supplementary Fig. 40). This distortion may be lost on addition of a bridging hydroxyl between the CeO 4 reconstructions (e.g. H 4 , see Fig. 6), which is above the distorted environment, or the distortion may be averaged at non-zero temperatures due to rapid interconversion of different local environments with similar energies.   The above results indicate that the concentration of surface hydroxyl groups has a great impact on the NMR shifts of surface oxygen ions. Furthermore, in order to reproduce the experimental 17 O NMR spectra, both dissociated water and CeO 4 -t reconstructions must be included in the calculations. Thus, the ceria (100) surface can be regarded as a combination of CeO 4 -t and O-t surface units, where the under-coordinated O 2C ions have been converted to bridging hydroxyl groups and terminal hydroxyl groups have formed on some under-coordinated cerium ions.
The 1 H NMR chemical shifts were also calculated using DFT, confirming the assignment of the 1 H NMR signals at 2-16 ppm and 2.5 ppm to bridging (-OH B ) and terminal (-OH T ) hydroxyl groups on the surface (Fig. 6 and Table 1) 38,39 . The calculated 1 H shift for -OH T is the most negative, and since the lowest frequency signal in the experimental 1 H NMR spectrum is the relatively sharp peak at 2.5 ppm, this resonance is assigned to -OH T . The broad signal is attributed to -OH B . Different -OH B environments are associated with a range of chemical shifts and the distribution is wider for the model with three dissociatively adsorbed H 2 O molecules (M 3 ) than that for two (M 2 ); in particular, the very large shift of H 4 in M 2 is due to hydrogen bonding to the oxygen ions of H 2 and H 3 . This at least partially explains why the experimental -OH B resonance is broad and why the spectral line width for NCs-H 2 17 O is broader than for NCs-17 O 2 , given the higher hydroxyl content of the former. An inhomogeneous distribution of dissociated water and variable hydrogen bonding may also contribute to the broadness of the signals.
Based on the quantitative 1 H NMR data and the above assignments from the DFT calculations, the fractions of CeO 4 -t and O-t surface units comprising the (100) facets of ceria nanocubes can be determined (Table 2). This is based on the fact that each CeO 4 -t surface unit contains one characteristic terminal hydroxyl group (-OH T ) and either three (M 2 , Fig. 2a)  .5% for CeO 4 -t), supporting the assignment of these models. 17 O DNP NMR spectroscopy. Recent developments in dynamic nuclear polarization (DNP) provide new opportunities to characterize the surface structure of solid materials 34,43,44 . Direct DNP involves transferring polarization from unpaired electrons directly to the nucleus of interest, with the unpaired electrons typically being added in the form of organic biradicals; because the biradicals are external to the particles, and the hyperpolarization mechanism has a 1/r 6 distance dependence, the surface can be selectively hyperpolarized and hence observed in the NMR spectrum (surface enhanced NMR spectroscopy, SENS    (Fig. 7a, b). For NCs-17 O 2 , the enhancement factor for the peak at 970 ppm is~8, while the surface signals for NCs-H 2 17 O can only be observed in the "on" spectrum, indicating that hyperpolarization is more efficient for these species than for the bulk, and therefore that these resonances are indeed surface oxygen species. The DNP build-up time, T DNP , can also be fitted to distinguish external and internal 17 O nuclei 34 , since nuclei close to the surface hyperpolarize faster and hence have a shorter T DNP . For NCs-17 O 2 , the T DNP values for the peaks at 970, 880, and 870 ppm are much smaller than for the bulk signal at 875 ppm, implying that the former arise from surface species in NCs-17 O 2 ( Fig. 7c and Table 3). Broader peaks are observed for the 17 O DNP SENS spectra than for the room temperature 17 O spectra, which can be attributed to the freezing out of motional averaging of the dynamic surface sites at the low temperatures required for DNP, as previously observed for ceria (111) facets 34 .
The 17 O DNP spectrum of NCs-H 2 17 O has spinning sidebands which overlap with other resonances due to the lower spinning speeds achievable at 100 K and the higher field at which the DNP experiments were performed (which results in a smaller separation of sidebands in ppm, for the same spinning frequency). Therefore, 17 O DNP projection magic angle turning and phase adjusted sideband separation (MATPASS) NMR experiments were performed to resolve the isotropic resonances ( Supplementary Fig. 43) 45,46 . Four non-bulk resonances at 1012, 970, 895, and 853 ppm can be deconvoluted, and were used to fit the saturation recovery data and obtain the T DNP s (Fig. 7d and Table 3). Again, these peaks are associated with shorter T DNP s than the peak at 875 ppm arising from the bulk part of the and I 0 are the signal intensities at delay t and at equilibrium, respectively, and β is the stretching exponent (0 < β < 1) ( Table 3). Table 3 The build-up time (T DNP ) and stretching exponent (β) of different peaks extracted from the 17 17 O spectral assignments, however, although DNP SENS spectroscopy generally provides a stronger signal-to-noise ratio compared to conventional NMR spectroscopy, due to the restricted spinning rates and broader surface signals at low temperature, certain species can be resolved better with the latter. The strategy introduced here can be applied to gain insight into the surface structures of oxide nanocrystals and materials with polar surfaces.

Methods
Preparation of ceria nanocubes. In a typical synthesis procedure 47 , 1.96 g Ce (NO 3 ) 3 ·6H 2 O was added into 40 mL distilled water. After stirring for 5 min, 30 mL NaOH solution (pH = 14) was slowly added into the mixture before it was vigorously stirred for another 30 min at room temperature. The mixture was then transferred into a 100 mL Teflon-lined hydrothermal reactor and heated at 453 K for 24 h before it was allowed to cool to room temperature. The resulting white sediment was centrifuged, washed with distilled water and dried at 353 K overnight. Finally, the solid was annealed in a tube furnace at 573 K for 5 h in flowing oxygen gas to obtain calcined ceria nanocubes.
Characterization. Powder X-Ray Diffraction (XRD) characterization was performed with a Philips X'Pro X-ray diffractometer with Cu Kα irradiation (λ = 1.54184 Å) operating at 40 kV and 40 mA. High-Resolution Transmission Electron Microscope (HRTEM) images were recorded on a JEOL JEM-2010 instrument at an acceleration voltage of 200 kV. X-ray Photoelectron Spectra (XPS) were measured on a Thermo ESCALAB 250 X with Al Kα (hν = 1486.6 eV) as the excitation source. The binding energies in XPS spectra were referenced to C 1 s = 284.8 eV.
Brunauer-Emmett-Teller (BET) specific surface area information was obtained from nitrogen adsorption at 77 K on a Micromeritics ASAP 2020 system. Raman spectra were acquired with a Bruker Multi RAM FT-Raman spectrometer using 514 nm light from a He-Ne laser source. The content of Na ions was analyzed by an Optima 5300DV inductively coupled plasma mass spectrometer (ICP-MS) while the N content was determined with a Heraeus CHN-0-Rapid elemental analyzer. 17 17 O labeled ceria nanocubes were mixed with radical solution (16 mM TEKPol 44 in dried tetrachloroethane, TCE) in an Ar-filled glove box. 17 O chemical shifts of the DNP NMR spectra were referenced to bulk ceria at 875 ppm at 100 K.
Details of DFT calculations. All spin-polarized DFT calculations were carried out using the Vienna Ab initio Simulation Package (VASP) 48 . The Perdew-Burke-Ernzerhof (PBE) functional 49 with the Hubbard U correction (DFT + U) 50 were used for all calculations. The effective U value of 5.0 eV was only applied to the localized Ce 4f orbitals 51,52 ; our previous study shows that the calculated chemical shifts from PBE + U (5.0 eV) are in quantitative agreement with the experimental values 28 . The projector augmented wave method 53 was used to describe the interaction between core and valence electrons. A plane-wave kinetic energy cutoff of 500 eV was used for all calculations. For geometry optimization, all of the atoms were allowed to relax until the Hellman-Feynman forces were lower than 0.02 eV Å −1 . For electronic minimization, we used an energy convergence criterion of 10 −5 eV for optimizing geometries and a higher criterion of 10 −8 eV for chemical shift and electric field gradients (EFGs) calculations 28 . The optimized lattice parameter of ceria using PBE + U (5.0 eV) is 5.448 Å, which is in reasonable agreement with the experimental value (5.411 Å) 54 .
We used a 2 × 2 surface cell to model the ceria (100) surface. The ceria (100) surface slab model with 12 oxygen layers was found to be sufficiently thick, i.e., the middle layers of this model mimic the bulk environment in terms of chemical shift (Supplementary Figs. 9,12,15,18,22,30,33,36 and 38). All the slabs contain a large vacuum gap (>10 Å) to remove the slab-slab interactions. The k-point mesh was sampled by using a 2 × 2 × 1 Monkhorst-Pack grid.
We used the same method as our previous work 28 to calculate chemical shifts, quadrupole coupling constants (C Q ) and asymmetry parameters (η). For the electric EFG calculations to obtain C Q and η of oxygen species, we used the experimental quadrupole moment (Q) of −0.02558 barns 55 for 17 O. For calculating the isotropic chemical shift (δ iso ), we used the following equation: where δ cal is the unaligned DFT chemical shift, δ ref is the reference chemical shift. The averaged value of the unaligned DFT chemical shifts of oxygen species in the middle layers (layers 4-9) of every prototype slab models is 835 ppm. By aligning 835 ppm to the corresponding experimental value of 877 ppm, we obtained the δ ref of 42 ppm. The average adsorption energies of each water molecule (Ε ads ) on the (100) surface with the O-t or CeO 4 -t model were calculated as the following: where A is the surface area of the slab, n is the number of adsorbed water molecules, m is the number of CeO 2 bulk (i.e., Ce 4 O 8 ) units in the slab model, μ is the chemical potential, and G is the Gibbs free energy. We assumed that the surfaces are in thermodynamic equilibrium with gas phase H 2 O. So, μ[H 2 O] (p,T) can be calculated as follows: where p 0 is the standard state pressure (0.1 MPa); enthalpy (H) and entropy(S) terms were taken from the website of NIST 58 . As the DFT total energies of the solid components can be regarded as good approximations of corresponding Gibbs free energies 57 , we then obtained: ð5Þ Note that the vibration contributions and the pV (V denotes volume) term of solid components were not considered.

Data availability
The data that support the findings of this study are available from the corresponding author upon reasonable request.