Size Dependence of Lattice Parameter and Electronic Structure in CeO 2 Nanoparticles

Intrinsic properties of a compound (e.g., electronic structure, crystallographic structure, optical and magnetic properties) define notably its chemical and physical behavior. In the case of nanomaterials, these fundamental properties depend on the occurrence of quantum mechanical size effects and on the considerable increase of the surface to bulk ratio. Here, we explore the size dependence of both crystal and electronic properties of CeO2 nanoparticles (NPs) with different sizes by state-of-the art spectroscopic techniques. X-ray diffraction, X-ray photoelectron spectroscopy, and high-energy resolution fluorescence-detection hard X-ray absorption near-edge structure (HERFD-XANES) spectroscopy demonstrate that the as-synthesized NPs crystallize in the fluorite structure and they are predominantly composed of CeIV ions. The strong dependence of the lattice parameter with the NPs size was attributed to the presence of adsorbed species at the NPs surface thanks to Fourier transform infrared spectroscopy and thermogravimetric analysis measurements. In addition, the size dependence of the t2g states in the Ce LIII XANES spectra was experimentally observed by HERFD-XANES and confirmed by theoretical calculations.


INTRODUCTION
CeO2-based nanoparticles (NPs) offer unique redox properties that open promising possibilities for applications in catalysis, 1,2 energy storage, 3,4 biomedicine 5 , and nuclear activities. 6 Quantum mechanical size effects, combined with a considerable increase of the surface to bulk ratio, are responsible for the unique properties of nanometer-sized particles, including electronic and geometric structure, and optical and magnetic properties. 7,8 A thorough understanding of the dependence of these properties on particle size is of great importance not only for the design of next generation materials.
In this context, our work focuses on studying the size-dependence of both crystallographic and electronic structures of CeO2 NPs as these two fundamental properties are of technological importance and theoretical interest and broad prospects. 2 The change of unit cell dimensions with decreasing particle size has been previously reported, but remains a subject of discussion. Different hypotheses have been put forward to explain this phenomenon: surface stress induced by the presence of sorbed species and partial reduction of Ce IV to Ce III . [9][10][11] Furthermore, the electronic structure and its size-dependence, is of fundamental interest as energetic and catalytic properties notably lie on it. 2 In the present work, the crystal structure of as-synthesized CeO2 NPs was characterized by using x-ray diffraction (XRD) and transmission electron microscopy (TEM) giving access to their size and lattice parameter. Fourier transform infrared spectroscopy (FTIR) and thermogravimetric analysis (TGA) was performed to determine species potentially absorbed at the surface.
Furthermore, we probed the electronic structure of CeO2 NPs using high-energy resolution fluorescence-detection hard X-ray absorption near-edge structure (HERFD-XANES) spectroscopy at the Ce LIII edge. Thanks to the use of an X-ray emission spectrometer, such inner-shell spectroscopy provides an element-selective probe of the electronic state and allows observing spectral features with significantly enhanced energy resolution compared to usual data limited by Ce LIII edge core hole life-time broadening (Supporting information Figure 1) 12,13 .

Nanoparticles obtained by hydrothermal treatment
Ceria nanoparticles samples were synthesized by alkaline precipitation of cerium ammonium sulfate precursor followed by hydrothermal condensation in a pressurized autoclave at different temperatures 14,15 . In detail, a 1M Ce(IV) solution was prepared by dissolving cerium(IV) ammonium sulfate dehydrate (Alfa Aesar) in deionized water; cerium(IV) hydroxide was directly precipitated by adding an excess of ammonium hydroxide (Sigma Aldrich, 25% in water) under constant stirring for 3 hours. A yellow cerium(IV) hydroxide precipitate was recovered by centrifugation, repeatedly washed with deionized water and hydrothermally treated in a stainless steel reactor vessel with Teflon insert (total free volume 12 ml). Typically, 200 mg of cerium(IV) hydroxide were suspended in 10 ml deionized water and heated for 3 h under autogenous pressure at different temperatures. After cooling, the solid residue was recovered, washed with deionized water, dehydrated with ethanol and acetone and dried overnight in a chemical fume hood. The resulting dry powders were analyzed by XRD with a Rigaku Miniflex 600 diffractometer. The crystallite size of the nanopowders was estimated from the XRD pattern using the Scherrer equation and averaging the results of 8 selected peaks in the 2θ range between 25 and 80°.

Nanoparticles obtained by thermal treatment in dry conditions.
In order to obtain samples with larger crystallites size, the dry powder samples obtained by hydrothermal treatment were calcined for 1 h at temperatures ranging from 350 to 950 °C in an open furnace. The so obtained nanoparticle samples were analyzed by XRD and labelled on the basis of the respective estimated crystallite size. The nomenclature and the synthesis route of the different nanoparticle samples are reported in detail in Table 1.
Considering that the sample Ce_2 experienced damages due to the exposure to the beam during the HERFD-XANES measurement, this compound has been discarded from this discussion on the oxidation state determination and on the electronic structure. Further details on this phenomenon are provided in the Supporting information Figure 2.

Transmission Electron Microscopy
Transmission electron microscopy (TEM) studies were performed using an aberration (image) corrected FEI™ Titan 80-300 operated at 300 kV providing a nominal information limit of 0.8 Å in TEM mode and a resolution of 1.4 Å in STEM mode. TEM micrographs have been recorded using a Gatan US1000 slowscan CCD camera, while STEM images have been recorded using a Fischione high-angle annular dark-field (HAADF) detector with a camera length of 195 mm. The samples for analysis have been prepared by dropping coating with a suspension of the nanoparticles in ultrapure water on carbon coated copper grids.

Fourier transform infrared spectroscopy
Dehydrated ceria NPs were analysed by FTIR in attenuated total reflectance mode with an Alpha Platinum Bruker spectrometer equipped with ZnSe crystal. FTIR spectra were were obtained at room temperature in the wavenumber range from 600 to 4000 cm -1 with a resolution of 4 cm −1 .

Thermogravimetric analysis
The thermal behaviour of ceria NPs was investigated using a Netzsch STA 449C DTA/TG using an alumina crucible and in air atmosphere. The temperature was controlled by a Pt-PtRh (10 %) thermocouple. Measurements were carried out at a constant heating and cooling rates of 10 o C/min between 40 and 700°C.

Raman
Raman measurements of nanocrystalline samples were performed at room temperature with a Horiba Jobin-Yvon T64000 spectrometer using a Kr+ laser with excitation wavelength of 647 nm. A 50x objective was used to irradiate powder samples and collect the back-scattered light.
The analyses were performed with an incident laser power in the 4-10 mW; no effect of laser power was observed for the resulting spectra in this range.

X-ray Photoelectron Spectroscopy
XPS measurements were performed with a Physical Electronics Quantera Scanning X-ray Microprobe. This system uses a focused monochromatic Al Kα X-ray (1486.7 eV) source for excitation and a spherical section analyzer. The instrument has a 32 element multichannel detection system. The X-ray beam is incident normal to the sample and the photoelectron detector is at 45° off-normal. High energy resolution spectra were collected using a pass-energy of 69.0 eV with a step size of 0.125 eV. For the Ag 3d5/2 line, these conditions produced a FWHM of 0.92 eV ± 0.05 eV. The binding energy (BE) scale is calibrated using the Cu 2p3/2 feature at 932.62 ± 0.05 eV and Au 4f7/2 at 83.96 ± 0.05 eV. The sample experienced variable degrees of charging. Low energy electrons at ~1 eV, 20μA and low energy Ar + ions were used to minimize this charging.
The binding energy scale was charge corrected referencing the Ce 3d3/2 4f 0 (u''') line at 916.7 eV. 16,17 The quantification and peak fitting was performed using PHI MultiPak version 9.6.1.7 software, where the experimental results were fitted to 10 peaks, defined as v 0 , v, v', v'', v''', u 0 , u, u', u'', and u'''. 16 In this scheme, v, v'', v''', u, u'', and u''' were associated with Ce IV , while v 0 , v', u 0 , and u' were associated with Ce III . The relative areas of the fitted peaks were measured in order to determine the relative concentration in the surface.

High-Energy Resolution Fluorescence-Detected X-ray Absorption Near Edge Structure
HERDF-XANES measurements were conducted at the CAT-ACT beamline (ACT station) of the KIT synchrotron light source (Karlsruhe Institute of Technology, Karlsruhe, Germany). 18,19 The incident energy was selected using the (111) reflection of a double Si crystal monochromator.
The X-ray beam was focused to 500 x 500 µm onto the sample. XANES spectra were measured in high-energy-resolution fluorescence detected (HERFD) mode using an X-ray emission spectrometer. 12,19 The sample, analyzer crystal, and a single diode VITUS Silicon Drift Detector (KETEK, Germany were arranged in a vertical Rowland geometry. The Ce HERFD-XAS spectra at the LIII edge were obtained by recording the maximum intensity of the Ce Lα1 emission line (4839 eV) as a function of the incident energy. The emission energy was selected using the 〈331〉 reflection of four spherically bent Ge crystal analyser (with a bending radius R = 1 m) aligned at a 80.7° Bragg angle. The experimental energy resolution was 1.15 eV obtained by measuring the full width at half maximum of the elastically scattered incident beam with an energy of 4.8404 keV. During the measurements a slit with the dimensions 500 x 500 µm was used in front of the sample, cutting of tails in the pprofile of the incident beam. This potentially led to a slight improvement of the experimental resolution, i.e. 1 eV (it is an estimation). The experimental resolution measured at ID26, ESRF using the same analyzer crystals was 0.9 eV 20 . The sample, crystals and detector were confined in a box filled with He and a constant He flow was maintained in order to minimize the loss of intensity due to absorption and scattering of the X-rays. The data were not corrected for self-absorption effects. The sample exposure to the beam was minimized to account for possible beam damage and checked by first collecting short XANES scans (~10 seconds) to look for irradiation effect.

Theoretical calculations
The spectra of bulk CeO2 and CeO2 in 2nm were performed in a manner described in 21-24 using the FEFF 9.6. code. Similar to the work of Li et al. and Plakhova et al., we show here only part of the absorption spectra, which corresponds to the 2p-5d transitions, and omit multi-electron excitations from the experimental data, which appear at higher incident energy.

Ce valence in the as-synthesized CeO2 nanoparticles.
Our X-ray diffraction (XRD) and transmission electron microscopy (TEM) data (Supporting Information Figure 3 and Figure 4) show that the as-synthesized CeO2 NPs crystallize in the Fm-3m fluorite structure (space group 225). Depending on the experimental conditions (and particularly the annealing temperature), the average crystallite diameters vary from 2.0 ± 0.1 to 91 ± 12 nm. These XRD-refined parameters are gathered in the Table 1 and will be more thoroughly discussed in a following section.

<Table 1 about here>
The oxidation state and electronic structure of Ce was assessed using Ce LIII edge HERFD-XANES and XPS, which corresponding spectra are respectively given in Figure 1 and in Figure 2.

<Figure 1 about here>
The HEFRD-XANES spectra of all the investigated CeO2 NPs exhibit a single pre-edge peak aligned with that of the bulk-CeO2 reference spectrum. This pre-edge peak (noted A in Figure 1) originates from the 2p transition to a mixed 5d-4f valence state 22,25 and is characteristic of the Ce valence of the probed sample. Indeed, a single peak is observed in the pre-edge region of a pure Ce IV compound, since the photo absorption process excite an electron to the 4f level, formally empty in the initial state. However, in the case of a Ce III ion, the interaction between the 4f electron in the initial state and the second electron excited by the photon leads to a splitting of the pre-edge feature into two groups of transition, whose energy position is related to the electron-electron interactions in the 4f level. 20 On the other hand, the Ce 3d XPS spectrum of Ce III PO4 reference 28 has two distinct sets of doublets: v 0 at 880.6 eV and u 0 at 897.9 eV as a result of Ce 3d5/2 4f 2 ejection, and v' at 884.5 eV and u' at 900.8 eV as a result of the Ce 3d5/2 4f 1 final state, neither of which register a meaningful peak area in this data. Furthermore, from the peak fitting performed (Supporting Information Figure 5), no characteristic band feature of Ce III was found for samples across all crystallite sizes, corroborating the XANES findings that only tetravalent cerium is present.

Size dependence of the lattice parameter
The unit cell parameter variation as a function of the NPs' size has been reported for several oxide cation. The second model, which is most commonly admitted, attributes the variation to the surface stress resulting from the difference of coordination between atoms on the surface and in the bulk 9,10 . This effect becomes more pronounced as the particle size reduces, i.e. as the contribution of the surface atoms to the structural characteristics increases. From our HERFD-XANES and XPS findings, the presence of Ce III and hence of the oxygen vacancy, have been discarded, which means that the observed lattice expansion might then be only due to surface stress. To corroborate this assumption, the formation of species present at the NPs surface has been studied by FTIR and TGA measurements. Each FTIR spectrum (  reported for CeO2 and other nanocrystals. [41][42][43] Several factors can contribute to the changes in the Raman peak position and linewidth of the T2g peak with NP size. These include phonon confinement, strain, broadening associated with the size distribution, defects and surface effect. [41][42][43][44][45][46] In most studies, the red shift is majorly attributed to the lattice expansion and associated strain that occurs when oxygen vacancies are created which leads to the reduction of Ce IV (ionic radius 0.970 Å 47 ) in Ce III (ionic radius 1.143 Å 47 ). However, the creation of O vacancies and the reduction of Ce IV in Ce III induce a local symmetry distortion and new Raman bands located around 550 and 595 cm -1 are observed 48 . The absence of both new Raman bands and detection of Ce III from our HERFD-XANES measurements allows us to discard this hypothesis for the T2g red-shift. One possible explanation could be that the stress generated by the presence of the adsorbed species at the NPs surface that would enhance the downward shift and broadening of the T2g.

<Figure 5 about here>
Size dependence of the electronic structure Bulk CeO2 exhibits three characteristic features A, B and C with a doublet structure for B and C leading to a total of 5 bands indicated by A, B1, B2, C1 and C2 in Figure 1. The pre-edge peak (noted A) originates from the dipole-forbidden 2p transition to a mixed 5d-4f valence state while the B and C arises from transitions from 2p3/2 → 5d5/2 orbitals. The splitting of B1 and C1 into a doublet structure is due to the crystal field splitting of 5d orbitals. 49 These edge features have been assigned to screened (B1 and B2) and unscreened (C1 and C2) excited states. 22,50 . B1 and B2 features described the 2p → 5d transition with 4f 1 L configuration while C1 and C2 are representatives of the 2p → 5d transition with 4f 0 L configuration, where L corresponds to the orbital angular momentum. 23,51 In the CeO2 fluorite structure, each Ce atom is surrounded by 8 oxygen atoms located at the corners of a cube creating a cubic crystal field belonging to the Oh point symmetry group. Due to this cubic crystal field, the Ce IV 5d 0 configuration is split into the eg and t2g bands corresponding to B1, C2 and B2, C1 respectively. 23,52 The Ce IV valence corresponds to a 5d 0 configuration implying that in the HERFD-XANES process t2g is firstly filled with electrons while the eg is empty as the transferred energy is not sufficient. Here the experimental crystal-field energy splitting of Ce 5d in bulk CeO2 is ca. 4 eV. This value of energy gap between eg and t2g is in good agreement with previously published values. [53][54][55] Now, looking at the experimental HERFD-XANES spectra of CeO2 NPs, one can observe that all the A, B1, B2, C1 and C2 feature are presented at the same energy position as in bulk CeO2. A value of ca. 4 eV is found for the experimental crystal-field energy splitting of Ce 5d in bulk CeO2 NPs, indicating that this energy gap is not affected by the particle size. However, one can note that the eg feature intensity remains constant for both NPs and bulk CeO2 while the t2g intensity is proportional to the particle size. This experimental observation is corroborated by our theoretical calculations showing that the simulated HERFD-XANES spectra of 2 nm CeO2 exhibit a t2g intensity smaller than that of bulk CeO2. The stability of the eg feature is also well reproduced.
One possible explanation lies in the presence of adsorbed species at the NPs surfaces. In the case of bulk CeO2, the corresponding HERFD-XANES spectra is a direct measurement of the electronic structure of bulk Ce atoms. However, in the case of our NPs, the measured spectra correspond to the average electronic structure of both Ce atoms in the bulk and at the surface. This implies that the observed t2g variation originates from the electronic structure of surface Ce atoms. We showed in the previous section that Ce remains in the IV oxidation state and that the fraction of adsorbed species is inversely proportional to the particle size. In other word, their content is increasing with the surface Ce atoms to bulk Ce atoms ratio. Considering that the eg level is empty in Ce 5d 0 , the bonding between the surface Ce atoms and the adsorbed species requires the delocalization of the t2g electrons, hence explaining the observed decrease of the t2g intensity on the Ce LIII HERFD-XANES spectra. One can also assume that this bonding affects the crystal field by creating new d levels. This larger degeneracy of the t2g level is clearly observable for the sample Ce_5.6 which exhibits a broader t2g feature (Figure 1). <Figure 6 about here>

CONCLUSION
In this work, we have synthesized fluorite Ce IV O2 NPs and studied the effect of the NP size on both local and electronic structure. By analogy with other metal oxides, we have shown that the lattice parameter expands with decreasing particle size. The presence of mainly Ce IV , demonstrated by XPS and HERFD-XANES, indicates that the unit cell size-dependence is not linked to the Ce valence but to surface stress. Indeed, our TGA and FTIR data confirms the presence of surface hydroxyl and carbonate groups that have a tensile effect on the crystalline lattice. Additionally, the size-dependence of the electronic structure, and especially of the t2g feature in the Ce LIII XANES spectrum, have been experimentally evidenced and confirmed with theoretical calculations.     Theoretical calculations predicts a lower t2g intensity for the 2 nm CeO2.