Malvina Massonnet

Laurent Claparede

Julien Martinez

Philippe Martin

Myrtille O J Y Hunault

Damien Prieur

Adel Mesbah

Nicolas Dacheux

Dr Nicolas Clavier
email: nicolas.clavier@icsm.fr

Influence of sintering conditions on the structure and the redox speciation of homogenous (U,Ce)O 2+δ ceramics : a synchrotron study

Keywords: uranium oxide, XAS, structure, nuclear fuel, O/M ratio

Although uranium-cerium dioxides are frequently used as surrogate material for (U,Pu)O 2-δ nuclear fuels, there is currently no reliable data regarding the oxygen stoichiometry and the redox speciation of the cations in such samples. In order to fill this gap, this manuscript details a synchrotron study of highly homogeneous (U,Ce)O 2±δ sintered samples prepared by wet-chemistry route. HERFD-XANES spectroscopy led to determine accurately the O/M ratios (with M = U + Ce). Under reducing atmosphere (pO 2  610 -29 atm at 650°C), the oxides were found close to O/M = 2.00 while the O/M ratio varied with the sintering conditions under argon (pO 2  310 -6 atm at 650°C). They globally appear to be hyperstoichiometric (i.e. O/M > 2.00), the departure from the dioxide stoichiometry decreasing with both the cerium content in the sample, and the sintering temperature. Nevertheless, such deviation from the ideal O/M = 2.00 ratio was found to generate only moderate structural disorder from EXAFS data at the U-L 3 edge, as all the samples retained the fluorite-type structure of the UO 2 and CeO 2 parent compounds. The determination of accurate lattice parameters thanks to S-PXRD measurements led to complement the data reported in the literature by various authors. These data were consistent with an empirical relation linking the unit cell parameter, the chemical composition and the O/M stoichiometry, showing that this latter can be evaluated simply within a ± 0.02 uncertainty.

Introduction

Uranium-plutonium mixed dioxides (U,Pu)O 2-δ are currently used as fuels in several pressurized-water reactors worldwide, and constitute one of the reference fuels for some of the concepts developed for the fourth generation of nuclear reactors, such as sodium-cooled fast reactor (SFR) [START_REF] Kelly | Generation IV International Forum: A decade of progress through international cooperation[END_REF] . While some countries (e.g. France) already chosed to reprocess UOx spent fuel in order to minimize the radiotoxicity of ultimate wastes and to save resources [START_REF] Poinssot | Actinide recycling within closed fuel cycles[END_REF] , the spent (U,Pu)O 2-δ assemblies are currently stored, pending for a solution of storage or reprocessing. This latter option is now envisaged in France, with the aim to refabricate new fuel elements, and then to stabilize the plutonium stockpile [START_REF] Courtin | Pu multi-recycling scenarios towards a PWR fleet for a stabilization of spent fuel inventories in France[END_REF] . Such a process first implies to master the quantitative dissolution of the (U,Pu)O 2-δ spent fuel, which is a mandatory step before any operation of partitioning. Nevertheless, if the dissolution of UO x has been extensively documented [START_REF] Shabbir | Kinetics of Dissolution of Uranium Dioxide in Nitric Acid .I[END_REF][START_REF] Gonzalez | Dissolution of Uranium-Dioxide Pellets in Nitric-Acid[END_REF][START_REF] Bruno | Uranium(Iv) Dioxide and Simfuel as Chemical Analogues of Nuclear Spent Fuel Matrix Dissolution -a Comparison of Dissolution Results in a Standard NaCl/NaHCO 3 Solution[END_REF][START_REF] Marc | Dissolution of uranium dioxide in nitric acid media: what do we know?[END_REF][START_REF] Ikeda | Kinetic-Study on Dissolution of UO 2 Powders in Nitric-Acid[END_REF][START_REF] King | Modelling the oxidative dissolution of UO 2[END_REF][START_REF] Pierce | Dissolution kinetics of UO 2 (cr)[END_REF][START_REF] Bertolotto | Effect of surface orientation on dissolution rate and surface dynamics of UO 2 single crystals in nitric acid[END_REF] , that of (U,Pu)O 2-δ mixed oxides remains less understood, partly due to the high specific activity of plutonium that restrains the possibilities of the study [START_REF] Desigan | Dissolution behavior of fast reactor MOX nuclear fuel pellets in nitric acid medium[END_REF][START_REF] Desigan | Dissolution behaviour of simulated MOX nuclear fuel pellets in nitric acid medium[END_REF][START_REF] Serrano | Influence of low temperature air oxidation on the dissolution behaviour of UO 2 and MOX spent fuel[END_REF] . Especially, only few works discussed the impact of the microstructural parameters on the dissolution rate in acidic media [START_REF] Ziouane | Impact of the plutonium content on dissolution kinetics of (U 1-x Pu x )O 2± powders[END_REF] . Furthermore, the links between dissolution rate and the cation redox speciation in the solid are generally not studied. These latter are of particular importance owing to the complex redox properties of actinide cations. Indeed, while uranium and plutonium are mainly tetravalent in the pristine fuel, they can endure either oxidation or reduction during irradiation, respectively. Also, the presence of aliovalent cations such as soluble fission products (Nd, La, …) into the UO 2 matrix is expected to impact the uranium redox speciation. As a result, the fuel matrix mainly consists of a mixture of U(IV), U(V) and even U(VI), on the one hand, and Pu(IV) and Pu(III) on the other, which gives rise to a large variety of O/M ratios (with M = U+Pu) [START_REF] Degueldre | Redox state of plutonium in irradiated mixed oxide fuels[END_REF][START_REF] Vauchy | Room-temperature oxidation of hypostoichiometric uranium plutonium mixed oxides U 1-y Pu y O 2-x -A depth-selective approach[END_REF] .

As tetravalent plutonium, cerium (IV) exhibits a complete solubility into the UO 2 fluorite-type structure, and (U,Ce)O 2±δ oxides are frequently considered as model compounds for (U,Pu)O 2±δ fuels [START_REF] Kim | Applicability of CeO 2 as a surrogate for PuO 2 in a MOX fuel development[END_REF] . Even if they do not constitute perfect surrogates, for example due to differences in the U-Ce-O and U-Pu-O ternary phase diagrams, cerium still possesses similar stable oxidation states than plutonium in oxide compounds, as well as close ionic radius in the eight-fold coordination (0.97 Å for Ce(IV) vs. 0.96 Å for Pu(IV)) [START_REF] Shannon | Revised Effective Ionic-Radii and Systematic Studies of Interatomic Distances in Halides and Chalcogenides[END_REF] . Hence, some efforts have been made both to prepare uranium-cerium dioxides samples with different morphologies (including nanopowders, thin films or dense pellets) [START_REF] Krishnan | Synthesis, characterization and thermal expansion measurements on uranium-cerium mixed oxides[END_REF][START_REF] Martinez | An original precipitation route toward the preparation and the sintering of highly reactive uranium cerium dioxide powders[END_REF][START_REF] Eloirdi | X-ray photoelectron spectroscopy study of the reduction and oxidation of uranium and cerium single oxide compared to (U-Ce) mixed oxide films[END_REF][START_REF] Kulyako | Preparation of Solid Solutions of Uranium and Cerium Oxides from Their Nitric Acid Solutions Using Microwave Radiation[END_REF] and in some cases to investigate their behavior during dissolution tests [START_REF] Tocino | Dissolution of uranium mixed oxides: The role of oxygen vacancies vs the redox reactions[END_REF] . In such studies, several biases can be pointed out, and preclude a reliable determination of the sample oxygen stoichiometry, expressed through the O/M ratio with M = U + Ce.

Most of the authors assumed that uranium and cerium remained tetravalent all along the fabrication process of the samples, without bringing any experimental evidence. Also, the differences in both the fabrication method, the samples morphology, and the techniques used to determine the O/M ratio, can lead to a limited representativity of the results. Indeed, powder metallurgy processes were frequently used to manufacture the samples, which is now well-known to induce heterogeneities in the cation distribution that can localy induce an incomplete formation of the (U,Ce)O 2±δ solid solution (i.e. out-of-equilibrium systems) [START_REF] Herrero | Charge compensation mechanisms in Nd-doped UO 2 samples for stoichiometric and hypo-stoichiometric conditions: Lack of miscibility gap[END_REF] .

Similarly, the investigation of thin films or nanosized powders, as well as the use of surface techniques such as X-ray Photoelectron Spectroscopy (XPS) can increase the sensitivity of the samples towards surface oxidation [START_REF] Eloirdi | X-ray photoelectron spectroscopy study of the reduction and oxidation of uranium and cerium single oxide compared to (U-Ce) mixed oxide films[END_REF][START_REF] Prieur | Charge Distribution in U 1-x Ce x O 2+y Nanoparticles[END_REF] .

In the prospect of using uranium-cerium dioxide as a surrogate material, its density has to be as close as possible to those encountered in the fuel, i.e. about 95% of the theroretical density.

Such value is generally achieved through a sintering process based on a thermal treatment at high temperature (around 1700°C) in a controled reducing atmosphere. However, there is currently no reliable data regarding the oxygen stoichiometry and the redox speciation of the cations in (U,Ce)O 2±δ dense samples, that can be used to link the sintering process parameters (including temperature, duration and oxygen partiel pressure) with the final microstructural and structural properties of the ceramics. In order to fill this gap, this manuscript describes a synchrotron study of highly homogeneous (U,Ce)O 2±δ samples. These latter were obtained from nanometric powders prepared by wet chemistry method, already presenting a homogenous distribution of the cations at the sub-micronic scale and a very high specific surface area. These characteristics ensured the fast diffusion of cations in the solid during heat treatements, then the rapid formation of solid solutions at the equilibrium state. The structural long and short range orders of the samples were then explored by coupling Synchrotron Powder X-Ray Diffraction (S-PXRD) and Extended X-ray Absorption Fine Structure (EXAFS) spectroscopy. The redox speciation of the cations was determined by HERFD-XANES (High Energy Resolution Fluorescence Detected -X-ray Absorption Near Edge Spectroscopy).

Experimental

Preparation of the powdered samples and sintering. The synthesis of the (U,Ce)O 2±δ starting powders was adapted from the protocol initially reported by Martinez et al. [START_REF] Martinez | An original precipitation route toward the preparation and the sintering of highly reactive uranium cerium dioxide powders[END_REF] , and based on the precipitation and rapid ageing of mixed hydroxides. All the usual chemicals were supplied by Merck and were of analytical grade, while uranium was kindly provided by CETAMA under the form of metal chips. In a first step, uranium metal pieces were dissolved in concentrated hydrochloric acid (6M) to obtain a 0.5M U(IV) solution following the protocol already described in our previous publications [START_REF] Trillaud | Synthesis of size-controlled UO 2 microspheres from the hydrothermal conversion U(IV) aspartate[END_REF] . A second solution containing Ce(IV) was obtained from the dissolution of cerium sulfate salt in HCl. These two solutions were mixed in the desired molar ratio (i.e. x Ce = e e = 0.15, 0.25 and 0.50), then poured in a large excess of 2M NH 3 (about 400%) under magnetic stirring, resulting in the immediate formation of a (U,Ce)(OH) 4 precipitate. This latter was let under stirring for 30 minutes, in order to favour the grain growth and ageing into the (U,Ce)O 2 .nH 2 O form [START_REF] Rai | Uranium(IV) Hydrolysis Constants and Solubility Product of UO 2 .xH 2 O(am)[END_REF] . The precipitate was then separated from the supernatant by centrifugation at 14000 rpm during 10 minutes, and washed twice with deionized water and once with ethanol. It was finally dried at room temperature in an inert glovebox filled with argon (O 2 content below 0.1 ppm) then calcined at 700°C for 4 hours under Ar/H 2 4% in order to eliminate volatile compounds remaining from the synthesis process.

The accurate chemical composition of the samples was further determined through the complete dissolution of a fraction of powder in aqua regia, followed by the measurements of U and Ce concentrations in the resulting solutions by Inductively-Coupled Plasma Atomic Emission Spectroscopy (ICP-AES, Spectro Arcos). For each composition considered, an average of U and Ce measurements was made at different wavelengths (i.e. λ = 448.691 nm, 418.660 nm, 413.765 nm and 413.380 nm for cerium and λ = 385.958 nm, 409.014 nm, 367.007 nm and 279.394 nm for uranium), and led to x Ce = e e molar ratios equal to 0.14; 0.26 and 0.49, respectively. These values confirmed the quantitative precipitation of both cations during the synthesis, as expected from previous results [START_REF] Martinez | An original precipitation route toward the preparation and the sintering of highly reactive uranium cerium dioxide powders[END_REF] . They will be used therafter to label the samples studied.

Before sintering, the powders were sieved (200 µm mesh) and shaped as 5 mm diameter pellets by uniaxial pressing (500 MPa) at room temperature. The obtained green pellets (showing a mass of about 200 mg) were then sintered in various operating conditions in terms of temperature, heat treatment duration and atmosphere. For this latter, two options were considered, to establish either reducing (Ar/H 2 4%) or slightly oxidant (Ar) conditions in the furnace. In both cases, the corresponding oxygen partial pressure was measured by a Setnag Jok'air analyzer (internal furnace set at 650°C), leading to values close to pO 2  610 -29 atm and pO 2  310 -6 atm, respectively. The different samples prepared are summarized in Table 1. In all the cases, heating rates of 2°C.min -1 were considered, with a cooling rate of 6°C.min - 1 . It is also to note that, due to equipment constraints, it was not possible to maintain a temperature plateau at T = 1600°C, this temperature being only briefly reached by the furnace. For simplification purposes, the holding time is then indicated to be equal to zero in the following. In these conditions, the samples might not have reached thermal equilibrium, even if the slow heating rate guaranteed a sample temperature close to 1600°C. Nevertheless, datapoints obtained at this temperature were analyzed with caution, owing to the potential differences in sintering and redox kinetics compared to the others. The diffraction patterns obtained from both data series were refined by the Rietveld method to extract unit cell parameters and average crystallite sizes, using the Cox-Hastings pseudo-Voigt profile function [START_REF] Thompson | Rietveld Refinement of Debye-Scherrer Synchrotron X-Ray Data from Al 2 O 3[END_REF] implemented in the Fullprof_suite program [START_REF] Frontera | FullProf as a new tool for flipping ratio analysis[END_REF] .

HERFD-XANES. High-energy resolution fluorescence detected XANES (HERFD-XANES)

data were measured at the MARS beamline of the SOLEIL synchrotron (Saint-Aubin, France) 31, 32 . The storage ring was operating in top-up mode at an electron current of 500 mA, 2.5

GeV. The beam size on sample was 150 μm × 150 μm FWHM (H×V). Spectra were measured at the U M 4 -edge (3728 eV) and the Ce L 3 -edge (5723 eV) using the double-crystal monochromator (DCM) equiped with a pair of Si(111) crystals. Higher harmonics rejection and vertical focusing was achieved using the Si strip of each mirror inserted before and after the DCM with a 4 mrad incidence angle. The incident energy was calibrated using the absorption K-edge of potassium of a KBr pellet (3608.4 eV). The incident X-ray flux on the sample position was 1.9×10 [START_REF] King | Modelling the oxidative dissolution of UO 2[END_REF] ph/s at 3.5 keV. HERFD-XANES was measured using the crystal-analyzer emission spectrometer in the Rowland geometry and a KETEK single element silicon solid state detector. The M β emission line of U (3339 eV) was analyzed using the 220 reflection of a Si(220) bent diced crystal analyzer with a curvature radius of 1 meter.

The energy resolution of the emission spectrometer was 0.55 eV. The L α emission line of Ce (4839.2 eV) was analysed using a Ge(331) bent cristal analyser. The energy resolution of the emission spectrometer was 0.89 eV. The samples were oriented at 45° with respect to the incident beam. A He-filled balloon was used to reduce the scattering of the incident and emitted X-rays by the air between the sample and the crystal analyzer and the detector.

Samples were prepared as pellets for each compound diluted in boron nitride. All spectra collected were normalized at the maximum of absorption using the Athena Software [START_REF] Ravel | HEPHAESTUS: data analysis for Xray absorption spectroscopy using IFEFFIT[END_REF] , then were fitted as a linear combination of different references to quantify the contribution of U(IV), U(V) and U(VI), on the one hand, and of Ce(IV) and Ce(III), on the other.

For uranium, a UO 2.00 single crystal was chosen as pure U(IV) standard, while a U 4 O 9

spectrum previously collected at the ESRF-ID26 beamline was used as a mixed standard for U(IV)/U(V) with a 1/1 ratio [START_REF] Kvashnina | Chemical State of Complex Uranium Oxides[END_REF] . Additionally, U 3 O 8 was taken as a mixed standard for U(V)/U(VI) with a 2/1 ratio 34 while UO 2 (NO 3 ) 2 •5H 2 O was selected as pure U(VI) standard.

For cerium, CeO 2 and CePO 4 were chosen as references for Ce(IV) and Ce(III), respectively.

All fits were obtained with a quality factor of Χ 2 < 0.04.

From the linear combination results, it was then possible to determine the different O/M molar ratios as follows :

O/U = mol.%(UO 2 )  2 + mol.%(U 4 O 9 )  2.25 (1.) O/Ce = mol.%(CeO 2 )  2 + mol.%(Ce 2 O 3 )  1.5 (2.) O/(U+Ce) = (1-x Ce )  (O/U) + x Ce  (O/Ce) ( 3.
)

EXAFS. Uranium U-L 3 EXAFS measurements were performed at European Synchrotron Radiation Facility (ESRF, Grenoble) on the HZDR-operated Rossendorf Beamline (BM20) [START_REF] Scheinost | ROBL-II at ESRF: a synchrotron toolbox for actinide research[END_REF] .

EXAFS data were recorded at 15K using an He cryostat. A Si(111) double crystal-monochromator coupled with collimating and focusing Rh-coated mirrors was used for the measurements. U-L 3 XAS data were recorded in the transmission mode using Ar/N 2 filled ionization chambers and in fluorescence mode with an electrically cooled (Cryo-Pulse 5 Plus)

18-element germanium detector (Ultra-LEGe, GUL0055, Mirion Technologies). The energy was calibrated using the Y K edge (17038 eV) of a Y metallic reference foil.

The EXAFS oscillations were fitted using the Artemis software included in the Demeter package [START_REF] Ravel | HEPHAESTUS: data analysis for Xray absorption spectroscopy using IFEFFIT[END_REF] . Fourier transform was carried out on the k3-weighed data between 3.5 and 13.5

Å -1 using the Hanning function. The FT data were then fitted in the [START_REF] Martin | A XAS study of the local environments of cations in (U, Ce)O 2[END_REF] . The value of the amplitude reduction factor ( ) was fixed to 0.92 [START_REF] Epifano | Extreme multi-valence states in mixed actinide oxides[END_REF] .

Other parameters were obtained from the fit, including inner potential shift (E 0 ), bond distances (d), Debye-Waller factors ( 2 ), and coordination numbers. For this latter, exception was made for the third shell, where the ideal number (24) was fixed.

Results and discussion

Characterization of the starting powder

In a first step, the structure and the cationic homogeneity of the starting powders obtained after heating at 700°C under Ar/H 2 atmosphere for 4 hours were investigated. The PXRD patterns reported in Figure 1 confirmed that all the samples presented the expected fluoritetype structure characteristic of U Additionally, SEM and EDS investigations were conducted to point out the morphology of the powders and to study their homogeneity in terms of cationic distribution. The results obtained for x Ce = 0.26 are presented as an example in Figure 2, with similar features being obtained for all the chemical compositions studied. SEM observations confirmed that the powder samples consisted of nanoscale crystallites assembled as micrometric aggregates, in good agreement with PXRD results. The agglomeration of the elementary crystallites most likely resulted from heating at 700°C. Nevertheless, it did not promote a strong grain growth, since the average crystallite size remained typically close to 10 nm. Hence, the reactivity of the powders towards densification was preserved, with specific surface areas typically between 10 and 30 m 2 .g -1 [START_REF] Martinez | An original precipitation route toward the preparation and the sintering of highly reactive uranium cerium dioxide powders[END_REF] .

The statistical distribution of the U and Ce cations within the powder samples was then studied by EDS analyses. From Figure 2, it can be seen that the distribution of the e molar ratio, illustrating the chemical composition of the sample, follows a Gaussian law. Although not strictly identical, the value of the centroid (x Ce = 0.232) matches the expected value and that coming from ICP-AES analysis, the slight differences being assigned to the conditions of acquisition that preclude a fully quantitative analysis. More importantly, the standard deviation around the average x Ce value appeared to be very limited (σ = 0.012). As such, 95%

of the datapoints are located within a range 0.208 < x Ce < 0.256. Comparable results were obtained for the other composition studied, and are supplied as supplementary information (Figure S1). Hence, no U-or Ce-hot-spots were detected, contrarily to the typical microstructures of samples prepared by powder metallurgy processes, i.e. mixture of oxide powders [START_REF] Devi | Plutonium heterogeneity in MOX fuel: A quantitative analysis[END_REF] . This sample series can also be considered to be more homogeneous than some other oxide compounds prepared from the initial precipitation of low-temperature precursors [START_REF] Claparede | Impact of the cationic homogeneity on Th 0.5 U 0.5 O 2 densification and chemical durability[END_REF] , in which the presence of large amounts of cerium in the starting mixture could lead to polyphasic systems [START_REF] Abraham | Actinide oxalates, solid state structures and applications[END_REF] .

From these results, the powder samples prepared during this work appear to be highly homogenous, and are expected to be strongly reactive towards sintering due to their nanometric grain size. As such, they ensure the rapid diffusion of oxygen atoms and cations during the heat treatments performed at high temperature, thus the preparation of sintered samples at the thermodynamic equilibrium.

HERFD-XANES

Representative selection of HERFD-XANES spectra recorded at U-M 4 and Ce-L 3 edges for the various U 1-x Ce x O 2 δ sintered samples studied, as well as spectra of references are compiled in Figure 3. The spectra collected for the other samples are supplied as supporting information (Figure S2). As demonstrated in previous works [START_REF] Ravel | HEPHAESTUS: data analysis for Xray absorption spectroscopy using IFEFFIT[END_REF][START_REF] Manaud | Hydrothermal Conversion of Uranium(IV) Oxalate into Oxides: A Comprehensive Study[END_REF][START_REF] Welcomme | Oxidation as an Early Stage in the Multistep Thermal Decomposition of Uranium(IV) Oxalate into U 3 O 8[END_REF] , HERFD-XANES provides a remarkable resolution in energy that allows the separation of the characteristic peaks of U(IV), U(V) and U(VI), and gives an accurate insight on the redox speciation of uranium. As such, the spectrum of UO 2 only presents one large peak assigned to U(IV) at around 3725 eV, while that of U 4 O 9 exhibits two peaks with comparable intensities corresponding to U(IV) and U(V) contributions, this latter around 3726 eV. Comparatively, the spectrum associated to U 3 O 8 usually shows a large signal located around 3727 eV that accounted for U(V) and U(VI) (not shown here). The spectra recorded from the different U 1-x Ce x O 2 δ sintered samples prepared are typically comprised between those of UO 2 and U 4 O 9 , meaning that they mainly consist of U(IV) with variable amounts of U(V). In order to quantify the proportion of the different oxidation states of uranium within the samples, HERFD-XANES spectra were fitted through a linear combination of reference spectra. In these latter, we assumed that UO 2.00 was completely composed of U(IV), U 4 O 9 was in a ratio U(IV):U(V) = 1:1, and that U(V):U(VI) = 2:1 in U 3 O 8 . From these values and the contribution of each reference spectra, the average oxidation state of uranium was determined and gathered in Table 3 while Figure 4 presents the fit results obtained for the U 0.74 Ce 0.26 O 2 δ sample sintered at T = 1600°C under Ar atmosphere.

For all the samples studied, the quality factor X 2 remained below 0.04.

All the results evidenced the absence of U(VI) traces in our samples, which notably differs from the findings of Prieur et al. [START_REF] Prieur | Charge Distribution in U 1-x Ce x O 2+y Nanoparticles[END_REF] , who systematically detected variable amounts of U(VI) in nanocrystalline U 1-x Ce x O 2 δ , mainly due to the physical form of their samples and their preparation route, i.e. hydrothermal conversion (T = 200°C, t = 4 hours) of mixed hydroxide under aerated conditions. In our study, sintering at high temperature promotes the reduction of U(VI) into U(V) or even U(IV), depending on the sintering atmosphere considered (i.e. the oxygen partial pressure). As such, samples sintered under argon include variable amounts of U(V), that are ranging from 5 to 35% depending on the sintering temperature. Conversely, all the samples densified under reducing Ar/H 2 mixture led only to a very small proportion of U(V), systematically close to 5%. Owing to the atmosphere chosen, which is expected to yield a complete reduction of uranium into U(IV), this value is likely to reflect a slight reoxidation of the samples after the heat treatment. This latter could occur right after pulling the pellets out of the furnace, i.e. when exposing them to ambient air, and/or during the preparation of the XAS samples, which required mechanical crushing of the pellets. In both cases, uranium was probably oxidized at the extreme surface of the solids, thus explaining the small fraction of U(V) measured herein.

Compared to uranium, the signal recorded at the L 3 -edge of cerium appeared to be much more complex. Particularly, CeO 2 is characterized by three distinct features: a pre-edge peak (5722 eV), as well as two doublets at around 5729/5733 and 5741/5743 eV, originating from 2p3/2  5d5/2 transitions. On the other hand, the spectrum of CePO 4 monazite, which comprises pure Ce(III) [START_REF] Bregiroux | Solid-state synthesis of monazite-type compounds containing tetravalent elements[END_REF] , only presents one characteristic large peak, centered at around 5728 eV. As for uranium, the data associated to the different U 1-x Ce x O 2+δ sintered samples mostly depends on the atmosphere chosen for the heat treatment at high temperature. Surprisingly, the proportion of Ce(III) remained negligible under reducing atmosphere, while it varied from 9 up to 67 % under argon. almost completely in similar conditions [START_REF] Riess | O 2 Chemical Potential of Non-stoichiometric Ceria, CeO 2-x , Determined by a Solid Electrochemical Method[END_REF] . As such, tetravalent uranium appears to have a protective effect over the reduction of Ce(IV) into Ce(III), resulting in stoichiometric samples

with O/M close to 2.00 (Table 4). Under argon, the increase of the partial pressure in oxygen led U(IV) to oxidize into U(V).

Correlatively, Ce(IV) was reduced to counter-balance the charge, in good agreement with the compensation mechanisms reported in the literature for several UO 2 -Ln 2 O 3 systems [START_REF] Herrero | Charge compensation mechanisms in Nd-doped UO 2 samples for stoichiometric and hypo-stoichiometric conditions: Lack of miscibility gap[END_REF][START_REF] Bes | New insight in the uranium valence state determination in U y Nd 1-y O 2±x[END_REF] .

Indeed, the incorporation of trivalent rare earth elements in the fluorite-type structure of UO 2 is balanced by the partial oxidization of U(IV) into U(V), although with a small fraction of oxygen vacancies [START_REF] Herrero | Charge compensation mechanisms in Nd-doped UO 2 samples for stoichiometric and hypo-stoichiometric conditions: Lack of miscibility gap[END_REF] . Nevertheless, it is important to note that the U(V)-Ce(III) compensation was never complete, still resulting in hyper-stoichiometric samples. This feature, which could appear to be counter intuitive, was already observed for (U,Pu)O 2 mixed oxides [START_REF] Fouquet-Metivier | Study of the influence of americium on thermodynamic and structural properties of (U,Pu)O 2±x mixed oxides[END_REF] . Also, it is important to note that the fraction of U(V), and correlatively that of Ce(III), varies with both the sintering temperature and the total amount of cerium incorporated in the sample (Figure 5).

EXAFS at the U-L 3 edge

As HERFD-XANES showed that the most important impact on the samples' stoichiometry was obtained when varying the sintering temperature from 1300°C to 1600°C under argon, a complementary EXAFS study was conducted to investigate the local environment of the uranium cation in these samples. The comparison of the U-L 3 EXAFS spectra plotted in the R-space for all the x = 0.26 samples sintered under argon atmosphere is provided in Figure 6.

The pseudo radial distribution function (RDF) modulus systematically exhibited the same features, with a first peak close to 2 Å corresponding to the apparent distance of the first shell -O(1), and a second one located around 3.8 Å, mainly due to the -interactions, with a small contribution of the -O(2) shell. The spectra mostly differ from the magnitude of the RDF, which is mainly linked to the coordination numbers and/or to the structural disorder. As such, the increase of the intensity with the sintering temperature could be linked both with the evolution of the O/M ratio towards the ideal 2.00 value, as well as to the grain growth phenomena associated with sintering, which promotes the expansion of the coherent domain lengths, resulting in an improved crystallinity. Accordingly, the coordination number on the first shell increases with the sintering temperature, but remains below the theoretical value of 8 for uranium in the UO 2.00 structure: this defect is thus directly linked with the presence of Ce(III) in the samples, that lower the oxygen content in the solid.

The RDF assigned to the pellet sintered under argon at 1300°C, which exhibits the highest O/M ratio determined in this work (O/M = 2.06), appeared to be shifted towards lower apparent distances. This feature is in good agreement with an oxidized sample, which is usually assigned to a smaller unit cell volume (see the XRD section hereafter), and then to shorter U-O(1) bond lengths (Table 5). Still, the distance measured for this sample (d = 2.343(4) Å) is only 1% smaller than the value reported by Martin et al. [START_REF] Martin | A XAS study of the local environments of cations in (U, Ce)O 2[END_REF] for a stoichiometric sample (O/M = 2.00), although with a slightly different cerium content (x Ce = 0.25). Even if hyper-stoichiometry was found to generate a limited contraction of the first coordination shell, distortion effects were still evidenced by higher Debye-Waller factors. Indeed, these latter directly account for structural disorder, as the thermic agitation could be considered to be negligible for measurements performed at 15K. Conversely to the first coordination layer, the second and third shells were less impacted, as the U-U and U-O(2) distances remained close to 3.84 and 4.48 Å, respectively, for all the sintering temperatures considered.

The data extracted from the EXAFS spectra of U 0.74 Ce 0.26 O 2 δ sintered samples under reducing Ar/H 2 atmosphere led to less significative variations, once again in good agreement with the results coming from HERFD-XANES, as their O/M stoichiometry was systematically found close to 2.00. Hence, on the one hand, neither interatomic distances nor Debye-Weller factors were found to vary significantly, except for the sample sintered at 1600°C, probably due to the absence of an isothermal plateau at the targeted temperature. On this basis, U-O(1), U-U, and U-O(2) distances appeared in very good agreement with the data reported by Martin et al. [START_REF] Martin | A XAS study of the local environments of cations in (U, Ce)O 2[END_REF] for stoichiometric samples, owing to the uncertainties attached with both measurements series. On the other hand, the coordination number for the first two shells (U-O(1) and U-U) was found to increase slightly but continuously from 1300°C to 1600°C, even if this variation remains in the same order of than the uncertainties attached with the measurement. This probably stemed from the grain growth occurring during the sintering process, which enhanced the contribution of bulk versus surface. Indeed, nanometric grain size are generally associated to the predominance of surface species that are characterized by incomplete coordination layer, thus decreasing the global N value [START_REF] Manaud | Hydrothermal Conversion of Thorium Oxalate into into ThO 2 •nH 2 O oxide[END_REF] .

Table 5.

Best fit results for the first three coordination shells at the uranium L 3 edge. The numbers between parentheses indicate the uncertainty on the last digit.

First shell : U-O (1)

Second shell : U-U

1500°C-10h Ar 2.366(4) 7.4(

1300°C-10h

Ar (blue) and 1600°C (mustard), including best fits (solid lines). The FT window was taken over the k-space range from 3.5 to 13.5 Å -1 and magnified by k 3 .

X-Ray Diffraction

As explained in the introduction, the structure of uranium-cerium dioxyde solid solutions has been widely explored in the literature, involving both stoichiometric, hyper-stoichiometric and sub-stoichiometric samples regarding oxygen. A large domain of chemical compositions has also been assessed, that goes from pure UO 2 containing some mol.% in cerium, to highly Ce-enriched samples. Different sets of unit cell parameters coming from these studies have been compiled in Figure 7 to give an overview of the impact of Ce content and O/M ratio on the structure of U 1-x Ce x O 2±δ mixed oxides.

Even if a precise measurement of the O/M stoichiometry was frequently neglected by the various authors, most of the results reported for stoichiometric samples are distributed on a straight-line accounting for the Vegard's law (Figure 7b). Nevertheless, one can observe that almost all the datapoints lie slightly below the theoretical line drawn from pure UO 2 and CeO 2 data, meaning that the samples analyzed probably presented a slight deviation from the ideal O/M = 2.00 stoichiometry. This feature could be explained by the very high tendency of U(IV) to oxidize in air, that has been observed in the present study when dealing with samples sintered under reducing Ar-H 2 atmosphere, and which is even more strengthened when dealing with powders.

Overall, the sub-stoichiometric domain was scarcely investigated, probably due to the difficulty to obtain such samples. This fits well with the results obtained from the HERFD-XANES study performed in this work, where even reducing conditions produced stoichiometric samples composed of U(IV) and Ce(IV). When O/M ratio below 2.00 was reached, the value of the unit cell parameter increased in regards of the Vegard's law. This tendency was explained by the presence of significant amounts of Ce(III), and by the formation of oxygen vacancies to counterbalance the charge defect. Nevertheless, while the values published by Tagawa et al. remained close to the Vegard's law [START_REF] Tagawa | Oxidation-Reduction Properties of Mixed Oxides in the Cerium-Uranium-Oxygen System[END_REF] , those from Lorenzelli appeared to be strongly different and might probably be considered with caution [START_REF] Lorenzelli | The System UO 2 -CeO 2 -High-Temperature Crystallographic Study[END_REF] (Figure 7a). Also, it is important to note that when the amount of cerium incorporated in the samples increased (typically x Ce > 0.60), the unit cell parameter got closer to the Vegard's law, indicating almost negligible deviation from the stoichiometry despite the conditions applied.

In the hyper-stoichiometric domain (Figure 7c), the deviation from O/M = 2.00 is accompanied by the decrease of the unit cell parameter, in good agreement with what is generally observed for UO 2+x samples [START_REF] Manaud | Hydrothermal Conversion of Uranium(IV) Oxalate into Oxides: A Comprehensive Study[END_REF] . This tendency is particularly marked for samples enriched in uranium for which Nawada et al. have reported samples with O/M molar ratio as high as 2.28 [START_REF] Nawada | Oxidation and Phase-Behavior Studies of the U-Ce-O System[END_REF] . However, as detailed previously, all the compounds with x Ce > 0.60 almost fit with the Vegard's law. Hence, cerium-enriched U 1-x Ce x O 2 δ solid solutions appear to be weakly impacted by both the physical form of the sample and the operating conditions (temperature, atmosphere) that all lead to stoichiometric samples. The results obtained in this study, either by laboratory PXRD or by Synchrotron measurements, confirm the trends presented above. The unit cell parameters obtained by Rietveld refinement are gathered in Table 6, while an example of fit is supplied for each technique as supplementaty information (Figure S3). Confidence parameters attached to the Rietveld refinements are also supplied as supplementary information in Tables S1 andS2.

Both series of values are consistent with each other, even if the unit cell parameters determined by PXRD generally stand slightly above those obtained by S-PXRD. This small discrepancy might originate from the differences in the experimental setups, but also from the preparation schedule of the samples. Indeed, laboratory PXRD were generally performed shorty after the fabrication of the samples, while these latter were stored for several weeks prior to synchrotron measurements, probably leading to a limited oxidation of uranium at the surface. variations of the unit cell parameter were observed, that were typically about 0.1% of the value calculated for the stoichiometric samples from equation (4.). Also, although the unit cell parameter decreases linearly versus δ for x Ce = 0.14, no clear trend can be deduced from the datapoints obtained for higher cerium contents. In order to go further, the structural data collected in this work was then compared to the relation reported by Sali et al. [START_REF] Sali | Oxidation behavior of (U 1-y Ce y )O 2.00 ; (y=0.21, 0.28 and 0.44) solid solutions under different oxygen potentials. Thermogravimetric and in situ X-ray diffraction studies[END_REF]

Conclusion

In this work, the use of nanometric and highly reactive uranium-cerium dioxide powders prepared by wet-chemistry route led to the fabrication of homogenous and dense U 1-x Ce x O 2+δ solid solutions after sintering at high temperature. As such, these samples allowed to study thoroughly the impact of the operating conditions chosen for the heat treatment (firing temperature, oxygen partial pressure), on the structure and redox speciation of the final ceramics.

For this latter, HERFD-XANES spectroscopy led to determine accurately the oxygen / metal molar ratios (i.e. O/M with M = U + Ce) in all the samples prepared. Under reducing atmosphere (PO 2 ~ 610 -29 atm), the oxides were found to be close to O/M = 2.00. Even if a limited fraction of the uranium (typically 5% or less) was found to be oxidized as U(V), it was more likely to arise from the storage and the preparation of the samples for synchrotron measurements. Hence, one can consider that in the furnace, the dioxide compounds were The structural data reported herein then constitute a starting point for the evaluation of the impact of the O/M stoichiometry on several characteristics of dense uranium-cerium dioxide pellets, such as microstructure and chemical durability.

Associated Content

Supporting Information Available:

-Statistical distribution of the Ce/(U+Ce) ratio for x Ce = 0. The Supporting Information is available free of charge on the ACS Publications website.

  (4.) Such a deviation from the expected value could be correlated with the partial oxidization of U(IV) into U(V) or even U(VI) in the samples, as recently evidenced by Prieur et al.[START_REF] Prieur | Charge Distribution in U 1-x Ce x O 2+y Nanoparticles[END_REF] . Indeed, despite the storage of the samples in an inert glovebox (O 2 < 0.1 ppm, i.e. P(O 2 ) < 10 - 2 Pa), their very high reactivity associated with their nanoscale size probably led to an oxidative ageing during PXRD sample preparation and/or measurement, both conducted under ambient air.

Figure 1 .

 1 Figure 1.PXRD diagrams of U 1-x Ce x O 2+δ powder samples after heat treatment at T = 700°C under Ar/H 2 atmosphere for 4 hours. The signal assigned to the sample holder (austenite with trace amounts of ferrite) is marked by *.

Figure 2 .

 2 Figure 2. SEM micrograph of U 0.74 Ce 0.26 O 2+δ sample after heat treatment at T = 700°C under Ar/H 2 atmosphere for 4 hours (left) and statistical distribution of the x Ce = Ce/(U+Ce) molar ratio determined by EDS analyses (right).

Figure 3 .

 3 Figure 3. Normalized HERFD-XANES spectra at the U-M 4 (asamples; b -references) and Ce-L 3 (csamples; d -references) edges for various U 1-x Ce x O 2+δ samples sintered under argon atmosphere.

Figure 4 .

 4 Figure 4. Observed (black), calculated (red) and difference (blue) HERFD-XANES spectra at the U-M 4 (left) and Ce-L 3 (right) edges for U 0.74 Ce 0.26 O 2 δ sintered at T = 1600°C under Ar atmosphere.

Figure 5 .

 5 Figure 5. Variation of the O/U (), O/Ce () and O/M () molar ratios under argon atmosphere as a function of (a) the sintering temperature (x Ce = 0.26) and of (b) the chemical composition (T = 1600°C).

Figure 6 .

 6 Figure 6. Uranium L 3 -edge k 3 -weighed EXAFS data (b) and Fourier transform (a) for U 0.74 Ce 0.26 O 2+δ samples sintered under Ar at 1300°C (black), 1400°C (red), 1500°C (blue) and 1600°C (mustard), including best fits (solid lines). The FT window was taken over the k-space range from 3.5 to 13.5 Å -1 and magnified by k 3 .

Figure 7 .

 7 Figure 7.Variation of the unit cell parameters of U 1-x Ce x O 2±δ reported in the literature for (a) sub-stoichiometric samples with O/M < 2.00 - : Lorenzelli et al. 52 ;  : Tagawa et al. 51  : Markin et al. 49 ; (b) stoichiometric samples with O/M = 2.00 -: Dörr et al. 54 ;  : Krishnan et al. 20 ;  : Martin et al. 36 ;  : Krishnan et al. 55 ;  -Nagarajan et al. 56 ;  : Kim et al. 57 ;  : Cao et al. 58 ;  : Markin et al. 49 ;  : Kurosaki et al. 59 ;  : Designan et al. 13 ;  : Prieur et al. 60 ;  : Zinkevich et al. 61 ; (c) hyperstoichiometric samples with O/M > 2.00 -Nawada et al. 53  (873 K),  (1123 K),  (1273 K);  : Markin et al. 49 ;  : Tagawa et al. 51 . The dashed lined represents the Vegard's law extrapolated from pure O 2 38 and CeO 2 26 data.

Figure 8 .

 8 Figure 8. Variation of the unit cell parameters of U 1-x Ce x O 2+δ samples prepared in this work as a function of the deviation from stoichiometry. The dotted lines account for the relation proposed by Sali et al. 62 .

  stoichiometric, with U(IV) preventing cerium from the reduction into Ce(III). Conversely, the O/M ratio in the samples prepared under argon (PO 2 ~ 210 -6 atm) varied with the sintering conditions. They globally appeared to be hyper-stoichiometric (i.e. O/M > 2.00), the departure from the dioxide stoichiometry decreasing with both the cerium content in the sample, and the sintering temperature. The reduction of the Ce(IV) present in the precursor into Ce(III) was then not sufficient to counter-balance the oxidation of U(IV) into U(V) under the operating conditions chosen. Nevertheless, such deviation from the ideal O/M = 2.00 ratio was found to generate only moderate structural disorder from EXAFS data at the U-L 3 edge, mainly in the first shell of coordination of the cations. Indeed, whatever the sintering temperature and atmosphere, all the samples retained the fluorite-type structure of the UO 2 and CeO 2 end-members. The determination of accurate lattice parameters thanks to S-PXRD measurements led to complement the data already reported in the literature by various authors. These results were also consistent with the mathematic expression proposed by Sali et al. to link the unit cell parameter, the chemical composition and the deviation from the stoichiometry. The fair agreement observed confirms that this relation can be used as a first approximation to estimate simply the O/M stoichiometry in uranium-cerium mixed oxides, typically within a ± 0.02 uncertainty.

  14 and x Ce = 0.49 sample -Normalized HERFD-XANES spectra at the U-M 4 and Ce-L 3 edges -Example of PXRD and SPXRD patterns refined by the Rietveld method -Unit cell parameters and confidence parameters obtained after the Rietveld refinement of PXRD and SPXRD

Table 1 .

 1 Sintering conditions applied to the U 1-x Ce x O 2+δ powder samples during this study.

	x Ce	Sintering temperature (°C)	Holding time (hours)	Atmosphere
	0.14 1400	10	Ar
		1600	0	Ar
		1400	10	Ar/H 2 4%
		1600	0	Ar/H 2 4%
	0.26 1300	10	Ar
		1400	10	Ar
		1500	10	Ar
		1600	0	Ar
		1300	10	Ar/H 2 4%
		1400	10	Ar/H 2 4%
		1500	10	Ar/H 2 4%
		1600	0	Ar/H 2 4%
	0.49 1400	10	Ar
		1600	0	Ar
		1400	10	Ar/H 2 4%
		1600	0	Ar/H 2 4%
	SEM observations and statistical EDS analyses. SEM observations were carried out on
	pristine samples using a FEI Quanta 200 ESEM FEG microscope equipped with a Large Field
	Detector (LFD) and a Back-Scattered Electron Detector (BSED). A low acceleration voltage
	of 5-10 kV coupled with low vacuum conditions (i.e. 50 Pa water vapor) was chosen to

amounts of ferrite. The first could generate an additional large peak between 10 and 20° (2), while the second could occasionate small intensity diffraction lines, notably around 2 = 43 and 50° (see PDF file 00-023-0298).

  1-x Ce x O 2±δ solid solutions. Nevertheless, the associated unit

	cell parameters determined from Rietveld refinement appeared to be significantly lower than
	that expected from stoichiometric compounds with	e	= 2.00 (Table 2). Indeed, if one
	considers the formation of an ideal solid solution, and the values reported in the literature for
	parent end-members (UO 2 : a = 5.4713 Å 38 ; CeO 2 : a = 5.4097 Å 39 ), the variation of the unit
	cell parameter (expressed in Å) versus x Ce should follow a linear trend with :
	a = 5.4713 -0.0616  x Ce

Table 2 .

 2 Unit cell parameters and average crystallite size of the U 1-x Ce x O 2+δ powder samples obtained after heat treatment at T = 700°C under Ar/H 2 atmosphere for 4 hours, coming from Rietveld refinement. The values obtained from the Vegard's law for stoichiometric compouds (O/(U+Ce) = 2.00) are supplied for comparison.

	x Ce	Unit cell parameter (Å) Vegard's law PXRD	Average crystallite size (nm)
	0.14	5.4627	5.4571(1)	17(1)
	0.26	5.4553	5.4390(3)	8(1)
	0.49	5.4411	5.4389(3)	8(1)

Table 3 .

 3 Contribution of the different species to the average oxidation state (OS) of uranium and cerium, as determined from linear combination fitting of HERFD-XANES data. The numbers between parentheses indicate the uncertainty on the last digit. More surprisingly, cerium is also fully tetravalent, while CeO 2 would turned into Ce 2 O 3

	x Ce	Sintering conditions	Atm. U(IV) U(V) U OS	Ce(III) Ce(IV) Ce OS
	0.14 1400°C -10h Ar/H 2 94 (1) 6 (1) 4.06	3 (2)	97 (2)	3.97
		1600°C -0h	Ar/H 2 96 (1) 4 (1) 4.04	0 (2)	100 (2) 4.00
	0.26 1300°C -10h Ar/H 2 93 (1) 7 (1) 4.07	2 (2)	98 (2)	3.98
		1400°C -10h Ar/H 2 94 (1) 6 (1) 4.06	1 (2)	99 (2)	3.99
		1500°C -10h Ar/H 2 94 (1) 6 (1) 4.06	0 (2)	100 (2) 4.00
		1600°C -0h	Ar/H 2 95 (1) 5 (1) 4.05	0 (2)	100 (2) 4.00
	0.49 1400°C -10h Ar/H 2 96 (1) 4 (1) 4.04	0 (2)	100 (2) 4.00
		1600°C -0h	Ar/H 2 95 (1) 5 (1) 4.05	0 (2)	100 (2) 4.00
	0.14 1400°C -10h Ar	74 (1) 26(1) 4.26	67 (2)	33 (2)	3.32
		1600°C -0h	Ar	80 (1) 20(1) 4.20	54 (2)	46 (2)	3.45
	0.26 1300°C -10h Ar	65 (1) 35(1) 4.35	46 (2)	54 (2)	3.54
		1400°C -10h Ar	82 (1) 18(1) 4.18	21 (2)	79 (2)	3.79
		1500°C -10h Ar	94 (1) 6 (1) 4.06	0 (2)	100 (2) 4.00
		1600°C -0h	Ar	89 (1) 11(1) 4.11	9 (2)	91 (2)	3.91

Table 4 .

 4 Determination of O/U, O/Ce and O/M molar ratios in the various samples investigated from the linear combination fitting of HERFD-XANES data.

	x Ce Sintering conditions	O/U Ar/H 2 Ar Ar/H 2 Ar O/Ce	O/M Ar/H 2 Ar
	0.14 1400°C -10h	2.03	2.13 1.98	1.66	2.02	2.06
	1600°C -0h	2.02	2.10 2.00	1.73	2.02	2.05
	0.26 1300°C -10h	2.03	2.17 1.99	1.77	2.02	2.06
	1400°C -10h	2.03	2.09 1.99	1.90	2.02	2.04
	1500°C -10h	2.03	2.03 2.00	2.00	2.02	2.02
	1600°C -0h	2.03	2.05 2.00	1.96	2.02	2.03
	0.49 1400°C -10h	2.02	2.03 2.00	2.00	2.01	2.02
	1600°C -0h	2.03	2.02 2.00	2.00	2.02	2.01

  1-x Ce x O 2±δ reported in the literature for (a) sub-stoichiometric samples with O/M < 2.00 - : Lorenzelli et al. 52 ;  : Tagawa et al. 51  : Markin et al. 49 ; (b) stoichiometric samples with O/M = 2.00 -: Dörr et al.

[START_REF] Dorr | Study of the Formation of UO 2 -PuO 2 Solid-Solution by Means of UO 2 -CeO 2 Simulate[END_REF]

;  : Krishnan et al.

[START_REF] Krishnan | Synthesis, characterization and thermal expansion measurements on uranium-cerium mixed oxides[END_REF]

;  : Martin et al.

[START_REF] Martin | A XAS study of the local environments of cations in (U, Ce)O 2[END_REF]

;  : Krishnan et al.

[START_REF] Krishnan | Heat capacity measurements on uranium-cerium mixed oxides by differential scanning calorimetry[END_REF]

;  -Nagarajan et al.

[START_REF] Nagarajan | Oxygen Potential Studies on Hypostoichiometric Uranium-Cerium Mixed-Oxide[END_REF]

;  : Kim et al.

[START_REF] Kim | The thermal conductivity and lattice parameter measurements in a low Ce content (U 1-y Ce y )O 2 mixed oxide[END_REF]

;  : Cao et al.

[START_REF] Cao | Differential interplay between Ce and U on local structures of U 1-x Ce x O 2 solid solutions probed by X-ray absorption spectroscopy[END_REF]

;  : Markin et al.

[START_REF] Markin | Uranium-Cerium-Oxygen Ternary Phase Diagram[END_REF]

;  : Kurosaki et al.

[START_REF] Kurosaki | Thermal conductivity of (U,Ce)O 2 with and without Nd or Zr[END_REF]

;  : Designan et al.

[START_REF] Desigan | Dissolution behaviour of simulated MOX nuclear fuel pellets in nitric acid medium[END_REF]

;  : Prieur et al.

[START_REF] Prieur | A spectroscopic hike in the U-O phase diagram[END_REF]

;  : Zinkevich et al.

[START_REF] Zinkevich | Thermodynamic modelling of the ceriumoxygen system[END_REF]

; (c) hyperstoichiometric samples with O/M > 2.00 -Nawada et al.

[START_REF] Nawada | Oxidation and Phase-Behavior Studies of the U-Ce-O System[END_REF]

 (873 K),  (1123 K),  (1273 K);  : Markin et al.

[START_REF] Markin | Uranium-Cerium-Oxygen Ternary Phase Diagram[END_REF]

;  : Tagawa et al.

[START_REF] Tagawa | Oxidation-Reduction Properties of Mixed Oxides in the Cerium-Uranium-Oxygen System[END_REF]

. The dashed lined represents the Vegard's law extrapolated from pure O 2

[START_REF] Leinders | Accurate lattice parameter measurements of stoichiometric uranium dioxide[END_REF]

and CeO 2

[START_REF] Prieur | Charge Distribution in U 1-x Ce x O 2+y Nanoparticles[END_REF]

data.

Table 6 .

 6 Unit cell parameter of the U 1-x Ce x O 2+δ sintered samples (expressed in Å), as determined by Rietveld refinement of PXRD and S-PXRD data.

	x Ce Sintering conditions	PXRD Ar/H 2	Ar	S-PXRD Ar/H 2	Ar

Acknowledgments

The authors thank the SOLEIL and ESRF synchrotrons for providing beamtime. They are grateful to J. Lautru for performing SEM-EDS analyses and to P-H. Imbert for his help in PXRD analyses. They also thank CEA for funding the PhD work of M. Massonnet. This study received funding from the GENIORS project (H2020 Euratom Research and Innovation Programme under grant agreement n°755171).

Table of Contents graphic

Synopsis

This paper reports the synchrotron investigation of homogeneous (U,Ce)O 2+δ oxides sintered in various atmospheres. Under reducing conditions, O/M ratio appeared close to 2.00 using HERFD-XANES, while it was hyper-stoichiometric under argon, and decreased with the cerium content and the sintering temperature. Such deviation was found to generate moderate structural disorder from EXAFS. Finally, Synchrotron-PXRD data led to propose a mathematic expression linking the unit cell parameter, the chemical composition and the deviation from the stoichiometry.


J C Nappé A

PH. GROSSEAU A , B. GUILHOT B F Audubert C

PH. IACCONI D M Beauvy C

M Benabdesselam

Keywords: Ti 3 SiC 2, irradiation, ions lourds, krypton, MEB, AFM, DRX sous Incidence Rasante

Les carbures, de par leurs propriétés remarquables, sont pressentis comme matériau de structure autour du combustible du réacteur de génération IV. Parmi ceux étudiés, Ti 3 SiC 2 se distingue car il associe les propriétés des céramiques à celles des métaux. Cependant, son comportement sous irradiation n'est pas connu. Des caractérisations ont été réalisées sur des échantillons irradiés aux ions Kr à 75 MeV. Elles ont permis de mettre en exergue que TiO 2 (formé en surface de Ti 3 SiC 2 ) est pulvérisé par l'irradiation et que la maille cristalline de Ti 3 SiC 2 se dilate suivant c.

Conductivité thermique 37 W.m -1 .K -1 [START_REF] Barsoum | Thermal properties of Ti 3 SiC 2[END_REF] Capacité calorifique 110 J.mol -1 .K -1 [START_REF] Barsoum | Thermal properties of Ti 3 SiC 2[END_REF] Dilatation thermique 9,0x10 La surface des matériaux est observée par Microscopie Électronique à Balayage (MEB) et Microscopie à Force Atomique (AFM). Le MEB est un Jeol JSM 6400 utilisé sous une tension d'accélération de 15 kV et avec un détecteur à électrons secondaires. L'AFM est un Nanoscope III A utilisé en mode contact avec une sonde de constante de raideur 0,12 N.m -1 en nitrure de silicium.

La structure dans la zone irradiée de Ti 3 SiC 2 a été analysée par Diffractométrie des Rayons X sous Incidence Rasante (DRX-IR). Le diffractomètre est un D5000 de Siemens à anticathode de cuivre (λ = 1,54 Å).

Résultats et discussion

Lors du recuit post-polissage, une couche blanche est apparue à la surface de nos échantillons ; celle-ci pourrait être provoquée par une oxydation de Ti 3 SiC 2 . En effet, ce matériau est très facilement oxydable et il est probable qu'un oxyde se soit formé malgré l'atmosphère d'argon. De plus, d'après la littérature [START_REF] Gao | On physical and thermochemical properties of high-purity Ti 3 SiC 2[END_REF], l'oxydation de Ti 3 SiC 2 débute par la formation d'une couche de TiO 2 avant la formation d'une couche TiO 2 + SiO 2 à l'interface Ti 3 SiC 2 -TiO 2 ; la couleur blanche de la surface peut donc laisser supposer la présence de TiO 2 .

Les matériaux ont donc été irradiés en présence d'une couche d'oxyde en surface. En conséquence la caractérisation des dégâts d'irradiation devra prendre en compte cet oxyde. Dans un second temps, cette microscopie permet d'évaluer la rugosité des échantillons grâce à une calibration en z. La rugosité est alors évaluée par le paramètre R a défini par la norme ISO 4287 par :

( )

0 1 . a R z x dx = ∫ (1)
où ℓ est la longueur sur laquelle est mesuré z(x) [START_REF] Zani | La mesure de rugosité ? Quelques normes… et plusieurs dizaines de paramètres[END_REF].

Le tableau 3 présente les rugosités moyennes de chaque échantillon ; elle est calculée à partir de la rugosité mesurée sur une dizaine d'images représentatives de l'état de surface de chaque échantillon. Ces mesures confirment quantitativement les évolutions observées par microscopies. Ainsi, à température ambiante l'augmentation de la fluence diminue la rugosité ; il y a pulvérisation des reliefs jusqu'à obtenir un état de surface plan. Par contre, l'irradiation à 500 °C n'a pas comme conséquence la réduction de la rugosité, bien que l'état de surface soit légèrement différent de celui du témoin. Ainsi, on note que le paramètre c évolue fortement. Ceci provient du fait que Ti 3 SiC 2 a une structure hexagonale, donc une forte sensibilité suivant c. Ainsi, on peut supposer que l'insertion des atomes de krypton mais aussi le déplacement des atomes dans le matériau se fait préférentiellement le long de cet axe. Enfin, on remarque que le paramètre c diminue avec l'augmentation de la température ce qui peut laisser penser à une diffusion des atomes de krypton ou à un recuit des défauts. Mais ces hypothèses sont à confirmer. Enfin, en ce qui concerne Ti 3 SiC 2 , sa maille cristalline se dilate suivant l'axe c, certainement à cause de l'insertion des atomes de krypton et du déplacement des atomes dans la zone endommagée.

Conclusion

3 3 . 2 (F

 32 .1 1 M Mi ic cr ro os sc co op pi ie e É Él le ec ct tr ro on ni iq qu ue e à à B Ba al la ay ya ag ge e Les images obtenues par MEB pour les 4 échantillons sont rassemblées sur la figure 1. Sur le témoin on observe la présence de reliefs sur une surface plane. Une analyse par EDX a permis de détecter la présence d'oxygène sur toute la surface de l'échantillon, aussi bien sur la partie plane que sur les reliefs, ce qui confirme la présence d'un oxyde. (a) échantillon témoin (b) irradié à température ambiante à 10 14 cm -ma ag ge es s M ME EB B, , g gr ro os ss si is ss se em me en nt t x x2 20 00 00 0 L'irradiation n'a pas été sans effet sur l'état de surface de Ti 3 SiC 2 . En effet, on observe tout d'abord une diminution des reliefs avec l'augmentation de la fluence ; l'oxyde semble être pulvérisé et donc peu « résistant » à cette irradiation à l'ambiante. Par contre, l'irradiation à haute température a un effet totalement différent : les reliefs restent intacts alors que la partie plane semble s'endommager. L'oxyde serait donc plus « résistant » à une irradiation en température qu'à l'ambiante. 3 3. .2 2 M Mi ic cr ro os sc co op pi ie e à à F Fo or rc ce e A At to om mi iq qu ue e L'AFM permet dans un premier temps de confirmer les observations réalisées en MEB quant à la « résistance » ou non de l'oxyde à l'irradiation. La figure 2 présente les images obtenues par AFM. Fi ig gu ur re e 2 2 : : I Im ma ag ge es s A AF FM M, , s sc ca an n d de e 4 45 5x x4 45 5 µ µm m 2 2 : : ( (a a) ) é éc ch ha an nt ti il ll lo on n t té ém mo oi in n, , ( (b b) ) i ir rr ra ad di ié é à à t te em mp pé ér ra at tu ur re e a am mb bi ia an nt te e à à ) ) i ir rr ra ad di ié é à à t te em mp pé ér ra at tu ur re e a am mb bi ia an nt te e à à

3 3 .

 3 .3 3 D DR RX X s so ou us s I In nc ci id de en nc ce e R Ra as sa an nt te e La DRX-IR devrait permettre de lever l'incertitude sur la couche blanche apparue après recuit mais également de connaître l'évolution des différentes phases dans la partie irradiée ainsi que d'évaluer les changements cristallographiques. La figure 3 présente les diffractogrammes réalisés à des angles d'incidence α de 1° et 3°. La première remarque que l'on peut formuler est que du TiO 2 , sous sa forme cristallographique rutile, s'est bien formé sur les échantillons avant irradiation. La profondeur de pénétration des rayons X est évaluée à 230 nm dans Ti 3 SiC 2 et 300 nm dans TiO 2 pour α = 1° et à 720 nm dans Ti 3 SiC 2 et 960 nm dans TiO 2 pour α = 3° ; comme le parcours moyen projeté est de 7,9 µm (cf. 2.2) la zone analysée pour les deux angles est bien une zone irradiée. α = 1° α = 3° F Fi ig gu ur re e 3 3 : : D DR RX X s so ou us s I In nc ci id de en nc ce e R Ra as sa an nt te e à Ensuite, on peut remarquer la pulvérisation de la couche d'oxyde à température ambiante : celle-ci disparaît non seulement avec l'augmentation de la fluence, comme observé en microscopies, mais aussi avec la pénétration des rayons X. On en conclut que le rutile formé ne « résiste » pas à cette irradiation, surtout à forte fluence.

  Cette recherche sur les dommages d'irradiation dans Ti 3 SiC 2 débute et les caractérisations ont surtout porté sur l'oxyde TiO 2 formé après le recuit des échantillons. Néanmoins, ces premiers résultats sont prometteurs. Tout d'abord, le rutile n'est pas « résistant » à une irradiation à 75 MeV au krypton à température ambiante : il est en effet pulvérisé par le faisceau d'ion. Par contre, une irradiation à 500 °C permettrait la formation d'anatase et augmenterait la « résistance » de la couche d'oxyde. Une hypothèse reste à confirmer : l'anatase est-il plus « résistant » que le rutile ?

  L'objectif de cette étude est donc de mieux appréhender le comportement de Ti 3 SiC 2 sous irradiation. Les échantillons ont été obtenus par frittage sous charge d'une poudre de Ti 3 SiC 2 . Ce matériau est rarement pur : en effet, la synthèse de Ti 3 SiC 2 implique une proportion non négligeable de poudre non transformée. On estime que notre matériau contient 75 % de Ti 3 SiC 2 , 20 % de TiC et 5 % TiSi 2 .Les échantillons ont été irradiés aux ions krypton 86 Kr 18+ au Grand Accélérateur National d'Ions Lourds (GANIL) à Caen. L'énergie des ions était de 75 MeV pour un débit de fluence moyen de 9x10 9 cm -2 .s -1 . Deux paramètres ont pu être modulés pour les irradiations : la fluence et la température. Ainsi, trois irradiations différentes ont été réalisées ; le tableau 2 récapitule leurs paramètres.

		-6 K -1	[5]
	T Ta ab bl le ea au u 1 1 : : P Pr ro op pr ri ié ét té és s d de e T Ti i 3 3S Si iC C 2 2
	2. Matériaux et techniques expérimentales
	2 2. .1 1 P Pr ré ép pa ar ra at ti io on n d de es s é éc ch ha an nt ti il ll lo on ns s
	Les échantillons sont tout d'abord polis afin d'obtenir une surface plane. Puis ils sont recuits à
	800 °C pendant 4 heures sous atmosphère d'argon afin de relâcher les contraintes créées lors du
	polissage. Enfin, les échantillons sont irradiés aux ions lourds afin de simuler l'impact des produits
	de fission et des atomes de recul des désintégrations alpha dans le matériau. En première
	approximation, on considérera que les contraintes observées ne sont dues qu'à l'irradiation.
	2 2. .2 2 É Éc ch ha an nt ti il ll lo on ns s e et t i ir rr ra ad di ia at ti io on ns s
	Température /°C	d'irradiation	Fluence /cm -2
	25		10 14
	25		10 15
	500		10 15

T Ta ab bl le ea au u 2 2 : : P Pa ar ra am mè èt tr re es s d d' 'i ir rr ra ad di ia at ti io on n d de es s é éc ch ha an nt ti il ll lo on ns s Le code de calcul TRIM a permis d'évaluer divers paramètres relatifs à cette irradiation. Ainsi, le parcours moyen projeté est de 7,9 µm, le pouvoir d'arrêt électronique est de 1,6x10 4 keV.µm -1 et le pouvoir d'arrêt nucléaire est de 66 keV.µm -1 . 2 2. .3 3 T Te ec ch hn ni iq qu ue es s d de e c ca ar ra ac ct té ér ri is sa at ti io on n Afin d'expliciter les phénomènes observés, les caractérisations des échantillons irradiés sont comparées à celles d'un témoin, préparé dans les mêmes conditions et non irradié.

  On note également la disparition des deux phases secondaires TiC et TiSi 2 en surface.Le comportement sous irradiation de notre échantillon à 500 °C est également intéressant. Les microscopies avaient fait apparaître une couche d'oxyde non pulvérisée. La DRX-IR d'une part confirme cette observation, d'autre part renseigne sur la composition de cet oxyde : il n'est pas constitué que de rutile. En effet, la forme stable de TiO 2 à température ambiante, l'anatase, est également présente. Des investigations sont en cours pour comprendre ce phénomène, mais il semblerait que cette irradiation du rutile à 500 °C, température proche de la température de transition anatase → rutile (700 °C), provoque un changement de phase ; un essai de recuit dans les mêmes conditions que celles de l'irradiation permettrait d'éclaircir la présence d'anatase. De plus, une hypothèse à vérifier serait que l'anatase se forme en surface du rutile ; par conséquent, il serait plus « résistant » et donc protègerait le rutile de l'irradiation. Ceci expliquerait l'observation de l'oxyde non pulvérisé en microscopies et la présence des deux oxydes en DRX-IR.Une dernière remarque porte sur la raie à 2θ = 40,9° de Ti 3 SiC 2 ; en effet, celle-ci, qui correspond à la diffraction du plan 008, est fortement décalée en fonction des paramètres d'irradiation. Ce décalage est dû à une variation des paramètres de mailles. Le tableau 4 présente une évaluation du paramètre de maille de Ti 3 SiC 2 pour chaque échantillon et chaque angle d'incidence.

	Angle d'incidence	Fluence /cm -2	Température d'irradiation /°C	Paramètres de maille a /Å c /Å
		-	-	3,065 17,65
	1°	10 14 10 15	25 25	3,065 17,68 3,058 17,89
		10 15	500	3,061 17,76
		-	-	3,065 17,66
	3°	10 14 10 15	25 25	3,065 17,71 3,061 17,89
		10 15	500	3,064 17,78
	T Ta ab bl le ea au u 4 4 : : P Pa ar ra am mè èt tr re es s d de e m ma ai il ll le e d de e T Ti i 3 3S Si iC C 2 2 e en n f fo on nc ct ti io on n d de es s p pa ar ra am mè èt tr re es s d d' 'i ir rr ra ad di ia at ti io on n