# Impact of sintering parameters on the microstructure of
homogeneous U_1 - xCe_xO_2+δceramics

Nicolas Clavier, Malvina Massonnet, Laurent Claparede, Renaud Podor,
Paul-henri Imbert, Julien Martinez, Nicolas Dacheux

► To cite this version:

Nicolas Clavier, Malvina Massonnet, Laurent Claparede, Renaud Podor, Paul-henri Imbert, et al.. Impact of sintering parameters on the microstructure of homogeneous

U_1 - xCe_xO_2+δceramics.JournaloftheAmericanCeramicSociety, 2025, 108(5), pp.e20376.10.1111/jac.05024007

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Impact of sintering parameters on the
microstructure of homogeneous U₁-xCe x O₂+δ
ceramics

N. Clavier ¹*, M. Massonnet ¹, L. Claparède ¹, R. Podor ¹, P.-H. Imbert ¹,
J. Martinez ², N. Dacheux ¹

1 ICSM, Univ Montpellier, CEA, CNRS, ENSCM, Bagnols/Cèze, France

2 CEA, DES, ISEC, DMRC, Univ Montpellier, Marcoule, France

* Corresponding author:

Dr. Nicolas CLAVIER
ICSM, Univ Montpellier, CEA, CNRS, ENSCM
Site de Marcoule
BP 17171
30207 Bagnols sur Cèze
France

Phone : + 33 4 66 33 92 08

Fax : + 33 4 66 79 76 11

nicolas.clavier@icsm.fr
**Abstract**: The effects of atmosphere and cerium content on the densification and the final microstructure of homogeneous $U_{1-x}Ce_xO_{2+\delta}$ solid solutions ($x$ = 0.10; 0.25; 0.50) were investigated. Dilatometric studies first revealed that while the cerium content only slightly modifies sintering under Ar/H$_2$ atmosphere, a change of the gas to argon dramatically modifies densification kinetics. As a result, samples prepared under Ar/H$_2$ exhibit a dense microstructure with micrometric grains. Conversely, samples sintered under argon appeared to be less densified but with larger grains. These changes were correlated with the variation of the final O/M stoichiometry ($M$ = U+Ce) and illustrated by the construction of sintering maps. Finally, grain growth was found to be driven by grain boundary motion when O/M ratio remained close to 2.00, while usual power laws did not apply for the most hyper-stoichiometric samples. The first values of activation energy for the sintering of $U_{1-x}Ce_xO_{2+\delta}$ solid solutions under Ar/H$_2$ atmosphere were also determined.

**Keywords**: nuclear fuel, uranium oxide, sintering, atmosphere, mechanism
# 1. Introduction

Uranium and plutonium mixed oxides, known as MOx (U,Pu)O$_{2\pm\delta}$, are currently used in 22 PWR reactors in France. They are produced by a powder metallurgy process based on a co-grinding step of the oxide powders, followed by dilution of this primary blend in UO$_2$. The microstructure obtained after sintering is then characterised by plutonium-rich zones distributed within a matrix composed mainly of uranium dioxide [1]. In the future, MOx fuels and their life-cycle could be modified by two major developments. On the one hand, the reprocessing of spent MOx fuels, which is not performed today, is envisaged for current Pressurized Water Reactors (PWRs) or for future plants, in order to optimize plutonium management [2]. On the other hand, the potential development of the fourth reactor generation, including sodium-cooled fast neutron reactors, implies a modification of the fabrication process, in particular to incorporate higher plutonium contents [3, 4]. In both cases, a fuel with a homogeneous distribution of cations within its structure is required. Much work is therefore being done to develop alternative synthesis routes for these fuels, most of which involve wet chemistry methods [5-8].

Obtaining oxide powders with different physico-chemical characteristics compared with those currently used in industry also implies revisiting the sintering of the materials in order to control the final microstructure of the ceramic. In fact, the grain size, the amount and distribution of porosity within the material, as well as the cationic homogeneity, are determined by the thermal cycle applied to the material. In this context, while the temperature and duration of the heat treatment are obviously first order parameters, in the case of uranium and plutonium oxides, the nature of the atmosphere used is critical [9, 10]. Due to the multiple valences that uranium and plutonium can adopt in solid phases, the dioxygen partial pressure (P(O$_2$)) within the sintering atmosphere will affect the O/M ratio (with M = U + Pu) within the material [11], and thus will condition the nature of the defects formed in the solid and the diffusion kinetics [12, 13]. Hence, numerous studies have already been devoted to the impact of the sintering atmosphere on the densification of UO$_{2+x}$ oxides [10, 14], as well as (U,Pu)O$_2$ MOx fuels [15-17]. Nevertheless, for the latter, authors mainly investigated powder mixtures, for which the formation of a solid solution during the heat treatment [18] can bias the analysis of sintering mechanisms. Conversely, if the sintering of homogeneous mixed oxide powders prepared by innovative methods has been studied [19, 20], only a few works have focused on the influence of the heat treatment atmosphere for these particular samples.
In this context, this paper reports a multi-parametric study of the sintering of nanoscale $U_{1-x}Ce_xO_{2+\delta}$ oxide powders prepared via the initial precipitation of mixed hydroxides, with $x = 0.10$; 0.25 and 0.50. The first two compositions are close to the Pu-content found in the primary $UO_2-PuO_2$ blends used for MOx fabrication, and that of typical PWR MOx fuel, while the $x = 0.50$ sample mainly presents an academic interest. Previous work has already shown that this synthesis method significantly lowers the sintering temperature, while leading to materials with an extremely homogeneous cation distribution [6, 21]. Cerium is used herein as a surrogate for plutonium, due to its similar properties in terms of ionic radius and redox behavior [22]. First, a dilatometric study was performed to evaluate the effect of the chemical composition and the sintering atmosphere on the shrinkage kinetics. These data also made it possible to delimit temperature domains favorable to the densification of the samples, which were then explored in order to establish sintering maps. Based on the differences observed in terms of both density and average grain sizes when varying cerium content and $P(O_2)$ value in the sintering atmosphere, additional experiments were carried out in order to investigate the grain growth mechanisms in more details, and to evaluate the activation energy associated with sintering.

## 2. Experimental

**Preparation and characterization of the starting powders.** $U_{1-x}Ce_xO_{2+\delta}$ nano-powders were obtained following the protocol initially developed by Martinez *et al.* [6], and adapted by Massonnet *et al.* [23]. This latter is based on the co-precipitation of U(IV) and Ce(IV) as mixed hydroxides, followed by their rapid aging in solution into oxides. U(IV) solution with a concentration about 0.5 mol.L⁻¹ was obtained by dissolving uranium metal chips (kindly supplied by CETAMA) in concentrated hydrochloric acid (6 mol.L⁻¹) [24]. Separately, Ce(NH₄)₄(SO₄)₄·2H₂O (Merck, ≥ 98% purity) was dissolved in 2 mol.L⁻¹ HCl. These two solutions were mixed in the desired molar ratio (i.e. $\frac{Ce}{U+Ce} = x_{Ce} = 0.10$, 0.25 and 0.50), then poured in a large excess of 2 mol.L⁻¹ NH₃ (about 400%) under magnetic stirring, resulting in the immediate formation of a precipitate. This latter was let under stirring for 30 minutes, in order to favor particles growth and ageing into the oxide form following:

$$ 
\begin{aligned}
1-x U^{4+} + x Ce^{4+} + 4 NH_3 \cdot H_2O & \rightarrow U_{1-x}Ce_x(OH)_4 + 4 NH_4^+ \\
& \rightarrow U_{1-x}Ce_xO_2 \cdot nH_2O + (2-n) H_2O + 4 NH_4^+
\end{aligned} 
\quad (1) 
$$
The precipitate was separated by centrifugation at 14000 rpm, washed twice with deionized water and once in ethanol, then dried in an inert Ar-glovebox to avoid rapid oxidation of uranium (IV). Final calcination at 700°C for 4 hours under Ar/H₂ 4% led the structural water, which could lead the pellets to break during their densification process, to be eliminated, and set the O/M ratio close to 2.00.

The main characteristics of these starting powders, already detailed in our previous study [23], are summarized in supplementary materials (Figure S1, Table S1). They all present a single fluorite-type structure, characteristic of the UO₂+x and CeO₂ end-members, and exhibit a typical crystallite size in the 10-20 nm range. This morphology is confirmed by SEM observations, which show submicrometric particles assembled in larger aggregates, that can reach up to 100 µm in length. It should be noted that these powders were stored in vials under air atmosphere, which could induce partial re-oxidation owing to their reactivity. Finally, the cerium doping rate in the samples was measured to be close to expected values after full dissolution of the powders and further ICP-AES analyses (Spectro Arcos). The values xCe = 0.10; 0.25 and 0.50 were further retained in the text for simplicity's sake.

**Shaping and sintering.** Before sintering, the powders were shaped as 5 mm diameter discs by uniaxial pressing (500 MPa) at room temperature. 200 mg of powder were poured into a tungsten carbide die, after addition of zinc stearate on the walls for lubrication, leading to green pellets of about 1.5-2 mm height with relative densities typically between 50 and 52% TD (Theoretical Density). These latter were finally sintered in alumina boats 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/H₂ 4% - P(O₂) ≈ 6×10⁻²⁹ atm at T = 650°C) or neutral (Ar - P(O₂) ≈ 10⁻⁶ atm) conditions in the furnace. In both cases, the dioxygen partial pressure P(O₂) was measured before entering the dilatometer by a Jok'air analyzer (supplied by Setnag). The latter is composed by an electrochemical zirconia sensor set in an internal furnace operating at 650°C, allowing to determine dioxygen partial pressures ranging between 10⁻³⁵ and 0.25 atm.

**Dilatometric measurements.** Dilatometric measurements were conducted on a vertical Setaram Setsys Evolution apparatus. All the pellets were placed between two alumina plates to avoid contamination of the sample environment, with a restraining force of 5g, then heated up to the desired temperature under Ar/H₂-4% or Argon, with a heating rate ranging from 2 to 10°C.min⁻¹. Cooling was operated down to room temperature at 6°C.min⁻¹. A blank
experiment accounting for the dilatation of the alumina sample holders was recorded for each experiment and substracted to the samples signal for correction.

**XRD.** X-Ray Diffraction (XRD) patterns were recorded using a Bruker D8 diffractometer equipped with a Lynxeye detector in the reflection geometry with Göbel mirror and using Cu Kα₁,₂ radiation (λ<sub>average</sub> = 1.54184 Å). Using modelling clay, sintered pellets were stuck to a rotating steel sample handler (ferrite), which may cause additional diffraction peaks around 45, 65 and 82°. XRD patterns were recorded at room temperature in the 25 – 100° range (2θ), with a step size of Δ(2θ) = 0.01° and a total counting time of about 2h15 per sample. The data collected were refined by the Le Bail method to extract unit cell parameters using the Cox-Hastings pseudo-Voigt profile function [25] implemented in the Fullprof_suite program [26]. The refined parameters were zero shift, unit cell parameters, background, profile shape parameters, and peak asymmetry. The microstructure parameters were assessed using an isotropic size model.

**SEM observations and grain size determination.** Scanning Electron Microscope (SEM) observations were carried out on the sintered samples using a FEI Quanta 200 ESEM FEG microscope equipped with a CBS detector (Concentric BackScattered detector). The samples were polished to a mirror grade, but did not go through chemical or thermal etching. Images were recorded in the Back-Scattered Electron (BSE) mode at 3 kV, under high vacuum and at low probe current, resulting in a crystallographic orientation contrast. It was then possible to determine the average grains size in the samples by image analysis using the SEraMic method reported by Podor *et al.* [27].

Each series of images was processed using the SEraMic plugin implemented in the Fiji image analysis software [28]. Typically, 500 to 1000 grains were considered for each sample, which allowed us to access grain-size distribution with satisfactory counting statistics. Also, different zones of the pellets were considered (typically in the center and close to the edge) to evidence any grain-size gradient. The equivalent circular diameter G (μm) has been calculated from the area A (μm²) of each grain given by the software as follows:

$$G = 2 \cdot (A/\pi)^{1/2} \qquad (2.)$$
**EDS measurements.** Using the same microscope than described above, statistical Energy Dispersive X-ray Spectroscopy (EDS) measurements were performed on both starting powers and sintered pellets. For each of them, around 100 datapoints were analyzed at various locations of the sample, allowing to point out the distribution of the Ce/(U+Ce) mole ratio. UO₂ and CePO₄ references were used as standards in order to achieve semi-quantitative data.

**Density measurements.** The geometrical density of sintered samples was determined by measurements of pellets thickness and diameter using a precision caliper. This value led to an estimation of the global porosity within the samples. Each measurement was repeated 10 times which allowed to estimate an uncertainty of about 1.5%TD, mainly coming from the precision of the caliper used and from the geometrical defects of the pellets. Theoretical density was derived from the unit cell parameters obtained from XRD data.

# 3. Results

## 3.1. Dilatometric study

The evaluation of the optimal conditions required to obtain dense samples was first carried out by means of dilatometric studies (Figure 1). The latter also highlight the influence of the chemical composition and the heat treatment atmosphere on the sintering process. Under Ar/H₂ atmosphere (P(O₂) ≈ 6 × 10⁻²⁹ atm at T = 650°C), the curves obtained show similar trends regardless of the cerium content studied. Initially, a slight swelling, associated with the thermal expansion of the samples (typically 1 to 2%), is observed up to about 800°C. This is in good agreement with the prior heat treatment of the powders, which limits their reactivity up to 700°C. Nevertheless, it is likely that redox reactions take place during this first part of the heat treatment, owing to the partial oxidation of the starting powders during storage. Such ageing of the samples is associated with an hyper-stoichiometric O/M ratio which further decreases down to 2.00 when heating under reducing Ar/H₂.

The temperature range from 800 to 1300°C is subsequently marked by a strong shrinkage (above 15% for the three compositions studied), characteristic of the sintering of the samples. It is associated with a large peak on the derivative curves (Figure 1c), which account for the axial strain rate. For x<sub>Ce</sub> = 0.10 and 0.50, this peak contains a shoulder at the highest temperatures, while it is even split in two distinct signals for x<sub>Ce</sub> = 0.25. The corresponding temperatures range from 1000 to 1100°C, then from 1250 to 1330°C,
depending on the chemical composition. However, no correlation between the maximum axial
strain rate temperatures and the cerium doping was evidenced. Also, the origin of these two
contributions remains unclear, and might be linked with morphological differences between
the samples. Indeed, the nanocrystalline powders prepared by the wet chemistry route chosen
for this work tend to agglomerate, forming aggregates whose size can vary depending on the
batches. As such, the two steps observed could correspond to densification within the
agglomerates, then between them, as it was already demonstrated for several other actinide
oxides prepared by wet-chemistry method [29]. Yet, the investigation of this effect is beyond
the scope of this study. Moreover, the temperature range concerned by these phenomenon
remains far from the sintering conditions studied in this work (vide infra). The impact of the
agglomerates is therefore probably eliminated at high temperatures, and does not affect the
results discussed below.

Above 1300°C, only a slight residual shrinkage is observed, also evidenced by the
presence of a small peak on the derivative curves, typically set between 1400 and 1550°C.
This probably marks the end of densification and the beginning of a grain growth step, but can
also act the onset of slight dedensification phenomena, like it is the case for x<sub>Ce</sub> = 0.50. The
sintering temperature obtained through the use of nanometric and homogeneous powders thus
appears significantly lower than that usually reported for similar oxides prepared by powder
metallurgy (i.e. typically around 1700°C), in good agreement with the previous results
reported for this synthesis route [21].

While the chemical composition of the sample does not significantly modify the
profile of the dilatometric curves, the latter evolves strongly with the sintering atmosphere.
**Figure1b** shows the comparison of the data obtained during the sintering of U<sub>0.9</sub>Ce<sub>0.1</sub>O<sub>2+δ</sub>
under argon and Ar/H<sub>2</sub> atmospheres. One should note that the experiment under Ar/H<sub>2</sub> is a
replicate of the one presented in Figure 1a, and appears slightly different. As the two
experiments have been performed with the same starting powder, it is likely that the partial
oxidation of our samples during storage might induce some small differences, mainly a 50°C
shift in the maximal axial strain rate temperature in this case. This strengthens the difficulty of
clearly linking sintering temperature and cerium doping in these samples.

When sintering under argon, the behaviour of the sample remains unchanged until
about 700°C. Above this temperature, however, a slight shrinkage can be observed between
800 and 1000°C, probably due to the adjustment of the stoichiometry in oxygen. Indeed,
recent works showed that the sintering of U<sub>1-x</sub>Nd<sub>x</sub>O<sub>2+δ</sub> oxide powders under argon can lead to
the transient formation of U<sub>3</sub>O<sub>8</sub>, which finally reduced back to UO<sub>2</sub> around 1000°C [30].
Owing to the molar volume of both phases, a similar phenomenon could explain the shrinkage observed in this study. Sintering then starts at around 1100°C and is characterised by a significant and extremely rapid shrinkage of the sample. As a result, densification is complete at 1300°C, which seems very low, even when compared with works exploring the oxidative sintering of UO₂ [10]. However, at the very end of sintering, a slight de-densification can be observed (typically between 1550 and 1600°C). This phenomenon has often been associated with the presence of carbon residues at high temperature [31], resulting from the use of organics during the preparation process, which can be excluded here due to the synthesis method chosen. Therefore, the de-densification is most likely due to redox phenomena, such as U(IV) oxidation or Ce(IV) reduction, which will be discussed later in this paper.

<figure><img src="image_2.png" /><figcaption>**Figure 1.** Variation of the relative pellet thickness of U₁-xCeₓO₂+δ samples sintered under Ar/H₂ atmosphere (a) with xCe = 0.10 (black), 0.25 (red) and 0.50 (blue). Variation of the relative linear shrinkage of U₀.₉Ce₀.₁O₂+δ (b) sintered under Ar (black) or Ar/H₂ (red) atmosphere. The corresponding derivative curves which account for the axial strain rate are shown in figures (c) and (d).</figcaption></figure>

In addition, a statistical EDS study was carried out in order to demonstrate the evolution of the U-Ce homogeneity during the sintering process. For the initial powders, even
if the volume probed by the electron beam (typically about 1 µm³) encompasses several nanometric grains, it still allows to evidence some variations in the U/Ce distribution that can be due to different precipitation kinetics. In sintered pellets, this approach does not only demonstrate the single-phase nature of the samples and helps us to monitor (semi-quantitatively) the variation of the composition, but also allows us to quantify the homogeneity of the latter. In this sense, these analyses provide more information than conventional EDS mapping, which in the case of homogeneous compounds only provides equivalent spatial visualization of the various elements studied.

<figure><img src="image_3.png" /><figcaption>**Figure 2.** Statistical distribution of the Ce/(U+Ce) mole ratio, obtained by EDS analyses, within starting powders (light colours) and sintered samples obtained at the end of the dilatometric study performed under argon (dark colours) : x<sub>Ce</sub> = 0.10 (black), 0.25 (red) and 0.50 (blue). Note that intermediate shade on the graph comes from the superimposition of light and dark colours and does not account for a particular set of data.</figcaption></figure>

Thus, **Figure 2** presents the distribution of the Ce/(U+Ce) mole ratio within both starting powders and sintered pellets obtained at the end of the dilatometric measurement (argon atmosphere). As expected from the wet chemistry route used herein, the powders show a very narrow distribution of their chemical composition around the target value. The distribution can be approximated as a Gaussian curve, the centroid of which corresponds well to the expected composition, the slight differences being assigned to the conditions of acquisition that preclude a fully quantitative analysis. Similar results were obtained for sintered samples, with even more homogeneous cation distributions, as a result of the
interdiffusion operating jointly with the densification. Thus, neither UO₂ nor CeO₂ hotspots were detected in the samples, showing that the sintering process did not lead to phase segregation, even in the presence of redox phenomena involving the cations present in the samples.

## 3.2. Sintering map

On the basis of the results obtained in the dilatometric study, several operating conditions were selected in order to construct the sintering map of two U₁-xCeₓO₂+δ samples, with x<sub>Ce</sub> = 0.10 and x<sub>Ce</sub> = 0.25 (i.e. 10 and 25 mol.% of cerium in cations). In fact, these compositions correspond to the range of existence of the solid solution for which the deviations from the ideal stoichiometry O/M = 2.00 are likely to be the most important [23], and thus to have a significant impact on the microstructure of the sintered pellets. The densification of these samples was therefore carried out under Ar or Ar/H₂, for temperatures between 1400 and 1600°C, and considering dwell times varying from 0 to 10 hours. The condition with T = 1600°C and t = 0h corresponds to the dilatometry experiments presented above, during which the targeted temperature was only briefly reached by the furnace, due to equipment limitations. All the sintering conditions applied to the samples are summarized in **Table 1**. For each sample, the density was evaluated by geometric measurements, while the grain size was determined by image analysis, according to the procedure described in [27] and recalled in the 'Experimental' section of this paper.

<table><caption>**Table 1.** Sintering conditions applied to the U₁-xCeₓO₂+δ powder samples during this study.</caption><thead><tr><th>x<sub>Ce</sub></th><th>Sintering temperature (°C)</th><th>Holding time (hours)</th><th>Atmosphere</th></tr></thead><tbody><tr><td rowspan="3">0.10; 0.25</td><td>1400</td><td>5</td><td>Ar; Ar/H<sub>2</sub> 4%</td></tr><tr><td>1500</td><td>1; 5; 10</td><td>Ar; Ar/H<sub>2</sub> 4%</td></tr><tr><td>1600</td><td>0; 5; 10</td><td>Ar; Ar/H<sub>2</sub> 4%</td></tr></tbody></table>

In order to calculate accurately the relative density of the samples, XRD measurements were performed on the samples after sintering to determine the unit cell parameter. The patterns collected for samples with x<sub>Ce</sub> = 0.10 are summarized in **Figure 3**, while those obtained for x<sub>Ce</sub> = 0.25 are supplied as supplementary material (Figure S2). For both data series, all the patterns exhibit the classical XRD lines of the fluorite-type structure of UO₂.
although slight differences can be detected between the different diffractograms, both in terms of relative intensity and of XRD peaks position. These variations are partly due to the physical form of the sample itself, as the measurements were made on sintered pellets which can induce textural effects such as preferential orientation of certain grains. Nevertheless, the main explanation for these differences lies in the chemical characteristic of the samples, as the redox speciation of U and Ce varies depending on the sintering conditions. Indeed, the unit cell parameter of $U_{1-x}Ce_xO_{2+\delta}$ oxides is well-known to depend on the O/M stoichiometry in the sample, which has already been shown to vary as a function of the atmosphere, the cerium content, and the sintering temperature [23, 32]. As such, the empirical relation originally proposed by Sali et al. [32], and recently revised by Massonnet et al. [23] was used with:

$$a (\AA) = 5.4704 - 0.060 \times x_{Ce} - 0.07 \times \delta \quad (3.)$$

The results obtained are summarized in Table 2, and show a very good agreement with previous results obtained by HERFD-XANES measurements [23]. These latter were performed at room temperature, after the various sintering heat treatments. All the samples sintered under Ar/H₂ atmosphere exhibit O/M ratios very close to 2.00, owing to the associated uncertainty. The unit cell parameters obtained are also in line with those expected from the formation of stoichiometric solid solutions $U_{1-x}Ce_xO_{2.00}$ according to Vegard's law [33]. Thus, it can be concluded that both uranium and cerium ended up to be almost completely tetravalent under these operating conditions. When the sintering was performed under argon, hyper-stoichiometric samples were obtained (i.e. O/M > 2.00). In fact, our previous work using HERFD-XANES measurements showed that, for a similar cerium content, the compounds prepared under argon atmosphere systematically present multiple valences of the cations, i.e. a mixture of Ce(III) and Ce(IV) on the one hand, and of U(IV) and U(V), on the other hand [23]. Moreover, the U(V) content always appears higher than that of Ce(III), leading to an overall hyper-stoichiometry in oxygen. Nevertheless, the deviation from the ideal oxygen stoichiometry seems to decrease with both the temperature and the cerium content, in good agreement with the U-Ce-O ternary diagram [34, 35]. This is also in good agreement with previous results showing that uranium average oxidation state in $U_{0.74}Ce_{0.26}O_{2+\delta}$ decreased from 4.35 to 4.06 when raising the sintering temperature from 1300 to 1500°C, while that of cerium changed from 3.54 to 4.00 [23]. Finally, the determination of O/M ratios allowed the calculation of the theoretical density of our materials, taking into account the redox speciation of the cations within the samples. In our case, the latter only
generate slight variations of the density, but must be carefully considered to get accurate values of relative densities when building sintering maps.

<table><caption>**Table 2.** Structural features obtained from refinement of XRD data. O/M ratios were calculated using the empirical formula proposed by Massonnet *et al.* [23], and are supplied with a ± 0.02 uncertainty. Theoretical densities (d, in g.cm⁻³) were determined from the unit cell parameter values.</caption><thead><tr><th rowspan="2">x<sub>Ce</sub></th><th rowspan="2">Sintering conditions</th><th colspan="3">Ar - 4% H<sub>2</sub></th><th colspan="3">Ar</th></tr><tr><th>a (Å)</th><th>d (g.cm<sup>-3</sup>)</th><th>O/M</th><th>a (Å)</th><th>d (g.cm<sup>-3</sup>)</th><th>O/M</th></tr></thead><tbody><tr><td rowspan="3">0.10</td><td>1400°C - 5h</td><td>5.4644(1)</td><td>10.59</td><td>2.00</td><td>5.4590(1)</td><td>10.67</td><td>2.08</td></tr><tr><td>1500°C - 10h</td><td>5.4654(2)</td><td>10.58</td><td>1.99</td><td>5.4595(1)</td><td>10.66</td><td>2.07</td></tr><tr><td>1600°C - 10h</td><td>5.4639(1)</td><td>10.59</td><td>1.99</td><td>5.4603(2)</td><td>10.65</td><td>2.06</td></tr><tr><td rowspan="3">0.25</td><td>1400°C - 5h</td><td>5.4563(1)</td><td>10.03</td><td>1.99</td><td>5.4537(1)</td><td>10.07</td><td>2.02</td></tr><tr><td>1500°C - 10h</td><td>5.4554(1)</td><td>10.04</td><td>2.00</td><td>5.4521(1)</td><td>10.09</td><td>2.04</td></tr><tr><td>1600°C - 10h</td><td>5.4558(1)</td><td>10.04</td><td>1.99</td><td>5.4528(1)</td><td>10.08</td><td>2.03</td></tr></tbody></table>

<figure><img src="image_4.png" /><figcaption>**Figure 3.** XRD patterns of the U<sub>0.9</sub>Ce<sub>0.1</sub>O<sub>2+δ</sub> sintered pellets prepared under Ar/H<sub>2</sub> or Ar at 1400°C – 5h (black); 1500°C – 10h (blue); and 1600°C – 10h (red).</figcaption></figure>
For the lowest cerium content studied ($x_{Ce} = 0.10$), the measured densities appeared to be globally high, and typically above 90% TD (Figure 4a), even after a heat treatment of 5 hours at 1400°C. When heating under argon, an increase of the sintering temperature led to a set of values close to 94% TD, in very good agreement with the dilatometric study that shows a plateau in the linear shrinkage between 1400°C and 1600°C. In Ar/H₂ atmosphere, similar results were obtained at 1500°C, although the longest heat treatment performed seems to induce a de-densification, which is not observed by dilatometry. Nevertheless, and contrary to what was observed under argon, increasing the temperature to 1600°C led to an increase in density which seems to be very close to the calculated value, whatever the heating time considered.

The results obtained for $x_{Ce} = 0.25$ show overall lower relative density values, ranging from 82 to 98% TD (Figure 4b). The incorporation of cerium thus appears to be unfavourable for sintering, although the dilatometric study shows a decrease in the temperature associated with the maximum shrinkage rate. Such behaviour has already been reported for mixed oxides prepared by powder metallurgy, and frequently attributed to the homogenisation of the cation distribution prior to densification [9]. In this work, very homogeneous powders were used, reducing the influence of solid solution formation on the sintering mechanisms. The lower density observed for $x_{Ce} = 0.25$ is then probably linked to a slowest diffusion of cerium in the samples.

<figure><img src="image_5.png" /><figcaption>**Figure 4.** Variation of the relative density of $U_{1-x}Ce_xO_{2+\delta}$ sintered samples during sintering at 1400 (blue triangles), 1500 (red circles) and 1600°C (black squares) under Ar (full symbols) or Ar/H₂ atmosphere (open symbols) for $x_{Ce} = 0.10$ (a) and $x_{Ce} = 0.25$ (b).</figcaption></figure>
One can also notice that for both compositions, higher densities were generally obtained under Ar/H₂, especially at the highest temperature investigated. This observation can be linked to the changes in the O/M ratio in the samples during the heat treatment. Indeed, Dehaudt *et al.* [36] showed that for small deviations from the oxygen stoichiometry (typically 0.01 < x < 0.05 in UO₂+x), uranium diffusion increases with x. For higher O/U ratios, sintering mechanisms evolve due to the formation of U₄O₉-y and the possible activation of surface diffusion, leading the activation energy to increase. During this study, it is probable that the higher P(O₂) in argon atmosphere led to the formation of U₄O₉-y clusters in the samples, thus affecting the final density.

The SEM micrographs of the sintered pellets, a selection of which is shown in **Figure 5**, are in good agreement with the trends identified from the dilatometric study and the density measurements. In fact, all the samples are composed of polygonal grains, characteristic of sintered ceramics, although a significantly higher porosity can be observed for compounds containing 25% cerium and sintered under argon atmosphere. Despite some cracks and polishing scratches, the images were processed through the SEraMic plugin implemented in the Fiji image analysis software (see experimental procedure in [27], and typical results provided as supplementary data in **Figure S3**) and show very clear differences in terms of grain size depending on the atmosphere considered. Thus, grain growth is favoured under argon, with average grain sizes generally 5 to 10 times larger than when sintering in a reducing atmosphere (**Table 3**). This result is consistent with the numerous studies reported in the literature on the UO₂ end-member and associated solid solutions, where an increase in the partial pressure of oxygen in the atmosphere used for heat treatment systematically leads to an increase in grain size [30, 37].

<table><caption>**Table 3.** Average grain sizes (equivalent circular diameters, in µm) of U₁-xCeₓO₂+δ sintered samples prepared in this work, expressed with a ± 2σ standard deviation.</caption><thead><tr><th rowspan="2">T (°C)</th><th rowspan="2">t (h)</th><th>x<sub>Ce</sub> = 0.10</th><th rowspan="2">Ar</th><th>x<sub>Ce</sub> = 0.25</th><th rowspan="2">Ar</th></tr><tr><th>Ar/H<sub>2</sub></th><th>Ar/H<sub>2</sub></th></tr></thead><tbody><tr><td>1400</td><td>5</td><td>0.9 ± 0.4</td><td>6.0 ± 3.3</td><td>0.8 ± 0.3</td><td>5.4 ± 2.9</td></tr><tr><td rowspan="2">1500</td><td>1</td><td>0.7 ± 0.3</td><td>6.8 ± 4.1</td><td>0.8 ± 0.3</td><td>5.3 ± 2.6</td></tr><tr><td>5</td><td>1.5 ± 0.6</td><td>7.4 ± 4.5</td><td>1.1 ± 0.5</td><td>8.9 ± 5.9</td></tr><tr><td rowspan="3">1600</td><td>10</td><td>1.8 ± 1.0</td><td>9.2 ± 6.2</td><td>1.9 ± 1.0</td><td>12.3 ± 9.1</td></tr><tr><td>0</td><td>1.3 ± 0.2</td><td>12.3 ± 7.9</td><td>1.8 ± 1.0</td><td>5.7 ± 6.6</td></tr><tr><td>5</td><td>4.5 ± 2.4</td><td>18.0 ± 11.3</td><td>3.7 ± 2.8</td><td>17.4 ± 13.0</td></tr></tbody></table>
<figure><img src="image_6.png" /><figcaption>**Figure 5.** SEM micrographs of U$_{1-x}$Ce$_x$O$_{2+\delta}$ samples sintered under various conditions of heat treatment and atmosphere.</figcaption></figure>
The density and grain size values discussed above were also used to plot the sintering maps shown in **Figure 6**. For clarity sake, the error bars have been omitted from these graphs, but can be found in **Figure 4** and **Table 3**, respectively for the relative density and grain size values. To allow a clear comparison of the collected data, the sintering trajectories were plotted for a constant chemical composition on the one hand (**Figures 6a and b**), and a constant sintering atmosphere (**Figures 6c and d**), on the other hand. For each of the two cerium contents considered, the differences illustrated by the SEM images are clearly highlighted. Thus, the use of a reducing atmosphere leads to almost complete densification of the ceramic, albeit with little grain growth. Conversely, samples sintered under argon have much larger grain sizes, but densification appears to be limited. Furthermore, the maximum density value decreases slightly with the cerium content, from 95% TD for $x_{Ce} = 0.10$ to 92% TD for $x_{Ce} = 0.25$.

<figure><img src="image_7.png" /><figcaption>**Figure 6.** Sintering maps of $U_{1-x}Ce_xO_{2+\delta}$ samples. Data are compared for similar compositions with $x_{Ce} = 0.10$ (a) and $x_{Ce} = 0.25$ (b) (atmosphere : Ar/H$_2$ - ■ and Ar - ●); and similar sintering atmospheres, i.e. Ar/H$_2$ (c) and Ar (d) ($x_{Ce} = 0.1 - \bullet$ and $x_{Ce} = 0.25 - \bigcirc$). Error bars were omitted on purpose to allow better</figcaption></figure>
vizualisation of the data. Dashed lines are presented only as eye-guides and do not result from any mathematical fit.

Comparison of the data obtained in a reducing atmosphere also shows that all the measurement points can be grouped into a single trajectory, despite a slight dispersion, probably due to the small grain size. This single trajectory implies that a given relative density value corresponds to a single grain size, whatever the conditions chosen in terms of temperature and duration of the sintering heat treatment, but also in terms of chemical composition. This peculiarity, which has already been reported for several oxides [38, 39], including oxygen-stoichiometric (U,Pu)O₂.₀₀ [40], therefore implies that the mechanisms driving densification and grain growth do not evolve with the cerium content. In contrast to this observation, the data obtained after sintering in argon atmosphere clearly show two different trajectories depending on the cerium content considered. These differences result from the complex redox interplay between the cations and the variation of the U(V)/Ce(III) charge compensation as a function of temperature and cerium content in the sample [35].

### 3.3. Grain growth mechanisms

In order to refine our understanding of the mechanisms controlling grain growth and leading to the microstructural differences highlighted on the sintering maps, a systematic study of the grain growth of U₁-xCeₓO₂+δ solid solutions was carried out by varying the sintering time at 1500°C and 1600°C. As previously evidenced, these two temperatures correspond to the range of sintering maps where grain growth is the most efficient and takes precedence over densification. By way of example, **Figure 7** shows the grain size distribution for samples sintered under argon, the results obtained under Ar-4%H₂ being presented as supplementary material (**Figure S4**). It appears that for the two cerium contents considered, and whatever the heat treatment duration between 1 and 10 hours, the normalized grain size distribution systematically follows an identical sigmoidal trend. This so-called self-similarity results from the invariance of each grain size class as a function of time (with a constant ratio of G/Ḡ) [41].

Growth can therefore be considered normal, which *de facto* rules out the existence of exaggerated growth phenomena during the various heat treatments carried out. Furthermore, similar results were obtained for the two atmospheres studied, indicating that the variation in
the O/M ratio (under the effect of the redox speciation of the U and Ce cations), is not, in the range covered by this study, likely to cause exaggerated grain growth.

Based on a normal grain size distribution, growth can be expressed by the following relationship:

$$G^n - G_0^n = k_0 \times e^{\left(\frac{-Ea}{RT}\right)} \times t \quad (4.)$$

where G is the average grain size at time t, G₀ is the initial grain size, k₀ is a rate constant and n is an integer characteristic of the prevailing diffusion mechanism involved in grain growth [42].

Since the synthesis route used leads to the preparation of nanometric powders, G₀ can be neglected in front of G. The expression for grain growth can then be simplified, and it becomes possible to determine the value of the exponent n, characteristic of the grain growth mechanism, from the representation of ln(G) as a function of ln(t):

$$n \ln(G) = \ln(t) - \frac{Ea}{RT} + \ln(k_0) \quad (5.)$$

The variation of ln(G) was then examined as a function of ln(t) considering three different thermal treatment durations (Figure 8). The resulting plots were fitted using a linear regression. For most of the datasets, correlation coefficients R² > 0.96 were obtained, while three samples led to less satisfying results, i.e. for xCe = 0.10 when working under argon, and for xCe = 0.25 under Ar/H₂ at 1500°C. Still, two different behaviours can be observed depending on the conditions considered. When using Ar/H₂ atmosphere, and for all the samples prepared for xCe = 0.25, which correspond to a final oxygen stoichiometry close to O/M = 2.00, a value of n ≈ 2 is systematically obtained. This corresponds to a growth mechanism driven by grain boundary motion within a pure material. This situation thus corresponds to a total solubility of cerium in the UO₂ lattice, in good agreement with the predominance of U(IV) and Ce(IV) in this series of samples, and with the existence of an ideal and complete solid solution in the UO₂-CeO₂ binary diagram [33].
<figure><img src="image_8.png" /><figcaption>**Figure 7.** Conservation of grain size distribution for U₁-xCeₓO₂+δ samples sintered under argon atmosphere, with xCe = 0.10 (a,b) and xCe = 0.25 (c,d): T = 1500°C during 1h (▼), 5h (♦), 10h (▲), and T = 1600°C during 0h (■), 5h (●) and 10h (▲).</figcaption></figure>

Conversely, the data obtained for the sintering of U₀.₉₀Ce₀.₁₀O₂+δ under argon led to very low R² values during the linear fitting procedure, resulting in very high and questionable values of n, which are even higher than those predicted by the models usually considered. The result obtained therefore has no physical meaning [43], and shows that grain growth under these conditions of chemical composition and atmosphere can no longer be described by a power law. A similar result was already reported for UO₂ samples doped with large quantities of Cr₂O₃, leading to the appearance of exaggerated growth phenomena [43]. In the present case, no such phenomenon was observed, but drastic grain growth was still reported. The probable presence of a large fraction of U(V) at high temperature within the sample under these conditions [35] therefore strongly modifies the diffusion processes that prevail during sintering, for example by activating surface diffusion, or evaporation-condensation mechanisms leading to the control of grain growth by the pores [44, 45].
<figure><img src="image_9.png" /><figcaption>**Figure 8.** Variation of ln G versus ln t during the sintering of U$_{1-x}$Ce$_x$O$_{2+δ}$ samples with x$_{Ce}$ = 0.10 (a) and x$_{Ce}$ = 0.25 (b) at T = 1500°C (black) or 1600°C (red) under Ar (full symbols) or Ar/H$_2$ (open symbols) atmosphere. The value of the n exponent determined is indicated for each sintering condition.</figcaption></figure>

### 3.4. Activation energy

To complete the study of sintering mechanisms, the activation energy associated with the densification process was determined in a final step. For this purpose, the constant heating rate method (CHR), already used in the literature for the study of actinide oxides [29, 36, 40, 46], was selected. This latter is based on the expression of the densification rate, which can be separated into terms depending on temperature, grain size and density, such as :

$$ \frac{d\rho}{dt} = A \times \frac{f(\rho)}{T \times G^n} \times e^{-\frac{Ea}{RT}} \quad (6.) $$

Where A is a constant, f(ρ) is a function dependent only on density, G is the average grain size, and n is an exponent characteristic of the predominant diffusion mechanism. In non-isothermal sintering experiments, the following relationship can then be obtained using constant values of heating rate:

$$ \ln [T \times \frac{d\rho}{dT} \times \frac{dT}{dt}] = -\frac{Ea}{RT} + \ln[f(\rho)] + \ln(A) + n \times \ln(G) \quad (7.) $$

The activation energy can then be deduced from the plot of Ln [T × (dρ/dT) × (dT/dt)] versus 1/T, provided that the data is recorded at constant values of ρ and G. The sintering map plot
has previously shown that this condition is satisfied, with each relative density value corresponding to only one grain size, whatever the sintering conditions for a given cerium content. The different data points associated to an arbitrarily defined value of ρ are then obtained by varying the heating rate during the dilatometry experiment. The value of ρ is deduced from the linear shrinkage of the sample according to :

$$ \rho = \left[ \frac{1}{1 - \frac{\Delta L}{L_0}} \right]^3 \times \rho_0 \quad (8.) $$

This relationship assumes isotropic shrinkage and negligible contribution of creep induced by the contact dilatometer. This point has been checked by comparing diameter/height ratios between green and sintered pellets (see **Table S2** supplied as supplementary material). Equation 8 also implies the conservation of the chemical composition of the sample during sintering. Under these conditions, the activation energy associated with the sintering of U₁-xCeₓO₂+δ solid solutions could only be determined under reducing atmosphere (Ar-4%H₂), as the use of argon led to a significant change in the O/M ratio during heat treatment. The data obtained for three heating rates (2, 5 and 10°C.min⁻¹) and considering 4 density values (60, 65, 70 and 75% TD) are shown in **Figure 9**.

<figure><img src="image_10.png" /><figcaption>**Figure 9.** Determination of the apparent activation energy for the densification of U₁-xCeₓO₂.₀₀ samples under Ar-4%H₂ with x<sub>Ce</sub> = 0.10 (a) and 0.25 (b). The data were extracted at 4 different densities for each dataset - 60 % (■), 65 % (●), 70 % (▲), 75 % (▼) – considering three heating rate values (2, 5 and 10°C.min⁻¹).</figcaption></figure>
From these plots, the mean activation energy reaches 265 ± 40 kJ.mol⁻¹ for x<sub>Ce</sub> = 0.10, and 320 ± 70 kJ.mol⁻¹ for x<sub>Ce</sub> = 0.25. Given the associated uncertainty, these two values can be considered to be similar, which appears to be in good agreement with the unique trajectory highlighted on the sintering maps. In addition, these values appear to be significantly lower than those reported in the literature for UO₂ and (U,Pu)O₂ mixed oxides, with no values reported to our knowledge for (U,Ce)O₂ compounds (Table 4). Only the value reported by Lahiri *et al.* seems to be in agreement with our results, but in this case the authors did not provide any clear evidence for an accurate measurement of the final O/M ratio [47].

<table><caption>**Table 4.** Values of activation energies obtained during this work for the sintering of U₁ₓCeₓO₂.₀₀ solid solutions under Ar-4%H₂. The values are compared with selected data coming from the literature, obtained by the CHR method.</caption><thead><tr><th>Sample</th><th>Ea (kJ.mol<sup>-1</sup>)</th><th>Reference</th><th>Sample</th><th>Ea (kJ.mol<sup>-1</sup>)</th><th>Reference</th></tr></thead><tbody><tr><td>UO<sub>2.00</sub></td><td>429 ± 8</td><td>[36]</td><td>U<sub>0.70</sub>Pu<sub>0.30</sub>O<sub>2.00</sub></td><td>482</td><td>[48]</td></tr><tr><td>UO<sub>2.09</sub></td><td>242 ± 6</td><td>[36]</td><td>U<sub>0.89</sub>Pu<sub>0.11</sub>O<sub>2.00</sub></td><td>635 ± 25</td><td>[46]</td></tr><tr><td>UO<sub>2.17</sub></td><td>299 ± 9</td><td>[36]</td><td>U<sub>0.85</sub>Pu<sub>0.15</sub>O<sub>2.00</sub></td><td>528 ± 7</td><td>[40]</td></tr><tr><td>UO<sub>2.00</sub></td><td>287</td><td>[47]</td><td>U<sub>0.85</sub>Am<sub>0.15</sub>O<sub>2±δ</sub></td><td>580 ± 8</td><td>[29]</td></tr><tr><td>U<sub>0.90</sub>Ce<sub>0.10</sub>O<sub>2.00</sub></td><td>265 ± 40</td><td>This work</td><td>U<sub>0.75</sub>Ce<sub>0.25</sub>O<sub>2.00</sub></td><td>320 ± 70</td><td>This work</td></tr></tbody></table>

## 4. Discussion

All the results presented in this study show a clear difference in the sintering behaviour of U₁ₓCeₓO₂+δ solid solutions, depending on the atmosphere used. Under Ar/H₂ atmosphere, XRD analysis confirms that the sintered samples obtained are stoichiometric in oxygen, with an O/M ratio very close to 2.00, while previous HERFD-XANES measurements showed that these samples are exclusively composed of U(IV) and Ce(IV) [23]. Nevertheless, at high temperature, cerium is expected to slightly reduce into Ce(III) (typically until O/M = 1.95 at 1000°C for x = 0.1) [35], leading to a solid solution with fluorite-like structure with few defects. This results in a higher sintering temperature, in good agreement with the results previously reported in the literature for UO₂, where the use of a reducing atmosphere leads to an increase in the temperature required for a complete densification [10]. The samples
prepared under Ar/H₂ in the course of this study also show a dense, small-grain microstructure, on which the cerium content has little influence. The synthesis route used, which leads to very homogeneous solid solutions, has thus favoured the predominance of a single sintering mechanism, illustrated by the unique trajectory observed on the sintering map. Simultaneously, grain growth follows a classical power law with exponent n ≈ 2, and then appears to be controlled by grain boundaries motion, without any strong solute drag effect associated with the precipitation of Ce-based secondary phases in the material. This result is in very good agreement with the findings of Tocino *et al.* [49], who probed the grain boundaries of several (U,M)O₂±δ solid solutions prepared by oxalic precipitation and sintered under reducing conditions, using TEM-EDS. When the dopant was heterovalent, like in the case of neodymium, a segregation of the latter was observed at the grain boundary. Conversely, doping with tetravalent cations, such as thorium or cerium, led to a homogeneous chemical composition between the grains and the boundaries. The sintered pellets prepared in our study are likely to behave the same way, owing to the similarities between the preparation methods (wet chemistry processes), and the predominance of U(IV) and Ce(IV) in the samples.

The activation energy associated with sintering was also found to be significantly lower than the values reported in the literature. In the case of actinide oxides, a decrease in activation energy due to sintering is generally associated with a change in oxygen stoichiometry. In our case, this modification of the O/M ratio probably occurs through the reduction of Ce(IV) into Ce(III) at high temperature [35]. Moreover, this decrease in the value of Ea is probably enhanced by the use of nanometric powders, as evidenced by the significant decrease in temperature leading to complete densification of the samples. Such a variation in activation energy has already been observed for other oxide ceramics sintered from nanopowders, such as Y-stabilized ZrO₂ or Al₂O₃ [50, 51]. Furthermore, the use of homogeneous starting powders also helps to reduce the energy cost associated with the formation of the solid solution. Indeed, this latter phenomenon is usually reported to result in an increase in the sintering temperature of mixed oxides when starting from heterogeneous mixtures (i.e. typically for powder metallurgy processes) [29]. The Ea values obtained in this study, which are comparable to those obtained using advanced sintering techniques such as SPS (close to 100 kJ.mol⁻¹ for UO₂ [52]), thereby corroborating the synthesis route's potential for the fabrication of dense, homogeneous model materials for nuclear fuels.

The microstructure of the samples prepared in argon differs significantly from those obtained in a reducing atmosphere. The higher value of P(O₂) leads to a slightly lower
densification of the pellets, but a much larger grain size. This latter feature is mainly linked to
an increase in global diffusion coefficients due to the formation of oxygen interstitials defects
associated to the partial oxidation of U(IV) to U(V) [53], evidenced by the O/M ratios
exceeding 2.00 determined for these samples at room temperature, and should reach even
higher values at high temperature following thermodynamic calculations (O/M ≈ 2.15 at
1000°C for x = 0.10 with P(O₂) = 10⁻⁶ atm.) [35]. However, this oxidation can occasionally
lead to de-densification phenomena, known as solarisation. These were recently detailed by
Miranda *et al.* for a MOx sample with the composition U₀.₈₉Pu₀.₁₁O₂+x, and a dioxygen partial
pressure close to that used in this work during argon treatments (P(O₂) ≈ 10⁻⁶ atm.) [54]. The
authors describe a heterogeneous microstructure, with a grain size that is half as small at the
periphery as at the centre of the pellet, and the presence of over-oxidised micro-domains with
the M₃O₇ type (M = U, Pu). However, these characteristics were not observed during the
present study. In fact, the average grain size, resulting from the analysis of more than 1000
grains distributed in different zones of the sample, does not show any marked variation
between the centre and the periphery of the pellet. Furthermore, the XRD analysis does not
reveal the presence of secondary phases within the samples. Thus, only increased porosity is
observed under argon, and might be correlated to the slight dedensification observed by
dilatometry in some cases under these conditions. The solarisation effect thus appears to very
limited in this study. As the conditions in terms of atmosphere and cation composition are
close to that used by Miranda *et al.* (with Ce mimicking Pu herein), it is likely that
dedensification is hindered due to the characteristics of the starting powder, and particularly
to the very high homogeneity of the cation distribution within the samples which limits the
formation of phases of higher oxygen stoichiometry such as M₃O₇, which were not observed
in our study.

If the general microstructural features observed for samples prepared under argon
remains similar, two distinct sintering paths are observed on the sintering maps depending on
the cerium content considered. Therefore, if densification appears to be adversely affected by
the presence of cerium, this latter seems to lead to a slightly larger maximum grain size. In
order to assess the role of cerium, it is necessary to consider it in two distinct temperature
ranges. At the lowest temperature studied (1400°C) and for the shortest heating times at
1500°C, the evolution of the microstructure is mainly marked by densification. This
temperature range also corresponds to the domain in which the presence of U(V)/Ce(III) is
greatest in the sample with composition xCe = 0.25, as shown in our previous work [23]. For
extended heating periods at 1500°C and 1600°C, microstructural evolution is predominantly
associated with grain growth. At these temperatures, the final O/M ratio returned to a value close to the stoichiometry of 2.00 for $x_{Ce} = 0.25$, while notable portions of U(V) and Ce(III) remained in the $x_{Ce} = 0.10$ sample. Consequently, the presence of these aliovalent cations, in conjunction with that of point defects in the crystal lattice, is likely to affect the diffusion of species and therefore the development of the microstructure differently, depending on the cerium content considered.

## 5. Conclusion

The impact of atmosphere and cerium content on the sintering of $(U_{1-x}Ce_x)O_{2+\delta}$ solid solutions was studied using nanometric, homogeneous powders, minimizing biases from solid solution formation during heat treatment. The observed effects mainly stem from variations in cation redox speciation during sintering. XRD measurements estimated the O/M (M = U + Ce) ratio in sintered samples, allowing for correlations between microstructure and U(IV)/U(V) and Ce(III)/Ce(IV) speciation, using a sintering map approach.

Ar/H₂ atmosphere maintained ideal oxygen stoichiometry (O/M = 2.00) with predominant U(IV) and Ce(IV), resulting in dense ceramics with limited grain size. In contrast, argon atmosphere caused partial uranium oxidation, leading to Ce(III) for charge compensation. Still, hyper-stoichiometric oxygen content was systematically measured, which increased structural defects and diffusion, favoring grain growth but limiting densification. Cerium content is then a key-parameter, regulating defect formation in conjunction with P(O₂) value.

Sintering maps aligned with observed grain growth mechanisms in $(U_{1-x}Ce_x)O_{2+\delta}$ solutions. If the growth appeared mainly controlled by the motion of the grain boundaries, it was shown that significant deviations from O/M = 2.00, linked with the presence of Ce(III) and U(V), altered kinetics, preventing description by conventional models. In return, redox speciation changes under argon precluded activation energy determination, while reducing conditions yielded values of 260-320 kJ.mol⁻¹, lower than those reported for stoichiometric $(U_{1-x}Pu_x)O_{2.00}$, indicating the powders' reactivity.

Combination of synthesis method, chemical composition, and sintering conditions enabled preparation of solids with various microstructures. This work offered insights into $U_{1-x}Ce_xO_{2+\delta}$ sintering mechanisms and produced model materials with controlled cation
distribution, redox speciation, and microstructure, suitable for studying properties of interest such as chemical durability or thermos-physical data.

**Acknowledgments.** The authors would like to thank J. Lautru and for performing SEM observations and M. Munoz for her he.lp in the determination of Ea values. 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 Program under grant agreement n°755171).

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