Role of Microstructure and Surface Defects on the Dissolution Kinetics of CeO 2 , a UO 2 Fuel Analogue

: The release of radionuclides from spent fuel in a geological disposal facility is controlled by the surface mediated dissolution of UO 2 in groundwater. In this study we investigate the in ﬂ uence of reactive surface sites on the dissolution of a synthesized CeO 2 analogue for UO 2 fuel. Dissolution was performed on the following: CeO 2 annealed at high temperature, which eliminated intrinsic surface defects (point defects and dislocations); CeO 2 ‑ x annealed in inert and reducing atmospheres to induce oxygen vacancy defects and on crushed CeO 2 particles of di ﬀ erent size fractions. BET surface area measurements were used as an indicator of reactive surface site concentration. Cerium stoichiometry, determined using X-ray Photoelectron Spectroscopy (XPS) and supported by X-ray Di ﬀ raction (XRD) analysis, was used to determine oxygen vacancy concentration. Upon dissolution in nitric acid medium at 90 ° C, a quanti ﬁ able relationship was established between the concentration of high energy surface sites and CeO 2 dissolution rate; the greater the proportion of intrinsic defects and oxygen vacancies, the higher the dissolution rate. Dissolution of oxygen vacancy-containing CeO 2 ‑ x gave rise to rates that were an order of magnitude greater than for CeO 2 with fewer oxygen vacancies. While enhanced solubility of Ce 3+ in ﬂ uenced the dissolution, it was shown that replacement of vacancy sites by oxygen signi ﬁ cantly a ﬀ ected the dissolution mechanism due to changes in the lattice volume and strain upon dissolution and concurrent grain boundary decohesion. These results highlight the signi ﬁ cant in ﬂ uence of defect sites and grain boundaries on the dissolution kinetics of UO 2 fuel analogues and reduce uncertainty in the long term performance of spent fuel in geological disposal.


INTRODUCTION
Spent nuclear fuel is a heterogeneous ceramic material composed primarily of UO 2 , with a minor component of actinides and fission products. The internationally supported strategy for the safe disposal of this nuclear waste material is within a geological disposal facility, 1 where the release of radionuclides to the environment will be dominated by the interaction of the UO 2 matrix with groundwater. To assess the long-term performance of the geological disposal site toward the containment of radionuclides, a safety case is being prepared, which assesses the mechanism and kinetics of fuel dissolution; accordingly, a large number of laboratory experiments have been focused on determining the dissolution kinetics of UO 2 under a wide variety of temperature and redox conditions. 2,3 However, dissolution rates determined from natural uraninite (UO 2 ) ore weathering indicate that rates measured in the laboratory are orders of magnitude greater than in nature. 4,5 This phenomenon has been widely considered and is attributed to a number of factors including artifacts of specimen preparation, solution saturation state, and changes in surface area with time. 6 Clearly, it is important to the development of a robust postclosure safety case for spent fuel disposal that such uncertainty is reduced.
In the current study, we consider the role of "energetically reactive sites", which contain fewer, and weaker, chemical bonds than those on defect-free surfaces or in the bulk, in the determination of laboratory dissolution rates of spent UO 2 fuel. These sites, which may include natural crystal defects (point defects and dislocations), grain boundaries, or sample preparation-induced artifacts (e.g., polishing scratches or sharp edges on crushed particles), comprise atoms that have greater reactivity than those in the defect-free surfaces or in the bulk, thus may dissolve more rapidly. 7,8 For example, the dissolution of UO 2 and a CeO 2 analogue for UO 2 have been found to be influenced by sample crushing 9,10 and polishing; 11 dissolution rates were overestimated by 3 orders of magnitude due to the reactive surface sites induced through these sample preparation techniques. 11 Natural defects, especially randomly distributed oxygen vacancy defects, dominate the lattice structure of spent UO 2 fuel, due to the incorporation of trivalent rare earth fission products in the UO 2 lattice. 12 It has been hypothesized that the presence of such energetically reactive defect sites may influence the dissolution rate. 13−18 However, the extent of such an effect on the overall dissolution rate is difficult to observe when other factors, such as the enhanced solubility of U(VI) over U(IV), strongly influence the dissolution behavior. Recent work by the current authors has shown that these seemingly minor features may significantly influence the initial dissolution rate of UO 2 fuel analogues 11,19 and, therefore, should be taken into consideration alongside other important factors (notably oxidation, solubility, and radiolysis) when understanding dissolution mechanisms of spent fuel.
In an attempt to preclude the dominant effects of U(IV) oxidation, the high solubility of U(VI) and radiolysis on the dissolution kinetics, we here report the role of energetically reactive features on the dissolution of a UO 2 analogue, CeO 2 , that was developed to closely resemble the microstructure of UO 2 fuel. 20 Both UO 2 and CeO 2 crystallize in the same fluoritetype structure (Fm3̅ m) and can be engineered to have similar grain sizes and crystallographically randomly orientated grains. We describe an evaluation of how energetically reactive sites, including intrinsic surface defects and oxygen vacancies, influence dissolution kinetics. Through quantification of these effects, we attempt to improve our understanding of the uncertainties associated with dissolution rates of spent fuel in geological disposal conditions.

EXPERIMENTAL METHODS
2.1. CeO 2 Preparation. Cerium dioxide monoliths were prepared according to Stennett et al., 20 at a sintering temperature of 1700°C. Monoliths were crushed using a percussion mortar and ball mill, sieved to four different size fractions, 25−50 μm, 75−150 μm, 300−600 μm, and 2−4 mm, and washed, all according to ASTM C1285 (the Product Consistency Test). 21 Prior to use, the particles were inspected by Scanning Electron Microscopy (SEM) to ensure no fine particles <1 μm in size remained adhered to particle surfaces. Particles in the size fraction 25−50 μm were subjected to further heat treatment; annealing in air was performed in a standard muffle furnace heated to 300, 400, 600, 800, 1000, and 1250°C at a ramp rate of 5°C min −1 and held for 4 h. Annealing in inert (Ar) and reducing (5% H 2 /95% N 2 ) atmospheres was performed in a standard tube furnace, sealed, and purged with gas for 2 h prior to heating to 1000°C at a ramp rate of 5°C min −1 and held for 4 h. Following dissolution, particles were dried by patting with tissue and placed in an inert-atmosphere desiccator prior to analysis.
2.2. Particle Characterization. The surface area of each crushed size fraction and the 25−50 μm heat-treated particles was determined using the Brunauer, Emmett, and Teller (BET) method, using a nitrogen adsorbate. Particles were degassed for 3 h at 200°C and analyzed using a Beckman Coulter SA3100 instrument. The surface oxidation state of annealed particles was determined using a Kratos Axis Ultra X-ray Photoelectron Spectrometer (XPS) with a monochromatic Al Kα source. The spectral intensities recorded were converted to surface oxidation state concentrations by first subtracting a Shirley-type background 22 and then obtaining accurate peak positions by fitting peaks using a mixed Gaussian/Lorenzian line shape. All photoelectron binding energies were referenced to C 1s adventitious contamination peaks at a binding energy of 285 eV.
Powder X-ray Diffraction (XRD) patterns were acquired using a Bruker D2 Phaser diffractometer operating in reflection mode at 30 kV and 10 mA with Cu Kα 1 radiation. Data were collected between 20 < 2θ < 60°at 2°min −1 and a step size of 0.02°. Rietveld analysis of phases identified in the diffraction patterns was performed using the refinement software, Topas (Bruker), and strain was calculated using the Double-Voigt approach. 23 Secondary electron images of particles were acquired using a Hitachi TM3030 SEM, operating at an accelerating voltage of 15 kV and a working distance of 18 mm.
2.3. CeO 2 Dissolution. Samples of 0.1 g of each size fraction of CeO 2 particles were placed in 50 mL PTFE vessels, which had been cleaned according to ASTM C1285. 21 Each vessel was filled with 40 mL of 0.01 M HNO 3 (pH 2.0), sealed, and placed within a Carbolite oven. For 25−50 μm CeO 2 particles with no annealing treatment, experiments were performed at 40, 70, and 90°C (±0.5°C). All other experiments were performed at 90 (±0.5)°C. Each experiment was performed in triplicate with duplicate blanks, and sampling was conducted at regular intervals from 0 to 35 days. During each sampling, an aliquot (1.2 mL) of the supernatant liquid in each vessel was removed and filtered (0.22 μm) prior to analysis by Inductively Coupled Plasma − Mass Spectroscopy (ICP-MS) (Agilent 4500 Spectrometer). Solution data expressed as the normalized weight loss (N L , expressed in g m −2 ) were calculated from the Ce concentrations after normalization by the surface area S (m 2 ) of the sample in contact with the solution (assuming that all the surface is "reactive") and by the mass loading of the element considered in the solid (i.e., f i is expressed as the ratio between the mass of the considered element and the overall mass of the leached sample), according to eq 1 24,25 where m i (g) corresponds to the total amount of the element i measured in the solution.
Derivation of eq 1 as a function of dissolution time gives the normalized dissolution rate of Ce (R L (Ce)), expressed in g m −2 d −1 ) 26 where C Ce (g L −1 ) is the concentration of Ce in solution, and V (L) is volume of leachate. In this expression, the f Ce and S values are usually assumed to remain almost constant during the leaching experiments, which can be considered as a valid assumption at the beginning of the dissolution tests for powdered samples.

RESULTS
3.1. Characterization of Defect Structures in CeO 2 . Particles from the 25−50 μm size fraction were annealed in air at temperatures ranging from 300−1250°C. One sample was analyzed without annealing for comparison. High temperature annealing in air lead to a reduction in surface area, as shown in Figure 1. For example, annealing at 600°C gave a surface area of 0.20 ± 0.01 m 2 g −1 , while at 1000°C the surface area was 0.11 ± 0.01 m 2 g −1 . We hypothesize that the surface area decrease reflects the removal of "sharp edges" and other intrinsic surface defects in the CeO 2 particles, during heating. When the annealing temperature was increased to the range 700 to 1250°C, a sharp drop in surface area was observed. This may be due to agglomeration of particles at these higher temperatures. Dissolution rate investigation was performed on samples annealed at 600 and 1000°C; both were representative of the removal of "sharp edges" and intrinsic surface defects, but samples annealed at 1000°C additionally represented particles with a significantly lower surface area.
An attempt to generate oxygen vacancies in particles of CeO 2 in the 25−50 μm size fraction was made by annealing at 1000°C in the absence of oxygen (inert or reducing environments). The creation of an oxygen vacancy in CeO 2 is accompanied by the release of two electrons from lattice O 2− , resulting in the reduction of Ce 4+ ions to Ce 3+ . 27 Reduction from CeO 2 to

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Research Article Ce 2 O 3 occurs through the formation of CeO 2-x intermediate phases; 28 to confirm the presence of oxygen vacancies, the oxidation state of Ce was determined using XPS, shown in Figure 2. Trivalent Ce was identified in the particle surfaces (top ∼10 nm), confirming that Ce 4+ reduction to Ce 3+ had occurred. The Ce 3d XPS data were resolved using ten components; 29 Table 1 describes each of the components found in the current study according to the accepted Burroughs nomenclature. 30 These data are in excellent agreement with previously published XPS data for partially reduced CeO 2 31,32 and show that samples annealed in an inert or reducing environment were not fully reduced to Ce 2 O 3 but contained a combination of identifiable contributions from both Ce 3+ and Ce 4+ oxidation states at the sample surface. This indicates the formation of partially reduced CeO 2 with a stoichiometry of CeO 2-x and the generation of oxygen vacancies. These defects have been previously characterized as Frenkel-type defects. 33 The fraction of Ce 3+ (denoted α) was determined from Ce 3d peak area analysis, according to eq 3. On the basis that half an oxygen vacancy is formed per Ce 3+ created, the deviation, x, from the ideal oxygen stoichiometry was determined for each sample, as shown in Table 2 Annealing in a reducing (H 2 /N 2 ) atmosphere resulted in CeO 2-x with the greatest Ce 3+ fraction (α = 0.370 ± 0.019) and a stoichiometry of CeO 1.82 , while annealing in an inert (Ar) atmosphere gave a higher Ce 3+ fraction than annealing in air under the same conditions (α = 0.221 ± 0.011 and α = 0.080 ± 0.004, respectively). As the Ce 3+ fraction is directly related to the concentration of oxygen vacancies generated, it can be assumed that the oxygen vacancy concentration is proportional to the Ce 3+ fraction of each sample.
The crystal structure of nonstoichiometric CeO 2-x was determined using X-ray diffraction. Because the samples were  Peak deconvolution was performed and labeled according to the accepted Burroughs nomenclature 30 for Ce 3d as described in Table 1.

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Research Article found to be chemically unstable upon exposure to air, they were loaded into the diffractometer within minutes of being removed from the annealing furnace. By comparison to the known correlation of the fluorite lattice parameter with the oxygen stoichiometry in the CeO 2-x system, 34 the three main diffraction peaks identified in Figure 3 were assigned to CeO 1.75 , CeO 1.81 , and CeO 2 . The second phase is in reasonable agreement with the XPS analysis of this sample, which gave a stoichiometry of CeO 1.82 ( Table 2). The CeO 1.75 phase was not identified by XPS; this may be due to the rapid oxidation, as described below. The spatial distribution of the phases within the samples was not investigated, however, since Ce 3+ species have previously been found to accumulate at grain boundaries within partially reduced CeO 2 , 35 grain boundaries may host CeO 1.75 and CeO 1.81 . The identification of these phases following annealing in a reducing atmosphere is consistent with the formation of oxygen vacancies. 34 With prolonged exposure to ambient conditions (air, for up to 200 h), the relative intensity of the peaks assigned to CeO 1.75, CeO 1.81 , and CeO 2 changed (Figure 3). Quantitative Rietveld analysis of the distribution of phases as a function of time is shown in Figure 4. Initially, the sample was composed of ∼15% CeO 1.75 , ∼68% CeO 1.81 , and ∼16% CeO 2 (±1.0%). After 56 h, CeO 1.75 was no longer observed, and the distribution of phases remained at 4.5 ± 0.9% CeO 1.81 and 95.2 ± 1.3% CeO 2 ( Figure  4) until 200 h. The increase in the content of oxygen, corresponding to a decrease in oxygen vacancies, was found to occur at a rate of (1.40 ± 0.14) × 10 −3 mol h −1 during the first 24 h of exposure to ambient conditions. This process was associated with a change in the volume of the fluorite unit cell, as calculated from Rietveld-refined lattice parameters. The fluorite unit cell was found to contract, from 167.62 ± 3.4 Å 3 for CeO 1.75 to 164.97 ± 3.30 Å 3 for CeO 1.81 and to 157.58 ± 3.15 Å 3 for CeO 2 . This volume reduction is consistent with the oxidation of Ce 3+ to Ce 4+ ; Ce 3+ has a larger ionic radius than Ce 4+ (1.03 and 0.97 Å, respectively). 36 Overall, the sample annealed in a H 2 /N 2 atmosphere underwent a 6% volume contraction within several hours of exposure to oxygen under ambient atmospheric conditions. The lattice strain, as calculated using Rietveld analysis of the CeO 2 phase, was found to significantly decrease during oxidation, from a value of ε = 0.092 ± 0.01 at 2 h to ε = 0.034 ± 0.01 after 200 h, consistent

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Research Article with the observed change in lattice volume. Due to the rapid nature of these chemical and structural changes, all dissolution experiments were performed within 30 min of sample annealing to minimize the effects of air oxidation.
3.2. CeO 2 Dissolution. Cerium dioxide dissolution experiments were performed under aggressive conditions (0.01 M HNO 3 , 90°C) to attain quantitative dissolution kinetic data within several weeks. It has been suggested that reduction of Ce 4+ to Ce 3+ may be induced by nitrous acid (HNO 2 ) formed through nitric acid instability at high acidity (>0.5 M); 13 however, this is not expected to influence the dissolution reaction in the current experiments, which were at an acidity much less than 0.5 M.
The dissolution of CeO 2 can be described by two distinct regimes, as shown in Figure 5; the first, rapid regime is far from solution saturation and thus represents the kinetically controlled dissolution rate, R k . The second regime is representative of near-solution saturation, controlled by the solubility of CeO 2 and concentration of Ce(OH) 2 2+ in solution. This is less rapid due to thermodynamic effects that occur close to equilibrium and is denoted R t . To understand the role of defects in the dissolution of CeO 2 , it was necessary to focus only on the kinetic regime of dissolution; therefore, we herein report R k only. Generally, the change between the kinetic and the thermodynamically controlled dissolution regimes occurred at ∼7 days, unless otherwise stated. Figure 5 shows the normalized mass loss of Ce (N L , g m −2 ) from nonannealed 25− 50 μm particles of CeO 2 as a function of time at 40, 70, and 90°C . The normalized dissolution rate of Ce was R k = (1.90 ± 0.74) × 10 −4 g m −2 d −1 at 90°C. The dependence of dissolution on temperature gave an activation energy of 30.4 ± 4 kJ mol −1 , assuming an Arrhenius-type relationship. This is consistent with previous work on CeO 2 and other fluorite-type dioxides such as ThO 2 and PuO 2 (E a = 20−37 kJ mol −1 ) 13,25,37 and is indicative of a surface-controlled dissolution mechanism.
3.3. Effect of Defect Annealing/Surface Area on CeO 2 Dissolution Kinetics. The dissolution rates of 25−50 μm particles of CeO 2 annealed in air, and nonannealed CeO 2 of four different particle sizes, are shown in Table 3 and Figure 6.
The surface area normalized dissolution rates were observed to increase with increasing surface area. This behavior is unexpected, since normalization to the surface area should result in similar dissolution rates. Samples of CeO 2 that were crushed and sieved to different size fractions clearly showed this correlation, with dissolution rates increasing from R k = (4.17 ± 1.13) × 10 −5 g m −2 d −1 for 2−4 mm particles to R k = (1.38 ± 0.28) × 10 −4 g m −2 d −1 for particles in the 75−150 μm size fraction. The exposure of grain boundaries during particle crushing may be responsible for enhancing the reactive surface area, resulting in the observed trend, as follows: each particle is composed of a number of grains, with a grain size of 5−30 μm. As the particle size decreases, from 2−4 mm to 75−150 μm, the ratio of particle size to the number of grains also decreases. Because the grain size remains constant, the shrinking size of the particle exposes more grain boundaries to the dissolution medium. Grain boundaries are known to preferentially dissolve due to the presence of a greater number of energetically

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Research Article reactive surface sites (e.g., defects) compared to the surfaces. 11 Once the smallest particle size is reached, each particle comprises only a few grains, with a high number of grain boundaries exposed to solution, which leads to the most rapid dissolution rates ( Figure 6). Similarly, thermally annealed particles of CeO 2 with the same particle size (25−50 μm) exhibited a factor of 7 decrease in their dissolution rate compared with nonannealed particles (R k = (2.98 ± 0.50) × 10 −5 g m −2 d −1 and (2.67 ± 0.30) × 10 −5 g m −2 d −1 , for 600 and 1000°C respectively), as shown in Figure  7. Because the reduction in surface area in these samples was associated with the high temperature annealing of intrinsic defects and sharp edges generated through sample crushing, it can be concluded that these energetically reactive features influence the dissolution kinetics. This is in agreement with the work of Claparede et al. 13 who found that increasing the sintering temperature of Th 1−x Ce x O 2 powders led to a reduction in dissolution rate, attributed to the elimination of crystal defects and amorphous domains. The current work extends this hypothesis to samples prepared by crushing, generating surface defects in the form of "sharp edges", as proposed by Corkhill et al. 11 3.4. Effect of Oxygen Vacancies on Dissolution Kinetics. For CeO 2 samples annealed in different atmospheres at 1000°C, the samples with the greatest oxygen vacancy content were found to dissolve at the most rapid rates. For example, the dissolution rate of CeO 2 annealed in Ar was slightly enhanced compared with CeO 2 annealed in air at the same temperature, by a factor of 2 ( Table 3). The dissolution of CeO 1.82 (annealed in H 2 /N 2 ) showed a significantly enhanced dissolution rate (Table 3, Figure 7). Samples of this material were analyzed by SEM at several time points during dissolution; in contrast to particles of stoichiometric CeO 2 , which did not change their shape or morphology upon 1 or 35 days of dissolution (Figure 8a−c), examination of the CeO 1.82 particles revealed a dramatic transformation. Prior to dissolution, these particles were 25−50 μm in size ( Figure  6d), but within 1 day they were observed to break apart into smaller fragments ∼5 μm in size, with a morphology suggestive of individual grains (Figure 8e). After 35 days of dissolution, some larger particles remained, but most of the sample had decomposed into single grain-sized fragments (Figure 8f). Postdissolution BET analysis of these samples after 1 day of dissolution gave a surface area of 2.49 ± 0.01 m 2 g −1 , an increase by a factor of 5 compared with the initial surface area ( Table 3). Normalization of the dissolution rate data to this surface area value gave a rate of R k = (4.06 ± 0.75) × 10 −4 g m −2 d −1 , 15 times greater than for air or Ar annealed samples of the same particle size (Figure 7). Due to the extremely rapid dissolution of this material, it was necessary to calculate the R k between 0 and 1 day of dissolution, after which time the

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Research Article normalized release of Ce was constant. When analyzed by XPS after 1 day of dissolution, these samples gave a surface stoichiometry of CeO 1.96 , which indicates that a rapid oxidation of CeO 2-x occurred, concurrent with a significant reduction in the oxygen vacancy content.  (4) where A is the solubility limit of CeO 2 , and b is the rate constant. Expanding eq 4 to account for the factors that are expected to contribute to the dissolution kinetics (surface area, oxygen vacancy content, and the different relative solubilities of Ce 3+ and Ce 4+ ) a first order dissolution rate expression can be derived for the CeO 2 samples investigated in this study where S is the measured surface area (after dissolution in the case of CeO 2-x ), S 0 is a reference surface area of 1 m 2 g −1 , α is the fraction of Ce 3+ (representing the oxygen vacancy content) at the particle surface as determined by XPS, A 3 and A 4 correspond to the solubility limits of Ce 3+ and Ce 4+ respectively, and b 3 and b 4 are the rate constants for Ce 3+ and Ce 4+ . A genetic algorithm, which can be applied to solve constrained optimization problems, 38 was used to fit the individual parameters in eq 5, providing optimum solubility and rate constant values for Ce 3+ and Ce 4+ based on the dissolution data obtained in this study; the data and model fits are shown in Figure 9. The modeled Ce 3+ and Ce 4+ solubilities, A 3 and A 4 , gave best-fit values of (5.10 ± 0.54) × 10 −4 mol dm −3 and (1.59 ± 0.08) × 10 −6 mol dm −3 , respectively (errors represent the 1σ confidence interval). These are in reasonable agreement with geochemically modeled solubility values, for example, Ce 4+ solubility was calculated using PHREEQC (LLNL database) to be 4.01 × 10 −6 mol dm −3 . When considering only CeO 2 annealed at various temperatures in air, and CeO 2 particles of different sizes (shown in Figures 9a and b, respectively), the rate constant for Ce 3+ was found to be b 3 = (0.245 ± 0.06) d −1 . For Ce 4+ the scatter in the experimental data, combined with the low absolute solubility limit, resulted in poorly defined estimates for b 4 ; a value of the order 1.00 × 10 −7 d −1 is tentatively suggested. Because the model to data fit was in agreement for CeO 2 (Figure 9a and b), and the solubilities of the different Ce oxidation states were similar to geochemically modeled solubility values, it can be surmised that the parameters in eq 5 adequately describe the dissolution rate of stoichiometric CeO 2 . Figure 9c shows the dissolution data and model fit for CeO 2-x samples annealed in Ar and H 2 /N 2 atmospheres. The model fit to the parameters in eq 5 agrees somewhat with samples annealed in Ar; however, the model fit to the parameters is not in agreement with data from samples annealed in H 2 /N 2 , despite normalization to the post-dissolution surface area and consideration for the elevated content of the more highly soluble Ce 3+ species in this sample (eq 5). Surface area data in Table 3 show that during dissolution, the surface area of CeO 2-x annealed in a H 2 /N 2 atmosphere increased by a factor of 5 after 1 day of dissolution. The first order dissolution model described above predicts that a surface area increase of a factor of 50 would be required to create a good fit to the parameters in eq 5, assuming all other values are correct. Specific surface area, as measured by BET, is routinely accepted to be the same as reactive surface area. However, recent studies have discussed that this may not necessarily be the case due to different activation energies of different high energy surface sites, e.g.,

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Research Article grain boundaries and oxygen vacancies. 39 It is possible that the BET surface area measurements taken here, 1 day after dissolution, underestimated the reactive surface area of these samples during the initial stages of dissolution due to the presence of a high proportion of exposed grain boundaries, which are known to be significantly more reactive than the bulk.

Physical
Effects of Oxidation on the Kinetics of Dissolution. As described above, not only the enhanced chemical solubility of Ce 3+ influenced the dissolution kinetics of CeO 2-x but also the physical effects leading to a change in the sample surface area played a significant role. The mechanism through which this is postulated to occur for CeO 2-x investigated in the current study is described below.
Upon contact with air or an oxic solution, the Ce 3+ ions in CeO 2-x , present as a result of charge compensation for oxygen vacancies, were rapidly oxidized to Ce 4+ . Due to the difference in ionic radius between Ce 3+ and Ce 4+ (with Ce 4+ the smaller cation), this oxidation process was associated with a contraction of the fluorite unit cell volume, on the order of ΔV = −3.25 ± 0.06 Å 3 according to Rietveld analysis of XRD data (a 6.0 ± 0.1% volume decrease relative to the starting volume). Ceramic materials that have undergone volume change-related phase transition exhibit significant internal lattice strain; according to Rietveld analysis, the lattice strain was initially high in CeO 2-x , reducing by a factor of 2.6 during oxidation to CeO 2 . Additionally, the presence of oxygen vacancies results in enhanced oxygen mobility, especially at grain boundaries where it is expected that a higher proportion of Ce 3+ exists; 35 this facilitates preferential dissolution of grain boundaries. 11 In this study, during the dissolution of CeO 1.82 to CeO 1.96 , the combined influence of lattice strain and enhanced oxygen mobility, created by the removal of oxygen vacancies, resulted in the disintegration of particles, preferentially along grain boundaries, producing individual grain-sized fragments after 1 day of dissolution (Figure 8e−f). Importantly, this resulted in an increase in reactive surface area, which exposed fresh surfaces for dissolution and enhanced the overall dissolution rate. After 1 day, the dissolution rate was observed to be more or less constant, likely because there is reduced oxygen atom mobility within the nearly stoichiometric CeO 1.96 . Hence, the combined roles of oxygen vacancies and grain boundaries should be considered significant in defining the dissolution kinetics of nonstoichiometric CeO 2 and other fluorite-type materials.
The dual role of oxygen vacancies and grain boundaries in dissolution has been observed in other fluorite-type materials, albeit those comprisising a solid solution of different chemical species. For example, Horlait et al. 17 reported the "crumbling" of Ce 1−x Ln x O 2-x/2 materials along grain boundaries during dissolution. This was associated with an increase in reactive surface area by up to a factor of 5. It was postulated that the incorporation of Ln 3+ played a significant role in the dissolution mechanism through changes to the lattice volume. 17,40 Similarly, Finkeldei et al. 41 found that defect fluorite and pyrochlore structures in the ZrO 2 −Nd 2 O 3 group preferentially dissolved along grain boundaries and at triple junctions, leading to disintegration. Substitution of elements into a fluorite lattice results in a volume change due to the difference in ionic radius of the substituting element; 36 the current study highlights the equally important role of oxygen vacancies on lattice volume change when only a single chemical species is present (CeO 2 ), confirming the importance of this defect feature in dissolution rate kinetics.
The association of defect structures with grain boundaries and their influence on the dissolution of CeO 2 and ThO 2 analogues for spent fuel was recently hypothesized by Corkhill et al., 11 who showed that the dissolution of grain boundaries was influenced by the crystallographic orientation of the grains and the corresponding mean misorientation angle of the grain boundaries. Boundaries with higher mean misorientation angles were found to dissolve at faster rates than those with low mean misorientation angles; it was hypothesized that higher misorientation angle grain boundaries contained a greater proportion of defects, with a high reactive surface area, which led to the enhanced dissolution rates. This study and others 17,18 have highlighted the important role of grain boundaries and particularly their association with defect structures (e.g., oxygen vacancies) on dissolution processes in spent fuel analogues. This underlines the requirement for new methodologies capable of linking grain boundary structure with dissolution kinetics, to fully understand their role in the dissolution of spent fuel materials. 42 4.3. Implications for the Dissolution of Spent Fuels. It was recently demonstrated for a suite of fluorite type materials, including CeO 2 , CaF 2 , and UO 2 , that the surface stability is correlated with the proportion of high energy surfaces, even when different chemical processes of dissolution occur, for example for CeO 2 and CaF 2 . 8 ThO 2 has also been shown to confirm this hypothesis. 11,19 Together with the resulted presented herein, these findings highlight the potential for energetically reactive surface sites to play a role in UO 2 dissolution.
Spent UO 2 fuel forms a complicated defect structure during fission within a reactor, and it is not yet clear the extent to which different types of reactive surface sites may influence the dissolution kinetics of spent fuel; however, studies on SIMFUEL have shown that doping with trivalent rare elements (to simulate fission products) resulted in lattice contraction 12 and a loss of cubic symmetry. On the basis of the results presented in the current study, we can hypothesize that such a lattice modification may lead to grain boundary decohesion. Evidence supporting this hypothesis includes a study of UO 2 fuel stored in aerated, moist environments, which was found to degrade along its grain boundaries and become heavily fractured. 43 The effects of lattice volume change on the integrity of grain boundaries in these materials, and the extent to which it may affect the dissolution kinetics, requires further exploration. Recent work has shown that Mixed Oxide Fuels (MOx), containing Pu 3+ , with a PuO 2-x stoichiometry of PuO 1.61 , 44 may also be prone to accommodating oxygen vacancies, 45 although the distribution of such defects between grains and the grain boundaries is currently not known. In light of the current limited knowledge of the atomic-scale structure of spent fuels, further work is required on inactive analogues, UO 2 , and spent fuel materials to ascertain the effects of reactive surface sites on dissolution kinetics, as distinct from oxidative dissolution or radiolysis effects, to reduce the uncertainty associated with the prediction of spent fuel dissolution within a geological disposal facility.

CONCLUSIONS
We present an investigation of the role of energetically reactive surface sites on the initial dissolution rate of CeO 2 to ascertain whether these features may result in overestimation of dissolution rates in the laboratory. Reactive surface sites and "sharp edges" were simulated by crushing samples to different

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Research Article size fractions and through high temperature annealing. Oxygen vacancy defects in CeO 2-x were generated by high temperature annealing in oxygen-free conditions. Surface area was used as a measurement of "sharp edges" and intrinsic defects, and the total Ce 3+ fraction measured by XPS was used as a measurement of the oxygen vacancy concentration. The relative dissolution rates of these materials showed that there was a quantifiable relationship between energetically reactive surface sites and dissolution rate, which was dependent upon reactive surface site concentration and the solubilities of Ce 3+ and Ce 4+ ; the greater the concentration of reactive surface sites, the higher the dissolution rate. The elimination of oxygen vacancies in CeO 2-x was found to significantly influence the dissolution rate; this was associated with changes in the lattice volume and lattice strain, manifested as grain boundary decohesion and increased surface area. Thus, it is clear that reactive surface sites, including artifacts of sample preparation, intrinsic material defects, and grain boundaries, have the potential to significantly enhance the dissolution of spent oxide fuel. We show that such effects can be quantified, thus it is possible to reduce the uncertainty associated with laboratory measurements of UO 2 dissolution, albeit in a simplified analogue system. It will be essential to develop further careful studies designed to interrogate the effect of reactive surface features on the durability and dissolution of materials such as UO 2 and MOx, as distinct from solubility, surface area, and radiation effects.