*4.2. Sample Microstructure*

Swift heavy ion irradiation of CeO<sup>2</sup> has been performed on samples produced by various synthesis and processing procedures, resulting in a range of microstructures with grain sizes from the nm-scale to bulk. The microstructure of a material influences its properties, including mechanical behavior, transport properties, and radiation response. For example, grain boundaries serve as defect sinks during irradiation with low-energy ions, leading to an enhanced radiation tolerance of nanocrystalline materials due to their high grain boundary densities [70]. This is in contrast to the reduced stability of nanocrystalline CeO<sup>2</sup> reported for SHI irradiation experiments [43]. Tracy et al. [46] and Cureton et al. [52] have shown that upon irradiation with 946 MeV <sup>197</sup>Au ions, nanocrystalline CeO<sup>2</sup> (grain size: 20 nm) exhibits greater unit cell swelling [52] (Figure 6a) and redox changes [46] compared with microcrystalline CeO<sup>2</sup> (grain size: 2 µm).

The grain size also has an influence on the phase stability of ceria. The irradiationinduced formation of hypostoichiometric Ce11O<sup>20</sup> has been observed for both micro- and nanocrystalline materials, but to a much larger extent for the latter (Figure 6b,d) [43,46,52]. This phase transition is linked to the reduction of cerium cations and associated oxygen expulsion processes described in Section 3.2 [52]. The unit cell parameter in Ce11O<sup>20</sup> is larger than that of the initial fluorite phase and further increases with ion fluence, indicating that defects continue to accumulate in this hypostoichiometric phase (Figure 6a). The phase transition is apparent in nanocrystalline CeO<sup>2</sup> at much lower fluences, and Ce11O<sup>20</sup> grows at a faster rate compared with microcrystalline CeO<sup>2</sup> (Figure 6d).

The greater unit cell swelling in nanocrystalline CeO<sup>2</sup> (Figure 6a) can be explained by the ion-track formation mechanism discussed in Section 3.2. SHI tracks form in CeO<sup>2</sup> via expulsion of oxygen anions in the radial direction, away from the ion path. This causes reduction of cerium cations in the track core where oxygen is depleted, while the track shell is enriched with oxygen point defects and small defect clusters. As shown by Takaki et al. [42], oxygen can be expelled by tens of nm, which corresponds to the grain size of samples used in the study shown in Figure 6. During quenching of the excited track region, some of the

oxygen will diffuse back to the core and recombine with oxygen vacancies, eliminating defects and decreasing the number of reduced cerium cations. In nano-ceria, however, the fraction of oxygen that diffuses back can be assumed to be reduced due to losses to grain boundaries. For a given fluence, this leads to a larger unit cell increase as compared with microcrystalline CeO2. This scenario is supported by previous X-ray absorption measurements (Figure 6c) [46], revealing increased redox changes in nanocrystalline ceria (edge shift of 4.3 eV compared with 2.0 eV in the microcrystalline material). It further explains the enhanced formation of hypostoichiometric Ce11O<sup>20</sup> in nano-ceria. This discussion shows that the microstructure of CeO<sup>2</sup> must be considered when comparing results from different SHI irradiation experiments. Systematic research is needed to quantify the swelling and redox changes of CeO<sup>2</sup> as a function of grain size, particularly in the 1 nm–1 µm range, for which oxygen diffusion may control the radiation response. *Quantum Beam Sci.* **2021**, *5*, x FOR PEER REVIEW 11 of 24

**Figure 6.** (**a**) Fluence-dependent change in unit cell parameter based on XRD pattern analysis for microcrystalline CeO2 (blue, grain size = 2 μm), nanocrystalline CeO2 (red, grain size = 20 nm), and the Ce11O20 phase produced in nanocrystalline samples (**black**), all relative to the unit cell parameter of unirradiated CeO2. (**b**) X-ray diffraction patterns of irradiated nanocrystalline CeO2 as a function of fluence, displaying the emergence of new peaks corresponding to the Ce11O20 phase, as indicated with arrows. (**c**) X-ray absorption spectra of the cerium K-edge in CeO2 before irradiation (blue) and after irradiation to a fluence of 5 × 1013 ions/cm2 (red) in nanocrystalline (**top**) and microcrystalline (**bottom**) samples. (**d**) Phase fraction of Ce11O20 relative to the fluorite phase as a function of ion fluence for microcrystalline (blue) and nanocrystalline (red) CeO2. Irradiation was performed with 946 MeV Au ions. These data were adapted from Cureton et al. [53] (**a**,**b**,**d**) and Tracy et al. [47] (**c**). The grain size also has an influence on the phase stability of ceria. The irradiationinduced formation of hypostoichiometric Ce11O20 has been observed for both micro- and **Figure 6.** (**a**) Fluence-dependent change in unit cell parameter based on XRD pattern analysis for microcrystalline CeO<sup>2</sup> (blue, grain size = 2 µm), nanocrystalline CeO<sup>2</sup> (red, grain size = 20 nm), and the Ce11O<sup>20</sup> phase produced in nanocrystalline samples (**black**), all relative to the unit cell parameter of unirradiated CeO<sup>2</sup> . (**b**) X-ray diffraction patterns of irradiated nanocrystalline CeO<sup>2</sup> as a function of fluence, displaying the emergence of new peaks corresponding to the Ce11O<sup>20</sup> phase, as indicated with arrows. (**c**) X-ray absorption spectra of the cerium K-edge in CeO<sup>2</sup> before irradiation (blue) and after irradiation to a fluence of 5 <sup>×</sup> <sup>10</sup><sup>13</sup> ions/cm<sup>2</sup> (red) in nanocrystalline (**top**) and microcrystalline (**bottom**) samples. (**d**) Phase fraction of Ce11O<sup>20</sup> relative to the fluorite phase as a function of ion fluence for microcrystalline (blue) and nanocrystalline (red) CeO<sup>2</sup> . Irradiation was performed with 946 MeV Au ions. These data were adapted from Cureton et al. [52] (**a**,**b**,**d**) and Tracy et al. [46] (**c**).

#### nanocrystalline materials, but to a much larger extent for the latter (Figure 6b,d) [43,47,53]. *4.3. High-Temperature Conditions*

This phase transition is linked to the reduction of cerium cations and associated oxygen expulsion processes described in Section 3.2 [53]. The unit cell parameter in Ce11O20 is larger than that of the initial fluorite phase and further increases with ion fluence, indicating that defects continue to accumulate in this hypostoichiometric phase (Figure 6a). The phase transition is apparent in nanocrystalline CeO2 at much lower fluences, and Ce11O20 grows at a faster rate compared with microcrystalline CeO2 (Figure 6d). The greater unit cell swelling in nanocrystalline CeO2 (Figure 6a) can be explained by the ion-track formation mechanism discussed in Section 3.2. SHI tracks form in CeO2 via expulsion of oxygen anions in the radial direction, away from the ion path. This causes reduction of cerium cations in the track core where oxygen is depleted, while the track shell is enriched with oxygen point defects and small defect clusters. As shown by Takaki Irradiation temperature is a key parameter to consider for cerium dioxide as an analogue for nuclear fuels. Nuclear light water reactor (LWR) fuel operating conditions range from room temperature at reactor startup to a typical maximum of ~1200 ◦C under normal operation. In general, increased temperature enhances defect recovery due to higher defect mobility, but it might also enhance defect production and promote more complex defects due to higher initial temperatures within an ion-induced thermal spike. The profound effect of irradiation temperature on defect production in CeO<sup>2</sup> is demonstrated by the flux effect discussed in Section 4.1 (Figure 5c). During ion-beam experiments, high temperatures are typically achieved by mounting samples on stages with resistive coils that heat the material.

et al. [42], oxygen can be expelled by tens of nm, which corresponds to the grain size of samples used in the study shown in Figure 6. During quenching of the excited track region, some of the oxygen will diffuse back to the core and recombine with oxygen vacancies, eliminating defects and decreasing the number of reduced cerium cations. In nanoceria, however, the fraction of oxygen that diffuses back can be assumed to be reduced due to losses to grain boundaries. For a given fluence, this leads to a larger unit cell in-Prior SHI irradiation studies of CeO<sup>2</sup> have demonstrated a systematic decrease in the saturation level of swelling [54] and the ion track diameter [32,33] with increasing irradiation temperature (Figure 7a,b). Both changes are consistent with thermally-driven defect recovery due to enhanced defect mobility; however, a more comprehensive understanding is provided by consideration of the thermal-spike model of track formation. This mathematical model describes the interaction of swift heavy ions with a material in terms

crease as compared with microcrystalline CeO2. This scenario is supported by previous X-

crystalline ceria (edge shift of 4.3 eV compared with 2.0 eV in the microcrystalline material). It further explains the enhanced formation of hypostoichiometric Ce11O20 in nanoceria. This discussion shows that the microstructure of CeO2 must be considered when comparing results from different SHI irradiation experiments. Systematic research is needed to quantify the swelling and redox changes of CeO2 as a function of grain size, particularly in the 1 nm–1 μm range, for which oxygen diffusion may control the radiation

response.

of a rapid increase in temperature over picosecond timescales induced by the high energy deposition within a nm-sized track region, followed by rapid quenching that freezes in structural damage [67,71]. The initial sample temperature is an input parameter in the thermal-spike model [49] that is added to the transient temperature spike and affects the final track diameter; higher temperatures typically yield larger ion tracks. of a rapid increase in temperature over picosecond timescales induced by the high energy deposition within a nm-sized track region, followed by rapid quenching that freezes in structural damage [67,71]. The initial sample temperature is an input parameter in the thermal-spike model [50] that is added to the transient temperature spike and affects the final track diameter; higher temperatures typically yield larger ion tracks.

Irradiation temperature is a key parameter to consider for cerium dioxide as an analogue for nuclear fuels. Nuclear light water reactor (LWR) fuel operating conditions range from room temperature at reactor startup to a typical maximum of ~1200 °C under normal operation. In general, increased temperature enhances defect recovery due to higher defect mobility, but it might also enhance defect production and promote more complex defects due to higher initial temperatures within an ion-induced thermal spike. The profound effect of irradiation temperature on defect production in CeO2 is demonstrated by the flux effect discussed in Section 4.1 (Figure 5c). During ion-beam experiments, high temperatures are typically achieved by mounting samples on stages with resistive coils

Prior SHI irradiation studies of CeO2 have demonstrated a systematic decrease in the saturation level of swelling [54] and the ion track diameter [32,33] with increasing irradiation temperature (Figure 7a,b). Both changes are consistent with thermally-driven defect recovery due to enhanced defect mobility; however, a more comprehensive understanding is provided by consideration of the thermal-spike model of track formation. This mathematical model describes the interaction of swift heavy ions with a material in terms

*Quantum Beam Sci.* **2021**, *5*, x FOR PEER REVIEW 12 of 24

*4.3. High-Temperature Conditions* 

that heat the material.

**Figure 7.** (**a**) Change in unit cell parameter from XRD pattern analysis as a function of irradiation temperature for CeO2 irradiated with 200 MeV 132Xe ions, relative to unirradiated reference samples heated under identical conditions [55]. (**b**) Ion track diameters determined by inelastic thermal-spike calculations [55] (red) and measured based on TEM images [32,33] (**black**) as a function of irradiation temperature. (**c**) Effect of thermal annealing on the relative change in unit cell parameter in CeO2 previously irradiated with 946 MeV 197Au ions [46]. Dashed and solid lines are to guide the eye. This figure was adapted from (**a**,**b**) Cureton et al. [55], (**b**) Sonoda et al. [32,33], and (**c**) Palo-**Figure 7.** (**a**) Change in unit cell parameter from XRD pattern analysis as a function of irradiation temperature for CeO<sup>2</sup> irradiated with 200 MeV <sup>132</sup>Xe ions, relative to unirradiated reference samples heated under identical conditions [54]. (**b**) Ion track diameters determined by inelastic thermal-spike calculations [54] (red) and measured based on TEM images [32,33] (black) as a function of irradiation temperature. (**c**) Effect of thermal annealing on the relative change in unit cell parameter in CeO<sup>2</sup> previously irradiated with 946 MeV <sup>197</sup>Au ions [45]. Dashed and solid lines are to guide the eye. This figure was adapted from (**a**,**b**) Cureton et al. [54], (**b**) Sonoda et al. [32,33], and (**c**) Palomares et al. [45].

mares et al. [46]. In CeO2, the thermal spike model predicts an increase in track diameter as a function of increasing irradiation temperature up to 700 °C [55] (Figure 7b). This prediction is not supported by TEM characterization, which shows an opposite trend [32,33]. This discrepancy either indicates that the thermal-spike model does not fully capture all aspects of ion-matter interactions at elevated temperatures, or that the model and experiment describe two different track regions. The thermal spike approach accounts for the entire track region (i.e., the full range of delta electron pathways and associated electron-phonon coupling), and the deduced track diameter represents the size of the track core plus the shell (see Section 3.2). TEM characterization, on the other hand, is sensitive to changes in electron density, and the measured track diameter mostly represents the smaller track core, In CeO2, the thermal spike model predicts an increase in track diameter as a function of increasing irradiation temperature up to 700 ◦C [54] (Figure 7b). This prediction is not supported by TEM characterization, which shows an opposite trend [32,33]. This discrepancy either indicates that the thermal-spike model does not fully capture all aspects of ion-matter interactions at elevated temperatures, or that the model and experiment describe two different track regions. The thermal spike approach accounts for the entire track region (i.e., the full range of delta electron pathways and associated electron-phonon coupling), and the deduced track diameter represents the size of the track core plus the shell (see Section 3.2). TEM characterization, on the other hand, is sensitive to changes in electron density, and the measured track diameter mostly represents the smaller track core, which is enriched in (high-Z) cerium cation defects [32,33]. Under these assumptions, the discrepancy between TEM data and thermal spike calculations could indicate that the track core shrinks with increasing irradiation temperature, while the shell thickness increases. This is consistent with XRD results and the reported reduced unit cell expansion at higher irradiation temperature, since the track core is primarily responsible for ioninduced swelling (oxygen vacancies and associated Ce3+ cations). Systematic ion-beam studies over a range of temperatures (including cryogenic) are required to gain further insight into the manner in which track formation is modified by increases in the irradiation temperature. For example, conventional scanning transmission EM imaging (which is more sensitive to changes at cation sublattice) coupled with annular bright-field (ABF) imaging (which more sensitive to changes at anion sublattice) could reveal changes in ion track core and shell sizes at various irradiation temperatures.

In addition to the in situ heating experiments described above, where temperature is applied during ion-beam exposure, samples can be thermally annealed after irradiation to elucidate defect kinetics and damage recovery mechanisms [45]. Synchrotron XRD measurements of CeO<sup>2</sup> irradiated with 946 MeV <sup>197</sup>Au ions and subsequently annealed within a hydrothermal diamond anvil cell [14] revealed a two-step defect recovery mechanism with corresponding activation energies of 1.0 and 2.1 eV (Figure 7c). These activation energies were attributed to O-interstitial migration and Ce-vacancy migration, respectively, but the

reoxidation of Ce3+ to Ce4+ after oxygen vacancy annihilation was not considered [72]. Unlike isostructural ThO2, the damage recovery in ceria remained incomplete up to 800 ◦C, with a unit cell parameter increase of ~0.03% relative to an unirradiated reference sample remaining at this highest achieved temperature [45]. This suggests that defect clusters with relatively high binding energies, such as 2Ce3+–V<sup>O</sup> <sup>2</sup><sup>−</sup> complexes, are stable up to 800 ◦C and require higher annealing temperatures for recovery.

High-temperature calorimetry measurements of previously irradiated CeO<sup>2</sup> (using 1100 MeV and 2200 MeV <sup>197</sup>Au ions) revealed that defect recovery is enhanced within an oxygen atmosphere compared with heating in an inert environment [53]. This suggests that recovery processes related to the reoxidation of ion induced Ce3+ cations to Ce4+ play an important role in the annealing of SHI damage in CeO<sup>2</sup> and must be considered [53]. Thus, ex situ annealing experiments are useful for identifying and characterizing the different defects that form in CeO<sup>2</sup> during SHI irradiation.
