*4.1. Ion Beam Conditions*

The irradiation response of CeO<sup>2</sup> has been studied using a wide range of ion species ( <sup>127</sup>I–238U), energies (0.5–30 MeV/u), d*E*/d*x* (~15–45 keV/nm), ion fluxes (10–10<sup>10</sup> ions/cm<sup>2</sup> s), and ion fluences (1011–10<sup>16</sup> ions/cm<sup>2</sup> ) [32–56]. The ion energy and energy loss strongly influence the induced structural damage as seen in unit cell parameter changes with increasing fluence for various irradiation conditions (Figure 5a). For SHI irradiations within the electronic d*E*/d*x* regime, there typically exists a material dependent energy loss threshold above which ion tracks will form [23]. Track formation has been documented by TEM in SHI irradiated CeO<sup>2</sup> for an energy loss of ~16 keV/nm [37], which suggests a lower threshold when compared with other fluorite-structured materials. For example, UO<sup>2</sup> exhibits a threshold between ~22–29 keV/nm [66]. However, the d*E*/d*x* threshold for track formation has not been accurately determined for CeO<sup>2</sup> over a wide range of ion species and energies; this should be the subject of future research.

gies; this should be the subject of future research.

threshold between ~22–29 keV/nm [66]. However, the d*E*/d*x* threshold for track formation has not been accurately determined for CeO2 over a wide range of ion species and ener-

[68], indicative of a quadratic relation between track diameter and d*E*/d*x* value. While the

**Figure 5.** (**a**) Relative change in unit cell parameter based on XRD pattern analysis as a function of fluence for CeO2 irradiated with 200 MeV 132Xe (green, dE/dx = 27 keV/nm), 946 MeV 197Au (red, dE/dx = 44 keV/nm), and 167 MeV 132Xe (blue, dE/dx = 27 keV/nm). (**b**) 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) with 167 MeV 132Xe (top) and 946 MeV 197Au (bottom). (**c**) Relative change in the unit cell parameter, determined by XRD pattern analysis, for CeO2 irradiated with 1694 MeV 197Au ions at ion fluxes of ~109 ions/cm2/s (red) and ~1010 ions/cm2/s (blue). Dashed lines in (**a**) and (**b**) are fits based on a single-impact model. These data are based on work published by Tracy et al. [46] (**a**,**b**) and unpublished work (**a**,**c**). The energy loss governs the nature and extent of the radiation damage induced in a material. In most cases, a higher energy loss induces a higher energy density within the track region, which produces more defects and results in the formation of defect clusters [54]. Sonoda et al. [37] demonstrated that the track size increases with increasing d*E*/d*x* in CeO2, which agrees well with thermal spike calculations [67] based on the Szenes model **Figure 5.** (**a**) Relative change in unit cell parameter based on XRD pattern analysis as a function of fluence for CeO<sup>2</sup> irradiated with 200 MeV <sup>132</sup>Xe (green, dE/dx = 27 keV/nm), 946 MeV <sup>197</sup>Au (red, dE/dx = 44 keV/nm), and 167 MeV <sup>132</sup>Xe (blue, dE/dx = 27 keV/nm). (**b**) 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) with 167 MeV <sup>132</sup>Xe (top) and 946 MeV <sup>197</sup>Au (bottom). (**c**) Relative change in the unit cell parameter, determined by XRD pattern analysis, for CeO<sup>2</sup> irradiated with 1694 MeV <sup>197</sup>Au ions at ion fluxes of ~10<sup>9</sup> ions/cm2/s (red) and ~10<sup>10</sup> ions/cm2/s (blue). Dashed lines in (**a**,**b**) are fits based on a single-impact model. These data are based on work published by Tracy et al. [46] (**a**,**b**) and unpublished work (**a**,**c**).

amount and type of defects, as well as track size, show a clear dependence on energy loss, redox changes of the cerium cations appear to be only weakly dependent on the d*E*/d*x* (Figure 5b). This behavior is not well understood, and it remains unclear if cation reduction also has a critical d*E*/d*x* threshold akin to track formation and whether or not they are the same. The energy loss alone cannot fully explain the observed radiation behavior, as demonstrated by the large change in unit cell parameter values in CeO2 (Figure 5a) induced by two different ion irradiation experiments using nearly the same d*E*/d*x* (~27 keV/nm for both 167 MeV 132Xe and 200 MeV 132Xe ions). This is explained by the additional impact of ion energy, also known as the velocity effect [23,69]. SHIs lose their energy to the electron subsystem by collisions with electrons, exciting them to high-energy states that are sometimes sufficient for ionization from the target atoms. The maximum energy imparted to these so-called delta electrons is determined by the ion velocity: higher velocity ions yield electrons with higher kinetic energies, allowing them to travel further away The energy loss governs the nature and extent of the radiation damage induced in a material. In most cases, a higher energy loss induces a higher energy density within the track region, which produces more defects and results in the formation of defect clusters [53]. Sonoda et al. [37] demonstrated that the track size increases with increasing d*E*/d*x* in CeO2, which agrees well with thermal spike calculations [67] based on the Szenes model [68], indicative of a quadratic relation between track diameter and d*E*/d*x* value. While the amount and type of defects, as well as track size, show a clear dependence on energy loss, redox changes of the cerium cations appear to be only weakly dependent on the d*E*/d*x* (Figure 5b). This behavior is not well understood, and it remains unclear if cation reduction also has a critical d*E*/d*x* threshold akin to track formation and whether or not they are the same.

from their initial positions. For irradiations with comparable energy loss values, ions with higher velocities (kinetic energies) will deposit their energy over a larger volume. This results in larger ion tracks, but lower energy densities within those tracks, yielding less pronounced in-track material modifications (Figure 5b) [47,55]. Differential scanning calorimetry measurements by Shelyug et al. [54] further illustrated this velocity effect. A comparison of the enthalpy of radiation damage (the energetic difference between pristine and irradiated samples) in CeO2 irradiated with 1100 and 2200 MeV 197Au ions revealed that the higher velocity ions produced tracks with lower defect concentrations, although the track diameters were larger than those produced by the lower velocity ions. These results were corroborated by neutron total scattering The energy loss alone cannot fully explain the observed radiation behavior, as demonstrated by the large change in unit cell parameter values in CeO<sup>2</sup> (Figure 5a) induced by two different ion irradiation experiments using nearly the same d*E*/d*x* (~27 keV/nm for both 167 MeV <sup>132</sup>Xe and 200 MeV <sup>132</sup>Xe ions). This is explained by the additional impact of ion energy, also known as the velocity effect [23,69]. SHIs lose their energy to the electron subsystem by collisions with electrons, exciting them to high-energy states that are sometimes sufficient for ionization from the target atoms. The maximum energy imparted to these so-called delta electrons is determined by the ion velocity: higher velocity ions yield electrons with higher kinetic energies, allowing them to travel further away from their initial positions. For irradiations with comparable energy loss values, ions with higher velocities (kinetic energies) will deposit their energy over a larger volume. This results in larger ion tracks, but lower energy densities within those tracks, yielding less pronounced in-track material modifications (Figure 5b) [46,54].

Differential scanning calorimetry measurements by Shelyug et al. [53] further illustrated this velocity effect. A comparison of the enthalpy of radiation damage (the energetic difference between pristine and irradiated samples) in CeO<sup>2</sup> irradiated with 1100 and 2200 MeV <sup>197</sup>Au ions revealed that the higher velocity ions produced tracks with lower defect concentrations, although the track diameters were larger than those produced by the lower velocity ions. These results were corroborated by neutron total scattering measurements and fitting of a single impact model to the measured damage accumulation. To date, no dedicated studies of the velocity effect have been performed on CeO2. Future research should further investigate the influence of SHI velocity on the induced damage structure.

In addition to ion mass and energy (i.e., d*E*/d*x*), as well as ion velocity, the ion flux on the sample has a substantial effect on the observed radiation response. Irradiation-induced material modifications are often studied in CeO<sup>2</sup> by irradiation to high fluences, at which ion tracks overlap (e.g., ~10<sup>13</sup> ions/cm<sup>2</sup> ). To reach these fluence values within reasonable irradiation times, high ion fluxes (fluence per unit time, given in ions/cm2/s) are often used. The flux used in a given experiment also depends on the accelerator and the beam mode utilized (e.g., pulsed versus continuous); these can vary greatly among facilities.

During irradiation with a high ion flux, relatively large amounts of energy are deposited in the sample over a short time interval. For sufficiently high fluxes, the resulting increase in thermal energy can outrace its dissipation, yielding high sample temperatures. As shown in Section 4.3, the irradiation temperature can influence the radiation behavior in insulators like CeO2. In contrast, a lower ion flux allows more time for the dissipation of thermal energy, and therefore produces less bulk sample heating and reduced mobilities of irradiation induced defects. This impedes the recovery processes, yielding higher defect concentrations and more extensive material modifications. This is demonstrated by the swelling behavior of CeO<sup>2</sup> irradiated with 1694 MeV Au ions at two different fluxes but otherwise identical irradiation conditions (Figure 5c). The higher flux irradiation leads to a faster unit cell parameter increase as a function of ion fluence, consistent with a larger ion track (ion track size is proportional to the slope of the initial linear region). However, the saturation value of swelling, which is caused by the concentration of defects within tracks, is greatly reduced compared to the low-flux irradiation (Figure 5c). This shows that the ion-beam flux is an important parameter that must be considered when comparing results from different irradiation experiments. It remains unclear how ion-matter interactions are impacted over a large range of fluxes, whether there is an effect beyond the increase in temperature, and whether or not there is a critical flux value below which thermal effects can be neglected. Systematic studies are needed to quantify the effect of ion-beam flux on defect formation and recovery processes.
