*5.2. Dependence of Radiation Response on the A-Site Cation Species*

As CeO<sup>2</sup> is utilized as an analogue to study radiation effects in nuclear fuel materials (e.g., UO<sup>2</sup> and ThO2), it is particularly important to compare the SHI irradiation responses of these materials. Despite all three having the same fluorite structure, each A-site cation has a distinct electronic structure, resulting in varying behavior under highly ionizing irradiation. As mentioned previously, the track formation is very different between CeO<sup>2</sup> and UO2, with the latter exhibiting no observable ion tracks after irradiation with fission

fragments (d*E*/d*x* ~18–22 keV/nm) [66]. This suggests that UO<sup>2</sup> is able to dissipate the energy deposited by a SHI much more efficiently than CeO<sup>2</sup> under similar irradiation conditions. This behavior may be related to differences in the types of defects formed, as suggested by a molecular dynamics (MD) investigation [64]. In MD simulations 99% of SHI irradiation-induced defects were produced on the oxygen sublattice in UO2, in contrast to CeO2, where cerium and oxygen defects are produced in stoichiometric quantities after ion impact (redox changes not considered). The production of appreciable quantities of both cation and anion defects in CeO<sup>2</sup> led to a larger quantity of surviving defects after track quenching [64].

While the radiation responses of ThO<sup>2</sup> and CeO<sup>2</sup> are more similar, with both exhibiting a core-shell type track morphology, the extent of structural changes within individual ion tracks differs between these materials due to the accessible cation valence states (monovalent Th4+ versus Ce4+/Ce3+) [83]. The formation of Ce3+ cations with larger ionic radius and the correspondingly complex oxygen defect structure in CeO<sup>2</sup> yields more pronounced swelling and microstrain build-up in this material, relative to ThO2, for which this redox-driven defect mechanism is inactive (Figure 9) [46,52,83]. Instead, the SHI radiation response of ThO<sup>2</sup> appears to be based solely on the accumulation of point defects and small, simple defect clusters [83]. The situation is more complex in UO2, given its multiple accessible U cation oxidation states (U3+, U4+, U5+, and U6+), enabling cation reduction or oxidation. Raman spectroscopy and XRD measurements have shown that UO<sup>2</sup> undergoes some oxidation during SHI irradiation, which causes minor unit cell contraction (Figure 9) [52]. *Quantum Beam Sci.* **2021**, *5*, x FOR PEER REVIEW 16 of 24

**Figure 9.** Relative change in unit cell parameter from XRD measurements as a function of fluence for microcrystalline (squares) and nanocrystalline (circles) UO2 (green), ThO2 (red), and CeO2 (blue) irradiated with 946 MeV 197Au ions. The shading displays the variation in irradiation-induced unit cell parameter changes between microcrystalline (2 μm) and nanocrystalline (20 nm) samples for each material. Adapted from Cureton et al. [53]. **Figure 9.** Relative change in unit cell parameter from XRD measurements as a function of fluence for microcrystalline (squares) and nanocrystalline (circles) UO<sup>2</sup> (green), ThO<sup>2</sup> (red), and CeO<sup>2</sup> (blue) irradiated with 946 MeV <sup>197</sup>Au ions. The shading displays the variation in irradiation-induced unit cell parameter changes between microcrystalline (2 µm) and nanocrystalline (20 nm) samples for each material. Adapted from Cureton et al. [52].

Changes in radiation behavior among CeO2, ThO2, and UO2 are particularly evident when structural modifications are compared between microcrystalline and nanocrystalline materials. As shown in Figure 6c, ion-induced redox processes are more efficient in nanocrystalline CeO2 (as discussed in Section 4.2), leading to a larger saturation level of swelling at high ion fluences (Figure 9). Since such redox effects are absent in ThO2, its overall swelling behavior is very similar for both nano- and microcrystalline materials. The largest discrepancy in unit cell parameter changes after SHI irradiation is found in microcrystalline and nanocrystalline UO2 (Figure 9). The former oxidizes under SHI irradiation, yielding unit cell contraction, while the latter exhibits a significant degree of Changes in radiation behavior among CeO2, ThO2, and UO<sup>2</sup> are particularly evident when structural modifications are compared between microcrystalline and nanocrystalline materials. As shown in Figure 6c, ion-induced redox processes are more efficient in nanocrystalline CeO<sup>2</sup> (as discussed in Section 4.2), leading to a larger saturation level of swelling at high ion fluences (Figure 9). Since such redox effects are absent in ThO2, its overall swelling behavior is very similar for both nano- and microcrystalline materials. The largest discrepancy in unit cell parameter changes after SHI irradiation is found in microcrystalline and nanocrystalline UO<sup>2</sup> (Figure 9). The former oxidizes under SHI irradiation, yielding unit cell contraction, while the latter exhibits a significant degree of swelling.

swelling. Characterization by X-ray diffraction and Raman spectroscopy suggest that the

boundaries, implying that pronounced redox changes are induced during SHI irradiation

These results highlight the manner in which the electronic structure of the cation dramatically changes the response of fluorite-structured oxides to swift heavy ion irradiation. This raises concerns about the use of CeO2 as an analogue material for UO2 in radiationdamage studies, at least for swift heavy ion (or fission-fragment) irradiation. The data shown in Figure 10 again emphasize that the grain size of a material plays a crucial role in ion-matter interactions, with its specific effects showing a strong dependence on com-

If aliovalent dopants are added to CeO2 in sufficiently high concentrations, ordering of these new cations can occur alongside ordering of the defects produced on the anion sublattice to maintain charge neutrality. Even in undoped CeO2, defects can order and change the symmetry of the material if they accumulate in large quantities. Thus, dopant and defect ordering can yield new fluorite-derivative structures [84], with bixbyite-structured lanthanide sesquioxides and pyrochlore-structured lanthanide/transition metal oxides being two commonly-studied examples. These materials can be considered as defectrich (sesquioxides) and heavily doped (pyrochlores) variants of CeO2, and both exhibit anion-deficient fluorite-derivative structures (Figure 10) [85]. The following section

*5.3. Radiation Effects in Structurally-Related Lanthanide Oxides* 

[53].

position.

Characterization by X-ray diffraction and Raman spectroscopy suggest that the increase in structural disorder in nanocrystalline UO<sup>2</sup> results from oxygen loss to grain boundaries, implying that pronounced redox changes are induced during SHI irradiation [53].

These results highlight the manner in which the electronic structure of the cation dramatically changes the response of fluorite-structured oxides to swift heavy ion irradiation. This raises concerns about the use of CeO<sup>2</sup> as an analogue material for UO<sup>2</sup> in radiation-damage studies, at least for swift heavy ion (or fission-fragment) irradiation. The data shown in Figure 10 again emphasize that the grain size of a material plays a crucial role in ion-matter interactions, with its specific effects showing a strong dependence on composition. *Quantum Beam Sci.* **2021**, *5*, x FOR PEER REVIEW 17 of 24 summarizes the main SHI irradiation effects observed in these materials, which provide further insight into the radiation response of CeO2.

**Figure 10.** Ce-bearing oxides with fluorite, bixbyite, and pyrochlore structures viewed along the (100) direction (**top**) and the corresponding (222) plane anion layers (**bottom**). Blue and green spheres represent cations, while red spheres represent oxygen anions. Unit cells are delineated with black lines. The bixbyite structure can be characterized as a fluorite-derivative with 1/8 of the anions replaced by constitutional vacancies, while the pyrochlore structure is a fluorite-derivative with ordering of two cation species and ¼ of the anions replaced by constitutional vacancies. **Figure 10.** Ce-bearing oxides with fluorite, bixbyite, and pyrochlore structures viewed along the (100) direction (**top**) and the corresponding (222) plane anion layers (**bottom**). Blue and green spheres represent cations, while red spheres represent oxygen anions. Unit cells are delineated with black lines. The bixbyite structure can be characterized as a fluorite-derivative with 1/8 of the anions replaced by constitutional vacancies, while the pyrochlore structure is a fluorite-derivative with ordering of two cation species and <sup>1</sup> 4 of the anions replaced by constitutional vacancies.

#### The bixbyite structure is characteristic of most lanthanide oxides for which the lanthanide element is in the trivalent oxidation state (Ln3+). This structure is a derivative of *5.3. Radiation Effects in Structurally-Related Lanthanide Oxides*

the fluorite structure, but with ordered constitutional vacancies replacing ¼ of the anion sites and the remaining atoms relaxed towards these vacant sites (Figure 10) [86]. The responses of bixbyite materials to SHI irradiation have been characterized using a range of ion energies and masses [30,87–90]. This prior work revealed a strong dependence of the radiation response on the cation ionic radius. The magnitude of the induced structural changes generally increases with cation size (and therefore decreases with cation mass, due to the contraction that occurs across the lanthanide series). Sesquioxides with small cations tend to retain their bixbyite structures under swift heavy ion irradiation, those with medium cations tend to undergo transformations to high temperature polymorphs, and those with large cations tend to amorphize. These modifications, which are generally proportional in magnitude to d*E*/d*x*, are attributed to the displacement of anions into con-If aliovalent dopants are added to CeO<sup>2</sup> in sufficiently high concentrations, ordering of these new cations can occur alongside ordering of the defects produced on the anion sublattice to maintain charge neutrality. Even in undoped CeO2, defects can order and change the symmetry of the material if they accumulate in large quantities. Thus, dopant and defect ordering can yield new fluorite-derivative structures [84], with bixbyite-structured lanthanide sesquioxides and pyrochlore-structured lanthanide/transition metal oxides being two commonly-studied examples. These materials can be considered as defect-rich (sesquioxides) and heavily doped (pyrochlores) variants of CeO2, and both exhibit aniondeficient fluorite-derivative structures (Figure 10) [85]. The following section summarizes the main SHI irradiation effects observed in these materials, which provide further insight into the radiation response of CeO2.

stitutional vacancies which, when sufficiently extensive, can yield collective atomic relaxation to form accessible polymorphic or amorphous structures [30]. These processes provide insight into the likely behavior of anion-deficient CeO2−*x* materials under irradiation. While Ce2O3 preferentially adopts a hexagonal structure, unlike most of the lanthanide sesquioxides, it is stable in cubic bixbyite-like phases starting at slightly higher oxygen contents [91,92]. Radiation damage mechanisms similar to those observed in the lanthanide sesquioxides have been reported for CeO2, with the displace-The bixbyite structure is characteristic of most lanthanide oxides for which the lanthanide element is in the trivalent oxidation state (Ln3+). This structure is a derivative of the fluorite structure, but with ordered constitutional vacancies replacing <sup>1</sup> 4 of the anion sites and the remaining atoms relaxed towards these vacant sites (Figure 10) [86]. The responses of bixbyite materials to SHI irradiation have been characterized using a range of ion energies and masses [30,87–90]. This prior work revealed a strong dependence of the

date, the response of Ce2O3 to swift heavy ion irradiation has not been characterized. However, based on the ionic radius of Ce, which is large among the lanthanides, amorphization is expected to be the dominant response of this material. This suggests that cerium reduction and the concomitant introduction of oxygen vacancies will reduce the radiation

radiation response on the cation ionic radius. The magnitude of the induced structural changes generally increases with cation size (and therefore decreases with cation mass, due to the contraction that occurs across the lanthanide series). Sesquioxides with small cations tend to retain their bixbyite structures under swift heavy ion irradiation, those with medium cations tend to undergo transformations to high temperature polymorphs, and those with large cations tend to amorphize. These modifications, which are generally proportional in magnitude to d*E*/d*x*, are attributed to the displacement of anions into constitutional vacancies which, when sufficiently extensive, can yield collective atomic relaxation to form accessible polymorphic or amorphous structures [30].

These processes provide insight into the likely behavior of anion-deficient CeO2−*<sup>x</sup>* materials under irradiation. While Ce2O<sup>3</sup> preferentially adopts a hexagonal structure, unlike most of the lanthanide sesquioxides, it is stable in cubic bixbyite-like phases starting at slightly higher oxygen contents [91,92]. Radiation damage mechanisms similar to those observed in the lanthanide sesquioxides have been reported for CeO2, with the displacement of oxygen being a dominant mode of defect production (see Section 3.2) [50]. To date, the response of Ce2O<sup>3</sup> to swift heavy ion irradiation has not been characterized. However, based on the ionic radius of Ce, which is large among the lanthanides, amorphization is expected to be the dominant response of this material. This suggests that cerium reduction and the concomitant introduction of oxygen vacancies will reduce the radiation tolerance of CeO<sup>2</sup> by making possible the oxygen displacement-driven transformation mechanisms previously observed in several lanthanide sesquioxides. To clarify this behavior, a detailed study of the swift heavy ion irradiation response of CeO2−*<sup>x</sup>* materials as a function of *x* would be useful.

Like the bixbyite-structured oxides, the responses of pyrochlore-structured materials to SHI irradiation have been extensively studied, due in large part to their potential applications in the immobilization of nuclear wastes [93]. These materials exhibit the general formula A2B2O7, where A is a large trivalent cation and B is a smaller tetravalent cation [94]. While Ce most often occupies the A-site position due to its relatively large ionic radius, it can occupy the B-site if paired with a larger A-site cation such as La [95]. Pyrochlore materials adopt a fluorite-derivative superstructure, differing from the fluorite structure in that two cations are ordered on the face-centered cubic cation sublattice, while 1/8 of the anions are replaced with constitutional vacancies, and the remaining anions are relaxed towards these vacant sites (Figure 10). The potential utility of these materials for nuclear waste immobilization arises, in large part, from their chemical flexibility, since a wide range of aliovalent cations of various sizes can be incorporated onto the two cation sites. Due to this compositional variability, research on the radiation responses of pyrochlore materials proves instructive with respect to the possible effects of extensive chemical doping on the radiation responses of cerium oxides.

Pyrochlore materials show clear compositional trends in radiation tolerance. Like the lanthanide sesquioxides, cation ionic radii are the primary determinant of these trends [28,96–99]. For pyrochlore materials the ratio of the A- and B-site cation radii, *r*A/*r*B, governs radiation tolerance. When this ratio is large, due to the inclusion of relatively large A-site cations or small B-site cations, the energy of cation antisite defect formation is large and the irradiation-induced disorder on the cation sublattice cannot easily be incorporated into the material's crystalline structure [100]. This typically yields amorphization in response to SHI irradiation. In contrast, for materials with small cation radius ratios, cation antisite defects are relatively easily accommodated by the structure and disordering to a highly radiation tolerant defect-fluorite structure is typical [100]. This order-disorder transformation entails the mixing of A- and B-site cations onto a single face-centered cubic cation site and the mixing of oxygen and constitutional vacancies onto a fluorite-like anion sublattice.

Since Ce is relatively large among the lanthanides, pyrochlore materials that include this element on the A-site usually feature large cation ionic radius ratios, making amorphization a likely response to swift heavy ion irradiation. This indicates that doping of CeO<sup>2</sup> with

additional cations, particularly smaller transition metal elements, such as the fission fragments found in nuclear fuels and nuclear wastes, might reduce the radiation tolerance of this material. This doping, if sufficiently extensive, could make accessible irradiation-induced phase transformation pathways to amorphous phases, as well as short-range structural modifications resulting from local defect ordering [98,101,102]. Thus, deviation from the ideal CeO<sup>2</sup> chemical composition due to the introduction of other atomic species appears likely to have a deleterious effect on radiation tolerance in this system.
