*3.5. Summary of Formation Processes of Hillocks and Ion Tracks*

To understand the difference between nanostructure formation in amorphizable and non-amorphizable ceramics, it is important to describe the process in terms of melting and successive recrystallization.

It is convenient to start the discussion with CeO2, which is one of the non-amorphizable ceramics. According to Ref. [38], hillocks are found to be spherical in CeO<sup>2</sup> irradiated with 200 MeV Au. It was found that hillocks (spherical objects) have crystalline features, where the lattice orientation of hillocks was aligned with that of the matrix. This points out to the process consisting of the following three steps as explained in Figure 8a. (1) A molten region is created along the ion path. A part of the molten region protrudes above the surface because of the thermal pressure and additional pressure due to volume change caused by solid-liquid transition. (2) During cooling, the molten region embedded in the matrix begins to recrystallize. The partial recrystallization results in ion tracks smaller than those expected from the size of the melt. The shape change (spheroidization) of the protruded part strongly suggests that the protruded part remains liquid for a long period of time which is long enough for the molten protrusion to change its shape. The protruded part of the molten region can spheroidize if the surface tension is strong enough. (3) A droplet at the surface starts to recrystallize epitaxially using the matrix as a template lattice, so that a crystalline nanosphere having the same crystal orientation as that of the matrix is formed. This result strongly suggests that the molten region embedded in the matrix is solidified before the protruded part of the melt is solidified. It is reasonable to assume that this sequence of the solidification process applies to all SHI-irradiated ceramics. Such a sequence of *Quantum Beam Sci.*  solidification process is supported by the MD simulation of the nanostructure formation in CaF **2020**, *4*, x FOR PEER REVIEW 11 of 15 <sup>2</sup> [16].

**Figure 8.** Schematic formation processes of ion tracks and hillocks in (**a**) CeO2, (**b**) fluorides (CaF2, SrF2, and BaF2), (**c**) STO and Nb-STO, and (**d**) amorphizable ceramics (YIG, LiNbO3, ZrSiO4, and **Figure 8.** Schematic formation processes of ion tracks and hillocks in (**a**) CeO<sup>2</sup> , (**b**) fluorides (CaF<sup>2</sup> , SrF2, and BaF<sup>2</sup> ), (**c**) STO and Nb-STO, and (**d**) amorphizable ceramics (YIG, LiNbO<sup>3</sup> , ZrSiO<sup>4</sup> , and GGG).

GGG). **4. Conclusions**  Amorphizable ceramics such as LiNbO3, ZrSiO4, and Gd3Ga5O12 were irradiated with 200 MeV Au ions at an oblique incidence angle. Line-like homogeneous ion tracks and bell-shaped hillocks are observed by TEM. The ion track and hillock diameters are similar for all the amorphizable ceramics, although the hillock diameter is found to be slightly larger than the ion track diameter. The TEM The likely process of nanostructure formation in fluorides (CaF2, SrF2, and BaF2) irradiated with 200 MeV Au is presented in Figure 8b. According to our previous study [36], most of the crystalline hillocks in these fluorides are nearly semispherical, although some of the hillocks have nearly spherical shape. Since recrystallization plays an important role in both fluorides and CeO2, the formation process in the fluorides should be similar to that of CeO<sup>2</sup> (Figure 8a). The difference between the spherical shape of hillocks and non-spherical shape can be explained by the difference in volume of protrusion.

are found to be amorphous which is in contrast to the crystalline feature of hillocks observed in the non-amorphizable ceramics. Therefore, it can be concluded that STO and Nb-STO are intermediate ceramics between amorphizable and non-amorphizable ceramics. No marked difference is observed between hillock formation in STO and that in Nb-STO. The material dependence of nanostructure formation can be ascribed to the intricate recrystallization process. The present results support that (1) simplicity of lattice structure and (2) the strength of ionic bonding can be the factors that determine

**Author Contributions:** Conceptualization, N.I.; TEM observation, N.I. and T.T.; Sample preparation, N.I.; Ion irradiation, N.I. and H.O.; Manuscript writing, N.I. All authors have read and agreed to the published version

**Acknowledgments:** The authors are grateful to the technical staff of the tandem accelerator at JAEA-Tokai for supplying high-quality ion beams. One of the authors (N.I.) thanks A. Iwase and A. Kitamura for their constant

1. Toulemonde, M.; Assmann, W.; Dufour, C.; Meftah, A.; Trautmann, C. Nanometric transformation of the matter by short and intense electronic excitation: Experimental data versus inelastic thermal spike model.

**Funding:** Part of the present work was financially supported by JSPS KAKENHI Grant Number 20K05389.

the recrystallization effectiveness.

of the manuscript.

**References** 

support during the research.

**Conflicts of Interest**: The authors declare no conflict of interest.

If the volume of protrusion is large, the hillock shape tentatively has an unstable shape because of its high aspect ratio of height to width. It is conceivable that the unstable shape can rapidly turn into a stable spherical shape. Similar spherical hillocks have been already reported in some ceramics (Gd2Zr2O<sup>7</sup> [50] and YIG [51]) irradiated with high-energy fullerene ions with very high Se, supporting the proposition that larger volume of the protrusion is the key to the formation of spherical hillocks.

The likely process of nanostructure formation in STO and Nb-STO is presented in Figure 8c. Although the first and second steps of the process in the figure are the same as those in Figure 8b, the third step of the process is different. Even though the molten region embedded in the matrix recrystallizes partially, the protruded part of the melt failed to recrystallize, resulting in amorphization. The failure of recrystallization only in the hillock region can be ascribed to oxygen deficiencies as discussed above.

The likely process in amorphizable ceramics (YIG, LiNbO3, ZrSiO4, and GGG) is presented in Figure 8d. The process consists of the following three steps. (1) A molten region is created along the ion path. A part of the molten region protrudes above the surface. (2) During cooling, the molten region embedded in the matrix starts to solidify, resulting in the amorphization of the molten region. Herein, the size of the molten region corresponds to that of the ion tracks. (3) The protruded part of the melt also starts to amorphize. This means that the hillock diameter is always similar to the ion track diameter. A subtle change of hillock shape leading to a slightly larger hillock diameter than the ion track diameter is not specified in the schematic, since this effect produces only a small difference between the hillock diameter and ion track diameter.
