**1. Introduction**

Long nanometer-sized damage trails are created in ceramics continuously along the trajectories of swift heavy ions (SHIs), if the energy transfer from a SHI to an electron system of ceramics is sufficiently high [1–3]. Such characteristic damage is called an ion track. The mechanism of ion track formation has been extensively studied so far, and it has been one of the central topics in the research on ion-solid interactions. Ceramics can be categorized into two groups; amorphizable and non-amorphizable ceramics. If amorphous ion tracks are created, the ceramics are called amorphizable ceramics. The electronic stopping power dependence of ion track sizes in many amorphizable ceramics has been successfully predicted using the thermal spike model [4–8]. According to the model, the amorphous ion track formation is attributable to a local temperature rise sufficient to cause local melting along an ion path. On the other hand, there are non-amorphizable ceramics in which a crystal structure within an ion track region is not amorphized [9–14]. It has been found that in non-amorphizable ceramics, ion track size is markedly smaller than the size of the melt predicted by the thermal spike models [13,14]. Recent molecular dynamics (MD) simulation has revealed that the small ion tracks in non-amorphizable ceramics are attributable to fast recrystallization after transient melting [15–18]. It has been pointed out that the ionic nature of atomic bonding in non-amorphizable ceramics may be responsible for such fast recrystallization in non-amorphizable ceramics [9,19]. However, there is

currently no consensus on which material property makes the distinction between amorphizable and non-amorphizable ceramics. Therefore, it is important to examine the material dependence of ion track formation in terms of amorphization/recrystallization.

Ion track formation caused by SHIs is often accompanied by the formation of hillocks (so-called surface ion tracks) [20–35]. Our recent studies revealed that both ion tracks and hillocks are amorphous in the case of amorphizable ceramics (Y3Fe5O<sup>12</sup> (YIG)) [36,37], whereas crystalline hillocks are found in the case of non-amorphizable ceramics (CaF2, SrF2, BaF2, and CeO2) [36,38]. Since the surface protrusion is a direct consequence of local melting along the ion path (melting of the ion track region), the observation of crystalline hillocks in non-amorphizable ceramics also provides a strong evidence of recrystallization after melting of the ion track region. It was also found that the hillock diameter always coincides with the diameter of a melt predicted by the thermal spike model for both amorphizable and non-amorphizable ceramics. This means that a hillock diameter value is affected by a melting process, but it remains unchanged after the subsequent recrystallization process. It is likely that a hillock size reflects melting, whereas an ion track size reflects both melting and subsequent recrystallization. Therefore, a comparative analysis of ion tracks and hillocks allows us to elucidate the whole processes of melting and amorphization/recrystallization. Moreover, there must be a variety of hillock and ion track morphologies due to an intricate recrystallization process, which can be the origin of the material dependence of nanostructure formation.

We recently proposed a method for precise measurement of a hillock size by transmission electron microscopy (TEM) [36–38]. The method is useful for the direct observation of a hillock side-view. It allows the accurate measurement of hillock dimensions and the identification of hillock crystal structure. In our previous study, we have studied hillocks and ion tracks in non-amorphizable ceramics such as CaF2, SrF2, and BaF2, whereas only one amorphizable ceramic (YIG) has been studied [36,37]. In the present study, we have further studied the relationship between the hillock diameter and ion track diameter for various types of ceramics. First, we show results of the TEM observations for SHI-irradiated amorphizable ceramics such as LiNbO3, ZrSiO4, and Gd3Ga5O<sup>12</sup> (GGG) and then for SrTiO<sup>3</sup> (STO) and 0.5 wt% niobium-doped STO (Nb-STO), whose hillock formation has not been fully explored. The electrical resistivity of STO increases by more than nine orders of magnitude by doping with 0.5 wt% Nb, whereas its crystal structure remains unaffected by the doping [39]. The effect of Nb doping on its hillock morphology is also investigated in this study. Based on the TEM investigations of both amorphizable and non-amorphizable ceramics, we discuss how the SHI-induced nanostructure formation depends on the intricate recrystallization process.
