*3.4. Factors That Determine the Recrystallization Process*

The presence of recrystallization process separates non-amorphizable ceramics from amorphizable ceramics. Two factors that determine the recrystallization process have been proposed; (1) simplicity of lattice structure and (2) the strength of ionic bonding. The previous literature [15] proposed that a simple lattice structure with the smallest number of the peaks in the pair correlation function is in correlation with the recrystallization efficiency. Actually, amorphous ion tracks and hillocks are observed in YIG and GGG that have complicated crystal structure, whereas crystalline ion tracks and hillocks are observed in rather simple structured compounds (CaF2, SrF2, BaF2, and CeO<sup>2</sup> with fluorite structure). STO has a relatively simple cubic structure with space group of Pm3m, where there are only 5 atoms in the unit cell. The relatively simple crystal structure of STO can be the origin of the recrystallization of the ion track region. However, creation of amorphous hillocks in STO demonstrates that STO and Nb-STO are intermediate ceramics between amorphizable and non-amorphizable ceramics. Here, it is worth noting that STO has a perovskite structure which is composed of TiO<sup>2</sup> planes and SrO planes, which make the structure somehow complicated. This unique structure of STO seems to be responsible for the intermediate behavior of ion-induced nanostructure formation. Therefore, we believe that the correlation of recrystallization effectiveness with the simplicity of the crystal structure is one of the promising hypotheses, and its validity should be further examined.

Another possible factor is the strength of ionic bonding, i.e., materials with a higher degree of ionicity recrystallize easily [19,56]. Non-amorphizable ceramics include many ionic crystals. It is conceivable that long-range ionic forces rather than short-range covalent interaction contribute to rapid recrystallization [19,57]. STO has mixed ionic-covalent bonding properties. While a hybridization of the O-2p states with the Ti-3d states within the TiO<sup>6</sup> octahedra leads to a pronounced covalent bonding, Sr2<sup>+</sup> and O2- ions exhibit an ionic bonding character. Although STO is one of the complex oxides, the ionic bonding character in STO may be also responsible for the partial recrystallization of ion tracks. Therefore, the two factors mentioned above is important to explain why STO and Nb-STO are intermediate ceramics between amorphizable and non-amorphizable ceramics.

It is worth discussing why the hillock region fail to recrystallize, whereas the ion track region recrystallizes in STO. The previous MD simulation demonstrated that oxygen atoms settle in their original sites faster than metal atoms in SHI-irradiated MgO and Al2O3, and metallic atoms then adjust to a layer of oxygen that has already been built [15]. The study concluded that that the ability of oxygen atoms to reach their equilibrium sites governs the recrystallization process after melting. It is conceivable that in STO, oxygen loss in the hillock region effectively hinders recovery of the lattice structure. The hillock region tends to be more oxygen deficient than the ion track region, since oxygen atoms tend to escape from the irradiated surface. An important role of oxygen deficiencies should be further investigated in the future.
