**4. Conclusions**

Using the MD method, we simulated the nanopore formation process by applying a thermal spike to single crystal CeO2. The nanopore was formed abruptly at around 0.3 ps after the irradiation and grew to its maximum size at 0.5 ps. Then, it shrank in the time to 1.0 ps and was finally equilibrated. The nanopore size increased with increasing effective stopping power *gSe* (i.e., the thermal energy deposited per unit length in the specimen), but it saturated when *gSe* was 0.8 keV/nm or more. This finding will provide useful information for precise control of the size of the nanopores. We classified oxygen Frenkel pairs into seven types using the distance between the vacant site and the corresponding oxygen atom. Irrespective of the value of *gSe*, the number of interstitial ions became the maximum immediately after irradiation. Subsequently, interstitial ions occupied the vacancies to lower the system energy. When *gSe* was low, the vast majority of Frenkel pairs were the short-distance type and when *gSe* was high, both short-distance and long-distance types of Frenkel pairs were produced.

The present study has clarified the essence feature of the nanopore formation process by irradiation; however, there are several issues that should be addressed in further investigations: (i) the MD simulation box is small compared with the radius of cylindrical hole. (ii) The length to width ratio of the track deviates from that of actual experiment. (iii) Several MD simulations per *Se* are required to confirm quantitative information.

**Author Contributions:** Conceptualization, Y.S. and A.I.; methodology, Y.S.; software, Y.S.; validation, Y.S. and R.K.; investigation, R.K.; data curation, R.K.; writing—original draft preparation, Y.S.; writing—review and editing, N.I. and A.I.; visualization, R.K.; supervision, A.I.; project administration, Y.S.; funding acquisition, N.I. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by JSPS KAKENHI Grant Numbers 16K06963 and 20K05389.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Acknowledgments:** Tomoaki Akabane (a former graduate student at Ibaraki University, currently with Fuji Film Medical IT Solutions, Inc. (Tokyo, Japan)) is acknowledged for the development of the program for molecular dynamics simulation.

**Conflicts of Interest:** The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.
