*Article* **Simulation of Two-Dimensional Images for Ion-Irradiation Induced Change in Lattice Structures and Magnetic States in Oxides by Using Monte Carlo Method**

**Akihiro Iwase \* and Shigeru Nishio**

The Wakasa Wan Energy Research Center (WERC), 64-52-1 Nagatani, Tsuruga, Fukui 914-0192, Japan; snishio@werc.or.jp

**\*** Correspondence: aiwase@werc.or.jp or iwase@mtr.osakafu-u.ac.jp

**Abstract:** A Monte Carlo method was used to simulate the two-dimensional images of ion-irradiationinduced change in lattice structures and magnetic states in oxides. Under the assumption that the lattice structures and the magnetic states are modified only inside the narrow one-dimensional region along the ion beam path (the ion track), and that such modifications are affected by ion track overlapping, the exposure of oxide targets to spatially random ion impacts was simulated by the Monte Carlo method. Through the Monte Carlo method, the evolutions of the two-dimensional images for the amorphization of TiO<sup>2</sup> , the lattice structure transformation of ZrO<sup>2</sup> , and the transition of magnetic states of CeO<sup>2</sup> were simulated as a function of ion fluence. The total fractions of the modified areas were calculated from the two-dimensional images. They agree well with the experimental results and those estimated by using the Poisson distribution functions.

**Keywords:** high energy irradiation; ion track overlapping; oxides; Monte Carlo simulation for two-dimensional images; lattice structures and magnetic states; binomial and Poisson distribution functions
