*3.1. X-ray Di*ff*raction*

Figure 4 shows FIA-XRD patterns from undoped YAG crystals irradiated with 200 MeV Xe14<sup>+</sup> ions to various fluences ranging from 0 to 5 <sup>×</sup> <sup>10</sup><sup>13</sup> ions/cm<sup>2</sup> . Before the irradiation, relatively strong four peaks were observed, all of which were assigned to diffractions from the garnet structure: 55.8◦ for (4 2 2), 124.6◦ for (9 2 1), 135.7◦ for (9 3 2), and 150.3◦ for (7 7 2) [14]. Because the garnet structure includes many atoms in a unit cell, many peaks are reported in the powder diffraction patterns. However, our samples showed only limited peaks due to high crystallinity. After the irradiation to <sup>1</sup> <sup>×</sup> <sup>10</sup><sup>11</sup> ions/cm<sup>2</sup> , the same peaks were observed, while the intensity ratios and the diffraction angles slightly changed. At the fluence of 1 <sup>×</sup> <sup>10</sup><sup>12</sup> ions/cm<sup>2</sup> , new four peaks were added, which were also assigned to the garnet structure: 65.1◦ to (4 4 0), 72.0◦ to (5 3 2), 88.6◦ to (5 5 2), and 105.2◦ to (6 5 3) [14]. Because of the partial amorphization, the single crystal was partly broken down to smaller grains facing various directions, i.e., poly-crystallization. Consequently, the new peaks were allowed to be observed. At the fluence of 1 <sup>×</sup> <sup>10</sup><sup>13</sup> ions/cm<sup>2</sup> and higher, all the peaks disappeared indicating the full amorphization of the YAG crystal. Amorphization of Nd-doped YAG crystals was already reported by Rutherford backscattering spectrometry (RBS)-channeling [15] and TEM [10]. *Quantum Beam Sci.* **2020**, *4*, x FOR PEER REVIEW 7 of 13 × 1011 ions/cm2, the same peaks were observed, while the intensity ratios and the diffraction angles slightly changed. At the fluence of 1 × 1012 ions/cm2, new four peaks were added, which were also assigned to the garnet structure: 65.1° to (4 4 0), 72.0° to (5 3 2), 88.6° to (5 5 2), and 105.2° to (6 5 3) [14]. Because of the partial amorphization, the single crystal was partly broken down to smaller grains facing various directions, i.e., poly-crystallization. Consequently, the new peaks were allowed to be observed. At the fluence of 1 × 1013 ions/cm2 and higher, all the peaks disappeared indicating the full amorphization of the YAG crystal. Amorphization of Nd-doped YAG crystals was already reported by Rutherford backscattering spectrometry (RBS)-channeling [15] and TEM [10].

**Figure 4.** FIA-XRD patterns of undoped YAG sa**m**ples in unirradiated state and irradiated with 200 MeV Xe14+ ions to various fluences ranging from 1 × 1011 to 5 × 1013 ions/cm2. The patterns are shifted for vertical direction for clarity. **Figure 4.** FIA-XRD patterns of undoped YAG samples in unirradiated state and irradiated with 200 MeV Xe14<sup>+</sup> ions to various fluences ranging from 1 <sup>×</sup> <sup>10</sup><sup>11</sup> to 5 <sup>×</sup> <sup>10</sup><sup>13</sup> ions/cm<sup>2</sup> . The patterns are shifted for vertical direction for clarity.

later. A chained horizontal line at 1.8295 indicates the index in the unirradiated state at the wavelength of 632.8 nm from literature [16]. After the irradiation to 1 × 1011 ions/cm2, a very weak and broad enhancement peak was observed at 6 μm in depth with the full width at half maximum (FWHM) of ~4 μm. Since the deviation from the unirradiated value was so small for the data at 1 × 1011 and 3 × 1011 ions/cm2 that the deviation from the unirradiated value was plotted with five times

*3.2. Refractive Index Profiling* 

magnification around the unirradiated value.
