*3.3. Fe2O<sup>3</sup>*

The XRD intensity at a diffraction angle of ~33◦ and 36◦ (corresponding to diffraction planes of (104) and (110)) normalized to those of unirradiated Fe2O<sup>3</sup> films on C-Al2O<sup>3</sup> and SiO<sup>2</sup> glass substrates as a function of the ion fluence is shown in Figure 5 for 90 MeV Ni+10, 100 MeV Xe+14 and 200 MeV Xe+14 ion impact. It appears that the XRD intensity degradation is nearly independent of the diffraction planes and substrates. The XRD intensity degradation per unit fluence YXD is given in Table 4, together with the sputtering yields [60] and stopping powers (SRIM2013). The X-ray (Cu-kα) attenuation length LXA is obtained to be 8.8 µm [80] and the attenuation depth is 2.5 and 2.7 µm for the diffraction angle of ~33◦ and 36◦ , respectively, which are much larger the film thickness of ~100 nm and thus the X-ray attenuation correction is unnecessary. The appropriate energy for the XRD vs. S<sup>e</sup> plot, using half-way approximation (E − Se`/2) with the film thickness ` of ~100 nm, again gives nearly the same as E\* for sputtering, in which the energy loss of the carbon foil of 100 nm is taken into account.

**Figure 5.** XRD intensity normalized to unirradiated films of Fe2O<sup>3</sup> as a function of ion fluence for 90 MeV Ni (, •, ∇, N), 100 MeV Xe (o, ∆, +, x) and 200 MeV Xe (•, ♦, H, T ) ions. Diffraction peaks at ~33◦ of Fe2O<sup>3</sup> films on C-Al2O<sup>3</sup> substrate ( (90 MeV Ni), o (100 MeV Xe), • (200 MeV Xe)), ~36◦ of films on C-Al2O<sup>3</sup> (• (90 MeV Ni), + (100 MeV Xe), ♦ (200 MeV Xe)), ~33◦ of films on SiO<sup>2</sup> glass substrate (∇ (90 MeV Ni), ∆ (100 MeV Xe), H (200 MeV Xe)) and ~36◦ of films on SiO<sup>2</sup> glass substrate (N (90 MeV Ni), x (100 MeV Xe), T (200 MeV Xe)). Data of 100 MeV Xe are from [60]. Linear fit is indicated by dotted lines. An estimated error of XRD intensity is 10%.

**Table 4.** XRD data of Fe2O<sup>3</sup> films. Ion, energy (E in MeV), XRD intensity degradation (YXD), E\* = E-∆E (energy loss in carbon foil of 100 nm) (MeV) and electronic (Se\*) and nuclear (Sn\*) stopping powers in keV/nm and projected range Rp\* (µm) calculated using SRIM2013. Sputtering yield Ysp from [60]. Results by low energy (100 keV Ne) ion are also given.


Similarly to SiO<sup>2</sup> and ZnO, the characteristic length (LEQ) is estimated to be 4.5, 4.3 and 4.1 nm for 90 MeV Ni+10, 100 MeV Xe+14 and 200 MeV Xe+14, respectively, from the empirical formula of the single-electron loss cross-section σ1L(10−<sup>16</sup> cm<sup>2</sup> ) of 0.56 (90 MeV Ni+10), 0.59 (100 MeV Xe+14) and 0.61 (200 MeV Xe+14) [83,84]. Here, σ1L = σ1L(Fe) + 1.5σ1L(O). LEQ is much smaller than the film thickness and the charge-state effect does not come into play.

Figure 6 shows XRD intensity degradation YXD vs. electronic stopping power (Se) (SRIM2013 and TRIM1997) together with the sputtering yields Ysp vs. Se. Both YXD and Ysp follow the power-law fit and the exponent using TRIM1997 gives a slightly larger fit than those using SRIM2013. The exponent of lattice disordering is two times larger than that of sputtering (Nsp is exceptionally close to unity, in contrast to the SiO<sup>2</sup> and ZnO cases). The change in the lattice parameter appears to scatter depending on the substrate and diffraction planes, and is not proportional to the ion fluence. The average of the lattice parameter change in the (104) and (110) diffractions of Fe2O<sup>3</sup> on C-Al2O<sup>3</sup> is −0.2, −0.3% (an estimated error of 0.1%) and nearly zero at ~1 <sup>×</sup> <sup>10</sup><sup>12</sup> cm−<sup>2</sup> for 200 MeV Xe, 100 MeV Xe and 90 MeV Ni ion impact. The dependence of the lattice parameter change on the ion fluence and S<sup>e</sup> is complicated, and is to be investigated.

**Figure 6.** XRD dgradation per unit fluence YXD of polycrystalline Fe2O<sup>3</sup> films (•, o) and sputtering yield Ysp (N, x) as a function of the electronic stopping power (Se) in keV/nm. Power-law fits are indicated by dashed lines and S<sup>e</sup> is calculated using SRIM2013 (•, N) and TRIM1997 (o, x): (•) YXD = (0.028 Se) 2.28 (SRIM2013), (o) YXD = (0.029Se) 2.54 (TRIM1997), (N) Ysp = (2.2 Se) 1.05 (SRIM2013) and (x) Ysp = (1.16 Se) 1.25 (TRIM1997). Sputtering data and power-law fit to the sputtering yields (TRIM1997) from [60].
