**4. Discussion**

The process of inward diffusion of oxygen from the LBE side and outward diffusion of Fe from the steel matrix mutually governed the oxide formation at the boundary between the steel surface and LBE. The cold working is a good simulation of the microstructural evolution under radiation damage in dislocation defects and interstitial atom types of

defects. In the case of the corrosion behavior exhibited by the cold-worked austenitic stainless-steels in LBE, the cold working accelerated the formation of the duplex oxide layer and the ferritization via Ni dissolution [10] at 500–550 ◦C in 1000–3000 h. As shown in Figure 5c, even at 450 ◦C and in 330 h experimental conditions, Ni dissolution was observed in the irradiated region and not in the nonirradiated region. As shown in Figure 6, oxide formation was enhanced via ion irradiation in LBE even at a low oxygen concentration by the formation of radiation defects. In the nonirradiated region, the oxide layer can grow in LBE with an oxygen concentration dissolved in LBE under thermal equilibrium. The thermal equilibrium state is also applicable to the irradiated region because oxidation reactions occur after ion irradiation. However, the number of Fe atoms diffusing outward might increase through site changes with vacancies, which might be trapped by impurities or the strain field induced via ion irradiation, leading to more Fe self-diffusion than that found under normal thermal activity. The activation energy of Fe self-diffusion in α-Fe is 2.87 eV, in which the vacancy formation energy (Evf) and migration energy (Evm) are 1.61 and 1.3 eV, respectively [17]. The diffusion coefficient (D) is calculated by D = D0exp(−(Evf + Evm)/kT, where D<sup>0</sup> is 8.0 <sup>×</sup> <sup>10</sup>−<sup>5</sup> <sup>m</sup>2/s, k is 8.62 <sup>×</sup> <sup>10</sup>−<sup>5</sup> eV/K, and T is 723 K. The thermal diffusion length (Ld) is described by L<sup>d</sup> = (6Dt)1/2, and L<sup>d</sup> of Fe was calculated to be 1.4 nm for the specimen subjected to the corrosion test performed at 450 ◦C for 330 h. Therefore, Fe self-diffusion does not affect oxide formation at the specimen surface. However, after ion irradiation, assuming all vacancies exist even at RT, when Evf = 0, which means the neighbor of the diffusive atom is a vacancy, D exhibits its maximum value and L<sup>d</sup> is 580 µm. The actual L<sup>d</sup> is smaller than this maximum value because of the void formation and residual vacancies trapped by the strain field induced by radiation damage. From an SRIM calculation shown in Figure 1b, the total number of vacancies was estimated to be 1.5 <sup>×</sup> <sup>10</sup><sup>19</sup> <sup>m</sup>−<sup>2</sup> around 1 <sup>µ</sup>m depth, induced by the displacement damage of 20 dpa, which is considered average damage through 2 µm depth. This is just the case of Evf = 0, then, L<sup>d</sup> shows a maximum value of 580 µm.

On the contrary, using the void size of 1.3 nm and the density of 3 <sup>×</sup> <sup>10</sup><sup>24</sup> <sup>m</sup>−<sup>3</sup> for 316L irradiated by 4 MeV-Au ions at 450 ◦C up to about 20 dpa from Reference [13], the number of vacancies included in the total voids was estimated to be 4.0 <sup>×</sup> <sup>10</sup><sup>17</sup> <sup>m</sup>−<sup>2</sup> , assuming that the one void had 100 vacancies. From these rough estimations, the number ratio of residual (invisible) vacancies is 0.0267 (4.0 <sup>×</sup> <sup>10</sup>17/1.5 <sup>×</sup> <sup>10</sup>19). Then, a mean free path (MFP) of vacancy diffusion is approximately 15 µm. This value is reasonable because recombining with interstitials and/or disappearance into sink sites reduces the MFP to be several micrometers. However, this might be a limitation of the simulation method that employed (ex situ) the corrosion test after ion irradiation.

In contrast, oxygen atoms diffuse inward from the surface as interstitial atoms. The migration energy of an interstitial atom (Eim) is 0.89 eV [14]. Here, D = D0exp(−Eim)/kT, where D<sup>0</sup> is 1.79 <sup>×</sup> <sup>10</sup>−<sup>7</sup> <sup>m</sup>2/s, k is 8.62 <sup>×</sup> <sup>10</sup>−<sup>5</sup> eV/K, and T is 723 K. The oxygen diffusion length (Ld) was calculated to be 910 µm according to L<sup>d</sup> = (6Dt)1/2. Therefore, oxygen can sufficiently diffuse into the material in this corrosion experiment in LBE. Comparing the EDS line spectra shown in Figure 5b,c, the inward oxygen diffusion lengths of the nonirradiated and irradiated regions are comparable. However, in the irradiation region, the oxygen concentration increased about six times more than that of the nonirradiated case. From these rough estimations, two reasons for the enhanced oxide formation in the case of ion irradiation in 316L are considered: (1) enhanced Fe diffusion caused by vacancy diffusion after ion irradiation and (2) enhancement of O interstitial diffusion induced via radiation damage. This enhances the oxidation reaction between Fe, Cr, and O. Based on the results of this study, it is suggested that radiation-induced diffusion during irradiation enhances the oxidation much more than that after irradiation.
