**2. Methodology**

From the available positron annihilation techniques, we applied positron annihilation lifetime spectroscopy (PALS), coincidence Doppler broadening spectroscopy (CDBS), and a pulsed low-energy positron system (PLEPS).

Generally, the lifetimes of positrons, which are trapped in monovacancies, determined both experimentally and theoretically lie in the interval of 150–300 ps for metals [41]. The lifetimes of positrons trapped in small vacancy clusters have been calculated and experimentally verified many times. As the lattice relaxation around the cluster has a relatively small influence on positron annihilation parameters, it was not included in the calculations. The results show that the lifetime of a positron trapped by di-vacancy does not differ much from that for monovacancy (an increase is about 10 ps for Fe). The lifetime increases rapidly when the cluster grows into two-dimensional tri-vacancy and further into three-dimensional tetra-vacancy [41]. For very large clusters (over 50 vacancies), the lifetime saturates around 450–500 ps. For large voids, the trapping may be limited mainly by positron diffusion to the defect.

Theoretical calculations have revealed that the dislocation line is only a shallow trap for positrons [42,43] (binding energy <0.1 eV). On the other hand, the lifetimes of trapped positrons observed in plastically deformed metals [44] are only slightly lower than the lifetimes of positrons trapped in vacancies. Smedskjaer [45] suggested that the pure dislocation line is a weak positron trap and explained the long lifetimes seen in experiments by point-like defects (vacancies, jogs) associated with the dislocation. For example, the binding energy of 0.92 eV for a vacancy to the edge-dislocation line was calculated in [46] for Fe. Once a positron arrives at the core of the dislocation, it diffuses very quickly (pipe diffusion) until it finds a vacancy attached to the dislocation or a jog of the dislocation; it is then trapped and annihilates there. This explanation is supported also by further calculations [43,47–49]. Calculated lifetimes of positrons trapped in dislocations and corresponding binding energies are listed in Table 2.


**Table 2.** Calculated lifetimes τ and binding energies EB of positrons trapped in the core region of dislocation line and defects associated with dislocation [43,47,48].

The specific trapping rates νD for dislocations were obtained by a combination of positron lifetime measurement and transmission electron microscopy (TEM) or other techniques capable of determining dislocation density (e.g., X-ray diffraction profile) [49]. The values of νD lie in the range of about 10−5–10−<sup>4</sup> m2s−<sup>1</sup> for metals. Thermally activated de-trapping of positrons trapped in a dislocation core (initial shallow trap) may occur at elevated temperatures, which makes νD temperature-dependent [50].

Table 2 shows calculated lifetimes τ (ps) of positrons trapped in bulk, vacancies, and dislocations. The different lifetimes for screw and edge dislocations in Fe single crystals were reported in detail in [48,49]. According to this work, screw dislocations exhibit larger specific trapping rates νD and lifetimes than edge ones. Similarly, to vacancies in the previous section, it can be shown that the minimum dislocation density detectable by PAS lifetime spectroscopy is ρD ~10<sup>12</sup> m<sup>−</sup>2. On the other hand, if ρD ~10<sup>16</sup> m<sup>−</sup>2, almost all positrons are trapped at dislocations (saturated trapping), and only the contribution of the trapped positrons is resolved in the PAS spectrum.

Positrons may be trapped in metals also by a grain boundary (GB). Nevertheless, trapping in GBs is likely only when the mean linear dimension of grains does not exceed a few μm. This means the grain size is comparable to (or smaller than) the positron diffusion length L+, and some fraction of positrons have a chance to reach a GB by diffusion motion. The transport of a positron to GBs limits substantially the positron trapping rate in GBs [51].

The relative values of the energy value for the ground state of a delocalized positron in different materials are different. This makes for possible positron trapping in a precipitate with a lower level of positron ground state energy. An excellent review paper about positron applications in radiation-induced defect studies has been published [52]. During the last few decades, many additional destructive and non-destructive methods have been applied with the aim of making progress in the characterization of complex information about defects' formation and their annealing and/or reannealing [53]. It is necessary to mention that some effects (neutron embrittlement and annealing of defects) are occurring at the same time, and the final microstructure depends on the level of neutron flux/fluence and the temperature of the treatment. Based on previous studies combining Mössbauer spectroscopy (MS) [54,55], positron annihilation spectroscopies (PAS) [56–70], and transmission electron microscopy (TEM) [62,64,68], we recognized that the PALS, as well as CDBS measurements, can yield substantial information about types and concentration of vacancies and their behavior after annealing [63–75]. Positrons trapped in open volume defects, i.e., radiation-induced vacancies, dislocations, microvoids, etc., annihilate with a lower probability than in the perfect area of the same material; thus, the positron lifetime grows with the size of the defects. The production of vacancy defects is directly attributed to radiation damage [59,63]. This was confirmed also by precise TEM studies [76,77]. Nevertheless, the interpretation of results depends on several uncertainties, and the reproducibility could be limited. Generally, we assume that specimens are homogenous. This condition, which is not fully fulfilled in the case of commercial RPV steels, is important for the application of the standard trapping model (STM) [78] in the evaluation of PALS measurements. In inhomogeneous specimens, positrons can be partially attracted by other trapping centers and the various implantation sites, which affects the positron data [79,80]. Therefore, the diffusion-trapping model (DTM) [81] was developed and successfully applied [82,83]. The DTM was several times improved, and its application for the pulsed positron beam technique is described in detail in [84]. The pulsed low-energy positron system (PLEPS) [85–87], which enables the measurement of irradiated specimens if their activities are lower than 1 MBq, was applied also for radiation degradation of RPV steels, although the pick/background ratio became significantly worse. This technique enables the depth profiling study of specimens (in the case of steels up to 550 nm) and can reduce the 60Co radiation contribution to the lifetime spectra to a minimum.

#### **3. Investigated Specimens, Experimental Treatment, and Experimental Techniques**

In this work, Russian RPV steel specimens from 15Kh2MFAA (from Greifswald Unit 7, producers: Atomstroyexport JSC, Moscow, Russia & Škoda Works, Plzen, Czech Republic) commercially used in VVER-440 V-213 type reactors including the Mochovce 34 NPP, Slovenské elektrárne in Slovakia (today under physical start-up) are studied from the perspective of radiation damage and structural recovery after the annealing [88]. The investigated material was cut into 10 pieces, creating five pairs of specimens with dimensions of 10 mm × 10 mm × 0.2 mm. The specimens were polished in a mirror-like way to create

perfect surface conditions before the surface radiation load. The chemical composition of the investigated specimens of 15Kh2MFAA steel was shown above in Table 1.

The radiation damage was experimentally simulated by proton irradiation (H+) in a 500 kV implanter of the Research Centre for Ion Beams and Plasma Technologies SlovakION within the Slovak University of Technology in University Science Park CAMBO Trnava (Slovakia) [89]. Each specimen was implanted (irradiated) with protons with an energy of 500 keV and a hydrogen fluence of 1 × 10<sup>18</sup> cm<sup>−</sup>2. The total radiation damage achieved a value of up to 1 DPA. The layers were implanted at up to 3 μm according to the SRIM calculation for Fe-2.5Cr-0.6Mo implantation by H ions, and the highest level of radiation damage was at a depth of ~2.3 μm (Figure 2).

**Figure 2.** SRIM calculations of DPA for 500 keV H+ ions incident on Fe-2.5Cr-0.6Mo. The detailed K-P calculation was used with a total number of ions in the calculation of 5 × 104.

The investigated specimens were observed by positron annihilation techniques due to their strong sensitivity to small vacancy defects formed during the process of irradiation/implantation. The radiation load affected mostly surface and subsurface layers, and therefore slow positrons were firstly applied for verification of a defect accumulation and observation of a defect depth profile up of to 520 nm. For that, a pulsed low-energy positron system (PLEPS) with the high-intensity positron source NEPOMUC at the FRM-II reactor in Technical University of Munich, Garching, Germany [90,91] was used.

Later, positron annihilation lifetime spectroscopy (PALS) and coincidence Doppler broadening spectroscopy (CDBS) [92] with a conventional positron source of 22Na (Institute of Nuclear and Physical Engineering, Slovak University of Technology, Bratislava, Slovakia) were applied at the Institute of Nuclear and Physical Engineering, Bratislava. The measurements were performed with expectations that only ~20% of positrons can provide a measurable signal from the implanted region up to 3 μm [93], while these techniques investigate materials up to 150 μm.

A PALS spectrum with a total count of ≈10<sup>6</sup> was measured by three Hamamatsu H3378 photomultipliers tubes coupled with BaF2 scintillators (Hamamatsu Photonics, Hamamatsu City, Shizuoka Pref., Japan) and powered by Ortec 556 HV sources (ORTEC/AMETEK, Oak Ridge, Tennessee, USA) in an air-conditioned box (Figure 3a) at room temperature. The START signal for the lifetime measurement is ~1.2 MeV gamma photons emitted by the positron source 22Na. The STOP signal, the annihilation energy of 511 keV, terminates the timing of the positron lifetime measurement, which is directly recorded and stored by DRS4 digitizer chip (RADEC, Koblenz, Switzerland). The own software QtPALS (Petriska, M., Institute of Nuclear and Physical Engineering, Slovak University of Technology, Bratislava, Slovakia) was used for pulse processing and spectrum construction. The data were treated by LT 9 software (Kansy, J., Institute of Physics and Chemistry of Metals, Katowice, Poland).

**Figure 3.** Air-conditioned unit setup for PALS (**a**) and CDB instrument in Institute of Nuclear and Physical Engineering, Bratislava (**b**).

CDB techniques [94] observed spectra with about 10<sup>6</sup> counts by two HPGe detectors GC2019 (ORTEC/AMETEK, Oak Ridge, Tennessee, USA) with Gaussian resolution function 1.9 keV at 1.33MeV (Figure 3b) cooled by the cooling system Cryo-JT. As a high voltage source, a dual high-voltage power supply Canbera3125 (Canberra Industries, Inc./Mirion Technologies, Inc., Meriden, CT, USA) is used. The standard multi-channel analyzer and spectra amplifier was replaced by digital components—DAQ Adlink-PCI (ADLINK Technology, Inc., Taoyuan City, Taiwan). The momentum window for a calculation of the S parameter is |pL| < 2.5 × <sup>10</sup>−3m0c, and for the W parameter, it is 15 × 10−<sup>3</sup> m0c < |pL| < 25 × 10−<sup>3</sup> m0c. Pulse amplitudes were collected and evaluated by own software – QtPALS and QtCDB (Petriska, M., Institute of Nuclear and Physical Engineering, Slovak University of Technology, Bratislava, Slovakia).

After the observation of the radiation damage, the specimens were gradually annealed at 200, 300, 400, 450, 475, 500, and 525 ◦C for detection of the optimal annealing temperature in the process of structural recovery. The post-irradiation annealing was performed in a compact vacuum tube furnace MTI GSL-1800x (MTI Corporation, Richmond, CA, USA). The specimens were annealed for 2 h in a ~6.4 × 10−<sup>9</sup> vacuum bar and after that cooled down in the air for about 45 min. The specimens were then observed by the PALS technique, whereas the annealing process affected the whole depth of the specimen.
