# Mechanisms of radiation-induced G-phase precipitation in Fe-MnNiSi ferritic model alloys at 400 °C

Quentin Tencé, E. Meslin, Isabelle Mouton, B. Decamps, Raphaëlle Guillou, Béchade Jean-Luc, Erik Elkaim, Anna Fraczkiewicz, M. Nastar

► To cite this version:

Quentin Tencé, E. Meslin, Isabelle Mouton, B. Decamps, Raphaëlle Guillou, et al., Mechanisms of radiation-induced G-phase precipitation in Fe-MnNiSi ferritic model alloys at 400 °C. Acta Materialia, 2025, 301, pp.121502. 10.1016/j.actamat.2025.121502. emse-05328752

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# Mechanisms of radiation-induced G-phase precipitation in Fe-MnNiSi ferritic model alloys at 400 °C

<figure><img src="image_2.png" /></figure>

Quentin Tencé<sup>a</sup>, Estelle Meslin<sup>a,∗</sup>, Isabelle Mouton<sup>b,c</sup>, Brigitte Décamps<sup>d</sup>, Raphaëlle Guillou<sup>c</sup>, Jean-Luc Béchade<sup>a</sup>, Erik Elkaim<sup>e,†</sup>, Anna Fraczkiewicz<sup>f</sup>, Maylise Nastar<sup>a</sup>

## ARTICLE INFO

### Keywords:

- Point defects

- Precipitation

- Transmission electron microscopy (TEM)

- X-Ray diffraction (XRD)

- Atom probe tomography (APT)

## ABSTRACT

A high-purity Fe-0.7Mn-1.8Ni-0.8Si model reactor pressure vessel alloy was irradiated with 22.5 MeV Fe⁹⁺ ions at 400 °C, producing a radiation dose of 1–2 dpa at a depth of 1 µm, following by annealing at the same temperature for up to 34 weeks. Irradiation led to the formation of four Mn-Ni-Si-enriched features: spherical precipitates in the bulk and on dislocation lines, sandwich-like precipitates, and toroidal segregation on dislocation loops. High-resolution transmission electron microscopy and synchrotron X-ray diffraction identified bulk precipitates as G-phase, exhibiting L2₁ symmetry, a cube-on-cube orientation with the matrix, and semi-coherent interfaces. Atom probe tomography showed that the bulk G-phase precipitates have the formula Ni₁₆ (MnₓFe₁₋ₓ)₆ Si₇, with increased Fe substitution in the Mn sublattice under irradiation. G-phase precipitates exhibited thermodynamic stability during post-irradiation annealing, while sandwich-like phases dissolved, indicating metastability. Irradiation reduces the matrix solubility limit, which is evidenced by the reduced volume fraction of G-phase precipitates observed in post-irradiation annealed samples. Heterogeneous precipitation of the G-phase on dislocation lines likely occurs through radiation-induced segregation (RIS) of Ni, Si, and Mn. Bulk sandwich-like precipitates with a dense Ni-Si-enriched phase in the center are strongly evidenced to form through a two-step mechanism: the SIAs clustering into a dense NiSi phase, followed by the kinetics of vacancy-solute clustering, leading to the precipitation of the less dense G-phase.

## 1. Introduction

Lattice radiation damage and solute clusters are microstructural features that significantly affect the mechanical properties of nuclear materials. For instance, reactor pressure vessel (RPV) steels of pressurized water reactors (PWR) experience hardening embrittlement [1–9]. The nanometer-sized segregated solute clusters are recognized as the primary contributors to the embrittlement trend curves of RPV steels [1,10,11]. Atom Probe Tomography (APT), which provides the composition and size distribution of the solute clusters, was used to identify the role of composition on the embrittlement trend curve. In addition to Cu, recent trend laws also consider the concentrations of Ni, Si and Mn, as well as the irradiation temperature, in their long-term operation models [11–13].

Up to now, there is no consensus on the phase diagram and mechanisms that control the redistribution of these solutes in ferritic steels

and their model alloys under irradiation. The mechanisms of solute redistribution operating under irradiation are diverse and can occur sequentially or concurrently. They are generally categorized into homogeneous and heterogeneous solute segregation, as well as radiation-enhanced precipitation (REP) and radiation-induced precipitation (RIP) [14]. The increase in lattice point defects (PDs) under irradiation leads to radiation enhanced diffusion (RED), thereby accelerating diffusion-controlled phenomena such as REP. Under irradiation, thermal precipitation driving forces compete with radiation-induced solute redistribution mechanisms. Among the radiation-induced solute redistribution mechanisms, let us mention the RIS [15–18] and the PD-induced precipitation of non-coherent precipitates [14,19].

Eventually, precipitates may dissolve when ballistic mixing dominates over RED [20,21] or when the supersaturation of PDs increases

<footnote><sup>a</sup> Université Paris-Saclay, CEA, Service de recherche en Corrosion et Comportement des Matériaux, SRMP, Gif Sur Yvette, 91191, France</footnote>

<footnote><sup>b</sup> SIMAP, Univ. Grenoble Alpes, CNRS, Grenoble INP, F-38000, Grenoble, France</footnote>

<footnote><sup>c</sup> Service de Recherche en Matériaux et procédés Avancés, CEA Saclay, Université Paris-Saclay, 91191 Gif-Sur-Yvette, France</footnote>

<footnote><sup>d</sup> IJClab, Laboratoire de Physique des 2 infinis Irène Joliot-Curie, Université Paris-Saclay, Orsay, 91400, France</footnote>

<footnote><sup>e</sup> Soleil, Synchrotron, L'Orme des Merisiers, Saint-Aubin, BP 48, Gif-sur-Yvette cedex, 91192, France</footnote>

<footnote><sup>f</sup> MINES Saint-Etienne, Université de Lyon, CNRS, UMR 5307 LGF, Centre SMS, 42023, Saint-Etienne, France</footnote>

<footnote>* Corresponding author.
E-mail address: estelle.meslin@cea.fr (E. Meslin).</footnote>
the solubility limit of interstitial species such as carbon or oxygen [22, 23].

In Cu-rich RPV steels or Fe-Cu model alloys, one observe REP of Cu-rich precipitates [24], and in low-Cu ferritic alloys containing less than 0.1 wt% Cu such as French RPVs, one observe the formation of Cu-rich clusters induced by irradiation [25,26]. In low-Cu Fe-Cu alloys, the so-called Cu-rich clusters were claimed to be formed sequentially after RIS of Cu dragged by vacancies on PDs sinks. The formation mechanism of a Cu-rich secondary phase at PDs sinks likely initiates with a positive RIS of Cu, resulting in local Cu supersaturation. However, it can also be expected that the bulk solubility of Cu is reduced by irradiation. Recent experiments clearly demonstrate a shift in the equilibrium Cu composition of an iron volume in contact with a Cu volume under electron irradiation [27]. A strong interaction was highlighted between the formation of these Cu-rich precipitates and the development of precipitates rich in Mn and Ni (MNPs) [3,28–30]. Significant mole fractions of MNPs precipitate after the formation of Cu-rich precipitates, while Mn-Ni rich clusters form at higher radiation doses in Cu-free steels [29]. Besides, in Cu-bearing steels, the MNPs are appended to Cu rich co-precipitates (CRPs) [30] and may form core shell structures [31]. It is worth noting that, although not discussed in the initial publications, Si plays a significant role in the formation of MNPs [32]. Si enters indeed into the composition of the identified MnNi-bearing intermetallic phases such as the G-phase (Ni₁₆Mn₆Si₇) and Γ₂ (Ni₃Mn₂Si) phases. Unfortunately, the phase diagrams of these multi-component systems, including that of the quaternary model alloy Fe(Mn,Ni,Si), is not clearly established, or at least, there is no consensus [33,34]. Thermocalc predicts for most of the commercial RPV steels at low temperature, the precipitation of either the G-phase or Γ₂-phase or both [33,34]. High-resolution synchrotron X-ray diffraction (HR-XRD) analysis revealed that the MNSPs in 5 out of the 6 neutron-irradiated Cu-bearing commercial steels are consistent with an intermetallic G-phase [35]. In low-Cu RPV steels, APT analysis highlight solute-rich clusters, which hardly reach a few nanometers in size [32,36,37]. HR-XRD tend to show the precipitated phase is the Γ₂-phase in the high-Ni CM6 alloy and the G-phase in the medium-Ni LG alloy [35]. However, the small size of the solute clusters and the presence of cementite phase in the analyzed samples have made the interpretation of the X-ray diffraction spectra particularly challenging [35].

To assess potential effects of irradiation on the precipitation of MNSPs, post-irradiation annealing treatments were performed. For instance, APT analyses of a neutron-irradiated Cu-free FeMnNi model alloy, both before and after annealing at 400 °C, revealed partial dissolution of MnNi clusters upon annealing [38]. The ≈2-nm-diameter Ni-, Si- and Mn-enriched nanoclusters formed in the neutron irradiated base and weld high nickel VVER-1000 metals had dissolved into the matrix after 24 h at 450 °C [36]. A few post-irradiation annealing (PIA) treatments were performed on various RPV steels at temperatures above 425 °C. For sufficiently long annealing times, it is almost always observed that a portion of the precipitates formed under irradiation dissolves [3,31,32,36]. In Ni-rich steels, a small fraction of the largest MNSPs remained and began to coarsen over longer times [3,32]. Unfortunately, in most of the PIA studies, the annealing temperature was higher than the irradiation temperature by at least 100 °C, making it difficult to distinguish the effects of irradiation from those of temperature. In conclusion, our current understanding of phase equilibria in the various ferritic steels and the impact of irradiation on these equilibria is still incomplete.

Besides, the debate remains open regarding the formation mechanisms of the solute-segregated zones in these alloys. As mentioned above, the precipitation kinetics of the G-phase differed in the presence of Cu, involving a two-step phase selection: first, the precipitation of the Cu-rich phase, followed by the formation of the “late blooming phase” MNPs. In low-Cu steels, it was proposed that the small solute clusters in the vicinity of SIA or vacancy defects revealed by atom probe tomography (APT) and transmission electron microscopy (TEM)

are not precipitates but rather coherent segregated zones resulting from a RIS [39], other groups argue that the solute-segregated zones are precursors or precipitates of a secondary phase [3,30,40,41]. According to the first group, precipitation has not occurred, and the observed solute clusters are non-equilibrium objects that grow with a very low rate, have a composition which is not necessarily the equilibrium composition, and are systematically attached to a PD cluster [39]. However, according to the second group, solute clusters should evolve into precipitates with compositions determined by the phase diagram at the irradiation temperature, with nucleation occurring through both homogeneous and heterogeneous mechanisms depending on temperature and the nominal composition [41]. A diffraction pattern highlighting a change in the symmetry of the solute clusters could have settled the debate, but as explained above the crystallographic analysis of a small quantity of nanoscale solute clusters is very difficult, even with a high resolution X-ray diffraction technique [35]. In duplex stainless steels (DSS), long-term thermal aging results in the formation of large G-phase precipitates (approximately 8 nm), which was extensively studied [42–45]. APT and TEM characterizations of the ferrite portion of an annealed DSS at 673 K, have highlighted a two-step nucleation process, first the nucleation of a coherent metastable phase then its transformation into G-phase precipitates at the critical size of 2.6 nm and with a critical composition of Ni₁₆Si₃.₅(Fe,Cr)₃.₅Mn₆ [42]. Note that the structural change of precipitates into brittle silicides certainly has an impact on their obstacle strength against gliding dislocations and on the embrittlement of the materials. The question of whether the solute clusters formed under irradiation in low alloy steels are coherent or have a different crystallographic structure than the matrix is therefore an important topic. In addition, most of the investigated secondary phases in RPV steels have atomic densities significantly different from the parent phase. Secondary phases with atomic density that differs from the matrix can be seen as an efficient PDs sinks that may totally change the competition of solute and PDs agglomeration reactions [14,19,46]. To our knowledge, the kinetic pathways of precipitation in RPV steels have not been analyzed in light of this point-defect-induced mechanism.

To get more insight into the formation mechanism of MNPs, we report in this article a comprehensive analysis of the solute redistribution in a Cu-free Fe-based model alloy of RPV steels: Fe-0.7Mn-1.8Ni-0.8Si (at.%). It contains all solutes contributing to the composition of the intermetallic G-phase, based on the phase diagram at 290 °C by Jacob et al. [34]. We expect the chosen composition to promote the formation of the G-phase. We proceed to ion irradiation (400 °C, $10^{-6}$ to $10^{-5}$ dpa $s^{-1}$), to accelerate the kinetics of the radiation damage evolution, to promote the formation of precipitates as large as possible, with the aim of achieving a deeper understanding of the underlying precipitation mechanisms. Even though these conditions differ from those experienced by RPV materials under neutron irradiation (290 °C, $10^{-10}$ dpa $s^{-1}$) [3,30,39–41], the use of charged particles remains relevant for studying the precipitation mechanisms of LBPs under irradiation, as it is shown by Almirall et al. [12].

As-irradiated samples are then annealed at the temperature of irradiation to assess the thermal stability of the radiation-induced solute clusters. The as-irradiated and post-irradiation annealed samples are characterized by transmission electron microscopy (TEM), both conventional and high resolution (HR), atom probe tomography (APT) and high-resolution synchrotron X-ray diffraction (HR-XRD). To discuss the results, we rely on our understanding of the thermodynamic and diffusion properties, the phenomena of RIS in these systems, and we also consider the role played by a point defect supersaturation in phase selection.

In Section 2, we introduce the experimental details, including the selection and elaboration method of the model alloy, the ion irradiation conditions, and the three characterization techniques. After a general description of the microstructure, Section 3 focuses on the effect of irradiation and post-irradiation annealing on the volume fraction, size,
<table><caption>Fig. 1. Chemical composition of the studied alloy, as-received from EMSE (Nominal composition).</caption><thead><tr><th></th><th>Mn</th><th>Si</th><th>Ni</th><th>C</th><th>S</th><th>O</th><th>N</th><th>Fe</th></tr><tr><th></th><th>at.%</th><th>at.%</th><th>at.%</th><th>wppm</th><th>wppm</th><th>wppm</th><th>wppm</th><th>-</th></tr></thead><tbody><tr><th>Nominal content</th><td>0.64</td><td>0.76</td><td>1.7</td><td>&lt;5</td><td>&lt;5</td><td>&lt;5</td><td>&lt;5</td><td>bal.</td></tr><tr><th>±</th><td>0.06</td><td>0.04</td><td>0.1</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr></tbody></table>

composition, morphology, and lattice parameter of each population of solute-rich clusters/precipitates. Then, in Section 4, we rely on the experimental results to analyze the selection of phases and propose a kinetic path of solute redistribution mechanisms and especially G-phase precipitation.

## 2. Experimental details

### 2.1. Materials

The studied alloy is a high-purity quaternary alloy Fe-0.7Mn-1.8Ni-0.8Si (at. %), with a composition chosen to promote the precipitation of the G-phase. The solute proportions are selected to closely match those of the reference G-phase Ni₁₆Mn₆Si₇, in such a way that, in the Ni-Si-Mn ternary diagram disregarding the contribution of iron, the solid solution under study is located in the vicinity of point G [10,34, 47]. Additionally, the solute concentrations are adjusted to minimize the destabilizing effects of Ni and Mn on the Body-Centered Cubic (BCC) structure while maximizing the precipitation driving force. As a result, this alloy will be referred to as the 'G-alloy' in the following text. It was prepared using cold crucible induction melting at École des Mines de Saint-Étienne (EMSE, France), followed by forging and austenitizing at 1473 K. The alloy was then recrystallized at 973 K for 24 h to obtain a BCC microstructure. The final microstructure exhibits a bimodal grain size distribution: 100 µm grains and clusters of 1 µm grains, likely resulting from the recrystallization process. The BCC structure was confirmed by conventional Electron Backscatter Diffraction (EBSD) at EMSE to ensure the absence of residual austenite. The ingot slices were mechanically polished to a thickness of 100 µm, then punched into 3 mm diameter discs, which were annealed at 973 K for 24 h in a vacuum of 10⁻⁷ mbar, followed by air cooling. Prior to irradiation, the discs were electro-polished on one side in a 95% methanol - 5% perchloric acid solution (–42 °C, 24 V) to remove the hardened layer.

### 2.2. Irradiation experiments and thermal annealing treatments

Neutron irradiation of the materials is modeled by ion irradiation conducted within the JANNuS-Saclay facility [48,49]. The sample were irradiated with the accelerator Epimethée with 22.5 MeV Fe⁹⁺ ions, at a flux of 7.8 ± 2.0 10¹⁰ ions cm⁻² s⁻¹ at 400 °C. The irradiation, conducted in 7 steps, lasted for 37 h and 20 min, with fast cooling up to room temperature and pauses during the night. Dose and ion implantation depth profiles are calculated using the binary collision approach of Norgett, Robinson and Torrens (NRT) [50], using Iradina simulation [51] in quick calculation mode with a displacement energy of 40 eV. The selected irradiation conditions are aimed at achieving a relatively uniform dose profile, ranging from 1 to 2 dpa at a depth of 1 µm, corresponding to 7 10⁻⁶ to 1.3 10⁻⁵ dpa s⁻¹ (Fig. 2). This depth choice not only falls within the dose range where LBPs are known to precipitate (doses greater than 1 dpa, [29]) but also helps mitigate the surface effects and the effects of the ion implantation peak [52]. The maximal implantation depth is equal to 4 µm. We chose the temperature of 400 °C for two main reasons. On the one hand, this temperature is in the stable temperature range of the G-phase in RPV model alloys according to recent thermodynamic calculations (below 450 °C [34]) thereby promoting the formation of the G phase. On the other hand, the atomic diffusion is fast enough to conduct post-irradiation annealing within weeks (between 1 to 52 weeks at 425 °C

<figure><img src="image_3.png" /><figcaption>Fig. 2. Evolution of the dose and atomic fraction of implanted ions as a function of depth in the investigated alloy. The depth and the corresponding dose analyzed by APT and cross-sectional TEM lamellas are reported. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

according to Almirall et al. [3]) to monitor the precipitate stability at the same temperature as the irradiation one. Thus, both thermal and radiation contributions to the formation of MNSP may be investigated. Irradiated samples were annealed in a vacuum of 10⁻⁷ mbar at 400 °C for 2 weeks and 34 weeks.

### 2.3. Microstructural characterization

#### Transmission electron microscopy

After irradiation, TEM cross-sectional samples were lifted out by Focused ion-Beam (FIB) FEI Helio 650 NanoLab dual-beam Scanning Electron Microscopy (SEM). The irradiation defects introduced by Ga ions of the FIB were cleaned by flash electro-polishing with an electrolyte composed of 48% of perchloric acid in ethanol at 9 V during 0.02 s at –46 °C. [53,54]. Loop and precipitate contrast analyses were performed using a Conventional TEM (CTEM) 200 kV FEI TECNAI G2 (LaB₆ filament) located at the CEA Saclay SRMP. High-Resolution Scanning TEM (HR STEM) images of the precipitates were obtained using a Cs-probe corrected FEI TITAN TEM (FEG) in analysis mode at CentraleSupélec (France), as well as with a JEOL ARM 200F double Cs-corrected TEM. TEM operation were performed at 200 kV on the three instruments. The sample thickness was estimated by Convergent Beam Electron Diffraction (CBED) technique along a [200] reflection [55].

#### Atom probe tomography

Atom Probe Tomography (APT) needle-shaped specimens were extracted and sharpened using FIB. Analyses were performed in a CAMECA LEAP 4000X HR at 60K, in laser pulsing energy mode with a wavelength of 382 nm, a pulse energy of 40 pJ, and a pulse repetition rate of 200 kHz. All the APT specimens were analyzed in similar evaporation conditions to focus on the irradiation and annealing effects on the analyzed samples. The IVAS 3.8.4 software by CAMECA was used for 3D reconstructions, based on interplanar distances along identified crystallographic directions. The data processing was done with IVAS and Python. The mass spectrum peak deconvolution procedure, is described in the supplementary material. To analyze the chemical composition of the solute-rich precipitates formed under irradiation, atomic fraction profiles were obtained in two different ways: proxigrams with a bin size of 0.5 nm, and 1D concentration profiles across solute-rich
areas along the Z-direction, with a diameter of 3 nm and a bin size of 1 nm.

### High resolution synchrotron X-ray diffraction

HR-XRD analyses were carried out at the CRISTAL beamline of the SOLEIL synchrotron facility. Using a synchrotron X-ray beam offers two key advantages for investigating the crystallographic structure of nano-precipitates: a high-energy X-ray beam of 15.626 keV to enhance diffracted signals, and a monochromatic beam to improve diffraction peak resolution. Additionally, the high flux allows for the detection of very small particles present in low volume fractions. The energy allowed us to discriminate the metallic fluorescence's signals by the XPAD detector while keeping a good angular resolution and also to distinguish the matrix peaks from the secondary phase peaks. The analyses were performed in reflection mode with a constant incident angle of 5° to minimize the contribution of the underlying non-irradiated matrix to the diffracted signal. To improve counting statistics, data acquisition was carried out while rotating the samples. It increases the number of diffracting particles and reduces preferential orientation.

An XPAD2 hybrid pixel 2D detector, known for its excellent sensitivity and high signal-to-noise ratio, was used to collect the HR-XRD diffraction patterns.

The detector's angular acquisition range is 12°, and its position was scanned from 12° to 48° in 2θ with 1° step and an acquisition time of 40 min per diagram. Raw data processing was carried out using ImageReducer software by Soleil, and the Rietveld refinement was performed using the MAUD software [56,57]. Cagliotti parameters were determined through the analysis of a LaB₆ standard powder.

## 2.4. Volume fraction of the precipitates

To estimate the volume fraction of precipitates and monitor its evolution during post-irradiation annealing, we use a lever-rule-based calculation relying on chemical concentration measurements obtained by APT. This choice is motivated by the difficulty of accurately counting precipitates without being affected by the 2D projection effects of the TEM images or the sampling effect induced by APT (see Section 3.5).

Assuming that all enriched solute precipitates and features have the same composition, we estimate the precipitate volume fraction, $f_V$, with the following lever-rule:

$$f_V C_X^P + (1 - f_V) C_X^{\text{mat}} = C_X^{\text{nom}} \quad (1)$$

where $C_X^P$ (X = Ni, Si, Mn) and $C_X^{\text{mat}}$ are the atomic fractions of solute X in the precipitate and the matrix, respectively, and $C_X^{\text{nom}}$ is the nominal fraction of atoms X. The volume fraction $f_V$ is thus given by the following formula:

$$f_V = \frac{C_X^{\text{nom}} - C_X^{\text{mat}}}{C_X^P - C_X^{\text{mat}}} \quad (2)$$

Further details regarding the calculation of $C_X^P$, $C_X^{\text{mat}}$ and $C_X^{\text{nom}}$, as well as the associated uncertainties, are provided in the supplementary material.

# 3. Results

## 3.1. Defect-free microstructure before irradiation

Prior to irradiation, both APT and TEM analyses confirm that the microstructure is free from defects. The residual dislocation density measured after thermal treatments is $4.10^{-9}$ µm$^{-2}$ (Fig. 3a). Additionally, conventional XRD analyses were conducted on the as-received material using a D8 Advance Bruker laboratory X-ray powder diffractometer (Cu Kα radiation, Bragg-Brentano geometry). The results further confirm the presence of a fully BCC microstructure (Fig. 3b). The chemical composition determined by APT matches the nominal composition of the studied alloys (Table 1) showing no chemical heterogeneity, except for Si enrichment near the crystallographic low-index poles (Fig. 9a), attributed to the laser-mode analysis [58].

<table><caption>**Table 1**
Number density of each family of irradiation defects (spherical, sandwich, loop and dislo).</caption><thead><tr><th>Condition<br>(×10<sup>16</sup>)</th><th>AI<br>cm<sup>-3</sup></th><th>PIA2<br>cm<sup>-3</sup></th><th>PIA34<br>cm<sup>-3</sup></th></tr></thead><tbody><tr><td>Spherical</td><td>6.27</td><td>9.26</td><td>1.52</td></tr><tr><td>Sandwich “G/NS/G”</td><td>1.04</td><td>0.80</td><td>—</td></tr><tr><td>Loop</td><td>0.21</td><td>—</td><td>—</td></tr><tr><td>Dislo</td><td>0.42</td><td>0.16</td><td>—</td></tr></tbody></table>

## 3.2. Solute redistribution under irradiation

The microstructure significantly changed after irradiation. Once combined to the chemical contrast of the APT analyses and the 3D visualization, the irradiation defects can be divided in 4 families, all shown in Fig. 4:

* Spherical precipitates enriched in Mn, Ni and Si, called “G-phase”.

* “Sandwich G/NS/G” precipitates, so called because of the anisotropic distribution of the Mn, Ni, Si and Fe atoms. The central region, enriched in Ni, Si, and Fe, is devoid of Mn, while the outer regions are enriched in all four elements, albeit with varying concentrations.

* Linear or circular-enriched features. This population may correspond to the formation of precipitates on dislocations. They are called “Dislo”.

* Toroidal Mn, Ni and Si-rich features having a diameter of about 10 nm. They correspond to dislocation loops enriched in solute atoms. They are called “Loops”.

The number density of each family measured from the APT volumes is reported in Table 1. After two weeks of annealing, the number density of spherical precipitates increased by approximately 47% (see Table 1), while that of sandwich precipitates and Dislos decreased by about 20% and 60%, respectively. After 34 weeks, dislocation lines were no longer visible, and only bulk spherical precipitates were detected throughout the entire APT volume. Although the increase in the number of spherical precipitates after two weeks of annealing could, in principle, be interpreted as a transformation of the Dislo and Sandwich precipitates, as well as the Loops, this explanation is inconsistent with the decreasing trend observed at longer annealing times and should therefore be considered with caution. More plausibly, this discrepancy arises from sampling effects inherent to APT analysis.

Note that a few Janus-like precipitates [59], were also observed. Although not discussed in detail, they are included in the volume fraction estimations. These objects share the same Ni-Si composition and G-phase identity as the sandwich precipitates. An example is provided in the supplementary material.

## 3.3. G-phase and sandwich (G/NS/G) precipitates

We begin by analyzing the crystallographic structure using conventional TEM, high-resolution TEM, and high-resolution synchrotron XRD, followed by the chemical composition analysis of the precipitates using APT.

### 3.3.1. Crystallographic structure analysis

**Conventional TEM.** Diffraction contrast images performed by conventional TEM reveal the presence of dislocation loops and an additional contrast, which may result from the presence of secondary phase precipitates. Both are distributed throughout the entire irradiated depth. To distinguish between loops and secondary phase precipitates, Dark Field (DF) imaging is performed using an additional diffraction spot of the SADP, indicated by a yellow arrow (Fig. 5b). The resulting DF image, shown in Fig. 5a, shows that the secondary phase precipitates correspond to two of the previously mentioned families: spherical and
<figure><img src="image_4.png" /><figcaption>**Fig. 3.** Characterization of the studied material prior to irradiation: (a) TEM bright-field image and (b) diffraction pattern obtained from laboratory conventional XRD measurements with $\lambda_{Cu} = 1,54$ Å. Double peaks correspond to $K\alpha_1$ and $K\alpha_2$.</figcaption></figure>

sandwich-shaped precipitates. In the case of the latter, DF imaging illuminated only the outer part of the object, suggesting that the outer layers of the sandwiches share the same crystallographic structure as the spherical ones. Both types have an average diameter of 8 ± 2 nm.

**High resolution imaging.** To go further, HR-STEM analyses were performed on the precipitates. A magnified view is shown in Fig. 6a. The BCC ferritic matrix is imaged along the (011) zone axis near a precipitate. The corresponding FFT (Fast Fourier Transform) pattern is presented in Fig. 6b. The BCC pattern of the matrix is identified, along with a FCC-type pattern, also in the (011) zone axis, with a lattice parameter approximately four times larger than that of the matrix. Besides, the precipitate and matrix exhibit a cube-on-cube orientation relationship along the investigated zone axis. Note that the same symmetry and orientation relationship was found in Duplex Stainless Steels (DSS) [60,61] and in ferrito-martensitic (FM) steels [62–65].

In Fig. 6c, we overlay two simulated diffraction patterns with the same orientation as the FFT-derived diffraction pattern: the α-Fe-BCC structure in the (011) zone axis to model the matrix, and the G phase structure $Ni_{16}Mn_6Si_7$ in the (011) zone axis to model the precipitate phase. The simulated diffraction patterns closely match the experimental ones.

The crystallographic orientations of the FFT-derived diffraction pattern are reported in Fig. 6g to identify the facets orientations on Fig. 6a. As expected, the interface projection lengths follow the order [111] < [200] < [110]. This ordering, from the least dense to the most dense interface, is consistent with the predictions of Wulff theory based on a simple interfacial energy model, which relates the interface energy to the number of interatomic bonds broken during interface formation.

The crystallographic structure of the G phase was also identified along a (012) zone axis in HR-TEM mode (Fig. 6d to f) confirming the lattice parameter ratio (equal to 4) and the cube-on-cube relationship between the α-Fe matrix and the G-phase precipitate.

The unit cell of phase G can be described as a 2 × 2 × 2 assembly of $L2_1$ ($Ni_2MnSi$) unit cells, with Mn atoms in face-centered cubic (FCC) positions at the vertices and centers of the faces, Si atoms at the edge centers and center of the unit cell, and Ni atoms in tetrahedral positions. By replacing 8 Mn atoms and 4 Si atoms with vacancies, we obtain the 116-atom unit cell of the G-phase [66,67]. The perfect stoichiometry of the G-phase is $Ni_{16}Mn_6Si_7$, which corresponds to the nominal composition: 55.17 Ni - 24.13 Si - 20.7 Mn (at.%).

Furthermore, high-resolution images also revealed Moiré fringes in STEM bright-field images (Fig. 6h). It remains unclear whether these fringes are located at the α-Fe matrix/G-phase interface or are associated with sandwich-like precipitates, potentially arising from the

spacing difference between the Ni–Si-enriched core of the sandwich structure and the G-phase at the edges. In both cases, it would result from a lattice mismatch between the precipitated zone and the matrix.

**High-resolution synchrotron XRD.** To obtain a statistically reliable analysis of the crystal structure and to precisely deduce the lattice parameter of the second-phase precipitate formed, high-resolution synchrotron XRD experiments were conducted. The experimental X-ray diffraction pattern obtained from the as-irradiated sample is given in Fig. 7. The theoretical positions of the BCC matrix and G-phase precipitate peaks are added also. Due to the small size of the precipitates (<10 nm in diameter) and their low atomic fraction, the peaks associated with the secondary phase exhibit low intensity and are broadened, overlapping with the matrix signal.

Nevertheless, we report for the first time the observation of distinct diffraction peaks and “shoulders”, which indicate the precipitation of G-phase-structured nano-precipitates in irradiated RPV model alloys.

The key findings derived from the diffraction pattern given in Fig. 7a are outlined below:

* The two peaks at 21° and 42° align with the theoretical positions of the (333)$_G$ and (339)$_G$ peaks.

* The shoulder of the (110)$_{Fe}$ matrix peak near 24° likely corresponds to the convolution of the (531)$_G$ and (600)$_G$ peaks of the G-phase.

* The (440)$_G$ peak, expected to be as intense as the (333)$_G$ peak, is not visible in the diffraction pattern. However, it is likely convoluted with the (110)$_{Fe}$ matrix peak. Notice that the convolution is also observed in the electron diffraction pattern (Fig. 5b), where the (044)$_G$ spot coincides with the (011)$_{Fe}$ spot.

Assuming the alloy is a two-phase system comprising α-Fe and G-phases, the lattice parameters determined by Rietveld refinement using MAUD software for the precipitated G-phase is 11.1414 ± 0.0419 Å, are slightly lower than its bulk counterpart, 11.1674 ± 0.0006 Å [68]. The atomic density of the precipitated G phase is thus equal to $\rho_G = 116/11.1414^3 = 0.0839$ Å⁻³.

The lattice parameter obtained by Rietveld refinement for the α-Fe matrix is 2.87116 ± 2 × 10⁻⁵ Å, corresponding to an atomic density of $\rho_a = 2/2.87116^3 = 0.0845$ Å⁻³. Consequently, the atomic density reduction of the precipitated G-phase relative to the parent phase is $\Delta\rho/\rho \approx -0.7\%$ and the corresponding volume mismatch is $\Delta V/V = \rho_a(1/\rho_G - 1/\rho_a) \approx 0.7\%$.

Note that, in the literature, the lattice parameter reported for the G-phase after HR-Synchrotron XRD measurements performed in a Cu-free, medium-Ni LG alloy is equal to 11.268 ± 0.020 Å, slightly higher than the bulk value [35].
<figure><img src="image_5.png" /><figcaption>Fig. 4. (a) Families of precipitates formed under irradiation and identified by APT. (b) The corresponding solute atomic fraction profile. (c) 3D APT volume of the irradiated microstructure displayed using a green isoconcentration interface defined at a combined Mn+Ni+Si concentration of 15 at.% and with Ni atoms. A schematic representation of a sandwich precipitate is given in (a). Dotted lines in (b) illustrate the way the precipitate composition is measured on each analyzed precipitate. The cross-sectional view of Dislo precipitates is represented on the APT volume in (c). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

### 3.3.2. *Chemical analysis*

For the chemical analysis of features formed under irradiation, APT is preferred over techniques such as STEM-EDS or EELS because the composition of nanometer-sized precipitates can significantly be affected by the surrounding Fe-rich matrix. However, we must be aware of potential artifacts that may occur during APT analysis. In particular, as mentioned in Section 3.1, the use of the laser mode analysis is responsible for the artificial enrichment in Si along crystallographic poles (§ 7.4.3 or § 7.6.6 from the book of Gault [58], visible on Fig. 9a). Details of the measurement protocol, data processing but also on

APT artifact and their consequences on the present data are provided in the supplementary materials.

For each feature type, the average composition was determined from composition profiles obtained from 10 precipitates whenever possible, or from as many precipitates as could be intercepted in the APT tips when fewer than 10 were available. The histogram showing the average compositions of each precipitate family is presented in Fig. 8. Note that the graph includes compositions not only after irradiation (AI) but also after thermal annealing for up to 2 and 34 weeks (labeled Post-Irradiated Annealing, PIA2 and PIA34, respectively).
<figure><img src="image_6.png" /><figcaption>**Fig. 5.** (a) Inverted TEM-DF image of the irradiated microstructure, obtained by selecting an additional reflection marked with an arrow on the SADP in (b). (c) A portion of the DF-TEM image from (a), shown at the same scale as the 3D APT volumes (d) containing Mn-, Ni-, and Si-rich precipitates. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

The precipitates are compared to the reference G-phase, Ni₁₆Mn₆Si₇. The spherical precipitates have the closest Ni/Si ratio to the reference G-phase and share the same crystallographic structure (Section 3.3.1). They are identified as G-phase. The outer layers of the sandwich-shaped precipitates display the same contrast as G-phase precipitates in CTEM analysis and exhibit a similar chemical composition, leading to their classification as G-phase as well.

In contrast, the middle layer of these sandwich-shaped precipitates, primarily enriched in Ni and Si, is designated as the “NS” phase. Thus, these structures are referred to as “G/NS/G” precipitates.

Regarding the presence of iron within precipitates, although it is detected in most MNSPs analyzed by APT, it was often disregarded and considered as an artifact in the analysis of irradiated RPV steels, especially because the size of radiation-induced features were very small (a few nanometers). Consequently, when MNSPs are treated as distinct phases, the contribution of Fe is ignored.

In this study, as demonstrated in Section 3.3.1 and detailed in the supplementary materials, precipitates average size is sufficiently large to support the reliability of our estimation of Fe content as representing the actual composition. However, uncertainty remains regarding the partitioning of Fe between the Mn and Ni sublattices. First-principles calculations of the G-phase lattice parameter, with either the Ni or Mn sublattice fully occupied by Fe, predict a reduction in the lattice parameter upon substitution of either Ni or Mn with Fe [67]. Therefore,

both substitutions can account for the reduction in the precipitated G-phase lattice parameter compared to the bulk value.

Simple concentration estimates, based on the measured compositions in Fig. 8 and virtual partitioning of Fe between the Ni and Mn sublattices, yield a (Mn+Fe) concentration of approximately 17%, which closely matches the site fraction of the Mn sublattice. Similarly, the (Ni+Fe) concentration is approximately 64%, significantly exceeding the 55% site fraction of the Ni sublattice. As a consequence, the partitioning of Fe into the Mn sublattice appears to be the most plausible mechanism. Therefore, we propose that the precipitated G-phase can be represented by the formula $Ni_{16}(Mn_xFe_{1-x})_6Si_7$ with $x \approx 0.6$.

### 3.4. RIS and RIP

We observe in Fig. 4 that Mn, Ni, and Si likely segregate at dislocation loops (called ‘Loop’) and lines (called ‘Dislo’), in agreement with previous studies [36]. This solute enrichment may result from either a one-step radiation-induced segregation (RIS) mechanism or a two-step solute redistribution process: RIS followed by heterogeneous radiation-induced precipitation (RIP). Notably, the Ni/Si and Mn/Si molar fraction ratios in the decorated dislocation loops are very similar to the nominal ratios found in the G-phase (Fig. 8).

Previous analyses of RIS at lower radiation doses have demonstrated a direct correlation between the RIS composition and sample's nominal
<figure><img src="image_7.png" /><figcaption>**Fig. 6.** G-phase precipitate in [011] zone axis (a) High-resolution STEM BF image, and corresponding FFT patterns: experimental (b) and simulated (c); G-phase precipitate in [012] zone axis: (d) High-resolution TEM image, and corresponding FFT patterns: experimental (e) and simulated (f); (g) Schematic representation of the G-phase in [011] zone axis; Interface orientations were deduced from (b) and (c); (h) STEM-BF image of spherical features displaying Moiré fringes imaged close to a [011] zone axis of the matrix. (FFT simulations were performed using the Single Crystal ® software.). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

composition [39]. However, unlike previous findings, the atomic fraction of Fe in this study is quite low (below 17 at.%), whereas reported RIS profiles show it can reach up to 80 at.%.

### 3.5. Dissolution and coarsening of precipitates upon thermal annealing

To assess the stability of radiation-induced features and gain insight into their nature, the irradiated samples were annealed at the irradiation temperature (400 °C). Microstructural evolution, including chemical composition, volume fraction, and number density of each precipitate family, was monitored by extracting APT tips after 2 different annealing times. The results are shown in the histogram of Fig. 8, in Figs. 9 and 10 and in the Tab.2 of the supplementary material. The results labeled as PIA 2 and PIA 34, correspond to post-irradiation annealing for 2 and 34 weeks, respectively.

In the as-irradiated condition, the 4 families of solute-segregated zones described in Section 3.2 are visible. After 2 weeks, the decorated

dislocation loops ('Loop') are not any more visible in the whole volume comprising approximately $0.6 \times 10^8$ ions. They were thus dissolved. After the same annealing time, the spherical, sandwich and 'Dislo' precipitates are still visible. After 34 weeks, the observed dislocation lines are not visible any more, and only bulk spherical precipitates are detected throughout the entire APT volume, comprising approximately $1.6 \times 10^8$ ions.

Between AI condition and PIA34, the spherical precipitates have significantly increased in diameter from approximately 8 to 14 nm while the overall volume fraction calculated as described in Section 2.4 decreased from $1.31 \pm 0.21\%$ à $0.75 \pm 0.21\%$ (Fig. 10a). For all the remaining precipitates, the Mn partition inside the precipitates is homogeneous, indicating that the sandwich precipitates were dissolved, or evolved into spherical precipitates. Also, it should be noted that the matrix composition in the immediate vicinity of the spherical precipitate becomes enriched in Ni and Si while being depleted in Mn
<figure><img src="image_8.png" /><figcaption>**Fig. 7.** HR X-ray diffraction pattern of the irradiated sample (black) presented alongside the G-phase (blue) simulated at the same wavelength with CrystalDiffract software. The mains peaks corresponding to the BCC matrix and the G-phase are indicated by red and blue markers, respectively. The red and green boxes are magnified views of the main peaks. The lattice parameters for both the precipitate phase and the matrix determined by Rietveld refinement are given at the top. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

(Fig. 9b). This effect was visible after 2 weeks and became even more pronounced after 34 weeks.

To analyze this quantitatively, we tracked the composition changes in both the matrix and the spherical precipitates, as they are the only precipitate family that remains throughout the annealing process. The precipitate composition extracted from the profile analysis in Fig. 8 is plotted in Fig. 10b. The matrix composition evolution measured in APT volumes far from the precipitated zones is reported in Fig. 10c. It shows that the spherical precipitates are depleted in Ni and Si and enriched in Mn, whereas the matrix exhibits the opposite trend, with enrichment in Ni and Si and depletion in Mn.

# 4. Discussion

## 4.1. Equilibrium and structural properties of the G phase

The CALPHAD models of the Fe–Mn–Ni–Si system do not predict significant departures from the ideal stoichiometry of the G-phase. For the current nominal composition, the most recent CALPHAD model predicts a four-phase equilibrium at 290 °C consisting of the Fe-based bcc matrix, Ni₇₅Si₂₅, a C15 phase (Ni₂Mn₃Si), and a large volume fraction of the G-phase, Ni₁₆Mn₆Si₇, among the three ordered phases [34]. As noted by the authors, the ordered phases can incorporate a significant amount of iron.

There remains no consensus regarding the partitioning between phases, the composition of phases, or their volume fractions. Nevertheless, regardless of whether iron is present in the precipitates, all thermodynamic studies agree that the molar fractions of Ni, Mn, and Si, relative to the total of the three, match the nominal values of the perfectly stoichiometric G-phase: Ni₁₆Mn₆Si₇. During thermal annealing, the complete dissolution of Ni–Si precipitates suggests that Ni–Si-phase is not a stable phase in this alloy. The accelerated dissolution of Ni-Mn-Si-rich dislocation loops (“Loop”) compared to the precipitates along dislocation lines (“Dislo”) may be attributed to the slightly smaller size (based on the composition profiles, see Fig. 4) of the solute enrichments on dislocation loops relative to the Dislo precipitates. Furthermore, the higher iron content in Loops, relative to spherical, sandwich and Dislo precipitates, likely contributes to their destabilization. After 34 weeks of annealing, precipitates near dislocation lines and dislocation loops were dissolved, whereas the bulk precipitates have grown significantly in size, with their radius increasing from 8 to 14 nm.

The overall volume fraction of precipitates decreases, suggesting that irradiation lowers the solubility limit of at least one solute species in the BCC parent phase. Additionally, the composition of bulk precipitates is converging towards the nominal stoichiometry of the G-phase Ni₁₆Mn₆Si₇: Fe, Ni and Si are diffusing out, while Mn is incorporating
<figure><img src="image_9.png" /><figcaption>**Fig. 8.** Precipitate average compositions, extracted from 1D concentration profiles, with 3 nm diameter cylinders oriented along the z direction, except for G/NS/G precipitates, oriented in the direction normal to the G/NS interface, without undertaking Ni/Fe deconvolution. Error bars are standard deviations. The shadowed bar refers to the nominal composition of the perfectly stoichiometric G-phase Ni₁₀Mn₆Si₇. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

<figure><img src="image_10.png" /><figcaption>**Fig. 9.** Evolution of the microstructure of the irradiated alloys after annealing at 400 °C during 2 and 34 weeks; (a) APT analyses performed in identical conditions (40 pJ, 60 K, 200 kHz); (b) Atomic fraction proxigrams were constructed using an isoconcentration interface defined at a combined Mn+Ni+Si concentration of 15 at.%. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>
<figure><img src="image_11.png" /><figcaption>**Fig. 10.** (a) Evolution upon annealing of the precipitate volume fraction using the method described in Section 2.4 and detailed in the supplementary material; (b) Precipitate composition evolution extracted from the 1D-profile analysis in Fig. 8; (c) Solute atomic fraction in the matrix extracted from APT volumes far from the precipitated zones in as-irradiated and post-irradiation annealed samples. The dashed line corresponds to the minimum value of the Mn concentration at the vicinity of the precipitate interfaces. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

into the precipitates (Figs. 9 and 10). This trend aligns with thermodynamic models predicting Ni/(Ni+Si+Mn) and Mn/(Ni+Si+Mn) ratios of 16/29 and 6/29 respectively.

Interestingly, the composition profiles of Ni and Si deviate from typical steady-state growth profiles (Fig. 9b). No local minimum is observed at the precipitate/matrix interface, nor do negative gradients extend from the bulk to the interface. Instead, the profiles resemble more to dissolution profiles, with Ni and Si diffusing from the precipitates into the matrix. This is further confirmed by the formation of a Ni- and Si-enriched “cloud” surrounding the precipitates. After 34 weeks of annealing, the Ni and Si profiles become nearly flat, indicating the cessation of dissolution kinetics. The Ni and Si concentrations in the matrix and precipitates likely approach equilibrium, estimated at 1.3 at.% Ni and 0.5 at.% Si in the matrix, and 55.8 at.% Ni and 23.2 at.% Si in the precipitates (see Table 11). Those Ni and Si molar fractions in the precipitate correspond to the absolute values of the perfectly stoichiometric G-phase Ni₁₆Mn₆Si₇. However, the Mn concentration profile after 34 weeks still displays a growth profile with a distinct minimum at the interface. Assuming local equilibrium of Mn atoms at the interface, the Mn concentration on the matrix side corresponds to the solubility limit of Mn in the matrix. As shown in Fig. 10c, this Mn solubility reported in blue dashed line, is estimated to be approximately 0.2 at.%, a value that remains nearly constant between 2 and 34 weeks, suggesting it is close to the equilibrium Mn concentration in the matrix. Notably, within the precipitates, the Mn profile exhibits a “shoulder”, contrasting with the flat Ni and Si profiles observed after 34 weeks (Fig. 9b). This suggests Mn diffusion is significantly slower than that of Ni and Si within the G-phase.

Moreover, a mirror symmetry between the Mn concentration gradient and that of Fe tends to show that Fe atoms leaving the precipitates are replaced by Mn atoms. We observe that the molar fraction ratios (Fe + Mn)/Si and Ni/Si are even closer to the nominal ratio of Ni₁₆Mn₆Si₇ than the ratios Mn/Si and Ni/Si (Fig. 8). Additionally, first principles DFT calculations of substitutional energy at 0 K suggest that substituting Mn with Fe is more favorable than substituting Ni or Si by Fe [67]. Thus, it is highly likely that Fe occupies the same sublattice as Mn, forming a G-phase with the chemical formula: Ni₁₆(MnₓFe(1-x))₆Si₇. Based on our composition measurements (Fig. 8), we propose that x is equal to 0.6. Note that the DFT calculations yield a lattice parameter of 11.15 Å for Ni₁₆Mn₆Si₇ and 11.03 Å for Ni₁₆Fe₆Si₇ [67]. Applying linear Vegard's law to the Mn fraction x in the Mn sublattice gives a lattice parameter of 11.10 Å, corresponding to a relative variation of -0.4% from the nominal G-phase. In comparison, the lattice parameter measured by HR-XRD shows a relative variation of -0.23% with respect to the bulk value. Although the measured decrease is slightly smaller,

the sign is consistent. Several experiments [42,43] and models [34,67] have reported the presence of iron in the G-phase formed in other iron-based alloys, such as the δ-ferrite phase of duplex stainless steels (DSS) where the G-phase contains up to 15 at.% of Fe. In such alloys, the stable G-phase formed in significant volume fraction, is suitable for reliable crystallographic and chemical analyses that enables its identification. The DFT-based thermodynamic modeling of the G-phase composition predicts a Fe fraction of about 13 at.% with the Fe atoms distributed in the sublattices of the G-phase. Note that, in the DSS complex composition, the Mn and the Ni sublattices are shared by several other solute species such as Mo or Cr.

## 4.2. Radiation-induced solute redistribution phenomena

Dislocation loops have almost the same composition than the bulk spherical precipitates. DFT-based modeling of solute-point defect flux couplings and RIS in dilute binary alloys FeX(X = Mn, Ni, Si, Cr, P) — when treated separately as if the Fe-matrix was containing only one solute species at a time — do not explain the observed composition profiles at dislocations [69]. In a kinetic regime dominated by the elimination of point defects at sinks, there is no effect of the radiation flux but a significant effect of temperature and of the microstructure sink strength $k^2$ on RIS that may differ from one species to the other. At 400 °C and for $k^2 = 5.10^{14}$ m⁻², the RIS enrichment factor is roughly twice greater for Mn than for Ni and Si in the matrix [69]. Thereby, such modeling would not lead to the stoichiometry of the G-phase but to a segregated zone significantly richer in Mn. However, these calculations are performed in the infinite dilute limit as if solute atoms do not interact with each other. On the other hand, there were systematic investigations of radiation-induced segregation in three different commercial ferritic–martensitic alloys showing strong RIS of Ni and Si but no RIS of Mn at grain-boundaries [70]. These alloys also contain many other detectable impurities among which Cu and Mo and a significant amount of Cr (around 8–10 at.%). Nevertheless, the enrichment of both Ni and Si at grain-boundaries did not appear to exhibit any dependence on the composition of Cr and/or the other minor elements such as Mn that varies between 0.45 to 0.64 wt%. Eventually, in commercial high-Ni, low-Cu RPV steels with a composition comparable to the alloy in the present study, low-dose neutron irradiation (<0.3 dpa) leads to RIS of Ni and Si and of Mn to a lesser extent to dislocations [36]. Our observation of Mn–Ni–Si solute rich clusters at dislocation lines may be due to the fact that the radiation dose is too high to access the initial stage of RIS. We would only observe the subsequent stage associated with the precipitation of the G phase. As proposed in some theoretical studies, the thermodynamic and kinetic interaction of Mn,
Ni and Si with the SIA clusters might be involved in the nucleation mechanism of the dislocation loops [39]. In model Fe-Ni-Mn alloys, the observed clustering mechanism of Mn and Ni could be associated with dislocation loops, with Ni atoms being more concentrated in the inner part of the loop and Mn atoms at the outer part [71]. Whether for thermodynamic or kinetic reasons, there is a small probability that the resulting ratio of solute segregation perfectly matches the G-phase stoichiometry unless the segregated zone is a G-phase precipitate. Besides, the content in Fe of the present dislocation loops being almost similar (within ≈10 at.%) to the spherical G-phase precipitates tends to show that the solute enriched zones around the dislocation loops are G-phase precipitates. The analytic characterizations of dislocation loops previously published were performed on low-dose irradiated samples (a few tenths of dpas) [36,39,72,73]. At such low doses, heterogeneous radiation-induced precipitation may not have occurred yet.

Solute enrichments tend to be more homogeneously distributed around dislocation loops compared to dislocation lines, where an iso-concentration surface of $Mn+Ni+Si = 15$ at.% reveals small spherical-shape precipitates of rather similar size and periodically distributed along the dislocation line. A recent phase-field modeling study of precipitates at grain boundaries, formed due to RIS has revealed patterns of small precipitates that resist to coarsening [74]. This phenomenon occurs when solute advection—specifically, the net solute flux driven by radiation-induced point defect fluxes-dominates over thermal diffusion. The observed pattern along dislocation lines provides a potential illustration of this mechanism.

Sandwich precipitates consist of two distinct phases: a dense Ni–Si central phase and an outer G-phase. Unlike isotropic core–shell morphologies, these precipitates exhibit parallel interfaces (G/NS and NS/G) aligned along the (111) direction of the BCC matrix (Fig. 5). Given that the precipitates maintain a cube-on-cube orientation relationship with the matrix, this (111) direction is also shared by the FCC-based precipitates. Notably, these interfaces do not correspond to the invariant plane (011)$_{BCC}$ of the BCC-to-G phase transformation. As a result, they are unlikely to be coherent with the BCC matrix and may serve as sinks for point defects. The composition of the Ni–Si-rich phase is closer to $Ni_2Si$ than $Ni_3Si$, although both phases are denser than the BCC matrix [75,76].

Spherical precipitates are semi-coherent and faceted, with their Mn sublattice partially occupied by Fe. While the composition measurements in Fig. 8 have a notable margin of error, we observe on average that the precipitates and decorated dislocation loops contain 6–17 at. % Fe and 8–10 at. % less Mn than the stoichiometric G-phase. Regarding the Si content in precipitates, it is generally higher than the nominal G-phase value, except within loop segregated volumes.

An increased volume fraction of precipitates suggests that at least one of the solutes forming the precipitates has a reduced solubility limit in the matrix. Indeed, under irradiation conditions, Table 11 shows a significant decrease in the concentration of Ni and Si in the Fe matrix compared to thermal conditions, while the local-equilibrium atomic fraction of Mn at the interface is higher under irradiation. Although the absolute concentration values of dilute species measured in the matrix far from the segregated zone should be interpreted with caution due to overlapping peaks in the APT spectrum, we use them to estimate the precipitate volume fraction via the lever-rule described in Section 2.4. As shown in Table 11, Ni is the solute that primarily determines the precipitate volume fraction. As expected, the volume fraction decreases from 1.36% under irradiation to 0.75% after 34 weeks of thermal annealing while the corresponding Ni-solubility limit increases from 0.95 at.% to 1.29 at.%. We can conclude that the initial system is supersaturated in Mn, Si, and Ni. Irradiation reduces the Ni solubility limit by approximately 25% and the Si solubility limit by around 40%. Furthermore, in this system, Ni is the solute that primarily determines the volume fraction.

Surprisingly, the molar fraction of Mn at the precipitate/matrix interface is higher under irradiation. It reaches approximately 0.5

at.% under irradiation, compared to about 0.22 at.% after 34 weeks of thermal annealing. However, radiation-induced precipitates contain lower Mn levels and higher Fe levels than the annealed precipitates, potentially increasing the Mn molar fraction at the interface. Additionally, a negative solute gradient is observed between the matrix and the precipitate, suggesting that precipitate growth is ongoing. This growth likely continues during thermal annealing, involving the exchange of Fe atoms from the precipitate with Mn atoms from the matrix. Even after 34 weeks of annealing, a Mn concentration gradient remains in both the matrix and the precipitate, indicating that the growth process involves adjustments to the Fe/Mn composition ratio within the precipitate. The initial formation of Ni–Si–(Fe) precipitates, followed by G-phase precipitation at the interface that gradually incorporates the Ni–Si–Fe phase, may first deplete Mn and subsequently lead to its diffusion into the precipitate.

### 4.3. The role of forced ballistic mixing

Irradiation-induced ballistic mixing may also contribute to the partial occupation of the Mn sublattice by both Mn and Fe in the G-phase, as well as the increased Mn concentration at the interface. Besides, precipitates located near dislocation loops and lines show slightly higher Fe content compared to those in the bulk matrix. Near point defect sinks, the excess of point defect concentration is very small discarding any significant influence of these defects on the Fe-content of this phase. However, a lower concentration of point defects slows down atomic diffusion. As a result, the balance between ballistic mixing and restorative reactions mediated by atomic diffusion tends to even more favor ballistic mixing close to these sinks.

A ballistic mechanism affecting only the Mn sublattice is plausible only if Mn diffusion is significantly slower than that of Ni and Si. However, Mn does not appear to diffuse particularly slowly compared to Ni and Si in the BCC matrix. DFT-based calculations of solute diffusivity in the infinite dilute limit (interactions between solutes are ignored) highlight that SIA is almost invariably comprised of Mn [77]. Thereby, SIA and Mn diffuse at the same speed. On the other hand, vacancy and SIAs almost equally contribute to the diffusion of Ni and Si. Vacancy-mediated diffusion of Mn is almost as fast as Si and at least one order of magnitude faster than Ni [77,78]. Besides, an increase of Mn concentration in Fe was shown to enhance Mn diffusion [79]. Note that observations of thermal annealed RPV steels irradiated with neutrons arrive at the same conclusion: Mn would diffuse faster than Ni and Si in the matrix [31]. In conclusion, whether in a kinetic regime dominated by recombination reactions between SIA and vacancies or in a regime dominated by the elimination of these same point defects at sinks, we expect that the Mn species will not diffuse significantly slower than Ni and Si. On the other hand, we do not know the diffusion of these three species in the ordered G-phase. The profile of Mn in the precipitates of the annealed samples is not flat, unlike that of Ni and Si, which could be due to slower diffusion of Mn in the G-phase compared to Ni and Si. However, it is worth noting that under irradiation, the profile of Mn in the precipitates is rather flat, similar to that of Ni and Si. Although this might seem to contradict the notion that Mn diffuses more slowly than Si and Ni in the G-phase, it is important to note that subtle diffusion competition can be masked by radiation-enhanced diffusion.

### 4.4. Complex kinetic paths of precipitation under irradiation

Although only one fluence was analyzed, the morphology of precipitates and their evolution upon annealing provide insight into the kinetic steps and mechanisms of precipitation of the bulk precipitates. The positive radiation-induced segregation (RIS) of Mn, Ni, and Si at point defect sinks reduces the nucleation barrier for the G-phase. As expected, we observe the precipitation of the thermodynamically stable G-phase at dislocation loops and dislocation lines.
<table><caption>**Fig. 11.** Solute atomic fraction (at.%) measured in APT needles of as-received sample from EMSE (Nominal). Solute atomic fraction (at.%) of the matrix extracted from APT volumes far from the precipitated zones in as-irradiated samples (AI-m); and 2-weeks (PIA2-m) and 34-weeks (PIA34-m) post-irradiation annealed samples. The volume fraction in % is deduced for each solute from the level rule with the nominal content, the solute atomic fraction in the matrix and in the precipitated phase (AI-p, PIA2-p, and PIA34-p) taken from Fig. 8 (method described in Section 2.4 and detailed in the supplementary material); Note that for Mn, the atomic fraction indicated in parentheses corresponds to the minimum value of the concentration profile at the vicinity of the precipitate interface. The minimum species-specific volume fraction in bold corresponds to the expected volume fraction.</caption><thead><tr><th></th><th>Mn (at.%)</th><th>Si (at.%)</th><th>Ni (at.%)</th></tr></thead><tbody><tr><td>Nominal</td><td>0.64 ± 0.06</td><td>0.76 ± 0.04</td><td>1.7 ± 0.1</td></tr><tr><td>Al-m</td><td>0.58 ± 0.08 (0.50 ± 0.01)</td><td>0.29 ± 0.06</td><td>0.95 ± 0.1</td></tr><tr><td>Al-p</td><td>10.0 ± 1.6</td><td>26.4 ± 1.4</td><td>55.9 ± 2.4</td></tr><tr><td>Al-f<sub>V</sub> (%)</td><td>1.47 ± 0.35</td><td>1.80 ± 0.14</td><td><strong>1.36 ± 0.21</strong></td></tr><tr><td>PIA2-m</td><td>0.58 ± 0.06 (0.29 ± 0.01)</td><td>0.36 ± 0.06</td><td>0.99 ± 0.08</td></tr><tr><td>PIA2-p</td><td>14.1 ± 1.7</td><td>24.2 ± 0.9</td><td>55.2 ± 1.4</td></tr><tr><td>PIA2-f<sub>V</sub> (%)</td><td>2.53 ± 0.28</td><td>1.68 ± 0.15</td><td><strong>1.31 ± 0.20</strong></td></tr><tr><td>PIA34-m</td><td>0.57 ± 0.16 (0.22 ± 0.02)</td><td>0.50 ± 0.06</td><td>1.29 ± 0.12</td></tr><tr><td>PIA34-p</td><td>16.0 ± 1.4</td><td>23.2 ± 1.3</td><td>55.8 ± 1.8</td></tr><tr><td>PIA34-f<sub>V</sub> (%)</td><td>2.66 ± 0.26</td><td>1.15 ± 0.16</td><td><strong>0.75 ± 0.21</strong></td></tr></tbody></table>

In this system, solute atoms are supersaturated and are expected to diffuse rapidly through radiation-enhanced diffusion, aggregating to form homogeneously distributed G-phase precipitates within the matrix. However, a substantial fraction of the precipitates in the matrix adopt a sandwich-like morphology (see Tab.2 in supplementary material), indicative of a more complex kinetic pathway. At the core of these sandwich-shaped precipitates, we identify a metastable Ni–Si–Fe phase, which dissolves upon annealing. The G-phase observed at the periphery of this metastable phase likely forms on pre-existing NS precipitates, suggesting that the NS phase nucleates first, followed by G-phase precipitation at the NS/matrix interface. Thus, the thermodynamically stable G-phase appears to precipitate after the radiation-induced precipitation of the Ni–Si–Fe phase, which itself would form following a radiation-induced segregation of Mn, Ni, and Si. Although it is difficult to track all these stages, at low fluence, the authors agree that the observed solute clusters contain all three solutes [30,39,40]. To demonstrate that the metastable Ni–Si–Fe phase acts as a precursor triggering the homogeneous precipitation of the G-phase, Ni–Si-rich clusters without Mn should be observable at low fluence. To our knowledge, such features have not been clearly reported in the literature. However, the figure 4 in the Ref. [36] obtained via APT in the base metal of VVER-1000 RPV materials caught our attention because it tends to show that Mn leaves the solute clusters at a neutron radiation fluence of around $10^{24} \text{ m}^{-2}$.

The kinetic pathways under irradiation are particularly sensitive to the thermodynamic and kinetic properties of both vacancies and self-interstitial atoms (SIAs). For instance, excess vacancies under irradiation are expected to aggregate and form voids. However, generally in metals under irradiation, the initial aggregation reactions involve SIAs, which form dislocation loops and/or precipitates of a phase denser than the matrix. SIAs have a greater formation energy than vacancies, diffuse faster, and most point defect sinks have a higher absorption bias for SIAs. It is only at a later stage that voids, vacancy dislocation loops, or phases less dense than the matrix start growing. Under irradiation, the nucleation barrier of the PD clusters is a function of the PDs mobilities. In particular, the incubation time for nucleation of PDs clusters results from a competition between the elimination rates of SIAs and vacancies [14,80]. The G-phase is a less dense phase characterized as an $L_{21}$ ordered phase with vacancies [75]. Whether

it is Ni$_2$Si or Ni$_3$Si, the Ni–Si–Fe (NS) phase is certainly denser than the matrix. The excess in SIAs might have promoted the precipitation of the NS phase. A similar precipitation mechanism was demonstrated for the γ-Fe–Ni phase in dilute BCC Fe(Ni) solid solutions [19]. As they transform into two substitutional atoms occupying two lattice sites in the dense phase, SIAs reduce the excess energy carried by the SIAs and accommodate the volume mismatch between the precipitated phase and the matrix. This precipitation mechanism operates even more readily on a dislocation loop enriched with solute atoms from the precipitated phase. This is presumably the case for solutes such as Ni and Si, for which positive RIS was reported on all types of defect sinks, as described earlier. The precipitation of a phase with different atomic density than the matrix leads to a loss of coherence of some of the precipitate/matrix interfaces. Semi-coherent or incoherent interfaces then become recombination centers of point defects. The diffusion and elimination of point defects on the semi-coherent or incoherent interfaces of the dense NiSi-rich precipitates might induce positive RIS of Ni, Si, and Mn. The solute enrichment and lattice disorder of the semi-coherent interface may reduce the barrier for the nucleation of the G-phase. The G-phase is less dense than the matrix. Its precipitation and grows implies the absorption of vacancies. The precipitation of the low-density G-phase close to the dense Ni–Si–Fe (NS) precipitates allows to reach a steady-state elimination regime of the excess point defects. Locally, the amount of absorbed SIAs by the NS precipitates should be equal to the amount of absorbed vacancies by the G-phase [19]. Such a precipitation mechanism could explain the anisotropic structure of the sandwich precipitates and the alignment of phases along a preferential direction of the matrix. In Fig. 8, the slightly elevated Si content observed in the bulk spherical precipitates relative to the expected nominal value may indicate a precipitation mechanism initiated by a sandwich-like metastable precursor. Over time, the Ni–Si core of this precursor could gradually dissolve or transform, ultimately yielding a complete G-phase precipitate that is slightly enriched in Si.

To corroborate this vacancy-induced precipitation of the G-phase, we do not observe voids, which suggests that most of the vacancies are absorbed by the G-phase precipitates. Therefore, even though MNSPs are stable phases, their nucleation in the matrix might be delayed because they involve the elimination of vacancies from the matrix, which is a complex process dependent on the overall kinetics of PDs.
In particular, the precipitation of a dense phase, even if it is not the stable phase, is favored in steels because it facilitates the elimination of SIAs, which have a formation energy at least one eV higher than that of vacancies, while the mixing energy of the phase is commonly a few 0.01 eV. What matters in the driving force is not the binding energy of the defect with solute atoms, but rather the formation energy of the defect times the eigenstrain of the secondary phase [19,46]. Therefore, even if the concentration of SIAs is very low in the matrix, we have shown in a low alloy Fe-Ni model alloy that the chemical potential of the SIA, which constitutes the driving force for elimination, is sufficiently high to modify the phase selection [19]. Similarly to the nucleation of voids, we may experience a delay in the nucleation of less dense phases compared to what one would expect from an REP mechanism. The nucleation incubation time of oversized particles such as G-phase precipitates will depend on the rate of aggregation of SIAs into SIA-solute clusters.

In RPV alloys at ≈300 °C, although they are usually considered to be supersaturated, MNSPs primary nucleate heterogeneously [30]. At the present temperature of 400 °C, the precipitation driving force is lower, which should further favor heterogeneous precipitation over homogeneous precipitation. Note that near PD sinks, the PD supersaturation is low, and the PD-induced precipitation mechanism does not operate. Therefore, we do not observe sandwich precipitates, but rather G-phase precipitates resulting from the direct precipitation of the stable G-phase. We have not observed Ni–Si–Fe precipitates at dislocation loops or lines because the driving force for G-phase precipitation is stronger. However, we anticipate that enrichment (or segregation) of Si and Ni on small SIAs-clusters could lead to the formation of mixed solutes-SIAs clusters, which might eventually transform into Ni–Si–Fe precipitates. Besides, there are G-phase precipitates that are not sandwich precipitates. Their core NS-phase may have dissolved, or they could have formed on small vacancy clusters that they absorbed. It is also possible that the bias in SIA absorption by the NS-precipitates is strong enough to induce a precipitation driving force high enough to directly nucleate the G-phase in volume. In a growing population of dislocation loops and dense precipitates, we expect a decrease of the SIAs supersaturation and an increase in the solubility limit until the point where the dense precipitates cease to grow or disappear in favor of vacancy agglomeration reactions. At steady state, if reached, the number of vacancies eliminated in vacancy clusters and less dense precipitates should be approximately equal to the number of SIAs eliminated in SIA clusters and dense precipitates.

The NS phase acting as a catalyst for the precipitation of the G-phase could explain the proposed mechanical behavior laws, highlighting the crucial role of Ni in low-Cu steels [10,11]. Ni would control both precipitation stages in the matrix. The higher the Ni content, the larger the fraction of the nickel-rich dense phase, and the greater the propensity to form the G-phase. In iron, the solubility of Cu is even lower under irradiation [27], likely because self-interstitial atoms (SIAs) participate in the precipitation of the FCC Cu-phase, which is significantly denser than the BCC matrix. Similarly, we expect an effect of SIAs on the solubility limit of Cu in RPV steels. The high bias in SIA elimination within the Cu-rich precipitates would promote the agglomeration of vacancies to form MNSP phases. Indeed, we observe that MNSPs form in the vicinity of the copper precipitates [30]. Therefore, the homogeneous precipitation of MNSPs would be a process that would occur after the precipitation of a dense phase such as a Cu-rich FCC phase or a Mn-free metastable dense phase. The volume fraction of both the high-density and low-density phases would result from the thermodynamic and kinetic properties of the alloy and its PDs but also from the overall evolution of the microstructure.

## 5. Conclusion

A high-purity Fe-0.7Mn-1.8Ni-0.8Si model reactor pressure vessel (RPV) alloy was irradiated with 22.5 MeV Fe⁹⁺ ions at 400 °C, to produce a uniform radiation dose profile ranging from 1 to 2 dpa at a depth

of 1 µm. Post-irradiation annealing (PIA) were subsequently performed at 400 °C for 2 and 34 weeks. Radiation damage, with a focus on solute-segregated zones, was characterized using transmission electron microscopy (TEM), atom probe tomography (APT), and high-resolution synchrotron X-ray diffraction (HR-XRD).

HR-XRD reveals a significant volume fraction of a secondary phase with L₂₁ crystallographic structure and with a lattice parameter of 11.1414 ± 0.0419 Å. Combined HR-TEM and APT analysis of the nano-features forming under irradiation clearly reveal four distinct types of Mn–Ni–Si-enriched clusters:

* Bulk spherical precipitates: Transmission electron microscopy (TEM) diffraction patterns indicate they are semi-coherent G-phase precipitates with a cube-on-cube orientation relationship with the matrix. In parallel, APT report the same homogeneously distributed clusters with a presumed chemical formula Ni₁₆ (MnₓFe₁₋ₓ)₆ Si₇.

* Bulk sandwich precipitates: These features have a Mn-free middle part and Ni, Mn, and Si enriched outer part. While the crystallographic structure of the middle part could not be determined, its composition and the available phase diagrams suggest it is an ordered phase with the symmetry of either Ni₂Si or Ni₃Si with an atomic density higher than the BCC matrix. The outer parts exhibit the same stoichiometry and the same crystallographic structure as the G-phase spherical precipitates.

* Toroidal Mn–Ni–Si-rich segregation and spherical precipitates along dislocation lines: Mn–Ni–Si-rich toroids correspond to enriched dislocation loops, with compositions consistent with the stoichiometry of spherical G-phase precipitates. The precipitates along the dislocation lines are monodisperse in size and smaller than those found in the matrix. Both features associated with dislocations are likely the result of radiation-induced precipitation subsequent to RIS; however, the advanced kinetics make it difficult to determine the specific RIS behavior of Ni, Si, and Mn.

After PIA, the bulk G-phase precipitates grow from 8 nm to 14 nm in diameter after 34 weeks, demonstrating their thermodynamic stability. In contrast, the sandwich-shaped Ni–Si-enriched middle part are metastable phases, as they dissolve or evolve into G-phase precipitates during the same period. Dislocation loops enriched with solutes dissolve within 2 weeks of annealing, while dislocation line precipitates persist after 2 weeks but disappear after 34 weeks.

Irradiation reduces the matrix solubility limit, evidenced by the significantly larger volume fraction of G-phase precipitates observed in irradiated samples. The radiation-induced solubility limit of Ni determined the volume fraction of the precipitated G-phase. We attribute the decrease in the Ni solubility limit to the radiation-induced supersaturation of vacancies, which promotes the precipitation of the G-phase due to its lower density compared to the matrix.

Based on the measured chemical composition and lattice parameter of the G-phase, together with DFT studies showing a decreasing lattice parameter with increasing Fe content and the anti-symmetry observed in the annealed Fe and Mn diffusion profiles, we propose that Fe partially substitutes for Mn in the sublattice. Consequently, the G-phase can be represented by the chemical formula Ni₁₆ (MnₓFe₁₋ₓ)₆ Si₇. The Fe atomic fraction (1 - x) in the Mn-sublattice varies between 0.44 in bulk precipitates and 0.59 in dislocation loops, respectively corresponding to 9% and 12% per atom of the G-phase. The higher Fe concentration in precipitates near point defect (PD) sinks is likely due to ballistic mixing between Fe and Mn. However, after 34 weeks of annealing, approximately 20 at.% of Fe atoms are lost, indicating that irradiation affects the G-phase composition.

Consistent with previous studies, heterogeneous G-phase precipitation occurs on dislocation loops and lines, likely driven by positive radiation-induced segregation (RIS) of Ni, Si and Mn solutes. The Mn-depleted core of sandwich-shaped precipitates suggests that homogeneous nucleation of G-phase begins with the precipitation of a
metastable Ni–Si–Fe phase, which dissolves after annealing. The precipitation of the Ni–Si–Fe phase is likely driven by a supersaturation of SIAs, which promotes the formation of phases denser than the matrix. Our findings indicate that this dense phase, analogous to the Cu-rich precipitates in Cu-bearing RPV steels, can act as a critical precursor to homogeneous G-phase precipitation. Besides, the Ni–Si–Fe phase should be investigated as a potential hardening feature in low-Cu steels. Based on our findings, we underscore the importance of managing the synergistic effects of solutes and point defect supersaturations on radiation-induced precipitation.

### CRediT authorship contribution statement

**Quentin Tencé:** Writing – original draft, Validation, Software, Methodology, Investigation, Formal analysis, Data curation. **Estelle Meslin:** Writing – review & editing, Writing – original draft, Visualization, Validation, Supervision, Resources, Project administration, Methodology, Funding acquisition, Formal analysis, Conceptualization. **Isabelle Mouton:** Writing – review & editing, Validation, Supervision, Methodology, Investigation. **Brigitte Décamps:** Validation, Supervision, Methodology. **Raphaëlle Guillou:** Writing – review & editing, Validation, Resources, Investigation, Formal analysis. **Jean-Luc Béchade:** Writing – review & editing, Validation, Supervision, Methodology, Investigation, Formal analysis. **Erik Elkaim:** Writing – review & editing, Validation, Methodology, Investigation. **Anna Fraczkiewicz:** Resources, Conceptualization. **Maylise Nastar:** Writing – review & editing, Writing – original draft, Visualization, Validation, Supervision, Software, Resources, Methodology, Investigation, Funding acquisition, Formal analysis, Data curation, Conceptualization.

### Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

### Acknowledgments

The research was supported by the Cross-cutting basic research Program of Division Energy of CEA (RTA Program), the RMATE project (CEA), and by the French government, managed by the French National Research Agency, under the “Investissements d’avenir” program (No. ANR-11-EQPX-0020). The authors would like to gratefully acknowledge the JANNuS Saclay facility for irradiating the samples. They also express their gratitude to M. Vallet from LMPS Paris Saclay for his assistance with the Titan TEM.

### Appendix A. Supplementary data

Supplementary material related to this article can be found online at https://doi.org/10.1016/j.actamat.2025.121502.

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