# Synergistic effects of Mn, Ni, and Si on the formation of Mn-Ni-Si-rich clusters in reactor pressure vessel model steels irradiated at high neutron fluence

Deepak Sharma, Auriane Etienne, Philippe Pareige, Bertrand Radiguet

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Deepak Sharma, Auriane Etienne, Philippe Pareige, Bertrand Radiguet. Synergistic effects of Mn, Ni, and Si on the formation of Mn-Ni-Si-rich clusters in reactor pressure vessel model steels irradiated at high neutron fluence. Acta Materialia, 2025, 298, pp.121397. 10.1016/j.actamat.2025.121397. hal-05250684

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Submitted on 11 Sep 2025

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Synergistic effects of Mn, Ni, and Si on the formation of Mn-Ni-Si-rich clusters in reactor pressure vessel model steels irradiated at high neutron fluence

Deepak Sharma¹,#,*, Auriane Etienne¹, Philippe Pareige¹, Bertrand Radiguet¹

¹Univ Rouen Normandie, CNRS, INSA Rouen Normandie, Groupe de Physique des Matériaux, UMR 6634, F-76000 Rouen, France

#Current affiliation of the author: Materials Innovation Centre, School of Engineering, University of Leicester, Leicester LE1 7RH, UK

*Corresponding author's email address: ds809@leicester.ac.uk

Abstract

The bulk composition of reactor pressure vessel (RPV) steels influences the formation of embrittling Mn-Ni-Si (MNS)-rich clusters or precipitates under neutron irradiation. As part of the STRUMAT-LTO European project, this study examines the individual and synergistic effects of Mn, Ni, and Si concentrations on MNS-rich cluster formation at high neutron fluences using atom probe tomography. The results indicate that cluster number density increases with bulk Ni and Mn content, with the effect of each element being more pronounced in alloys containing higher amounts of the other – highlighting a Mn-Ni synergy. In contrast, Si has a negligible impact on cluster formation in the investigated composition ranges. Comparisons between experimental data and predictions from Thermo-Calc and the MILAGROS tool suggest that the formation of MNS-rich clusters involves radiation-induced segregation via flux coupling effects. These findings provide new insights into the mechanisms governing solute clustering in irradiated RPV steels, with implications for long-term reactor operation and material performance.

Keywords

Reactor pressure vessel steels; Irradiation effect; Atom probe tomography; Solute clustering; Irradiation hardening
# 1. Introduction

Life extension of the existing nuclear power plants (NPPs) is much needed to support the transition to clean energy and to meet climate goals by 2050 [1]. One critical issue with the long-term operation of the NPPs is the embrittlement of the reactor pressure vessel (RPV) steel under neutron irradiation. Indeed, the RPV is an irreplaceable component. Therefore, the in-service degradation of its mechanical properties can limit the safe operational lifetime of the NPP.

The embrittlement is demonstrated by an upward shift in the ductile-to-brittle transition temperature ($\Delta TT$) [2-4]. It is generally correlated with the increase in the yield stress ($\Delta\sigma$) resulting from irradiation hardening [5-7]. The current long-term operation assessments are done by predicting the shift in $\Delta TT$ by using embrittlement trend curves (ETCs) published in relevant codes and standards by the regulatory authorities [8-10]. ETCs show that embrittlement increases with neutron fluence [2-4] and that this increase is correlated with the bulk concentration of certain solutes or impurities such as P, Cu, or Ni - where a chemical factor, obtained by statistical correlation, is used to account for the influences of the different solutes. The existing ETCs are based on fluence data corresponding to a maximum of 40 years of operation, and can hardly be applied to life extension for up to 80 years - which is the need of the hour for sustaining nuclear power as the clean source of energy [1, 11, 12]. According to reference [8], current models significantly underpredict the changes in $\Delta TT$ at high neutron fluence due to the unaccounted microstructural changes happening at higher neutron fluence. Given that, it appears important to better understand the influence of bulk solute concentrations on the microstructure and mechanical properties after neutron irradiation at high fluence.

The impurity Cu in early RPV steels was recognised to be the main cause of embrittlement due to the formation of Cu-rich precipitates [13-18]. The Cu content was then reduced to < 0.1 wt %
in the next generation of RPV steels. However, Pareige *et al.* [19], in the 1990s, reported that the low-Cu steels still embrittle at higher neutron fluence, primarily because of the formation of Mn-Ni-Si (MNS)-rich clusters. Many studies [20–31] have reported similar observations in low-Cu RPV steels. The formation of these MNS-rich clusters is influenced by the RPV steel composition, especially Mn, Ni, and Si [21, 32–34]. However, there is a limited understanding of the individual and synergistic effects of Mn, Ni, and Si. Such information will not only help in improving the already existing ETCs but will also be useful for designing material for the next generation of RPVs and for better understanding the solute clustering mechanisms.

It has been reported that Ni is responsible for significantly intensifying the radiation embrittlement of the VVER materials containing lower Cu and P [35, 36]. A higher Ni content (~1.5 wt %) led to significant embrittlement in VVER-1000 weld material [37]. Mn has been shown to suppress the deleterious effect of Ni [38]. However, a higher amount of Mn in steel with higher Ni content leads to a significant increase in hardness [39]. Similar observations were recently reported by Kolluri *et al.* [9], where Mn has no significant effect on hardening if the Ni content is lower (0.58 wt % to 0.96 wt %). However, the addition of Mn in steel with high Ni content leads to a significant rise in $\Delta TT$, suggesting a synergy between Mn and Ni. These studies are based on mechanical tests. The microstructural information in terms of the changes in the size, shape, number density, volume fraction, and composition of the clusters are also important to provide physical explanation of the ETCs. Atom probe tomography (APT) is one such technique that can provide such information at the nanometer scale. The recent APT studies [21, 32, 33] on understanding the role of Mn and Ni do provide us with such information, but despite these efforts, data are scarce at higher fluence. In addition, Si also influences the formation of MNS-rich clusters [19]; therefore, it is also important to understand if Si has any synergistic effects with Mn and Ni.
Moreover, despite several efforts in the literature [25,27,40,41], there is no consensus on the clustering mechanism at higher fluence: whether it is radiation-induced or radiation-enhanced.

Hence, as part of the STRUMAT-LTO project, several chemically tailored RPV steels were produced to understand the individual and synergistic effects of Mn, Ni, and Si on the formation of MNS-rich clusters. APT was used in this work to gather the microstructural information from the unirradiated and neutron-irradiated samples. Vickers microhardness tests were used to correlate the microstructural changes and irradiation hardening at high neutron fluence, as a function of bulk composition. CALPHAD calculations were performed to better understand the clustering mechanism.

## 2. Materials and methods

### 2.1. Materials

Out of the several chemically tailored RPV model steels produced for the STRUMAT-LTO project, six steels, namely A, B, C, F, G, and H, were chosen for this work. The nominal chemical compositions (in at %) of these steels are shown in Table 1. Except for Mn, Ni, and Si, the bulk concentrations of most solutes are nearly identical across all the steels. Alloys A to C have low Mn (~0.4 at%), medium Si (~0.5 at%), and a progressively increasing level of Ni from nearly 0 to 2 at %. Alloys F and G also have an increasing level of Ni (approximately 1 and 2 at %, respectively) but with a high Mn level (~1.3 at%). The Si content remains similar to that in Alloys A, B, and C, although it is slightly higher (~0.6 at %). Finally, Alloys G and H contain approximately the same amount of Mn and Ni but Alloy H has a higher Si level (~1 at %). These systematic variations in chemical compositions allowed us to identify the effects of:

- Ni in low (A to C) and high (F and G) Mn steels

- Mn in medium (B and F) and high (C and G) Ni steels
- Si in high Mn and high Ni steels (G and H)

<table><caption>Table 1. The nominal chemical compositions (at %) for the alloys used in this work.</caption><thead><tr><th>Alloy</th><th>C</th><th>Mo</th><th>V</th><th>Cr</th><th>Mn</th><th>Ni</th><th>Si</th><th>Cu</th><th>P</th><th>Fe</th></tr></thead><tbody><tr><td>A</td><td>0.51</td><td>0.41</td><td>0.11</td><td>2.37</td><td>0.43</td><td>0.02</td><td>0.55</td><td>0.09</td><td>0.018</td><td>Balance</td></tr><tr><td>B</td><td>0.51</td><td>0.41</td><td>0.11</td><td>2.34</td><td>0.38</td><td>0.94</td><td>0.52</td><td>0.09</td><td>0.018</td><td>Balance</td></tr><tr><td>C</td><td>0.56</td><td>0.4</td><td>0.11</td><td>2.28</td><td>0.38</td><td>1.89</td><td>0.47</td><td>0.09</td><td>0.018</td><td>Balance</td></tr><tr><td>F</td><td>0.56</td><td>0.41</td><td>0.11</td><td>2.29</td><td>1.38</td><td>0.96</td><td>0.65</td><td>0.09</td><td>0.018</td><td>Balance</td></tr><tr><td>G</td><td>0.51</td><td>0.4</td><td>0.11</td><td>2.2</td><td>1.38</td><td>1.88</td><td>0.63</td><td>0.09</td><td>0.019</td><td>Balance</td></tr><tr><td>H</td><td>0.56</td><td>0.4</td><td>0.11</td><td>2.21</td><td>1.32</td><td>1.89</td><td>1.01</td><td>0.09</td><td>0.019</td><td>Balance</td></tr></tbody></table>

The base composition of these model steels was derived from the typical composition of VVER-1000 RPV steel [42], and then the systematic variations in Mn, Ni, and Si were made. The samples were manufactured in an open induction furnace with a special iron charge that contained secondary elements. Cast iron was used to maintain the required level of carbon content. The alloying elements (Mn, Ni, and Si) were added in the form of master alloys. The desired level of impurity elements (Cu, P, and S) was obtained by adding Cu, Fe-P compound (with 25 % P), and Fe-S compound (with 36.4 % S), respectively. The impurity levels here, as shown in Table 1, are close to the upper limits of a VVER-1000 RPV steel.

The casting process was used to produce ingots of weight 25 kg from each melt. This was followed by heating the ingots for 4 h at 800 °C. Ingots were then forged into bars with a cross-section of 50 mm × 50 mm. The forging was carried out at temperatures ranging from 900 °C to 1200 °C. The sink heads of the ingots were removed. The forged bars were subsequently hot-rolled into plates with a thickness of 8 mm and a width ranging from 200 mm – 210 mm. Rolling was performed at 1180 °C with a preheating of about 2 h. The finished plates were subsequently cut into pieces of lengths 600 mm to 700 mm.

The 8 mm thick plates were then heat-treated for 10 h at 655 °C. This was followed by hardening and tempering treatments to achieve target strength levels. The hardening stage included heating the samples from 655 °C to 940 °C (for A, C, F, G, and H) and to 960 °C (for B) for 20
min, followed by water quenching down to room temperature. The tempering stage consisted of heating the plates to 655 °C (for A, F, and G) and 675 °C (for C and G) for 10 h and 19 h, respectively. Alloy B was heated to 675 °C for 14 h. The tempering was carried out in the air. A bainitic microstructure was obtained in all the alloys. Some islands of ferrite were observed in Alloy A [43].

## 2.2. Irradiation conditions

The produced samples were irradiated with neutrons as part of LYRA-10 irradiation experiments [44]. The irradiation was jointly performed by NRG and JRC at the high flux reactor (HFR) in Petten, Netherlands. The irradiation was carried out for 16 HFR cycles by irradiating the samples for 467 days of full power, with a nominal reactor power level of 45 MW. This achieved a nominal fast neutron fluence (E > 1 MeV) of about $1.11 \times 10^{20} \text{ n cm}^{-2}$. The average irradiation temperature over the 16 cycles was 283 °C, with individual cycle averages ranging from 280 °C to 288 °C. The nominal flux (E > 1 MeV) value was kept around $2.75 \times 10^{12} \text{ n cm}^{-2} \text{ s}^{-1}$. This is higher (by slightly more than two orders of magnitude) than the typical design flux for a pressurised water reactor (PWR) RPV. More details on the irradiation experiments can be found in the reference [44]. The designed lifetime fluence for a typical PWR RPV is $4 \times 10^{19} \text{ n cm}^{-2}$ [42] – which is equivalent to 32 effective full power years (EPFY). Hence, the nominal fluence received by the current samples corresponds to 89 EPFY. The dose is estimated to be 0.18 displacement per atom (dpa).

## 2.3. Metallography and Vickers microhardness

The unirradiated and the neutron-irradiated steels were then sectioned into small samples of dimensions 10 mm × 5 mm × 0.5 mm in the hot cell facility of Helmholtz-Zentrum Dresden-Rossendorf, Dresden, Germany. The sectioned samples were then mounted in epoxy using a hot mounting method at Groupe de Physique des Matériaux (GPM), Rouen, France. The samples were
subsequently mechanically ground to 9 µm using diamond pads, followed by sequential polishing
down to 0.04 µm diamond suspension.

To understand the irradiation hardening behaviour of the steels as a function of different compositions, Vickers microhardness tests were carried out on a NANOVEA CB500 micro-indentation machine. The indentations were made using a load of 5 N with a dwell time of 10 s. Twenty readings were taken for each sample, and average values are presented here.

2.4. Atom probe tomography

Data obtained from APT offer a three-dimensional description of chemical heterogeneities at
the nanometer scale but are highly localised (approximately 50 × 50 × 200 nm). To ensure the
representativeness of the results, two chunks were extracted from different locations on the
polished samples using focused ion beam (FIB) milling. At least three tips were prepared from
each chunk using FIB annular milling. The final stage of tip preparation included a low-energy
cleanup at 2 kV and 90 pA to reduce the Ga damage of the tips.

The APT characterisation was carried out on AMETEK-CAMECA's LEAP 5000 XR at the
GENESIS platform of GPM, Rouen, France. All the samples were analysed in voltage mode, at a
temperature equal to 55 K. The pulse fraction and pulse frequency were kept as 20 % of the standing
voltage and 200 kHz, respectively. The detection rate was varied from 0.1 % to 0.3 % during
analysis to keep a constant evaporation flux, as the sample diameter changes during analysis. At
least 10 million atoms were collected from each alloy to enable the examination of an object density
exceeding 5 × 10²¹ per m³.

The APT data were reconstructed using the IVAS commercial software (version 3.8.10) from
AMETEK-CAMECA. The initial several thousand atoms were discarded during reconstruction as
the tip was being aligned and had a higher Ga and O concentration during the start of the APT
analysis. A standard image compression factor value of 1.65 was used for the reconstruction, whilst
the *k* values were determined by calibrating the *d* spacing values for the poles, such as (011), (002),
or (222). The atom files were then saved from these reconstructions. These files were then imported
into GPM 3DSAT software (CNRS IDDN: IDDN.FR.001.430017.000.S.P.2020.000.10000) to
perform further analysis. Each peak (mass-to-charge ratio) of the mass spectrum was identified and
decomposed based on the natural abundances of several isotopes of different elements.
Subsequently, the global composition of the samples was calculated from the decomposed data.
The matrix composition was calculated by decomposing the mass spectrum obtained from volumes
containing no clusters.

The clusters in unirradiated and irradiated samples were identified using the isoposition method (IPM). Further information on IPM can be seen in reference [45]. It is based on three parameters: a composition threshold (*C*<sub>th</sub>) value, the maximum distance between atoms (*d*<sub>max</sub)), and the minimum number of core atoms (*N*<sub>min</sub>). The *C*<sub>th</sub> value was used to first filter the potentially clustered atoms. *C*<sub>th</sub> is defined as the local concentration of the solutes measured at 0.01 % relative occurrence in the randomised datafile. Visual inspection of the APT volumes reveals that the solute clusters are enriched in Mn, Ni, Si, Cu, and P, without displaying any distinct structural features such as a Cu-rich core (Fig. 1). Such cluster morphologies are typically observed in low-Cu steels (< 0.1 wt %) [28,46,47]. Accordingly, Mn, Ni, Si, Cu, and P were grouped as core atoms to calculate the *C*<sub>th</sub> value whilst searching for the MNS-rich clusters.
<figure><img src="image_2.png" /><figcaption>Fig. 1. Close-up view of typical solute clusters observed in irradiated alloys A, B, C, F, G, and H. Only Cu, Mn, and Ni atoms are displayed here, without applying any data filtering.</figcaption></figure>

The atomic distance method was then used to assign the filtered atoms to the clusters – the atoms (core and non-core atoms) within the $d_{max}$ of 0.4 nm were assigned to the same cluster. If the number of core atoms are lower than $N_{min}$, the corresponding clusters are not kept, and the corresponding atoms are brought back to the matrix. The $N_{min}$ values were decided based on the fact that zero clusters were present in the random solid solution.

After the identification step, a shell of matrix atoms around the clusters is generally considered as cluster atoms [48]. These surrounding shells were eliminated using a two-step erosion method. The first erosion step was applied to establish the boundary between the clusters and the matrix, whilst the second erosion step was conducted to identify the core of the clusters.

The diameter ($D$), number density ($N$), and volume fraction ($f_v$) of clusters were calculated using the first erosion data. The diameter of each cluster was calculated using the expression: $D = 2 \times \sqrt[3]{\frac{3nV_{at}}{4\pi Q}}$ – which is the equivalent spherical diameter. Here, $n$ is the number of atoms in each
cluster, $V_{at}$ is the atomic volume of BCC Fe, and $Q$ is the detection efficiency of LEAP 5000 XR – which is 0.52. The $N$ was calculated as the total number of clusters identified/total volume analysed. The total volume ($V_T$) analysed is given by the expression: $V_T = \frac{n_1 \times V_{at}}{Q}$, where $n_1$ is the total number of atoms collected from all the tips of each sample. The $f_v$ of the clusters is given by:

$$f_v = \frac{\text{Total number of atoms in the clusters}}{\text{Total number of atoms collected}}$$

The second erosion data was used to create separate volumes containing only cluster cores. The mass/charge peaks obtained from these volumes were also treated the same way as mass/charge peaks from the bulk volume: The mass/charge peaks were identified and decomposed using the natural abundance of the elements to calculate the cluster composition.

## 2.5. CALPHAD calculations

Single-point equilibrium calculations were performed in the Thermo-Calc software (version 2017a). This was done to understand the phase transformation behaviour of different steels, used in this work, under equilibrium conditions. The exact compositions (Table 1) were used for these calculations. The calculations were performed at 283 °C to match the irradiation condition. The TCFe8 database was used for all the calculations, and no restriction was made on the possible phases.

# 3. Results

## 3.1. Microstructure

Fig. 2 and Fig. 3 present atom maps illustrating the distribution of solute atoms (Mn, Ni, Si, Cu, P, and altogether (MNS)) in unirradiated and irradiated samples, respectively. Regions enriched with these elements were identified using IPM. A visual analysis of these maps indicates
that neutron irradiation has induced clustering of the solute elements, with the clustering tendency
increasing progressively from Alloy A to Alloy H.
<figure><img src="image_3.png" /><figcaption>Fig. 2. Filtered atom maps for Alloy (a) A, (b) B, (c) C, (d) F, (e) G, and (f) H under unirradiated conditions. All the solutes look quite homogeneously distributed.</figcaption></figure>
<figure><img src="image_4.png" /><figcaption>Fig. 3. Filtered atom maps of neutron-irradiated Alloy (a) A, (b) B, (c) C, (d) F, (e) G, and (f) H. The regions enriched in solutes are highlighted, showing the irradiation-induced solute clusters.</figcaption></figure>
## 3.2. APT vs nominal composition

The average global compositions of all unirradiated and irradiated alloys, as measured using APT, are presented in Table 2. In unirradiated alloys, these compositions represent the matrix compositions since no cluster is observed. For irradiated alloys, the matrix compositions – also shown in Table 2 – were determined by excluding cluster atoms (prior to erosion) from the global volumes.

The comparison of APT global compositions with nominal values (Table 1) shows that the measured amounts of C, Mo, Mn, V, and Cr are lower than their nominal concentrations. This reduction occurs because these elements are carbide formers [19,21,24], and since APT analyses very localised regions, it may not capture carbides, making these variations expected [21]. However, in Alloy A, the difference is relatively small, suggesting a lower volume fraction of carbides compared to the other alloys.

APT measurements detected slightly higher Ni concentrations overall, except for Alloy C in the irradiated condition and Alloys B, C, and F in the unirradiated condition, where lower amounts were observed. Similarly, Si concentrations in APT global compositions were slightly higher than the nominal values, except for Alloys B and C in the irradiated state and Alloys A, B, and C in the unirradiated state, where lower concentrations were found. Nonetheless, the solute concentrations in the APT volume follow the same trend as the nominal composition for Mn, Ni, and Si, and their concentrations are sufficient to study their effects as expected.

A slightly lower amount of Cu was detected (0.05 to 0.07 at. % instead of 0.09 at %). It could be due to its preferential evaporation during APT analysis [49]. Similarly, a very slight underestimation of P was observed (~0.015 at % instead of 0.018 at %). It could be due to some P
segregation to grain boundaries during heat treatments. Such small differences between APT and
nominal compositions are expected and have been reported previously [5,21].

Additionally, the concentrations of Mn, Ni, Si, Cu, and P in the irradiated matrix are a bit lower
than in the global composition, as these elements tend to form MNS-rich clusters. However, the
concentrations of Mn, Ni, and Si remaining in the irradiated matrix are close to their overall global
values. This suggests that a significant fraction of these solutes remains available for further
clustering under higher irradiation doses. At elevated doses, it is plausible that both the number
density and size of MNS-rich clusters would increase, potentially accompanied by changes in their
nature or composition.
<table><caption>Table 2. The average global and matrix APT compositions obtained from different tips of Alloys A, B, C, F, G, and H under irradiated conditions are presented in this table. The average global APT compositions for all these alloys under unirradiated conditions are also shown. All the values are in at %.</caption><thead><tr><th>Sample</th><th>C</th><th>Mo</th><th>V</th><th>Cr</th><th>Mn</th><th>Ni</th><th>Si</th><th>Cu</th><th>P</th></tr></thead><tbody><tr><td colspan="10">Global APT composition for unirradiated samples</td></tr><tr><td>A</td><td>0.47 ±<br>0.04</td><td>0.34 ±<br>0.04</td><td>0.08 ±<br>0.01</td><td>2.19 ±<br>0.14</td><td>0.34 ±<br>0.01</td><td>0.03 ±<br>0.07</td><td>0.51 ±<br>0.01</td><td>0.04 ±<br>0.01</td><td>0.015 ±<br>0.001</td></tr><tr><td>B</td><td>0.11 ±<br>0.01</td><td>0.29 ±<br>0.03</td><td>0.03 ±<br>0.01</td><td>1.22 ±<br>0.16</td><td>0.27 ±<br>0.02</td><td>0.85 ±<br>0.04</td><td>0.50 ±<br>0.03</td><td>0.03 ±<br>0.01</td><td>0.016 ±<br>0.001</td></tr><tr><td>C</td><td>0.11 ±<br>0.07</td><td>0.30 ±<br>0.02</td><td>0.05 ±<br>0.01</td><td>1.29 ±<br>0.15</td><td>0.28 ±<br>0.01</td><td>1.81 ±<br>0.12</td><td>0.44 ±<br>0.01</td><td>0.05 ±<br>0.01</td><td>0.015 ±<br>0.001</td></tr><tr><td>F</td><td>0.11 ±<br>0.01</td><td>0.29 ±<br>0.01</td><td>0.06 ±<br>0.01</td><td>1.42 ±<br>0.12</td><td>1.04 ±<br>0.02</td><td>0.92 ±<br>0.03</td><td>0.66 ±<br>0.01</td><td>0.04 ±<br>0.01</td><td>0.015 ±<br>0.001</td></tr><tr><td>G</td><td>0.17 ±<br>0.01</td><td>0.30 ±<br>0.05</td><td>0.03 ±<br>0.01</td><td>1.53 ±<br>0.13</td><td>1.09 ±<br>0.06</td><td>1.92 ±<br>0.1</td><td>0.66 ±<br>0.01</td><td>0.05 ±<br>0.01</td><td>0.015 ±<br>0.002</td></tr><tr><td>H</td><td>0.13 ±<br>0.01</td><td>0.19 ±<br>0.04</td><td>0.04 ±<br>0.01</td><td>1.55 ±<br>0.14</td><td>1.18 ±<br>0.06</td><td>1.93 ±<br>0.25</td><td>1.03 ±<br>0.01</td><td>0.05 ±<br>0.01</td><td>0.014 ±<br>0.004</td></tr><tr><td colspan="10">Global APT composition for irradiated samples</td></tr><tr><td>A</td><td>0.50 ±<br>0.42</td><td>0.40 ±<br>0.11</td><td>0.11 ±<br>0.02</td><td>2.34 ±<br>0.27</td><td>0.34 ±<br>0.09</td><td>0.03 ±<br>0.01</td><td>0.59 ±<br>0.09</td><td>0.06 ±<br>0.01</td><td>0.018 ±<br>0.01</td></tr><tr><td>B</td><td>0.17 ±<br>0.06</td><td>0.33 ±<br>0.03</td><td>0.05 ±<br>0.04</td><td>1.72 ±<br>0.12</td><td>0.32 ±<br>0.01</td><td>1.04 ±<br>0.05</td><td>0.51 ±<br>0.01</td><td>0.071 ±<br>0.02</td><td>0.013 ±<br>0.009</td></tr><tr><td>C</td><td>0.24 ±<br>0.15</td><td>0.35 ±<br>0.02</td><td>0.04 ±<br>0.01</td><td>1.69 ±<br>0.06</td><td>0.29 ±<br>0.01</td><td>1.86 ±<br>0.02</td><td>0.45 ±<br>0.02</td><td>0.05 ±<br>0.01</td><td>0.008 ±<br>0.002</td></tr><tr><td>F</td><td>0.16 ±<br>0.08</td><td>0.31 ±<br>0.01</td><td>0.06 ±<br>0.01</td><td>1.63 ±<br>0.09</td><td>1.21 ±<br>0.06</td><td>1.12 ±<br>0.03</td><td>0.70 ±<br>0.02</td><td>0.061 ±<br>0.01</td><td>0.012 ±<br>0.001</td></tr><tr><td>G</td><td>0.29 ±<br>0.06</td><td>0.35 ±<br>0.01</td><td>0.03 ±<br>0.01</td><td>1.67 ±<br>0.79</td><td>1.04 ±<br>0.04</td><td>1.93 ±<br>0.04</td><td>0.68 ±<br>0.03</td><td>0.05 ±<br>0.01</td><td>0.015 ±<br>0.005</td></tr><tr><td>H</td><td>0.16 ±<br>0.09</td><td>0.28 ±<br>0.01</td><td>0.04 ±<br>0.01</td><td>1.70 ±<br>0.01</td><td>1.06 ±<br>0.04</td><td>1.95 ±<br>0.05</td><td>1.06 ±<br>0.02</td><td>0.05 ±<br>0.01</td><td>0.012 ±<br>0.002</td></tr><tr><td colspan="10">Matrix APT composition for irradiated samples</td></tr><tr><td>A</td><td>0.50 ±<br>0.4</td><td>0.40 ±<br>0.1</td><td>0.11 ±<br>0.02</td><td>2.33 ±<br>0.2</td><td>0.33 ±<br>0.09</td><td>0.03 ±<br>0.01</td><td>0.58 ±<br>0.09</td><td>0.05 ±<br>0.01</td><td>0.016 ±<br>0.009</td></tr><tr><td>B</td><td>0.16 ±<br>0.09</td><td>0.33 ±<br>0.03</td><td>0.03 ±<br>0.01</td><td>1.72 ±<br>0.1</td><td>0.29 ±<br>0.01</td><td>0.93 ±<br>0.09</td><td>0.45 ±<br>0.05</td><td>0.05 ±<br>0.01</td><td>0.007 ±<br>0.004</td></tr><tr><td>C</td><td>0.22 ±<br>0.18</td><td>0.35 ±<br>0.02</td><td>0.035 ±<br>0.01</td><td>1.71 ±<br>0.06</td><td>0.24 ±<br>0.02</td><td>1.57 ±<br>0.11</td><td>0.33 ±<br>0.02</td><td>0.03 ±<br>0.01</td><td>0.003 ±<br>0.001</td></tr><tr><td>F</td><td>0.12 ±<br>0.1</td><td>0.32 ±<br>0.01</td><td>0.06 ±<br>0.01</td><td>1.65 ±<br>0.09</td><td>1.05 ±<br>0.08</td><td>0.84 ±<br>0.18</td><td>0.56 ±<br>0.1</td><td>0.04 ±<br>0.01</td><td>0.007 ±<br>0.002</td></tr><tr><td>G</td><td>0.29 ±<br>0.06</td><td>0.36 ±<br>0.01</td><td>0.03 ±<br>0.01</td><td>1.71 ±<br>0.08</td><td>0.69 ±<br>0.04</td><td>1.08 ±<br>0.04</td><td>0.38 ±<br>0.02</td><td>0.02 ±<br>0.01</td><td>0.008 ±<br>0.002</td></tr><tr><td>H</td><td>0.16 ±<br>0.09</td><td>0.28 ±<br>0.01</td><td>0.04 ±<br>0.01</td><td>1.74 ±<br>0.01</td><td>0.81 ±<br>0.1</td><td>1.28 ±<br>0.28</td><td>0.74 ±<br>0.13</td><td>0.02 ±<br>0.01</td><td>0.006 ±<br>0.001</td></tr></tbody></table>
### 3.3. Cluster characteristics

The number density ($N$), volume fraction ($f_v$), and the diameter ($D$) of MNS-rich clusters measured in irradiated steels are reported in Table 3. It is important to note that the neutron flux used in this study is approximately two orders of magnitude higher than that typically encountered under PWR RPV conditions. As a result, the characteristics of the solute clusters observed here may differ from those formed under comparable dose levels in actual PWR environments. Previous studies [50,51] have shown that higher flux conditions generally result in increased number densities of solute clusters, reduced average cluster size, and lower solute enrichment. Nonetheless, the primary objective of this study is to assess the influence of bulk composition.

The influence of Ni bulk content on cluster size is noticeable in low-Mn steels, where the cluster diameter increases from ~2 nm to ~2.9 nm across Alloys A to C. However, this trend does not persist in high-Mn steels, as seen in the comparisons between Alloys F and G or F and H. When examining pairs B/F and C/G, the effect of Mn on cluster size appears minimal, leading to only a slight reduction in average diameter with increasing Mn content.

<table><caption>Table 3. The average values for number density, volume fraction, and diameter of the MNS-rich clusters that were observed in irradiated samples. The error bars are the standard deviations.</caption><thead><tr><th>Sample</th><th>Number density, N (× 10<sup>23</sup> m<sup>-3</sup>)</th><th>Volume fraction, f<sub>v</sub> (%)</th><th>Diameter, D (nm)</th></tr></thead><tbody><tr><td>Alloy A</td><td>4.5 ± 1.8</td><td>0.24 ± 0.08</td><td>2.04 ± 0.48</td></tr><tr><td>Alloy B</td><td>14.3 ± 1.7</td><td>1.45 ± 0.28</td><td>2.52 ± 0.66</td></tr><tr><td>Alloy C</td><td>17.1 ± 2.9</td><td>2.49 ± 0.30</td><td>2.90 ± 0.60</td></tr><tr><td>Alloy F</td><td>32.6 ± 1.2</td><td>3.38 ± 0.22</td><td>2.64 ± 0.44</td></tr><tr><td>Alloy G</td><td>49.3 ± 1.4</td><td>4.29 ± 0.23</td><td>2.42 ± 0.46</td></tr><tr><td>Alloy H</td><td>48.1 ± 3.6</td><td>4.37 ± 0.22</td><td>2.52 ± 0.44</td></tr></tbody></table>

In contrast, the effects of Mn and Ni on cluster number density are more pronounced. In all cases, an increase in bulk Ni content leads to an increase in number density. For instance, in low-Mn steels (A to C, with Ni increasing from nearly 0 to 2 %), the cluster number density increases
from $4.5 \times 10^{23}$ to $17.1 \times 10^{23} \text{ m}^{-3}$. Similarly, comparisons between alloys B and F, as well as C and G, indicate that higher Mn bulk content leads to increased cluster density in both medium- and high-Ni steels. Notably, Mn has a stronger effect on cluster density than Ni. Adding 1 % Mn to low-Mn, medium-Ni steel (B) results in an increase of $18.3 \times 10^{23} \text{ m}^{-3}$ in cluster density (F compared to B), whereas adding 1 % Ni to Alloy B increases the density by only $2.8 \times 10^{23} \text{ m}^{-3}$ (C compared to B). Likewise, adding 1 % Mn to C raises the cluster density by $32.2 \times 10^{23} \text{ m}^{-3}$ (G compared to C), whilst adding 1 % Ni to F increases it by $16.7 \times 10^{23} \text{ m}^{-3}$ (G compared to F).

Additionally, the impact of 1 % Ni is more significant in high-Mn steels ($+16.7 \times 10^{23} \text{ m}^{-3}$ from F to G) than in medium-Mn steels ($+2.7 \times 10^{23} \text{ m}^{-3}$ from B to C). A similar trend is observed when adding 1 % Mn, which has a greater effect in high-Ni steels ($+32.2 \times 10^{23} \text{ m}^{-3}$ from G to C) than in medium-Ni steels ($+18.3 \times 10^{23} \text{ m}^{-3}$ from B to F). This strong interaction between Mn and Ni suggests a synergistic effect, where their combined influence on clustering is greater than the sum of their individual effects.

Since the volume fraction depends on both cluster size and density, and the effect of bulk Mn and Ni on cluster size is relatively small, the trends observed for cluster density also apply to volume fraction. A comparison of Alloys G and H provides insight into the effect of bulk Si (ranging from 0.32 % to 0.51 %) in high-Mn, high-Ni steels. No significant differences in N, $f_v$, and D were observed, suggesting that Si has no impact on MNS-rich cluster formation in high Mn/Ni RPV steels.

The average core compositions of clusters in irradiated alloys, as measured by APT, are presented in Table 4. It is evident from the table that these clusters predominantly consist of Fe. Examining solute levels, the relative amount of Mn, Ni, and Si in the clusters increases following the same trend as their levels in the bulk material. The clusters in Alloy A contain a higher amount
of Cr, whilst those in the other alloys exhibit approximately the same Cr content. A slightly higher but still comparable amount of Cu appears in the clusters of Alloys A and B, whereas Alloys C and F show clusters with a similar Cu content, lower than that of Alloys A and B but higher than in Alloys G and H. The clusters in Alloys G and H contain the lowest Cu levels, with both alloys displaying approximately the same content. It seems that higher bulk Mn and Ni contents tend to reduce the Cu level into clusters. However, according to Table 2, the remaining Cu in the matrix is lower in steels with more Mn and Ni, indicating that more Cu has clustered. Since no Cu-rich precipitate is observed, a possible explanation is that in steels containing more Mn and Ni, more solute clusters are formed (Table 3), so that less Cu per cluster is available. The P content is highest in the clusters of Alloy A, whilst the clusters in the other alloys exhibit approximately the same amount. The clusters in Alloy A also contain a higher amount of V, whereas the clusters in the remaining alloys show nearly identical V levels. Additionally, C is present in the clusters of all the alloys, with the highest concentration found in the clusters of Alloy A.

<table><caption>Table 4. The average compositions of clusters (in at %) observed in alloys A, B, C, F, G, and H. The balance is Fe.</caption><thead><tr><th>Alloy</th><th>Mn</th><th>Ni</th><th>Si</th><th>Cr</th><th>Mo</th><th>Cu</th><th>P</th><th>V</th><th>C</th></tr></thead><tbody><tr><td>A</td><td>1.9 ±<br>0.9</td><td>2.8 ±<br>0.45</td><td>2.5 ±<br>0.55</td><td>3.1 ±<br>0.65</td><td>0.05 ±<br>0.02</td><td>1.2 ±<br>0.9</td><td>0.70 ±<br>0.30</td><td>0.09 ±<br>0.05</td><td>0.63 ±<br>0.42</td></tr><tr><td>B</td><td>2.05 ±<br>0.4</td><td>9.1 ±<br>1.2</td><td>4.4 ±<br>1.5</td><td>1.3 ±<br>0.1</td><td>0.02 ±<br>0.01</td><td>1.2 ±<br>0.4</td><td>0.20 ±<br>0.16</td><td>-</td><td>0.04 ±<br>0.03</td></tr><tr><td>C</td><td>2.6 ±<br>0.2</td><td>12.5 ±<br>0.7</td><td>5.6 ±<br>0.7</td><td>1.2 ±<br>0.2</td><td>0.10 ±<br>0.06</td><td>0.90 ±<br>0.10</td><td>0.13 ±<br>0.07</td><td>0.01 ±<br>0.01</td><td>0.23 ±<br>0.21</td></tr><tr><td>F</td><td>6.4 ±<br>0.1</td><td>10.3 ±<br>0.3</td><td>5.8 ±<br>0.4</td><td>1.2 ±<br>0.1</td><td>0.17 ±<br>0.07</td><td>0.91 ±<br>0.08</td><td>0.14 ±<br>0.03</td><td>0.03 ±<br>0.03</td><td>0.11 ±<br>0.06</td></tr><tr><td>G</td><td>6.4 ±<br>0.3</td><td>12.75 ±<br>0.6</td><td>5.6 ±<br>0.4</td><td>1.15 ±<br>0.1</td><td>0.17 ±<br>0.06</td><td>0.55 ±<br>0.04</td><td>0.10 ±<br>0.04</td><td>0.02 ±<br>0.01</td><td>0.23 ±<br>0.08</td></tr><tr><td>H</td><td>5.4 ±<br>0.2</td><td>11.6 ±<br>0.4</td><td>6.8 ±<br>0.6</td><td>1.15 ±<br>0.1</td><td>0.12 ±<br>0.05</td><td>0.54 ±<br>0.07</td><td>0.11 ±<br>0.04</td><td>0.02 ±<br>0.01</td><td>0.11 ±<br>0.09</td></tr></tbody></table>
### 3.4. Enrichment factor

The enrichment factor ($C_{cluster}/C_{matrix}$) for different elements was calculated for all the alloys, to better understand the changes in the cluster composition. The enrichment factor for carbon was found to be approximately 1 for Alloys A and C, and for other alloys, it was less than 1. The enrichment factors for V and Mo were also less than 1 for all the alloys. This means that V, Mo, and carbon do not have much influence on the formation of MNS-rich clusters. The enrichment factor of Cr for Alloy A was found to be 1.3, and for other alloys, the enrichment factor was less than 1. A higher enrichment factor of Cr for Alloy A is associated with higher Cr content in the bulk. This also suggests that Cr has some participation in the formation of MNS-rich clusters in Alloy A. Overall, these elements (C, V, Mo, and Cr) do not have any influence on the formation of MNS-rich clusters, except for the influence of Cr seen for Alloy A.

The enrichment factor values for Mn, Ni, Si, Cu, and P are plotted in Fig. 4. They are systematically higher than 5. The enrichment factor for Mn increased from alloys A to C. As only the amount of Ni was increased for these alloys, it seems that increasing the amount of Ni in the bulk leads to an increase in Mn in the clusters. This is in line with the synergy between Mn and Ni shown previously. The enrichment factor of Mn decreased for Alloy F when Ni content was decreased, although Mn content was increased. The enrichment factor of Mn again increased for Alloy G when the Ni content was increased. The enrichment factor for Mn decreased for Alloy H. This is associated with the increase in the bulk Si content.

The highest enrichment factor of Ni was observed for Alloy A. The enrichment factor of Ni decreased from Alloy B to C, although the Ni content was increased. The enrichment factor of Ni increased for Alloy F as the amount of Mn was added and the amount of Ni was decreased. The enrichment factor for Alloy G did not change with respect to Alloy F, although the amount of Ni
was added; however, the amount of Mn remained constant. The observations from the enrichment factors of Mn and Ni suggest that Mn and Ni favour each other in cluster formation: As the amount of Ni is increased in the bulk, the amount of Mn will increase in the clusters, and vice versa. The enrichment factor of Ni for Alloy H decreased due to the addition of Si.

The enrichment factor values for Si and Cu for Alloys A to G varied in the clusters with the same trend as the variation in the bulk Ni content, suggesting that Ni, Si, and Cu favour each other. However, the enrichment of Si and Cu decreased for Alloy H, although Si content was higher for this alloy. The enrichment factor for P was found to be the highest for Alloy A, but the enrichment factor variations for P did not show any trend with composition, as for Mn, Ni, Si, and Cu.
<figure><img src="image_5.png" /><figcaption>Fig. 4. The enrichment factor plots for Mn, Ni, Si, Cu, and P in alloys A, B, C, F, G, and H.</figcaption></figure>
### 3.5. Hardening

The results from microhardness measurements are reported in Table 5. The hardening values ($\Delta H_v$) were calculated from the measured average hardness values for the unirradiated and irradiated alloys. Since absolute hardening depends not only on microstructural change but also on the initial hardness [52], the relative hardening (in %) of each alloy is also reported in this table.

<table><caption>Table 5. The average hardness values ($H_{v0.5}$) obtained for alloys A, B, C, F, G, and H in the unirradiated and the irradiated conditions, and corresponding relative (%) and absolute hardening.</caption><thead><tr><th>Alloy</th><th>Hardness unirradiated</th><th>Hardness irradiated</th><th>Change in hardness (%)</th><th>Hardening</th></tr></thead><tbody><tr><td>A</td><td>268 ± 11</td><td>335 ± 16</td><td>25.0</td><td>67 ± 20</td></tr><tr><td>B</td><td>217 ± 3</td><td>283 ± 9</td><td>30.4</td><td>66 ± 10</td></tr><tr><td>C</td><td>227 ± 4</td><td>323 ± 15</td><td>42.3</td><td>96 ± 16</td></tr><tr><td>F</td><td>216 ± 5</td><td>300 ± 7</td><td>38.9</td><td>84 ± 9</td></tr><tr><td>G</td><td>231 ± 3</td><td>374 ± 12</td><td>61.9</td><td>143 ± 13</td></tr><tr><td>H</td><td>220 ± 9</td><td>359 ± 13</td><td>63.2</td><td>139 ± 16</td></tr></tbody></table>

Hardening increases for Alloy C, which correlates with an increase in the number density and cluster size. In contrast, Alloy F exhibits reduced hardening compared to Alloy C, despite having a higher number density and cluster size. For Alloys G and H, a sharp increase in hardening is observed, consistent with the rise in cluster number density and size. Overall, the hardening trend does not strictly follow the trends in cluster number density and size, although a general tendency towards higher hardening in more solute-rich alloys is evident. This is illustrated in Fig. 5 (a) and (b), which shows the variation in absolute and relative hardening as a function of $\sqrt{N.D}$ and the combined bulk concentration of Mn, Ni, and Si ($C_{Mn} + C_{Ni} + C_{Si}$), respectively. In addition to experimental uncertainties, these deviations may arise from the influence of other microstructural features, such as carbide number density, dislocation forests, and self-interstitial atom (SIA) loops.
<figure><img src="image_6.png" /><figcaption>Fig. 5. Absolute and relative changes in Vickers microhardness for the six steels, plotted as a function of (a) the square root of the product of cluster number density and size, and (b) the combined bulk concentration of Mn, Ni, and Si.</figcaption></figure>

<figure><img src="image_7.png" /></figure>

Absolute and relative hardening were converted into an increase in yield stress ($\Delta\sigma$) using the relation: $\Delta\sigma = 3.33 \times \Delta H_v$ [32], facilitating comparison with other data and the interpretation of the results. The changes in the $\Delta\sigma$ values are plotted in Fig. 6.

<figure><img src="image_8.png" /><figcaption>Fig. 6. The average change in yield stress ($\Delta\sigma$) for all the alloys, calculated from the hardness values, is presented in this figure. The $\Delta\sigma$ values were calculated using the relation: $\Delta\sigma = 3.33 \times \Delta H_v$. The figure also showcases the relative change (%) in ($\Delta\sigma$).</figcaption></figure>

# 4. Discussion

## 4.1. Effect of the bulk composition on solute clustering
The effects of bulk composition on solute clusters can be interpreted in several ways. One possible explanation is that these clusters represent stable phases formed through enhanced precipitation driven by vacancy supersaturation. In this scenario, a higher bulk content increases the precipitation driving force, leading to a greater number density and volume fraction, which aligns with experimental observations.

To clarify this point, first, single-point equilibrium calculations were performed using Thermo-Calc. Precipitation of seven distinct phases (ferrite (α), FCC1, FCC2, $M_{23}C_6$, $M_6C$, $M_3P$, and MnS) was predicted at 283 °C with the current composition of the alloys. The corresponding volume fraction (%) of these phases for different alloys is shown in Table 6. Majorly ferrite and carbides cover the major volume fraction of these phases. The sulfides and phosphides are present in low-volume fractions. The composition of the FCC1 phase suggests that these are Cu (~98 %) precipitates, which could thermodynamically form in small amounts in these alloys – such a phase was not observed, as Cu is associated with Mn, Ni, Si, and P in the clusters. The FCC2 phase roughly contains 40 % Ni, 30 % Fe, 30 % Mn, and very slight amounts of Cu, Cr, Si, and Mo. No MNS-rich clusters/phase/precipitates were predicted in these calculations. Although the FCC2 phase does not have the same composition as that of the MNS-rich clusters (Table 4), if we consider the FCC2 phase to be MNS-rich clusters, then a significant difference between the predicted precipitation (Table 6) and observed clustering (Table 3) was observed. In fact, for Alloy A, no FCC2 is predicted, whereas solute clusters are observed. These observations suggest that the formation of MNS-rich clusters involves a radiation-induced mechanism, and not (only) a radiation-enhanced mechanism.

Table 6. The volume fraction (%) of different phases predicted using single-point equilibrium simulations for different alloys is shown in this table. The significant difference between the
predicted precipitation and observed clustering (Table 3) indicates that the formation of MNS-rich clusters is due to the radiation-induced mechanism.

<table><thead><tr><th>Alloy</th><th>α Fe</th><th>FCC1</th><th>FCC2</th><th>M<sub>23</sub>C<sub>6</sub></th><th>M<sub>6</sub>C</th><th>M<sub>3</sub>P</th><th>MnS</th></tr></thead><tbody><tr><td>A</td><td>97.46</td><td>0.077</td><td>-</td><td>2.06</td><td>0.31</td><td>0.067</td><td>0.027</td></tr><tr><td>B</td><td>96.68</td><td>0.078</td><td>0.076</td><td>2.07</td><td>0.30</td><td>0.069</td><td>0.027</td></tr><tr><td>C</td><td>95.67</td><td>0.063</td><td>1.62</td><td>2.305</td><td>0.24</td><td>0.07</td><td>0.027</td></tr><tr><td>F</td><td>94.87</td><td>0.058</td><td>2.43</td><td>2.29</td><td>0.26</td><td>0.067</td><td>0.027</td></tr><tr><td>G</td><td>93.64</td><td>0.039</td><td>3.868</td><td>2.07</td><td>0.30</td><td>0.061</td><td>0.027</td></tr><tr><td>H</td><td>93.60</td><td>0.041</td><td>3.717</td><td>2.29</td><td>0.25</td><td>0.068</td><td>0.027</td></tr></tbody></table>

The compositions (at %) of the FCC2 phase predicted by Thermo-Calc calculations in different alloys are shown in Table 7 and compared with APT measurements. In particular, the measured Fe content in clusters is largely higher than the predicted one. It is known that Fe atoms from the matrix can be detected within clusters due to various bias sources, such as the local magnification effect [21,53] – which leads to trajectory overlap [54] and is influenced by the spatial resolution of the instrument. Thus, a "corrected" composition, $X_i^{cor}$, is also reported in Table 7. It assumes that the Fe level measured into clusters by APT is overestimated, and should be the one predicted by Thermo-Calc. The corrected compositions are given by:

$$X_i^{cor} = X_i^{meas} \cdot \frac{1 - X_{Fe}^{cor}}{1 - X_{Fe}^{meas}}$$

where $i$ = Mn, Ni, Si, Cu or P, $X_{Fe}^{meas}$ and $X_{Fe}^{cor}$ are the levels of Fe into clusters measured by APT and predicted by Thermocalc (set to 30%), respectively.

Looking at chemical compositions, it becomes very clear that the predicted FCC2 phase does not match with the observed MNS-rich clusters. These significant differences in the predicted and the observed or corrected phase compositions either confirm that the formation of MNS-rich clusters is hardly explained by a simple radiation-enhanced mechanism or suggest that another phase not predicted through the TCFe8 database can precipitate.
<table><caption>Table 7. The table presents the composition (at %) for the MNS-rich clusters observed in the APT volumes and for the NiFeMn phase predicted in Thermo-Calc calculations. The table also showcases the corrected APT compositions.</caption><thead><tr><th>Alloy</th><th>Condition</th><th>Fe</th><th>Mn</th><th>Ni</th><th>Si</th><th>Cr</th><th>Mo</th><th>Cu</th><th>P</th><th>V</th><th>C</th></tr></thead><tbody><tr><td rowspan="3">A</td><td>Observed</td><td>86.93</td><td>1.97</td><td>2.77</td><td>2.52</td><td>3.12</td><td>0.05</td><td>1.22</td><td>0.70</td><td>0.09</td><td>0.63</td></tr><tr><td>Corrected</td><td>30</td><td>14.6</td><td>21.5</td><td>19.2</td><td>-</td><td>-</td><td>9.2</td><td>5.4</td><td>-</td><td>-</td></tr><tr><td>Predicted</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td rowspan="3">B</td><td>Observed</td><td>81.74</td><td>2.05</td><td>9.12</td><td>4.36</td><td>1.28</td><td>-</td><td>1.21</td><td>0.20</td><td>-</td><td>0.04</td></tr><tr><td>Corrected</td><td>30</td><td>8.5</td><td>37.6</td><td>18.2</td><td>-</td><td>-</td><td>5</td><td>0.8</td><td>-</td><td>-</td></tr><tr><td>Predicted</td><td>30.57</td><td>27.54</td><td>39.17</td><td>0.30</td><td>1.15</td><td>0.01</td><td>1.25</td><td>-</td><td>-</td><td>-</td></tr><tr><td rowspan="3">C</td><td>Observed</td><td>76.74</td><td>2.62</td><td>12.47</td><td>5.64</td><td>1.17</td><td>0.10</td><td>0.90</td><td>0.13</td><td>-</td><td>0.23</td></tr><tr><td>Corrected</td><td>30</td><td>10.3</td><td>49.6</td><td>18.0</td><td>-</td><td>-</td><td>3.5</td><td>0.5</td><td>-</td><td>-</td></tr><tr><td>Predicted</td><td>33.16</td><td>19.81</td><td>43.75</td><td>0.99</td><td>0.91</td><td>0.01</td><td>1.37</td><td>-</td><td>-</td><td>-</td></tr><tr><td rowspan="3">F</td><td>Observed</td><td>74.99</td><td>6.42</td><td>10.30</td><td>5.77</td><td>1.17</td><td>0.17</td><td>0.91</td><td>0.14</td><td>0.03</td><td>0.11</td></tr><tr><td>Corrected</td><td>30</td><td>19.2</td><td>30.9</td><td>17.02</td><td>-</td><td>-</td><td>2.7</td><td>0.4</td><td>-</td><td>-</td></tr><tr><td>Predicted</td><td>30.28</td><td>35.92</td><td>31.60</td><td>0.06</td><td>0.96</td><td>0.01</td><td>1.16</td><td>-</td><td>-</td><td>-</td></tr><tr><td rowspan="3">G</td><td>Observed</td><td>73.09</td><td>6.38</td><td>12.75</td><td>5.57</td><td>1.15</td><td>0.17</td><td>0.55</td><td>0.10</td><td>0.02</td><td>0.23</td></tr><tr><td>Corrected</td><td>30</td><td>19</td><td>31.9</td><td>16.8</td><td>-</td><td>-</td><td>1.6</td><td>0.3</td><td>-</td><td>-</td></tr><tr><td>Predicted</td><td>30.24</td><td>30.09</td><td>37.24</td><td>0.23</td><td>0.98</td><td>0.01</td><td>1.22</td><td>-</td><td>-</td><td>-</td></tr><tr><td rowspan="3">H</td><td>Observed</td><td>74.11</td><td>5.43</td><td>11.58</td><td>6.84</td><td>1.15</td><td>0.12</td><td>0.54</td><td>0.11</td><td>0.02</td><td>0.11</td></tr><tr><td>Corrected</td><td>30</td><td>16.3</td><td>34.9</td><td>19.5</td><td>-</td><td>-</td><td>1.6</td><td>0.3</td><td>-</td><td>-</td></tr><tr><td>Predicted</td><td>30.46</td><td>29.71</td><td>37.43</td><td>0.41</td><td>0.78</td><td>0.01</td><td>1.19</td><td>-</td><td>-</td><td>-</td></tr></tbody></table>

Previous studies [20,55] suggested that G-phase – composed of (Ni, Fe, Mo)55%, Si24%, (Mn, Cr)21% – or $\Gamma_2$-phase – consisting of Ni50%, Si16.7%, Mn33.3% – could precipitate in RPV steels when irradiated at about 300 °C or below. However, the chemical composition of solute clusters measured by APT significantly deviates from these expected phases. To facilitate a more meaningful comparison between experimental data and theoretical predictions, Fe atoms detected by APT can be excluded from the analysis, based on the strong assumption that their presence is an artefact of the technique. Therefore, using the corrected composition – based solely on Mn, Ni, and Si – the resulting cluster compositions are compared with those of the G and $\Gamma_2$ phases in Fig. 7. This comparison reveals a marked difference between the observed clusters and the $\Gamma_2$-phase. Whilst the cluster compositions are more similar to the G-phase, some deviations remain – particularly a deficiency in Mn and an excess of Ni in Alloys B and C.
<figure><img src="image_9.png" /><figcaption>Fig. 7. Comparison of the relative Mn, Ni, and Si contents measured in cluster cores of the six alloys with the compositions expected for the G-phase and Γ₂-phase.</figcaption></figure>

However, the assumption that all Fe detected in the clusters is an artefact of APT and that only Mn, Ni, and Si should be considered has several limitations. First, this approach completely overlooks the presence of Cu and P, which are also involved in cluster formation. Second, APT-related biases are likely to affect smaller clusters more significantly. If Fe detection were purely an artefact, its apparent concentration in cluster cores should decrease with increasing cluster size – which is not observed, as shown in Fig. 8 (a). Finally, if the Fe content were indeed fully artificial, the concentrations of Mn, Ni, and Si in the cluster cores should remain consistent across all cases (assuming they reflect the fixed G-phase composition with an amount of "artificial" Fe). However, as illustrated in Fig. 8 (b), these concentrations vary and appear to correlate with the bulk composition: the higher the Mn or Ni content in the matrix, the higher their corresponding concentrations in the clusters. These observations suggest that the Fe detected in cluster cores is unlikely to be solely an artefact of the APT technique.
<figure><img src="image_10.png" /><figcaption>Fig. 8. (a) Average level of Fe measured in cluster core as a function of average cluster radius for each alloy; (b) Measured concentrations of Mn, Ni, and Si in cluster core as a function of bulk Mn, Ni, and Si concentrations.</figcaption></figure>

To estimate the extent to which matrix atoms are introduced into cluster cores due to trajectory
overlap, a chemical composition correction model was developed by Hatzoglou *et al.* [56–58].
More recently, Jenkins *et al.* [59] combined field evaporation modelling with atomic position
blurring to account for both trajectory overlaps and spatial resolution effects. Their findings suggest
that the proportion of matrix atoms detected in cluster cores depends on cluster-reduced field
evaporation, cluster size, and instrument lateral resolution.
For a LEAP 5000 XR, the lateral resolution in RPV steel is estimated to be around 0.4 nm. Considering clusters with a 1 nm radius – which is smaller than the experimentally measured cluster radii in our alloys, thereby maximising the estimated APT bias – and assuming a reduced evaporation field between 0.80 to 0.95 (low-field clusters) as per Jenkins et al. [59], the maximum Fe content measured in a solute-only cluster core is expected to be below 40 %. In the current study, approximately 75 % Fe was measured in cluster cores. According to Jenkins et al. [59], such Fe content can be measured in 1 nm radius clusters with a low evaporation field (80–85 % of the matrix evaporation field) and an actual Fe content of about 50 %. This suggests that the majority of Fe detected in cluster cores is indeed part of the clusters, which is not compatible with enhanced precipitation of the G-phase.

A second possible mechanism for solute cluster formation is the radiation-induced segregation of solutes onto defect clusters, such as small vacancy and/or SIA clusters [60]. In that case, solute clusters can contain a lot of Fe, and solute enrichment into clusters should be dependent on the bulk composition. According to reference [61], these mobile defect clusters can be immobilised by the solute, which then acts as segregation sites due to the coupling of fluxes between solutes and point defects. Castin et al. [62] developed an Object Kinetic Monte Carlo model to quantify solute clustering due to these mechanisms in RPV steels. The cluster volume fraction predicted by this model as a function of irradiation conditions and steel compositions was implemented in the MILAGROS tool (Machine learning based prediction of descriptors of NiMnSiPCu-rich clusters in RPV/VVER materials under irradiation, by giving the chemical composition of the material and the irradiation conditions as inputs) developed by Castin et al. [61,62]. The volume fractions predicted by this tool in the case of Alloys A, B, C, F, G, and H are reported in Table 8. Even if the calculated volume fractions are a bit lower than the measured ones, the model reproduces
experimental observation relatively well, including clustering in Alloy A. This suggests that radiation-induced mechanisms actively contribute to solute clustering (and possibly precipitation at high doses) in these irradiation conditions.

<table><caption>Table 8. Comparison of the solute cluster fraction obtained from APT measurements, the volume fraction predicted by Thermo-Calc (enhanced precipitation), and the MILAGROS tool (radiation-induced segregation).</caption><thead><tr><th>Alloys</th><th>f<sub>a</sub> (%) APT</th><th>f<sub>v</sub> (%) Thermo-Calc</th><th>f<sub>v</sub> (%) MILAGROS</th></tr></thead><tbody><tr><td>A</td><td>0.24 ± 0.08</td><td>-</td><td>0.002</td></tr><tr><td>B</td><td>1.45 ± 0.28</td><td>0.076</td><td>0.48</td></tr><tr><td>C</td><td>2.49 ± 0.30</td><td>1.62</td><td>1.19</td></tr><tr><td>F</td><td>3.38 ± 0.22</td><td>2.43</td><td>1.29</td></tr><tr><td>G</td><td>4.29 ± 0.23</td><td>3.87</td><td>3.16</td></tr><tr><td>H</td><td>4.37 ± 0.22</td><td>3.72</td><td>3.67</td></tr></tbody></table>

## 4.2. Theoretical hardening vs experimental

The irradiation hardening observed in the material is dependent on several factors, such as the number density of carbides, solute clusters, dislocations, and the size of the clusters, both in non-irradiated and irradiated microstructures. To understand the hardening results (Fig. 6) well, the experimental hardening values were plotted against the theoretical hardening values in Fig. 9.

For theoretical calculations, the Dispersed Barrier Hardening model was used to calculate the critical resolved shear stress (CRSS) contribution of the solute clusters ($\tau_{sc}$). The model is given by the following relation: $\tau_{sc} = \alpha_{sc}\mu b\sqrt{ND}$; where $\alpha_{sc}$ is the obstacle strength, $\mu$ is the shear modulus of the material, $b$ is the Burgers vector, and $D$ is the cluster diameter. Here, the values for $\alpha_{sc}$, $\mu$, and $b$ were taken as 0.1, 83 GPa [63], and 0.248 nm, respectively. The hardening or the increase in the yield stress for RPV steels due to irradiation can be expressed by the relation: $\Delta\sigma = M(\sqrt{\tau_{forest}^2 + \tau_{carbide}^2 + \tau_{sc}^2} - \sqrt{\tau_{forest}^2 + \tau_{carbide}^2})$; where $\tau_{forest}$ is the CRSS contribution from
the dislocation forests and $\tau_{carbide}$ is the CRSS contribution from the carbides. M is Taylor's factor whose value is 3.05. Since the exact information about carbides and dislocation forests was not available for this work; therefore, the $\tau_{forest}$ and $\tau_{carbide}$ were adapted from the typical values of these components for RPV steels from reference [64]. The values are 62 MPa and 36 MPa, respectively.

It is clear from Fig. 9 that the theoretical hardening trend does not exactly match the experimental hardening trend. This is because the exact information on the number density of carbides and dislocations in the initial state, and/or another irradiation-induced feature, such as SIA clusters, is not known. It was understood in section 3.2 that Alloy A might have a lower number density of carbides compared to other alloys. A better correlation between mechanical properties and microstructure requires to use of data from complementary techniques providing information about other microstructural features. Such data were collected during the STRUMAT-LTO project, and the results are published in another paper [65].

<figure><img src="image_11.png" /><figcaption>Fig. 9. The comparison of experimental hardening values with the theoretical hardening values obtained for alloys used in this work.</figcaption></figure>
**5. Conclusions**

In this study, the microstructure of six RPV model steels with varying Mn, Ni, and Si levels was characterised using APT before and after high-dose neutron irradiation. In all cases, solute clusters enriched in Mn, Ni, and Si, along with smaller amounts of Cu and P, were observed. Notably, a significant presence of Fe was detected in the cluster cores. The influence of bulk Mn, Ni, and Si content on solute clustering can be summarised as follows:

- Cluster size increases with Ni content in low-Mn steels but remains unaffected by Ni in medium-Mn steels. Neither Mn nor Si has a discernible impact on cluster size.

- Cluster number density increases with Ni bulk content in both low- and medium-Mn steels. For a given Ni concentration, a higher Mn content leads to an increased cluster number density, with the Mn effect being more pronounced than that of Ni. A synergistic interaction between Mn and Ni is observed. Si, in contrast, has a minimal influence on cluster number density.

To further interpret these findings, experimental results were compared with predictions from Thermo-Calc and the MILAGROS tool. These comparisons strongly suggest that solute clustering cannot be solely explained by a radiation-enhanced precipitation mechanism; rather, flux coupling effects must be considered.

Finally, irradiation-induced hardening was assessed through Vickers microhardness measurements and correlated with microstructural observations. The calculated hardening trend aligns with experimental measurements, though some discrepancies persist. These deviations are likely due to the influence of additional microstructural features beyond the solute clusters identified by APT.

Addressing these factors will be the focus of a future study.
Acknowledgments

Experiments were performed on GENESIS platform instruments supported by the Région Haute-
Normandie, the Métropole Rouen Normandie, CNRS via LABEX EMC3, and the French National
Research Agency via “Investissements d’avenir” program (ANR-11-EQPX-0020). LEAP
experiments have been performed thanks to the GENESIS+ project. The European Union and
Région Normandie have contributed to the realisation of the GENESIS+ project. GENESIS+ is
cofunded via the European Regional Development Fund. This work was partially supported by the
CNRS Federation IRMA - FR 3095. The reported research was performed in the framework of the
Horizon 2020 project named STRUMAT-LTO. This project has received funding from the
EURATOM under grant agreement number 945272.
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