Fast-Neutron Radiolysis of Sub- and Supercritical Water at 300–600 °C and 25 MPa: A Monte Carlo Track Chemistry Simulation Study

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The integration of supercritical water (SCW) technology in proposed Generation IV nuclear reactors marks a significant advancement in the evolution of nuclear energy. To achieve optimal water chemistry control and enhance reactor efficiency, safety, and sustainability, it is critical to thoroughly understand the radiation chemistry and behavior of transient species within the reactor core. This knowledge is particularly vital for the development of SCW-cooled reactor (SCWR) designs, including their SCW-cooled small modular reactor (SCW-SMR) variants. These reactors are designed to operate at temperatures between 300 and 600 °C and at a nominal pressure of 25 MPa. Our study focuses on the radiolysis of de-aerated, pure water by 2 MeV monoenergetic neutrons, mirroring the fast-neutron flux in a typical reactor setting. We provide a detailed analysis of the time-dependent chemical yields (G values) for both radical (e⁻_aq, H^●, and ^●OH) and molecular (H₂ and H₂O₂) primary species that are either formed or destroyed from 1 picosecond (ps) to 1 millisecond (ms). Given the unique operating conditions of SCWRs/SMRs, our findings are expected to be highly relevant and valuable to those working in the SCWR and SCW-SMR field.

Abstract

(1) Background: Supercritical water-cooled reactors (SCWRs) and their smaller modular variants (SMRs) are part of the ‘Generation IV International Forum’ (GIF) on advanced nuclear energy systems. These reactors operate beyond the critical point of water (t_c = 373.95 °C and P_c = 22.06 MPa), which introduces specific technical challenges that need to be addressed. The primary concerns involve the effects of intense radiation fields—including fast neutrons, recoil protons/oxygen ions, and γ rays—on the chemistry of the coolant fluid and the integrity of construction materials. (2) Methods: This study employs Monte Carlo simulations of radiation track chemistry to investigate the yields of radiolytic species in SCWRs/SMRs exposed to 2 MeV neutrons. In our calculations, only the contributions from the first three recoil protons with initial energies of 1.264, 0.465, and 0.171 MeV were considered. Our analysis was conducted at both subcritical (300 and 350 °C) and supercritical temperatures (400–600 °C), maintaining a constant pressure of 25 MPa. (3) Results: Our simulations provide insights into the radiolytic formation of chemical species such as e⁻_aq, H^●, H₂, ^●OH, and H₂O₂ from ~1 ps to 1 ms. Compared to data from radiation with low linear energy transfer (LET), the G(e⁻_aq) and G(^●OH) values obtained for fast neutrons show a similar temporal dependence but with smaller amplitude—a result demonstrating the high LET nature of fast neutrons. A notable outcome of our simulations is the marked increase in G(^●OH) and G(H₂), coupled with a corresponding reduction in G(H^●), observed during the homogeneous chemical stage of radiolysis. This evolution is attributed to the oxidation of water by the H^● atom according to the reaction H^● + H₂O → ^●OH + H₂. This reaction acts as a significant source of H₂, potentially reducing the need to add extra hydrogen to the reactor’s coolant water to suppress the net radiolytic production of oxidizing species. Unlike in subcritical water, our simulations also indicate that G(H₂O₂) remains very low in low-density SCW throughout the interval from ~1 ps to 1 ms, suggesting that H₂O₂ is less likely to contribute to oxidative stress under these conditions. (4) Conclusions: The results of this study could significantly impact water-chemistry management in the proposed SCWRs and SCW-SMRs, which is crucial for assessing and mitigating the corrosion risks to reactor materials, especially for long-term operation.

1. Introduction

Together with hydropower, nuclear energy offers considerable potential to reduce greenhouse gas emissions and air pollutants during operation compared to coal or gas-powered plants. This positions it as an essential alternative to burning fossil fuels in the fight against climate change and its consequences. The importance of this perspective was highlighted at the IAEA International Conference on Climate Change and the Role of Nuclear Power, held in Vienna, Austria, from 7 to 11 October 2019 [1]. Beyond its environmental benefits, nuclear power presents a solution to the increasing energy needs spurred by worldwide population growth and economic development. This has sparked heightened interest in the advancement and implementation of novel nuclear technologies, including ‘small modular reactors’ (SMRs) [2,3,4]. In contrast to their traditional, larger counterparts, SMRs are characterized by their compact size, lower power output, and modular construction. Currently, more than 70 reactor designs are under development worldwide, with commercial deployment anticipated between 2030 and 2040. These designs often incorporate cooling systems from existing, conventional nuclear reactors, showcasing an innovative approach to nuclear energy generation.

Our study focuses on SMRs cooled by supercritical water (SCW), which operate under a pressure of 25 MPa and temperatures ranging from 300 to 600 °C from core inlet to outlet. These systems are scaled-down, lower-power, modular versions of the larger ‘supercritical water-cooled reactor’ (SCWR) concept, functioning under similar temperature and pressure conditions. The benefits of using SCW systems for power generation stem from the increased thermodynamic efficiency achieved through higher operating temperatures. These systems can attain efficiencies of over ~45%, compared to ~33% for currently operational light water reactors, resulting in significant capital cost savings. Significantly, the SCWR has been recognized by the ‘Generation IV International Forum’ (GIF) as one of six innovative nuclear energy designs selected for further research and development [4,5,6,7,8,9].

The long-term viability of SCWRs and their SCW-SMR variants critically hinges on precise water chemistry management. A key challenge for all SCWR designs is understanding how water radiolysis affects material performance. As the coolant circulates through the SCWR reactor core, the combined effects of neutron and γ-radiation fields induce the formation of various free radicals and molecular products. These include the hydrated electron (e⁻_aq), the hydrogen atom (H^●), molecular hydrogen (H₂), the hydroxyl radical (^●OH), hydrogen peroxide (H₂O₂) and its decomposition product O₂, the hydronium ion (H₃O⁺), the hydroxide ion (OH⁻), and the hydroperoxyl/superoxide anion radicals (HO₂^●/O₂^●−, depending on pH) [10,11,12,13]. Oxygen (O₂) is also produced as a secondary radiolytic product through the following reactions [13,14]:

^●OH + H₂O₂ → HO₂^● + H₂O, k₁ = 4.2 × 10⁸ M⁻¹ s⁻¹ at 300 °C

(1)

followed by

^●OH + HO₂^● → O₂ + H₂O

(2)

and

HO₂^● + HO₂^● → O₂ + H₂O₂.

(3)

Under the conditions proposed for SCWRs, the physical and chemical properties of water undergo dramatic changes as it transitions from subcritical to supercritical states (see, e.g., [15]). The chemical species formed through radiolysis can aggressively interact with metal alloys in this highly reactive environment, potentially accelerating corrosion processes. This corrosion can significantly impact in-core materials, particularly fuel cladding, leading to fuel failures and the dispersal of fuel fragments and fission products into the coolant. Moreover, these chemical species can also affect the transport of radioactive materials from the core to downstream piping components, thereby enhancing out-of-core radiation fields and increasing exposure risks for reactor maintenance personnel [7].

Another key aspect of controlling SCWR water chemistry requires the ability to mitigate the effects of water radiolysis. It should be noted that the common practice of adding excess molecular hydrogen, hydrazine (N₂H₄), or ammonia (NH₃) in concentrations sufficient to suppress net radiolysis (see, e.g., [16,17,18]) may not be effective in an SCWR [7].

The extreme conditions of high temperature and pressure, combined with the intense flux of ionizing radiations, render the experimental characterization of water radiolysis under expected SCWR/SCW-SMR operating conditions exceedingly challenging, if not unfeasible. As a result, computer simulations become crucial for investigating the radiation chemistry of the SCWR coolant. While experiments and simulations have examined the radiolytic yields (G values) of water decomposition products at temperatures up to 350 °C [13], most studies on radiolysis in SCW, ranging from 380 to 700 °C, have primarily relied on modeling (e.g., see [19] and the references therein). Recent experimental research investigating temperatures beyond the critical point of water (t_c = 373.95 °C and P_c = 22.06 MPa), with findings extending up to 500 °C, has been comprehensively reviewed by Lin and Katsumura [20].

In this work, we present Monte Carlo track chemistry simulations of the time-dependent G values for the primary species (e⁻_aq, H^●, H₂, ^●OH, and H₂O₂) resulting from the radiolysis of neutral, de-aerated water by monoenergetic 2 MeV neutrons. These simulations cover the temperature range from 300 to 600 °C at a pressure of 25 MPa. We selected 2 MeV neutrons because the in-reactor fission-neutron flux spectrum peaks around this energy [13,21,22]. Calculations spanned from 1 picosecond (ps) to 1 millisecond (ms). Concerning densities at 25 MPa for the studied temperatures, below the critical point of water, they are 0.743 g/cm³ at 300 °C and 0.625 g/cm³ near the reactor core inlet (350 °C). For SCW, densities are 0.167 g/cm³ at 400 °C, 0.090 g/cm³ at 500 °C, and 0.071 g/cm³ at the reactor core outlet (600 °C) [23]. All available data on the physicochemical properties of SCW (such as dielectric constant, K_w, viscosity, etc.) up to 600 °C have been incorporated into the calculations.

2. Fast-Neutron Irradiation of Water

The interactions of neutrons are highly dependent on their kinetic energy (see, e.g., [22,24,25]). For ‘fast’ neutrons, with kinetic energies ranging from ~0.5 to 10 MeV, slowing down primarily occurs through multiple successive ‘billiard-ball’ elastic collisions with atomic nuclei, following the laws of energy and momentum conservation from classical particle physics. During these interactions, a portion of the neutron’s kinetic energy is transferred to the nucleus. In fast-neutron radiolysis of water, neutrons are predominantly moderated through interactions with both hydrogen (proton) and oxygen nuclei, creating a spectrum of recoil-ion energies ranging from zero up to the energy of the incident neutrons. These proton and oxygen ion recoils are widely spaced along the neutron path. Their maximum ranges, or track lengths, are considerably shorter than the average distance between two successive neutron interactions. For instance, the mean free path of a 2 MeV incident neutron in water at 25 °C is about 4 cm, whereas the maximum ranges for recoil protons and oxygen ions at this energy are ~75.5 and 1.5 μm, respectively [25,26]. Consequently, they can be considered to behave independently of each other. Under normal irradiation conditions (i.e., in the absence of dose-rate effects), their energy is deposited locally within isolated, dense tracks near the neutron collision sites—the points where the recoils are generated—with no overlapping reaction zones from neighboring tracks. As a result, the water radiolysis chemistry observed should be similar to that induced by independent, high ‘linear energy transfer’ (LET) protons and oxygen ions. This understanding of the track structure underpins the approach used in this work to calculate the radiolysis yields for fast neutrons by simply summing the individual G values for each of these recoil ions, weighted by their fraction of total neutron energy deposited [13,25,27,28].

In the neutron energy range of interest, oxygen ion recoils play a minor role in the fast-neutron radiolysis of water due to their relatively low average energies. Studies have demonstrated that in light water, proton recoils absorb ~93% of the neutron energy, with the remaining energy absorbed by oxygen ions [21,29]. When calculating radiation chemical yields due to 2 MeV neutrons, we consider only the contributions from the first three recoil protons (i.e., from the first three neutron collisions). After three collisions, subsequent recoil protons have only a negligible impact on radiolysis due to their minimal contribution to the dose (see, e.g., [27,30]). The ‘average’ energy loss—important to note, as average values are relevant when dealing with a beam comprising many neutrons—after n collisions can be determined using the following equation [24,25,27]:

$$\overline{\ln \left({\displaystyle \frac{E_0}{E_n}}\right)}\hspace{0.17em}\hspace{0.17em}=\hspace{0.17em}\hspace{0.17em}n\hspace{0.17em}\xi$$

(4)

where

$$\xi \hspace{0.17em}\hspace{0.17em}=\hspace{0.17em}\hspace{0.17em}1\hspace{0.17em}\hspace{0.17em}+\hspace{0.17em}\hspace{0.17em}{\displaystyle \frac{{\left(A\hspace{0.17em}\hspace{0.17em}-\hspace{0.17em}\hspace{0.17em}1\right)}^2}{2\hspace{0.17em}A}}\hspace{0.17em}\ln \left({\displaystyle \frac{A\hspace{0.17em}-\hspace{0.17em}1}{A\hspace{0.17em}+\hspace{0.17em}1}}\right)$$

(5)

Here, A refers to the atomic number of the recoil ion. For collisions involving protons, where A = 1, Equation (5) is not explicitly defined. However, the limit as A approaches unity is applicable, and in this case, ξ = 1. Consequently, the average kinetic energy of the neutron after n individual elastic scattering collisions can be expressed as

$$E_n\hspace{0.17em}=\hspace{0.17em}{E}_0\hspace{0.17em}{e}^{-n}$$

(6)

where $E_0$ = 2 MeV is the initial kinetic energy of the neutron. Based on this formulation, we can deduce the following initial energies for the three considered protons: $E_{p_1}$ = ($E_0$–$E_1$) = 1.264 MeV, $E_{p_2}$ = 0.465 MeV, and $E_{p_3}$ = 0.171 MeV. The neutron (proton recoil) yields were then calculated using the following equation:

$$G(\mathrm{X})\hspace{0.17em}\hspace{0.17em}=\hspace{0.17em}\hspace{0.17em}{\displaystyle \frac{{\displaystyle \sum _{\mathrm{i}=1}^{3}G{\left(\mathrm{X}\right)}_{p_{\mathrm{i}}}\hspace{0.17em}{E}_{p_{\mathrm{i}}}}}{E_{\mathrm{T}}}}$$

(7)

where $G{\left(\mathrm{X}\right)}_{p_{\mathrm{i}}}$ is the yield of species X associated with the recoil proton p_i (i = 1 to 3), and

$$E_{\mathrm{T}}\hspace{0.17em}=\hspace{0.17em}{\displaystyle \sum _{\mathrm{i}=1}^3{E}_{p_{\mathrm{i}}}}$$

(8)

is the sum of all recoil proton energies.

3. Monte Carlo Track Chemistry Simulations

The radiolysis of both subcritical (300 and 350 °C) and supercritical (400–600 °C) water at a pressure of 25 MPa was simulated using the latest version of our Monte Carlo track chemistry code, IONLYS-IRT [31], detailed elsewhere [19,32,33]. Briefly, the IONLYS step-by-step program models the initial physical and physicochemical stages of radiation up to ~1 ps in a 3D environment. It provides a complex, highly non-homogeneous spatial distribution of reactants at the end of the physicochemical stage, including e⁻_aq, H^●, H₂, ^●OH, H₂O₂, H₃O⁺, OH⁻, HO₂^●/O₂^●−, ^●O^●(³P), O^●−, and others. The results serve as the initial conditions for the subsequent chemical stage, where the various radiolytic species randomly diffuse and react until all track processes are complete. This stage is handled by our IRT program, utilizing the ‘independent reaction times’ (IRT) method [34,35,36]. This computationally efficient stochastic simulation technique applies the independent pairs approximation to simulate reaction times without following the trajectories of diffusing species. The implementation of this method has been described previously [37], and its accuracy in providing time-dependent chemical yields across a wide range of irradiation conditions has been validated through comparisons with full random flights (or step-by-step) Monte Carlo simulations that precisely follow reactant trajectories (for a review, see [31]).

The reaction scheme, rate constants, and diffusion coefficients for reactive species in our IRT program for pure liquid water at 300 and 350 °C follow those used in previous studies [19,25,33,38]. Beyond the critical point, we applied the SCW radiolysis database from Liu et al. [39,40], specifically using their reported reaction rate constants for the three temperatures selected for this study: 400, 500, and 600 °C at 25 MPa. Consistent with prior assumptions, we assumed that the diffusion coefficients for all species scaled proportionally with the self-diffusion of compressed SCW at these temperatures, as documented by Lamb et al. [41] and Yoshida et al. [42]. Furthermore, the static dielectric constants and the ionic products of SCW (K_w) were obtained from Lemmon et al. [23] and Bandura and Lvov [43], respectively. As discussed previously (see, e.g., [32]), in our calculations we also assumed that the thermalization distance of subexcitation-energy electrons (e⁻_sub)—those with kinetic energies below ~7.3 eV, the first-electronic excitation threshold of condensed water—and the prompt geminate electron–cation (H₂O^●+) recombination occurring prior to thermalization of the e⁻_sub are influenced solely by changes in water density at all selected temperatures above 400 °C.

From a microscopic perspective, we opted to overlook the heterogeneous structural nature of SCW [44], which arises from the existence of large local density fluctuations (or water ‘clustering’) associated with criticality. In our simulations, we treated the overall instantaneous representation of SCW as a uniform medium, characterized by a mean density equal to the bulk water density (ρ).

Finally, we accounted for the fact that the three considered recoil protons completely stopped in the water due to their limited ranges. Using the SRIM software (version SRIM-2013, see Ziegler et al. [45]), we calculated their trajectories and energies as functions of penetration depth in SCW. Figure 1 schematically illustrates the total penetration lengths into SCW at 400 °C and 25 MPa (ρ = 0.167 g/cm³) for these protons. The chemistry observed under these conditions represents an average over the proton energies, from their initial energies $E_{p_{\mathrm{i}}}$(i = 1 to 3) down to zero.

To avoid complexities arising from variations in the moving protons’ energies, we used a simplifying approximation, saying that the energies of the three considered recoil protons remained constant as they traversed the water medium. The constant track average energy values, ${\overline{E}}_{p_{\mathrm{i}}}$, were determined using the SRIM software [45] and our own Monte Carlo track structure simulations, as previously detailed [46]. At 25 MPa, these energies were ~0.722, 0.230, and 0.080 MeV at 300 °C; 0.715, 0.233, and 0.086 MeV at 350 °C; 0.731, 0.242, and 0.086 MeV at 400 °C; 0.746, 0.249, and 0.086 MeV at 500 °C; and 0.756, 0.257, and 0.083 MeV at 600 °C. The corresponding LETs for these protons, as determined by our Monte Carlo code, are ~24.0, 46.1, and 57.5 keV/μm at 300 °C; 20.2, 38.9, and 48.7 keV/μm at 350 °C; 5.32, 10.1, and 12.9 keV/μm at 400 °C; 2.88, 5.39, and 6.98 keV/μm at 500 °C; and 2.17, 4.14, and 5.50 keV/μm at 600 °C, respectively.

To reproduce the effects of 2 MeV neutrons, we simulated short track segments (typically ~15–150 μm) for each of the first three generated recoil protons. Within these segments, the energy and LET of the protons remained well-defined and nearly constant. Consequently, our model calculations provided ‘track segment’ yields for a well-defined LET over time. We chose the number of individual proton histories (usually ~10–100, based on proton energy) to minimize statistical fluctuations in the chemical yield averages while still meeting acceptable computational time limits. We then calculated the neutron yields of the various radiolytic species by summing the corresponding weighted G values for each recoil proton, according to Equations (7) and (8).

It is important to note that radiation chemical yields are traditionally quantified as G values, where G(X) represents the total number of species X formed or destroyed per 100 eV of absorbed energy. In this paper, G values are expressed in units of molecules per 100 eV. For conversion to SI units, 1 molecule/100 eV ≈ 0.10364 µmol/J [10].

4. Results and Discussion

Figure 2a–e and Figure 3a–e display the time evolutions of G(e⁻_aq), G(H^●), G(H₂), G(^●OH), and G(H₂O₂) as derived from our simulations of the radiolysis of pure, de-aerated water by 2 MeV neutrons. The results cover the period from ~1 ps to 1 ms at temperatures of 300, 350, 400, 500, and 600 °C, respectively, all at 25 MPa. For comparison, Figure 3 also includes experimental data obtained from various authors [13,30,47,48,49]. Despite the relative scarcity of G values for fast neutron radiolysis, especially beyond the critical point in the SCW regime, there is generally good agreement between our computed yield values and the existing measurements. This agreement between experimental data and modeling a posteriori supports the validity of the assumptions used in our calculations, thereby affirming the reliability of our Monte Carlo code.

Currently, the only available measured value at very high temperatures and pressures for comparison with our results is that of Edwards [49] at 400 °C and 24.8 MPa (ρ = 0.163 g/cm³), which is G(e⁻_aq) ~ 0.59 ± 0.19 molecule/100 eV. Unfortunately, the exact timing of this measurement remains uncertain. According to prior studies [50,51], it could have been conducted on a timescale of a few microseconds, which aligns well with our calculations (see Figure 3a).

As illustrated in Figure 3, our simulations operate under the assumption that the initial yields of radiolytic species, which form within the first picosecond, are not dependent on temperature [53]. Therefore, any observed variations in these species’ yields across different temperatures stem solely from the chemical reactions that govern their formation and decay during track expansion by diffusion. It is crucial to recognize, however, that temperature significantly impacts the initial spatial distribution of these species within the tracks, which in turn influences their reaction kinetics [38].

Compared to low-LET radiation data from ⁶⁰Co γ rays, fast electrons, or ~300-MeV protons (see [19] and references therein), our computed G(e⁻_aq) and G(^●OH) values for fast neutrons show a similar temperature dependence across the studied range but with reduced amplitude. This pattern underscores the high-LET nature of fast neutrons. Indeed, with higher LET radiation, there is an increased occurrence of radical–radical reactions due to the greater local concentration of radicals along the radiation tracks. Many of these reactions occur before the radicals can diffuse into the bulk solution, resulting in fewer radicals escaping through combination or recombination reactions during track expansion [10,31,54,55].

A notable outcome of our simulations is the marked increase in G(^●OH) and G(H₂), coupled with a corresponding decrease in G(H^●), observed at times greater than ~0.1 μs. As discussed earlier, this significant change is attributed to the oxidation of water by the H^● atom during the homogeneous chemical stage of radiolysis, as described by the following reaction [56,57,58,59]:

H^● + H₂O → ^●OH + H₂, k = (3.2 ± 0.4) × 10⁴ M⁻¹ s⁻¹ at 300 °C

(9)

This reaction is normally insignificant at room temperature; however, it rapidly accelerates at higher temperatures, as demonstrated by its increasing rate constants: 7.7 × 10⁴ M⁻¹ s⁻¹ at 400 °C, 3.7 × 10⁵ M⁻¹ s⁻¹ at 500 °C, and 1.3 × 10⁶ M⁻¹ s⁻¹ at 600 °C, under a pressure of 25 MPa [39]. As illustrated in Figure 2 and Figure 3, the reaction notably boosts the production of ^●OH and H₂ at temperatures exceeding 300 °C. Specifically, there is an increase of ~6 G-units in the radiolytic formation of ^●OH radicals and molecular hydrogen in SCW between 400 and 600 °C.

To enhance the presentation of these findings, Figure 4a–e displays the time-dependent cumulative yield variations, ΔG(H₂), for each reaction involved in the formation and decay of H₂, as determined through our simulations. Notably, this figure underscores the pivotal role of reaction (9); its significance becomes increasingly pronounced at higher temperatures, especially in SCW, emphasizing its critical influence under these conditions.

There are primarily two reasons why reaction (9) is crucial for the control and management of water chemistry in proposed SCWRs and their SCW-SMR variants. First, the radiolytic generation of oxidizing species, such as ^●OH radicals, can trigger oxidative stress, potentially leading to the corrosion of materials under supercritical conditions. This affects critical components like fuel cladding, reactor vessels, and other structural elements, vital for maintaining integrity under the high-temperature and high-pressure operating conditions characteristic of these reactors [7,60,61,62]. Second, in conventional pressurized water reactors, adding excess H₂ to the coolant water is a common strategy to suppress net water radiolysis and inhibit the formation of oxidizing radiolytic products (see, e.g., [16,17,18,22,63,64,65]). While it remains uncertain whether this procedure would be equally effective under SCWR conditions [7,62,66,67], the radiolytic formation of H₂ via reaction (9) could impact the minimum concentration of excess H₂, referred to as the ‘critical hydrogen concentration’, required to prevent the formation of oxidative products from water radiolysis.

A few words should be added about our calculated temporal dependence of G(H₂O₂). As is well established, the primary mechanism for H₂O₂ formation during the track stage of radiolysis is the combination of two ^●OH radicals [10,13]:

^●OH + ^●OH → H₂O₂, k₁₀ = 9.87 × 10⁹ M⁻¹ s⁻¹ at 300 °C.

(10)

At 300 and 350 °C, within the subcritical water regime, our simulations predict a continuous increase in G(H₂O₂), from an initial value of ~0.17 molecule/100 eV to ~0.9 molecules/100 eV at 1 ms (see Figure 3e). This temporal evolution resembles that found in previous studies using low-LET irradiation [19], but with higher H₂O₂ yields, consistent with the high-LET characteristics of fast neutrons. Higher molecular yields are expected due to increased radical–radical reactions at elevated LETs. The slight decrease in G(H₂O₂) when moving from 300 to 350 °C is explained by the faster diffusion of ^●OH radicals out of the tracks compared to their self-combination within the tracks, resulting in lower H₂O₂ yields [30,68]. Unlike in subcritical water, the efficiency of reaction (10) in low-density SCW irradiated at temperatures ranging from 400 to 600 °C with a pressure fixed at 25 MPa is relatively low. The rate constant for this reaction increases only slightly with temperature, from 1.4 × 10⁹ M⁻¹ s⁻¹ at 400 °C to 1.5 × 10⁹ M⁻¹ s⁻¹ at 500 °C, and to 1.9 × 10⁹ M⁻¹ s⁻¹ at 600 °C [39]. This rate shows significantly less temperature dependence than the diffusion rate of the ^●OH radicals out of the tracks, leading to the expectation of minimal G(H₂O₂) values above the critical point. This outcome, predicted earlier by Liu et al. [40] based on cage effect considerations, is confirmed by our Monte Carlo simulations, showing that G(H₂O₂) remains very low in low-density SCW (~0.04 molecule/100 eV or less) throughout the interval from ~1 ps to 1 ms, making it difficult to detect. Moreover, independent of H₂O₂’s thermal instability at high temperatures [20], our results suggest that H₂O₂ is less likely to contribute to oxidative stress under these conditions.

5. Conclusions

In this study, Monte Carlo track chemistry simulations were used to calculate the G values for the primary radiolytic species in pure, de-aerated water irradiated by monoenergetic 2-MeV neutrons at temperatures ranging from 300 to 600 °C, maintaining a constant pressure of 25 MPa. These conditions reflect those anticipated in proposed SCWRs and their smaller modular variants. The fast neutron yields were derived by primarily considering the first three elastically scattered recoil protons generated by the incident neutron, with initial energies of 1.264, 0.465, and 0.171 MeV, while effects from oxygen ion recoils were omitted.

Our simulations shed light on the radiolytic formation of chemical species such as e⁻_aq, H^●, H₂, ^●OH, and H₂O₂ over a time-frame from ~1 ps to 1 ms. A comparison with low-LET radiation data underscored the high-LET nature of fast neutrons. A significant finding from our study was the pronounced increase in G(^●OH) and G(H₂), alongside a notable decrease in G(H^●), during the homogeneous chemical stage of radiolysis. This change is attributed to the oxidation of water by H^● atoms, following the reaction H^● + H₂O → ^●OH + H₂. This reaction serves as a substantial source of H₂, potentially reducing the necessity to add excess hydrogen to the reactor’s coolant to mitigate the net radiolytic production of oxidizing species. Our simulations also indicated that unlike in subcritical water, G(H₂O₂) remains very low in low-density SCW, implying that H₂O₂ is less likely to contribute significantly to oxidative stress under these conditions.

The findings of this study could greatly influence water-chemistry management in proposed SCWRs and SCW-SMRs, which is vital for evaluating and mitigating corrosion risks to reactor materials, especially over long-term operation. Further experimental data are needed to more accurately characterize the temperature dependence of radiolytic yields, to validate our modeling calculations more comprehensively, and to clarify the potential role of the reaction of H^● atoms with water at high temperatures.