Radiolysis of Sub- and Supercritical Water Induced by ¹⁰B(n,α)⁷Li Recoil Nuclei at 300–500 °C and 25 MPa

Abstract

(1) Background: Generation IV supercritical water-cooled reactors (SCWRs), including small modular reactor (SCW-SMR) variants, are pivotal in nuclear technology. Operating at 300–500 °C and 25 MPa, these reactors require detailed understanding of radiation chemistry and transient species to optimize water chemistry, reduce corrosion, and enhance safety. Boron, widely used as a neutron absorber, plays a significant role in reactor performance and safety. This study focuses on the yields of radiolytic species in subcritical and supercritical water exposed to ⁴He and ⁷Li recoil ions from the ¹⁰B(n,α)⁷Li fission reaction in SCWR/SCW-SMR environments. (2) Methods: We use Monte Carlo track chemistry simulations to calculate yields (G values) of primary radicals (e⁻_aq, H^•, and ^•OH) and molecular species (H₂ and H₂O₂) from water radiolysis by α-particles and Li³⁺ recoils across 1 picosecond to 0.1 millisecond timescales. (3) Results: Simulations show substantially lower radical yields, notably e⁻_aq and ^•OH, alongside higher molecular product yields compared to low linear energy transfer (LET) radiation, underscoring the high-LET nature of ¹⁰B(n,α)⁷Li recoil nuclei. Key changes include elevated G(^•OH) and G(H₂), and a decrease in G(H^•), primarily driven during the homogeneous chemical stage of radiolysis by the reaction H^• + H₂O → ^•OH + H₂. This reaction significantly contributes to H₂ production, potentially reducing the need for added hydrogen in coolant water to mitigate oxidizing species. In supercritical conditions, low G(H₂O₂) suggests that H₂O₂ is unlikely to be a major contributor to material oxidation. (4) Conclusions: The ¹⁰B(n,α)⁷Li reaction’s yield estimates could significantly impact coolant chemistry strategies in SCWRs and SCW-SMRs. Understanding radiolytic behavior in these conditions aids in refining reactor models and coolant chemistry to minimize corrosion and radiolytic damage. Future experiments are needed to validate these predictions.

1. Introduction

Nuclear energy produces electricity with significantly lower carbon emissions compared to coal or gas power plants, making it a key component of sustainable, environmentally friendly energy solutions. The advent of Generation IV (Gen IV) nuclear reactors marks a major advancement in nuclear technology, aiming to meet the global need for cleaner, more efficient energy. These reactors, developed through the Generation IV International Forum (GIF) collaboration [1,2], focus on enhancing sustainability, safety, and economic viability.

Among the six innovative system designs proposed by GIF, the supercritical water-cooled reactor (SCWR) stands out as especially promising [2]. SCWRs are designed to operate at a pressure of 25 MPa and temperatures ranging from ~350 °C to as high as 625 °C, from core inlet to outlet [3], exceeding the critical point of water (t_c = 373.95 °C, P_c = 22.06 MPa) [4]. SCWRs offer substantial advantages over current advanced water-cooled Gen III/III+ reactors, which typically operate between ~250 and 330 °C. These benefits include higher thermodynamic efficiency (exceeding 45% compared to 28–32% in existing designs), reduced operational costs, a more compact and simplified plant design, improved safety features, and the ability to co-generate hydrogen (H₂) [2,3,5,6,7].

Currently, substantial research and development efforts are directed towards small modular reactors (SMRs), including compact, lower-power, and modular variants of the larger SCWR concept, which operate under comparable temperature and pressure conditions [2,8,9,10,11]. These SMR variants of full-scale SCWRs are particularly well-suited for deployment in developing countries and remote or isolated communities, where large-scale infrastructure may be limited and energy demand is lower. Their modularity allows for flexible scaling, factory fabrication, and easier transportation and installation, making them an attractive solution for decentralized, clean energy generation.

The long-term effectiveness of SCWRs and their SCW-SMR variants depends critically on precise water chemistry management. Understanding the impacts of intense radiation fields on SCW is vital, as the SCW coolant is constantly exposed to radiation in the reactor core. This exposure results in the formation of oxidative radiolytic species, including the hydroxyl radical (^•OH), hydrogen peroxide (H₂O₂), oxygen (O₂) as a decomposition product of H₂O₂, and the hydroperoxyl/superoxide anion radicals (HO₂^•/O₂^•−, the balance between HO₂^• and O₂^•− varying with pH) [12,13,14,15]. It should be noted that oxygen is also generated as a secondary radiolytic product via the reactions below, with their respective rate constants at 400 °C and 25 MPa [16,17]:

^•OH + H₂O₂ → HO₂^• + H₂O, k = 1.8 × 10⁷ M⁻¹ s⁻¹

(1)

followed by

^•OH + HO₂^• → O₂ + H₂O, k = 2.1 × 10⁹ M⁻¹ s⁻¹

(2)

and

HO₂^• + HO₂^• → O₂ + H₂O₂, k = 5.9 × 10⁶ M⁻¹ s⁻¹.

(3)

These highly reactive species can increase the corrosion rates of most metal alloys, significantly compromising the reactor core’s structural integrity and posing long-term risks [18,19,20]. Assessing the primary (or “escape”) yield (or G value, defined as the number of species formed or consumed per 100 eV of absorbed radiation energy) [3,15,21] of these radiolytic species as a function of temperature, density, and time during sub- and supercritical water radiolysis is crucial for devising effective corrosion control strategies. However, directly measuring these yields under the extreme in-core reactor conditions of high temperature, high pressure, and mixed radiation fields, is highly challenging, if not impractical. Consequently, experimental data on SCW radiolysis remain limited (e.g., see [21] and the references therein), making theoretical modeling and computer simulations the most viable approach for investigating the radiation chemistry of SCWR and SCW-SMR coolants [3,17,22,23,24].

Building on our previous work using Monte Carlo simulations of radiation track chemistry to quantify the yields of primary radical species—namely, the hydrated electron (e⁻_aq), hydrogen atom (H^•), and ^•OH radical—as well as molecular products such as molecular hydrogen (H₂) and H₂O₂ generated in SCWRs/SCW-SMRs under 2 MeV neutron irradiation, we now extend our investigation to the radiolysis of sub- and supercritical water induced by the ¹⁰B(n,α)⁷Li fission reaction.

Boron-10, a stable isotope of boron with a natural abundance of ~20%, possesses a high thermal neutron absorption capacity, with a neutron-capture cross-section of 3837 barns (1 barn = 10⁻²⁸ m²) [25,26]. Boron enriched in ¹⁰B and its chemical compounds—such as boric acid (H₃BO₃), boron carbide (B₄C), and various rare-earth or refractory metal borides—are extensively used in the nuclear industry for applications including neutron detection, shielding (for personnel and instruments), neutron poisoning, control rods, and nuclear material storage. For instance, H₃BO₃ is routinely added to the primary coolant of pressurized water reactors (PWRs) as a water-soluble neutron poison, or “chemical shim”, to regulate neutron flux and control core reactivity [27,28,29]. One referee also noted that, in the case of SCWRs, due to solubility issues near the critical point and phase changes in the turbines, it is more probable that boron will be used in control rods rather than being directly added to the coolant.

When a slow neutron is absorbed, it triggers a fission reaction that releases two energetic, primarily high-LET ions: a ⁴He²⁺ ion (α-particle) with a kinetic energy of 1.47 MeV and, in 94% of cases, a ⁷Li³⁺ nucleus in its first excited state with 0.84 MeV of kinetic energy. This excited lithium nucleus decays to its ground state with a half-life of ~10⁻¹³ s, emitting a 0.478 MeV γ-ray during this process [25]. The path length of these ions is approximately 5–10 μm in water [30,31]; they move relatively slowly and produce closely spaced ionizing events, forming tracks of sharply defined columns. Figure 1 illustrates the ¹⁰B(n,α)⁷Li neutron capture reaction.

The ⁴He and ⁷Li nuclei produced by the ¹⁰B(n,α)⁷Li fission reaction serve as sources of high-LET radiation in the primary coolant, significantly impacting the radiation chemistry of the reactor’s cooling water. This influences the formation of radiolytic species, which play a crucial role in corrosion, material degradation, and overall reactor performance. Consequently, a detailed understanding of these localized, high-LET radiation effects is essential for accurately modeling radiolytic species production and evaluating its implications on reactor longevity and safety.

In this study, we conduct Monte Carlo track chemistry simulations to determine time-dependent G values for primary radiolytic species (e⁻_aq, H^•, H₂, ^•OH, and H₂O₂) produced by the radiolysis of pure, deaerated water, initiated by the recoil ⁴He and ⁷Li heavy ions emitted in the ¹⁰B(n,α)⁷Li capture reaction. Aligned with the expected operating conditions of SCW-SMRs, these simulations span temperatures from 300 to 500 °C at a pressure of 25 MPa and cover timescales from 1 picosecond (ps) to 0.1 millisecond (ms). At 25 MPa, below water’s critical point, density decreases with increasing temperature while remaining in the liquid-like range—declining from 0.743 g/cm³ at 300 °C to 0.625 g/cm³ near the reactor core inlet (350 °C). Beyond the critical point, in the supercritical region, water experiences a steep drop in density, reaching low, gas-like values of 0.167 g/cm³ at 400 °C and 0.090 g/cm³ at the assumed reactor core outlet temperature of 500 °C [32]. Let us also note that the calculations incorporate all available physicochemical property data for SCW up to 500 °C, including temperature-dependent values of the dielectric constant, ionization constant (K_w), and viscosity. These properties are critical for accurately modeling the radiolytic behavior of water under supercritical conditions.

A primary aim of this study is to investigate the impact of water oxidation by H^• atoms [33,34], as in the following reaction:

H^• + H₂O → H₂ + ^•OH.

(4)

This reaction, though negligible at room temperature, rapidly accelerates at elevated temperatures [15,22,35,36]. It is pivotal in the nuclear industry for managing water chemistry and preserving the structural integrity of reactor materials. It primarily causes corrosion of in-core components through the formation of reactive oxidizing species like ^•OH and H₂O₂, along with its decomposition product, O₂. Under the conditions anticipated for SCWRs/SCW-SMRs, this corrosion could result in material degradation and the transport of radioactive corrosion products from the core to downstream piping components, thereby increasing exposure risks for reactor maintenance personnel throughout the plant (see, e.g., [3]).

2. Monte Carlo Track Chemistry Simulations

To model and simulate the radiolysis of subcritical (300 and 350 °C) and supercritical (400 and 500 °C) water at a pressure of 25 MPa using 1.47 MeV α-particles (⁴He²⁺) and 0.845 MeV lithium ions (⁷Li³⁺), we employed the latest version of our Monte Carlo track chemistry simulation code, IONLYS-IRT. Additionally, we utilized the SRIM (“Stopping and Range of Ions in Matter”) simulation program, widely recognized for its precise calculations of ion stopping powers and penetration ranges in diverse materials. This section will specifically address the updates made to the IONLYS-IRT program for this study. For a more comprehensive discussion of the simulation code and its underlying principles, we refer the reader to our previous publications [23,24,29,37,38], where these aspects are thoroughly addressed.

Briefly, the IONLYS program [39] simulates the initial physical and physicochemical stages of radiation up to ~1 ps in 3D, producing a highly non-homogeneous distribution of radiolytic species. Major products include e⁻_aq, H^•, H₂, ^•OH, H₂O₂, H₃O⁺, and OH⁻, among others, with e⁻_aq, ^•OH, and H₃O⁺ being most abundant. These outputs serve as initial conditions for the chemical stage, during which species undergo stochastic diffusion and reactions until all track processes are complete, as modeled by our IRT program [40] using the “independent reaction times” (IRT) method [41,42,43]. This efficient stochastic method applies the independent pairs approximation to simulate reaction times without tracking diffusing species trajectories. Its implementation and accuracy—validated against full step-by-step Monte Carlo simulations—are detailed in prior studies (see [44] for a review).

In our IRT program for pure liquid water at 300 and 350 °C, we employed a reaction scheme, rate constants, and diffusion coefficients that align with those reported in previous studies [15,23,37,45]. Above the critical point, we adopted the SCW radiolysis database from Liu et al. [17,22], specifically selecting their reaction rate constants for 400 and 500 °C at 25 MPa. We scaled diffusion coefficients for all species according to the self-diffusion of compressed SCW as documented by Lamb et al. [46] and Yoshida et al. [47]. Static dielectric constants and ionic products of SCW (K_w) were taken from Lemmon et al. [32] and Bandura and Lvov [48], respectively. Consistent with previous findings (e.g., see [38]), we assumed that the thermalization distances of subexcitation-energy electrons (e⁻_sub)—i.e., those with kinetic energies below ~7.3 eV, the first electronic excitation threshold of condensed water—and the prompt geminate electron-cation (H₂O^•+) recombination, which occurs before e⁻_sub thermalization, are governed solely by water density above 400 °C.

From a microscopic view, we overlooked the heterogeneous structure of SCW [49], due to significant local density fluctuations or “water clustering” associated with criticality. In our simulations, SCW was treated as a uniform medium with a mean density equal to that of bulk water (ρ) at the specified temperature and pressure.

In pre-simulations, we also considered the full stopping of both recoil nuclei (α-particle and lithium ion) in water due to their short ranges. Using SRIM software (version SRIM 2013 [50]), we calculated their energy-depth profiles in SCW. Figure 2 illustrates their total penetration lengths at 400 °C and 25 MPa (ρ = 0.167 g/cm³).

To simplify the model, ion energies were assumed constant during their travel. Average track energies (${\overline{E}}_{\mathrm{He}}$ and ${\overline{E}}_{\mathrm{Li}}$) were determined using SRIM [50] and our Monte Carlo track structure simulations, as previously described [29]. At 25 MPa, these average energies were ~0.658 and 0.298 MeV at 300 °C, ~0.655 and 0.302 MeV at 350 °C, ~0.658 and 0.302 MeV at 400 °C, and ~0.640 and 0.308 MeV at 500 °C. The corresponding LET values were ~170 and 166 keV/µm at 300 °C, ~142 and 140 keV/µm at 350 °C, ~38.2 and 37.4 keV/µm at 400 °C, and ~20.7 and 20.3 keV/µm at 500 °C.

The effective charges of helium and lithium ions were set to Z_eff = 1.8 and 1.7, respectively, to match the expected LET values. Simulations were performed over short ion track segments (typically, ~2–8 μm), where ion energy and LET remained nearly constant. This allowed for the calculation of “track segment” yields at well-defined LETs. Approximately 10 individual ion histories were simulated to ensure statistical reliability while maintaining computational efficiency [23,24,29,30].

Finally, the yields of primary free radicals and molecular products from the radiolysis of water induced by the ¹⁰B(n,α)⁷Li reaction were calculated by summing the G values of each recoil ion—obtained from our Monte Carlo simulations—weighted by their respective fractions of the total absorbed energy, according to [24,29,45]

$$G\left({\mathrm{X}}_i\right) = {\displaystyle \frac{G{\left({\mathrm{X}}_i\right)}_{\mathrm{He}} E_{\mathrm{He}} + G{\left({\mathrm{X}}_i\right)}_{\mathrm{Li}} E_{\mathrm{Li}}}{E_{\mathrm{T}}}},$$

(5)

where G(X_i)_He and G(X_i)_Li are the yields of species X_i associated with the recoil helium and lithium ions, respectively, and E_T = E_He + E_Li is the sum of the initial energies of the ion products of the reaction (i.e., 2.31 MeV). Numerically, Reaction (5) becomes

$$G\left({\mathrm{X}}_i\right) = 0.636 G{\left({\mathrm{X}}_i\right)}_{\mathrm{He}}+ 0.364 G{\left({\mathrm{X}}_i\right)}_{\mathrm{Li}}$$

(6)

as 63.6% of the energy is deposited by the 1.47 MeV α-particle and 36.4% by the 0.84 MeV lithium ion.

The absorption of the accompanying low-LET 0.478 MeV γ-ray in the aqueous solution (see Figure 1) is negligible within our region of interest. For reference, an electron of this energy has a range of ~1 mm in liquid water at 25 °C [51]—over 100 times the ~5–8 μm penetration depths of the He and Li ions. Therefore, its contribution was omitted from the G-value calculation in this study.

In this paper, G values are presented as molecules formed or consumed per 100 eV of absorbed radiation energy. To convert these values to SI units (micromolar per joule, μmol/J), 1 molecule/100 eV ≈ 0.10364 μmol/J. Note also that free radicals are represented by a “radical dot” (^•) in their chemical formula, placed at the position where the unpair electron resides.

3. Results and Discussion

3.1. Radiolysis of Sub- and Supercritical Water by ¹⁰B(n,α)⁷Li Fission Nuclei

Figure 3a–d shows the simulated temporal evolution of G values for radiolytic species (e⁻_aq, H^•, H₂, ^•OH, and H₂O₂) in pure, deaerated water irradiated by 1.47 MeV He²⁺ and 0.84 MeV Li³⁺ ions. The results cover the time range from ~1 ps to 0.1 ms at temperatures of 300 °C (Panel a), 350 °C (Panel b), 400 °C (Panel c), and 500 °C (Panel d), each at a pressure of 25 MPa. Although ¹⁰B has been extensively studied in nuclear technologies, its radiation-chemical yields have received limited attention. Currently, the only experimental G values suitable for comparison with our simulated yields under these conditions are those estimated by Christensen [52] at 289 °C. Furthermore, to our knowledge, no data are available on the temperature dependence of these yields in the SCW regime.

3.2. Comparison of the Yields of Each Species Across Different Temperatures

3.2.1. The Hydroxyl Radical (^•OH)

Figure 4 presents the time profile of G(^•OH) from simulations of the ¹⁰B(n,α)⁷Li radiolysis of pure, deaerated water by 1.47 MeV He²⁺ and 0.84 MeV Li³⁺ ions. The simulations span temperatures between 300 and 500 °C at a constant pressure of 25 MPa, cover densities ranging from 0.743 to 0.090 g/cm³, and extend up to ~0.1 ms. As depicted, the ^•OH yield of ~1.13 molecule/100 eV at ~1 μs estimated by Christensen [52] at 289 °C aligns closely with our calculations.

Reaction (4), in which H^• atoms react with SCW, is the primary driver of the sharp increase in ^•OH radical production at 400 and 500 °C and 25 MPa, within the “vapor-like” water density range of ~0.167–0.090 g/cm³. As mentioned above, this enhancement, observed during the homogeneous chemical stage of radiolysis, results from substantial increases in the rate constant, which reaches k = 7.7 × 10⁴ M⁻¹ s⁻¹ at 400 °C and 3.7 × 10⁵ M⁻¹ s⁻¹ at 500 °C, both at 25 MPa [22].

Interestingly, Figure 4’s comparisons with our previous studies on water radiolysis using 2 MeV fast neutrons, known for their relatively high LET [15,24,33,37,45], reveal that the G(^•OH) values for the ¹⁰B(n,α)⁷Li recoil nuclei display broadly similar temporal patterns across the studied temperature range. However, the notably lower amplitudes observed in this study imply an even higher LET associated with these recoil ions. Higher LET radiation results in more frequent radical–radical reactions due to an increased local concentration of radicals along the radiation tracks. Consequently, 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 (see, e.g., [12,44,53,54,55,56]).

As a result, our simulation findings suggest that ^•OH radical production in irradiated SCW coolant could have a significant impact on water chemistry management in proposed SCWRs and their SCW-SMR variants. This elevated concentration of oxidizing species may substantially increase the corrosion rate of critical reactor components, especially under the extreme high-temperature and high-pressure conditions characteristic of these reactors.

3.2.2. Molecular Hydrogen (H₂)

Figure 5a shows our calculated yields of molecular hydrogen over time from the radiolysis of sub- and supercritical water by the ¹⁰B(n,α)⁷Li recoil nuclei, spanning temperatures from 300 to 500°C at a constant pressure of 25 MPa, and times ranging from 1 ps to 0.1 ms. The data reveal a sharp increase in G(H₂) for times greater than ~0.1 μs at supercritical temperatures. This rise in H₂ yields closely parallels previous findings from the 2 MeV fast neutron radiolysis of SCW [24]. The cumulative yield variations (ΔG) for each reaction contributing to G(H₂), as shown in Figure 5b, underscore the pivotal role of Reaction (4) in generating molecular hydrogen, alongside hydroxyl radicals, at homogeneity, i.e., once the tracks have dissipated. As seen in the figure, the increase in H₂ from Reaction (4) reaches about 3 G-units at 400 °C (ρ = 0.167 g/cm³).

The extent to which the substantial radiolytic production of H₂ in the ¹⁰B(n,α)⁷Li radiolysis of water may affect the minimum concentration of excess hydrogen—referred to as the “critical hydrogen concentration” (CHC) [57,58,59]—required in the coolant water of proposed SCWRs or SCW-cooled SMRs to minimize, or ideally suppress, net water radiolysis and maintain fuel cladding integrity [3,60,61], remains uncertain. While the potential benefits of adding H₂ have been suggested, it is still unclear whether this approach would be as effective under supercritical conditions as it is in conventional pressurized water reactors, where the CHC has been measured to be around 0.4–0.6 mL/kg (~2 × 10⁻⁵ M) [60,62]. Our results strongly emphasize the need for further investigation into SCW chemistry in reactors to address this critical issue.

3.2.3. The Hydrogen Atom (H^•)

Figure 6a presents the time profiles of G(H^•) from the radiolysis of pure, deaerated sub- and supercritical water by the ¹⁰B(n,α)⁷Li recoil nuclei, covering temperatures from 300 to 500 °C at a constant pressure of 25 MPa, and times ranging from 1 ps to 0.1 ms.

Compared to fast-neutron radiolysis data [24], our computed G(H^•) values for the ¹⁰B(n,α)⁷Li 1.47 MeV He²⁺ and 0.84 MeV Li³⁺ fission nuclei exhibit similar time dependence across the studied range, further emphasizing the high-LET character of these radiation types. A particularly noteworthy result from our simulations in SCW is the significant increase in G(H^•) during the track stage of radiolysis, followed by a rapid decrease at times exceeding ~0.1 μs. To gain a deeper insight into the time-dependent variations in G(H^•), we can analyze the unfolding of the reactions involved. This is shown in Figure 6b,c, where we present the cumulative yield variations, ΔG(H^•), for the key reactions contributing to the formation and decay of H^• atoms, calculated at 400 and 500 °C, respectively.

As shown, the formation of G(H^•) in the tracks is primarily driven by the reaction between e⁻_aq and hydronium ions H₃O⁺ [23,63,64]:

e⁻_aq + H₃O⁺ → H^• + H₂O.

(7)

The rate constants for this reaction at 25 MPa are 1.1 × 10¹³ M⁻¹ s⁻¹ at 400 °C and 3.3 × 10¹³ M⁻¹ s⁻¹ at 500 °C [22]. Notably, the efficiency of this rapid charge recombination is enhanced by the low dielectric constant of SCW, with ε_s ≈ 2.50 at 400 °C and ε_s ≈ 1.57 at 500 °C [32]. In contrast, under subcritical conditions, the rate constants are substantially lower—7.2 × 10¹¹ and 1.9 × 10¹² M⁻¹ s⁻¹ at 300 and 350 °C, respectively [15]. These lower reaction rates, combined with higher dielectric constants (ε_s ≈ 21.5 at 300 °C and 14.9 at 350 °C [32]), contribute to the markedly reduced G(H^•) values observed at these temperatures.

A brief mention should be made of the reaction between hydrated electrons and water molecules, given below:

e⁻_aq + H₂O → H^• + OH⁻.

(8)

The rate constants for this reaction are ~3.0 × 10⁴ M⁻¹ s⁻¹ at 400 °C and ~6.6 × 10⁴ M⁻¹ s⁻¹ at 500 °C, under 25 MPa [22]. This reaction also contributes to the formation of H^• atoms near the end of track expansion and the onset of the homogeneous chemical stage of radiolysis. However, as shown in Figure 6b,c, its contribution to G(H^•) remains relatively minor compared to that of Reaction (7) under supercritical conditions.

Figure 6b,c show that H^• atoms are consumed via radical–radical recombination:

H^• + H^• → H₂,

(9)

and, more significantly at homogeneity, by the water oxidation Reaction (4), which produces ^•OH and H₂, as previously discussed. This latter reaction becomes largely dominant at 500 °C. It is noteworthy that the consumption of H^• radicals at 25 MPa via Reaction (9) is lower at 500 °C than at 400 °C, despite the higher rate constant for Reaction (9) at 500 °C (~1.0 × 10¹² M⁻¹ s⁻¹) compared to 400 °C (~5.0 × 10¹¹ M⁻¹ s⁻¹). This apparent discrepancy can be explained as follows: as the density of SCW decreases from 0.167 g/cm³ at 400 °C to 0.090 g/cm³ at 500 °C, the medium becomes increasingly gas-like. With fewer water molecules available to act as a barrier, the solvent “cage effect” is markedly reduced [17,22,65]. This decrease in the cage effect results in an increased escape of the species formed from water dissociation, including H^• radicals, as the proximity necessary for recombination becomes less favorable at higher temperatures.

Another reaction of the H^• atom and water,

H^• + H₂O → e⁻_aq + H₃O⁺,

(10)

also removes H^• atoms, competing with Reaction (4). It has been considered by various authors [15,22,35] at elevated temperatures and within the supercritical water regime. A key feature of this reaction is that it produces e⁻_aq and H₃O⁺ in close proximity, facilitating their rapid recombination to reform H^• atoms, especially above the critical point where the dielectric constant is substantially reduced. According to Liu et al. [22], this reaction is significant under subcritical conditions, but its rate constant decreases markedly beyond the critical point, making it negligible in SCW radiolysis. Our simulations, as shown in Figure 6b,c, align with Liu et al.’s findings: a relatively small contribution at homogeneity is observed at 400 °C, which completely disappears at 500 °C.

3.2.4. The Hydrated Electron (e⁻_aq)

As with ^•OH, H₂, and H^•, Figure 7a shows our calculated yields of e⁻_aq over time from the radiolysis of sub- and supercritical water induced by the ¹⁰B(n,α)⁷Li recoil nuclei. The results span temperatures from 300 to 500 °C at a constant pressure of 25 MPa, with a timescale ranging from 1 ps to 0.1 ms. Regardless of temperature, the data reveal a sharp decline in G(e⁻_aq) during track expansion, lasting until ~1 μs. In comparison with yields from low-LET radiation [23,63], the computed e⁻_aq yields for ¹⁰B(n,α)⁷Li recoil irradiation exhibit similar trends but with significantly lower values. As previously noted, this behavior is indicative of the high-LET nature of the ¹⁰B(n,α)⁷Li fission nuclei, a conclusion further supported by the close alignment of our G(e⁻_aq) values with previous findings from the 2 MeV fast neutron radiolysis of SCW [24].

To better understand the time-dependent variations in G(e⁻_aq), we can examine the unfolding of the underlying reactions. For illustration, Figure 7b presents the cumulative yield variations, ΔG(e⁻_aq), for the key reactions controlling the formation and decay of e⁻_aq during the radiolytic process, as determined from our simulations at 400 °C and 25 MPa. Notably, this figure underscores the pivotal role of Reaction (7), which is primarily responsible for the decay of G(e⁻_aq). In contrast, Reaction (8) at homogeneity contributes only minimally to the disappearance of e⁻_aq. As discussed earlier, Reaction (10) produces hydrated electrons and hydronium ions in close proximity, leading to their rapid recombination in SCW to reform H^• atoms, driven by the significantly reduced dielectric constant. Other reactions, such as e⁻_aq + ^•OH → OH⁻ and e⁻_aq + H^• (+H₂O) → H₂ + OH⁻, also contribute to the decay of G(e⁻_aq), but only to a minor extent. These contributions are omitted from Figure 7b for clarity.

A brief explanation is warranted regarding the more rapid decrease in G(e⁻_aq) at 400 °C compared to 500 °C, despite the fact that the rate constants for Reaction (7), which primarily governs the time evolution of G(e⁻_aq), are relatively similar at both temperatures [22]. This discrepancy stems from the lower density of the SCW medium at 500 °C, which diminishes the probability of recombination between e⁻_aq and H₃O⁺. As a result, the consumption of hydrated electrons is less at 500 °C than at 400 °C.

3.2.5. Hydrogen Peroxide (H₂O₂)

Figure 8 illustrates the temporal evolution of G(H₂O₂) calculated from the radiolysis of pure, deaerated sub- and supercritical water induced by the ¹⁰B(n,α)⁷Li recoil nuclei. As with other radiolytic species, the results span temperatures from 300 to 500 °C at a constant pressure of 25 MPa, with a timescale extending from 1 ps to 0.1 ms. Our simulations predict a decrease in G(H₂O₂) with increasing temperature from 300 to 350 °C during the track stage of radiolysis, with minimal G(H₂O₂) values observed above the critical point. These findings align well with previous reports on the temperature dependence of H₂O₂ yields in low-LET radiolysis of subcritical water up to 350 °C and in low-density SCW up to 700 °C (see, e.g., [15,23]). Notably, as previously mentioned, the temporal evolution at 300 and 350 °C mirrors that observed with low-LET radiation, but with higher H₂O₂ yields, consistent with the high-LET characteristics of ¹⁰B(n,α)⁷Li fission nuclei [29,30].

Hydrogen peroxide is the principal oxidizing molecular product generated during the radiolysis of water [12,15,23]. It is formed almost exclusively during the track stage of radiolysis through the combination of two ^•OH radicals produced in the radiolytic decomposition of water:

^•OH + ^•OH → H₂O₂.

(11)

The slight decrease in G(H₂O₂) from 300 to 350 °C can be explained by the faster diffusion of ^•OH radicals out of the tracks, which outpaces their self-recombination within the tracks, thereby leading to lower H₂O₂ yields [15,66,67].

Unlike in subcritical water, the efficiency of Reaction (11) in low-density SCW irradiated at temperatures between 400 and 500 °C under a pressure at 25 MPa is relatively low. The rate constant for this reaction increases only marginally with temperature, from 1.4 × 10⁹ M⁻¹ s⁻¹ at 400 °C to 1.5 × 10⁹ M⁻¹ s⁻¹ at 500 °C [17]. Under these conditions, minimal G(H₂O₂) values are expected above the critical point. This outcome, initially predicted by Liu et al. [17] based on cage effect considerations, is confirmed by our Monte Carlo simulations, which show that G(H₂O₂) remains very low—approximately 0.12 molecule/100 eV or less at 400 °C, and 0.04 molecule/100 eV or less at 500 °C—throughout the time range from ~1 ps to 0.1 ms, making experimental detection particularly challenging. Furthermore, irrespective of the thermal instability of H₂O₂ at high temperatures [21], our results suggest that H₂O₂ is unlikely to contribute significantly to material oxidation under these conditions.

4. Conclusions

In this study, Monte Carlo track chemistry simulations were used to calculate the G values of primary radiolytic species produced from the radiolysis of pure, deaerated water by ¹⁰B(n,α)⁷Li fission nuclei at temperatures ranging from 300 to 500 °C, under a constant pressure of 25 MPa. These conditions simulate those anticipated in proposed SCWRs and their small modular variants. The yields were primarily determined from the recoil ions, ⁴He and ⁷Li, produced by the boron-neutron capture reaction, with initial energies of 1.47 and 0.84 MeV, respectively. To the best of our knowledge, these are the first yield calculations conducted with high-LET ⁴He and ⁷Li ions under such extreme temperature and pressure conditions. Their realization was made possible by the recently published kinetic data from Liu et al. [17,22] on water radiolysis beyond the critical point. Our simulations provide new insights into the radiolytic formation of key chemical species, including e⁻_aq, H^•, H₂, ^•OH, and H₂O₂, over a timescale spanning from ~1 ps to 0.1 ms.

A key finding from our study was the marked increase in G(^•OH) and G(H₂), coupled with a notable decrease in G(H^•), during the homogeneous chemical stage of radiolysis. This change can be attributed to the oxidation of water by H^• atoms through the reaction H^• + H₂O → ^•OH + H₂. This reaction becomes a significant source of H₂, potentially reducing the need for adding excess hydrogen to the reactor’s coolant in order to counteract the net radiolytic production of oxidizing species. Furthermore, our simulations revealed that, unlike subcritical water, G(H₂O₂) remains remarkably low in low-density SCW. This suggests that H₂O₂ is unlikely to have a significant impact on material oxidation in SCW. This finding has important implications for corrosion risk management and water chemistry strategies in SCWR and SCW-SMR systems, particularly during long-term operation.

Our findings highlight the intricate interplay between various radical species and their potential to either mitigate or exacerbate oxidative damage under extreme reactor conditions. However, further experimental data are required to more precisely characterize the temperature dependence of radiolytic yields produced by the ¹⁰B(n,α)⁷Li radiolysis of sub- and supercritical coolant water. Such data would allow for a more comprehensive validation of our model calculations. Additionally, further studies are needed to clarify the specific role of the reaction between H^• atoms and water at high temperatures, particularly its impact on the overall radiolytic behavior and its implications for reactor performance, safety, and material integrity during prolonged operational periods.