Spectrum-Dependent Burnable Poison Selection for Enhanced Safety and Neutronic Performance in an Epithermal Supercritical Carbon Dioxide-Cooled Reactor

Abstract

This study investigates the neutronic performance of burnable poisons (BPs) in an epithermal spectrum supercritical carbon dioxide (S-CO₂)-cooled reactor. Twelve candidate BP materials are systematically evaluated, including rare-earth oxides (e.g., HfO₂, Er₂O₃, Eu₂O₃, etc.) and boron-based compounds (B₄C and PACS). The deterministic neutron transport code KYLIN-I with the ENDF/B VI 45-group cross-section library is employed for analysis. According to the calculation results, Eu₂O₃ effectively suppresses the initial k_inf of the epithermal-spectrum fuel assembly to ~1.2 with a relatively low weight fraction (~2.6%) while maintaining a total temperature coefficient (TTC) lower than −1.4 pcm/K throughout the entire burnup period. HfO₂ and Er₂O₃, at approximately 15% weight fraction, achieve TTC values better than −2 pcm/K. Furthermore, both Eu₂O₃ and HfO₂ contribute to maintaining a low, stable power peaking factor (PPF) below 1.24 throughout the burnup process. This study provides a theoretical foundation and technical support for designing an efficient and safe S–CO₂-cooled nuclear reactor. It highlights the importance of selecting BP materials that are well-adapted to the neutron spectrum and optimizing the fuel assembly configuration accordingly.

1. Introduction

Advanced gas-cooled reactor (AGR) technology has been widely developed worldwide. Currently, the gas-cooled reactor designs generally employ the helium Brayton cycle system. Examples include the high-temperature gas-cooled pebble-bed reactor (HTGR) in China [1] and the high-temperature engineering test reactor (HTTR) in Japan [2]. The helium Brayton cycle can achieve core outlet temperatures exceeding 850 °C. However, it imposes stringent requirements on high-temperature-resistant structural materials [3]. Another promising coolant for gas-cooled reactors is S–CO₂ [4,5]. The critical point of CO₂ occurs at a pressure of 7.38 MPa and a temperature of 31.1 °C. S–CO₂ exhibits high thermodynamic efficiency within the temperature range of 450–600 °C, making it well-suited for nuclear energy applications [6]. Other outstanding properties, such as high density, low viscosity, and compact turbomachinery, further improve its potential.

In the 2000s, research institutions in the United States, such as the Massachusetts Institute of Technology (MIT) [7,8,9] and Sandia National Laboratories (SNL) [10] published a series of studies exploring both direct and indirect applications of the S–CO₂ Brayton cycle in nuclear engineering. The innovative reactor design concept, which utilizes S–CO₂ as a direct coolant, has the potential to further enhance economic performance and simplify system configuration [11,12]. Building on this advantage, several studies have proposed the S–CO₂-cooled reactor as a transportable micro-reactor [13,14,15].

Unlike light water, S–CO₂ coolant has inherent limitations in neutron moderation and weak temperature reactivity feedback. Researchers have proposed installing moderator rods into the S–CO₂ gas-cooled reactor’s fuel assembly to enhance the neutron moderation. Due to the nature of AGR, only solid moderators are suitable for the S–CO₂ reactor core. By comparing different moderator materials and their configurations, an optimized design for an S–CO₂ gas-cooled reactor fuel assembly was developed, also known as a “weak moderation” assembly [16,17]. Meanwhile, the solid moderator shifts the neutron energy spectrum from fast to the epithermal energy range [18].

Besides reactivity feedback mechanisms, the auxiliary reactivity control methods are essential for ensuring the safety of S–CO₂ reactor cores, such as the burnable poison (BP) reactivity control method [19]. Compared with control rod mechanisms, BPs offer greater flexibility, as they can be integrated into fuel assemblies without requiring additional space for facility configurations [20,21]. The application of BPs for reactivity control has been extensively investigated across various advanced reactor types. These include rectangular and plate-shaped assembly water-cooled small modular reactors (SMRs) [22,23,24,25], liquid metal-cooled fast-spectrum nuclear reactors (LMCRs) [26,27], and high-temperature gas-cooled reactors (HTGRs). For HTGRs, the feasibility of using BPs has been well studied under both thermal and fast neutron spectra [28,29]. Additionally, BP design concepts are also applicable to micro-transportable gas-cooled reactors that have a similar design to the S–CO₂-cooled reactor [30,31]. Theoretically, the BP-based reactivity control method applies to any nuclear reactor.

BP materials control reactivity by interacting with neutrons through absorption reactions such as (n, γ), (n, α), and (n, p). Core design characteristics significantly influence the practical performance of BP design. Variations in the neutron spectrum have a significant effect on reactor core features. Previously, Hwanyeal Yu [32] studied 90% enriched ¹⁰B B₄C or Hf as a “replaceable fixed absorber (RFA)” in a 36.2 WM_th S-CO₂-cooled micro modular reactor (MMR). Zhang et al. [33] also employed B₄C in discrete BP rods in a 15 MW_th S–CO₂-cooled microreactor to control radial power distribution. Zong’s paper [34] presents the effects of B₄C, Er₂O₃, and Gd₂O₃ on the reactivity disturbance characteristics of the S–CO₂ reactor.

This work focuses on weakly moderated S–CO₂ reactor assemblies, where the neutron absorption cross-sections of candidate isotopes exhibit overlapping resonance peaks in the epithermal energy range. To address this challenge, this study employs the neutronics simulation code KYLIN-I to model epithermal S–CO₂ fuel assemblies and evaluate the performance of a series of BP materials. The numerical simulations are designed to isolate the effect of the epithermal neutron spectrum on BP performance by minimizing the influence of other variables in the neutronic analysis.

The objective of this study is to identify a suitable BP material for the “weak moderation” epithermal-spectrum S–CO₂-cooled reactor and to evaluate its effect on neutronic performance. This paper is organized as follows. Section 2 introduces the candidate BP materials for epithermal reactors and provides an overview of the simulation framework. Section 3 presents the BP performance results for S–CO₂ fuel assemblies. The evaluation metrics include reactivity suppression, temperature feedback behavior, burnup characteristics, and power distribution flattening, thereby enabling a comprehensive assessment of the design performance.

2. Methodology

2.1. Absorber Material Selection

The neutronic design of BPs in epithermal reactors should follow key principles: (1) At the start of operation, BPs must introduce enough negative reactivity to suppress excess reactivity. (2) During operation, BPs should provide consistent reactivity control, enable uniform fuel burnup, and ensure optimal power distribution within the assembly. (3) At the end of the burnup cycle, the reactivity release caused by BP addition should be minimized [32,33]. To meet these design principles, an ideal BP material should have a high-neutron-absorption cross-section, and its transmutation products in the depletion chain should have significantly lower absorption cross-sections. Additionally, the natural abundances of neutron-absorbing isotopes within the BP material must be considered, as they directly affect reactivity control.

According to the literature review, this study conducts a detailed investigation of various rare earth elements as potential BP materials. The selected candidates include hafnium (Hf) [35], europium (Eu) [36], dysprosium (Dy) [37], cadmium (Cd) [38], erbium (Er) [39], samarium (Sm) [40], lutetium (Lu) [41], and holmium (Ho) [42]. It also examines boron (B) and gadolinium (Gd), two well-established BP materials in pressurized water reactors (PWRs), to provide a basis for comparison with rare earth candidates. Data on the (n, γ) cross-section variations with neutron energy for major rare earth element neutron absorption nuclides have been collected from the ENDF/B-VI data library and summarized in Figure 1. Furthermore, the oxides of these rare earth elements all exhibit high melting points, good thermal conductivity, and minimal radiation-induced swelling, making them well-suited for use as BPs in nuclear reactors.

This study also identifies polycarborane-siloxane-ethynyl polymer (PACS), with the molecular formula (B₁₀H₁₀C₂)_a((CH₃)SiO)_b(C₂)_c, as a promising BP material. PACS uniquely combines neutron moderation provided by hydrogen atoms with boron-based neutron absorption [43]. Furthermore, it exhibits excellent thermal stability, enabling it to maintain structural integrity and functionality under high-temperature and high-pressure environments. This study selected two types of PACS materials, PACS-L and PACS-J, with H/B proportions of 84:10 and 34:10 as candidate BP materials. While irradiation stability in polymeric composites has been studied [44,45], direct irradiation data specific to PACS under S–CO₂-cooled radiation conditions remain unavailable. Therefore, this work focuses on evaluating the neutronic performance of PACS materials. Stability concerns under irradiation may be addressed through optimized BP loading methods or compositional adjustments in future work. A set of key parameters for the candidate BP materials selected in this study is summarized in

Table 1. The primary material properties parameters of candidate BP materials.

Candidate BP Materials	Primary Neutron Absorber Isotopes	Natural Abundance of Absorbing Nuclides	Density (g/cm3)	Melting Point (°C)
Gd2O3	155Gd	0.1480	7.40	2330
	157Gd	0.1565
Er2O3	166Er	0.3350	8.64	2387
	167Er	0.2287
Eu2O3	151Eu	0.4781	7.30	2350
	153Eu	0.5219
HfO2	176Hf	0.0526	9.68	2758
	177Hf	0.1860
	178Hf	0.2728
	179Hf	0.1362
	180Hf	0.3508
CdO	113Cd	0.1222	8.15	900
Sm2O3	149Sm	0.1382	8.35	2325
Ho2O3	165Ho	1.0000	8.36	2330
Dy2O3	164Dy	0.2826	7.81	2330–2350
Lu2O3	176Lu	0.0260	9.42	2487
B4C	10B	0.1982	2.52	2450
PACS-L	10B		0.9	>1200
PACS-J	10B		1.0	>1200

.

2.2. Fuel Assembly Configuration

This study incorporates the candidate materials into simulated reactor fuel assemblies and calculates the corresponding neutronic parameters. Their performance is then assessed to identify suitable BP candidates for an epithermal-spectrum S–CO₂-cooled reactor core. To examine how the neutron spectrum affects BP performance, two different fuel assembly models are created: an epithermal-spectrum fuel assembly (ES-FA) representing a mildly moderated S–CO₂-cooled reactor core and a fast-spectrum fuel assembly (FS-FA) without ZrH₂ rods. Both configurations are shown in Figure 2.

The fuel assembly models in this study are based on the published design of a “weak moderation” S–CO₂-cooled reactor. The reactor core has a thermal power of 100 MW_th, with S–CO₂ coolant entering the core at 671 K and exiting at approximately 850 K. Each fuel assembly has a hexagonal geometry and consists of 61 rods. The fuel rods are composed of UO₂ with a ²³⁵U enrichment of 19.75%, and the cladding material is high-nickel-content stainless steel. In the ES-FA assembly model, 13 ZrH₂ moderator rods are incorporated. The key geometric and material parameters of the fuel assemblies are summarized in

Table 2. Benchmark epithermal-spectrum nuclear reactor fuel assembly major parameters.

Design Parameters	Value
Radius of the fuel rod	3.5 mm
Number of rod cells	61
Rod pitch	0.9 cm
Thickness of cladding	0.5 mm
Assembly box thickness	2 cm
Density of UO2 fuel	10.4 g/cm3
235U enrichment	19.75%
Supercritical CO2 coolant density	0.11519 g/cm3
Temperature of fuel	900 K
Temperature of coolant	773 K
Solid moderator material	ZrH2

.

The integrated BP rod refers to a configuration in which the BP material is directly incorporated into the nuclear fuel. Fabrication methods include surface coating of fuel pellets or sintering a uniformly mixed BP–UO₂ matrix [46]. Figure 3 shows schematic diagrams of BP-coated and uniformly mixed integrated BP rods. In this study, a heterogeneous neutronic model of the S–CO₂-cooled fuel assembly is used to reflect the spatial heterogeneity of BP material distribution. Specifically, fuel rods containing a homogenized BP–UO₂ mixture are modeled as separate material cells with unique isotopic compositions and densities, unlike standard UO₂ fuel rods.

2.3. KYLIN-I

The KYLIN-I code is used for neutron transport and burnup calculations in this study. It employs a point-and-line approach for geometric modeling, enabling accurate representation of complex geometries through a combination of straight lines and circular arcs. The neutron transport equation is solved using a flow-coupled collision probability method. KYLIN-I uses the subgroup method to account for resonance self-shielding in cross-section calculations. This method is widely applied in recently developed neutronic analysis codes, such as SHARK [47], NECP-X [48], and MPACT [49].

During development, KYLIN-I was verified and validated against IAEA benchmark problems, with results for k_inf and key nuclide density changes during burnup matching reference results [50]. A series of sensitivity studies was conducted to determine the optimal conditions for neutronic calculations. Section 3 will present some results.

3. Results and Discussion

3.1. Sensitivity Analysis

3.1.1. Code Benchmark

A benchmark was performed comparing KYLIN-I with the Monte Carlo method (MCM) code OpenMC [51] using the ES-FA model. It should be noted that BP–UO₂ rods were replaced with fuel rods in this benchmark to eliminate the influence of BP materials. As shown in Figure 4, the k_inf from KYLIN-I is 423 pcm higher than OpenMC. This study initially employs KYLIN-I to quantify the neutronic characteristics of BP candidates and then uses OpenMC to reassess the impact of code sensitivity on critical design performance. The OpenMC simulations are performed with 300 batches, including 100 inactive batches. Each batch uses 500,000 source neutrons.

3.1.2. Multi-Group Energy Structure

The KYLIN-I code has been developed and validated using multiple standard multigroup cross-section libraries, including the 45- and 190-group neutron libraries derived from the ENDF/B-VI evaluated nuclear data library. A series of comparisons between these two multigroup neutron libraries was conducted to assess their sensitivity regarding the performance of BP material. Figure 5 shows the k_inf results for various ES-FA fuel assemblies with different BP configurations, as calculated by KYLIN-I using both the 45- and 190-group neutron cross-section libraries. For ES-FA cases containing BP materials, the k_inf differences between the two libraries generally range from 200 to 500 pcm.

However, the current 190-group neutron library lacks cross-section data for several necessary BP materials, such as Er₂O₃, Eu₂O₃, Gd₂O₃, and HfO₂. To ensure consistency in the neutronic analysis across all BP candidates, subsequent coefficients calculated were performed using the 45-group cross-section library [52]. The outstanding BP cases would be re-evaluated using the OpenMC continuous energy cross-section library.

3.1.3. Mesh Subdivision and Burnup

Geometric mesh subdivision has a significant influence on the accuracy of KYLIN-I neutron transport calculations, particularly in BP material performance studies where self-shielding effects are prominent. To evaluate this sensitivity, fuel, and BP pin cells are divided into a varying number of annular rings radially, with each ring assigned homogeneous materials such as UO₂ or BP–UO₂ mixtures.

Burnup calculations evaluated irradiation effects across all mesh configurations. The KYLIN-I code employs a predictor–corrector (PC) scheme for burnup, whereby neutron transport and depletion calculations are performed twice within each burnup step. The nuclide density $\mathit{N}{\left(t\right)}_s$ at step s is computed as shown in Equation (1):

$$\mathit{N}{\left(t\right)}_s=0.5[\mathit{exp}\left({\mathit{A}}_{P}t\right)\mathit{N}{\left(0\right)}_s+\mathit{exp}\left({\mathit{A}}_{\mathrm{C}}t)\right.\mathit{N}{\left(0\right)}_s$$

(1)

where A is the transition matrix that incorporates the neutron flux and reaction cross-sections at step s, the subscripts P and C denote the predictor and corrector steps, respectively. $\mathit{N}{\left(0\right)}_s$ represents the nuclide density at the beginning of step s, which serves as the initial composition for both the predictor and corrector. To evaluate mesh sensitivity, a case study was performed simulating 5 wt% Gd₂O₃ in UO₂ fuel at a power density of 25 W/g during burnup. In this sensitivity analysis, the five-ring rod cell case, which has the finest structure, serves as the reference case. Figure 6 shows pin cells with five- and three-ring annular mesh subdivisions, along with the evolution of k_inf and its deviation from the reference case during burnup.

The results indicate that while the two-ring pin cell case exhibits significant deviations from the five-ring reference throughout burnup, the three- and four-ring models show much more minor differences, typically within ±10 pcm. In particular, the k_inf values for the three-ring case deviate by less than 5 pcm from the reference, demonstrating sufficient accuracy for BP performance analysis. Therefore, a three-ring radial subdivision is adopted in this study to strike a balance between computational efficiency and numerical precision. The entire mesh division used in the corresponding analysis of ES-FA is shown in Figure 7.

3.1.4. Initial ²³⁵U Content Maintenance

When moderator rods and BP–UO₂ rods are introduced into the S–CO₂-cooled FA model, the effective ²³⁵U loading is reduced. To maintain a consistent reactivity benchmark, two compensation strategies are proposed and evaluated in sensitivity analysis, as summarized in Figure 8.

In the “UO₂ material method,” a single modified UO₂ material definition, which is adjusted for either ²³⁵U enrichment or numerical density (ND), is applied globally in all fuel rods, corresponding to a homogeneous adjustment.

In contrast, the “material cell method” applies separate adjustments to individual material cells. Particularly, standard fuel rods compensate for ²³⁵U loss due to moderator volume displacement, while BP–UO₂ rods compensate for loss caused by BP insertion. This yields two distinct UO₂ material definitions, representing a heterogeneous adjustment.

As shown in Figure 8, the reactivity compensation strategy varies with the assembly configuration. In the ES-FA, both moderator rods and BP–UO₂ rods are incorporated, so the adjustment accounts for the combined loss of ²³⁵U due to volume displacement. Conversely, the FS-FA includes only BP–UO₂ rods without moderator rods, meaning the compensation is designed solely to offset the loss of ²³⁵U caused by the BP insertion.

The above BP rods with a 5 wt% Gd₂O₃ UO₂ mixture calculation case are used to assess the effectiveness of two compensation strategies under different spectral conditions. The corresponding input parameters are summarized in

Table 3. Summary of KYLIN-I input parameters for ²³⁵U compensation adjustment methods and k_inf at the beginning of life (BOL) with various adjustment cases.

	Assembly Type	Enrichment of 235U	ND (g/cm3)	Adjusted Enrichment kinf (BOL)	Adjusted ND kinf (BOL)
UO2 material method	ES-FA	25.997%	13.69	1.32779	1.26405
	FS-FA	20.61%	10.85	1.36988	1.35064
Material cells method (Standard fuel/ BP–UO2 mixture)	ES-FA	30.37%/21.18%	16.03/11.17	1.32657	1.26265
	FS-FA	19.75%/21.18%	10.4/11.17	1.36910	1.35076
Only UO2 fuel assembly		19.75%	10.4	1.38359	1.38359

. For the “material cell method,” parameters are specified separately for UO₂ in standard fuel rods and in BP–UO₂ mixture rods. A reference model, consisting of 61 pure UO₂ fuel rods without moderator rods or BP materials, was also created to examine the inherent burnup behavior of the fast-spectrum S–CO₂-cooled reactor fuel assembly, referred to as the “Only UO₂ fuel assembly” case.

Several burnup calculations were performed using the parameters listed in Table 3. The total burnup depth and step scheme were determined based on the “Only UO₂ fuel assembly” case, in which k_inf approaches 1 after 300 GWd/tU. The burnup step scheme consists of 310 steps: the first two are 0.05 GWd/tU, followed by nine steps of 0.1 GWd/tU, and the remaining 299 steps at 1 GWd/tU each. This depth exceeds the typical refueling burnup of PWRs. Such a high burnup level may pose significant challenges to fuel and cladding materials. However, in this conceptual material selection study, this high burnup depth is selected to distinguish differences in BP depletion rates.

This burnup scheme is consistently applied to all subsequent BP cases throughout this study. The operation condition is simulated at full power, with a power density of 25 W/g. The k_inf results at BOL are also shown in Table 3. Compared to the reference “Only UO₂ FA” case, adding Gd₂O₃ BP causes reactivity suppression depending on the spectrum. In FS-FA, the initial k_inf decreases from 1.38359 to about 1.370, while in ES-FA, the reduction exceeds approximately 1.327 or 1.264. This significant difference comes from the shift in the neutron spectrum toward the epithermal range caused by the moderator rods, where both ²³⁸U resonances and Gd isotopes have notably higher absorption cross-sections.

The depletion curves are shown in Figure 9. The ²³⁵U enrichment adjustment leads to higher initial k_inf values than the UO₂ ND adjustment under both the material cells method and the UO₂ material method. The reason for this is the decrease in ²³⁸U content and lower neutron absorption. Enrichment adjustment also leads to greater Δk_inf during burnup. In contrast, the UO₂ ND adjustment maintains the proportion of ²³⁵U and ²³⁸U, resulting in more stable neutronic performance. The divergence of k_inf value between the ²³⁵U enrichment and UO₂ ND adjustment methods is more significant in ES-FA assemblies than in FS-FA configurations, as moderator rods amplify the neutron absorption capability of the BP and ²³⁸U.

Comparing Figure 9a,b, the UO₂ material method and the material cells method produce similar depletion curves. The material cells method treats the fuel rod parameters independently based on their poison content, offering greater flexibility to model different types of burnable poisons with various weight fractions. Therefore, the material cells method with ND adjustment is selected for subsequent studies to ensure consistency in total fissile material inventory across all computational models.

3.2. Reactivity Suppression

A straightforward opinion about BP design is that increasing the weight fraction (wt%) of BP in the BP–UO₂ mixture rods results in stronger suppression of reactivity. However, the long-term reactivity control is significantly related to the burnup chains of different neutron absorbers. This part of the study chose B₄C and CdO simulation cases to illustrate the impact of the burnup chain. B₄C-type BP materials have a simple neutron reaction as shown in Equation (2).

$${}_5{}^{10}B+n=\left[{}_5{}^{11}B\right]\ast \to {}_3{}^{7}Li+{}_2{}^{4}He$$

(2)

Another class of candidate BP materials demonstrates long-term reactivity control, such as CdO and HfO₂. When exposed to neutron irradiation, CdO generates isotopes with relatively high-neutron-absorption cross-sections, including ¹⁰⁷Ag, ¹⁰⁹Ag, and ¹¹⁵In. Figure 10 shows the abundances of Cd isotopes and neutron reaction products.

Figure 11 shows the k_inf evolutions with burnup of FS-FA and ES-FA assemblies containing different weight fractions of B₄C and CdO poison. The burnup curves for B₄C exhibit significant differences at the initial depletion in both assembly types. However, as burnup progresses, the curves gradually approach each other. Under an epithermal neutron spectrum, the burnup curves of B₄C ES-FA calculation cases collapse into a single line around 150 GWd/tU. Initial differences in reactivity suppression due to varying B₄C weight fraction are minimized by its high depletion rate, which is further enhanced by the inclusion of moderator rods.

Conversely, because of the in situ generation of isotopes with high-neutron-absorption cross-sections, the reactivity suppression effect remains stable throughout the entire burnup process. The burnup curves for different CdO weight fraction cases evolve in parallel, and the assemblies’ k_inf decreases steadily. Therefore, CdO is better suited as a control rod material rather than a burnable poison.

To further evaluate the BP materials listed in Table 1, a series of calculations was performed to determine the poison weight fractions required to achieve a BOL k_inf of 1.200 in both the FS-FA and ES-FA models. The baseline BOL k_inf are 1.26265 for ES-FA and 1.35076 for FS-FA. Although the achieved k_inf values exhibit slight deviations from the exact target, the corresponding reactivity suppression Δk_inf values are precisely quantified for each poison, and their weight fractions are provided in

Table 4. Weight fractions of poisonous materials in BP–UO₂ mixture rods for FS-FA and ES-FA models to achieve initial k_inf values of 1.2 and burnup depths when k_inf values ≈ 1.

	ES-FA			FS-FA
Poisonous Materials	Weight Fraction (wt%)	BOL Δkinf (pcm)	Burnup Depth kinf ≈ 1 (GWd/tU)	Weight Fraction (wt%)	BOL Δkinf (pcm)	Burnup Depth kinf ≈ 1 (GWd/tU)
B4C	1.3	6230	119	2.3	14,812	258
CdO	25	6404	78	31	14,231	125
Dy2O3	6.5	5890	95	19	15,395	153
Er2O3	16	6350	83	27	15,306	137
Eu2O3	2.6	5874	95	7	15,272	161
Gd2O3	10	6301	97	19	14,480	153
HfO2	15	5960	93	27	15,266	143
Ho2O3	8	6677	101	16	15,197	185
Lu2O3	6	5952	85	13	14,948	136
Sm2O3	7	5838	90	20	15,002	142
PACS-L	5.7	6277	105	5.4	15,283	113
PACS-J	3	6457	109	3.3	15,283	129

.

In Table 4, to control the initial k_inf of assemblies ~1.2, the weight fractions of poisonous materials in FS-FA assemblies generally range from 10 wt% to 30 wt%. Only the B-based materials have weight fractions below 10 wt%. In ES-FA, except for PACS, the weight fractions of other candidates are about half of those in FS-FA. The addition of moderator rods effectively enhances the initial suppression of reactivity. For B₄C, Dy₂O_3, Eu₂O_3, and Ho₂O₃, these four poisonous materials require much smaller amounts and demonstrate superior reactivity control capabilities under the epithermal spectrum.

Figure 12 presents the burnup curves of FS-FA and ES-FA assemblies with BP material candidates; the initial k_inf values are adjusted to approach 1.200 by optimizing weight fractions as specified in Table 4. The curves are displayed to the point where k_inf reaches approximately 1, allowing for a comparative assessment of the FA’s depletion rates associated with each BP material. In Figure 12, a general observation is that the ES-FA consistently exhibits a quicker depletion rate and lower weight fractions for all types of BP candidates due to the thermalized neutron spectrum. In the ES-FA, boron-based materials, B₄C and PACS, reach a deeper burnup level when k_inf approaches 1 compared to rare-earth element materials. Among the remaining materials, the ES-FA with Ho₂O₃ exhibits a slower k_inf decrease rate, followed sequentially by Gd₂O₃, Dy₂O₃, and Eu₂O₃.

The loading density of each BP material and the cumulative Δk_inf over the entire 300 GWd/tU burnup process are summarized in

Table 5. The amount of poison loaded in a single BP–UO₂ mixture rod in ES-FA, FS-FA, and Δk_inf during 300 GWd/tU.

Poisonous Materials	ES-FA		Poisonous Materials	FS-FA
	Poison Content (g/cm2)	300 GWd/tU Δkinf (pcm)		Poison Loading Content (g/cm2)	300 GWd/tU Δkinf (pcm)
B4C	0.0126	45,337	B4C	0.9718	23,966
PACS-J	0.0115	46,952	Ho2O3	0.5145	27,501
PACS-L	0.0197	48,959	Eu2O3	0.1966	30,612
Ho2O3	0.2573	45,054	Dy2O3	0.5708	33,185
Gd2O3	0.2846	48,429	Gd2O3	0.5408	33,319
Dy2O3	0.1953	48,233	HfO2	1.0053	34,551
Eu2O3	0.0730	47,020	Sm2O3	0.6424	36,907
HfO2	0.5585	49,318	Er2O3	0.8973	35,391
Sm2O3	0.2248	51,276	Lu2O3	0.4710	36,512
Lu2O3	0.2174	52,003	PACS-J	0.0127	40,596
Er2O3	0.5317	50,992	CdO	0.9718	38,492
CdO	0.7837	51,762	PACS-L	0.0187	40,596
Non-BP	0	52,717	Non-BP	0	39,422

. The non-BP reference cases show that the maximum achievable reactivity release for ES-FA is 52,717 pcm, and 39,422 pcm for FS-FA. According to BP optimization principles, an ideal BP should minimize its impact on reactivity release Δk_inf while effectively suppressing initial excess reactivity k_inf (BOL).

The reactivity release of FS-FA is apparently lower than that of ES-FA, and the PACS brings a relatively small improvement to the Δk_inf over a burnup depth of 300 GWd/tU. In the ES-FA, several rare-earth-based BPs exhibit close Δk_inf to the non-BP reference case, which are Lu₂O₃ (52,003 pcm), CdO (51,762 pcm), Sm₂O₃ (51,276 pcm), and Er₂O₃ (50,992 pcm). Figure 13 presents the variation in the ²³⁵U nuclide density of ES-FA with different BP candidates. The incorporation of the BP significantly affects the depletion rate of the fissile nuclide. PACS-L is capable of increasing the ²³⁵U depletion speed. In contrast, the ES-FA with Lu₂O₃ retains the highest ²³⁵U nuclide density.

3.3. Temperature Reactivity Feedback Coefficients

The negative temperature reactivity feedback is one of the important inherent control mechanisms of a nuclear reactor core. Unlike PWRs, which utilize a coolant density change to provide stable negative reactivity feedback, the epithermal-spectrum S–CO₂-cooled reactor lacks this feature. Therefore, it is necessary to require that the addition of BP material assist in enhancing temperature feedback.

The fuel temperature coefficient (FTC) results for the FS-FA with BP candidates are summarized in

Table 6. Summary of fuel temperature coefficients (pcm/K) for FS-FA containing different BP candidates at 0, 75, and 150 GWd/tU.

	Fuel Temperature Reactivity Coefficients (pcm/K)
Poisonous Materials BP Mass Fraction	0 GWd/tU	75 GWd/tU	150 GWd/tU
Only UO2 fuel assembly	−0.68	−0.74	−0.70
B4C–2.3%	−0.34	−0.62	−0.56
Ho2O3–16%	−0.24	−0.2	−0.3
Eu2O3–7%	−0.14	−0.2	−0.26
Dy2O3–19%	−0.2	−0.12	−0.26
Gd2O3–19%	−0.36	−0.58	−0.28
HfO2–27%	−0.66	−0.6	−0.5
Sm2O3–20%	−0.26	−0.36	−0.24
Er2O3–27%	−0.44	−0.42	−0.24
Lu2O3–13%	−0.26	−0.36	−0.2
PACS-J–3.3%	−1.56	−1.72	−1.90
CdO–31%	−0.46	−0.5	−0.56
PACS-L–5.4%	−1.84	−2.06	−2.14

. The BP weight fractions used in these calculations are consistent with those listed in Table 4. FTC values are computed over a temperature range of 890–910 K at each burnup step. These FS-FA results serve as a reference for subsequent comparisons with ES-FA. In Table 6, it is evident that most BPs decrease the magnitude of the FTC, except for PACS, where the hydrogen atoms have a thermalized neutron spectrum, thereby enhancing the neutron resonance absorption of ²³⁸U.

Table 7. Summary of fuel, moderator, and total temperature coefficients (pcm/K) for ES-FA containing different BP candidates at 0, 50, and100 GWd/tU.

Poisonous Materials		Temperature Reactivity Coefficients (pcm/K)			Poisonous Materials		Temperature Reactivity Coefficients (pcm/K)
		0	50	100			0	50	100
		(GWd/tU)					(GWd/tU)
B4C-1.3%	M	0	0.06	0.1	Eu2O3-2.6%	M	−0.08	0	0.06
	F	−1.5	−1.76	−1.94		F	−1.7	−1.54	−1.52
	T	−1.5	−1.7	−1.84		T	−1.78	−1.54	−1.46
PACS-J-3%	M	0	0.06	0.06	HfO2-15%	M	−0.06	0.04	0.06
	F	−1.8	−2.1	−2.2		F	−2.1	−2	−1.96
	T	−1.8	−2.04	−2.1		T	−2.16	−1.96	−1.9
PACS-L-5.7%	M	0	0.06	0.06	Sm2O3-7%	M	0.14	0.12	0.1
	F	−2	−2.34	−2.46		F	−1.64	−1.6	−1.54
	T	−2	−2.28	−2.4		T	−1.5	−1.48	−1.44
Ho2O3-8%	M	0	0.06	0.06	Lu2O3-6%	M	0.06	0.14	0.1
	F	−1.5	−1.54	−1.64		F	−1.5	−1.46	−1.36
	T	−1.5	−1.48	−1.58		T	−1.44	−1.32	−1.26
Gd2O3-10%	M	0.1	0.14	0.14	Er2O3-16%	M	−0.22	0	0
	F	−1.88	−1.82	−1.78		F	−2.1	−1.86	−1.6
	T	−1.78	−1.68	−1.64		T	−2.32	−1.86	−1.6
Dy2O3-6.5%	M	0	0.06	0.08	CdO-25%	M	0	0.06	0.04
	F	−1.5	−1.52	−1.52		F	−1.7	−1.6	−1.44
	T	−1.5	−1.46	−1.44		T	−1.7	−1.54	−1.4

M: moderator temperature coefficients; F: fuel temperature coefficient; T: total temperature coefficients.

shows the FTC, moderator temperature coefficients (MTC), and total temperature coefficients (TTC) of ES-FA with BP candidates. The MTC temperature range is from 890 K to 910 K. The FTCs and MTCs are calculated from the isolated temperature oscillations of the fuel rods and ZrH2 moderator rods, while the TTCs are determined during simultaneous temperature changes. Apart from Er₂O₃, Eu₂O₃, and HfO₂, which demonstrate negative MTC at the BOL, the MTC of the remaining BP cases is slightly positive, suggesting these materials can effectively trigger negative temperature reactivity. Under an epithermal neutron spectrum, the increased proportion of resonance interactions amplifies the FTC magnitude. Among the BP candidates, the top four materials that maximize TTC are HfO₂, Er₂O₃, Gd₂O₃, and Eu₂O₃. The PACS material continuously shifts the neutron spectrum toward epithermal energies, resulting in higher temperature reactivity feedback.

3.4. Flattening of Power Distribution

Achieving uniform power distribution in epithermal S–CO₂-cooled fuel assemblies is essential for improving safety. The evenness of power distribution can be measured by the assembly PPF, which is defined as the ratio of the maximum power density to the average power density of the fuel rods. Figure 14 shows the PPF values for FS-FA and ES-FA with BP candidates at the beginning, middle, and end of burnup stages. Excluding the effect of BP, the PPF values of ES-FA at three burnup stages are 1.0292, 1.0231, and 1.0184, respectively, compared to 1.0002, 1.0008, and 1.0025 for FS-FA.

A clear finding from Figure 14 is that the PPFs in ES-FA are generally higher than those in FS-FA because moderator rods boost the fission rate in neighboring fuel rods. Compared to the Only UO₂ FS-FA, the PPFs of FS-FA containing BP materials other than PACS show only minor differences. At the BOL, the PPF of the Only UO₂ FS-FA is lower than that of cases with BP materials. However, by 150 GWd/tU, the PPF results are reversed. The candidate BPs tend to have small neutron absorption cross-sections in the fast neutron energy range, leading to a limited effect on power distribution. Other factors influencing PPF include the fuel content and adjustments in fuel ND, which are discussed in Section 3.1.4. These factors can cause uneven distributions of fissile ²³⁵U, resulting in high PPF values at the BOL.

Among these rare-earth element poisons, ES-FA’s PPF with HfO₂ consistently remains lower than others, indicating its ability to sustain effective power distribution control throughout the burnup process. For ES-FA containing B₄C, the PPFs are generally lower than those of other compound materials, although they are relatively higher at BOL. This behavior results from the strong neutron absorption capability and rapid depletion rate of B₄C. As a result, its influence on the PPF becomes negligible at burnups of 50 and 100 GWd/tU. The ES-FA, which contains PACS and exhibits both neutron moderation and absorption capabilities, continues to demonstrate lower PPFs compared to other assemblies, highlighting excellent performance. Among ES-FA, the BPs that effectively reduce the PPF are PACS, HfO₂, and Eu₂O₃.

3.5. BP Performance Assessment

Reactivity suppression, temperature reactivity feedback, burnup behavior, and power distribution flattening have been evaluated. Based on the results, a comprehensive BP material selection can be made.

Eu₂O₃ exhibited outstanding performance as BP in epithermal S–CO₂-cooled reactors. With a low mass fraction of 2.6%, Eu₂O₃ achieved effective reactivity suppression while maintaining a stable total temperature coefficient (TTC below −1.4 pcm/K) and ensuring flat power distributions (PPF ≤ 1.24) throughout the burnup process.

HfO₂ demonstrated distinct advantages for long-term BP applications. At a higher mass fraction (~15%), HfO₂ not only provided stronger suppression of reactivity and improved temperature reactivity feedback (TTC < −2 pcm/K) but also produced neutron absorption products that maintained spectral adaptability, ensuring effective reactivity control up to 93 GWd/tU. This characteristic makes HfO₂ an ideal candidate for long-term reactor operation. In addition, Er₂O₃ was particularly effective in enhancing temperature feedback, showing the most negative TTC (−2.32 pcm/K initially) among rare-earth BPs.

The innovative PACS materials addressed trade-offs between moderation and absorption by utilizing hydrogen’s spectral softening and boron’s capture capabilities. PACS-L is especially well balanced for high burnup (>105 GWd/tU) and TTC (−2 pcm/K), offering a pathway for next-generation BP material development.

As mentioned in Section 3.1.1, this study reassesses the k_inf and TTC at BOL of the design cases with Eu₂O₃, HfO₂, Er₂O₃, and PACS-J candidates using OpenMC. A comparison of the results from KYLIN-I and OpenMC is presented in

Table 8. Comparison of k_inf and TTC at BOL with KYLIN-I and OpenMC.

	KYLIN-I		OpenMC
	Initial kinf	TTC (pcm/K)	Initial kinf	TTC (pcm/K)
Eu2O3-2.6%	1.20391	−1.78	1.19942 ± 0.00007	−1.96
HfO2-15%	1.20305	−2.16	1.19893 ± 0.00007	−2.42
Er2O3-16%	1.19960	−2.32	1.19466 ± 0.00007	−2.49
PACS-L-5.7%	1.19988	−1.80	1.19550 ± 0.00007	−2.04

. The OpenMC simulation settings are consistent with those used in Figure 4 ES-FA benchmark.

Since KYLIN-I employs a 45-group multi-group while OpenMC uses a continuous energy cross-section library, the initial k_inf values obtained with KYLIN-I are systematically higher than those from OpenMC by 400–500 pcm, stable with the benchmark results. In addition, OpenMC adopts a 300 K temperature gap to calculate the TTC, resulting in values that are generally more negative than those from KYLIN-I. Nevertheless, this discrepancy does not alter the relative performance of BP in enhancing the reactivity feedback of the ES-FA. The above comparison demonstrates that the code’s sensitivity does not affect the evaluation and selection of BPs. The ranking and selection of BP in this study guides engineering design of epithermal-spectrum S–CO₂-cooled reactors.

4. Conclusions

The findings from this study confirm that aligning the neutron spectrum is a crucial principle for selecting BPs in an epithermal-spectrum S–CO₂-cooled reactor. The specific neutron cross-section characteristics and isotope transmutation pathways of different materials determine their performance rankings. The Eu₂O₃, HfO₂, Er₂O₃, and PACS four materials are selected as suitable epithermal-spectrum reactor BP materials.

It should be noted that, even though the neutron spectrum is thermalized by ZrH₂ moderator rods, the required weight fractions for HfO₂ and Er₂O₃ are around 15%. Such high weight fractions can adversely affect the thermal conductivity and manufacturability. Therefore, future work will focus on optimizing the assembly configuration. For example, the next study will adjust the positions of the moderator and BP rods. The selection of BP materials is based on the intrinsic neutronic merits of Eu₂O₃, HfO₂, Er₂O₃, and PACS. The goal is to reduce the required BP weight fractions while enhancing the effectiveness of reactivity control. Meanwhile, in the practical engineering design, materials may be selected or combined based on the reactor’s anticipated operational period and power density to achieve strong reactivity suppression at the BOL and sustained control throughout the lifetime of an epithermal S–CO₂-cooled reactor.