First-principles simulation of radiation shielding performance in TaS₂–HDPE composites using Geant4

Abstract

High atomic number (Z) fillers in polymer matrices provide lightweight alternatives to conventional radiation shielding. Previous studies have examined fillers such as CdO, $\hbox {WO}_3$, and $\hbox {Bi}_2\hbox {O}_3$. However, no prior work has investigated tantalum disulfide ($\hbox {TaS}_2$) in polymer composites for gamma-ray shielding, leaving a clear gap in the literature. Here, we report the photon attenuation performance of high-density polyethylene (HDPE) composites containing 10–50 wt% $\hbox {TaS}_2$ over 0.06–2.0 MeV, evaluated by Geant4 Monte Carlo simulations and validated with XCOM data. At 80 keV, where enhancement is most pronounced, the 50 wt% composite achieved a mass attenuation coefficient of 2.88 ± 0.04 $\hbox {cm}^2$/g, corresponding to a 15.9 ± 0.21 improvement over pure HDPE. Composites with 35, 20, and 10 wt% $\hbox {TaS}_2$ showed enhancements of 11.55 ± 0.05, 7.07 ± 0.03, and 4.04 ± 0.02 times, respectively. Benchmarking against micro-CdO–HDPE confirmed competitive or superior attenuation across the photon spectrum. These results establish TaS₂–HDPE as a tunable, non-toxic, and effective candidate for next-generation radiation shielding applications.

Introduction

Radiation shielding materials are essential in applications such as medical imaging, nuclear power, aerospace, and security systems, where effective attenuation of ionizing radiation is required to protect personnel and equipment. Traditionally, high-density metals like lead have been employed due to their high atomic numbers and superior attenuation properties. However, concerns regarding toxicity, weight, and fabrication challenges have prompted the search for alternative materials with comparable shielding performance but improved safety and manufacturability.

Beyond metals, glass- and alloy-based systems have also been explored. Recent reviews have summarized radiation shielding glasses, including borate, phosphate, silicate, tellurite, Pb-Pb-, and Bi-based systems¹, emphasizing both their tunable performance and limitations such as brittleness or Pb-toxicity. Geant4-based studies on phosphate and borate bioactive glasses have further confirmed the sensitivity of attenuation parameters to composition in the diagnostic X-ray range². Alloy-based systems such as Fe–Ni alloys³ have demonstrated strong photon and neutron shielding but often require complex processing. Together, these advances highlight the diversity of candidate materials while reinforcing the need for simpler, safer, and more versatile alternatives.

Polymer-based composites containing high atomic number (high-Z) fillers are promising candidates for radiation shielding. Such materials combine the attenuation efficiency of heavy elements with the lightweight, corrosion-resistant, and easily processable nature of polymers. Studies on $\hbox {BaTiO}_3$- and $\hbox {CaWO}_4$-reinforced polymers⁴ showed that increasing filler content (up to 20%) improves gamma-ray attenuation. At the same loading, $\hbox {CaWO}_4$ composites outperformed those with $\hbox {BaTiO}_3$. Monte Carlo work on LDPE/W composites⁵ found that tungsten additions up to 25 wt% enhance gamma-ray attenuation, and that filler proportion is more important than particle size. Simulations of glass fiber/PEEK composites with $\hbox {Gd}_2\hbox {O}_3$⁶ showed that higher $\hbox {Gd}_2\hbox {O}_3$ content strengthens both gamma-ray and fast neutron shielding. The 50 wt% sample outperformed paraffin and concrete and also reduced secondary radiation. $\hbox {B}_4$C/$\hbox {CrB}_2$-reinforced polymers⁷ also provided effective dual gamma-neutron protection. The BCCrB-50 composite had the highest attenuation and strong radiation resistance, making it a potential environmentally friendly alternative for nuclear applications. Ternary polyester/polyacrylonitrile composites reinforced with $\hbox {Gd}_2$($\hbox {SO}_4$)$_3$ have also been investigated, showing that gamma shielding improves with higher gadolinium content while neutron protection benefits from polyacrylonitrile loading⁸.

Among the polymers used for radiation shielding, high-density polyethylene (HDPE) is a widely used thermoplastic valued for its low cost, chemical stability, and mechanical strength. Its high hydrogen content makes it effective for neutron shielding, but its low-Z constituents limit gamma-ray attenuation. To overcome this limitation, high-Z fillers such as $\hbox {WO}_3$⁹, $\hbox {Bi}_2\hbox {O}_3$¹⁰, and CdO¹¹ have been incorporated into HDPE matrices, yielding improved performance. In $\hbox {WO}_3$–HDPE composites, both filler size and weight fraction strongly influence attenuation. Smaller $\hbox {WO}_3$ nanoparticles and higher loadings significantly improved performance, particularly at low photon energies, with results approaching those of conventional lead shielding. $\hbox {Bi}_2\hbox {O}_3$–HDPE systems also showed substantial improvements: increasing $\hbox {Bi}_2\hbox {O}_3$ content (10–50 wt%) enhanced gamma-ray attenuation across 0.0595–1.333 MeV. At 0.0595 MeV, the HVL of pure HDPE was 23 times higher than that of the 50 wt% composite, confirming the superior low-energy efficiency of $\hbox {Bi}_2\hbox {O}_3$. Similarly, CdO–HDPE composites exhibited marked improvements, especially at low energies. Nano-CdO fillers outperformed micro-CdO, with a relative increase of about 16% at 40 wt% loading and 59.53 keV, underscoring the role of particle size in enhancing shielding performance.

While these oxide- and metal-based fillers have demonstrated significant improvements in gamma-ray attenuation, they also present notable drawbacks. CdO raises toxicity concerns, $\hbox {Bi}_2\hbox {O}_3$ and $\hbox {WO}_3$ are heavy and can reduce processability, and their effectiveness is largely confined to low photon energies. This motivates the search for alternative fillers that combine high attenuation efficiency with safety, stability, and versatility. In this context, tantalum disulfide ($\hbox {TaS}_2$) represents a promising polymer-filler option. The heavy element tantalum (Z = 73) provides strong photon attenuation, particularly above its K-edge (67.4 keV), while the sulfide structure supports good dispersion in polymer matrices. Unlike CdO, $\hbox {TaS}_2$ offers a unique balance of high attenuation capability and lower toxicity risk. Yet, despite these advantages, no prior work has investigated $\hbox {TaS}_2$-based polymer composites for radiation shielding, leaving a clear gap in the literature. Addressing this gap forms the central motivation of the present study.

In this study, we investigate HDPE composites reinforced with $\hbox {TaS}_2$, focusing on their gamma-ray shielding performance. Photon mass attenuation coefficients ($\mu /\rho$) are evaluated using Geant4 simulations and validated against the NIST XCOM database¹². Composites with varying $\hbox {TaS}_2$ loadings are analyzed from 0.06 to 2.0 MeV, and results are benchmarked against CdO–HDPE¹¹ as well as conventional lead, concrete and concrete-based shielding¹³. The goal is to establish the shielding potential of $\hbox {TaS}_2$–HDPE as a lightweight, processable, and non-toxic alternative for next-generation radiation protection.

Materials and methods

Material composition

The investigated composites consist of high-density polyethylene (HDPE) as the polymer matrix and tantalum disulfide (TaS₂) as the high-Z filler. TaS₂ is composed of tantalum (Z = 73) and sulfur (Z = 16) atoms arranged in layered S–Ta–S units, covalently bonded within each layer and stacked via weak van der Waals forces¹⁴. This structure allows TaS₂ to be exfoliated into ultrathin sheets, which, when embedded in polymers, can introduce multiple interfaces that enhance photon attenuation.

Composite densities were calculated using the rule of mixtures from the known densities of HDPE (0.955 g/$\hbox {cm}^3$) and $\hbox {TaS}_2$ (6.86 g/$\hbox {cm}^3$). Simulated composites containing 10–50 wt% $\hbox {TaS}_2$ were prepared, with elemental compositions (Ta:S ratio and C/H content from HDPE) implemented consistently in both Geant4 and XCOM to ensure direct comparability. Table 1 summarizes the input parameters, including composite densities, filler loadings, and elemental weight fractions, which were explicitly used in all calculations.

Table 1 Material properties of $\hbox {TaS}_2$–HDPE composites, including densities, filler loadings, and elemental weight fractions.

From a safety perspective, $\hbox {TaS}_2$ is not classified as highly toxic. Safety data sheets report that it may cause skin and eye irritation, and respiratory irritation if inhaled¹⁵. It has low aquatic toxicity, is not bioaccumulative, and is non-persistent in the environment. As with other fine powders, it should be handled using appropriate safety measures to minimize inhalation and skin contact. Encapsulating $\hbox {TaS}_2$ within the HDPE matrix reduces user exposure compared with loose powders. Indeed, studies indicate that fillers such as graphene-related materials emit a negligible release under acute exposure when embedded in polymer matrices¹⁶. However, particulate controls and standard occupational measures remain necessary during compounding and any post-processing that can generate dust. Although no substance-specific occupational exposure limits have been established for $\hbox {TaS}_2$, guidance can be taken from tantalum metal and oxide dusts, for which both OSHA and ACGIH specify limits of 5 mg/$\hbox {m}^3$ (respirable fraction)¹⁷. These limits represent legally enforceable U.S. regulatory standards (PEL) and internationally recognized occupational health guidelines (TLV), respectively.

Theoretical framework

When gamma radiation passes through matter, its intensity decreases due to absorption and scattering. The primary interaction mechanisms responsible for this attenuation are the photoelectric effect, Compton scattering, and pair production. The extent of attenuation is quantified by the mass attenuation coefficient ($\mu /\rho$), which represents the probability of photon interaction per unit mass. This coefficient depends on both photon energy and the atomic composition of the material.

The attenuation of a monoenergetic, collimated photon beam follows the Beer–Lambert law:

$$\begin{aligned} I = I_0 e^{-\mu x} \end{aligned}$$

(1)

where $I_0$ is the incident photon intensity, I is the transmitted intensity, $\mu$ is the linear attenuation coefficient ($\hbox {cm}^{-1}$), and x is the material thickness (cm). Rearranging Eq. 1, the linear attenuation coefficient can be expressed as:

$$\begin{aligned} \mu = \frac{1}{x}\ln \left( \frac{I_0}{I}\right) \end{aligned}$$

(2)

To compute the mass attenuation coefficient, $\mu$ is normalized by the material density $\rho$ (g/cm³):

$$\begin{aligned} \frac{\mu }{\rho } = \frac{1}{x\rho }\ln \left( \frac{I_0}{I}\right) \end{aligned}$$

(3)

For materials containing more than one element, the effective atomic number ($Z_{\textrm{eff}}$) is calculated using¹³:

$$\begin{aligned} Z_{\textrm{eff}} = \frac{\sum f_i A_i {(\mu /\rho )}_i}{\sum {\frac{f_j A_j}{Z_j}({\mu /\rho )}_j}} \end{aligned}$$

(4)

where $f_i$ is the molar fraction of element i in the mixture, $A_i$ and $Z_i$ are its mass number and atomic number, and ${(\mu /\rho )}_i$ is the mass attenuation coefficient of this element.

The mean free path (MFP) is defined as the average distance that a photon travels in a given material before undergoing an interaction. It is mathematically expressed as the reciprocal of the linear attenuation coefficient, i.e., $\text {MFP} = 1/\mu$. This parameter provides a measure of the penetrability of a material by incident photons and is crucial for assessing shielding effectiveness. Another important quantity is the half-value layer (HVL), which denotes the thickness of material required to reduce the intensity of a monoenergetic photon beam to half its original value. It is related to the attenuation coefficient by the expression $\text {HVL} = \ln (2)/\mu$. Both MFP and HVL are fundamental indicators used to evaluate and compare shielding materials, offering insight into how efficiently a material can attenuate ionizing radiation across different energy ranges.

Radiation protection efficiency (RPE) is calculated from the transmission factor of photons through a material according to:

$$\begin{aligned} \textrm{RPE}(\%) = \left( 1 - \frac{I}{I_0} \right) \times 100\% \end{aligned}$$

(5)

The definition above ensures that RPE values range from 0% (no attenuation) to 100% (complete attenuation). RPE provides a convenient, dimensionless measure of shielding performance that allows direct comparison between materials of different thicknesses and compositions. It has also been widely applied in radiation-shielding studies to benchmark gamma-ray absorbers.

Monte Carlo simulation using Geant4

Monte Carlo simulations were performed using the Geant4 (version 11.2.2) toolkit to model photon interactions in the $\hbox {TaS}_2$–HDPE composite. The world volume was modeled as an air-filled box with dimensions 5 cm (x) $\times$ 2.5 cm (y) $\times$ 2.5 cm (z). The 2 cm-thick $\hbox {TaS}_2$–HDPE absorber slab was centered at $x=0$, with its front surface normal to the incident beam.

A monoenergetic, narrowly collimated pencil beam was used as the photon source. The beam originated at $(x,y,z) = (-2.0,0,0)$ cm and propagated along the $+x$-axis toward the center of the absorber. Photon energies in the range 0.06–2.0 MeV were simulated, with $10^6$ primary events per energy point, defining the incident photon intensity $I_0$ used in attenuation calculation. The initial beam had zero divergence, ensuring a strictly narrow-beam configuration consistent with exponential attenuation theory.

A dedicated sensitive detector was positioned immediately downstream of the absorber, separated by a 1 mm air gap to prevent geometric overlap. The detector was modeled as an air-filled volume with a thickness of 5 mm and transverse dimensions matching those of the absorber in the $y-z$ plane (2.0 cm $\times$ 2.0 cm). This ensured full coverage of the transmitted photon beam and guaranteed that all photons passing through the absorber were recorded for the determination of the transmitted intensity I. The ratio $I/I_0$ was then used to calculate the mass attenuation coefficient at each energy.

Electromagnetic interactions were modeled with the G4EmStandardPhysics_option4 physics list. It provides high-precision treatments of photoelectric absorption, Compton scattering, and pair production, as well as detailed atomic de-excitation processes. This physics constructor is well suited for gamma-ray transport and has been validated for the energy range considered in this work¹⁸. Production cuts were set to 1 $\mu$m within the absorber region to ensure accurate modeling of low-energy secondary particles, while default range cuts were maintained elsewhere. Material definitions in Geant4 used the same densities and elemental weight fractions listed in Table 1, ensuring consistency with the XCOM calculations.

Theoretical comparison with XCOM

To validate the Geant4 simulation results, theoretical mass attenuation coefficients were obtained from the XCOM Photon Cross Sections Database. XCOM provides photon interaction data for elements and compounds based on evaluated atomic cross sections and is widely used in radiation shielding analyses. In XCOM, the mass attenuation coefficient of a composite material is determined from its elemental values using the mixture rule:

$$\begin{aligned} {\left( \frac{\mu }{\rho } \right) }_\text {composite} = \sum _i w_i \left( \frac{\mu }{\rho } \right) _i \end{aligned}$$

(6)

where $w_i$ is the weight fraction of the $i^\text {th}$ element in the composite, and $\left( \mu /\rho \right) _i$ is the elemental mass attenuation coefficient from XCOM. This method was applied to the $\hbox {TaS}_2$–HDPE composite by combining the contributions from tantalum, sulfur, carbon, and hydrogen. The theoretical values were then compared point-by-point with the Geant4 simulation results. The relative deviations (RD%) between XCOM and Geant4 values were computed using:

$$\begin{aligned} RD(\%) = \frac{(\mu /\rho )_{\text {XCOM}} - (\mu /\rho )_{\text {G4}} }{(\mu /\rho )_{\text {XCOM}}} \end{aligned}$$

(7)

Uncertainty estimation

To ensure the reliability of the simulated mass attenuation coefficients, statistical uncertainties were estimated based on the number of photons transmitted through the material. Assuming Poisson statistics, the absolute uncertainty in the transmitted photon count was estimated as $\delta I = \sqrt{I}$. Given that the initial number of photons $I_0$ is a fixed input in the simulation, its uncertainty was considered negligible. The uncertainty in the linear attenuation coefficient (see Eq. 2) was propagated from $\delta I$ as follows:

$$\begin{aligned} \delta \mu = \frac{1}{x} \cdot \frac{\delta I}{I} = \frac{1}{x\sqrt{I}}. \end{aligned}$$

(8)

The uncertainty in the mass attenuation coefficient $\mu /\rho$ was then obtained by normalizing $\delta \mu$ by the material density $\rho$, such that

$$\begin{aligned} \delta (\mu /\rho ) = \frac{\delta \mu }{\rho } = \frac{1}{x\rho \sqrt{I}}. \end{aligned}$$

(9)

The uncertainties in the mean free path (MFP) and half-value layer (HVL) were obtained by propagating the statistical errors according to standard error propagation rules, as expressed in the following equations:

$$\delta (\text {MFP}) = \frac{\delta \mu }{\mu ^2}, \quad \delta (\text {HVL}) = \frac{\ln (2)}{\mu ^2} \cdot \delta \mu .$$

For XCOM data, we assigned a fixed uncertainty of 2% for each value to account for theoretical modeling limitations. This value is supported by Hubbell’s comprehensive review of photon cross-section data, which suggests an envelope of uncertainty of approximately 1–2% (at 68% confidence level) for photon energies ranging from 5 keV to several MeV¹⁹. The upper bound of this range (2%) was chosen as a conservative estimate to ensure that all systematic deviations are captured, particularly when comparing composite materials with complex atomic compositions. The total uncertainty associated with the comparison between the Geant4-simulated and XCOM-derived mass attenuation coefficients was calculated using standard error propagation:

$$\begin{aligned} \delta _{\text {tot}} = \sqrt{\bigg (\frac{\delta (\mu /\rho )_{G4}}{(\mu /\rho )_{G4}}\bigg )^2 + \bigg (\frac{\delta (\mu /\rho )_{XCOM}}{(\mu /\rho )_{XCOM}}\bigg )^2 } \times 100\% \end{aligned}$$

(10)

Results and discussion

Attenuation coefficients and shielding parameters

Table 2 summarizes the Geant4- and XCOM-derived mass attenuation coefficients, together with the corresponding mean free path (MFP), half-value layer (HVL), and propagated uncertainties in the 60–300 keV range. This overview highlights the systematic improvements in attenuation performance with increasing $\hbox {TaS}_2$ loading. The complete dataset across the full energy spectrum is provided in Supplementary Table S1.

Fig. 1a shows the Geant4-simulated mass attenuation coefficients $(\mu /\rho )$ for pure HDPE and TaS₂–HDPE composites containing 10, 20, 35, and 50 wt% TaS₂ over the energy range 0.06–2.0 MeV. All compositions exhibit the expected energy dependence, with a pronounced peak at low energies driven by the photoelectric effect, followed by a monotonic decrease as Compton scattering becomes the dominant interaction mechanism.

At 80.0 keV, where attenuation enhancement is most significant, the 50 wt% composite reaches a $(\mu /\rho )$ of $2.88 \pm 0.04$ $\hbox {cm}^2$/g, corresponding to a $15.9 \pm 0.2$-fold improvement over pure HDPE. The 35 wt% composite improves attenuation by $11.55 \pm 0.05$ times, the 20 wt% composite by $7.07 \pm 0.03$ times, and the 10 wt% composite by $4.04 \pm 0.02$ times. The performance gain scales systematically with filler content, reflecting the strong photoelectric cross-section of tantalum in this energy range.

For comparison, the attenuation performance of ordinary concrete from XCOM is included in Fig. 1a. At 80 keV, concrete exhibits a mass attenuation coefficient of $\sim$0.201 $\hbox {cm}^2$/g, which is substantially lower than that of the $\hbox {TaS}_2$–HDPE composites. Even the 10 wt% sample (0.73 $\hbox {cm}^2$/g) surpasses concrete, while the 50 wt% composite achieves more than fourteen times higher attenuation at the same energy. In fact, all $\hbox {TaS}_2$–HDPE composites outperform concrete up to $\sim$300 keV, where the curves start to merge. Beyond 1 MeV, all compositions approach the attenuation level of pure HDPE. This behavior is consistent with theoretical expectations: the high-Z filler provides its greatest benefit between 80 and 200 keV (photoelectric regime), while differences diminish as Compton scattering becomes dominant at higher energies.

The effective atomic number ($Z_{\textrm{eff}}$) of the $\hbox {TaS}_2$–HDPE composites shows a clear increasing trend with higher $\hbox {TaS}_2$ content (Fig. 1b). This effect is particularly pronounced in the low- to medium-energy range, reaching a maximum value at 80 keV. The enhancement at this energy can be attributed to the dominance of photoelectric absorption, whose cross section scales strongly with atomic number, thereby amplifying the contribution of high-Z tantalum to the overall attenuation.

Figs. 1c and 1d present the mean free path (MFP) and half-value layer (HVL), respectively, as functions of photon energy for pure HDPE and $\hbox {TaS}_2$–HDPE composites. Both parameters exhibit the expected energy dependence: a pronounced decrease at low photon energies, a minimum in the intermediate-energy range, and a gradual increase at higher energies. Increasing the TaS₂ content systematically reduces both MFP and HVL, indicating enhanced attenuation efficiency.

Table 2 Mass attenuation coefficients ($\mu /\rho$), mean free path (MFP), and half-value layer (HVL) for $\hbox {TaS}_2$–HDPE composites at different weight fractions in the 60–100 keV energy range.

Fig. 1

Attenuation-related results for HDPE composites with varying TaS₂ content: (a) Mass attenuation coefficients (MAC), (b) effective atomic number ($Z_{\textrm{eff}}$), (c) mean free path (MFP), and (d) half-value layer (HVL). For reference, XCOM-derived data for ordinary concrete are included in (a), (c), and (d).

At 80.0 keV, the MFP reductions relative to pure HDPE are $77.30 \pm 0.08$%, $88.25 \pm 0.04$%, $93.93 \pm 0.03$%, and $96.41 \pm 0.05$% for the 10, 20, 35, and 50 wt% composites, respectively. The HVL exhibits identical percentage reductions with the same uncertainties at this energy, reflecting the direct proportionality between MFP and HVL. By contrast, the XCOM-derived HVL of lead at 80 keV is only $\sim$0.025 cm, whereas the 50 wt% $\hbox {TaS}_2$–HDPE composite reaches 0.143 cm. This highlights the superior attenuation efficiency of Pb due to its high density, but also shows that the composite achieves competitive performance on a mass-normalized basis.

As shown in Fig. 1d, all $\hbox {TaS}_2$–HDPE composites exhibit lower HVL values than concrete (gray dashed line) in the 80–100 keV range, confirming their superior attenuation efficiency at low photon energies. However, above $\sim$400 keV, concrete begins to outperform the composites, reflecting its higher density and greater effectiveness in the Compton-dominated regime. Notably, even at a relatively low filler loading of 20 wt%, the $\hbox {TaS}_2$–HDPE composite achieves an HVL of 0.47 cm at 80 keV, lower than values reported for brass- and $\hbox {B}_4$C-reinforced concretes (e.g., 0.66 cm for P50 at 81 keV)¹³. This indicates that modest $\hbox {TaS}_2$ additions can already deliver shielding performance competitive with heavily modified concretes. Above 1.0 MeV, differences among all compositions become minimal for both MFP and HVL.

Nevertheless, the results show that incorporating $\hbox {TaS}_2$ into HDPE substantially enhances gamma-ray attenuation in the low- to mid-energy range, and that filler loading can be tuned to match the energy distribution of specific radiation environments.

Fig. 2

Radiation protection efficiency (RPE) of pure HDPE and HDPE composites containing 10–50 wt% TaS₂ as a function of photon energy.

The radiation protection efficiency (RPE) was calculated using Eq. 5 for pure HDPE and $\hbox {TaS}_2$–HDPE composites with varying filler contents. The results (Fig. 2) show that pure HDPE exhibits low RPE values (10–35%) across the investigated photon energy range, consistent with its low-Z constituents. In contrast, the incorporation of $\hbox {TaS}_2$ markedly enhances RPE, particularly in the 60–300 keV region. For the 50 wt% composite, RPE values reach 99.2% at 60 keV, 99.99% at 80 keV, and 99.65% at 100 keV, demonstrating nearly complete attenuation in this energy range. This sharp improvement is directly linked to the Ta K-edge. At higher photon energies (>300 keV), the RPE values of all composites decrease and gradually converge toward those of pure HDPE.

The enhanced attenuation observed in the 60–300 keV range has direct implications for practical radiation shielding. Superficial and orthovoltage X-ray treatments, widely used in radiotherapy, typically employ photon beams between 50 and 320 kVp²⁰, corresponding to photon spectra extending up to 50–320 keV. The superior performance of $\hbox {TaS}_2$–HDPE composites in this interval therefore indicates their suitability for medical shielding applications, offering safer and more efficient alternatives to traditional Pb- or CdO-based materials.

In addition to medical and industrial contexts, the enhanced attenuation observed in the 60–300 keV range also has relevance for space radiation protection. Although galactic cosmic rays (GCRs) and solar energetic particles (SEPs) primarily consist of protons and heavy ions, their interactions with spacecraft materials produce abundant secondary photons in the tens to hundreds of keV range^21,22. Shielding against these secondary gamma rays is critical for protecting both crew and electronic systems. The superior low-to-mid energy attenuation of $\hbox {TaS}_2$–HDPE, combined with the intrinsic hydrogen-rich matrix of HDPE that is effective for neutron moderation and charged-particle slowing, highlights the potential of these composites as multifunctional shielding layers in spacecraft design.

Relative deviation from XCOM

The relative deviation (RD%) between the Geant4-simulated and XCOM-calculated mass attenuation coefficients was evaluated for each photon energy and composite ratio using Eq. 7, and the results are summarized in Table 3. Over the full energy range investigated (0.06–2.0 MeV), the RD% values remained within the total uncertainty (Eq. 10) for the majority of compositions. All deviations were below 3%, with the strongest agreement observed in the intermediate energy region (0.08–0.2 MeV), where all RD% values were well within the total uncertainty limits. However, at the lowest energy point (0.06 MeV), the RD% exceeded the total uncertainty for the 20%, 35%, and 50% $\hbox {TaS}_2$ composites, indicating a modest but noticeable discrepancy. This behavior is attributed to the enhanced sensitivity of photon–matter interactions in the photoelectric-dominated region around 60 keV. In this regime, even small differences in material composition or atomic cross-section modeling can lead to amplified deviations²³. Furthermore, for each beam energy, RD% was observed to increase systematically with increasing $\hbox {TaS}_2$ content.

Table 3 Relative deviation (RD%) between XCOM and Geant4 across TaS₂ weight fractions and energies.

Comparison with CdO–HDPE composites

To highlight the effect of filler atomic number and K-edge position, we compared the shielding performance of $\hbox {TaS}_2$–HDPE with experimental data for CdO–HDPE composites at 10, 20, 30, and 40 wt%¹¹. Cd was chosen as a benchmark because CdO–HDPE has been widely studied as a polymer composite shield. In addition, cadmium’s lower K-edge (26.71 keV) allows us to directly illustrate the advantage provided by tantalum’s higher K-edge (67.4 keV). In that study, both micro- and nano-sized CdO–HDPE were investigated. Here, we chose to compare with the micro-CdO–HDPE samples because our Geant4 model assumes a homogeneous bulk mixture with size-independent photon cross sections, making the micro samples more representative of the simulation conditions. The same photon energies and material thickness were used to assess the effect of replacing CdO with $\hbox {TaS}_2$. Table 4 presents the comparison results for photon energies from 59.53 keV to 1.4 MeV.

At the lowest energy considered (59.53 keV), CdO–HDPE shows higher $(\mu /\rho )$ for all loadings. This is due to Cd’s strong photoelectric effect above its K-edge and the fact that Ta’s K-edge is not yet reached. Increasing $\hbox {TaS}_2$content improves attenuation, but CdO remains superior at this energy.

At 80.99 keV, a distinct reversal is observed for all loadings: $\hbox {TaS}_2$–HDPE exhibits substantially higher $(\mu /\rho )$ than CdO–HDPE, with the advantage increasing at higher filler contents. This is due to the sharp rise in Ta’s photoelectric cross-section immediately above its K-edge, whereas Cd’s cross-section has already declined significantly. The largest relative performance gain of $\hbox {TaS}_2$ over CdO at this energy is seen at 40 wt%, showing that higher filler loading and the sharp increase in Ta’s photoelectric absorption above its K-edge combine to maximize attenuation.

Between 122 keV and 356 keV, $\hbox {TaS}_2$–HDPE maintains a clear advantage across all percentages. However, the relative difference compared to CdO–HDPE narrows slightly as the photoelectric contribution diminishes and Compton scattering becomes dominant. Increasing the $\hbox {TaS}_2$ fraction continues to improve attenuation, but the gains are more modest compared to the post-K-edge low-energy region. Above 600 keV, the differences between the two materials become small for all loadings. Nevertheless, $\hbox {TaS}_2$–HDPE retains a slight advantage in most cases, consistent with the higher atomic number of Ta enhancing pair-production cross-sections.

Table 4 Comparison of mass attenuation coefficients $(\mu /\rho )$ in $\hbox {cm}^2$/g for $\hbox {TaS}_2$–HDPE and CdO–HDPE composites at different weight fractions and photon energies.

Overall, the comparison shows that increasing filler content improves attenuation for both materials, but the magnitude and energy dependence of this improvement differ. CdO–HDPE is superior below $\sim$70 keV for all loadings, while $\hbox {TaS}_2$–HDPE becomes more effective above Ta’s K-edge. The performance gap between the two materials widens at higher loadings in the 70–300 keV range. These findings suggest that application-specific filler selection should consider both the operating energy spectrum and the maximum achievable filler fraction.

The complementary attenuation characteristics of CdO–HDPE and $\hbox {TaS}_2$–HDPE suggest potential benefits from their combined use in a graded-Z shielding configuration. In such an approach, layers of materials with different atomic numbers and absorption edges are stacked to optimize performance across a broad photon energy spectrum. By sequentially layering CdO-rich and $\hbox {TaS}_2$-rich composites, it may be possible to exploit the superior low-energy performance of CdO together with the post-K-edge attenuation of $\hbox {TaS}_2$, thereby broadening the effective shielding range for mixed or unknown photon spectra.

Similar graded-Z strategies have been successfully applied in other contexts. Atwell et al.²⁴ investigated two-layer shields such as Al–HDPE, Ta–HDPE, and W–HDPE, showing that layering high-Z metals with polymers can significantly enhance radiation protection compared to single-material configurations. Likewise, Daneshvar et al.²⁵ designed multilayer graded shields for satellite electronics using Al-bronze, Mo, and Cu, and demonstrated superior resistance against electron and proton irradiation. These examples highlight the effectiveness of combining materials with different atomic numbers and absorption edges, supporting the potential of CdO/$\hbox {TaS}_2$ polymer composites in graded-Z designs for gamma-ray shielding. Taken together, this concept emphasizes the importance of considering not only individual fillers but also their synergistic integration in multilayer architectures for next-generation radiation protection.

Conclusion

This study evaluated the photon attenuation performance of $\hbox {TaS}_2$–HDPE composites with varying filler contents using Geant4 Monte Carlo simulations validated against XCOM theoretical data. The results demonstrate that incorporating $\hbox {TaS}_2$ substantially enhances gamma-ray attenuation in the low- to mid-energy range. At the highest loading fraction, reductions in mean free path and half-value layer exceed 96% at 80 keV. Comparative analysis with experimental data for micro-CdO–HDPE showed that $\hbox {TaS}_2$–HDPE outperforms CdO-based composites above Ta’s K-edge (67.4 keV), with the most pronounced relative advantage in the 70–300 keV range. At energies below $\sim$70 keV, CdO remains more effective due to its lower K-edge and stronger photoelectric absorption. These findings highlight $\hbox {TaS}_2$–HDPE as a promising, tunable shielding material, with performance strongly dependent on both photon energy and filler fraction. The choice between $\hbox {TaS}_2$ and alternative fillers such as CdO should therefore be guided by the target energy spectrum and application-specific design requirements.

Although conventional shielding materials such as lead and concrete remain widely employed, they are limited by toxicity, high weight, and the need for large thicknesses. In contrast, $\hbox {TaS}_2$–HDPE is lighter, processable, chemically stable, and non-toxic, while providing competitive attenuation efficiency. At 80 keV, where enhancement is most significant, our composites outperform ordinary concrete and concrete-based alloys (e.g., brass- or $\hbox {B}_4$C-reinforced concretes). These results underscore their potential as safer, versatile candidates for next-generation radiation protection, with direct relevance to medical X-ray shielding and promising multifunctional applications in space environments.

Summary statement

$\hbox {TaS}_2$–HDPE composites offer tunable, high-efficiency gamma-ray attenuation, outperforming CdO–HDPE above Ta’s K-edge. Their energy-selective behavior makes them strong candidates for next-generation medical and space radiation shielding applications.