High-density lead-free alloys for compact and sustainable photon shielding: a Monte Carlo and benchmarking study

Abstract

The quest for next-generation radiation shielding hinges on finding lead-free alloys that balance high density with environmental safety. In this work, we targeted three transition metal arsenides (VAs, MoAs, and TaAs) to determine their efficacy against ionizing radiation across a wide energy range from 0.015 MeV to 15 MeV. By leveraging the Geant4 Monte Carlo toolkit and benchmarking against the XCOM database, we achieved high-fidelity simulations with deviations below 1%. Among the candidates, TaAs demonstrated the highest photon attenuation efficiency, characterized by a linear attenuation coefficient of μ = 1.463 cm⁻¹ at 0.5 MeV and a half-value layer of λ_½ = 0.47 cm at 0.5 MeV. Critically, at a thickness of 0.1 cm, TaAs delivers a dose reduction of over 50% relative to VAs. Statistical reliability was rigorously validated using the Kolmogorov–Smirnov test (p = 1.00), confirming no significant difference between simulated and theoretical XCOM data distributions. These findings establish TaAs not merely as a replacement for conventional materials, but as compact, lead-free shielding alternative optimized for space-constrained diagnostic systems.

Introduction

The mitigation of radiation exposure in medical diagnostics and nuclear facilities necessitates the continuous development of advanced shielding materials. However, a primary challenge lies in engineering barriers that reconcile high attenuation efficiency with lightweight and compact structural designs. Historically, radiation protection has relied on concrete and lead (Pb). While effective, Pb possesses significant drawbacks, including high toxicity, low mechanical strength, and a low melting point that can lead to radiation leakage under prolonged thermal exposure¹. Similarly, concrete-based materials are susceptible to dehydration and cracking over time, which compromises their structural integrity and absorption efficiency due to density fluctuations^2,3. To address these limitations, various material classes have emerged as potential candidates. Ceramic and glass systems offer transparency and ease of fabrication but are often limited by brittleness and lower adaptability in high-energy environments. Polymeric nanocomposites and ferrites provide flexible and tunable shielding properties through the incorporation of high-Z nanoparticles, such as bismuth or tungsten, yet they may struggle with thermal stability and high filler loading requirements^4–20. In contrast, alloys offer a superior balance of mechanical durability and high mass density, making them ideal for high-intensity environments^21–26. Recent studies have highlighted the transition toward lead-free alloy systems to reconcile high attenuation efficiency with environmental safety^26–29. Specifically, experimental and theoretical investigations into lead-free alloy compositions have demonstrated that optimizing the atomic mass and density can significantly enhance gamma-ray shielding performance³⁰. While other materials like polymeric nanocomposites and ferrites provide flexible shielding through high-Z nanoparticle fillers, transition metal alloys remain the most robust candidates for compact and sustainable shielding solutions.

This study addresses the need for high-performance shielding by investigating a new set of lead-free, transition metal arsenide-based alloys: VAs, MoAs, and TaAs. These materials were selected for their high mass densities—ranging from 6.88 to 12.21 g/cm³—as well as their chemically stable and cost-effective synthesis via traditional solid-state reaction. Utilizing the Geant4 Monte Carlo toolkit^31,32, we simulated the linear attenuation coefficients (μ) and various shielding parameters (mean free path, radiation protection efficiency, and effective atomic number) across a wide energy spectrum of 0.015–15 MeV. The results are rigorously benchmarked against the XCOM database, Phy-X and PAGEX software^33–35 and validated using the Kolmogorov–Smirnov test to establish TaAs as a highly compact and efficient solution for modern radiationenvironments. Finally, the scientific novelty of this work lies in investigating transition metal arsenides, a class of high-density materials largely unexplored for radiation protection. By establishing TaAs as a high-performance benchmark, this study provides the theoretical foundation required to shift from lead-based systems to more compact, high-Z alloy alternatives.

Materials and simulation framework

Three lead-free arsenide alloys (VAs, MoAs, and TaAs) were selected for this evaluation due to their optimal physicochemical profile, which combines chemical inertness, mechanical stability, and environmental safety with cost-effective fabrication. Critically, these alloys possess high densities of 6.88 g/cm³ (VAs), 8.72 g/cm³ (MoAs), and 12.21 g/cm³ (TaAs), a fundamental requirement for effective radiation shielding^36–38. The modeled materials correspond to polycrystalline powders synthesized via a direct solid-state reaction route, following protocols established in prior literature^39–41.

For the computational assessment, we employed the Geant4 Monte Carlo toolkit (a C + + based simulation framework) to model the transport and interaction of ionizing radiation within the target al.loys⁴². As a simulation toolkit, Geant4 requires users to possess a solid understanding of its structure and functionalities in order to effectively implement and customize its components. Users are expected to write their own code to tailor the simulations to specific applications. In this study, the Geant4 Monte Carlo toolkit was employed to simulate the linear attenuation coefficient (μ) of the selected alloys, based on the Beer–Lambert law⁴³:

1

Here, denotes the intensity of the incident (primary) photon beam, represents the intensity of the transmitted (attenuated) beam after passing through the material, and corresponds to the thickness of the sample. Initially, was obtained by simulating primary photons in the absence of any shielding material. Subsequently, the transmitted intensity was calculated after incorporating the simulated alloy samples into the geometry. In addition, Simulations were performed using G4EmLivermorePhysics physics list to accurately model low-energy electromagnetic interactions. Tracking was controlled with a 0.01 mm maximum step size and a 0.1 mm production cut for photons and electrons. Simple geometry has been used in this study. Figure 1 presents a schematic representation of the simulation geometry constructed using the Geant4 toolkit. The shielding sample, shown in pink, was modeled with a fixed thickness of 1 cm. A cylindrical sodium iodide (NaI) detector (yellow) with a radius of 7.5 cm and a length of 5 cm was placed at the left boundary of a cubic world volume measuring 50 × 50 ×  50 cm³. A sensitive detector volume scored uncollided primary photons to ensure narrow-beam geometry compliance. Statistical convergence was monitored, with runtimes averaging 30 min per energy point to ensure δ < 0.1%. On the opposite side, a photon source (in blue) emitting photons of varying energies was positioned to direct a beam toward the detector. To ensure a well-collimated pencil beam, two lead (Pb) collimators were included in the setup: one with a 1 cm inner radius adjacent to the sample, and another encasing the detector (in gray).

Fig. 1.

a A collimated beam of photons (green) hits a shielding material (pink). The secondaries shown in red are negatively charged particles. b The simulation geometry employed in this study using the Geant4 Monte Carlo toolkit. The blue cylinder represents the photon emitter, gray cylinders correspond to lead collimators, the pink disk denotes the shielding material under investigation, and the yellow cylinder represents the NaI detector used for photon detection.

Statistical convergence was strictly monitored to ensure the reliability of the results. By simulating 10⁶ primary photon histories per energy point, the relative statistical uncertainty (δ) for the transmitted flux was maintained at δ < 0.1%. The standard uncertainty σ(μ) for the linear attenuation coefficient (not shown) was calculated based on the propagation of these statistical fluctuations through the Beer-Lambert law:

2

where I is the number of detected photons.

The results are benchmarked with the data obtained from XCOM database produced by National Institute of Standards and Technology, Gaithersburg, MD according to:

3

From the simulated , different important shielding parameters were calculated such as half-value layer (), mean-free path (), transmission factor (), radiation protection efficiency (), kinetic energy released in a material per unit mass KERMA ( relative to the air, the dose rate at a distance from a source, and effective atomic number (). These parameters can be calculated using the following equations:

4

5

6

7

8

Here, is the atomic mass, is the number of atoms of the i^th constituent element, is the atomic number, and is the mass density⁴⁴.

9

10

Where is the gamma constant, is the activity of the source, and is the distance from the source. More details of these parameters can be found in the literature^45–49.

Results and discussion

Figure 2 shows the variation of the mass attenuation coefficient, or MAC, as a function of photon energy, on a log-log scale, for XAs samples with X = V, Mo, or Ta. The MAC values exhibit a clear three-region behavior, governing by the dominant photon interaction mechanism. In the low-energy range, below 0.1 MeV, the MAC values are significantly high for all investigated samples, as expected, due to the photo-electric effect (), which dominates this region. It is worth mentioning that is strongly dependent on the atomic number and explains why TaAs sample exhibits the highest MAC values, followed by MoAs and Vas. For example, at 0.015 MeV, the MAC records 74.776 cm²/g, 59.233 cm²/g, and 123.633 cm²/g for VAs, MoAs, and TaAs respectively. As energy increases, a steep decline is observed due to rapid drop in photo-electric cross-section. In the intermediate region, between up to 1 MeV, the MAC decreases more gradually as Compton scattering becomes the dominant interaction mechanism. In this region, attenuation is primarily affected by electron density rather than atomic number, resulting in narrowing the difference between the samples. However, TaAs alloy still has a slight advantage due to its higher density and overall interaction probability. As photon energy increases, above 1.022 MeV, the MAC continues to decrease but tends to flatten due to the onset of pair-production () mechanisms. The hierarchy TaAs > MoAs > VAs arises from the Z-dependence of the photoelectric and pair-production cross-sections, combined with the higher mass density of TaAs, which increases the overall interaction probability. In the Compton region, differences narrow because electron density rather than Z dominates.

Fig. 2.

Mass attenuation coefficient (MAC) as a function of photon energy for VAs, MoAs, and TaAs alloys used in this study.

To quantify and validate these findings, Table 1 shows a detailed comparison of the linear attenuation coefficients () for all alloy samples in this study calculated using both the Geant4 MC toolkit and the XCOM photon cross-section database across the photon energy range of 0.015–15 MeV. Additionally, the percentage difference () between the two datasets is included to assess the accuracy of the Geant4 simulations. Across all alloy samples and energies, the values show the expected energy dependence, high at low energies due to the dominance of and gradually decreasing as photon energy increases due to the transition to and, at higher energies, . The percentage differences between Geant4 and XCOM are consistently low, typically well below 1% for MoAs and TaAs alloys, and remain within the acceptable uncertainty margin for VAs alloys where minor discrepancies appear at certain energy points, such as 0.06 MeV to 0.2 MeV, but even the largest deviation does not exceed approximately 3.8% which reflects strong overall agreement. These results confirm that the accuracy and power of the Geant4 MC toolkit in calculating for different shielding materials. Moreover, the low values across three distinct alloy systems reinforce the robustness and general applicability of the simulation approach.

Table 1.

Linear attenuation coefficient (µ) for VAs, MoAs, and TaAs alloys were evaluated using both Geant4 MC toolkit and XCOM database over a range of photon energies of 0.15 MeV to 15 MeV. The corresponding percentage differences (Δ%) between the two methods are also reported.

Energy (MeV)	Linear attenuation coefficient μ (cm−1)
	VAs			MoAs			TaAs
	XCOM	Geant4	Δ%	XCOM	Geant4	Δ%	XCOM	Geant4	Δ%
0.015	514.4567	514.1333	0.0629	516.5125	516.5125	0.0000	1509.5614	1509.5614	0.0000
0.02	236.1539	235.2844	0.3682	564.0150	564.0150	0.0000	710.1344	710.1344	0.0000
0.03	77.1473	77.7474	0.7779	195.1373	195.1373	0.0000	242.6924	242.6924	0.0000
0.04	34.5727	34.9658	1.1369	89.2049	89.2049	0.0000	112.7202	112.7202	0.0000
0.05	18.6379	18.5114	0.6786	48.3662	48.3662	0.0000	62.3688	62.3688	0.0000
0.06	11.3732	11.0118	3.1780	29.3497	29.3497	0.0000	38.6926	38.6926	0.0000
0.08	5.4348	5.4386	0.0692	13.5457	13.5457	0.0000	69.1964	69.1964	0.0000
0.1	3.2465	3.2624	0.4883	7.6483	7.6483	0.0000	39.2684	39.2684	0.0000
0.15	1.5425	1.5666	1.5673	3.0633	3.0633	0.0001	14.1558	14.1558	0.0000
0.2	1.0708	1.0920	1.9735	1.8436	1.8436	0.0002	7.1760	7.1761	0.0000
0.3	0.7587	0.7553	0.4500	1.1147	1.1147	0.0003	3.1304	3.1304	0.0000
0.4	0.6352	0.6346	0.0986	0.8727	0.8727	0.0003	1.9605	1.9605	0.0002
0.5	0.5631	0.5616	0.2603	0.7490	0.7490	0.0006	1.4631	1.4631	0.0001
0.6	0.5129	0.5119	0.2000	0.6705	0.6705	0.0007	1.1968	1.1968	0.0003
0.8	0.4438	0.4461	0.5246	0.5703	0.5703	0.0008	0.9194	0.9194	0.0004
1	0.3962	0.4055	2.3301	0.5051	0.5051	0.0005	0.7720	0.7720	0.0003
1.5	0.3224	0.3259	1.0737	0.4090	0.4090	0.0002	0.5964	0.5964	0.0004
2	0.2822	0.2857	1.2453	0.3603	0.3603	0.0007	0.5274	0.5274	0.0001
3	0.2414	0.2473	2.4296	0.3152	0.3152	0.0005	0.4769	0.4769	0.0010
4	0.2225	0.2244	0.8590	0.2972	0.3172	6.7283	0.4648	0.4648	0.0009
5	0.2129	0.2113	0.7768	0.2903	0.2903	0.0000	0.4664	0.4664	0.0005
6	0.2081	0.2003	3.7825	0.2885	0.2885	0.0004	0.4739	0.4739	0.0001
8	0.2057	0.2123	3.2057	0.2928	0.2928	0.0003	0.4964	0.4964	0.0004
10	0.2076	0.2063	0.6211	0.3013	0.3013	0.0002	0.5219	0.5219	0.0007
15	0.2170	0.2172	0.0759	0.3250	0.3250	0.0009	0.5837	0.5837	0.00074

Figure 3 shows a graphical representation of the data in Table 1, versus photon energy, for the three lead-free alloys studied in this work as obtained via Geant4 simulations compared to XCOM theoretical values to capture the key photon interaction with alloy samples. Across the entire spectrum, TaAs displays the highest values, followed by MoAs and then VAs. For example, at 0.05 MeV, Geant4 yields 18.5 cm^− 1, 48.4 cm^− 1, and 62.4 cm^− 1 for VAs, MoAs, and TaAs alloys respectively. In the intermediate energy region, 0.5 MeV for instance, the values drop significantly across all alloy samples to 0.56 cm^− 1, 0.75 cm^− 1, and 1.46 cm^− 1 for VAs, MoAs, and TaAs respectively. This region is dominated by as mentioned elsewhere. As higher energies, for example 5 MeV, values further decline, with Geant4 giving 0.21 cm^− 1, 0.29 cm^− 1, and 0.47 cm^− 1 for VAs, MoAs, and TaAs respectively, preserving the trend of TaAs > MoAs > VAs. More importantly, the good agreement between the simulated via Geant4 MC toolkit and the theoretical data obtained from XCOM standard database confirms the high reliability of the Geant4 model in simulating photon attenuation behavior predicted by standard theoretical databases.

Fig. 3.

Linear attenuation coefficients (μ) versus photon energy for a VAs, b MoAs, and c TaAs, calculated using Geant4 and benchmarked against XCOM values. The strong agreement supports simulation reliability.

Following the close numerical and graphical agreement between the data simulated using Geant4 and the theoretical data from XCOM database for VAs, MoAs, and TaAs alloy samples, a statistical evaluation was conducted to further validate the consistency between the two datasets. Figure 4 shows the cumulative distribution functions ( of and applies the Kolmogorov-Smirnov ( test to quantitatively assess their distributional similarity along with the maximum deviation and the associated reported in each subplot. Starting with VAs alloy, the test yield a of 0.0761 and a of 1.00, indicating no statistically significant difference between the obtained from both Geant4 and XCOM. Similarly, MoAs and TaAs show values of 0.04 and 0.10, respectively, both with of 1.00. These far exceed the typical threshold of 0.05, confirming strong statistical agreement between the two datasets for all alloys investigated in this study^50–52. In addition, the nearly overlapping CDF curves visually reinforce this conclusion. The result further confirms Geant4 MC toolkit ability to simulate the ionizing radiation shielding properties with high statistical fidelity for dense, high-Z alloys.

Fig. 4.

Cumulative distribution functions (CDFs) of μ values obtained from Geant4 and XCOM for a VAs, b MoAs, and c TaAs. K–S test results confirm statistical consistency with p = 1.00 for all samples.

To better understand which interaction mechanism dominates at each energy region and how the material composition affects the interaction regime, Fig. 5 shows the percentage contribution of to the total as a function of photon energy for VAs, MoAs, and TaAs alloy samples. At low photon energies, below 0.1 MeV, the contribution from is minimal, below 10% for all alloys, due to the overwhelming dominance of the . In this regime, the is heavily affected by the presence of high-Z elements, explaining the low relative contribution from Compton interactions. As energy increases into the intermediate range, becomes the dominant interaction mechanism, with its contribution peaking (100%) near 1 MeV. Beyond 2 MeV, the Compton fraction declines as pair production mechanisms become significant, a trend most pronounced in the high-Z TaAs alloy. This behavior reinforces the established interaction hierarchy: governs shielding in the low-energy regime (favoring high-Z materials), whereas dominates attenuation across the intermediate energy range. Consequently, optimal material selection is strictly dependent on the incident radiation spectrum. To rigorously quantify the shielding efficiency of these alloys, we evaluated several key performance parameters.

Fig. 5.

Fractional contribution of Compton scattering to the total μ as a function of photon energy for VAs, MoAs, and TaAs, indicating interaction regime transitions.

Across the entire energy range, the total uncertainty in Geant4-derived µ does not exceed ~ 0.1%, in line with typical electromagnetic simulation studies.

Figure 6 presents the energy-dependent variation of two critical shielding parameters, (a) half-value layer () and (b) mean-free path () for the VAs, MoAs, and TaAs alloys. These parameters provide practical insight into the thickness requirements of shielding materials for effective gamma attenuation. Consistent with fundamental theory, both and exhibit a positive correlation with photon energy across all samples. This trend stems directly from the inverse relationship between incident energy and , necessitating thicker material layers to compensate for the reduced interaction probability at higher energy levels. The lowest and values are observed at low energies where the photoelectric effect dominates, while the highest values occur at high energies where pair production begins to emerge, but attenuation is less efficient. At all energy levels, TaAs alloy displays the lowest and values, followed by MoAs and then VAs. For instance, at 0.5 MeV, the values are approximately 0.47 cm, 0.92 cm, and 1.23 cm, for TaAs, MoAs, and VAs, respectively, corresponding to their respective values. This hierarchy remains consistent across the spectrum and emphasizes the superior shielding efficiency of TaAs due to its higher mass density and atomic number.

Fig. 6.

a Half-value layer and b mean free path as functions of photon energy for VAs, MoAs, and TaAs alloys.

Table 2 provides a comparative assessment of , , and at 0.5 MeV for the investigated arsenide alloys in this work alongside selected reference shielding materials, including Cr-based alloys, steel-based composites, and ordinary concrete. Among all listed materials, TaAs demonstrates the highest of 1.463 cm^− 1, outperforming even CrBi of 1.275 cm^− 1, which is the most effective among the literature-reported Cr alloys in this table. Consequently, TaAs also exhibits the lowest of 0.474 cm and of 0.684 cm values, indicating the most compact and efficient shielding configuration among all compared materials. In contrast, VAs has a lower of 0.563 cm^− 1, corresponding to and values of 1.231 cm and 1.776 cm, respectively, but still superior to common materials such as steel-scrap of 0.266 cm^− 1 and ordinary concrete of 0.340 cm^− 1, which require significantly more thickness to achieve equivalent attenuation. MoAs, with intermediate performance of 0.749 cm^− 1, 0.925 cm, and 1.335 cm, outperforms all steel-based and concrete references and even CrP and CrAs, making it a compelling candidate for mid-range shielding applications. Overall, the results highlight that the arsenide alloys investigated in this study, particularly TaAs, possess superior photon attenuation characteristics compared to several traditional and advanced shielding materials. The superiority of TaAs follows directly from enhanced photoelectric absorption at low energies due to its high Z constituents, sustained attenuation in the Compton region from higher electron density, and stronger pair-production probability above ~ 1.5 MeV. These mechanisms collectively explain the persistent ranking TaAs > MoAs > VAs across all energies.

Table 2.

Linear attenuation coefficent of arsenide-based alloys used in this study with those of conventional shielding materials and another alloys at a photon energy of 0.5 MeV.

Sample	μ (cm−1)	λ1/2 (cm)	λ (cm)	References
Vas	0.563	1.231	1.776	This work
MoAs	0.749	0.925	1.335
TaAs	1.463	0.474	0.684
CrBi	1.275	0.544	0.784	24
CrAs	0.547	1.267	1.828
CrP	0.482	1.438	2.075
Steel-scrap	0.266	2.606	3.759	53
Steel-magnetite	0.298	2.326	3.356
Ordinary concretes	0.340	2.039	2.941

Figure 7 maps the Air KERMA response across the photon energy spectrum. We observe a distinct two-phase behavior: a rapid exponential decay in the low-energy region that transitions into a stabilized decline at higher energies. Crucially, in the sub-0.1 MeV regime, TaAs outperforms the other alloys, generating the highest KERMA values. This dominance is not coincidental; it stems directly from the high density of the TaAs matrix, which amplifies photon interaction rates and forces a larger ejection of kinetic energy-carrying secondary particles into the adjacent air.As incident energy climbs toward 3 MeV, these material distinctions blur. The curves begin to converge, signaling the physical shift toward Compton scattering regime where interaction probability is largely indifferent to atomic number (Z). By the time we reach the upper energy limits, the profiles nearly overlap. At this stage, the shrinking interaction cross-sections become the limiting factor, restricting the efficiency of energy deposition in air regardless of the shielding medium’s density.

Fig. 7.

KERMA (kinetic energy released per unit mass) in air as a function of photon energy for VAs, MoAs, and TaAs, showing energy transfer behavior from photons to air across all alloys investigated in this work.

Figure 8 shows another important shielding parameter, effective atomic number () versus incident photon energy for VAs, MoAs, and TaAs alloy samples over the range of 0.01–15 MeV. At low photon energy levels, below 0.1 MeV, the values are at their highest, as is dominates. Here, TaAs shows the highest followed by MoAs and VAs respectively, reflecting the actual atomic number hierarchy of their constituent element (Ta > Mo > V). This ordering directly correlates with the superior attenuation observed in TaAs in previous figures and tables. As photon energy increases into region, values gradually converge, indicating reduced sensitivity to atomic numbers. is primarily influenced by electron density rather than Z, which explains the flattening of curves and the reduced gap between materials in this range. Beyond 3 MeV to 5 MeV, stabilizes, and in some cases, shows slight fluctuations due to the onset of, which again has a modest Z-dependence. However, the differences between the alloys remain consistent, with TaAs maintaining the highest throughout the spectrum. The high KERMA values at low energies reflect enhanced absorption via the photoelectric effect in high-Z TaAs, whereas the convergence at higher energies follows from the Z-independent nature of Compton scattering.

Fig. 8.

Effective atomic number versus photon energy for VAs, MoAs, and TaAs, illustrating Z-sensitivity at low energies and convergence under Compton-dominant conditions.

Figure 9 shows (a) the exposure buildup factor (EBF) and (b) the absorption buildup factor (EABF) as a function of photon energy across different selected penetration depths for VAs alloy samples. It is observed that EBF increases with both energy and penetration depth (mean-free path). In the low energy region, below 0.1 MeV, the EBF remains low for all depths due to the dominance of and minimal photon scattering. However, at intermediate energies, up to 1.5 MeV, the EBF rises sharply to peak near 1 MeV, a region where is the dominant interaction mechanism. To illustrate, at 1 MeV, the EBF escalates from ~ 3 at 1 mfp to over 10⁴ at 40 mfp, indicating a substantial accumulation of secondary photons within deep shielding layers. A parallel trend is observed for EABF in Fig. 9b, which scales positively with both incident energy and penetration depth. These results confirm that as optical thickness increases, scattering effects progressively govern the radiation field, resulting in elevated buildup factors that are critical for determining the safety margins of thick shielding configurations. The increase in EBF and EABF with energy and depth results from the higher probability of multiple Compton scatterings, which generate additional secondary photons within thicker shielding layers.

Fig. 9.

a Exposure buildup factor (EBF), b absorption buildup factor (EABF) for VAs alloy versus photon energy for VAs at different penetration depths (1–40 mfp).

Figure 10 shows the specific absorbed fraction of energy (SAFE) versus photon energy for VAs at different penetration depths (1–40 mfp). The idea from this parameter is to quantify the fraction of energy absorbed in the target region per unit incident energy. As expected, SAFE decreases with energy in the Compton-dominant region due to reduced efficiency but increases again slightly at higher energies as begins to contribute. SAFE also increases significantly with depth indicating enhanced energy deposition as the photon flux traverses deeper material. SAFE reflects how efficiently a material absorbs incident photon energy, meaning higher SAFE at greater depths corresponds to stronger energy deposition inside the shield. In contrast, increasing buildup factors indicate enhanced secondary-photon generation, which must be considered when designing thick shielding components.

Fig. 10.

specific absorbed fraction of energy (SAFE) versus photon energy for VAs at different penetration depths (1–40 mfp) for VAs sample.

Figure 11 displays the specific gamma-ray constant (Γ), expressed in R.m²/(Ci.hr), as a function of photon energy for VAs, MoAs, and TaAs, with an inset focusing on the lower energy region to highlight the effect of density on Γ behavior. Across the full energy spectrum, Γ exhibits a sharp inverse relationship with photon energy for all three alloys. This trend arises because higher-energy photons possess greater penetrability, thereby reducing the dose delivered per unit activity at a fixed distance. In the low-energy region, below 0.1 MeV, Γ values are elevated due to intense photon absorption and localized energy deposition. At 0.05 MeV, for example, TaAs shows a Γ value of ~ 1000 R.m²/(Ci.hr), compared to near 680 for MoAs and near 530 for VAs, marking a near 89% increase from VAs to TaAs. In the intermediate-energy region below 3 MeV, where dominates, the decline in Γ becomes more gradual. At 0.5 MeV, TaAs retains a higher exposure potential of about 60 R.m²/(Ci.hr) compared to ~ 50 for MoAs and ~ 40 for VAs. However, as energy exceeds 5 MeV, the curves converge; at 10 MeV, the difference becomes marginal (~ 30 for TaAs, ~ 28 for MoAs, and ~ 26 for VAs). As highlighted in the inset, the Γ value at low energy is strongly governed by the material density, with TaAs of 12.21 g/cm³, maintaining a consistently higher exposure constant than its lighter counterparts.

Fig. 11.

Specific gamma-ray constant as a function of photon energy for VAs, MoAs, and TaAs. The inset highlights the density-dependent variation of in the low-energy region.

Figure 12 shows the photon dose rate in air as a function of distance from monoenergetic gamma source shielded by VAs, MoAs, or TaAs alloys. The data reflects the expected decay in dose intensity, governed jointly by the inverse square law and the material-specific exponential attenuation. At the most critical shielding interface (0.1 cm), TaAs achieve the lowest dose rate, reducing exposure by over 50% relative to VAs. This superior performance is directly attributable to the high atomic number (Z) and density of the TaAs matrix. MoAs occupies an intermediate position, offering moderate dose reduction. This hierarchy persists at extended distances (0.5 cm and 1 cm); even at 5 cm, TaAs yields the lowest residual dose. These results underscore that intrinsic material properties remain the dominant factor in limiting exposure, particularly in compact shielding scenarios where maximizing attenuation within a constrained volume is essential. Overall, the bar graph confirms that TaAs provides the most effective near-field dose suppression due to its superior photon attenuation properties. These results validate TaAs as the optimal material among the studied alloys for high-intensity gamma radiation environments requiring compact and efficient shielding, while MoAs offers a suitable compromise between attenuation and material density.

Fig. 12.

Bar graph of photon dose rate in air at different selected distances from a gamma source shielded by VAs, MoAs, or TaAs.

Conclusion

This study rigorously evaluated the radiation shielding efficacy of three transition metal arsenide alloys (VAs, MoAs, and TaAs) using the Geant4 Monte Carlo toolkit. Our findings establish TaAs as the superior candidate for high-intensity photon attenuation. At 0.5 MeV, TaAs exhibited a linear attenuation coefficient of , representing about 160% improvement over VAs and significantly outperforming traditional shielding materials such as ordinary concrete and steel-based composites. Furthermore, TaAs demonstrated the lowest half-value layer , enabling a dose rate reduction of over 50% compared to VAs at a thickness of 0.1 cm. The strong statistical agreement with XCOM () confirms the reliability of these results. These findings do not merely replicate known data but advance the field by identifying transition metal arsenides as a high-performance class of materials previously overlooked in shielding literature. Ultimately, this study serves as a predictive roadmap for future experimental synthesis, establishing TaAs as a robust and compact lead-free solution for modern diagnostic and industrial applications where space constraints and sustainability are paramount.

Author contributions

Morad Khalid Hamad : Conceptualization, Data curation, Formal analysis, acquisition, Investigation, Methodology, Project administration, Resources, Software, Supervision, Validation, Visualization, Writing – original draft, Writing – review & editing.

Funding

Not applicable.

Data availability

All data related to this article are available from the corresponding author upon reasonable request.

Declarations

Competing interests

The author declares that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Declaration of using AI tool

During the preparation of this work, the author(s) used an AI tool in order to improve language and readability. After using this tool/service, the author reviewed and edited the content as needed and takes full responsibility for the content of the publication.