Gamma-ray and neutron shielding efficiency of Pb-free gadolinium based glasses

LOW ENERGY ACCELERATOR, RAY AND APPLICATIONS

Gamma-ray and neutron shielding efficiency of Pb-free gadolinium based glasses

V. P. Singh ，

N. M. Badiger，

S. Kothan，

S. Kaewjang，

T. Korkut，

H. J. Kim，

J. Kaewkhao

Nuclear Science and Techniques

Vol.27, No.4

Article number 103

Published in print 20 Aug 2016

Available online 26 Jul 2016

DOI：10.1007/s41365-016-0099-1

64800

The radiation shielding efficiency of material depends upon photon attenuation, exposure buildup factors and neutron removal capacity. A newly developed Pb-free gadolinium based glasses in compositions (80-x)B₂O₃-10SiO₂-10CaO-xGd₂O₃ (where x = 15, 20, 25, 30 and 35 mol%) had completely been investigated for their shielding efficiency with Geant4 simulation for mass attenuation coefficients and neutron total macroscopic cross section and by calculating exposure buildup factors. The exposure buildup factors for photon energy from 0.015 to 15 MeV had been calculated up to 40 mean free paths using five factors Geometric Progression method. The mass attenuation coefficients of the Pb-free glasses were simulated for energies from 223 to 2614 keV and compared with the possible available experimental results. The neutron shielding efficiency of these glasses was discussed by calculating neutron total macroscopic cross section for energies from 1 eV to 14.1 MeV. Present investigations are found to be very useful for applications in nuclear engineering.

GadoliniumNeutronGlassBuildup factorGeant4 simulation

1. Introduction

Radiation protection in nuclear installations has prime importance for personnel safety from the ionizing radiation. Shielding of radiation source to control radiation exposure is the area of radiological safety engineering in nuclear technology, which is considered and implemented during reactor design. Therefore, choice of appropriate radiation shielding is extremely crucial to fulfill the requirements of exposure control. Nowadays, radiation is associated with our life in power production, industries, agriculture, medical, petroleum, research work, etc. Initially lead (Pb) was considered as the best available radiation shielding materials for gamma-rays while low-Z materials (water, boron, lithium, hydrogenous, etc) are commonly applied for neutron shielding. A common shielding material for both gamma-ray and neutron is mixture of low- and high-Z elements, and are being used in nuclear reactors for core shielding. Transparent window (viewing window) in nuclear installations is required for visual inspection of high radiation components or equipment prepared using Pb and Pb-equivalent shielding materials. However, Pb has been found to be very hazardous material which required immediate attention. Over the past few years, there have been great deals of expressed concern about the toxicity of the Pb and reduction the utilization of Pb. The Pb toxicity in children as well as the adults has been studied [1, 2]. Some developments for Pb-free transparent glasses have been continuously found in literature aimed for superior Pb-free glasses.

Various types of heavy metal oxide glasses have been investigated as replacement of Pb based glasses. The mass attenuation coefficients of silicate glasses containing bismuth, barium and Pb oxides have been investigated [3, 4]. The gamma-ray interaction properties of bismuth borate glasses and zinc bismuth borate glasses have also been investigated [5, 6]. It has been found that Pb can be replaced with other suitable elements to provide the similar equivalent shielding properties. The physical, optical and photon interaction properties of the newly developed gadolinium based gamma-ray shielding materials are reported [7]. However, gamma-ray and neutron shielding efficiency of gadolinium based glasses for reactors application (i.e. photon energy: up to 10 MeV and neutron energy: up to 14.1 MeV) has not yet been reported.

The gamma-ray shielding efficiency is assessed by different types of interaction parameters such as mass attenuation coefficient, effective atomic number and effective electron density. The mass attenuation coefficient defines the interaction probability of photon in the medium. The intensity of gamma-ray beam through a medium follows attenuation law (I=I₀ e^-µt) for narrow, single energy for thin absorbing material, where I and I₀ are transmitted and initial photon intensities, µ is linear attenuation coefficient and t is the thickness of medium.

In broad beam, multi-energy gamma-ray or thick interacting material generate secondary photons. To account the secondary photons, the law is made applicable by introducing a correction factor called as buildup factor. Now the modified equation is I= B×I₀ e^-µt including the buildup factors, B [8]. The B value is unity when all the above conditions are satisfied. The buildup factor is the ratio of the total photon beam response (e.g. flux, dose or exposure) to the response of uncollided photon beam fraction at a point to the number arriving there without being scattered. The buildup is defined as the ratio of total value of a specified radiation quantity at any point to the contribution to that value from radiation reaching to the point without having undergone a collision in the passage of radiation through a medium [9]. The buildup factor corrects the response to uncollided photons so as to include the contribution of the scattered photons.

The compilation for buildup factors by various codes has been reported by American Nuclear Society in the report ANSI/ANS-6.4.3, 1991[10].The buildup factor data in the report covers energy range of 0.015-15 MeV and up to penetration depth of 40 mean free paths (mfp). The buildup factors in the ANSI/ANS-6.4.3,1991 report [10] are for 23 elements, Beryllium (Z=4) to Uranium (Z=92). Harima et al., [11] developed a fitting formula, called Geometric Progression (G-P) which gives buildup factors of the good agreement with the ANSI/ANS-6.4.3, 1991 report [10]. Harima [9] reviewed extensively and reported the gamma-ray buildup factors and its applications. The buildup factors for few elements and water were reported by Martin [8]. Various researchers investigated photon buildup factors for various low- and high-Z element containing compounds and mixtures; concretes [12], heavy metal oxide glasses [13], oxide dispersion strengthened oxides [14], superconductors [15], gel [16], drugs [17], human body parts, tissues and vitamins [18]. These studies showed that the G-P fitting is a useful and suitable technique for estimation of the buildup factors.

Geant4 code is widely used for the Monte Carlo simulation of the passage of particles transport through the matter. It is based on object-oriented programming and allows user to derive classes to describe the detector geometry, primary particle generator and physics processes models along electromagnetic, hadronic, and decay physics based on theory, materials and elements, experimental data or parameterizations. Most of physics process models include multiple scattering, ionization, Bremsstrahlung, positron annihilation, photo electric effect, Compton and Rayleigh scattering, pair production, synchrotron and transition radiation, Cherenkov effect, refraction, reflection, absorption, scintillation, fluorescence, and Auger electrons emission [19, 20]. The Geant4 simulation code covers a wide energy range of photon starting from 250 eV to the TeV. Recently Geant4 simulation code has been used for simulation of mass attenuation coefficients of scintillation detectors and silicates at various energies [21, 22].

In the present study, we have studied mass attenuation coefficients, exposure buildup factors and neutron total macroscopic cross section for Pb-free gadolinium based glasses. The mass attenuation coefficients were calculated using Geant4 simulation code. The exposure buildup factors were calculated using G-P fitting method for photon energy of 0.015 to 15 meV and up to 40 mean free paths [12]. The photon energy of 0.015 to 15 meV and mean free paths up to 40 are chosen because G-P fitting parameters of individual elemental are available for these energies. The neutron total macroscopic cross section was estimated using Geant4 simulation code for energy of 1 eV to 14.1 MeV.

2. Materials and Computational Method

Recently Pb-free gadolinium based glasses in compositions (80-x) B₂O₃-10SiO₂-10CaO-xGd₂O₃ (where x = 15, 20, 25, 30 and 35 mol%) have been developed by Kaewjang et al.[7]. These glasses contain the combination of low- and high-Z elements (B, O, Si, Ca and Gd), therefore the glasses exhibit the gamma-ray and neutron shielding properties. The densities of the glasses are 3.57 g. cm^-3, 3.84 g. cm^-3, 3.91 g. cm^-3, 4.18 g. cm^-3 and 4.41 g. cm^-3 for glasses with Gd₂O₃ of 15 mol%, 20 mol%, 25 mol%, 30 mol% and 35 mol%, respectively.

2.1 Mass attenuation coefficients

2.1.1 WinXcom software

The mass attenuation coefficient (µ/ρ) for the glasses is estimated using mixture rule as;

(μ / ρ)_{G l a s s} = \sum_{i}^{n} w_{i} {(μ / ρ)}_{i}

(1)

where $w_{i}$ is the weight fraction and ${(μ / ρ)}_{i}$ is mass attenuation coefficient of the i^th element. The quantity w_i is given by $w_{i} = n_{i} A_{i} / \sum_{j}^{n} n_{j} A_{j}$ with condition $\sum_{i}^{n} w_{i} = 1$ , where A_i is the atomic weight of the i^th element and n_i is the number of elements in the materials. The µ/ρ value at a particular energy of individual element is taken from WinXcom program developed by Gerward et al. [23].

2.1.2 Geant4 Simulation code

Attenuation features were investigated with Geant4 simulation code using a narrow beam geometry model. Geant4 geometry and trajectory are shown in the Fig. 1. The mass attenuation coefficients of glasses were determined by the transmission method according to attenuation law ( $I = I_{0} e^{- µ_{m} t}$ ), where I₀ and I are the incident and attenuated photon intensity, respectively, µ_m (cm².g^-1) is the mass attenuation coefficient and t is the mass thickness of the sample. Attenuation of photons is calculated by simulating all relevant physical processes and interactions before and after inserting the samples under the investigation. Photon interaction includes photoelectric effect, Compton scattering, pair production, Rayleigh scattering, and electrons interactions include Bremsstrahlung, multiple scattering and ionization. Atomic effects after photoelectric effect, as X-rays emission and Auger effect are included. So it is possible to have a vertex from photoelectric effect [24]. A good agreement between Geant4 model for electromagnetic processes and National Institute of Standards and Technologies data has been reported [24].

Fig.2.

Geant 4 geometry and trajectories

2.2 Exposure buildup factors

The computational work of the exposure buildup factors (EBF) for the glasses is done in three steps as [15];

1. Calculation of equivalent atomic number [25, 26]

2. Calculation of the G-P fitting parameters [25, 26]

3. Calculation of the exposure buildup factors [9, 11]

The buildup of photons is mainly due to multiple scattering events by Compton scattering, so that equivalent atomic number (Z_eq) is considered from the Compton scattering interaction process. The Z_eq for each glass is estimated by the ratio of (µ/ρ)_Compton / (µ/ρ)_Total, at a specific energy with the corresponding element at the same energy, where (µ/ρ)_Compton is the mass attenuation coefficient for Compton scattering and (µ/ρ)_Total is the total mass attenuation coefficient. These mass attenuation coefficients are calculated using WinXcom program [23]. The Z_eq of the glasses is calculated by logarithmic interpolation method as;

Z_{e q} = \frac{Z_{1} (\log R_{2} - \log R) + Z_{2} (\log R - \log R_{1})}{\log R_{2} - \log R_{1}}

(2)

where $Z_{1}$ and $Z_{2}$ are the atomic numbers of elements corresponding to the ratios $R_{1}$ and $R_{2}$ respectively and R is the ratio for the glass at a specific energy. Also, the G-P fitting parameters are calculated similar to the above logarithmic interpolation.

The G-P fitting parameters (b, c, a, X_k and d) are put in the given below equations for estimation of exposure buildup factors;

B (E, x) = 1 + \frac{(b - 1) (K^{x} - 1)}{K - 1} for   K \neq 1

(3)

B (E, x) = 1 + (b - 1) x for   K = 1,

(4)

where,

\begin{array}{l} K (E, x) = c x^{a} + d \frac{\tanh (x / X_{K} - 2) - \tanh (- 2)}{1 - \tanh (- 2)}, \\ for penetration depth (x) \leq 40 mfp \end{array}

(5)

where x is the source-detector distance for the medium in terms of mfp and b, the value of the exposure buildup factor at 1 mfp, K (E, x) is the dose multiplicative factor, and b, c, a, X_K and d are computed G-P fitting parameters which depends on the attenuating medium and source energy.

2.3 Standardization of G-P fitting Method

The present G-P fitting method for exposure buildup factors is standardized using the ANSI/ANS-6.4.3-1991 standard data [10]. The differences in EBF of Pb between present G-P fitting method and ANSI/ANS-6.4.3-1991 standard data are shown in Fig. 2. It is found that the differences between present G-P fitting method and ANSI/ANS-6.4.3-1991 data are negligible in low energy except at one energy and become very small in high energy regions. Therefore, present G-P fitting can be used for calculation of exposure buildup factors for compounds or mixture containing high atomic number elements.

Fig.2.

Difference (%) between ANSI/ANS-6.4.3, 1991 standard data and present G-P fitting work with respect to the calculated values of EBF for lead at some penetration depths up to 15 MeV.

2.4 Neutron Total Macroscopic Cross Section

Neutron total macroscopic cross sections (cm^-1) of the gadolinium based glasses are performed using Geant4 simulations code [19]. The Geant4 code was used to estimate total macroscopic cross sections for three different neutron sources as ²⁵²Cf, ²⁴¹Am/Be and the fission neutron from reactors.

3. Results and Discussion

The gamma-ray and neutron shielding efficiencies of newly developed Pb-free gadolinium based glasses are discussed using the mass attenuation coefficients, exposure buildup factors and neutron total macroscopic cross sections and shown graphically in Figs. 3 (a-e), 4 (a-e) and 5, respectively. The mol% contents of Gd₂O₃ in the glasses are shown in each figure (e.g. G15 means 15 mol% of Gd₂O₃). These shielding parameters are discussed in detail in next coming sections.

Fig. 3

(a-e). Mass attenuation coefficients for Gadolinium based glasses (a) Gd₂O₃ 15 mol% (b) Gd₂O₃ 20 mol% (c) Gd₂O₃ 25 mol% (d) Gd₂O₃ 30 mol% (e) Gd₂O₃ 35 mol% using Geant4 simulation, WinXcom and experiment.

Fig. 4

(a-e). Exposure buildup factors for Gadolinium based glasses versus photon energy (a) Gd₂O₃ 15 mol% (b) Gd₂O₃ 20 mol% (c) Gd₂O₃ 25 mol% (d) Gd₂O₃ 30 mol% (e) Gd₂O₃ 35 mol%

Fig. 5.

Neutron Total Macroscopic Cross Sections for Gadolinium Based Glasses

3.1 Mass attenuation coefficients

The mass attenuation coefficient (µ/ρ) for the selected glasses was calculated using Geant4 Monte Carlo simulation and WinXcom software, and shown in Fig. 3 (a-e). The µ/ρ values of all the glasses were estimated experimentally in low energy photon of 223 to 622 keV [7]. However, in Geant4 simulation any energy sources can be used for experimental setup; therefore, higher energies were considered.

The variation of µ/ρ with photon energy is divided in three regions, low, intermediate and high energy. The µ/ρ values for all the glasses with different composition of Gd₂O₃ show sharp reduction in low energy region and slower in intermediate energy region and finally seems to be independent in high energy region. Sharp reduction of µ/ρ values is due to photoelectric effect, where interaction cross section dependent upon atomic number (Z^4-5) and energy (1/E^7/2) [27] where the photon energy plays a vital role in photoelectric effect. Slow reduction in intermediate region is due to Compton scattering, where interaction cross section is directly proportional to Z. In high energy region, pair production is responsible for photon interaction.

From Fig. 3 (a-e), it is to be noted that the µ/ρ values for all the glasses increase with increase of Gd₂O₃ content. Therefore, gamma-ray shielding efficiency of glasses increases with the increase of Gd₂O₃ percentage. It is already reported that the Pb-free glasses are found to be more efficient for radiation shielding than commercial window, ordinary concrete and X-ray window [7]. The gamma-ray shielding efficiency of all the selected glasses is also compared with steel-magnetite concrete (ρ=5.11 g cm^-1) [28] and shown in Fig. 3 (a), Fig. 3 (b), Fig. 3 (c), Fig. 3 (d), Fig. 3 (e) for glasses containing Gd₂O₃ of 15 mol%., 20 mol%, 25 mol%, 30 mol% and 35 mol%, respectively. From the figure, it is found that the increase in Gd₂O₃ content in the glass increases mass attenuation coefficients, which are always higher than the steel-magnetite concrete. Considering the densities of the glasses and steel-magnetite with the mass attenuation coefficients, it is observed that the linear attenuation coefficients (density × mass attenuation coefficient) of glass containing Gd₂O₃ of 35 mol% are higher than the steel-magnetite in the energy range 223 to 340 keV. Similarly, linear attenuation coefficients are higher for glass containing Gd₂O₃ of 15 mol% than steel-magnetite in the energy range 223 to 287 keV. Therefore, it is concluded that the gadolinium based glasses become superior gamma-ray shielding material than steel-magnetite concrete in low energy region.

3.2 Exposure buildup factors

Variation of exposure buildup factors (EBF) for the selected glasses with photon energy (0.015 to 15 MeV) and for penetration depth up to 40 mean free paths are shown in Fig. 4 (a), Fig. 4 (b), Fig. 4 (c), Fig. 3 (d), Fig. 4 (e) for glass containing Gd₂O₃ of 15 mol%., 20 mol%, 25 mol%, 30 mol% and 35 mol%, respectively. The EBF for the glasses are small in low energy and large in high energy region. Also the EBF are found to be increasing with mean free path of the glass. The variation behavior of buildup factors shows that more photon buildups for high energy photons with large penetration depths whereas mass attenuation coefficients reduces up to intermediate photon energy. The variation of EBF can be explained by partial photon interaction process similar to the mass attenuation coefficients. Peaks in EBF (3.2×10³) are observed in photoelectric effect region at 60 keV which is near k-edge absorption of gadolinium (i.e. 50.2 keV).

The effective atomic number is derived by the photon attenuation coefficients, similarly for the Z_eq of a compound or mixture. The Z_eq describes the interaction characteristics of a compound or mixture similar to atomic number of an element. The EBF for the glass are small in low-energy due to dominance of photoelectric effect, where all the photons are completely removed from the glass. Therefore, the buildup factors in low energy are found to be of small and order of unity. With increase in photon energy, EBF increases due to multiple scattering as Compton scattering dominates. The multiple scattering of photon reduces the photon energy, finally removed by the photoelectric absorption. The pair production takes over the Compton scattering process in the photon energy excess of 1.022 MeV.

The reason for very large EBF in pair production region (high photon energy region) is explained by chemical composition (similar to equivalent atomic number) dependency of the glasses. In the pair production, interaction cross section is directly proportional to Z², subsequently low-Z_eq shows the small EBF. High EBF in pair production region is due to production of secondary photons due to annihilation of positron (generated after pair production) and electron. The removal of high energy photon (≥1.022 MeV) and generation of secondary photon (0.511 MeV) continues to buildup the photon in the glass. The thickness of the glass contributes additionally as the positron may escape from glass of lower thickness and photon buildup reduces, whereas buildup factor increases in large thickness of the glass.

3.3 Neutron total macroscopic cross section

Neutron total macroscopic cross sections (NTMCS) of the glasses calculated using Geant4 simulation code at ten different neutron energies from 1 eV to 14.1 MeV are shown in Fig. 5. For neutron energy of 1 eV, glass containing 15 mol % of Gd₂O₃ is the superior neutron shielding material, whereas at 100 keV glass containing 20 mol % is the superior neutron shielding material. Above 2 MeV neutrons, glass containing 35 mol% of Gd₂O₃ shows superiority. Here it is to be noted that better neutron shielding efficiency for high-Z glass (35 mol %) shows that the high-Z elements also contribute in neutron removal mechanism. Similar conclusions have also been reported using macroscopic removal cross section for fast neutron [13].

4. Conclusion

In this paper, the gadolinium based glasses in compositions (80-x) B₂O₃-10SiO₂-10CaO-xGd₂O₃ (where x = 15, 20, 25, 30 and 35 mol%) have been investigated for gamma-ray and neutron interaction for their shielding efficiencies. The results can be concluded as follows;

- Gamma-ray attenuation property of the gadolinium based glass increases with the Gd₂O₃ composition.

- Simulation results of mass attenuation coefficients for the glasses are in good agreement with theoretical and experimental results.

- Exposure buildup factors for the glasses decrease with increasing of the Gd₂O₃ compositions.

- Gadolinium based glasses become superior gamma-ray shielding material than steel-magnetite in low energy region.

- Increasing the Gd₂O₃ composition reduces neutron removal property of the glasses in low neutron energy, whereas it improves the property in high neutron energy.

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