Exploration of gamma radiation shielding features for titanate bismuth borotellurite glasses using relevant software program and Monte Carlo simulation code

Journal of Non-Crystalline Solids xxx (xxxx) xxx–xxx

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Exploration of gamma radiation shielding features for titanate bismuth borotellurite glasses using relevant software program and Monte Carlo simulation code G. Lakshminarayanaa,⁎, Ashok Kumarb, M.G. Dongc, M.I. Sayyedd, Nguyen Viet Longe,f, M.A. Mahdia a

Wireless and Photonic Networks Research Centre, Faculty of Engineering, Universiti Putra Malaysia, 43400 Serdang, Selangor, Malaysia Department of Physics, College of Engineering and Management, Punjabi University Neighbourhood Campus, Rampura-Phul, Punjab, India Department of Resource and Environment, School of Metallurgy, Northeastern University, Shenyang 110819, China d Physics Department, University of Tabuk, Tabuk, Saudi Arabia e Ceramics and Biomaterials Research Group, Ton Duc Thang University, Ho Chi Minh City, Vietnam f Faculty of Applied Sciences, Ton Duc Thang University, Ho Chi Minh City, Vietnam b c

A R T I C L E I N F O

A B S T R A C T

Keywords: Radiation shielding XCOM MCNP5 code Mass attenuation coefficient Mean free path Half-value layer

In this work, gamma radiation shielding parameters for six titanate bismuth borotellurite glasses were investigated. The mass attenuation coefficients (μ/ρ) have been calculated using XCOM software and MCNP5 code within the photon energy range 0.015–10 MeV. The (μ/ρ) values were then used to calculate the effective atomic number (Zeff), electron density (Ne), mean free path (MFP) and half-value layer (HVL) values. By using the Geometric progression (G–P) method, the exposure buildup factor (EBF) values at 0.015 MeV–15 MeV photon energy range, with penetration depths up to 40 mfp at intervals 1, 5, 10, 20, 30, and 40 mfp were evaluated. The 30 TeO2–30 B2O3–30 Bi2O3–10 TiO2 (mol %) glass possesses better gamma ray shielding effectiveness due to a higher value of (μ/ρ), Zeff and lower values of HVL and MFP. The studied glasses exhibit excellent gamma ray shielding features compared to different types of concretes.

1. Introduction In recent years, there has been growing interest among researchers to fabricate and apply different kinds of radiation shielding materials, which can effectively attenuate the harmful gamma and neutron radiations in various fields such as outer space exploration, nuclear reactors, nuclear medicine, nuclear waste storage sites, agriculture, and industries etc. [1–3]. Particularly, nowadays, at radiation sites (nuclear power plants etc.) various kinds of concrete are most commonly in use to protect the workers and surrounding environment from the neutral radiations direct or scattered and leakage effects. Here, concrete possesses advantages like cheap cost, ease of preparation for different types of construction, and relatively high density etc. [4]. However, several disadvantages associated with concrete like aggregates expansion, leaching, decrease in its structural strength and porosity due to radiolysis of water content and the evaporation of pore water under radiation heat and cracks formation etc. [5,6]. Additionally, concrete is opaque to visible light, which makes impossible for onsite workers to real-time monitoring of the situation inside nuclear radiation source.

⁎

On the other hand, glasses can be considered as suitable substitutes for absorbing gamma rays and neutrons instead of concrete because glasses are highly transparent to visible light, easy to fabricate, 100% recyclable and their mechanical and physical features can be altered to meet the requirements by adding other chemical compounds [7]. To understand the radiation shielding features of any material, several γ-ray interaction parameters such as mass attenuation coefficient (μ/ρ), effective atomic number (Zeff), electron density (Nel), mean free path (MFP), half-value layer (HVL), and total interaction crosssection (σt) estimation is an important aspect [8–11]. In general, before utilizing in practical onsite radiation protection applications, materials are first tested for their radiation shielding effectiveness using Monte Carlo simulations. Different research groups have been reported the mentioned γ-ray interaction parameters for numerous glass systems for their potential applications as radiation shielding materials ([7,12,13] and the references therein). In the present study, for TeO2-B2O3-Bi2O3-Ti2O glasses, by using XCOM program first we evaluated the (μ/ρ) values within the energy range 0.015–10 MeV, and from them, the γ-ray shielding parameters

Corresponding author. E-mail address: [email protected] (G. Lakshminarayana).

http://dx.doi.org/10.1016/j.jnoncrysol.2017.10.027 Received 26 July 2017; Received in revised form 11 October 2017; Accepted 13 October 2017 0022-3093/ © 2017 Elsevier B.V. All rights reserved.

Please cite this article as: Lakshminarayana, G., Journal of Non-Crystalline Solids (2017), http://dx.doi.org/10.1016/j.jnoncrysol.2017.10.027

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Table 1 Chemical composition (mol %) and elements (wt%) present in the studied glasses, including their density [14]. Sample code

S1 S2 S3 S4 S5 S6

(mol %)

Density (g/cm3) [14]

Chemical composition of elements (wt%)

TeO2

B2O3

Bi2O3

TiO2

Ti

B

Te

O

Bi

65 55 45 40 35 30

20 20 30 30 30 30

10 20 20 20 25 30

5 5 5 10 10 10

1.4229 1.2037 1.2607 2.5755 2.3794 2.2111

2.5702 2.1743 3.416 3.4892 3.2236 2.9955

49.2948 35.286 30.2384 27.4548 22.1943 17.6779

21.871 19.3065 21.0640 21.5155 20.2752 19.2104

24.8412 42.0295 44.0211 44.9649 51.9275 57.905

follows:

such as Zeff, Ne, MFP, HVL, and exposure buildup factor (EBF) values using Geometric progression (G–P) fitting method are derived for their potential applications as γ-ray shielding materials. Additionally, the μ/ρ values of the present glasses were calculated using MCNP5 simulation code and compared with XCOM results.

–ln μ=

() I I0

(1)

t

For the purpose of calculations of mass attenuation coefficients of each sample, 108 particles were used during the simulation.

2. Materials and method

2.2. Calculation of different radiation shielding parameters-theory

The selected glasses density values with the chemical composition (100-x-y-z) TeO2 - (x) B2O3 - (y) Bi2O3 - (z) TiO2 [(x = 20; y = 10, 20; and z = 5), (x = 30; y = 20; and z = 5), (x = 30; y = 20, 25, 30; and z = 10) (mol %)] were taken from Ref. [14]. The chosen 6 glasses were labelled as ‘S1’, ‘S2’, ‘S3’, ‘S4’, ‘S5’, and ‘S6’, for convenience (see Table 1).

2.2.1. Mass attenuation coefficient Electromagnetic radiation interacts with the certain material through different processes i.e. the photoelectric absorption, Compton absorption and scattering and electron-pair production. Associated with each of these interaction processes are linear interaction coefficients (μ), which measure the probability per unit path length that a photon of certain energy in a particular material will interact [15]. When a parallel beam of monoenergetic photons entering through a certain material, it is attenuated due to absorption and scattering. Attenuation due to absorption follows the Lambert-Beer law, which can be expressed as above Eq. (1) [16]. On the other hand, the mass attenuation coefficient (μ/ρ) measures the number of photons interacted with the interacting material and can be evaluated using XCOM software [17] based on the mixture rule, namely [18]:

2.1. MCNP5 simulation process MCNP5 is a Monte Carlo code for simulation of different physical interactions at large energy range. MCNP5 is fully three-dimensional and it utilizes extended nuclear cross-section libraries and uses physics models for particle types [2,7]. Fig. 1 shows the defined cross-sectional geometry setup in MCNP5 Monte Carlo code. In this work, γ-ray sources with various energies have been defined as a point isotropic source. The source has been defined in the mode card of the MCNP5 input file as a point source of photon energy in the range of 0.015–10 MeV. As it can be seen from Fig. 1, glass sample has been located as an attenuator sample between the source and detection area. A point isotropic radiation source was also placed at a point before the glass sample. MCNP5 calculations were done by using Intel® Core™ i7 -6700CPU 3.40 GHz computer hardware. To get absorbed dose amounts in the detection area, average flux tally F4 was utilized. This type of tally mash gives the sum of average flux in the cell. For the simulation process, Tally F4 value simulated by MCNP5 code without shielding material was ‘I0’, the value of Tally F4 simulated by MCNP5 with a certain thickness, ‘t’ of the shielding material was ‘I’. Then the linear attenuation coefficient of the shielding material, μ can be calculated as

Radiation source

5.48 ± 0.01 6.15 ± 0.01 5.930 ± 0.002 5.820 ± 0.001 6.060 ± 0.002 6.39 ± 0.01

(μ/ρ)glass =

∑ wi (μ/ρ)i i

(2)

where wi and (μ/ρ)i are the weight fraction and mass attenuation coefficient of the ‘i’th constituent element, respectively. It is the essential quantity to calculate many other parameters such as effective atomic number, electron density, half-value layer, mean free path etc. 2.2.2. Effective atomic number and electron density The effective atomic number (Zeff) for a composite material cannot represent by a single number. It has to be weighed differently for each of the various processes by which photons can interact with a material.

Tally

Glass sample

Pb shielding 2

Fig. 1. MCNP5 total simulation geometry.

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The mass attenuation coefficient values were used to calculate the Zeff of the selected glasses with the help of the following equation [19]:

∑j f j Z

j

μ ρ i μ ρ j

3

10

(3)

Ne = NA

nZeff Z = NA eff 〈A〉 ∑i ni Ai

(4)

where 〈A〉 is the mean atomic mass and NA is Avogadro constant. 2.2.3. Mean free path and half-value layer The mean free path (MFP) is the average distance a photon can travel in the material before being interacted. The MFP is the reciprocal of the linear attenuation coefficient and measured in (cm) [21]. Besides, the half value layer (HVL) represents the thickness of the shielding materials at which the intensity of the incident photons is reduced by one-half and can be calculated by the following relation:

HVL =

ln(2) μ

-1

10

2

10

-2

9x10

2

where fi, Ai, and Zi are the fractional abundances, the atomic weight, and the atomic number of the element ‘i’, respectively. The effective electron density (Ne) is another important quantity, which describes the number of electrons per unit mass of the interacting materials. The higher the value of Ne, the better is the chances of photon interaction. The effective electron density can be calculated by the relation [20]:

-2

8x10

2

Aj

() ()

------ Mass attenuation Coefficient (cm /g) ------>

∑i fiAi

------ Mass attenuation Coefficient (cm /g) ------>

Zeff =

S1 S2 S3 S4 S5 S6

1

10

0

10

S1 S2 S3 S4 S5 S6

-2

7x10

-2

6x10

-2

5x10

-2

4x10

1

2

10

3

10

4

10

5

10

10

------ Energy (MeV) ------>

-1

10

-2

10

-3

10

-2

10

-1

10

0

10

1

10

2

10

3

10

4

10

5

10

------ Energy (MeV) ------>

(5)

Fig. 2. Variation of the mass attenuation coefficients with incident photon energy for the selected glasses.

2.2.4. Exposure buildup factor The attenuation of the incident photon obeys the Lambert-Beer law (i.e. Eq. (1)) under three conditions: if the beam of a photon is monoenergetic, narrow and interacts with the thin absorbing medium [22]. If these three conditions are not met, the Lambert-Beer law can be reformulated as follows (I = BI0e− μt), where B represents the buildup factor. The buildup factor depends mainly on the incident photon energy and the nature of the medium. For the exposure buildup factor (EBF) calculation of the glass samples in this study, the logarithmic interpolation method was used with the help of G–P fitting parameters from particular equivalent atomic numbers (Zeq) of the glass samples. The EBF calculation method can be summarized in three steps as follows. The first step deals with the calculation of the Zeq values for the selected glasses. The second step concerns with the evaluation of G–P fitting parameters, while the values of EBF computations are illustrated in step three [23]. For the detailed knowledge on the EBF calculations, readers may refer to our recent studies [9,10,24–26].

photoelectric and the Compton effect are equal and E2 is the energy at which the probability of the Compton effect and the pair production are equal. The values of E1 and E2 are listed in Table 3. The (μ/ρ) values are found to decrease sharply in the low-energy region, decreases moderately in the medium energy region and a slight increase in their values is observed in the high-energy region. It is due to the fact that at low energies, the photoelectric absorption is the dominant process [27,28]. 4−5 The cross-section for photoelectric varies as Z E3.5 . In medium energy region, Compton scattering is predominant. The cross-section for Compton scattering varies as Z E . The (μ/ρ) values show significant variation for photon energies > 3 MeV because of the dominance of pair production process in the high-energy region, which has Z2 dependence [29]. Furthermore, discontinuities in values of (μ/ρ) are identified at some energy due to M, L and K-absorption edge of high Zelements (i.e., Bi) present in the samples [30]. The variation of the effective atomic number (Zeff) for all the selected glasses with photon energy is shown in Fig. 3. The values of the (Zeff) for these glasses are given in Table 4. The (Zeff) of samples decreases sharply up to 1 MeV, shows a minimum at 1.5 MeV and increases sharply beyond 1.5 MeV. The minimum values of (Zeff) are noticed for sample S1 whereas they are the maximum for the S6 sample. The similar kind of variations is observed for electron densities for all the studied glasses with photon energy and is presented in Fig. 4 and Table 5. Again the discontinuities in (Zeff) and electron densities are observed at some energies due to K-absorption edge of high Z-elements present in the glass samples. At nuclear radiation sites, generally, the evaluation of radiation shield thickness depends on the concept of half-thickness and the cumulative effect of succeeding materials layers. The mean free path (MFP) and half-value layer (HVL) have been calculated for all the glass samples and the obtained data are given in Tables 6 and 7, respectively. It is known that the MFP and HVL are crucial parameters to establish any glass or polymer or another kind of solid matrix as a better shielding material. Generally, for a superior radiation shielding material, lower MFP and HVL values are desired. The variation of the MFP

3. Results and discussion The chemical composition, wt% of each element and densities of the studied glasses in this work are presented in Table 1. The mass attenuation coefficients (μ/ρ) have been computed by applying XCOM program in a wide energy range of 1 keV to 100 MeV. The variation of the (μ/ρ) values with incident photon energy has been shown in Fig. 2 for all the glass samples for the whole energy range, whereas the values of (μ/ρ) are listed in Table 2 for the 15 keV to 10 MeV energy range. The (μ/ρ) values have also been calculated using MCNP5 simulation code and are tabulated in Table 2. The percentage deviation between the (μ/ ρ) values indicates that the (μ/ρ) calculated using both the methods are in good agreement up to energies of 6 MeV. Beyond 6 MeV, larger deviations in values are observed. Fig. 2 shows that the variation of (μ/ρ) values with chemical composition is large below E1 (low-energy region), negligible is between E1 and E2 (medium energy region) and is moderate above E2 (high-energy Region), where E1 is the energy at which the probability of the 3

0.015 0.02 0.03 0.04 0.05 0.06 0.08 0.1 0.15 0.2 0.3 0.4 0.5 0.6 0.8 1 1.5 2 3 4 5 6 8 9 10

Energy (MeV)

54.76 34.20 11.87 13.98 7.794 4.827 2.277 2.354 0.8727 0.4575 0.2136 0.1412 0.1094 0.0919 0.0728 0.06215 0.04866 0.04274 0.03762 0.03571 0.03507 0.03501 0.03573 0.03630 0.03692

54.74 34.07 11.80 13.95 7.786 4.825 2.268 2.348 0.8693 0.4559 0.2120 0.1399 0.1083 0.0909 0.0719 0.0606 0.0479 0.0423 0.0373 0.0353 0.03455 0.03414 0.03356 0.03304 0.03229

0.04 0.37 0.61 0.20 0.10 0.04 0.37 0.26 0.39 0.35 0.75 0.86 1.03 0.98 1.12 2.42 1.61 1.14 0.94 0.99 1.48 2.46 6.08 8.96 12.55

67.45 46.25 16.16 13.65 7.621 4.733 2.249 3.083 1.135 0.5832 0.2583 0.1630 0.1221 0.1001 0.07695 0.06462 0.04979 0.04373 0.03879 0.03713 0.03672 0.03688 0.03798 0.03871 0.03949

XCOM

% deviation

XCOM

MCNP5

S2

S1

67.41 46.07 16.11 13.62 7.605 4.722 2.232 3.071 1.130 0.5807 0.2562 0.1610 0.1207 0.0989 0.07599 0.06276 0.04885 0.04315 0.03839 0.03673 0.03615 0.03592 0.03555 0.03508 0.03429

MCNP5 0.06 0.39 0.32 0.25 0.20 0.23 0.75 0.37 0.42 0.42 0.79 0.95 1.13 1.13 1.24 2.87 1.87 1.31 1.01 1.05 1.53 2.58 6.38 9.37 13.15

% deviation 67.26 46.88 16.41 12.91 7.216 4.488 2.140 3.111 1.148 0.5901 0.2613 0.1648 0.1233 0.1010 0.07754 0.06508 0.05009 0.04395 0.03888 0.03713 0.03663 0.03673 0.03772 0.03840 0.03914

XCOM

S3

67.21 46.69 16.36 12.88 7.200 4.477 2.122 3.099 1.143 0.5877 0.2592 0.1631 0.1218 0.0998 0.07655 0.06322 0.04916 0.04337 0.03848 0.03673 0.03607 0.03578 0.03534 0.03485 0.03406

MCNP5 0.08 0.39 0.32 0.21 0.21 0.25 0.85 0.38 0.46 0.41 0.79 1.00 1.18 1.16 1.28 2.84 1.85 1.30 1.01 1.07 1.52 2.564428 6.299677 9.237229 12.95833

% deviation

Table 2 Mass attenuation coefficients of the studied glasses evaluated using XCOM program and MCNP5 code, and % deviation.

67.42 47.28 16.55 12.51 6.994 4.352 2.079 3.120 1.153 0.5927 0.2625 0.1655 0.1238 0.1013 0.07781 0.06528 0.05023 0.04406 0.03893 0.03713 0.03661 0.03667 0.03762 0.03829 0.039

XCOM

S4

67.37 47.09 16.50 12.47 6.979 4.341 2.060 3.107 1.147 0.5905 0.2604 0.1638 0.1223 0.1002 0.07683 0.06344 0.04930 0.04348 0.03853 0.03673 0.036044 0.035736 0.035262 0.034759 0.033967

MCNP5 0.07 0.38 0.27 0.24 0.21 0.26 0.89 0.39 0.53 0.43 0.78 1.00 1.19 1.11 1.24 2.81 1.83 1.30 1.01 1.06 1.55 2.55 6.27 9.22 12.91

% deviation 72.73 52.24 18.32 12.46 6.969 4.342 2.08 3.421 1.261 0.6445 0.2808 0.1744 0.1289 0.1047 0.07948 0.06626 0.05067 0.04445 0.03941 0.03772 0.03731 0.03747 0.03858 0.03933 0.04011

XCOM

S5

72.68 52.04 18.28 12.43 6.951 4.327 2.06 3.407 1.255 0.6418 0.2785 0.1726 0.1274 0.1034 0.07843 0.06428 0.04968 0.04384 0.03899 0.03731 0.03672 0.03649 0.03611 0.03561 0.03481

MCNP5

0.07 0.39 0.22 0.27 0.26 0.35 1.03 0.40 0.47 0.42 0.82 1.01 1.16 1.19 1.30 2.99 1.96 1.38 1.05 1.08 1.58 2.61 6.41 9.45 13.21

% deviation

77.28 56.50 19.83 12.41 6.948 4.333 2.081 3.681 1.354 0.689 0.2966 0.1821 0.1334 0.1075 0.08091 0.06710 0.05105 0.04479 0.03982 0.03823 0.03791 0.03815 0.03941 0.04022 0.04107

XCOM

S6

77.24 56.28 19.80 12.38 6.935 4.315 2.056 3.665 1.348 0.686 0.2942 0.1802 0.1317 0.1062 0.07984 0.06499 0.04999 0.04415 0.03939 0.03781 0.03731 0.03714 0.03684 0.03637 0.03556

MCNP5

0.06 0.41 0.15 0.23 0.30 0.42 1.18 0.43 0.47 0.46 0.80 1.03 1.24 1.21 1.31 3.14 2.06 1.43 1.08 1.11 1.59 2.64 6.51 9.58 13.41

% deviation

G. Lakshminarayana et al.

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Table 3 E1 and E2 for all the selected glass samples.

Table 4 Effective atomic number of all the studied glasses.

Sample code

E1 (keV)

E2 (MeV)

Energy (MeV)

S1

S2

S3

S4

S5

S6

S1 S2 S3 S4 S5 S6

328.90 382.94 386.38 391.60 409.52 428.26

151.06 152.42 153.10 153.79 154.48 155.17

0.015 0.02 0.03 0.04 0.05 0.06 0.08 0.1 0.15 0.2 0.3 0.4 0.5 0.6 0.8 1 1.5 2 3 4 5 6 8 10

60.55 65.11 64.64 55.94 55.24 54.28 51.73 59.78 51.78 44.02 33.70 28.55 25.84 24.30 22.70 21.91 21.33 21.62 22.87 24.29 25.67 26.94 29.12 30.89

67.58 71.93 71.56 60.92 60.17 59.18 56.55 67.36 60.16 52.50 40.90 34.37 30.73 28.57 26.24 25.08 24.17 24.49 26.01 27.73 29.38 30.89 33.46 35.52

68.44 72.71 72.23 61.87 60.91 59.65 56.37 67.50 59.34 50.95 38.79 32.20 28.56 26.43 24.15 23.03 22.13 22.43 23.88 25.54 27.14 28.63 31.19 33.27

68.01 72.47 72.03 62.30 61.27 59.90 56.39 67.75 59.34 50.74 38.43 31.80 28.16 26.01 23.76 22.64 21.75 22.04 23.45 25.08 26.67 28.13 30.66 32.71

70.55 74.53 74.14 64.97 63.89 62.50 58.90 70.24 62.34 54.00 41.40 34.30 30.29 27.93 25.36 24.08 23.05 23.36 24.90 26.66 28.38 29.95 32.65 34.84

72.57 76.09 75.69 67.44 66.35 64.92 61.24 72.21 64.75 56.68 44.00 36.56 32.27 29.66 26.85 25.43 24.28 24.60 26.25 28.14 29.97 31.63 34.49 36.80

E1 is the energy at which the probability of the photoelectric equals the probability of the Compton effect. E2 is the energy at which the probability of the Compton effect equals the probability of the pair production.

S1 S2 S3 S4 S5 S6

80

60

10

50

S1 S2 S3 S4 S5 S6

9 40

------ Electron Density (number of electrons/g) ------>

------ Effective atomic number ------->

70

30

20

0.1

1

10

------ Energy (MeV) -------> Fig. 3. Variation of the effective atomic numbers for the studied glasses with photon energy.

values with photon energies are depicted in Fig. 5. The MFP values are very small in the low-energy region (< 200 keV) for all the glass samples. Then they show an increasing trend up to 5 MeV and become maximum at 5 MeV. After that MFP values indicate a decreasing trend up to 500 MeV and become nearly constant above this energy. The MFP and HVL values are the lowest for S6 and are highest for S1. This indicates that the sample S6 is the best shielding glass out of the six glass samples under study. This is due to the fact that the Zeff for sample S1 is the minimum whereas it is maximum for the sample S6. Thus, the glass composition affects the MFP and HVL values of the samples. Here, we conclude that by altering the chemical composition of the glass samples, MFP or HVL values can be minimized to acquire desirable radiation shielding effectiveness. In Fig. 5, studied glasses MFP values have also been compared with MFP values of different types of concretes [31] generally used for γ- ray shielding. From Fig. 5, one can observe that all the glass samples under study possess the lower values of MFP as compared to seven types of concretes. Here, it confirms a fact that the shielding effectiveness of the present glass systems is better than standard concretes and the studied glasses can be used as potential gamma ray shielding materials. The exposure G–P fitting parameters have been computed at

8

7

6

5

4

3

2 0.1

1

10

------ Energy(MeV) ------> Fig. 4. Variation of the electron densities for the selected glasses with photon energy.

different energies for the studied glasses. The exposure buildup factor (EBF) values were obtained using GP fitting formula for the penetration depths of 1, 5, 10, 20, 30 and 40 mfp values. The variation of EBFs for all the glass samples with incident photon energy at various penetration depths are shown in Fig. 6. Gamma-rays are usually attenuated by interactions at the level of the electrons in the atoms of the shielding materials. The value of EBF is slightly greater than one up to 0.02 MeV for all the mfp values, increases moderately up to 0.04 MeV. Beyond 0.04 MeV, the EBF value decreases up to 0.15 MeV and shows an 5

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Table 5 Electron density of all the selected glasses.

Table 7 Half-value layer for all the studied glasses.

Energy (MeV)

S1

S2

S3

S4

S5

S6

Energy (MeV)

S1

S2

S3

S4

S5

S6

0.015 0.02 0.03 0.04 0.05 0.06 0.08 0.1 0.15 0.2 0.3 0.4 0.5 0.6 0.8 1 1.5 2 3 4 5 6 8 10

7.8 8.39 8.33 7.21 7.12 7 6.67 7.7 6.67 5.67 4.34 3.68 3.33 3.13 2.93 2.82 2.75 2.79 2.95 3.13 3.31 3.47 3.75 3.98

7.78 8.28 8.24 7.01 6.92 6.81 6.51 7.75 6.92 6.04 4.71 3.96 3.54 3.29 3.02 2.89 2.78 2.82 2.99 3.19 3.38 3.55 3.85 4.09

8.68 9.22 9.16 7.85 7.73 7.57 7.15 8.56 7.53 6.46 4.92 4.08 3.62 3.35 3.06 2.92 2.81 2.85 3.03 3.24 3.44 3.63 3.96 4.22

8.81 9.39 9.33 8.07 7.94 7.76 7.31 8.78 7.69 6.58 4.98 4.12 3.65 3.37 3.08 2.93 2.82 2.86 3.04 3.25 3.46 3.64 3.97 4.24

8.66 9.15 9.1 7.97 7.84 7.67 7.23 8.62 7.65 6.63 5.08 4.21 3.72 3.43 3.11 2.96 2.83 2.87 3.06 3.27 3.48 3.68 4.01 4.28

8.48 8.89 8.84 7.88 7.75 7.58 7.15 8.44 7.56 6.62 5.14 4.27 3.77 3.47 3.14 2.97 2.84 2.87 3.07 3.29 3.5 3.7 4.03 4.3

0.015 0.02 0.03 0.04 0.05 0.06 0.08 0.1 0.15 0.2 0.3 0.4 0.5 0.6 0.8 1 1.5 2 3 4 5 6 8 10

0.002 0.004 0.011 0.009 0.016 0.026 0.056 0.054 0.145 0.276 0.592 0.896 1.156 1.376 1.737 2.035 2.599 2.959 3.362 3.541 3.606 3.612 3.539 3.425

0.002 0.002 0.007 0.008 0.015 0.024 0.05 0.037 0.099 0.193 0.436 0.691 0.923 1.126 1.464 1.744 2.263 2.577 2.905 3.035 3.069 3.055 2.967 2.853

0.002 0.002 0.007 0.009 0.016 0.026 0.055 0.038 0.102 0.198 0.447 0.709 0.948 1.157 1.507 1.796 2.333 2.659 3.006 3.147 3.19 3.182 3.098 2.986

0.002 0.003 0.007 0.01 0.017 0.027 0.057 0.038 0.103 0.201 0.454 0.719 0.962 1.175 1.53 1.824 2.371 2.703 3.059 3.207 3.252 3.247 3.165 3.053

0.002 0.002 0.006 0.009 0.016 0.026 0.055 0.033 0.091 0.177 0.407 0.656 0.887 1.092 1.439 1.726 2.257 2.573 2.902 3.032 3.065 3.052 2.964 2.851

0.001 0.002 0.005 0.009 0.016 0.025 0.052 0.029 0.08 0.157 0.366 0.596 0.813 1.009 1.34 1.616 2.124 2.421 2.724 2.837 2.861 2.843 2.752 2.641

Energy (MeV)

S1

S2

S3

S4

S5

S6

0.015 0.02 0.03 0.04 0.05 0.06 0.08 0.1 0.15 0.2 0.3 0.4 0.5 0.6 0.8 1 1.5 2 3 4 5 6 8 10

0.003 0.005 0.015 0.013 0.023 0.038 0.08 0.078 0.209 0.399 0.854 1.292 1.668 1.986 2.507 2.936 3.75 4.27 4.851 5.11 5.203 5.212 5.107 4.943

0.002 0.004 0.01 0.012 0.021 0.034 0.072 0.053 0.143 0.279 0.63 0.998 1.332 1.624 2.113 2.516 3.266 3.718 4.192 4.379 4.428 4.409 4.281 4.118

0.003 0.004 0.01 0.013 0.023 0.038 0.079 0.054 0.147 0.286 0.645 1.023 1.368 1.67 2.175 2.591 3.367 3.837 4.337 4.542 4.604 4.591 4.471 4.308

0.003 0.004 0.01 0.014 0.025 0.039 0.083 0.055 0.149 0.29 0.655 1.038 1.388 1.696 2.208 2.632 3.421 3.9 4.414 4.628 4.693 4.686 4.567 4.406

0.002 0.003 0.009 0.013 0.024 0.038 0.079 0.048 0.131 0.256 0.588 0.946 1.28 1.576 2.076 2.49 3.257 3.712 4.187 4.375 4.423 4.404 4.277 4.114

0.002 0.003 0.008 0.013 0.023 0.036 0.075 0.043 0.116 0.227 0.528 0.859 1.173 1.456 1.934 2.332 3.066 3.494 3.93 4.094 4.128 4.102 3.971 3.81

------ Mean free path ------>

Table 6 Mean free path values for the studied glasses.

S1 S2 S3 S4 S5 S6 Ordinary concrete Basalt-magnetite concrete Hematite-serpentine concrete Ilmenite concrete Ilmenite-limonite concrete Steel-magnetite concrete Steel-scrap concrete

20

0 -3

10

-2

10

-1

10

0

10

1

10

2

10

3

10

4

10

5

10

6

10

----- Energy (MeV) ------>

increasing trend after that up to 15 MeV. For higher penetration depths, the EBF values show an increasing trend with energy and the trend becomes more sharp for the higher penetration depth values at higher energies. Sharp peaks are observed at 0.08 MeV for sample S1 and at 0.03 MeV, 0.08 MeV and 0.4 MeV for the remaining samples. These are due to the K-absorption edge of high Z-elements present in the samples. The low-value of buildup factor in the lower energy region is due to the predominance of the photoelectric effect in this energy region, which results in the fast removal of low-energy photons due to absorption thereby not allowing these photons to buildup. The Compton effect is a most dominant process in energy degradation of the incident photon in the medium energy region. In the medium energy region, the buildup factor values are very high for a given penetration depth due to the dominance of Compton effect, which only helps in the degradation of

Fig. 5. Variation of the MFP values with incident photon energy for the studied glasses and some standard concretes.

photon energy due to scattering process. This leads to the higher value of buildup factor, as large numbers of Compton events are required to degrade the energy of the photon and as a result of these photons exist for a longer time in the material. The pair-production phenomenon dominates over Compton effect for higher energies. The behavior in the high-energy region is similar to the behavior of buildup factor for high Z elements with energies. Further, it is identified that the EBF increases with an increase in penetration depth for a given compensator material. This occurs due to the reason that with an increase in penetration depth the probability of multiple scattering increases, which results in the 6

Journal of Non-Crystalline Solids xxx (xxxx) xxx–xxx

G. Lakshminarayana et al. 10

4

S2

4

10

S1

10

3

----- Buildup factor ----->

----- Buildup factor ----->

10

1 mfp 5 mfp 10 mfp 20 mfp 30 mfp 40 mfp

2

10

1

10

0

3

10

2

10

1

10

0

10

10

-2

10

-1

10

0

-2

1

10

10

----- Energy (MeV) ----->

10

1 mfp 5 mfp 10 mfp 20 mfp 30 mfp 40 mfp

S3

4

-1

0

10

10

2

10

1

10

0

1 mfp 5 mfp 10 mfp 20 mfp 30 mfp 40 mfp

3

----- Buildup factor ----->

----- Buildup factor ----->

3

10

2

10

1

10

0

10

10

-2

10

-1

10

0

1

-2

10

10

10

4

1 mfp 5 mfp 10 mfp 20 mfp 30 mfp 40 mfp

S5

10

3

10

2

10

1

10

0

0

10

1

10

1 mfp 5 mfp 10 mfp 20 mfp 30 mfp 40 mfp

S6

6

10

5

10

----- Buildup factor ----->

----- Buildup factor ----->

5

-1

10

----- Energy (MeV) ----->

----- Energy (MeV) ----->

10

10

1 mfp 5 mfp 10 mfp 20 mfp 30 mfp 40 mfp

4

10

S4

10

1

10

----- Energy (MeV) ----->

4

10

3

10

2

10

1

10

0

10 10

-2

10

-1

10

0

10

-2

1

10

-1

10

0

10

1

10

----- Energy (MeV) ----->

----- Energy (MeV) ----->

Fig. 6. Variation of EBFs with incident photon energy at different penetration depths for selected glass samples.

selected materials at a fixed value of incident energy. The EBF varies inversely with Zeq up to 3 MeV. It is because of the reason that due to multiple scattering, the low energy photons buildup within the material. There is a competition between the two interaction processes namely photoelectric effect and Compton scattering. But the probability of photoelectric effect in the low-energy region is more due to its Z dependence (∝ Z4–5) as compared to Compton scattering, which varies linearly with Z. So, there is a possibility of absorption of these photons by high Z elements, thereby reducing the number of photons in the scatter part, which results in the lowering of the buildup factor for high Z elements containing materials [30]. Beyond 3 MeV, the probability for pair production is considerably large, which has Z2 dependence and with further increase in energy, its probability increases. Consequently, a pair of electron and positron is

increase of multiple scattered photons, hence the increment in EBF values [32–34]. The variations of EBFs of studied glasses with incident photon energy at the penetration depths of 1, 5, 10, 20, 30 and 40 mfp are shown in Fig. 7. It is observed that EBF values are different for different glasses for a fixed penetration depth. For a penetration depth of 1 and 5 mfp, the value of EBF is maximum for S1 sample and is least for sample S6 for all energies except at 0.03 MeV and for energies above 8 MeV. But for penetration depths of 10, 20, 30 and 40 mfp, the value of buildup factor is maximum for S1 glass but is least for S6 sample for incident energies up to 3 MeV. But above this energy, the value of EBF is maximum for sample S6 and is least for S1 glass. The complete trend reversal takes place at 6 mfp penetration depths. The Zeq of S1 is the minimum and that of S6 is maximum among the 7

Journal of Non-Crystalline Solids xxx (xxxx) xxx–xxx

G. Lakshminarayana et al.

----- Buildup factor ----->

10

1

10

0

S1 S2 S3 s4 S5 S6

5 mfp

----- Buildup factor ----->

S1 S2 S3 s4 S5 S6

1 mfp

0

10

10

-2

-1

10

10

0

10

1

10

-2

----- Energy (MeV) ----->

10

10

1

-2

10

-1

10

2

10

1

0

10

10

0

1

10

-2

3

10

2

10

1

S1 S2 S3 s4 S5 S6

30 mfp

4

10

10

10

-1

0

10

10

1

5

----- Buildup factor ----->

----- Buildup factor ----->

10

1

----- Energy (MeV) ----->

----- Energy (MeV) -----> 10

10

S1 S2 S3 s4 S5 S6

3

10

0

10

0

10

20 mfp

----- Buildup factor ----->

----- Buildup factor ----->

10

-1

----- Energy (MeV) ----->

S1 S2 S3 s4 S5 S6

10 mfp

10

0

10

-2

10

-1

10

0

10

1

10

6

10

5

10

4

10

3

10

2

10

1

10

0

S1 S2 S3 s4 S5 S6

40 mfp

10

-2

10

-1

0

10

10

1

----- Energy (MeV) ----->

----- Energy (MeV) ----->

Fig. 7. Comparison of EBFs of studied glasses with incident photon energy at fixed penetration depths of 1, 5, 10, 20, 30 and 40 mfp, respectively.

the high Z material. So, for the incident energies above 3 MeV, the EBF is lesser for S1 glass sample due to the elimination of incident photons because of pair-production and for the penetration depth above 6 mfp, the buildup factor is more for the same material due to the multiple scattering of the 511 keV photons formed due to pair production [30].

created in the medium. Depending upon the energy of the incident photon, the pair of electron and positron possesses sufficient kinetic energy. The positron suffers a collision with the medium and finally annihilated, which results in the creation of a pair of 511 keV photons. For smaller values of penetration depth (e.g. 5 mfp) the thickness is not sufficient for these photons to get multiple scatterings and to add to the value of buildup factor. More is the Z of a medium; greater is the pair production cross section. Then, more number of photons is eliminated from the incident beam, which decreases the value of buildup factor for high Z materials. But for the thicknesses > 6 mfp, the 511 keV photons undergo multiple scattering, which results in the increment of multiple scattered photons, hence increases the value of buildup factor for the material having a higher value of cross section for pair production i.e.

4. Conclusions In summary, γ-ray shielding features for different compositions of TeO2-B2O3-Bi2O3-TiO2 (mol %) glasses were investigated in terms of μ/ ρ, Zeff, Ne, MFP, HVL, and EBF. The μ/ρ values are evaluated by both XCOM program and MCNP5 code, and up to 6 MeV, the small percentage deviation between the obtained μ/ρ values of both methods 8

Journal of Non-Crystalline Solids xxx (xxxx) xxx–xxx

G. Lakshminarayana et al.

demonstrate good agreement. Among the selected glasses, 30 TeO2–30 B2O3–30 Bi2O3–10 TiO2 glass possesses the best shielding properties, which means the addition of Bi2O3 enhances the shielding properties. The MFP values were compared with seven types of concretes and all glasses exhibit lower MFP values than the concretes, which indicates that the γ-ray shielding features of the studied glass samples are superior to several standard shielding concretes. The novelty of the work lies in the fact that the selected compositions are better shielding materials and the gamma-ray interactions studies have been conducted for the first time for these compositions.

(2017) 72–77. [14] N. Gupta, A. Kaur, A. Khanna, F. Gonzàlez, C. Pesquera, R. Iordanova, B. Chen, Structure-property correlations in TiO2-Bi2O3-B2O3-TeO2 glasses, J. Non-Cryst. Solids 470 (2017) 168–177. [15] S. Singh, A. Kumar, D. Singh, K.S. Thind, G.S. Mudahar, Barium–borate–fly ash glasses: as radiation shielding materials, Nucl. Inst. Methods Phys. Res. B 266 (2008) 140–146. [16] M.I. Sayyed, H. Elhouichet, Variation of energy absorption and exposure buildup factors with incident photon energy and penetration depth for boro-tellurite (B2O3TeO2) glasses, Radiat. Phys. Chem. 130 (2017) 335–342. [17] L. Gerward, N. Guilbert, K.B. Jensen, H. Levring, X-ray absorption in matter. Reengineering XCOM, Radiat. Phys. Chem. 60 (2001) 23–24. [18] M. Dong, B.O. Elbashir, M.I. Sayyed, Enhancement of gamma ray shielding properties by PbO partial replacement of WO3 in ternary 60TeO2–(40-x)WO3–xPbO glass system, Chalcogenide Lett. 14 (2017) 113–118. [19] F. Akman, R. Durak, M.F. Turhan, M.R. Kacal, Studies on effective atomic numbers, electron densities from mass attenuation coefficients near the K edge in some samarium compounds, Appl. Radiat. Isot. 101 (2015) 107–113. [20] A. Kumar, Gamma ray shielding properties of PbO-Li2O-B2O3 glasses, Radiat. Phys. Chem. 136 (2017) 50–53. [21] M.I. Sayyed, Half value layer, mean free path and exposure buildup factor for tellurite glasses with different oxide compositions, J. Alloys Compd. 695 (2017) 3191–3197. [22] M.I. Sayyed, S.I. Qashou, Z.Y. Khattari, Radiation shielding competence of newly developed TeO2-WO3 glasses, J. Alloys Compd. 696 (2017) 632–638. [23] V.P. Singh, M.E. Medhat, N.M. Badiger, Assessment of exposure buildup factors of some oxide dispersion strengthened steels applied in modern nuclear engineering and designs, Nucl. Eng. Des. 270 (2014) 90–100. [24] M.I. Sayyed, Y. Elmahroug, B.O. Elbashir, S.A.M. Issa, Gamma-ray shielding properties of zinc oxide soda lime silica glasses, J. Mater. Sci. Mater. Electron. 28 (2017) 4064–4074. [25] B.O. El-bashir, M.I. Sayyed, M.H.M. Zaid, K.A. Matori, Comprehensive study on physical, elastic and shielding properties of ternary BaO-Bi2O3-P2O5 glasses as a potent radiation shielding material, J. Non-Cryst. Solids 468 (2017) 92–99. [26] K.A. Matori, M.I. Sayyed, H.A.A. Sidek, M.H.M. Zaid, V.P. Singh, Comprehensive study on physical, elastic and shielding properties of lead zinc phosphate glasses, J. Non-Cryst. Solids 457 (2017) 97–103. [27] G.S. Mudahar, S. Modi, M. Singh, Total and partial mass attenuation coefficients of soil as a function of chemical composition, Appl. Radiat. Isot. 42 (2004) 13–18. [28] H.E. Hassan, H.M. Badran, A. Aydarous, T. Sharshar, Studying the effect of nano lead compounds additives on the concrete shielding properties for gamma-rays, Nucl. Inst. Methods Phys. Res. B 360 (2015) 81–89. [29] V.P. Singh, N.M. Badiger, J. Kaewkhao, Radiation shielding competence of silicate and borate heavy metal oxide glasses: comparative study, J. Non-Cryst. Solids 404 (2014) 167–173. [30] S. Kaur, A. Kaur, P.S. Singh, T. Singh, Scope of Pb-Sn binary alloys as gamma rays shielding material, Prog. Nucl. Energy 93 (2016) 277–286. [31] I.I. Bashter, Calculation of radiation attenuation coefficients for shielding concretes, Ann. Nucl. Energy 24 (1997) 1389–1401. [32] V.P. Singh, N.M. Badiger, N. Chanthima, J. Kaewkhao, Evaluation of gamma-ray exposure buildup factors and neutron shielding for bismuth borosilicate glasses, Radiat. Phys. Chem. 98 (2014) 14–21. [33] V.P. Singh, M.E. Medhat, N.M. Badiger, A.Z.M. Rahman, Radiation shielding effectiveness of newly developed superconductors, Radiat. Phys. Chem. (2015) 175–183. [34] S.R. Manohara, S.M. Hanagodimath, L. Gerward, K.C. Mittal, Exposure buildup factors for heavy metal oxide glass: a radiation shield, J. Korean Phys. Soc. 59 (2011) 2039–2042.

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