Comparative investigations of gamma and neutron radiation shielding parameters for different borate and tellurite glass systems using WinXCom program and MCNPX code

Accepted Manuscript Comparative investigations of gamma and neutron radiation shielding parameters for different borate and tellurite glass systems using WinXCom program and MCNPX code M.I. Sayyed, M.G. Dong, H.O. Tekin, G. Lakshminarayana, M.A. Mahdi PII:

S0254-0584(18)30377-8

DOI:

10.1016/j.matchemphys.2018.04.106

Reference:

MAC 20601

To appear in:

Materials Chemistry and Physics

Received Date: 5 January 2018 Revised Date:

6 April 2018

Accepted Date: 29 April 2018

Please cite this article as: M.I. Sayyed, M.G. Dong, H.O. Tekin, G. Lakshminarayana, M.A. Mahdi, Comparative investigations of gamma and neutron radiation shielding parameters for different borate and tellurite glass systems using WinXCom program and MCNPX code, Materials Chemistry and Physics (2018), doi: 10.1016/j.matchemphys.2018.04.106. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

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HVL (cm)

10 8 6 4

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BBi25 BBi30 BBi40 BBi50 BBi60 BBi65 Ordinary Hematite-serpentine Ilmenite Steel-scrap Ilmenite-limonite

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Graphical abstract

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Energy (MeV)

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Comparative investigations of gamma and neutron radiation shielding parameters for different borate and tellurite glass systems using WinXCom program and MCNPX code M.I. Sayyeda, M.G. Dongb, H.O. Tekinc,d, G. Lakshminarayanae,*, M.A. Mahdie

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a

Physics Department, University of Tabuk, Tabuk, Saudi Arabia Department of Resource and Environment, School of Metallurgy, Northeastern University, Shenyang 110819, China c Uskudar University, Vocational School of Health Services, Radiotherapy Department, Istanbul 34672, Turkey d Uskudar University, Medical Radiation Research Center (USMERA), Istanbul 34672, Turkey e Wireless and Photonic Networks Research Centre, Faculty of Engineering, Universiti Putra Malaysia, Serdang, 43400, Selangor, Malaysia

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Abstract

In the present article, for different chemical compositions of B2O3‒Bi2O3, B2O3‒Sb2O3, B2O3‒WO3‒La2O3, B2O3‒MoO3‒ZnO, and TeO2‒MO (M=Mg, Ba, and Zn) glasses, by applying WinXCom program we calculated the mass attenuation coefficient (µ/ρ) values, and from these

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values, the effective atomic number (Zeff), electron density (Ne), mean free path (MFP), halfvalue layer (HVL), and exposure buildup factor (EBF) values using Geometric progression (G‒P) fitting method, including macroscopic effective removal cross-section (ΣR) values for fast

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neutrons are evaluated for their potential applications as γ-ray and neutron radiation shielding

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materials. Moreover, the µ/ρ values of all the studied different glass compositions were computed using MCNPX simulation code and compared with WinXCom results. BBi65 glass has the highest µ/ρ, and Zeff values in the B2O3‒Bi2O3 glasses and lower values of MFP, HVL, and EBF. The maximum values of µ/ρ and Zeff are recorded for BSb70 in the B2O3‒ Sb2O3 glasses. It is found that the Zeff for B2O3‒Bi2O3 glasses is lower than those for B2O3‒ Sb2O3 glasses, which reveal that the B2O3‒Bi2O3 glasses have better shielding properties than the B2O3‒Sb2O3 glasses. The µ/ρ values of B2O3‒WO3‒La2O3 glasses are higher than those

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B2O3‒MoO3‒ZnO glasses, which indicate that B2O3‒WO3‒La2O3 glasses show preferable radiation shielding effectiveness comparing with B2O3‒MoO3‒ZnO glasses. The variation of different shielding parameters for the selected glasses was discussed according to the three

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photon interactions with matter (Photoelectric effect, Compton scattering, and pair production). The calculated µ/ρ and Zeff for the selected glasses have been compared with different glasses. HVL values are compared with ordinary, hematite-serpentine, ilmenite, steel-scrap and ilmenite-

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limonite concretes. It is found that ΣR values for B2O3‒Bi2O3, B2O3‒Sb2O3, B2O3‒WO3‒La2O3, B2O3‒MoO3‒ZnO, and TeO2‒MO (M=Mg, Ba, and Zn) glasses lie within the range 0.1312-

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0.2823 cm-1, 0.0876-0.0957 cm-1, 0.1180-0.1085 cm-1, 0.1066 - 0.1002 cm-1, and 0.1040-0.1075 cm-1, respectively.

Keywords: WinXCom; MCNPX code; Mass attenuation coefficient; Mean free path; Half-value layer

1. Introduction

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*Corresponding author‒E-mail: [email protected]; [email protected]

Due to the increasing applications of radioactive isotopes and nuclear energy in medicine,

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petroleum plants, nuclear power plants, outer space research, industries, and agriculture, among

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researchers there has been great attention paid to the development of novel radiation shielding materials to protect personnel from the hazardous radiation effects at the radiation sites [1, 2]. Particularly, at nuclear reactors, emitted radiations are neutrons, primary γ-rays that are originated from the reactor core and the secondary γ-rays created by neutrons interaction with substances external to the core. As a matter of fact, nowadays, traditionally, different types of concretes are in use at nuclear power plants and nuclear waste storage sites for radiation protection and shielding from gamma, X-ray, and other ultra-high energy radiations. Though

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concrete is cost-effective and shows structural flexibility for required constructions design, there exist some demerits with concretes like variation in their composition and water content and here, higher H2O content causes to deterioration of concrete structural strength and decrement in

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its density, further, H2O will be lost when concrete is subjected to prolonged exposures to the radiations as it becomes hot by radiation energies absorption. Further, concretes are utterly opaque to visible light and so, it is quite impossible to look through a concrete-based radiation

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shield [3, 4]. Generally, materials to be applicable for radiation shielding, need to possess homogeneity of density and chemical composition. In this regard, various alternative materials

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such as steel, composites, resins, alloys, and polymers etc. have been chosen and evaluated for the radiation shielding applications [5‒8]. Due to their optical transparency for visible light, cheap cost, ease of fabrication in different shapes and sizes with no variation in their density and composition with external fields, glasses recently are attracted many researchers to study them as

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promising materials for γ-rays and neutron radiation shielding [1, 2, 4, 6‒11]. Accurate values of various parameters like mass attenuation coefficient (µ/ρ), effective atomic number (Zeff), electron density (Ne), mean free path (MFP), and half-value layer (HVL), which

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determine the scattering and absorption of γ-rays in matter are necessary to judge a material’s practical application in radiation shielding. Usually, γ-rays interaction is dependent upon photon

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energy, density and an atomic number of elements present in the materials and high values of density and lower values of MFP and HVL are required for best radiation shielding applications [12]. Thus, as glass components, high atomic number (Z) metal-oxides/heavy metal oxides (HMOs) (e.g. PbO) show better shielding properties under γ and X-ray and other forms of harmful radiations. These HMO based glasses possess physical features such as high density, high dielectric constant, and wide optical transparency (~ 8 µm) including low glass transition

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temperature etc.[2]. But, due to the harmful effects of Pb toxic nature on human health and environment, nowadays, researchers are focusing more on other HMOs such as BaO and Bi2O3 as substitutes for the Pb in glasses for γ-rays shielding [11, 13]. Moreover, in glasses, for

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elements Bi (Z=83) and Pb (Z=82), both Bi3+ and Pb2+ ions have the same 6s2 electronic configurations and there exist much similarity in various properties like atomic weight, ionic radius and wide glass formation regions, and in toxicity, however, Bi is much safer than Pb.

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Here, to attenuate neutron radiation, one can consider the addition of ‘Li’ and ‘B’ elements to the glass network [4, 13].

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Among various kinds of oxide glasses, borates are most commonly used glass formers, since B2O3 shows excellent glass forming ability in a wide composition range even without the addition of any network modifiers and when modifier oxides like alkali (e.g. Li2O) or alkaline (e.g. MgO) or ZnO added to it, the covalent network of B2O3 modifies significantly to

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accommodate modifier ions by the formation of anionic sites and nonbridging oxygens (NBOs), due to conversion of BO3 structural units into BO4 units [14]. Moreover, borate glasses possess a high strength of covalent B‒O bond, wide optical transparency, and good thermal stability. On

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the other hand, TeO2-rich glasses exhibit low melting temperature, low-phonon energy, nontoxicity, high density, high refractive index (≥2),large third-order nonlinear optical susceptibility

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(χ(3)), high chemical durability, excellent optical transparency up to far-infrared region (~6 µm), and non-hygroscopic nature. However, TeO2 alone, unlike B2O3, doesn’t form glass itself (i.e. TeO2 is a conditional glass former) and it needs at least one modifier oxide like MgO or ZnO or another glass former (e.g. B2O3) in order to form the glass network, where both TeO3 and TeO4 functional groups exist [15]. Here, it should be worth mentioning that ZnO or WO3 and MoO3 at lower concentrations play network modifier role while at higher concentrations they have the

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ability to show glass network forming nature when introduced into the glass matrix [15‒17]. Here, homogeneity of the glass is directly related to the distribution of different structural units and modifier ions within the glass matrix. It is identified that lanthanum oxide (La2O3) acts as a

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network modifier during its addition to the glass network and forms NBOs [18]. In glasses, Sb2O3 inclusion could reduce the melting temperature, enhances the glass forming ability, and decreases the phonon energy of the glasses and creates NBOs when it acts as a modifier oxide

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[19].

In the present article, for different chemical compositions of B2O3‒Bi2O3, B2O3‒Sb2O3,

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B2O3‒WO3‒La2O3, B2O3‒MoO3‒ZnO, and TeO2‒MO (M=Mg, Ba, and Zn) glasses, by applying WinXCom program we calculated the µ/ρ values, and from these values, the Zeff, Ne, MFP, HVL, and exposure buildup factor (EBF) values using Geometric progression (G‒P) fitting method, including macroscopic effective removal cross-section values for fast neutrons are evaluated for

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their potential applications as γ-ray and neutron radiation shielding materials. Moreover, the µ/ρ values of all the studied different glass compositions were computed using MCNPX simulation code and compared with WinXCom results. For the studied glass compositions in this work, the

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density values were adopted from the Refs. [20‒24]. Compositions of the glasses with their densities are given in Table 1(i-iv). In addition, the description of elemental composition is

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given in Table 2(i-iv).

2. Theoretical background 2.1 Gamma‒ matter interactions Gamma radiation is a form of electromagnetic radiation in the high energy region of the electromagnetic spectrum. Gamma rays can interact with matter and this interaction can take several forms. Each interaction type brings different physical results. Although, gamma rays

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have different forms of interaction with matter only three dominant forms of interaction (i.e. photoelectric absorption, Compton scattering, and pair production) are crucial [25, 26]. 2.2 MCNPX simulation code

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Monte Carlo N-Particle Transport Code System-extended (MCNPX) version 2.6.0 (Los Alamos national laboratory, USA) general-purpose Monte Carlo code was applied for the determination of µ/ρ of investigated glass samples. MCNPX is a Monte Carlo code for simulation of various

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physical interactions at wide energy range. MCNPX is fully three-dimensional and it utilizes extended nuclear cross section libraries and uses physics models for particle types [27]. Similar

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to the methodology in this study, some MCNPX studies for different radiation applications can be found in the literature [28‒37]. Simulation parameters such as cell specifications, surface specifications, material specifications and position determinations of each simulation tools have been defined in input file according to their physical features. The input structure of MCNPX

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code has three major parts such as description of the problem geometry, defining the materials with their chemical combination and the structure of radiation source. The µ/ρ of each glass samples was measured in a narrow beam transmission geometry using point isotropic source

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with collimated and monoenergetic beam. In this study, each glass sample has been defined considering their elemental mass fractions and chemical composition as listed in Table 2. The

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present simulation geometry of mass attenuation coefficient calculations and the design and screenshot of MCNPX simulation setup is shown in Fig. 1 (a) and (b), respectively. The analysis of investigation was performed using the D00205ALLCP03 MCNPXDATA package, comprised of DLC-200/MCNPDATA cross-section libraries. This library typically extends ENDF/B-VI data from 20 MeV to 150 MeV. To obtain the absorbed dose amount in the detection field, average flux tally F4 has been used. In addition, 108 particles have been tracked as the number of

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particle (NPS variable). MCNPX calculations were done by using Intel® Core ™ i7 CPU 2.80 GHz computer hardware. Finally, the error rate has been observed less than 0.1% in the output file.

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2.3 WinXcom program

In this study, WinXcom program [38] was also used to calculate the gamma ray mass attenuation coefficients of the investigated glass samples. WinXcom program is a user friendly calculation

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program and input parameter specifications are quite understandable and easy to access. In the WinXcom program, material types were defined by their elemental fractions, which are totally

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the same as in MCNPX Monte Carlo code. Afterwards, the gamma ray energies have been defined. The attenuation coefficients of the selected glasses were finally calculated by the program. 2.4 Radiation shielding parameters

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2.4.1 Mass attenuation coefficients

The mass attenuation coefficient (µ/ρ) is the basic quantity through which the rest of other quantities, such as Zeff, Ne, HVL…etc can be calculated. The mass attenuation coefficient (µ/ρ)

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of a glass sample at a specific energy is the sum of the products of the weight fraction and the

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mass attenuation coefficient of the element i at that energy namely [39]:

⁄ =

( ⁄ ) (1)

where wi and (µ/ρ)i are the fractional weight and the total mass attenuation coefficient of the ith constituent in the glass sample. The mass attenuation coefficients of the elements constituting the glasses at certain energy were obtained from WinXcom program [38]. 2.4.2 Effective atomic number and electron density 7

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The effective atomic number (Zeff) is an important parameter that describes the multi-element materials in terms of equivalent elements and is used in radiation response characterization. In addition, the electron density (Ne) is the number of electron per unit mass [40]. In this work, the

values we can determine the electron density as described in [42]. 2.4.3 Half value layer and mean free path

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Zeff for the present glasses have been calculated using the Auto-Zeff software [41]. From the Zeff

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The half value layer (HVL) is the thickness of glass sample required to attenuate 50% of the incident gamma ray. Besides, the mean free path (MFP) is the average distance traveled by a

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photon (gamma ray) in the medium before an interaction occurs [43]. HVL and MFP were calculated using the following relations [44]: =

0.693

(2)

1 = (3)

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where µ is the linear attenuation coefficient (cm-1). The linear attenuation coefficient (µ) of the glass sample was calculated by multiplying the mass attenuation coefficient of the glass by its

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respective density.

2.4.4 Exposure buildup factor

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The buildup factor is the correction quantity used for attenuation calculations. It represents the contribution of collided part of gamma radiations. The exposure buildup factor (EBF) can be calculated for a glass samples using G-P fitting formula [1, 4, 36, 37, 45‒49]. Steps to calculate EBF can be summarized as follows: a. Calculations of equivalent atomic number (Zeq) The following relation was used to calculate the Zeq for the glasses envisaged in this work [50]: 8

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=

(

)+ −

−

(

− log R )

(4)

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where Z1 and Z2 are the atomic numbers for the elements corresponding to the ratio R1 and R2. b. Calculations of G-P fitting parameter

The G-P fitting parameters (b, c, a, Xk and d) are used for the calculation of EBF. Their

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values are available in standard reference ANSI/ANS-6.4.3 [51]. The EBF G-P fitting parameters for the present glasses can be calculated by the following relation: )* +,-./0 1,-./23 45)0 +,-./23 1,-./* 4 (,-./0 1,-./* )

[5]

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C =

where C1 andC2 are the values of G-P fitting parameters corresponding to the atomic numbers Z1 and Z2 respectively for a certain energy between for which Z1 < Zeq < Z2.. c. Calculations of EBF

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The G-P fitting parameters then used to calculate the EBF with the help of the following formulas: 9(:, <) = 1 +

=−1 ? (> − 1) for > ≠ 1 (6) >−1

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9 (:, <) = 1 + (= − 1)< for > = 1 (7) where K(E, x) is the photon dose multiplication factor which can be calculated using the

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following relation:

>(:, <) = D< E + F

tanh (< ⁄KL − 2) − tanh (−2) for < ≤ 40 NOP (8) 1 − tanh (−2)

here E represents the incident photon energy, x is source to detector distance in the medium in unit of mean free path (mfp), and b is the buildup factor at 1 mfp. 2.4.5 Macroscopic effective removal cross section for fast neutrons

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The removal cross-sections, ΣR (cm-1) for the glass systems investigated in this work were evaluated using the mass removal cross section, ΣR/ρ values for elements constituting the

∑S =

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material by using the following relations [52]: T (∑S / ) (9)

where Wi is the partial density which can be calculated using:

V (10)

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T =

3. Results and discussion

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where wi represents the weight fraction of the i constituent and ρs is the density of the sample.

Figs. 2-5 clearly explain the variation of µ/ρ values for B2O3‒Bi2O3, B2O3‒Sb2O3, B2O3‒WO3‒La2O3, B2O3‒MoO3‒ZnO, and TeO2‒MO (M=Mg, Ba, and Zn) glass compositions with incident photon energies, respectively. From these figures it is observed that the µ/ρ values

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attain their maximum values (in the range of 70-95 g/cm2, 15-37 g/cm2, 35-85 g/cm2 and 38-47 g/cm2 for glasses in Fig. 2-5, respectively) at lower photon energies (i.e. 0.015 MeV), where photoelectric effect predominates. Thereafter, the µ/ρ values for all selected glasses decrease

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sharply with increasing photon energy. For photon energy larger than 0.08 MeV, the µ/ρ values

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vary in a narrow range for all selected glasses and exhibit a less energy-dependent manner. This can be attributed to Compton effect, which is dominating in this intermediate energy range. As the photon energy becomes greater than 1 MeV, the µ/ρ values tend to be almost constant due to the dominance of pair production process [53]. It can be seen from Fig. 2 that the µ/ρ values increase with an increase in Bi2O3 modifier content in the B2O3-Bi2O3 glasses range from 25 to 65 mol % Bi2O3 and it is obvious that the BBi65 glass has the highest values of µ/ρ values and this is because this glass sample contains the highest amount of Bi (from Table 2, weight fraction

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of Bi= 83.0198 %). Also, it is clear from Fig. 2 that the variation of µ/ρ has discontinuities at around 0.1 MeV, which arise from photoelectric effect around the K-absorption edge of Bi. In addition, from Fig. 3 it is obvious that the µ/ρ values increase with the increase of Sb2O3 mol %

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and the maximum values of µ/ρ are recorded for BSb70 and the discontinuities in the µ/ρ values are clear at around 0.03 MeV due to photoelectric effect around the K-absorption edge of Sb. From Fig. 4 it can be seen that LBW50 glass has the highest values of mass attenuation

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coefficient and the µ/ρ values of B2O3-WO3-La2O3 glasses are higher than B2O3-MoO3-ZnO glasses, which indicate that B2O3-WO3-La2O3 glasses show preferable radiation shielding

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effectiveness comparing with B2O3-MoO3-ZnO glasses. Discontinuities in µ/ρ values were observed due to K-absorption edge at 20.00 keV, 38.92 keV and 69.53 keV for Mo, La, and W; respectively. As can be seen from Fig. 5, TBa10 possesses the maximum values of µ/ρ (except at 0.015 MeV) and the discontinuities in the values of µ/ρ occur at 0.04 MeV, which attributed to

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K-absorption edge of Te and Ba at 31.81 keV and 37.44 keV, respectively. Besides, we reported the mass attenuation coefficients of the selected glasses by using MCNPX (version 2.4.0) Monte Carlo code. The validation of modeled MCNPX code has been obtained by comparing the results

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with standard WinXcom data. In Table 3 (i) - (iv), we listed the µ/ρ values obtained by MCNPX code and WinXcom software. The results showed that MCNPX Monte Carlo values generally

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agreed well with WinXcom data. The difference between the MCNPX results values of µ/ρ and calculated WinXcom results can be estimated using the following relation: TZ[KD N − \] K ) × 100%Y (11) Diff. = Y( TZ[KD N

The difference (Diff.) between the MCNPX results and calculated WinXcom values of µ/ρ deduced from Eq. (11) are listed in Table 3 (i)-(iv).

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The Diff. in µ/ρ values are in the range of 0‒11.06 % for B2O3-Bi2O3 glasses, while the Diff. is very small (0‒7.44) for B2O3-Sb2O3 glasses, and the Diff. is in the range of between (0.016‒9.57)

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and (0.003‒7.52) for glasses in Table 3 (iii) and (iv), respectively. The calculated effective atomic numbers (Zeff) as a function of photon energy for B2O3‒Bi2O3, B2O3‒Sb2O3, B2O3‒WO3‒La2O3, B2O3‒MoO3‒ZnO, and TeO2‒MO (M=Mg, Ba, and Zn)

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glasses are presented in Figs. 6-9 respectively.

As can be seen from Fig. 6 the maximum value of Zeff is observed in the low energy region and

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the variation of Zeff is negligible between 0.03-0.8 MeV where the Compton scattering dominates, while the Zeff reaches its minimum value between 1-4 MeV. Besides, the Zeff for B2O3‒Bi2O3 glasses were found in the range of 17-46, 19-48, 23-52, 27-55, 30-58 and 32-60 for BBi25, BBi30, BBi40, BBi50, BBi60, and BBi65, respectively. In addition, Fig. 6 shows that the Zeff increases with the increase of Bi2O3 content. The calculated Zeff for B2O3‒Bi2O3 glasses are

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lower than those of lithium zinc bismuth borate glasses [13]. From Fig. 7 we can observe that the Zeff for B2O3‒Sb2O3 glasses changes in the same way as in Fig. 6, the maximum Zeff is found in the energy region of 0.04-0.08 MeV while the minimum Zeff

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is found in the energy region of 1-3 MeV. Also, from Fig. 7 it can be noticed that the Zeff are in

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the range of 9-22, 11-26, 13-29, 15-32, 17-33, 19-35 and 21-36 for BSb10, BSb20, BSb30, BSb40, BSb50, BSb60 and BSb70, respectively. It can be observed that the Zeff for B2O3‒Sb2O3 glasses is lower than those for B2O3‒Bi2O3 glasses. Besides, from Fig. 7, one can observe that Zeff increases with the addition of Sb2O3 in the B2O3‒Sb2O3 glasses. The lower values of Zeff for B2O3‒Sb2O3 glasses than B2O3‒Bi2O3 glasses reveal that the B2O3‒Bi2O3 glasses have better shielding properties than the B2O3‒Sb2O3 glasses. The calculated values of Zeff of B2O3‒Sb2O3 glass system are lower than those of 80TeO2-20WO3 and 80TeO2-20BaO glasses [54]. 12

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Fig. 8 illustrates the variation of Zeff for B2O3‒WO3‒La2O3 and B2O3‒MoO3‒ZnO glass systems. It can be seen from Fig. 8 that in the low photon energy, all the samples have high Zeff values and the Zeff for B2O3‒WO3‒La2O3 glasses are higher than those for B2O3‒MoO3‒ZnO glasses. At a

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lower photon energy (i.e. 0.015 MeV), the Zeff is equal to 37.7, 40.4 and 45.8 for LBW15, LBW25, and LBW50, while the Zeff of the B2O3‒MoO3‒ZnO glasses were found as 18.4, 19 and 19.6 for ZBMo10, ZBMo20 and ZNMo30, respectively. This behavior of Zeff in the low energy

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range can be explained on the basis of the dependence of cross-section of photoelectric process on the atomic number of elements as Z4-5. From Fig. 8, and for both glass systems, the minimum

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Zeff values were found in the energy range of 1-4 MeV. This can be attributed to Compton scattering process, which dominated in this energy range, and the interaction cross section is directly proportional to atomic number Z. On the other hand, the Zeff values increase with an increase in WO3 and MoO3 contents in the B2O3‒WO3‒La2O3 and B2O3‒MoO3‒ZnO glasses,

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respectively. The Zeff of the present B2O3‒MoO3‒ZnO glasses are slightly smaller than those of B2O3‒Bi2O3. Also, the Zeff values for B2O3‒WO3‒La2O3 glasses are lower than those reported for TeO2-WO3-PbO [55] and K2O-WO3-TeO2 [56].

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Fig. 9 shows the variation of the Zeff of 90TeO2-10MgO, 80TeO2-20MgO, 90TeO2-10BaO and 60TeO2-40ZnO glasses. The same general shape was observed for niobium tellurite glasses [57].

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It is clear that there are two energy regions in which the Zeff values are nearly constant. These two regions are 0.03-0.06 MeV and 0.8-3 MeV, respectively. Between these energy regions, there is a transition region with a rapid reduction in the Zeff values in the transition region. In addition, from Fig. 9 it can be seen that the Zeff values of TBa10 were maximum whereas those of TMg20 minimum. This is due to the fact that TBa10 contains high Z-element (i.e. Ba, Z=56), hence we can conclude that TBa10 is the superior γ-ray attenuator among the tellurite glasses

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presented in Fig. 9. The calculated Zeff for the selected glasses in Fig. 9 are higher than those for 80TeO2–20B2O3 [54], while the Zeff for TBa10 and TMg20 are higher than those for 80TeO2– 20K2O and 80TeO2–20V2O5 [54].

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The effective electron density (Ne) for B2O3‒Bi2O3, B2O3‒Sb2O3, B2O3‒WO3‒La2O3, B2O3‒MoO3‒ZnO, and TeO2‒MO (M=Mg, Ba, and Zn) glasses are shown in Figs. 10-13. A similar trend was noticed in the variation of the effective electron density values with the

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incident photon energy as Zeff since the Ne is directly proportional to the Zeff.

Mean free path is an important parameter, which plays a crucial role in understanding the

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exponential attenuation of photons. From the values of mass attenuation coefficient at different energies (Figs. 2-5) and density (Table 1), the values of MFP corresponding to each selected glass composition at different energies ranging from 0.015-10 MeV were calculated using Eq. 3, and the results are shown in Figs. 14-17. Fig.14 shows the variation of MFP with photon energy

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for the glasses (100-x) B2O3-xBi2O3, where (x=25, 30, 40, 50, 60 and 65 mol %). In the low photon energy region (E<0.015 MeV), the MFP for all glasses are roughly constant, while the MFP shows significant changes from 0.2 MeV up to 6 MeV. Since the MFP related to the mass

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attenuation coefficient, the variation of MFP can be explained on the same basis of the dominance of several partial photon interaction processes in different energy regions [58].

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Additionally, it was found that MFP values were decreased with increasing Bi2O3 concentration as well as the density, so from Fig. 14 we can see that BBi65 has the lowest MFP and this emphasize our estimation that the shielding properties of the B2O3-Bi2O3 glass system enhance with the addition of Bi2O3.

The variation of MFP for the glasses (100-x) B2O3-xSb2O3, where (x=10, 20, 30 40, 50, 60 and 70 mol %) is shown graphically in Fig. 15. It is clear that the MFP values of all

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compositions increase sharply in the energy range of 0.1-10 MeV. Besides, the MFP values are almost composition independent for energy less than 0.1 MeV. In this energy region (i.e. E<0.1 MeV), all the samples seem to have the same MFP values. It should be pointed out that SbB70

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and SbB10 have the lowest and highest MFP among the glass samples presented in Fig. 15 respectively. So, the addition of Sb2O3 to B2O3– Sb2O3 glasses, leads to decrease the MFP. Moreover, From Fig. 14 and Fig. 15, the MFP values of B2O3-Bi2O3 glasses are lower than in

Sb2O3 glasses. shows

the

energy

dependency

of

MFP

for

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Fig.16

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B2O3-Sb2O3, indicating that photons are more attenuated in B2O3-Bi2O3 glasses than the B2O3-

B2O3‒WO3‒La2O3 and

B2O3‒MoO3‒ZnO glasses. For photon energy lower than 0.06 MeV, values of MFP are very small and all samples possess almost the same MFP, while for E>0.06 MeV the values of MFP increase rapidly with the increase in energy. The MFP of the LBW15, LBW25, LBW50,

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ZBMo10, ZBMo20, and ZBMo30 glasses were 6 cm, 5.5 cm, 5 cm, 10.7 cm, 9.6 cm and 9 cm, respectively at 10 MeV. It can be seen very well that additional amounts of WO3 and MoO3 in B2O3‒WO3‒La2O3 and B2O3‒MoO3‒ZnO glasses content results in the decrease of MFP values.

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Besides, it is observed that the MFP values for the B2O3‒WO3‒La2O3 glasses are found to be lower than those for B2O3‒MoO3‒ZnO glasses. This indicates that at certain photon energy, the

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large thickness of B2O3‒MoO3‒ZnO glasses is required as compared to B2O3‒WO3‒La2O3 for providing the same gamma ray shielding. Fig. 17 shows the variation of MFP for 90TeO2-10MgO, 80TeO2-20MgO, 90TeO2-10BaO and 60TeO2-40ZnO glasses for different photon energies. The behavior of MFP with photon for these glasses is similar to the variation observed for the previous glasses presented in Figs. 14-16 and differences are only in the magnitude. TBa10 was found to provide superior shielding from

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gamma radiation since it possesses the lowest value of MFP. This is due to the fact that TBa10 contains relatively high Z element (i.e Ba), as well as this glass sample, has the highest density. The MFP for TMg10, TMg20, TBa10, and TZ40 are lower than BSb10-BSb50 glasses and

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ZBMo10- ZBMo30 glasses.

It is worth mentioning that it would be very interesting to compare the shielding properties of the selected glasses in terms of HVL with different types of concretes to assess the possibility of

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employed the present glass systems as a shielding material. For this purpose, we plotted the HVL for B2O3‒Bi2O3, B2O3‒Sb2O3, B2O3‒WO3‒La2O3, B2O3‒MoO3‒ZnO, and TeO2‒MO (M=Mg,

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Ba, and Zn) glasses along with different types of concretes [59] and the results are shown in Fig. 18-21.

From Fig. 18 it can be seen that all the BBi25-BBi65 glass samples have lower values of HVL than ordinary, hematite-serpentine, ilmenite, steel-scrap and ilmenite-limonite concretes from

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0.06 to 10 MeV. In addition, it is found that BSb50-BSb70 glasses have lower values of HVL than all aforementioned concretes from 0.1-10 MeV (Fig.19). BSb30 glass sample has found to have higher HVL than ilmenite from 0.8-8 MeV. Regarding the glasses BSb10 and BSb20, it

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should be noted that they have almost same values of HVL with ordinary and ilmenite-limonite concretes, respectively. When it comes to Fig. 20, all selected glasses in this figure were found to

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have lower HVL thus better shielding than ordinary, hematite-serpentine and ilmenite-limonite concretes, while ZBMo10 glass sample has almost the same values of HVL with ilmenite. Also, ZBMo20 glass sample was found to have slightly higher values of HVL than the steel-scrap concrete. From Fig. 21, it is clear that TMg10, TMg20, TBa10 and TZ40 glasses have lower HVL values than ordinary, hematite-serpentine, ilmenite, steel-scrap and ilmenite-limonite concretes and therefore show better gamma ray shielding properties than these concretes.

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The equivalent atomic numbers (Zeq) for B2O3‒Bi2O3, B2O3‒Sb2O3, B2O3‒WO3‒La2O3, B2O3‒MoO3‒ZnO, and TeO2‒MO (M=Mg, Ba, and Zn) glasses are tabulated in Table 4 (i-iv), respectively. In addition, the G-P fitting parameters (a, b, c, Xk, and d) are given in

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supplementary Tables S1-S12. The calculated equivalent atomic numbers (Zeq) and the G-P fitting parameters then used to calculate the exposure buildup factor EBF for the selected glasses and the results are shown in Figs. 22-25.Variation of EBF for the B2O3‒Bi2O3 glasses with

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photon energy (0.015-15 MeV) is shown in Fig. 22 (a-f). It can be seen that the values of EBF for all samples increase with increasing the penetration depths. Also, for all samples, the EBF

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values were found the minimum in the low energy region. The low value of EBF in the low energy region is due to the predominance of the photoelectric effect in this region, which results in the fast removal of low energy photons due to absorption thereby not allowing these photons to buildup. The EBF values increase moderately with energy in the intermediate energy region

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due to multiple scattering by Compton scattering. In the high-energy region, the EBF values show an increasing trend with energy and the trend becomes sharper for the higher penetration depth (especially at 40 mfp) values at higher energies. Besides, sharp peak in EBF was observed

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at 0.08 MeV due to the K- absorption edge of the high Z-element (i.e. Bi) present in the samples. Also, it is clear that as Bi2O3 content increase, the peak becomes sharper. The EBF for

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penetration depth of 40 mfp of the BBi25, BBi30, BBi40, BBi50, BBi60 and BBi65 glasses were 29.61, 47.17, 128.42, 1022.56, 5553.98 and 11740.68, respectively. The variations of EBF for B2O3‒Sb2O3 glasses with incident photon energy at different penetration depths are shown in Fig. 23 (a-g). The value of EBF is small up to 0.05 MeV for all samples, shows a sharp peak at 0.05 MeV (near the K-absorption edge of Sb), and increases moderately up to 0.5 MeV. The low value of EBF for E<0.05 MeV is due to predominance of the

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photoelectric effect (as discussed in the previous figure). Also, an inclusion of Sb2O3 in the B2O3-Sb2O3 glass system increases the sharpness of the peak. Beyond 0.5 MeV, the EBF value decreases very slowly at 1 mfp penetration depth, whereas for 5, 10 and 20 mfp penetration

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depths, the EBF decreases gradually up to 15MeV. For 40 mfp penetration depth, the EBF increases in the high energy region. The EBF shows significant variation in the high energy region at 40 mfp because of the dominance of pair production process in this energy region. In

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the pair production, interaction cross section is proportional to Z2. An additional amount of Sb2O3 in B2O3‒Sb2O3 glasses results in an increase in Zeq (see Table 4-ii) and hence the EBF

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values increase. For example, at 40 mfp the EBF for 10, 30 and 70 mol% and Sb2O3 were 10.09, 19.27 and 270.21, respectively at 15 MeV.

The variations of EBF with photon energy are illustrated in Fig. 24 (a-c) and Fig. 24 (d-f) for B2O3‒WO3‒La2O3 and B2O3‒MoO3‒ZnO glasses, respectively. It can be seen that the EBF

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values for all samples are low in the low energy region, increase sharply in the medium energy region, and show a decreasing trend for 1, 5, 10 and 20 mfp (except for LBW50 glass sample) whereas for the 40 mfp penetration depths, the EBF values increase in the high energy region.

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Photoelectric absorption predominates at low photon energy. It is an absorption process, which results in complete removal of the photons, and this explains the small values of EBF in the low

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energy region. In the intermediate energy region; the dominance of Compton scattering takes over the photoelectric absorption. Due to multiple scattering in this region, there is only small degradation of energy. The Compton scattering process does not remove the photon, it only degrades the energy of the photon. So, the lifetime of the photon is long, more the probability of photon to escape the material. Thus the EBFs are moderate in the medium energy region. In the high energy region, another absorption process starts dominating viz. pair production.

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Additionally, due to the high Z (La and W) content in LBW15, LBW25 and LBW50 glasses (Fig. 23 a-c), there is a sharp peak in EBF values at around absorption edge energies (~60 keV). Fig. 25 (a-d) shows the variation of EBF for the 90TeO2-10MgO, 80TeO2-20MgO, 90TeO2-

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10BaO and 60TeO2-40ZnO glasses with photon energy. It is noticed that the EBF for these glasses are small (in order of 1) in the low energy and reach a maximum value at 40 mfp for all samples in high-photon energy region. Besides, the values of the EBF increase by increasing the

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penetration depth. Also, sharp peak in EBF happens at 0.04 MeV near the k-absorption edge of Te and the peak height for TBa10 is very large as compared with TMg10, TMg20 and TZ40

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glasses. The dominance of three main photon interaction processes (i.e. Photoelectric absorption, Compton scattering and pair production) in different energy regions explain the variation of the EBF with photon energy (as discussed in previous figures). The EBF for the penetration depth of 40 mfps of the TMg10, TMg20, TBa10 and TZ40 glasses were 2582.79, 928.390, 7415.04 and

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3473.47, respectively at 15 MeV.

The effective removal cross-sections for fast neutron, ΣR (cm−1) of the B2O3‒Bi2O3, B2O3‒Sb2O3, B2O3‒WO3‒La2O3, B2O3‒MoO3‒ZnO, and TeO2‒MO (M=Mg, Ba, and Zn) glasses were

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evaluated using the relations mentioned above and the results were tabulated in Table 5 (i-iv). Referring to the Table 5, it can be noticed that the ΣR increases from 0.1312 cm-1 to 0.2823 cm-1

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with increasing mol% of the modifier (Bi2O3) from (25 to 65 mol%). The ΣR for B2O3‒Sb2O3 glasses were found in the range from (0.0876 cm-1to 0.0957 cm-1) with the mol% increase of the modifier (Sb2O3) from (10 to 70 mol%). For the B2O3‒WO3‒La2O3 glasses, the ΣR were found to decrease from 0.1180 cm-1to 0.1085 cm-1 with the percentage increase of the modifier (WO3) from 15 to 50 mol%, while the ΣR were found to decrease from 0.1066 cm-1to 0.1002 cm-1 with the percentage increase of the modifier (MoO3) from 10 to 30 mol% in the B2O3‒MoO3‒ZnO

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glasses. From Table 5 (iv) it can be seen that the ΣR were found in the range of 0.1040 cm-10.1075cm-1. From these results, we can conclude that B2O3- Bi2O3 glasses have higher neutron removal cross section thus better shields against neutron than the other glass systems in this

are higher than ordinary concrete (0.0937 cm−1) [59].

4. Conclusions

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work. It is found that the ΣR values of all the selected glass systems (except B2O3‒Sb2O3 glasses)

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The present study aimed at the investigation of B2O3‒Bi2O3, B2O3‒Sb2O3, B2O3‒WO3‒La2O3, B2O3‒MoO3‒ZnO, and TeO2‒MO (M=Mg, Ba, and Zn) glasses with respect to the gamma-ray

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interaction as well as fast neutron and a comparison was made with different glasses and concretes. The MCNPX code was applied for the determination of mass attenuation coefficients of investigated glass samples. The results showed that MCNPX Monte Carlo values generally agreed well with WinXcom data. For all glass samples, the µ/ρ and Zeff values attain their

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maximum values at lower photon energies (i.e. 0.015 MeV), where photoelectric effect predominates. The obtained results revealed that the µ/ρ values increase with an increase in Bi2O3 and Sb2O3 modifiers in the B2O3-Bi2O3 and B2O3‒Sb2O3 glasses, respectively, while the

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µ/ρ values increase with an increase in WO3 and MoO3 contents in the B2O3‒WO3‒La2O3 and B2O3‒MoO3‒ZnO glasses, respectively. Besides, the results showed that the Zeff for B2O3‒Sb2O3

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glasses is lower than those of B2O3‒Bi2O3 glasses, while the Zeff for B2O3‒WO3‒La2O3 glasses is higher than those of B2O3‒MoO3‒ZnO glasses. BBi65, BSb70, LBW50, TBa10 have highest µ/ρ and Zeff values and lowest HVL, MFP and EBF in the B2O3‒Bi2O3, B2O3‒Sb2O3, B2O3‒WO3‒La2O3, B2O3‒MoO3‒ZnO, and TeO2‒MO (M=Mg, Ba, and Zn) glasses, respectively. From the HVL results, we can conclude that the B2O3‒Bi2O3 glasses were found to have better shielding effectiveness than the B2O3‒Sb2O3 in the entire energy region.

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The B2O3‒WO3‒La2O3 glasses show preferable radiation shielding effectiveness comparing with B2O3‒MoO3‒ZnO glasses. It is found that the ΣR values of all the selected glass systems (except B2O3‒Sb2O3 glasses) are higher than ordinary concrete (0.0937 cm−1). Calculations of

show better fast neutron shielding than all other glasses.

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References

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fast neutron removal cross sections revealed that B2O3-Bi2O3 glasses envisaged in this work

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Table 1 (ⅰ-ⅰ). Nominal composition of the studied glass systems and their density [20‒24] Table 2 (ⅰ-ⅰ). Calculated wt% of the elements present in the studied glass systems of Table 1 (i), (ii), (iii), and (iv) Table 3 (ⅰ-ⅰ). Comparison of mass attenuation coefficients of the selected glasses using MCNPX and WinXCom Table 4 (ⅰ-ⅰ). Equivalent atomic number for different glass samples Table 5 (ⅰ-ⅰ). Fast neutrons effective removal cross sections of the studied glass systems Figure Captions

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Fig.1. (a) Representation of total simulation geometry. (b) The design and screenshot of MCNPX simulation setup from VE (Visual Editor) Fig. 2. Variation of mass attenuation coefficient values as a function of photon energy for glasses in Table 1 (i). Fig. 3. Variation of mass attenuation coefficient values as a function of photon energy for glasses in Table 1 (ii). Fig. 4. Variation of mass attenuation coefficient values as a function of photon energy for glasses in Table I (iii). Fig. 5. Variation of mass attenuation coefficient values as a function of photon energy for glasses in Table 1 (iv). Fig. 6. Variation of effective atomic number values as a function of photon energy for glasses in Table 1 (i). Fig. 7. Variation of effective atomic number values as a function of photon energy for glasses in Table 1 (ii). Fig. 8. Variation of effective atomic number values as a function of photon energy for glasses in Table 1 (iii). Fig. 9. Variation of effective atomic number values as a function of photon energy for glasses in Table 1 (iv). Fig. 10. Variation of electron density values as a function of photon energy for glasses in Table 1 (i). Fig. 11. Variation of electron density values as a function of photon energy for glasses in Table 1 (ii). Fig. 12. Variation of electron density values as a function of photon energy for glasses in Table 1 (iii). Fig. 13. Variation of electron density values as a function of photon energy for glasses in Table 1 (iv). Fig. 14. Variation of mean free path values as a function of photon energy for glasses in Table 1 (i). Fig. 15. Variation of mean free path values as a function of photon energy for glasses in Table 1 (ii). Fig. 16. Variation of mean free path values as a function of photon energy for glasses in Table 1 (iii). Fig. 17. Variation of mean free path values as a function of photon energy for glasses in Table 1 (iv). Fig. 18. Variation of half value layer as a function of photon energy for glasses in Table 1 (i). Fig. 19. Variation of half value layer as a function of photon energy for glasses in Table 1 (ii). 25

ACCEPTED MANUSCRIPT

AC C

EP

TE D

M AN U

SC

RI PT

Fig. 20. Variation of half value layer as a function of photon energy for glasses in Table 1 (iii). Fig. 21. Variation of half value layer as a function of photon energy for glasses in Table 1 (iv). Fig. 22. Variation of exposure buildup factors with photon energy for glasses in Table 1 (i) at different penetration depths (1, 5, 10, 20 and 40 mfp). Fig. 23. Variation of exposure buildup factors with photon energy for glasses in Table 1 (ii) at different penetration depths (1, 5, 10, 20 and 40 mfp). Fig. 24. Variation of exposure buildup factors with photon energy for glasses in Table 1 (iii) at different penetration depths (1, 5, 10, 20 and 40 mfp). Fig. 25. Variation of exposure buildup factors with photon energy for glasses in Table 1 (iv) at different penetration depths (1, 5, 10, 20 and 40 mfp).

26

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Table 1 (ⅰ-ⅰ). Nominal composition of the studied glass systems and their density [20‒24] (ⅰ) Density (g/cm3) (±0.005)

75B2O3-25Bi2O3

5.598

70B2O3-30Bi2O3

5.709

60B2O3-40Bi2O3

6.259

50B2O3-50Bi2O3

6.941

40B2O3-60Bi2O3

7.479

35B2O3-65Bi2O3

7.741

BBi25 BBi30 BBi40 BBi50

SC

M AN U

(ⅱ)

Sample code

RI PT

Glass composition (mol %)

BBi60 BBi65

Density (g/cm3) (±0.005)

Sample code

90B2O3-10Sb2O3

2.370

BSb10

80B2O3-20Sb2O3

TE D

Glass composition (mol %)

2.878

BSb20

3.341

BSb30

3.763

BSb40

50B2O3-50Sb2O3

4.120

BSb50

40B2O3-60Sb2O3

4.350

BSb60

4.645

BSb70

70B2O3-30Sb2O3

AC C

EP

60B2O3-40Sb2O3

30B2O3-70Sb2O3

27

ACCEPTED MANUSCRIPT

(ⅲ) Density (g/cm3) (±0.005)

60B2O3-15WO3-25La2O3

4.810

50B2O3-25WO3-25La2O3

5.131

25B2O3-50WO3-25La2O3

5.619

40B2O3-10MoO3-50ZnO

3.487

30B2O3-20MoO3-50ZnO

3.706

20B2O3-30MoO3-50ZnO

3.801

90TeO2-10MgO 80TeO2-20MgO 90TeO2-10BaO

SC

LBW50

ZBMo10 ZBMo20 ZBMo30

Sample code

5.388

TMg10

5.211

TMg20

5.573

TBa10

5.430

TZ40

AC C

EP

60TeO2-40ZnO

LBW25

Density (g/cm3) (±0.005)

TE D

Glass composition (mol %)

LBW15

M AN U

(ⅳ)

Sample code

RI PT

Glass composition (mol %)

28

ACCEPTED MANUSCRIPT

Table 2 (ⅰ-ⅰ). Calculated wt% of the elements present in the studied glass systems of Table 1 (i), (ii), (iii), and (iv) (i)

Bi

BBi25

9.6123

61.9367

BBi30

8.0285

66.5112

BBi40

5.6861

73.2764

BBi50

4.0372

BBi60

2.8133

BBi65

2.3126

TE D

(ii)

O

28.451

M AN U

B

SC

Elements Sample code

RI PT

Nominal composition (wt %)

25.4603 21.0375

78.039

17.9238

81.5736

15.6131

83.0198

14.6676

Nominal composition (wt %) Sample code

Elements Sb

O

21.1962

26.5227

52.2811

BSb20

EP

B

15.1739

42.7209

42.1052

BSb30

11.114

53.6408

35.2452

BSb40

8.1916

61.501

30.3074

BSb50

5.9875

67.4294

26.5831

BSb60

4.2658

72.0603

23.6739

BSb70

2.8838

75.7775

21.3387

AC C

BSb10

29

ACCEPTED MANUSCRIPT

(iii) Nominal composition (wt %) Elements W

La

O

LBW15

8.2108

17.4539

43.957

30.3783

LBW25

6.2052

26.3812

39.864

27.5496

LBW50

2.5167

42.7993

32.3365

22.3475

B

Mo

Zn

O

ZBMo10

10.4282

11.5679

39.4217

38.5822

ZBMo20

7.178

21.2331

36.1796

35.4093

ZBMo30

4.4217

29.4294

33.4304

32.7185

M AN U

RI PT

B

SC

Sample code

TE D

(iv)

Nominal composition (wt %)

Sample code

AC C

TMg20

TBa10

TZ40

Mg

O

77.7683

1.6459

20.5858

Te

Mg

O

75.2026

3.5812

21.2162

Te

Ba

O

72.2393

8.6385

19.1222

Te

Zn

O

59.6656

20.3842

19.9502

EP

Te

TMg10

Elements

30

ACCEPTED MANUSCRIPT

Table 3 (ⅰ-ⅰ). Comparison of mass attenuation coefficients of the selected glasses using MCNPX and WinXCom (i) BBi25

BBi30 WinXCom

MCNPX

BBi40 % Dev.

RI PT

Energy (MeV)

WinXCom

MCNPX

% Dev.

MCNPX

0.1

1.403

1.434

2.225

1.654

1.6556

0.097

2.155

2.158

0.139

0.2

0.5698

0.57024

0.077

0.3663

0.3682

0.519

0.4482

0.4498

0.357

0.3

0.3253

0.32696

0.510

0.1884

0.1891

0.372

0.2164

0.2187

1.063

0.4

0.1744

0.17513

0.419

0.1327

0.1334

0.528

0.1458

0.1476

1.235

0.5

0.1261

0.11216

11.055

0.1069

0.1072

0.281

0.1141

0.1159

1.578

0.6

0.1033

0.11038

6.854

0.09202

0.09215

0.141

0.09642

0.09667

0.259

0.8

0.08981

0.09012

0.345

0.07495

0.07498

0.040

0.07686

0.07698

0.156

1

0.07399

0.07412

0.176

0.06494

0.06504

0.154

0.06584

0.06592

0.122

2

0.06448

0.06493

0.698

0.04437

0.04467

0.676

0.04466

0.04478

0.269

3

0.04422

0.04436

0.317

0.03712

0.03814

2.748

0.03783

0.03794

0.291

4

0.03677

0.03698

0.571

0.03342

0.03357

0.449

0.03453

0.03467

0.405

5

0.03286

0.03307

0.639

0.03126

0.03129

0.096

0.03274

0.03287

0.397

6

0.03052

0.03061

0.295

7

0.02904

0.02919

0.517

8

0.02807

0.02818

0.392

9

0.02741

0.02763

0.803

10

0.02698

0.02711

11

0.0267

0.02692

12

0.02652

0.02661

13

0.02643

14

0.02639

15

0.0264

M AN U

TE D

% Dev.

SC

WinXCom

0.02999

0.167

0.03172

0.03194

0.694

0.0291

0.02921

0.378

0.03116

0.03121

0.160

0.02856

0.02901

1.576

0.03087

0.03091

0.130

0.02825

0.02845

0.708

0.03078

0.03098

0.650

EP

0.02994

0.02807

0.02823

0.570

0.0308

0.0314

1.948

0.824

0.02799

0.02809

0.357

0.03092

0.03112

0.647

0.339

0.02798

0.02805

0.250

0.03109

0.03145

1.158

0.02649

0.227

0.02803

0.02801

0.071

0.0313

0.03143

0.415

0.02641

0.076

0.02812

0.02802

0.356

0.03155

0.03187

1.014

0.02664

0.909

0.02823

0.0281

0.461

0.0318

0.03197

0.535

AC C

0.482

31

ACCEPTED MANUSCRIPT

Continue (i) Energy (MeV)

BBi50 WinXCom

BBi60

MCNPX

% Dev.

WinXCom

MCNPX

BBi65 % Dev.

WinXCom

MCNPX

% Dev.

2.656

2.6781

0.832

3.158

3.1598

0.057

3.413

3.420

0.211

0.2

0.5301

0.5343

0.792

0.612

0.6145

0.408

1.27

1.284

1.071

0.3

0.2445

0.2467

0.900

0.2725

0.2756

1.138

0.6529

0.6537

0.123

0.4

0.1589

0.1591

0.126

0.172

0.1737

0.988

0.2865

0.2901

1.257

0.5

0.1214

0.1254

3.295

0.1286

0.1298

0.933

0.1785

0.1801

0.896

0.6

0.1008

0.1034

2.579

0.1052

0.1076

2.281

0.1322

0.1336

1.059

0.8

0.07878

0.07881

0.038

0.08069

0.08078

0.112

0.1074

0.1103

2.700

1

0.06675

0.06698

0.345

0.06765

0.06798

0.488

0.08165

0.08198

0.404

2

0.04494

0.04494

0.000

0.04523

3

0.03854

0.03854

0.000

0.03925

4

0.03565

0.03565

0.000

0.03677

5

0.03421

0.03541

3.508

0.03569

6

0.03351

0.03434

2.477

0.03529

7

0.03322

0.03433

3.341

0.03528

8

0.03318

0.03477

4.792

9

0.03331

0.03355

0.721

10

0.03354

0.03433

2.355

11

0.03385

0.03459

2.186

12

0.03419

0.03512

13

0.03458

0.03548

14

0.03498

0.03517

15

0.03537

SC

M AN U 0.531

0.0681

0.0691

1.468

0.03956

0.790

0.04538

0.04596

1.278

0.03687

0.272

0.03961

0.04002

1.035

0.03678

3.054

0.03733

0.03769

0.964

0.03786

7.283

0.03642

0.03652

0.275

0.03874

9.807

0.03618

0.03639

0.580

TE D

0.04547

0.03945

11.158

0.03631

0.03656

0.689

0.03584

0.03766

5.078

0.03664

0.03697

0.901

0.03628

0.03984

9.813

0.03711

0.03731

0.539

0.03678

0.03671

0.190

0.03765

0.03782

0.452

EP

0.03549

2.720

0.0373

0.03844

3.056

0.03824

0.03841

0.445

2.603

0.03785

0.03877

2.431

0.03885

0.03891

0.154

0.543

0.03841

0.03966

3.254

0.03949

0.03996

1.198

0.03894

0.03955

1.567

0.04012

0.04062

1.246

AC C 0.03611

RI PT

0.1

2.092

32

ACCEPTED MANUSCRIPT

(ii) Energy (MeV)

BSb10 MCNPX

WinXCom

% Dev.

MCNPX

BSb30 % Dev.

WinXCom

MCNPX

0.2845

0.28591

-0.496

0.419

0.42011

0.265

0.553

0.177

0.2

0.1746

0.17924

2.658

0.217

0.21792

0.424

0.259

0.25987

0.336

0.3

0.1388

0.13946

0.476

0.157

0.15823

0.783

0.175

0.17698

1.131

0.4

0.1097

0.11024

0.492

0.115

0.11624

1.078

0.12

0.12893

7.442

0.5

0.09542

0.09602

0.629

0.0974

0.09792

0.534

0.0995

0.1004

0.905

0.6

0.08604

0.08623

0.221

0.0869

0.08736

0.529

0.0877

0.08812

0.479

0.8

0.07907

0.08014

1.353

0.0793

0.07963

0.416

0.0796

0.07981

0.264

1

0.06902

0.07011

1.579

0.0688

0.06918

0.552

0.0687

0.06881

0.160

2

0.06189

0.06198

0.145

0.0616

0.06193

0.536

0.0612

0.06132

0.196

3

0.04332

0.04395

1.454

0.0431

0.04392

1.903

0.0429

0.04308

0.420

4

0.03517

0.03523

0.171

0.0353

0.03521

0.255

0.0355

0.03572

0.620

5

0.03055

0.03068

0.426

0.031

0.03198

3.161

0.0315

0.03174

0.762

6

0.02758

0.02797

1.414

0.0283

0.02842

0.424

0.0291

0.02936

0.893

7

0.02555

0.02564

0.352

0.0265

0.02681

1.170

0.0275

0.02779

1.055

8

0.02408

0.02432

0.997

9

0.02298

0.02301

0.131

10

0.02214

0.02264

2.258

11

0.02149

0.02273

5.770

12

0.02096

0.02116

13

0.02054

0.02155

14

0.0202

0.02104

15

0.01993

0.0252

0.02532

0.476

0.0264

0.02662

0.833

0.0243

0.02441

0.453

0.0257

0.02593

0.895

0.0236

0.02384

1.017

0.0251

0.02536

1.036

0.0231

0.02331

0.909

0.0248

0.02513

1.331

EP

M AN U

SC

RI PT

0.1

0.954

0.0227

0.02298

1.233

0.0245

0.02479

1.184

4.917

0.0224

0.02253

0.580

0.0243

0.02443

0.535

4.158

0.0222

0.02239

0.856

0.0242

0.02436

0.661

0.022

0.02209

0.409

0.0241

0.02428

0.747

AC C 0.02009

0.55398

% Dev.

TE D

WinXCom

BSb20

0.803

33

ACCEPTED MANUSCRIPT

Continue (ii) Energy (MeV)

BSb40

BSb50 MCNPX

0.1

0.688

0.6891

0.16

0.822

0.823

0.15

0.301

0.3012

0.07

0.3431

0.2

0.193

0.1937

0.36

0.3

0.126

0.1268

0.4

0.102

0.5

% Dev.

WinXCom

MCNPX

% Dev.

0.07

0.9563

0.9570

0.09

0.3443

0.35

0.3852

0.3864

0.31

0.2117

0.2121

0.19

0.2299

0.2302

0.13

0.63

0.131

0.1323

0.99

0.1364

0.1376

0.88

0.1032

1.18

0.1035

0.1042

0.68

0.1055

0.1072

1.61

0.0885

0.0887

0.23

0.08929

0.08936

0.08

0.0901

0.0924

2.55

0.6

0.0798

0.0801

0.38

0.0801

0.0821

2.50

0.8

0.0685

0.0698

1.90

0.06829

0.06843

0.21

1

0.0609

0.0612

0.49

0.06057

0.06098

0.68

2

0.0428

0.0437

2.10

0.04257

3

0.0357

0.0372

4.20

0.03586

4

0.032

0.0323

0.94

0.03248

5

0.0298

0.0301

1.01

0.03057

6

0.0285

0.0298

4.56

0.02942

7

0.0276

0.0286

3.62

0.02873

8

0.027

0.0274

1.48

0.02832

9

0.0266

0.0272

2.26

10

0.0264

0.0268

1.52

11

0.0263

0.0267

1.52

12

0.0262

0.0264

0.76

13

0.0262

0.0263

14

0.0262

0.02621

15

0.0263

0.02612

RI PT

WinXCom

SC

% Dev.

0.08036

0.08128

1.14

0.06811

0.06927

1.70

0.06024

0.06122

1.63

M AN U

MCNPX

0.04274

0.40

0.04238

0.04311

1.72

0.03592

0.17

0.03603

0.03624

0.58

0.03283

1.08

0.03296

0.03316

0.61

0.03072

0.49

0.03131

0.03178

1.50

0.02965

0.78

0.03039

0.03122

2.73

0.02882

0.31

0.02989

0.0301

0.70

0.02843

0.39

0.02966

0.02998

1.08

TE D

WinXCom

BSb60

0.02843

1.14

0.0296

0.0297

0.34

0.02802

0.02812

0.36

0.02966

0.02962

0.13

0.02802

0.02804

0.07

0.02979

0.02958

0.70

0.02808

0.02799

0.32

0.02997

0.02947

1.67

0.38

0.02819

0.02796

0.82

0.03018

0.03023

0.17

0.04

0.02832

0.02789

1.52

0.03042

0.03056

0.46

0.68

0.02846

0.02781

2.28

0.03066

0.03075

0.29

AC C

EP

0.02811

34

ACCEPTED MANUSCRIPT

Continue (ii) Energy (MeV)

BSb70 MCNPX

% Dev.

0.1

1.091

1.014

7.05

0.15

0.4274

0.4315

0.2

0.2481

0.2492

0.3

0.1417

0.1425

0.4

0.1076

0.1079

0.5

0.09091

0.0912

0.6

0.08061

0.08078

0.8

0.06793

0.06798

1

0.05991

2

0.04219

3

0.0362

4

0.03345

5

0.03206

6

0.03136

7

0.03105

8

0.031

9

0.03109

10

0.03129

11

RI PT

WinXCom

0.96 0.44 0.56 0.28

M AN U

SC

0.32 0.21 0.07 0.10

0.04232

0.31

0.0374

3.31

0.03352

0.21

0.03212

0.19

0.03141

0.16

0.03114

0.29

0.0311

0.32

0.03092

0.55

0.03129

0.00

0.03155

0.03168

0.41

12

0.03185

0.03192

0.76

13

0.03218

0.03231

0.38

0.03251

0.03312

0.04

0.03285

0.03289

0.68

15

EP

AC C

14

TE D

0.05997

35

ACCEPTED MANUSCRIPT

(iii) Energy (MeV)

LBW15 MCNPX

% Dev.

WinXCom

% Dev.

WinXCom

MCNPX

% Dev.

2.319

0.303

0.1

1.122

1.124

0.15

0.4524

0.45943

1.554

0.5674

0.56983

0.178

0.8548

0.8569

0.246

0.2

0.2644

0.27011

2.160

0.3171

0.31916

0.428

0.4489

0.4496

0.156

0.3

0.1502

0.15116

0.639

0.1677

0.17028

0.650

0.2113

0.2126

0.615

0.4

0.1132

0.11773

4.002

0.1211

0.12215

1.538

0.1408

0.1417

0.639

0.5

0.0951

0.09788

2.923

0.09931

0.10755

0.867

0.1098

0.1126

2.550

0.6

0.08403

0.08477

0.881

0.08649

0.08704

8.297

0.09263

0.09297

0.367

0.8

0.07051

0.07133

1.163

0.07146

0.07211

0.636

0.07381

0.07418

0.501

1

0.06206

0.06248

0.677

0.0624

2

0.04319

0.04393

1.713

0.04328

3

0.03625

0.03788

4.497

0.03673

4

0.03272

0.03298

0.795

0.03355

5

0.03068

0.03097

0.945

0.03183

6

0.02943

0.02997

1.835

0.03084

7

0.02865

0.02867

0.070

8

0.02817

0.02829

0.426

9

0.02789

0.02793

0.143

10

0.02774

0.02789

0.541

11

0.02769

0.02772

12

0.02771

0.02762

13

0.02777

0.02771

14

0.02787

15

0.02799

2.312

RI PT

0.274

SC

1.466

0.06241

0.910

0.06326

0.06416

1.423

0.04394

0.016

0.0435

0.04399

1.126

0.03698

1.525

0.03792

0.03799

0.185

0.03359

0.681

0.03565

0.03593

0.785

0.03197

0.119

0.03469

0.03479

0.288

0.03095

0.440

0.03436

0.03498

1.804

TE D

0.178 1.462

MCNPX

LBW50

M AN U

WinXCom

LBW25

0.03032

0.357

0.0344

0.03493

1.541

0.03002

0.02998

0.066

0.03465

0.03501

1.039

0.02993

0.02997

0.133

0.03503

0.03512

0.257

0.02995

0.02991

0.134

0.03548

0.03556

0.225

0.108

0.03006

0.02985

0.134

0.03599

0.03637

1.056

0.325

0.03023

0.02998

0.699

0.03653

0.03691

1.040

0.216

0.03043

0.03005

0.827

0.03707

0.03768

1.646

AC C

EP

0.0303

0.02789

0.072

0.03066

0.02966

1.249

0.03763

0.03733

0.797

0.02801

0.071

0.03089

0.03099

3.262

0.03816

0.03751

1.703

36

ACCEPTED MANUSCRIPT

Continue (iii) Energy (MeV)

ZBMo10

ZBMo30

MCNPX

% Dev.

WinXCom

MCNPX

% Dev.

WinXCom

MCNPX

% Dev.

0.4804

0.15

0.3533

0.3672

3.79

0.4165

0.4256

2.14

0.4797

0.15

0.193

0.2016

4.27

0.2123

0.2256

5.90

0.2317

0.2469

6.16

0.2

0.1456

0.1497

2.74

0.1538

0.1596

3.63

0.1621

0.1698

4.53

0.3

0.1109

0.1156

4.07

0.1132

0.1214

6.75

0.1155

0.1198

3.59

0.4

0.09525

0.09698

1.78

0.09608

0.09997

3.89

0.09691

0.0989

2.01

0.5

0.08543

0.08782

2.72

0.08571

0.08987

4.63

0.086

0.0896

4.02

0.6

0.07829

0.07994

2.06

0.07833

0.07993

2.00

0.07838

0.0798

1.78

0.8

0.06816

0.06967

2.17

0.06802

0.07021

3.12

0.06787

0.06874

1.27

1

0.06103

0.06655

8.29

0.06083

2

0.04306

0.04487

4.03

0.04297

3

0.03578

0.03633

1.51

0.03593

4

0.03193

0.03287

2.86

0.03229

5

0.02964

0.03012

1.59

0.03017

6

0.02818

0.02981

5.47

0.02887

7

0.02723

0.02884

5.58

8

0.02659

0.02912

8.69

9

0.02616

0.02779

5.87

10

0.02588

0.02844

9.00

11

0.02569

0.02693

12

0.02557

0.02788

13

0.02551

0.02821

14

0.02549

15

0.02551

0.06358

4.33

0.06062

0.06169

1.73

0.04652

7.63

0.04288

0.04412

2.81

0.03877

7.33

0.03608

0.03724

3.11

0.03489

7.45

0.03265

0.03366

3.00

0.03336

9.56

0.03071

0.03214

4.45

0.02992

3.51

0.02955

0.03006

1.70

TE D

SC

RI PT

0.1

M AN U

WinXCom

ZBMo20

0.02896

3.14

0.02887

0.02912

0.86

0.02753

0.02811

2.06

0.02847

0.02887

1.39

0.02721

0.02787

2.37

0.02826

0.02869

1.50

0.02702

0.02759

2.07

0.02817

0.02821

0.14

4.60

0.02692

0.02713

0.77

0.02815

0.02817

0.07

8.29

0.02689

0.02701

0.44

0.0282

0.02789

1.11

9.57

0.0269

0.02676

0.52

0.02829

0.02761

2.46

AC C

EP

0.02805

0.02802

9.03

0.02695

0.02631

2.43

0.02841

0.02733

3.95

0.02697

5.41

0.02703

0.02604

3.80

0.02855

0.02712

5.27

37

ACCEPTED MANUSCRIPT

(iv)

WinXCom

TMg20

MCNPX

% Dev.

WinXCom

MCNPX

% Dev.

1.3400

1.3612

1.58

1.2090

1.2161

0.59

0.15

0.5056

0.5101

0.89

0.4648

0.4673

0.54

0.2

0.2814

0.2832

0.64

0.264

0.2693

2.01

0.3

0.1508

0.1517

0.60

0.1459

0.1467

0.55

0.4

0.1105

0.1172

6.06

0.1088

0.1094

0.55

0.5

0.09155

0.0927

1.26

0.09102

0.0915

0.53

0.6

0.08031

0.0824

2.60

0.08029

0.0823

2.50

0.8

0.06687

0.0677

1.24

0.06726

0.0679

0.95

1

0.05862

0.0591

0.82

0.05913

2

0.04133

0.0425

2.83

0.04167

3

0.03604

0.0374

3.77

0.03605

4

0.03387

0.0341

0.68

0.03359

5

0.03297

0.0332

0.70

0.03246

6

0.03266

0.0329

0.73

0.03196

7

0.03271

0.0327

0.03

8

0.03296

0.0326

1.09

9

0.03333

0.0334

0.21

10

0.03377

0.0339

0.38

11

0.03426

0.0346

12

0.03477

0.0349

13

0.03528

0.0354

14

0.03579

15

0.03629

0.0597

0.96

0.0427

2.47

0.0371

2.91

0.0339

0.92

0.0349

7.52

0.0327

2.32

TE D

M AN U

0.1

0.0319

0.22

0.03193

0.0321

0.53

0.03217

0.0323

0.40

0.03249

0.0327

0.65

0.99

0.03286

0.0334

1.64

0.37

0.03327

0.0336

0.99

0.34

0.03369

0.0341

1.22

EP

0.03183

AC C

RI PT

TMg10

SC

Energy (MeV)

0.0361

0.87

0.03411

0.0343

0.56

0.0364

0.30

0.03453

0.0347

0.49

38

ACCEPTED MANUSCRIPT

Continue (iv) TZ40 % Dev.

WinXCom

MCNPX

% Dev.

0.1

1.5220

1.5240

0.13

1.0550

1.0590

0.38

0.15

0.5634

0.5646

0.21

0.4138

0.4141

0.07

0.2

0.3066

0.3097

1.01

0.2411

0.2424

0.54

0.3

0.1581

0.1596

0.95

0.1385

0.1392

0.51

0.4

0.1133

0.1137

0.35

0.1055

0.1067

1.14

0.5

0.09267

0.0931

0.46

0.08927

0.0898

0.59

0.6

0.08066

0.0812

0.67

0.07926

0.0801

1.06

0.8

0.06661

0.0671

0.74

0.06685

0.0692

3.52

1

0.05815

0.0586

0.77

0.05896

2

0.04101

0.0414

0.95

0.04171

3

0.03612

0.0366

1.33

0.03613

4

0.03428

0.0347

1.23

0.03373

5

0.03366

0.0339

0.71

0.03264

6

0.03359

0.0339

0.92

0.03219

7

0.03383

0.0347

2.57

8

0.03426

0.0346

0.99

9

0.03479

0.0349

0.32

10

0.03539

0.0357

0.88

11

0.03601

0.0371

12

0.03664

0.0369

13

0.03727

0.0374

14

0.03789

15

0.03848

M AN U

MCNPX

0.0592

0.41

0.0421

0.94

0.0367

1.58

0.0341

1.10

0.0329

0.80

0.0327

1.58

TE D

WinXCom

0.0324

0.90

0.03225

0.0328

1.71

0.03252

0.0326

0.25

0.03288

0.0329

0.06

3.03

0.03327

0.0339

1.89

0.71

0.0337

0.0341

1.19

0.35

0.03414

0.0343

0.47

EP

0.03211

AC C

RI PT

TBa10

SC

Energy (MeV)

0.0381

0.55

0.03457

0.0349

0.95

0.0387

0.57

0.035

0.0363

3.71

39

ACCEPTED MANUSCRIPT

Table 4 (ⅰ-ⅰ). Equivalent atomic number for different glass samples (ⅰ)

BBi25

BBi30

BBi40

BBi50

BBi60

BBi65

0.015

19.05

20.38

22.81

25.04

27.25

28.33

0.02

23.04

24.61

27.52

30.19

32.87

34.21

0.03

24.20

25.80

28.72

31.38

33.94

35.25

0.04

25.01

26.64

29.55

32.20

34.73

0.05

25.65

27.28

30.19

32.81

35.30

0.06

26.16

27.80

30.71

0.08

26.98

28.64

31.53

0.1

44.45

47.37

52.56

0.15

46.55

49.47

54.64

0.2

47.79

50.72

55.84

0.3

49.30

52.20

0.4

50.21

53.05

0.5

50.75

53.65

0.6

51.13

0.8

51.56

SC 35.93

M AN U

36.49

35.75

36.94

34.11

36.51

37.65

57.24

61.59

63.72

59.21

63.44

65.46

60.37

64.48

66.46

TE D

33.32

61.68

65.67

67.54

58.09

62.42

66.36

68.17

58.64

62.96

66.79

68.60

EP

57.26

54.02

58.99

63.26

67.09

68.84

54.43

59.39

63.63

67.40

69.17

AC C

1

RI PT

Energy (MeV)

51.71

54.61

59.56

63.77

67.51

69.26

48.76

52.07

57.49

62.06

66.22

68.17

39.65

43.91

51.00

56.82

61.99

64.43

3

27.88

31.86

39.43

46.53

53.33

56.45

4

24.08

27.57

34.49

41.36

48.20

51.67

5

22.42

25.63

32.12

38.75

45.55

48.97

1.5 2

40

ACCEPTED MANUSCRIPT

21.49

24.54

30.81

37.26

43.97

47.37

8

20.55

23.39

29.30

35.59

42.14

45.52

10

20.10

22.87

28.60

34.72

41.19

44.57

15

19.74

22.46

28.09

34.02

40.41

43.74

Energy (MeV)

BSb10

BSb20

BSb30

BSb40

BSb50

0.015

11.27

13.45

15.16

0.02

11.55

13.81

15.56

0.03

11.95

14.29

16.07

0.04

20.21

25.06

28.69

0.05

20.79

25.73

29.37

0.06

21.24

26.23

0.08

21.90

26.93

0.1

22.34

27.43

0.15

23.07

0.2

23.49

BSb10

18.06

19.41

20.72

17.55

18.44

19.74

20.99

17.60

18.95

20.21

21.42

31.72

34.45

36.97

39.39

32.41

35.12

37.61

39.96

TE D

16.68

32.93

35.62

38.08

40.40

30.61

33.63

36.30

38.71

40.96

31.10

34.11

36.75

39.13

41.34

EP

29.87

28.19

31.85

34.85

37.43

39.74

41.87

28.67

32.32

35.27

37.83

40.07

42.18

AC C

0.3

BSb60

M AN U

(ⅰ)

SC

RI PT

6

23.96

29.16

32.79

35.77

38.25

40.51

42.52

24.30

29.47

33.11

36.03

38.53

40.73

42.71

24.48

29.66

33.27

36.19

38.65

40.85

42.82

0.6

24.57

29.78

33.40

36.32

38.75

40.94

42.90

0.8

24.71

29.92

33.47

36.43

38.83

41.04

43.01

1

24.81

29.94

33.54

36.40

38.90

41.03

43.01

0.4 0.5

41

ACCEPTED MANUSCRIPT

18.02

24.92

29.59

33.18

36.33

38.93

41.43

2

12.53

17.59

22.39

26.64

30.61

34.21

37.60

3

10.91

14.76

18.60

22.41

26.20

29.93

33.66

4

10.54

14.05

17.62

21.22

24.85

28.57

32.26

5

10.41

13.76

17.17

20.66

24.26

27.92

31.60

6

10.28

13.55

16.90

20.33

23.83

27.44

31.15

8

10.21

13.35

16.60

19.96

23.41

26.91

30.64

10

10.16

13.27

16.47

19.79

23.21

15

10.11

13.21

16.40

19.71

23.06

22.95

0.02

20.97

23.47

0.03

21.75

24.26

0.04

31.79

33.36

0.05

32.61

0.06

33.21

SC 26.61

30.29

21.13

21.71

22.30

28.90

23.27

25.30

27.16

29.59

23.92

26.03

27.94

37.25

24.29

26.44

28.34

34.14

37.87

24.54

26.71

28.62

34.70

38.34

24.74

26.90

28.81

AC C

0.08

28.45

TE D

20.44

30.38

LBW50 ZBMo10 ZBMo20 ZBMo30

EP

0.015

26.72

M AN U

(ⅰ) Energy (MeV) LBW15 LBW25

RI PT

1.5

40.34

44.80

54.12

25.01

27.19

29.11

41.21

45.70

54.98

25.19

27.39

29.29

42.47

46.98

56.11

25.48

27.69

29.59

0.2

43.19

47.73

56.75

25.65

27.85

29.75

0.3

44.08

48.62

57.49

25.90

28.11

29.90

0.4

44.54

49.12

57.91

25.95

28.17

30.05

0.1 0.15

42

ACCEPTED MANUSCRIPT

44.92

49.46

58.21

26.01

28.20

30.11

0.6

45.10

49.67

58.37

26.04

28.27

30.15

0.8

45.35

49.90

58.58

26.20

28.36

30.23

1

45.46

49.98

58.64

26.27

28.40

30.21

1.5

42.58

47.82

57.41

23.30

25.86

28.22

2

35.27

41.52

53.71

20.08

22.80

25.13

3

27.60

33.52

47.25

18.86

21.26

23.60

4

25.25

30.69

44.15

18.53

20.85

23.13

5

24.15

29.27

42.49

18.39

20.67

22.93

6

23.52

28.48

41.55

8

22.83

27.58

40.37

10

22.52

27.14

39.78

15

22.28

26.85

39.27

M AN U

SC

RI PT

0.5

20.53

22.80

18.13

20.37

22.65

18.11

20.32

22.57

18.05

20.29

22.51

AC C

EP

TE D

18.28

43

ACCEPTED MANUSCRIPT

(ⅰ) Energy (MeV)

TMg10

TMg20

0.015

23.30

22.16

24.83

24.92

0.02

23.44

22.35

24.92

25.04

0.03

23.74

22.69

25.15

25.26

0.04

43.77

41.51

46.66

43.81

0.05

44.26

42.07

47.04

44.25

0.06

44.60

42.48

47.33

44.55

0.08

45.05

42.99

47.68

44.93

0.1

45.32

43.34

47.90

0.15

45.73

43.83

48.21

0.2

45.96

44.11

48.37

0.3

46.21

44.43

48.60

0.4

46.33

44.59

0.5

46.45

44.71

0.6

46.52

44.75

0.8

46.56

1

46.62

45.54 45.75

TE D

45.97

48.74

46.18

48.77

46.24

44.83

48.82

46.28

44.90

48.82

46.31

EP

46.11

43.48

48.15

45.47

43.17

40.38

46.55

43.42

40.24

36.95

44.25

40.96

39.05

35.74

43.35

39.98

5

38.49

35.04

42.79

39.50

6

38.09

34.58

42.50

39.16

3 4

SC

M AN U 45.17

45.60

2

RI PT

TZ40

48.68

AC C

1.5

TBa10

44

8

37.61

34.09

42.05

38.73

10

37.39

33.83

41.82

38.53

15

37.26

33.71

41.73

38.42

RI PT

ACCEPTED MANUSCRIPT

(i)

0.1312 0.1951 0.2198 0.2483 0.2712 0.2823

TE D

(ii)

∑R (cm-1)

M AN U

Glass Sample BBi25 BBi30 BBi40 BBi50 BBi60 BBi65

∑R (cm-1)

(iii)

AC C

EP

Glass Sample BSb10 BSb20 BSb30 BSb40 BSb50 BSb60 BSb70

SC

Table 5 (ⅰ-ⅰ). Fast neutrons effective removal cross sections of the studied glass systems

0.0876 0.0909 0.0934 0.0954 0.0963 0.0950 0.0957

Glass ∑R (cm-1) Sample LBW15 0.1180 LBW25 0.1164 LBW50 0.1085 ZBMo10 0.1066 ZBMo20 0.1049 ZBMo30 0.1002 45

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(iv)

0.1040 0.1035 0.1033 0.1075

RI PT

∑R (cm-1)

AC C

EP

TE D

M AN U

SC

Glass Sample TMg10 TMg20 TBa10 TZ40

46

(a)

M AN U

SC

RI PT

ACCEPTED MANUSCRIPT

(b)

AC C

EP

TE D

Fig.1. (a) Representation of total simulation geometry. (b) The design and screenshot of MCNPX simulation setup from VE (Visual Editor)

47

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BBi25 BBi30 BBi40 BBi50 BBi60 BBi65

90

RI PT

80 70 60

SC

50 40 30 20 10 0 0.01

1

TE D

0.1

M AN U

Mass attenuation coefficient (cm2/g)

100

10

Energy (MeV)

AC C

EP

Fig. 2. Variation of mass attenuation coefficient values as a function of photon energy for glasses in Table 1 (i).

48

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BSb10 BSb20 BSb30 BSb40 BSb50 BSb60 BSb70

RI PT

35 30 25

SC

20 15 10 5 0 0.01

1

TE D

0.1

M AN U

Mass attenuation coefficient (cm2/g)

40

10

Energy (MeV)

AC C

EP

Fig. 3. Variation of mass attenuation coefficient values as a function of photon energy for glasses in Table 1 (ii).

49

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LBW15 LBW25 LBW50 ZBMo10 ZBMo20 ZBMo30

RI PT

70 60 50

SC

40 30 20 10 0 0.01

0.1

M AN U

Mass attenuation coefficient (cm2/g)

80

1

10

TE D

Energy (MeV)

AC C

EP

Fig. 4. Variation of mass attenuation coefficient values as a function of photon energy for glasses in Table I (iii).

50

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TMg10 TMg20 TBa10 TZ40

45

RI PT

40 35 30 25

SC

20 15 10 5 0 0.01

0.1

M AN U

Mass attenuation coefficient (cm2/g)

50

1

10

TE D

Energy (MeV)

AC C

EP

Fig. 5. Variation of mass attenuation coefficient values as a function of photon energy for glasses in Table 1 (iv).

51

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BBi25 BBi30 BBi40 BBi50 BBi60 BBi65

RI PT

50

SC

40

30

M AN U

Effective atomic number

60

20

10 0.01

0.1

1

10

TE D

Energy (MeV)

AC C

EP

Fig. 6. Variation of effective atomic number values as a function of photon energy for glasses in Table 1 (i).

52

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40 BSb10 BSb20 BSb30 BSb40 BSb50 BSb60 BSb70

RI PT

30

SC

25 20 15 10 5 0.01

1

TE D

0.1

M AN U

Effective atomic number

35

10

Energy (MeV)

AC C

EP

Fig. 7. Variation of effective atomic number values as a function of photon energy for glasses in Table 1 (ii).

53

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50 LBW15 LBW25 LBW50 ZBMo10 ZBMo20 ZBMo30

RI PT

40 35

SC

30 25 20 15

0.1

TE D

10 0.01

M AN U

Effective atomic number

45

1

10

Energy (MeV)

AC C

EP

Fig. 8. Variation of effective atomic number values as a function of photon energy for glasses in Table 1 (iii).

54

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TMg10 TMg20 TBa10 TZ40

RI PT SC

35

30

25

20 0.01

0.1

M AN U

Effectice atomic number

40

1

10

TE D

Energy (MeV)

AC C

EP

Fig. 9. Variation of effective atomic number values as a function of photon energy for glasses in Table 1 (iv).

55

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9.00E+023 BBi25 BBi30 BBi40 BBi50 BBi60 BBi65

RI PT

7.00E+023

SC

6.00E+023 5.00E+023

M AN U

Electron density (electron/g)

8.00E+023

4.00E+023 3.00E+023

0.1

TE D

0.01

1

10

Energy (MeV)

AC C

EP

Fig. 10. Variation of electron density values as a function of photon energy for glasses in Table 1 (i).

56

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BSb10 BSb20 BSb30 BSb40 BSb50 BSb60 BSb70

RI PT

6.00E+023

SC

5.00E+023

4.00E+023

M AN U

Electron density (electron/g)

7.00E+023

3.00E+023

2.00E+023 0.01

0.1

1

10

TE D

Energy (MeV)

AC C

EP

Fig. 11. Variation of electron density values as a function of photon energy for glasses in Table 1 (ii).

57

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LBW15 LBW25 LBW50 ZBMo10 ZBMo20 ZBMo30

RI PT

6.00E+023

SC

5.00E+023

M AN U

Electron density (electron/g)

7.00E+023

4.00E+023

3.00E+023 0.01

0.1

1

10

TE D

Energy (MeV)

AC C

EP

Fig. 12. Variation of electron density values as a function of photon energy for glasses in Table 1 (iii).

58

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RI PT

TMg10 TMg20 TBa10 TZ40

SC

4.00E+023

3.00E+023

M AN U

Electron density (electron/g)

5.00E+023

2.00E+023 0.01

TE D

0.1

1

10

Energy (MeV)

AC C

EP

Fig. 13. Variation of electron density values as a function of photon energy for glasses in Table 1 (iv).

59

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5

SC

3

2

M AN U

MFP (cm)

4

RI PT

BBi25 BBi30 BBi40 BBi50 BBi60 BBi65

1

0 0.1

TE D

0.01

1

10

Energy (MeV)

AC C

EP

Fig. 14. Variation of mean free path values as a function of photon energy for glasses in Table 1 (i).

60

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20

12 10 8

M AN U

MFP (cm)

14

RI PT

16

BSb10 BSb20 BSb30 BSb40 BSb50 BSb60 BSb70

SC

18

6 4 2 0.1

TE D

0 0.01

1

10

Energy (MeV)

AC C

EP

Fig. 15. Variation of mean free path values as a function of photon energy for glasses in Table 1 (ii).

61

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M AN U

SC

MFP (cm)

10

RI PT

LBW15 LBW25 LBW50 ZBMo10 ZBMo20 ZBMo30

0 0.01

0.1

1

10

TE D

Energy (MeV)

AC C

EP

Fig. 16. Variation of mean free path values as a function of photon energy for glasses in Table 1 (iii).

62

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6

RI PT

TMg10 TMg20 TBa10 TZ40

SC

2

M AN U

MFP (cm)

4

0 0.1

1

TE D

0.01

10

Energy (MeV)

AC C

EP

Fig. 17. Variation of mean free path values as a function of photon energy for glasses in Table 1 (iv).

63

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8 6 4 2

0.1

TE D

0 0.01

RI PT

HVL (cm)

10

SC

12

BBi25 BBi30 BBi40 BBi50 BBi60 BBi65 Ordinary Hematite-serpentine Ilmenite Steel-scrap Ilmenite-limonite

M AN U

14

1

10

Energy (MeV)

AC C

EP

Fig. 18. Variation of half value layer as a function of photon energy for glasses in Table 1 (i).

64

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8 6 4 2 0

0.1

TE D

0.01

RI PT

HVL (cm)

10

SC

12

BSb10 BSb20 BSb30 BSb40 BSb50 BSb60 BSb70 Ordinary Hematite-serpentine Ilmenite Steel-scrap Ilmenite-limonite

M AN U

14

1

10

Energy (MeV)

AC C

EP

Fig. 19. Variation of half value layer as a function of photon energy for glasses in Table 1 (ii).

65

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8 6 4 2 0

0.1

TE D

0.01

RI PT

HVL (cm)

10

SC

12

LBW15 LBW25 LBW50 ZBMo10 ZBMo20 ZBMo30 Ordinary Hematite-serpentine Ilmenite Steel-scrap Ilmenite-limonite

M AN U

14

1

10

Energy (MeV)

AC C

EP

Fig. 20. Variation of half value layer as a function of photon energy for glasses in Table 1 (iii).

66

HVL (cm)

10 8 6 4 2 0

0.1

TE D

0.01

SC

12

TMg10 TMg20 TBa10 TZ40 Ordinary Hematite-serpentine Ilmenite Steel-scrap Ilmenite-limonite

M AN U

14

RI PT

ACCEPTED MANUSCRIPT

1

10

Energy (MeV)

AC C

EP

Fig. 21. Variation of half value layer as a function of photon energy for glasses in Table 1 (iv).

67

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BBi25

1

mfp 1 5 10 20 40

10

100

m fp 1 5 10 20 40

EBF

10

BBi30

b

c

BBi40

m fp 1 5 10 20 40

RI PT

a

M AN U

SC

10

0

9 d 10 m fp

BBi50

TE D

AC C

EP

EBF

8

4

-2

10

1 5 10 20 40

10

10

-1

13 f 10 mfp

BBi60

13 e 10 mfp

1 5 10 20 40

10

1

1

10

-1

10

0

10

8

3

10

10

-2

1

10

10

1 5 10 20 40

10

3

BBi65

-2

-2

-1

10

10

Photonenergy(MeV)

0

10

Photonenergy(MeV)

1

10

10

-2

10

-1

10

Photonenergy(MeV)

Fig. 22. Variation of exposure buildup factors with photon energy for glasses in Table 1 (i) at different penetration depths (1, 5, 10, 20 and 40 mfp).

68

0

10

1

10

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(a)

BSb20

(b)

100

100

mfp 1 5 10 20 40

10

10

1

1

10

1

10

0.1

Photon energy (MeV)

1

9

BSb40

10

M AN U

10

100

mfp

1 5 10 20 40

8

10 EBF

4

BSb50

(e)

13

10

100

mfp 1 5 10 20 40

0.1

Photon energy (MeV)

10

(d)

10

1 0.1

1

10

13

1

10

Photon energy (MeV) (f)

BSb60

mfp

10

1 5 10 20 40

10

8

10

100

10

EBF

0.1

SC

1

0.01

EBF

BSb30

1 5 10 20 40

EBF

EBF

1 5 10 20 40

(c) mfp

RI PT

100

EBF

BSb10

mfp

1

0.1

3

10

-1

10 0.1

1

Photon energy (MeV)

BSb70

(g) mfp

100

10

4

10

0.01

0.1

1

Photon energy (MeV)

10

1 0.1

3

10

AC C

-1

10

0.01

0.1

1

1

0.01

0.1

1

Photon energy (MeV)

10

10

Photon energy (MeV)

Fig. 23. Variation of exposure buildup factors with photon energy for glasses in Table 1 (ii) at different penetration depths (1, 5, 10, 20 and 40 mfp).

69

10

-2

1

0.1

1

10

EP

EBF

1 5 10 20 40

10

TE D

0.01

9

10

-2

10

10

1

10

ACCEPTED MANUSCRIPT

14

10

EBF

LBW15

a mfp 1 5 10 20 40

b

10

c

LBW25

mfp 1 5 10 9 10 20 40

100

LBW50

mfp 13 1 10 5 10 20 40

100

1000

RI PT

9

10

10

100

8

10

10

4

10

4

1 0.1

1

10

10

1 0.1

1

1 0.1

10

1

10

3

-1

-1

-2

10 d

mfp 2 1 10 5 10 20 40

M AN U

10

e

ZBMo10

1

1

10

10

0

0

-2

10

-1

10

0

10

-2

10

2

10

ZBMo30

mfp 1 5 10 20 40

1

10

10 -1

10

0

10

Photonenergy(MeV)

AC C

Photonenergy(MeV)

1

10

f

0

10

EP

10

10

ZBMo20

mfp 2 10 1 5 10 20 40

TE D

EBF

SC

10

1

10

-2

10

-1

10

0

10

Photonenergy(MeV)

Fig. 24. Variation of exposure buildup factors with photon energy for glasses in Table 1 (iii) at different penetration depths (1, 5, 10, 20 and 40 mfp).

70

1

10

ACCEPTED MANUSCRIPT

1000

TMg10

1000

mfp 1 5 10 20 40

EBF

100

10

SC 1

0.01

M AN U

1 0.1 1 Photon energy (MeV)

3

2

10

TE D

100

0.01

EP

10

0.1

0.1 1 Photon energy (MeV)

10

TZ40

mfp

10

1 5 10 20 40

1

0.01

10

(d)

TBa10

(c) mfp

1000

EBF

1 5 10 20 40

100

10

10000

TMg20

(b) mfp

RI PT

(a)

1 5 10 20 40

1

10

0

10 1

10

0.1

1

Photon energy (MeV)

AC C

Photon energy (MeV)

0.01

Fig. 25. Variation of exposure buildup factors with photon energy for glasses in Table 1 (iv) at different penetration depths (1, 5, 10, 20 and 40 mfp).

71

10

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Highlights

RI PT

SC M AN U TE D EP

•

The µ/ρ increases with an increase in Bi2O3 content in the B2O3-Bi2O3 glasses. The Zeff increases with increasing Sb2O3 modifier in the B2O3‒Sb2O3 glasses. The µ/ρ attains maximum values at 0.015 MeV where photoelectric effect dominates. B2O3-WO3-La2O3 glasses show better shielding effectiveness than B2O3-MoO3-ZnO glasses. B2O3-Bi2O3 glasses show better fast neutron shielding effectiveness than all other glasses.

AC C

• • • •