Radiation shielding competence of newly developed TeO2-WO3 glasses

Accepted Manuscript Radiation shielding competence of newly developed TeO2-WO3 glasses M.I. Sayyed, S.I. Quashu, Z.Y. Khattari PII:

S0925-8388(16)33640-4

DOI:

10.1016/j.jallcom.2016.11.160

Reference:

JALCOM 39657

To appear in:

Journal of Alloys and Compounds

Received Date: 17 July 2016 Accepted Date: 10 November 2016

Please cite this article as: M.I. Sayyed, S.I. Quashu, Z.Y. Khattari, Radiation shielding competence of newly developed TeO2-WO3 glasses, Journal of Alloys and Compounds (2016), doi: 10.1016/ j.jallcom.2016.11.160. 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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Radiation shielding competence of newly developed TeO2-WO3 glasses M. I. Sayyeda,1, S. I. Quashu a, Z. Y. Khattari a,b b

Department of Physics, Faculty of Science, University of Tabuk, Tabuk, KSA Department of Physics, Faculty of Science, Hashemite University, Zarqa, Jordan

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a

Abstract

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Gamma rays shielding effectiveness of newly developed Tellurium oxide basedglasses have been investigated. We have used Geometric Progression (G-P) fitting method for calculating the equivalent atomic number for photon energy absorption (Zeq), absorption (EABF) and exposure (EBF) buildup factors at energies 0.015-15 MeV. The buildup factors were found to depend strongly on the photon energy and mean free path (mfp) 1. The EABF and EBF indicated that these types of glasses are suitable for shielding effectiveness and becoming more superior as the molar fraction of WO3 is increased in the glass compound. The present work should be useful for a possible utilizing of these glasses for optical and medical applications where radiation exposure is present.

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Keywords: G-P fitting; amorphous materials; shielding; lead free-glass; buildup factors.

1

Corresponding author: M.I. Sayyed, [email protected]

ACCEPTED MANUSCRIPT 1. Introduction In view of extensive use of heavy metal oxide, fluoride and oxyfluoride glasses in various applications as laser hosts, in fiber optics and as non-linear optical materials in medical or agriculture industry [1-4]. Among them, Tellurium oxide

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based glasses have attracted much attention in both basic science and engineering due to their potential utility in the field of fuel cells, sold state batteries, optical amplifiers and ultimately in non-linear optical micro-devices [4]. For these reasons, telluritebased glasses have become an attractive issue for many investigations ranging from

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the basic Raman, IR-spectra to study the optical properties while DSC2 for studying the thermal properties of these tellurite materials [1, 4]. Conventionally, lead-based glasses have been widely used for γ-ray radiation shielding and protection from other

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ionizing human harmful radiation because of its rich physical and chemical properties. Nowadays, lead-based glasses have been greatly restricted in various radiations shielding application due to their toxicant nature [5]. Many attempts have been reported in the literatures to replace them with lead-free materials or glasses suitable for radiation shielding. Examples of these materials, but not limited, heavy metal

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oxide based glasses such as bismuth oxides have already their impact and significance in many industrial applicatons [6].

The knowledge of how radiation interacts with optical materials is hidden in

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what is so called "buildup factors" which is conventionally known as radiation dose [7]. There are two types of buildup factor: (1) the energy absorption buildup factor and (2) the exposure buildup factor. These two factors are usually calculated by the

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widely used method of G-P least square fitting [7, 8]. For example, a progressive investigation has been performed by Singh et al. [6] who investigated the sheilding effect of γ-ray energy on some important Bismuth-based glasses by calculating the absorption and exposure buildup factors. On further attempt of the Inoue et al. [9] have detailed the γ-ray energy absorption (EABF) and exposure buildup factors (EBF) for different glasses with high ZnO contents in the energy range E∈ [0.015, 15] MeV up to a penetration depth of 40 mfp [9]. In these extensive reports they have employed the five parameter geometric progression (G-P) fitting method to determine both

2

DSC: Differential scanning calorimetry.

ACCEPTED MANUSCRIPT EABF and EBF for these different types of gassed materials. On the other hand, Chanthima et al., [10] have measured the mass attenuation coefficients, effective atomic number (Zeff) and electron density (Neff) of another class of silicate glasses contain Bi2O3, BaO and PbO which are of excellent transparent and shielding character. Other important research works are also appeared recently in the work of

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Kaewjaeng et al. who investigated the effect of BaO compound on the optical and radiation shielding on various silicate-based glass systems [11].

In the present study, we focus our attention on the tellurite-based glasses of the

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form (100-y)TeO2-yWO3 due to their attractive applications as mentioned above. The investigation will be performed on the most used molar fraction y=5, 10, 15, 20, 25 and 30 mol% in many applications [1]. The molecular formula and composition of

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these compounds used in this study is summarized in Table 1. Therefore, in this study, understanding the shielding properties of these compounds with X- or γ-ray has become essential for many bio-medical and industrial applications [1-3]. This interaction study may pinpoint the correlation between the their constitutes molar fraction of these compounds and typical natural radiation dose imposed on them

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owing its industrial and medical interests. In fact, the results of such investigations may help in designing and synthesizing new tellurite-related compounds which in turn are able to resist possible radiation damages at human body.

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2. Theoretical and computational background The computational work of buildup factor values and the G-P fitting

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parameters of the selected compounds are calculated by the well-known method of logarithmic interpolation from the equivalent atomic number

(Zeq) [7, 8]. The

computational work has been performed in three parts as follows. The first part concerns with the computation of the Zeq values for the selected compounds. The second part deals with the calculations of G-P fitting parameters and the values of buildup factor computations are illustrated in part three. The principles of this method relies on the well-known law in physics, namely Lambert-Beer law in its modified form as


=  (, ) ×
 

(1)

ACCEPTED MANUSCRIPT where I0 and I are the initial and the transmitted photon intensities respectively, µ is the linear attenuation coefficient (cm-1) and x is the sample thickness (cm). Here the multiplication factor Bi(E,x) is called buildup factor (i is either exposure or absorption) which accounts for the photon flux distribution when the ideal LambertBeer law conditions did not fulfill in the experimental conditions or setup. These

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conditions are listed elsewhere [8].

2.1 Calculation of the equivalent atomic number Zeq

The Zeq of a particular material is defined as the ratio R=(µ/ρ)Compton/(µ/ρ) Total

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of that material at a specific photon energy corresponding to the ratio of an element at the same photon energy. Thus, firstly the Compton partial mass attenuation coefficients, (µ/ρ)Compton and the total partial mass attenuation coefficients (µ/ρ)Total

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were obtained for elements of atomic number Z∈ (4, 57). These two ratios were calculated for the selected glass compounds for the incident photon energy E ∈ [0.015–15.0] MeV using the WinXcom computer program [12]. The logarithmic interpolation of Zeq has been performed using the relation [12, 13]

 ( ) (  )  

(2)

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 =

where Z1 and Z2 are the atomic numbers of the elements corresponding to the ratios

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R1 and R2 respectively. The ratio R for a compound satisfies the following inequality R1 < R < R2 at a specific photon energy. This simple procedure of calculating these

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parameters is exemplified by the 80TeO2-20WO3 compound at a certain incident photon energy of 1.0 MeV. The ratio (µ/ρ)

Compton/(µ/ρ) Total

of compound is 0.9239

which lies between the ratio 0.9278 and 0.9233 corresponding to elements Z1= 53 and Z2 = 54 respectively. Then, using these values in Eq. (1), the parameter Zeq = 53.85 is obtained. The effective atomic number (Zeff) is related to σa and σe through the following equation [12, 13]  =

 



(3)

ACCEPTED MANUSCRIPT where σa is the effective atomic cross section and σe is th total electronic cross section [12]. Also, the electron density (number of electrons per unit mass, (Neff) of the compound is defined as [13]: 

=

!! "# $

∑ &

(4)

where M = ∑) A) n) the molecular weight of the compound, Ai is is the atomic weight

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of the ith element, ni is the number of formula units of molecule and NA is the Avogadro’s number.

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2.2 Calculation of geometric progression (G-P) fitting parameters

In the second step, the standard reference database recently released from the American National Standards ANSI/ANS-6.4.3 [12, 14] which provides the various

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values of buildup factor (or consequently G-P fitting parameters) for 23 chemical elements, one compound (i.e., H2O) and two mixtures (i.e., air and concrete) in the energy range of E ∈ [0.015–15.0] MeV was used. This database has covered these GP fitting parameters for penetration depths up to 40 mfp. Then, the G-P fitting buildup factor coefficients of the used glasses compounds were then interpolated according to

+=

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the following formula [12, 15]:

, - . /, -.  /  

(5)

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where P1 and P2 are the values of the G-P fitting coefficients corresponding to element of atomic numbers Z1 and Z2 respectively at a given photon energy and Zeq is the

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equivalent atomic number of a given compound.

2.3 Calculation of energy exposure and absorption buildup factors Finally, the computed G-P fitting parameters {P1, P2} were then used to

generate the energy buildup factors (i.e., absorption and exposure) for the compounds at selected incident photon energies in the range 0.015
(, ) =

2

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1 + (5 − 1), 7 = 1

8 9

: 9

(7  − 1), 1 < 7 ≤ 40

1?@ℎ BCDE , 7 > 40 0

(6)

complicated tangent hyperbolic function which is given by 7(, ) = H I + J

KLMN (⁄OP Q) KLMN ( Q) 9 KLMN ( Q)

,  ≤ 40

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The function K(E, x) which represents the photon dose multiplication factor is rather a

(7)

where E is the incident photon energy and x is the penetration depth in units of mfp. The letters {a, b, c, d, Xk} are G-P fitting parameters. The parameter b represents the

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value of buildup factor at 1 mfp. These parameters are usually obtained by leastsquare fitting procedure. The dose function K(E,x) depends strongly on the incident

3. Results and Discussion

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photon energy E and penetration depth x.

3.1 Gamma ray buildup factors of the Te-based glasses compounds 3.1.1 Photon energy dependency

The molecular formula of the (1-y)TeO2-yWO3 binary system investigated in

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this study is presented in Table 1. The table also depicts the composition of each compound. This composition will be correlated with the EBF and EABF for each binary system in the subsequent discussion (see below). The change in the equivalent

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atomic numbers for different molar fractions with incident photon energy (Zeq) is presented in Figure 1. A sudden jump in Zeq at certain photon energy (i.e., 31.81 keV) is observed with two different values respectively near the K-absorption edge

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associated with lower atomic number element

52 128Te

associated with the high atomic number element

and another two values are

74 184W

at photon energy of 69.53

keV. The appeared jumped-values are primarily due to the non-uniform variation of EABF with energy at particular energy value (i.e., it is possible to obtained more than one value of Zeq for a given element at the same photon energy). In the case of WO3 at15% mol two set of values of Zeq are possible at 31.81 keV due to Tellurite Kabsorption edge, the value 27.01 is immediately below the absorption edge, and 44.85 immediately above the absorption edge of 50.36 for

184 74W

52 128Te

while these values are 45.51 and

element respectively. For the other molar fractions these K-

absorption edge values are approximately within 0.05-1.1 % of the above mentioned

ACCEPTED MANUSCRIPT K-edge values. The variations of Zeff and Ne with photon energy for the compounds at several molar fraction of WO3 are shown in Fig. 2 and Fig. 3 for total interaction processes in different energy regions where a dominance process can occur in each region: photoelectric absorption at low energies, Compton (incoherent) scattering at intermediate energies and pair production at high energies. The Ne is closely related to There are

several

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Zeff with the same behavior as it is evident from Fig.3.

discontinuous jumps in the low energies corresponding to photoelectric K, L-, and Mabsorption edge of Te and W as listed in Table 3. In fact, different energy regions can be identified from these two figures: low (E< 0.03 MeV), intermediate (0.03
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MeV) and high-wide (0.3
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The change in the equivalent atomic numbers with incident photon energy (Zeq) is exemplified for the investigated compounds at 5 mol% of WO3 which is shown in Table 2. The other values of Zeq for the compounds at different molar fractions are given in the supplementary information in Table S1-Table S5.These tables provide the Zeq along with the corresponding exposure and energy absorption

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G-P fitting parameters for the various glass compounds in the energy range E∈ [0.015,15] MeV. The energy absorption (EABF) and exposure (EBF) buildup factor for each of the studied compound at different molar fraction of WO3 is shown in Fig. 4 and Fig. 5 respectively as a function of photon incident energy with different mean

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free path (mfp) in the range mfp ∈ [1, 40] as indicated within each figure. Fig. 4 clearly shows a 128Te52 K-absorption edge of each compounds at E=31.81 keV where

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it attains a maximum value at 40 mfp for all molar fraction of WO3. It is also noted that these peaks in all EABF behavior diminished as the WO3 molar fraction increases. The calculated peak value ratio between 5 and 30 mol% is 2% indicates that the presence of WO3 molecule within the glass composition has a pronounced effect on the absorption factor in the studied energy range. In Fig. 5, two adjacent absorption peaks are present at E=31.81 keV and E=69.53 keV for 128Te52 and 74W184 respectively corresponding to the K-absorption edge of these two elements. Notably, the second peak height is correlated with the molar fraction of Tungsten (74W184) and vice versa keeping the energy separation (i.e.,△E= 37.72 keV) between them unchanged along the entire energy range and compositions studied in this work. The

ACCEPTED MANUSCRIPT curves have the same general shape as observed for another compounds and mixtures like alloys, concretes, superconductors, lead-free glasses and heavy metal oxide glasses [16-19]. It is concluded from Fig. 4 and Fig.5 that the EABF and EBF values are decreasing as the molar fraction of WO3 is increased (i.e., element of higher atomic number). Therefore, the addition of the Tungsten element to the compound

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makes it more effective in shielding applications. 3.1.2 Mean free path dependency

The variation of EABF and EBF with mfp at selected values of incident

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photon energy is shown in Fig. 6 and Fig. 7 respectively. Both Figures showing that at low photon energy, the behavior of EABF and EBF is mfp independent. At intermediate energy both buildup factor are almost WO3 molar ratio independent with

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a linear behavior. At high energy both factors showing larger values when compared with the other energy regions. From Fig. 6d and Fig.7d, it is evident that at 5 % molar fraction of WO3 is of greatest shielding effect.

4. Conclusions

In the present study, rich results have been gained about the shielding

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properties of some Te-based glasses with varied WO3 molar fraction. Moreover, the γray buildup factors (i.e., EBF and EABF) have been numerically calculated for these important compounds in the energy range E∈ [0.015,15] MeV up to ultimate penetration depths of 40 mfp. For radioprotection applications in energy range greater

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than 1.5 MeV and for all possible penetration depths tested, Te-based glasses with 5% mol of WO3 has shown excellent shielding efficiency than the other compounds. This

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work may point to an attractive buildup material for radioprotection.

Acknowledgment

The financial support from Hashemite University and University of Tabuk is gratefully acknowledged. Conflict of Interests Statements

The authors of this article being submitted to this Journal declare no conflict of interests.

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Figures Caption: Fig.1 Variation of Zeq with photon energy for investigated glass compounds.

Fig. 2 Effective atomic number (Zeff) investigated glasses with photon energy for total interaction from 1 KeV to 100 GeV.

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Fig. 3 Electron density (Ne) for investigated glasses with photon energy for total interaction from 1 KeV to 100 GeV.

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Fig. 4 Variation of energy absorption buildup factors of investigated glass with photon energy for (a) x=5 mol%, (b) x=10 mol%, (c) x=15 mol% (d) x=20 mol%, (e) x=25 mol% and (f) x=30 mol% of WO3.

Fig. 5 Variation of exposure buildup factors of investigated glass with photon energy for (a) x=5 mol%, (b) x=10 mol%, (c) x=15 mol% (d) x=20 mol%, (e) x=25 mol% and (f) x=30 mol% of WO3.

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Fig. 6 Variation of absorption buildup factors of investigated glass with penetration depths at (a) 0.015, (b) 0.15, (c) 1.5 and (d) 15 MeV.

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Fig. 7 Variation of exposure buildup factors of investigated glass with penetration depths at (a) 0.015, (b) 0.15, (c) 1.5 and (d) 15 MeV.

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References

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Na2O-Bi2O3 and TeO2-WO3-La2O3-MoO3 J. Optical Mater. 33 1858-1861

[3] Dorofeev VV et al., High-purity TeO2- WO3-(La2O3,-Bi2O3) J. Optical Mater. 33 1911-1915

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[4] Upender G, Ramesh S, Prasad M, Sathe VG and Mouli VC 2010 Optical band gap, glass transition temperature and structural studies of (100-x) TeO2-xAg2O-xWO3 J. Alloys and Compd. 504 468-474

[5] Fares H, Jlassi I, Elhouichet H and Ferid M 2014 Investigation of thermal, structural and optical properties of tellurite glass with WO3 adding J Non-Cryst.

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Solids 396-307 1-7

[6] Singh VR, Badiger NM and Kaewkhao 2014 Radiation shielding competence of silicate and bprate heavy metal oxide glasses: Comparative study J Non-Cryst. Solids 404 167-173

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[7] Harima Y, Sakamoto Y, Tanaka S and Kawai M 1986 Validity of the geometricprogression formula in approximation of gamma ray buildup factors Nucl. Sci. Eng. 94 24-28

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[8] Chilton AB, Shultis JK and Faw R, "Principle of Radiation Shielding," 1st ed. (Prentic-Halle, Englewood Cliffs, New Jersey, 1984) [9] Inoue T, Honma T, Dimitrov V and Komatsu T 2010 Approach to thermal properties and electronic polarizability from average single bond strength in ZnOBi2O3-B2O3 glasses J. Solid state Chem. 183 3078-3085 [10] Chanthima N, Kaewkhao and Limsuwan P 2012 Study of photon interaction and shielding properties of silicate glasses containing Bi2O3, BaO and PbO in the energy region of 1 keV to 100 GeV Ann. Nucl. Energy 41 119-124

ACCEPTED MANUSCRIPT [11] Kaewjaeng S, Kaewkhao J Limsuwan P and Maghanemi U 2012 Effect of BaO on Optical, Physical and Radiation Shielding Properties of SiO2-B2O3-Al2O3-CaONa2O Glasses System [12] Berg MJ, Hubbell JH, XCOM: Photon Cross Section Data base. Web Version 1.2, National Institute of Standards and Technology, Gaithersburg, MD 20899, USA,

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August 1999, Originally published at NBSIR 87-3597, XCOM: Photon Cross Section on a Personal Computer (July 1987), 1987-1999, 19990 Available from: http://physics.nist.gov/xcom

[13] Manohara SR, Hanagodimath SM 2007 Studies on effective atomic numbers and

Instrum. Methods Phys. Res. B 258 321-28

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electron densities of essential amino acids in the energy range 1 keV-100GeV Ncul.

[14] ANSI/ANS-6.4.3, Gamma ray attenuation coefficient and buildup factors for

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engineering materials, American Nuclear Society, La Grange Park, Illinois, 1991 [15] Harima Y 1983

An approximation of gamma buildup factors by modified

geometrical progression Nucl. Sci. Eng. 83 299–309

[16] Manohara SR, Hanagodimath and Gerward L 2009 Photon interaction and energy absorption in glass: A transparent gamma ray shield Ann. Nucl. Energy 393

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465-472

[17] Singh VP and Badiger NM 2014 Gamma ray and neutron shielding properties of some alloy materials Ann. Nucl. Energy 64 301-310 [18] Singh VP, Badiger NM and Medhat ME Assessment of Exposure Build-up

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Factors of Some Oxide Dispersion Strengthened Steel Applied in Modern Nuclear Engineering and Designs 2014 Nucl. Eng. Des. 270 90-100

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[19] Singh VP, Medhat ME, Badiger NM, Abu Zayed MSR 2015 Radiation shielding effectiveness of newly developed superconductors Radiat. Phys. Chem. 106 175-183

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60 55

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50

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Zeq

45 40 35

25 0.01

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30

0.1

1

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Fig. 1

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Photon energy (MeV)

x=5 x=10 x=15 x=20 x=25 x=30 10

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70

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60 50 40 30

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20

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1E-4

Fig. 2

x=5 x=10 x=15 x=20 x=25 x=30

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Effective atomic number (Zeff)

80

0.01

1

100

Photon energy (MeV)

10000

1000000

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x=5 x=10 x=15 x=20 x=25 x=30

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23

Electron density (N e×10 )

9

3

1E-4

0.01

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6

1

100

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Fig. 3

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Photon energy (MeV)

10000

ACCEPTED MANUSCRIPT (a)

mfp

10

EABF

2

10

(b)

x=5 mol%

1 5 10 20 25 35 40

3

(c)

x=10 mol%

mfp

x=15 mol%

mfp 1 5 20 20 25 35 40

1 5 20 20 25 35 40

1

10

0

4

10

(d)

10

2

10

(f)

mfp

x=20 mol%

1 5 10 15 20 30 40

3

EABF

(e)

mfp

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10

x=25 mol%

1 5 10 15 20 30 40

1

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0

10

-2

-1

0

1

-2

10

4

(a) mfp 1 5 10 20 25 35 40

3

2

10

(b)

x=5 mol%

1

10

0

(d)

-1

0

1

10 10 Photon energy (MeV)

3

2

10

(c)

x=10 mol%

10

1 5 20 20 25 35 40

(f) mfp mfp

x=20 mol%

x=15 mol%

mfp

(e)

mfp

1 5 10 15 20 30 40

10

EBF

-2

10

1 5 20 20 25 35 40

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10

4

1

10

mfp

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EBF

10

10

0

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Fig. 4

10

-1

10 10 Photon energy (MeV)

10

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10 10 Photon energy (MeV)

x=30 mol%

1 5 10 15 20 30 40

10

10

mfp

x=25 mol%

x=30 mol%

1 5 10 15 20 30 40

1 5 10 15 20 30 40

1

10

0

10

-2

10

Fig. 5

-1

0

10 10 Photon energy (MeV)

1

10

-2

10

-1

0

10 10 Photon energy (MeV)

1

10

-2

10

-1

0

10 10 Photon energy (MeV)

1

10

ACCEPTED MANUSCRIPT 1.014

3.0 ( b)

(a)

0.015 MeV 2.5

1.008

x=5 x=10 x=15 x=20 x=25 x=30

1.5

1.0 10000

(c )

(d)

1.5 MeV x=5 x=10 x=15 x=20 x=25 x=30

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x=5 x=10 x=15 x=20 x=25 x=30

6000

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40

8000

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EABF EABF

0.15 MeV

2.0

1.002

80

x=5 x=10 x=15 x=20 x=25 x=30

15 MeV

4000

2000

0

0

0

10

20

30

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Fig. 6

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Pnetration depth (mfp)

40

0

10

20

30

Pnetration depth (mfp)

40

ACCEPTED MANUSCRIPT 1.014 (a)

( b)

0.015 MeV

0.15 MeV x=5 x=10 x=15 x=20 x=25 x=30

2.0

EBF

1.008

1.002

1.0 18000

80

16000

15 MeV

x=5 x=10 x=15 x=20 x=25 x=30

14000

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40

(d)

1.5 MeV

x=5 x=10 x=15 x=20 x=25 x=30

12000 10000 8000

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EBF

(c )

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1.5

x=5 x=10 x=15 x=20 x=25 x=30

6000 4000 2000

0

0

-2000

0

10

20

30

Pnetration depth (mfp)

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Fig. 7

40

0

10

20

30

Pnetration depth (mfp)

40

ACCEPTED MANUSCRIPT W O Te

5 WO3-95TeO2

0.039649

0.200821

0.759530

10 WO3-90TeO2

0.079298

0.201148

0.719554

15 WO3-85TeO2

0.118946

0.201474

0.679579

20 WO3-80TeO2

0.158595

0.201801

0.639604

25 WO3-77.5TeO2

0.198244

0.202127

0.599629

30 WO3-75TeO2

0.237893

0.202454

0.559654

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Glass description

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Table 1 Chemical formula and composition of the investigated glasses xWO3-(100-x)TeO2 in (%).

ACCEPTED MANUSCRIPT Table 2 Equivalent atomic number (Zeq) and G-P exposure (EBF) and energy absorption (EABF) buildup factor coefficients for investigated glasses with 5 mol% WO3. EBF a

Xk

d

b

c

1.004 1.012 1.030 3.766 3.487 2.708 1.776 1.353 1.222 1.284 1.418 1.541 1.617 1.651 1.687 1.681 1.576 1.571 1.546 1.498 1.516 1.496 1.531 1.499 1.564

1.441 0.163 0.375 0.751 0.275 0.148 0.020 0.100 0.348 0.501 0.653 0.794 0.876 0.938 1.001 1.029 1.126 1.114 1.063 1.025 0.944 0.922 0.878 0.965 1.114

-0.483 0.574 0.192 0.092 -0.004 0.472 0.802 0.617 0.265 0.171 0.104 0.063 0.042 0.023 0.007 0.001 -0.022 -0.016 0.001 0.016 0.046 0.057 0.080 0.059 0.035

5.777 11.337 28.175 24.777 14.494 10.536 15.225 13.783 14.012 14.585 14.249 14.142 14.072 14.017 14.088 13.430 13.495 12.937 12.889 13.374 13.601 13.826 14.150 14.205 14.168

0.325 -0.560 -0.304 -0.077 -0.098 -0.096 -0.175 -0.292 -0.147 -0.093 -0.050 -0.042 -0.035 -0.025 -0.018 -0.016 -0.004 -0.006 -0.030 -0.043 -0.071 -0.080 -0.098 -0.078 -0.060

1.004 1.011 1.029 1.571 1.517 1.461 1.373 1.311 1.439 1.694 1.951 2.283 2.379 2.406 2.353 2.262 1.920 1.849 1.718 1.597 1.569 1.514 1.480 1.410 1.399

1.440 0.270 0.321 0.769 0.282 0.154 0.044 0.102 0.200 0.286 0.463 0.597 0.711 0.780 0.868 0.916 1.042 1.012 0.946 0.903 0.832 0.810 0.792 0.879 1.016

EABF a -0.481 0.311 0.251 0.098 0.073 0.310 0.699 0.600 0.409 0.325 0.202 0.149 0.105 0.081 0.052 0.037 0.002 0.013 0.038 0.056 0.085 0.097 0.111 0.086 0.063

Xk 6.111 17.487 18.483 18.497 12.688 18.402 14.197 13.478 13.892 13.932 13.837 13.872 13.871 13.731 13.631 13.501 13.639 13.103 13.230 13.543 13.792 14.006 14.290 14.350 14.293

RI PT

25.168 25.291 25.558 45.643 46.015 46.290 48.166 48.462 48.861 49.083 49.375 49.514 49.618 49.663 49.717 49.784 49.031 47.121 44.470 43.450 42.825 42.460 42.016 41.750 41.616

c

SC

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 15

b

M AN U

Zeq

AC C

EP

TE D

Energy (MeV)

Table 3 Photon energies (in KeV) of 128Te52 and 184W74 of absorption edges above 1.0 KeV.

Element Z

M5

M4

M3

M2

M1

L3

L2

L1

K

Te

52

-

-

-

-

1.006

4.341

4.612

4.939

31.81

W

74

1.809

1.872

2.281

2.575

2.82

10.21

11.54

12.1

69.53

d 0.322 -0.283 -0.188 -0.036 -0.066 -0.054 -0.227 -0.325 -0.225 -0.192 -0.115 -0.107 -0.084 -0.070 -0.054 -0.046 -0.023 -0.034 -0.062 -0.077 -0.104 -0.114 -0.125 -0.101 -0.084

ACCEPTED MANUSCRIPT • • •

AC C

EP

TE D

M AN U

SC

RI PT

•

Ability of Te-based glasses to protect from radiation exposure. Geometric Progression (G-P) fitting method is used for calculating the Zeq, EBF and EABF. Zeq values have been found to change with photon incident energy and WO3 composition. EABF and EBF were found to be the largest for 5% WO3 molar fraction other than other compounds at nearly 0.06 MeV and 40 mfp.