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Variation of energy absorption and exposure buildup factors with incident photon energy and penetration depth for boro-tellurite (B2O3-TeO2) glasses
Author’s Accepted Manuscript Variation of energy absorption and exposure buildup factors with incident photon energy and penetration depth for boro-tellurite (B2O3-TeO2) glasses M.I. Sayyed, H. Elhouichet www.elsevier.com/locate/radphyschem
PII: DOI: Reference:
S0969-806X(16)30368-1 http://dx.doi.org/10.1016/j.radphyschem.2016.09.019 RPC7276
To appear in: Radiation Physics and Chemistry Received date: 6 December 2015 Revised date: 28 July 2016 Accepted date: 11 September 2016 Cite this article as: M.I. Sayyed and H. Elhouichet, Variation of energy absorption and exposure buildup factors with incident photon energy and penetration depth for boro-tellurite (B2O3-TeO2) glasses, Radiation Physics and Chemistry, http://dx.doi.org/10.1016/j.radphyschem.2016.09.019 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 galley proof before it is published in its final citable 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.
Variation of energy absorption and exposure buildup factors with incident photon energy and penetration depth for boro-tellurite (B2O3-TeO2) glasses
M. I. Sayyed a,* H. Elhouichet b,c a
b
Department of Physics, Faculty of Science, University of Tabuk, Tabuk, KSA Laboratoire de Physico-Chimie des Matériaux Minéraux et leurs Applications, Centre National
de Recherches en Sciences des Matériaux, B.P. 95 Hammam-Lif, 2050, Tunisia c
Département de Physique, Faculté des Sciences de Tunis, University Tunis El Manar, 2092,
Tunisia.
Abstract In this work we have calculated the gamma ray energy absorption (EABF) and exposure buildup factors (EBF) of (100-x)TeO2 - xB2O3 glass systems (where x = 5, 10, 15, 20, 22.5 and 25 mol%) in the energy region 0.015–15 MeV up to a penetration depth of 40 mfp (mean free path). The five parameters (G-P) fitting method has been used to estimate both EABF and EBF values. Variations of EABF and EBF with incident photon energy and penetration depth have been studied. It was found that EABF and EBF values were higher in the intermediate energy region, for all the glass systems. Furthermore, borotellurite glass with 5 mol% B2O3, was found to present the lowest EABF and EBF values, hence it is superior gamma-ray shielding material. The results indicate that the boro-tellurite glasses can be used as radiation shielding materials.
Keywords: buildup factors; energy absorption; energy exposure; effective atomic number; G-P fitting; boro-tellurite glasses. *
Corresponding author: M.I. Sayyed, [email protected]
1
1. Introduction Radiation interaction with matter has to be taken into account for the building materials in nuclear facilities. How that interaction occurs and what are the results varies depending on the type of radiation. For example electrons in matter can interact with gamma ray or photon radiation resulting in scattered radiation. Energy can also be absorbed which can result in emission of heat, gamma radiation or charged particles. Alpha- and beta- particles are directly ionizing particles. They can easily be stopped as they interact strongly with matter. Indirect ionizing particles that are not charges themselves like neutrons, gamma ray and X-ray photons cause ionization by secondary particles. As they do not interact well with matter they become the main problem for radiation shielding in nuclear facilities (Kaplan, 1989). It is very important and useful to develop the mixture of materials that can be used as shield against nuclear radiation (Aly et. al, 2014; Singh, 2014). In such manner, glasses are promising materials because of their great homogeneity, range of composition, simplicity to manufacture, and excellent transparency. Furthermore its radiation shielding properties can be enhanced by the addition of oxide in the glass formula (Chanthima, 2012). Radiation shielding protective glasses is used in many hospital X-ray rooms, radiation therapy rooms, Screens for medical diagnostics, airport security X-ray screens, for materials testing, nuclear facilities, laboratories, X-ray and radiation protection spectacles. Furthermore, glasses are used in space technology to protect human beings and equipment from harmful radiation like cosmic rays (Manohara et al., 2011). Among several glass systems, oxide glasses are the most stable active ions host for practical applications such as optical and sensor devices, mainly due to their high chemical durability and thermal stability. Among them, tellurite glasses are the most promising and attractive materials for wide variety of laser applications (Fares et al. 2015). Further to their good optical properties such as, high refractive index and important transmission coefficient, tellurite glasses possess low melting temperature, high thermal stability, good resistances towards corrosion and moisture and good mechanical strength and chemical durability. Borate based glasses are the most suitable one for the design of new optical devices due to their good solubility of rare earth ions, easy preparation on large scales happing and cost effective properties. Compared to SiO2, P2O5, GeO2 host matrices, B2O3 is the better glass former compound and has lower price, higher stability and larger phonon energy. Recently, the trend has been turned to add two or more glass formers to form the glass materials for various scientific and technical applications 2
(Stambouli et. al, 2012; Fares et. al, 2014). The pure borate glasses possess low refractive index, high melting point and high phonon energy in the order of 1300 –1500 cm-1. It is interesting to note that glass systems containing B2O3 exhibit very good broad band properties, whereas significant improvement in luminescence intensities and lifetimes can be observed. Boro-tellurite glass represents favorable compromise between the requirements of low phonon energy and a relatively high thermal stability, high chemical durability and ease of fabrication. Considering these facts it is proposed to introduce B2O3 into tellurite glasses in order to improve their thermal and mechanical stabilities. Boro-tellurite glasses show exceptionally marked shielding towards successive gamma irradiation. This kind of glass is widely used in radiation shielding as a result of their large absorption cross-section for radiation, resistance to high radiation, and at the same time, small irradiation effects on their optical and mechanical properties (Bhat, 2004). Various researchers (Kaur and Singh, 2014; Kaewjang et al. 2014; Manohara et al., 2009; Osman et al. 2015; Singh et al. 2008; Singh et al. 2015; Yasaka et al. 2014) have reported that glass samples could be used as a radiation shielding material. The shielding of the gamma-ray requires information’s of effective atomic number, mean free bath, and buildup factors. The transmitted intensity of an incident radiation through a homogeneous material with the total attenuation coefficient μ follows Lambert’s Beer law. This law is expressed as I=I0 e- μx, where I is the transmitted intensity, I0 is the initial intensity, μ is the total attenuation coefficient of the material (in cm-1), and x is the thickness of the absorber (in cm). This equation is valid only under the condition that the beam should be monoenergetic, well collimated beam and passing through a thin absorber i.e. it applies only for collided part of the beam. The direction between uncollided and the collided (scattered) part makes it necessary to modify the computational methods for shields which are thick enough to considerable scattered component of the gamma-ray photons. The modified attenuation equation can be written as (I =B I0 e- μx) where B is the buildup factor. The factor B depends on linear absorption coefficient (μ), shield thickness (x), photon energy (E) and atomic properties of shield material (atomic number, scattering and absorption cross section). The buildup factor can be classified as: (1) exposure buildup factor which defined as that photon buildup factor in which the quantity of interest is the exposure and the detector response function is that of absorption in air; (2) energy absorption buildup factor is
3
the photon buildup factor in which the quantity of interest is the absorbed or deposited energy in the medium and the detector response function is that of absorption in the material. There are different methods to estimate the buildup factors such as G-P fitting method (Harima et.al, 1986); iterative method (Suteau and Chiron, 2005) and Monte Carlo method (Sardari et al., 2009). American Nuclear Society ( ANS, 1991) used G-P fitting method and provided a buildup factor data for 23 elements, one compound and two mixtures viz. water, air and concrete at 25 standard energies in the energy range of 0.015 to 15.0MeV with suitable interval up to the penetration depth of 40 mfp. The main objective of the present work is to calculate the energy absorption and exposure buildup factors by using the G-P fitting method for some Boro-tellurite (B2O3-TeO2) glasses which are given in Table 1 in the energy range 0.015-15 MeV up to penetration depths 40 mfp. The effect of some parameters, such as photon energy and penetration depth on both EABF and EBF, has been investigated. Buildup factors of the boro-tellurite glasses cannot be found in any standard database, therefore they are valuable or practical calculations in gamma ray shield purposes.
2. Material and computational method The glass system in the present work is boro-tellurite in composition (100-x)TeO2 xB2O3 where x = 5, 10, 15, 20, 22.5 and 25 mol%. The description of elemental composition is given in Table 1.
2.1 Total mass attenuation coefficient The interaction between a radiation particle and a matter is probabilistic. This probability is described by linear attenuation coefficient μ, for a certain way of interaction per unit pathlength. Linear attenuation coefficient is proportional to the number of atoms per unit volume of the shielding material. It is dependent on the density ρ of the material. It is derived by creating mass attenuation coefficient µ/ρ to lose this dependence (Kaplan, 1989). In case of mixture of elements, the mass attenuation coefficient is given by: µ⁄ρ
∑
(μ⁄ρ)
( )
where Wi is the weight fraction of element i. The mass attenuation coefficient, for the selected boro-tellurite glasses, has been calculated by the WinXcom program (Gerward et. al, 2004). 4
2.2. Effective atomic number (Zeff) and electron density (Ne) The effective atomic numbers of the glass samples was calculated using the following expression: ∑
( ) ( )
∑
( )
where fi is the fractional abundance of the element i relative to the number of atoms providing that Σfi= 1, Ai is the atomic weight, and Zj is the atomic number. Furthermore, the effective electron density is calculated using the following equation: ∑
( )
〈 〉
where 〈 〉 is the mean atomic mass and NA is Avogadro constant.
2.3 Energy absorption and exposure buildup factors The EABF and EBF values and the G-P fitting parameters of the boro-tellurite glasses were calculated using the methods of interpolation from the equivalent atomic number Zeq. Computations are divided in three steps: 1. Calculation of the equivalent atomic number Zeq; 2. Calculation of the G-P fitting parameters; 3. Calculation of the energy absorption and exposure buildup factors. The equivalent atomic number is a single parameter used to describe the boro-tellurite glasses properties in terms of equivalent elements. Zeq can be estimated from the ratio of the Compton partial mass attenuation coefficient relative to the total mass attenuation coefficient at specific photon energy, using the relation (Harima, 1983); (
)
(
)
( )
where Z1 and Z2 are the atomic numbers of the elements corresponding to the ratios R1 and R2, respectively, R is the ratio (µ/ρ) Compton/(µ/ρ) Total for the selected glasses at a specific energy. The values of Zeq of the selected glasses were then used to interpolate G-P fitting parameters (a, b, c, d and Xk) in the energy range 0.015–15 MeV, using the following interpolation expression (Harima, 1983): 5
(
)
(
)
( )
where P1 and P2 are the values of G-P fitting function coefficients, at a specific energy, corresponding to the atomic numbers Z1 and Z2, respectively. Finally, we used the G-P fitting parameters to compute the energy absorption and exposure buildup factors in the energy range 0.015-15 MeV up to penetration depth 40 mfp using the following formula (Harima, 1983): (
) (
( )
(
)
( )
)
( )
The function K(E, x) represents the photon dose multiplication factor which can be calculated using the following equation: (
)
( ⁄
)
( (
)
)
( )
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.
The change in the equivalent atomic numbers with incident photon energy is exemplified for the investigated glasses at 5 mol% of B2O3 which is shown in Table 2. The other values of Zeq for the glass samples 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 G-P fitting parameters for the various glass samples. These parameters have been used to calculate the buildup factor data.
3. Standardization of computational method In order to standardize the interpolation method discussed in the previous section, we have calculated the values of EBF for water up to 40 mfp in the selected energy range of 0.015–15 MeV using the (G-P) fitting method. The results obtained were compared with standard exposure buildup factor data of the American National Standards (ANSI/ANS-6.4.31991) for several selected energy between 0.015 and 15.0 MeV (Harima, 1993). The compared 6
values of EBF have been plotted and shown in Fig. 1. They are in good agreement with the standard data. This provides confidence in the results obtained for the boro-tellurite glasses. 4. Results and discussion The chemical composition of the boro-tellurite glasses is listed in Table 1. The variation of effective atomic number and electron density with incident photon energy for the glass samples has been shown in Fig. 2 and Fig.3, respectively. The variation in the Energy absorption buildup factor (EABF) and exposure buildup factor (EBF) values of the boro-tellurite glasses with photon energy are shown in the Figs. 4 and 5 (a– f) for different penetration depths (1, 5, 10, 20, 30 and 40 mfp). The EABF and EBF values for the selected glass samples as a function of penetration depths at photon energies 0.015, 0.15, 1.5, 3, 8 and 15 MeV are shown in Figs.6 and 7 (a-f).
4.1 Effective atomic number and effective electron density of boro-tellurite glasses The values of the mass attenuation coefficients of the glass samples used in this work were obtained from the software WinXCom (Gerward et al., 2004). Both atomic numbers and atomic masses of the elements were taken from a recent IUPAC report (Michael et al., 2013). We have used Eqs. 2 and 3 to calculate the values of the effective atomic number and effective electron density in the energy range of 1keV–100GeV. The variation of Zeff and Ne with photon energy for the glass samples has been shown in Figs.2 and. 3, respectively, for total interaction process. Obviously, the value of the effective atomic numbers (Zeff), for all the selected samples, increases with the increase of the photon energy up to 40 keV and sudden jumps occur at 30-40 KeV (Fig.2). These sudden jumps can be explained on the basis of k edge absorption of Te at around 31.81 keV. The values of the effective atomic numbers (Zeff), in the energy range 6 - 20 keV, are almost independent of the photon energy, for the glass samples. Thereafter, from 70 keV to 600 keV, a rapid decrease in the effective atomic number (Zeff) occurs with increasing the incident photon energy for all the glass samples; this can be explained based on the dependence of cross-section of photoelectric process which varies inversely with the photon energy as E-3.5. Furthermore, the maximum value for the effective atomic number (Zeff) was found for boro-tellurite glasses with 5 mol% B2O3. This can be explained on the basis of dependence of cross-section of photoelectric process on the atomic number of elements as Z4–5. The highest weight fraction of Te present in this sample (75.95%) and the weight fraction of Te are reduced 7
in the successive samples and hence the effective atomic numbers of the successive samples keeps on decreasing. Finally, the minimum effective atomic number was found to correspond, effectively, to boro-tellurite glasses with 25 mol% B2O3 since this sample contains the lowest weight fraction of Te (59.96%). With further increase of photon energy in the range 0.6 - 3.0 MeV, the value of Zeff becomes nearly independent of photon energy, for all the glass samples. This may be due to dominance of Compton scattering process. As the photon energy increases above 3.0 MeV, the value of Zeff slowly increases and becomes nearly constant above 50.0 MeV. This can be explained on the basis of dominance of pair production in this higher energy region. The Ne is closely related to Zeff with the same behavior as it is evident from Fig.3. 4.2 Variation of EABF and EBF with incident photon energy The variations of EABF and EBF, with photon energy, for all the glass samples and at different penetration depths, have been shown in Figs. 4 and 5 (a-f), respectively. Form these figures, it is seen that with increasing the incident photon energy, the values of the EABF and EBF, for all glass samples, increase up to a maximum value at intermediate energies, then starts decreasing. This can be explained in the basis of dominance of different partial photon interaction processes in different energy regions. However, in the low energy region, photoelectric effect is the dominant photon interaction process, so maximum number of photons will be absorbed and consequently, EABF and EBF values are reduced. Similarly, in the high energy region, another photon absorption process, that is pair production, is the dominant one. In the intermediate energy region, Compton scattering is the dominant process of photon interaction that only help in degradation of photon energy due to scattering and fails to completely remove the photon. So, more the life time of the photon is long, more the probability of photon to escape the material is important. This process results in increasing the values of the EABF and EBF. One can observe a sharp peak in EABF and EBF, at very high energy, and large penetration depth. This is due to build up of secondary gamma photons generated by electron-positron annihilation in the medium due to multiple scattering events. In fact, the increase in penetration depth of the materials leading to increase the thickness of the interacting material which in turn results in increasing the scattering events in the interacting medium, in particular for the material with the highest equivalent atomic number. Hence it results in large EABF and EBF values 8
Clearly from Fig.5 (a–f) there is a sharp peak at 40keV energy that may be due to k edge absorption of Te at around 31.81 keV. It worth noting that with increasing B2O3 concentration, the variation of EABF and EBF is identical and the only difference is in the magnitudes of EABF and EBF. Also, it is clearly seen considerable differences between EABF and EBF values have been observed as the B2O3 molar fraction changes. It is also noted that these differences diminished as the B2O3 molar fraction decreases. For example, at 0.6 MeV and for a penetration depth of 40 mfp, the difference between EABF and EBF values is 33.43 and 24.49 for B2O3 composition of 25 mol% and 5 mol%, respectively.
4.2 Variation of EABF and EBF with penetration depth Figs.6 and 7 shows an increase of EABF and EBF values with penetration depths for all the glass samples, at specific incident photon energies (0.015, 0.15, 1.5, 3, 8 and 15 MeV). At the lowest energy (Figs 6 and 7- a), the EABF and EBF values are roughly constant (≈ unity) above 5 mfp. The values of EABF and EBF vary according to the chemical composition except at photon energy 1.5 MeV, as shown in Figs 6 and 7 (c). It is seen that for the boro-tellurite glasses with low effective atomic numbers (Zeff) (e.g. for boro-tellurite glasses with 25 mol% B2O3), the EABF and EBF values are large. However, for the glasses with higher effective atomic numbers (for boro-tellurite glasses with 5 mol% B2O3), the EABF and EBF values are relatively weak. In contrast, at fixed photon energy 1.50 MeV (Figs.6 and 7.c), EABF and EBF values are nearly independent of chemical composition of the glasses and the magnitudes of the EABF and EBF have been reduced. It may be due to the reason that in this region, the Compton scattering process whose cross-section varies linearly with Zeq of the glasses is the main interacting process, thus no significant variation of EABF and EBF have been observed at this energy.
In high energy region (E ≥3 MeV), reversal in the trend of EABF and EBF values been observed at penetration depths 15 < x < 40 has, i.e. EABF and EBF values increase with 9
increasing Zeq (Fig.6 d-f and Fig. 7 d-f). This can be explained on the basis of dominance of pair production in this energy region. The cross-section of pair production process varies with equivalent atomic number as (Zeq)2. So, the glass with higher Zeq (5 mol% B2O3) has higher probability to undergo pair-production. As a result of this process, electron and positron must be formed with different kinetic energies depending on the energy of the incident photon energy. The electron-positron pair suffers several numbers of collisions when it moves through the glass sample and hence loses its energy. Since, the penetration depth of the glass sample is adequately large for the electron-positron pair to lose its energy with the glass sample and comes to rest. After that, this electron and positron can undergo annihilation process, which results in the creation of two new secondary gamma rays of 0.511 MeV. These secondary rays have energies in the dominance region of Compton scattering process. Hence, these photons will undergo energy degradation in multiple collisions before they completely absorbed within the glass sample by photoelectric absorption. So, the probability of photons to escape through the larger dimensions of glass sample increases, resulting in higher values for EABF and EBF(Singh et al., 2013) .
Finally, for a better radiation shielding material, a high value of Zeff and low value of buildup factor are desired. The Zeff values in the investigated glass systems decrease as the molar concentration of B2O3 is increased. Both the EABF and EBF values increase as the molar concentration of B2O3 is increased.. Obviously, the lower values of molar concentration of B2O3 in the boro-tellurite glass will improve the radiation shielding properties in terms of Zeff and buildup factor. Hence, we can conclude that boro-tellurite glass with 5 mol% B2O3 appears as best gamma ray shielding glass due to higher values for Zeff and lower values of both EABF and EBF. Conclusions In this work, we have investigated the shielding properties of for boro-tellurite glasses with different molar composition of B2O3. We have calculated the effective atomic number and electron density for total photon interaction in the energy range of 1 keV to 100 GeV. It has been found that the effective atomic numbers decrease with increasing B2O3 concentration. Furthermore, by Geometric Progression method (G-P), energy absorption buildup factors and exposure buildup factors were calculated for incident photon energy in the 10
range 0.015 MeV - 15 MeV, up to penetration depths of 40 mfp (mean free path). It was found that EABF and EBF possess maximum values in the intermediate energy region, where Compton scattering is the dominant photon interaction process. The EABF and EBF depend strongly on the chemical composition of the glass in the lower energy region, become nearly independent at the fixed energy of 1.5 MeV and show a small dependence in the higher energy region. For boro-tellurite glass with 5 mol% of B2O3, the EABF and EBF values are found the lowest in low-to-intermediate energy (<3 MeV), thus it is having superior gamma-ray shielding properties. The obtained results have scientific values to develop excellent shielding properties of materials and provide references to synthesize new materials for gamma rays shielding applications.
Acknowledgment The financial support from University of Tabuk is gratefully acknowledged.
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EBF
100000
40 mfp
10000
20 mfp
1000
10 mfp
G-P fitting ANS-6.4.3
100
1 mfp
10
1 0.01
0.1
1
10
Photon energy (MeV) Fig. 1 EBF of water obtained in the present work compared with those of the ANSI/ANS-6.4.3 standard for energy region 0.015–15MeVat1, 5, 10, 25 and 40 mfp. 14
Effective atomic number (Zeff)
70 x=5 x=10 x=15 x=20 x=22.5 x=25
60 50 40 30 20 10 1E-3
0.1
10
1000
100000
Photon energy (MeV) Fig. 2 The variation of effective atomic number (Zeff) of boro-tellurite glasses with incident photon energy for total interaction from 1 KeV to 100 GeV.
15
23
Electron density (N e×10 )
15 x=5 x=10 x=15 x=20 x=22.5 x=25
12
9
6
3 1E-3
0.1
10
1000
100000
Photon energy (MeV) Fig.3. The variation of Electron density (Ne) of boro-tellurite glasses with incident photon energy for total interaction from 1 KeV to 100 GeV.
16
3
10
(a)
2
(c)
x=10 mol%
mfp
1 5 10 20 25 35 40
10
EABF
(b)
x=5 mol%
mfp
x=15 mol%
mfp 1 5 20 20 25 35 40
1 5 20 20 25 35 40
1
10
0
10
(d)
10
(f)
mfp
x=20 mol%
1 5 10 15 20 30 40
2
EABF
(e)
mfp
1 5 10 15 20 30 40
x=22.5 mol%
mfp x=25 mol%
1 5 10 15 20 30 40
1
10
0
10
-2
10
-1
0
10 10 Photon energy (MeV)
1
10
-2
-1
10
0
10 10 Photon energy (MeV)
1
10
-2
10
-1
0
10 10 Photon energy (MeV)
Fig. 4 (a-f) The variation of EABF of boro-tellurite glass with incident photon energy for different molar fractions of B2O3.
17
1
10
mfp (a) 1 5 10 20 25 35 40
3
10
2
EBF
10
(b) mfp
x=5 mol%
(c)
x=10 mol%
x=15 mol%
mfp 1 5 20 20 25 35 40
1 5 20 20 25 35 40
1
10
0
10
3
10
(d)
(e)
mfp x=20 mol%
1 5 10 15 20 30 40
2
EBF
10
(f)
mfp 1 5 10 15 20 30 40
x=22.5 mol%
mfp x=25 mol%
1 5 10 15 20 30 40
1
10
0
10
-2
10
-1
0
10 10 Photon energy (MeV)
1
10
-2
10
-1
0
10 10 Photon energy (MeV)
1
10
-2
10
-1
Fig. 5 (a-f) The variation of EBF of boro-tellurite glass with incident photon energy for different molar fractions of B2O3.
18
0
10 10 Photon energy (MeV)
1
10
1.028
(a)
0.015 MeV
3.2
(b)
0.15 MeV
80
(c)
1.5 MeV
1.024 2.8
60
x=5 x=10 x=15 x=20 x=22.5 x=25
1.012 1.008 1.004
2.4 x=5 x=10 x=15 x=20 x=22.5 x=25
2.0
1.6
EABF
1.016
EABF
EABF
1.020
40 x=5 x=10 x=15 x=20 x=22.5 x=25
20
0
1.2 10
20
30
40
0
10
Penetration depth (mfp) (d)
(e)
3 MeV
60
x=5 x=10 x=15 x=20 x=22.5 x=25 10
20
30
40
EABF
EABF
80
0
40
0
10
(f)
0
0 10
20
30
Penetration depth (mfp)
40
0
10
20
30
Penetration depth (mfp)
Fig. 6 (a-f) The variation of EABF of boro-tellurite glass with penetration depths at specific incident photon energies (0.015, 0.15, 1.5, 3, 8 and 15 MeV).
19
40
x=5 x=10 x=15 x=20 x=22.5 x=25
1500
750
0
30
15 MeV
2250
40
Penetration depth (mfp)
20
Penetration depth (mfp)
8 MeV
40
0
30
x=5 x=10 x=15 x=20 x=22.5 x=25
120
20
20
Penetration depth (mfp)
EABF
0
40
1.028
80 (a)
0.015 MeV
2.8
(b)
(c)
0.15 MeV
1.024
60
EBF
1.016 x=5 x=10 x=15 x=20 x=22.5 x=25
1.012 1.008 1.004 0
10
20
EBF
2.4
1.020
EBF
1.5 MeV
2.0 x=5 x=10 x=15 x=20 x=22.5 x=25
1.6
1.2 30
40
0
10
Penetration depth (mfp)
20
30
40 x=5 x=10 x=15 x=20 x=22.5 x=25
20
0
40
0
10
Penetration depth (mfp)
20
30
40
Penetration depth (mfp)
60 (d)
(e)
3 MeV
(f)
8 MeV
160 40
15 MeV
2250
x=5 x=10 x=15 x=20 x=22.5 x=25
120
20
x=5 x=10 x=15 x=20 x=22.5 x=25
0 0
10
20
30
40
EBF
EBF
EBF
1500 80 x=5 x=10 x=15 x=20 x=22.5 x=25
40
0 0
10
Penetration depth (mfp)
20
30
Penetration depth (mfp)
40
750
0 0
10
Fig. 7 (a-f) The variation of EBF of boro-tellurite glass with penetration depths at specific incident photon energies (0.015, 0.15, 1.5, 3, 8 and 15 MeV).
Table 1: Chemical compositions of the investigated borotellurite glasses xB2O3-(100-x)TeO2 in (%).
Glass description
B
O
Te
5 B2O3-95TeO2
0.0155
0.2250
0.7595
10 B2O3-90TeO2
0.0311
0.2494
0.7196
15 B2O3-85TeO2
0.0466
0.2738
0.6796
20 B2O3-80TeO2
0.0621
0.2983
0.6396
22.5 B2O3-77.5TeO2
0.0699
0.3105
0.6196
20
20
30
Penetration depth (mfp)
40
25 B2O3-75TeO2
0.0777
0.3227
0.5996
Table 2 Equivalent atomic number (Zeq) and G-P exposure (EBF) and energy absorption (EABF) buildup factor coefficients for boro-tellurite glasses with 5 mol% B2O3.
Energ y (MeV)
EBF
EABF
Zeq B
c
a
Xk 6.085
0.015
23.78 7
1.00 5
1.23 4
0.35 9
0.02
23.92 3
1.01 3
0.22 9
0.48 0
11.23 1
0.03
24.21 8
1.03 6
0.37 3
0.20 0
24.51 7
0.04
44.87 4
3.80 2
0.66 3
24.49 0
0.05
45.33 0
3.27 4
0.23 6
0.09 1 0.05 6
0.06
45.63 6
2.66 4
0.11 4
0.56 4
11.55 8
0.08
46.04 0
1.73 8
0.02 5
0.79 0
14.95 3
0.1
46.29 4
1.29 1
0.16 4
0.51 2
13.77 2 21
14.07 8
d 0.27 7 0.44 7 0.26 3 0.06 7 0.07 2 0.10 4 0.20 2 0.24 8
b
c
a
Xk
1.00 5
1.23 0
0.35 5
6.997
1.01 2
0.29 4
0.29 6
16.01 1
1.03 5
0.33 0
0.24 8
17.23 4
1.55 4
0.67 7
0.10 0
19.46 2
1.49 5
0.24 5
0.03 6
11.96 7
1.44 2
0.13 4
0.38 1
17.89 1
1.34 9
0.05 6
0.65 7
14.14 5
1.27 4
0.15 0
0.51 3
13.57 8
d 0.27 1 0.25 8 0.17 9 0.03 8 0.03 5 0.07 4 0.22 8 0.27 5
0.15
46.67 0
1.22 8
0.39 1
0.23 7
14.13 6
0.2
46.87 7
1.34 0
0.50 5
0.17 2
14.49 8
0.3
47.10 1
1.46 8
0.67 6
0.09 7
14.31 9
0.4
47.20 0
1.59 0
0.82 2
0.05 6
14.15 3
0.5
47.29 8
1.66 2
0.90 5
0.03 4
14.14 6
0.6
47.36 4
1.69 2
0.96 3
0.01 8
13.99 5
0.8
47.40 7
1.72 0
1.02 2
14.06 9
1
47.41 2
1.71 5
1.04 8
1.5
46.55 7
1.59 2
1.13 8
2
44.42 1
1.58 7
1.12 1
0.00 3 0.00 3 0.02 5 0.01 9
3
41.72 6
1.55 8
1.06 5
0.00 0
12.82 9
4
40.69 0
1.50 9
1.02 3
0.01 5
13.32 2
5
40.11 3
1.51 4
0.95 0
0.04 2
13.54 9
6
39.69 6
1.48 6
0.93 2
0.05 2
13.73 0
8
39.24 1
1.49 8
0.89 3
0.07 2
14.03 1
10 15
39.00 4 38.87
1.45 9 1.49
0.96 4 1.08
0.05 6 0.03
14.15 0 14.22
13.43 0 11.36 6 12.77 4
22
0.13 0 0.09 5 0.04 8 0.03 9 0.03 2 0.02 3 0.01 7 0.01 4 0.00 2 0.00 6 0.02 8 0.04 1 0.06 5 0.07 3 0.09 0 0.07 4 -
1.44 2
0.23 6
0.37 2
13.95 5
1.86 7
0.29 2
0.32 3
13.96 1
2.07 8
0.49 1
0.18 9
13.90 2
2.39 8
0.63 1
0.13 7
13.88 3
2.47 0
0.74 6
0.09 4
13.88 0
2.47 6
0.81 1
0.07 1
13.73 9
2.39 6
0.89 6
0.04 4
13.63 9
2.29 3
0.94 1
13.51 5
1.92 7
1.05 9
0.03 1 0.00 2
1.85 0
1.03 0
0.00 7
13.08 6
1.71 9
0.95 8
0.03 3
13.19 3
1.59 5
0.91 5
0.05 0
13.56 8
1.55 5
0.85 3
0.07 6
13.82 6
1.49 4
0.83 7
0.08 5
14.04 6
1.44 5
0.82 3
0.09 7
14.24 6
1.37 6 1.35
0.89 4 1.00
0.07 8 0.06
14.34 6 14.39
13.58 2
0.20 5 0.19 4 0.11 0 0.10 1 0.07 8 0.06 6 0.05 0 0.04 2 0.02 0 0.02 9 0.05 6 0.07 1 0.09 4 0.10 2 0.11 1 0.09 2 -
9
3
7
9
7
0.06 1
1
3
2
1
0.08 0
HIGHLIGHTS 1. The shielding properties of boro-tellurite (B2O3-TeO2) glasses were evaluated. 2. Geometric progression (GP) method was used to calculate the gamma ray energy absorption (EABF) and exposure buildup factors (EBF). 3. The obtained data were calculated in the energy range 0.015–15 MeV, up to 40mfp. 4. The results indicate that the boro-tellurite glasses can be used as radiation shielding materials.
23
PII: DOI: Reference:
S0969-806X(16)30368-1 http://dx.doi.org/10.1016/j.radphyschem.2016.09.019 RPC7276
To appear in: Radiation Physics and Chemistry Received date: 6 December 2015 Revised date: 28 July 2016 Accepted date: 11 September 2016 Cite this article as: M.I. Sayyed and H. Elhouichet, Variation of energy absorption and exposure buildup factors with incident photon energy and penetration depth for boro-tellurite (B2O3-TeO2) glasses, Radiation Physics and Chemistry, http://dx.doi.org/10.1016/j.radphyschem.2016.09.019 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 galley proof before it is published in its final citable 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.
Variation of energy absorption and exposure buildup factors with incident photon energy and penetration depth for boro-tellurite (B2O3-TeO2) glasses
M. I. Sayyed a,* H. Elhouichet b,c a
b
Department of Physics, Faculty of Science, University of Tabuk, Tabuk, KSA Laboratoire de Physico-Chimie des Matériaux Minéraux et leurs Applications, Centre National
de Recherches en Sciences des Matériaux, B.P. 95 Hammam-Lif, 2050, Tunisia c
Département de Physique, Faculté des Sciences de Tunis, University Tunis El Manar, 2092,
Tunisia.
Abstract In this work we have calculated the gamma ray energy absorption (EABF) and exposure buildup factors (EBF) of (100-x)TeO2 - xB2O3 glass systems (where x = 5, 10, 15, 20, 22.5 and 25 mol%) in the energy region 0.015–15 MeV up to a penetration depth of 40 mfp (mean free path). The five parameters (G-P) fitting method has been used to estimate both EABF and EBF values. Variations of EABF and EBF with incident photon energy and penetration depth have been studied. It was found that EABF and EBF values were higher in the intermediate energy region, for all the glass systems. Furthermore, borotellurite glass with 5 mol% B2O3, was found to present the lowest EABF and EBF values, hence it is superior gamma-ray shielding material. The results indicate that the boro-tellurite glasses can be used as radiation shielding materials.
Keywords: buildup factors; energy absorption; energy exposure; effective atomic number; G-P fitting; boro-tellurite glasses. *
Corresponding author: M.I. Sayyed, [email protected]
1
1. Introduction Radiation interaction with matter has to be taken into account for the building materials in nuclear facilities. How that interaction occurs and what are the results varies depending on the type of radiation. For example electrons in matter can interact with gamma ray or photon radiation resulting in scattered radiation. Energy can also be absorbed which can result in emission of heat, gamma radiation or charged particles. Alpha- and beta- particles are directly ionizing particles. They can easily be stopped as they interact strongly with matter. Indirect ionizing particles that are not charges themselves like neutrons, gamma ray and X-ray photons cause ionization by secondary particles. As they do not interact well with matter they become the main problem for radiation shielding in nuclear facilities (Kaplan, 1989). It is very important and useful to develop the mixture of materials that can be used as shield against nuclear radiation (Aly et. al, 2014; Singh, 2014). In such manner, glasses are promising materials because of their great homogeneity, range of composition, simplicity to manufacture, and excellent transparency. Furthermore its radiation shielding properties can be enhanced by the addition of oxide in the glass formula (Chanthima, 2012). Radiation shielding protective glasses is used in many hospital X-ray rooms, radiation therapy rooms, Screens for medical diagnostics, airport security X-ray screens, for materials testing, nuclear facilities, laboratories, X-ray and radiation protection spectacles. Furthermore, glasses are used in space technology to protect human beings and equipment from harmful radiation like cosmic rays (Manohara et al., 2011). Among several glass systems, oxide glasses are the most stable active ions host for practical applications such as optical and sensor devices, mainly due to their high chemical durability and thermal stability. Among them, tellurite glasses are the most promising and attractive materials for wide variety of laser applications (Fares et al. 2015). Further to their good optical properties such as, high refractive index and important transmission coefficient, tellurite glasses possess low melting temperature, high thermal stability, good resistances towards corrosion and moisture and good mechanical strength and chemical durability. Borate based glasses are the most suitable one for the design of new optical devices due to their good solubility of rare earth ions, easy preparation on large scales happing and cost effective properties. Compared to SiO2, P2O5, GeO2 host matrices, B2O3 is the better glass former compound and has lower price, higher stability and larger phonon energy. Recently, the trend has been turned to add two or more glass formers to form the glass materials for various scientific and technical applications 2
(Stambouli et. al, 2012; Fares et. al, 2014). The pure borate glasses possess low refractive index, high melting point and high phonon energy in the order of 1300 –1500 cm-1. It is interesting to note that glass systems containing B2O3 exhibit very good broad band properties, whereas significant improvement in luminescence intensities and lifetimes can be observed. Boro-tellurite glass represents favorable compromise between the requirements of low phonon energy and a relatively high thermal stability, high chemical durability and ease of fabrication. Considering these facts it is proposed to introduce B2O3 into tellurite glasses in order to improve their thermal and mechanical stabilities. Boro-tellurite glasses show exceptionally marked shielding towards successive gamma irradiation. This kind of glass is widely used in radiation shielding as a result of their large absorption cross-section for radiation, resistance to high radiation, and at the same time, small irradiation effects on their optical and mechanical properties (Bhat, 2004). Various researchers (Kaur and Singh, 2014; Kaewjang et al. 2014; Manohara et al., 2009; Osman et al. 2015; Singh et al. 2008; Singh et al. 2015; Yasaka et al. 2014) have reported that glass samples could be used as a radiation shielding material. The shielding of the gamma-ray requires information’s of effective atomic number, mean free bath, and buildup factors. The transmitted intensity of an incident radiation through a homogeneous material with the total attenuation coefficient μ follows Lambert’s Beer law. This law is expressed as I=I0 e- μx, where I is the transmitted intensity, I0 is the initial intensity, μ is the total attenuation coefficient of the material (in cm-1), and x is the thickness of the absorber (in cm). This equation is valid only under the condition that the beam should be monoenergetic, well collimated beam and passing through a thin absorber i.e. it applies only for collided part of the beam. The direction between uncollided and the collided (scattered) part makes it necessary to modify the computational methods for shields which are thick enough to considerable scattered component of the gamma-ray photons. The modified attenuation equation can be written as (I =B I0 e- μx) where B is the buildup factor. The factor B depends on linear absorption coefficient (μ), shield thickness (x), photon energy (E) and atomic properties of shield material (atomic number, scattering and absorption cross section). The buildup factor can be classified as: (1) exposure buildup factor which defined as that photon buildup factor in which the quantity of interest is the exposure and the detector response function is that of absorption in air; (2) energy absorption buildup factor is
3
the photon buildup factor in which the quantity of interest is the absorbed or deposited energy in the medium and the detector response function is that of absorption in the material. There are different methods to estimate the buildup factors such as G-P fitting method (Harima et.al, 1986); iterative method (Suteau and Chiron, 2005) and Monte Carlo method (Sardari et al., 2009). American Nuclear Society ( ANS, 1991) used G-P fitting method and provided a buildup factor data for 23 elements, one compound and two mixtures viz. water, air and concrete at 25 standard energies in the energy range of 0.015 to 15.0MeV with suitable interval up to the penetration depth of 40 mfp. The main objective of the present work is to calculate the energy absorption and exposure buildup factors by using the G-P fitting method for some Boro-tellurite (B2O3-TeO2) glasses which are given in Table 1 in the energy range 0.015-15 MeV up to penetration depths 40 mfp. The effect of some parameters, such as photon energy and penetration depth on both EABF and EBF, has been investigated. Buildup factors of the boro-tellurite glasses cannot be found in any standard database, therefore they are valuable or practical calculations in gamma ray shield purposes.
2. Material and computational method The glass system in the present work is boro-tellurite in composition (100-x)TeO2 xB2O3 where x = 5, 10, 15, 20, 22.5 and 25 mol%. The description of elemental composition is given in Table 1.
2.1 Total mass attenuation coefficient The interaction between a radiation particle and a matter is probabilistic. This probability is described by linear attenuation coefficient μ, for a certain way of interaction per unit pathlength. Linear attenuation coefficient is proportional to the number of atoms per unit volume of the shielding material. It is dependent on the density ρ of the material. It is derived by creating mass attenuation coefficient µ/ρ to lose this dependence (Kaplan, 1989). In case of mixture of elements, the mass attenuation coefficient is given by: µ⁄ρ
∑
(μ⁄ρ)
( )
where Wi is the weight fraction of element i. The mass attenuation coefficient, for the selected boro-tellurite glasses, has been calculated by the WinXcom program (Gerward et. al, 2004). 4
2.2. Effective atomic number (Zeff) and electron density (Ne) The effective atomic numbers of the glass samples was calculated using the following expression: ∑
( ) ( )
∑
( )
where fi is the fractional abundance of the element i relative to the number of atoms providing that Σfi= 1, Ai is the atomic weight, and Zj is the atomic number. Furthermore, the effective electron density is calculated using the following equation: ∑
( )
〈 〉
where 〈 〉 is the mean atomic mass and NA is Avogadro constant.
2.3 Energy absorption and exposure buildup factors The EABF and EBF values and the G-P fitting parameters of the boro-tellurite glasses were calculated using the methods of interpolation from the equivalent atomic number Zeq. Computations are divided in three steps: 1. Calculation of the equivalent atomic number Zeq; 2. Calculation of the G-P fitting parameters; 3. Calculation of the energy absorption and exposure buildup factors. The equivalent atomic number is a single parameter used to describe the boro-tellurite glasses properties in terms of equivalent elements. Zeq can be estimated from the ratio of the Compton partial mass attenuation coefficient relative to the total mass attenuation coefficient at specific photon energy, using the relation (Harima, 1983); (
)
(
)
( )
where Z1 and Z2 are the atomic numbers of the elements corresponding to the ratios R1 and R2, respectively, R is the ratio (µ/ρ) Compton/(µ/ρ) Total for the selected glasses at a specific energy. The values of Zeq of the selected glasses were then used to interpolate G-P fitting parameters (a, b, c, d and Xk) in the energy range 0.015–15 MeV, using the following interpolation expression (Harima, 1983): 5
(
)
(
)
( )
where P1 and P2 are the values of G-P fitting function coefficients, at a specific energy, corresponding to the atomic numbers Z1 and Z2, respectively. Finally, we used the G-P fitting parameters to compute the energy absorption and exposure buildup factors in the energy range 0.015-15 MeV up to penetration depth 40 mfp using the following formula (Harima, 1983): (
) (
( )
(
)
( )
)
( )
The function K(E, x) represents the photon dose multiplication factor which can be calculated using the following equation: (
)
( ⁄
)
( (
)
)
( )
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.
The change in the equivalent atomic numbers with incident photon energy is exemplified for the investigated glasses at 5 mol% of B2O3 which is shown in Table 2. The other values of Zeq for the glass samples 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 G-P fitting parameters for the various glass samples. These parameters have been used to calculate the buildup factor data.
3. Standardization of computational method In order to standardize the interpolation method discussed in the previous section, we have calculated the values of EBF for water up to 40 mfp in the selected energy range of 0.015–15 MeV using the (G-P) fitting method. The results obtained were compared with standard exposure buildup factor data of the American National Standards (ANSI/ANS-6.4.31991) for several selected energy between 0.015 and 15.0 MeV (Harima, 1993). The compared 6
values of EBF have been plotted and shown in Fig. 1. They are in good agreement with the standard data. This provides confidence in the results obtained for the boro-tellurite glasses. 4. Results and discussion The chemical composition of the boro-tellurite glasses is listed in Table 1. The variation of effective atomic number and electron density with incident photon energy for the glass samples has been shown in Fig. 2 and Fig.3, respectively. The variation in the Energy absorption buildup factor (EABF) and exposure buildup factor (EBF) values of the boro-tellurite glasses with photon energy are shown in the Figs. 4 and 5 (a– f) for different penetration depths (1, 5, 10, 20, 30 and 40 mfp). The EABF and EBF values for the selected glass samples as a function of penetration depths at photon energies 0.015, 0.15, 1.5, 3, 8 and 15 MeV are shown in Figs.6 and 7 (a-f).
4.1 Effective atomic number and effective electron density of boro-tellurite glasses The values of the mass attenuation coefficients of the glass samples used in this work were obtained from the software WinXCom (Gerward et al., 2004). Both atomic numbers and atomic masses of the elements were taken from a recent IUPAC report (Michael et al., 2013). We have used Eqs. 2 and 3 to calculate the values of the effective atomic number and effective electron density in the energy range of 1keV–100GeV. The variation of Zeff and Ne with photon energy for the glass samples has been shown in Figs.2 and. 3, respectively, for total interaction process. Obviously, the value of the effective atomic numbers (Zeff), for all the selected samples, increases with the increase of the photon energy up to 40 keV and sudden jumps occur at 30-40 KeV (Fig.2). These sudden jumps can be explained on the basis of k edge absorption of Te at around 31.81 keV. The values of the effective atomic numbers (Zeff), in the energy range 6 - 20 keV, are almost independent of the photon energy, for the glass samples. Thereafter, from 70 keV to 600 keV, a rapid decrease in the effective atomic number (Zeff) occurs with increasing the incident photon energy for all the glass samples; this can be explained based on the dependence of cross-section of photoelectric process which varies inversely with the photon energy as E-3.5. Furthermore, the maximum value for the effective atomic number (Zeff) was found for boro-tellurite glasses with 5 mol% B2O3. This can be explained on the basis of dependence of cross-section of photoelectric process on the atomic number of elements as Z4–5. The highest weight fraction of Te present in this sample (75.95%) and the weight fraction of Te are reduced 7
in the successive samples and hence the effective atomic numbers of the successive samples keeps on decreasing. Finally, the minimum effective atomic number was found to correspond, effectively, to boro-tellurite glasses with 25 mol% B2O3 since this sample contains the lowest weight fraction of Te (59.96%). With further increase of photon energy in the range 0.6 - 3.0 MeV, the value of Zeff becomes nearly independent of photon energy, for all the glass samples. This may be due to dominance of Compton scattering process. As the photon energy increases above 3.0 MeV, the value of Zeff slowly increases and becomes nearly constant above 50.0 MeV. This can be explained on the basis of dominance of pair production in this higher energy region. The Ne is closely related to Zeff with the same behavior as it is evident from Fig.3. 4.2 Variation of EABF and EBF with incident photon energy The variations of EABF and EBF, with photon energy, for all the glass samples and at different penetration depths, have been shown in Figs. 4 and 5 (a-f), respectively. Form these figures, it is seen that with increasing the incident photon energy, the values of the EABF and EBF, for all glass samples, increase up to a maximum value at intermediate energies, then starts decreasing. This can be explained in the basis of dominance of different partial photon interaction processes in different energy regions. However, in the low energy region, photoelectric effect is the dominant photon interaction process, so maximum number of photons will be absorbed and consequently, EABF and EBF values are reduced. Similarly, in the high energy region, another photon absorption process, that is pair production, is the dominant one. In the intermediate energy region, Compton scattering is the dominant process of photon interaction that only help in degradation of photon energy due to scattering and fails to completely remove the photon. So, more the life time of the photon is long, more the probability of photon to escape the material is important. This process results in increasing the values of the EABF and EBF. One can observe a sharp peak in EABF and EBF, at very high energy, and large penetration depth. This is due to build up of secondary gamma photons generated by electron-positron annihilation in the medium due to multiple scattering events. In fact, the increase in penetration depth of the materials leading to increase the thickness of the interacting material which in turn results in increasing the scattering events in the interacting medium, in particular for the material with the highest equivalent atomic number. Hence it results in large EABF and EBF values 8
Clearly from Fig.5 (a–f) there is a sharp peak at 40keV energy that may be due to k edge absorption of Te at around 31.81 keV. It worth noting that with increasing B2O3 concentration, the variation of EABF and EBF is identical and the only difference is in the magnitudes of EABF and EBF. Also, it is clearly seen considerable differences between EABF and EBF values have been observed as the B2O3 molar fraction changes. It is also noted that these differences diminished as the B2O3 molar fraction decreases. For example, at 0.6 MeV and for a penetration depth of 40 mfp, the difference between EABF and EBF values is 33.43 and 24.49 for B2O3 composition of 25 mol% and 5 mol%, respectively.
4.2 Variation of EABF and EBF with penetration depth Figs.6 and 7 shows an increase of EABF and EBF values with penetration depths for all the glass samples, at specific incident photon energies (0.015, 0.15, 1.5, 3, 8 and 15 MeV). At the lowest energy (Figs 6 and 7- a), the EABF and EBF values are roughly constant (≈ unity) above 5 mfp. The values of EABF and EBF vary according to the chemical composition except at photon energy 1.5 MeV, as shown in Figs 6 and 7 (c). It is seen that for the boro-tellurite glasses with low effective atomic numbers (Zeff) (e.g. for boro-tellurite glasses with 25 mol% B2O3), the EABF and EBF values are large. However, for the glasses with higher effective atomic numbers (for boro-tellurite glasses with 5 mol% B2O3), the EABF and EBF values are relatively weak. In contrast, at fixed photon energy 1.50 MeV (Figs.6 and 7.c), EABF and EBF values are nearly independent of chemical composition of the glasses and the magnitudes of the EABF and EBF have been reduced. It may be due to the reason that in this region, the Compton scattering process whose cross-section varies linearly with Zeq of the glasses is the main interacting process, thus no significant variation of EABF and EBF have been observed at this energy.
In high energy region (E ≥3 MeV), reversal in the trend of EABF and EBF values been observed at penetration depths 15 < x < 40 has, i.e. EABF and EBF values increase with 9
increasing Zeq (Fig.6 d-f and Fig. 7 d-f). This can be explained on the basis of dominance of pair production in this energy region. The cross-section of pair production process varies with equivalent atomic number as (Zeq)2. So, the glass with higher Zeq (5 mol% B2O3) has higher probability to undergo pair-production. As a result of this process, electron and positron must be formed with different kinetic energies depending on the energy of the incident photon energy. The electron-positron pair suffers several numbers of collisions when it moves through the glass sample and hence loses its energy. Since, the penetration depth of the glass sample is adequately large for the electron-positron pair to lose its energy with the glass sample and comes to rest. After that, this electron and positron can undergo annihilation process, which results in the creation of two new secondary gamma rays of 0.511 MeV. These secondary rays have energies in the dominance region of Compton scattering process. Hence, these photons will undergo energy degradation in multiple collisions before they completely absorbed within the glass sample by photoelectric absorption. So, the probability of photons to escape through the larger dimensions of glass sample increases, resulting in higher values for EABF and EBF(Singh et al., 2013) .
Finally, for a better radiation shielding material, a high value of Zeff and low value of buildup factor are desired. The Zeff values in the investigated glass systems decrease as the molar concentration of B2O3 is increased. Both the EABF and EBF values increase as the molar concentration of B2O3 is increased.. Obviously, the lower values of molar concentration of B2O3 in the boro-tellurite glass will improve the radiation shielding properties in terms of Zeff and buildup factor. Hence, we can conclude that boro-tellurite glass with 5 mol% B2O3 appears as best gamma ray shielding glass due to higher values for Zeff and lower values of both EABF and EBF. Conclusions In this work, we have investigated the shielding properties of for boro-tellurite glasses with different molar composition of B2O3. We have calculated the effective atomic number and electron density for total photon interaction in the energy range of 1 keV to 100 GeV. It has been found that the effective atomic numbers decrease with increasing B2O3 concentration. Furthermore, by Geometric Progression method (G-P), energy absorption buildup factors and exposure buildup factors were calculated for incident photon energy in the 10
range 0.015 MeV - 15 MeV, up to penetration depths of 40 mfp (mean free path). It was found that EABF and EBF possess maximum values in the intermediate energy region, where Compton scattering is the dominant photon interaction process. The EABF and EBF depend strongly on the chemical composition of the glass in the lower energy region, become nearly independent at the fixed energy of 1.5 MeV and show a small dependence in the higher energy region. For boro-tellurite glass with 5 mol% of B2O3, the EABF and EBF values are found the lowest in low-to-intermediate energy (<3 MeV), thus it is having superior gamma-ray shielding properties. The obtained results have scientific values to develop excellent shielding properties of materials and provide references to synthesize new materials for gamma rays shielding applications.
Acknowledgment The financial support from University of Tabuk is gratefully acknowledged.
References
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EBF
100000
40 mfp
10000
20 mfp
1000
10 mfp
G-P fitting ANS-6.4.3
100
1 mfp
10
1 0.01
0.1
1
10
Photon energy (MeV) Fig. 1 EBF of water obtained in the present work compared with those of the ANSI/ANS-6.4.3 standard for energy region 0.015–15MeVat1, 5, 10, 25 and 40 mfp. 14
Effective atomic number (Zeff)
70 x=5 x=10 x=15 x=20 x=22.5 x=25
60 50 40 30 20 10 1E-3
0.1
10
1000
100000
Photon energy (MeV) Fig. 2 The variation of effective atomic number (Zeff) of boro-tellurite glasses with incident photon energy for total interaction from 1 KeV to 100 GeV.
15
23
Electron density (N e×10 )
15 x=5 x=10 x=15 x=20 x=22.5 x=25
12
9
6
3 1E-3
0.1
10
1000
100000
Photon energy (MeV) Fig.3. The variation of Electron density (Ne) of boro-tellurite glasses with incident photon energy for total interaction from 1 KeV to 100 GeV.
16
3
10
(a)
2
(c)
x=10 mol%
mfp
1 5 10 20 25 35 40
10
EABF
(b)
x=5 mol%
mfp
x=15 mol%
mfp 1 5 20 20 25 35 40
1 5 20 20 25 35 40
1
10
0
10
(d)
10
(f)
mfp
x=20 mol%
1 5 10 15 20 30 40
2
EABF
(e)
mfp
1 5 10 15 20 30 40
x=22.5 mol%
mfp x=25 mol%
1 5 10 15 20 30 40
1
10
0
10
-2
10
-1
0
10 10 Photon energy (MeV)
1
10
-2
-1
10
0
10 10 Photon energy (MeV)
1
10
-2
10
-1
0
10 10 Photon energy (MeV)
Fig. 4 (a-f) The variation of EABF of boro-tellurite glass with incident photon energy for different molar fractions of B2O3.
17
1
10
mfp (a) 1 5 10 20 25 35 40
3
10
2
EBF
10
(b) mfp
x=5 mol%
(c)
x=10 mol%
x=15 mol%
mfp 1 5 20 20 25 35 40
1 5 20 20 25 35 40
1
10
0
10
3
10
(d)
(e)
mfp x=20 mol%
1 5 10 15 20 30 40
2
EBF
10
(f)
mfp 1 5 10 15 20 30 40
x=22.5 mol%
mfp x=25 mol%
1 5 10 15 20 30 40
1
10
0
10
-2
10
-1
0
10 10 Photon energy (MeV)
1
10
-2
10
-1
0
10 10 Photon energy (MeV)
1
10
-2
10
-1
Fig. 5 (a-f) The variation of EBF of boro-tellurite glass with incident photon energy for different molar fractions of B2O3.
18
0
10 10 Photon energy (MeV)
1
10
1.028
(a)
0.015 MeV
3.2
(b)
0.15 MeV
80
(c)
1.5 MeV
1.024 2.8
60
x=5 x=10 x=15 x=20 x=22.5 x=25
1.012 1.008 1.004
2.4 x=5 x=10 x=15 x=20 x=22.5 x=25
2.0
1.6
EABF
1.016
EABF
EABF
1.020
40 x=5 x=10 x=15 x=20 x=22.5 x=25
20
0
1.2 10
20
30
40
0
10
Penetration depth (mfp) (d)
(e)
3 MeV
60
x=5 x=10 x=15 x=20 x=22.5 x=25 10
20
30
40
EABF
EABF
80
0
40
0
10
(f)
0
0 10
20
30
Penetration depth (mfp)
40
0
10
20
30
Penetration depth (mfp)
Fig. 6 (a-f) The variation of EABF of boro-tellurite glass with penetration depths at specific incident photon energies (0.015, 0.15, 1.5, 3, 8 and 15 MeV).
19
40
x=5 x=10 x=15 x=20 x=22.5 x=25
1500
750
0
30
15 MeV
2250
40
Penetration depth (mfp)
20
Penetration depth (mfp)
8 MeV
40
0
30
x=5 x=10 x=15 x=20 x=22.5 x=25
120
20
20
Penetration depth (mfp)
EABF
0
40
1.028
80 (a)
0.015 MeV
2.8
(b)
(c)
0.15 MeV
1.024
60
EBF
1.016 x=5 x=10 x=15 x=20 x=22.5 x=25
1.012 1.008 1.004 0
10
20
EBF
2.4
1.020
EBF
1.5 MeV
2.0 x=5 x=10 x=15 x=20 x=22.5 x=25
1.6
1.2 30
40
0
10
Penetration depth (mfp)
20
30
40 x=5 x=10 x=15 x=20 x=22.5 x=25
20
0
40
0
10
Penetration depth (mfp)
20
30
40
Penetration depth (mfp)
60 (d)
(e)
3 MeV
(f)
8 MeV
160 40
15 MeV
2250
x=5 x=10 x=15 x=20 x=22.5 x=25
120
20
x=5 x=10 x=15 x=20 x=22.5 x=25
0 0
10
20
30
40
EBF
EBF
EBF
1500 80 x=5 x=10 x=15 x=20 x=22.5 x=25
40
0 0
10
Penetration depth (mfp)
20
30
Penetration depth (mfp)
40
750
0 0
10
Fig. 7 (a-f) The variation of EBF of boro-tellurite glass with penetration depths at specific incident photon energies (0.015, 0.15, 1.5, 3, 8 and 15 MeV).
Table 1: Chemical compositions of the investigated borotellurite glasses xB2O3-(100-x)TeO2 in (%).
Glass description
B
O
Te
5 B2O3-95TeO2
0.0155
0.2250
0.7595
10 B2O3-90TeO2
0.0311
0.2494
0.7196
15 B2O3-85TeO2
0.0466
0.2738
0.6796
20 B2O3-80TeO2
0.0621
0.2983
0.6396
22.5 B2O3-77.5TeO2
0.0699
0.3105
0.6196
20
20
30
Penetration depth (mfp)
40
25 B2O3-75TeO2
0.0777
0.3227
0.5996
Table 2 Equivalent atomic number (Zeq) and G-P exposure (EBF) and energy absorption (EABF) buildup factor coefficients for boro-tellurite glasses with 5 mol% B2O3.
Energ y (MeV)
EBF
EABF
Zeq B
c
a
Xk 6.085
0.015
23.78 7
1.00 5
1.23 4
0.35 9
0.02
23.92 3
1.01 3
0.22 9
0.48 0
11.23 1
0.03
24.21 8
1.03 6
0.37 3
0.20 0
24.51 7
0.04
44.87 4
3.80 2
0.66 3
24.49 0
0.05
45.33 0
3.27 4
0.23 6
0.09 1 0.05 6
0.06
45.63 6
2.66 4
0.11 4
0.56 4
11.55 8
0.08
46.04 0
1.73 8
0.02 5
0.79 0
14.95 3
0.1
46.29 4
1.29 1
0.16 4
0.51 2
13.77 2 21
14.07 8
d 0.27 7 0.44 7 0.26 3 0.06 7 0.07 2 0.10 4 0.20 2 0.24 8
b
c
a
Xk
1.00 5
1.23 0
0.35 5
6.997
1.01 2
0.29 4
0.29 6
16.01 1
1.03 5
0.33 0
0.24 8
17.23 4
1.55 4
0.67 7
0.10 0
19.46 2
1.49 5
0.24 5
0.03 6
11.96 7
1.44 2
0.13 4
0.38 1
17.89 1
1.34 9
0.05 6
0.65 7
14.14 5
1.27 4
0.15 0
0.51 3
13.57 8
d 0.27 1 0.25 8 0.17 9 0.03 8 0.03 5 0.07 4 0.22 8 0.27 5
0.15
46.67 0
1.22 8
0.39 1
0.23 7
14.13 6
0.2
46.87 7
1.34 0
0.50 5
0.17 2
14.49 8
0.3
47.10 1
1.46 8
0.67 6
0.09 7
14.31 9
0.4
47.20 0
1.59 0
0.82 2
0.05 6
14.15 3
0.5
47.29 8
1.66 2
0.90 5
0.03 4
14.14 6
0.6
47.36 4
1.69 2
0.96 3
0.01 8
13.99 5
0.8
47.40 7
1.72 0
1.02 2
14.06 9
1
47.41 2
1.71 5
1.04 8
1.5
46.55 7
1.59 2
1.13 8
2
44.42 1
1.58 7
1.12 1
0.00 3 0.00 3 0.02 5 0.01 9
3
41.72 6
1.55 8
1.06 5
0.00 0
12.82 9
4
40.69 0
1.50 9
1.02 3
0.01 5
13.32 2
5
40.11 3
1.51 4
0.95 0
0.04 2
13.54 9
6
39.69 6
1.48 6
0.93 2
0.05 2
13.73 0
8
39.24 1
1.49 8
0.89 3
0.07 2
14.03 1
10 15
39.00 4 38.87
1.45 9 1.49
0.96 4 1.08
0.05 6 0.03
14.15 0 14.22
13.43 0 11.36 6 12.77 4
22
0.13 0 0.09 5 0.04 8 0.03 9 0.03 2 0.02 3 0.01 7 0.01 4 0.00 2 0.00 6 0.02 8 0.04 1 0.06 5 0.07 3 0.09 0 0.07 4 -
1.44 2
0.23 6
0.37 2
13.95 5
1.86 7
0.29 2
0.32 3
13.96 1
2.07 8
0.49 1
0.18 9
13.90 2
2.39 8
0.63 1
0.13 7
13.88 3
2.47 0
0.74 6
0.09 4
13.88 0
2.47 6
0.81 1
0.07 1
13.73 9
2.39 6
0.89 6
0.04 4
13.63 9
2.29 3
0.94 1
13.51 5
1.92 7
1.05 9
0.03 1 0.00 2
1.85 0
1.03 0
0.00 7
13.08 6
1.71 9
0.95 8
0.03 3
13.19 3
1.59 5
0.91 5
0.05 0
13.56 8
1.55 5
0.85 3
0.07 6
13.82 6
1.49 4
0.83 7
0.08 5
14.04 6
1.44 5
0.82 3
0.09 7
14.24 6
1.37 6 1.35
0.89 4 1.00
0.07 8 0.06
14.34 6 14.39
13.58 2
0.20 5 0.19 4 0.11 0 0.10 1 0.07 8 0.06 6 0.05 0 0.04 2 0.02 0 0.02 9 0.05 6 0.07 1 0.09 4 0.10 2 0.11 1 0.09 2 -
9
3
7
9
7
0.06 1
1
3
2
1
0.08 0
HIGHLIGHTS 1. The shielding properties of boro-tellurite (B2O3-TeO2) glasses were evaluated. 2. Geometric progression (GP) method was used to calculate the gamma ray energy absorption (EABF) and exposure buildup factors (EBF). 3. The obtained data were calculated in the energy range 0.015–15 MeV, up to 40mfp. 4. The results indicate that the boro-tellurite glasses can be used as radiation shielding materials.
23