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The investigation of gamma-ray and neutron shielding parameters of Na2O-CaO-P2O5-SiO2 bioactive glasses using MCNPX code
Results in Physics 12 (2019) 1797–1804
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The investigation of gamma-ray and neutron shielding parameters of Na2OCaO-P2O5-SiO2 bioactive glasses using MCNPX code
T
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H.O. Tekina,b, , O. Kilicogluc, E. Kavazd, E.E. Altunsoyb,e, M. Almatarif, O. Agarg, M.I. Sayyedf a
Uskudar University, Vocational School of Health Services, Radiotherapy Department, Istanbul 34672, Turkey Uskudar University, Medical Radiation Research Center (USMERA), Istanbul 34672, Turkey c Uskudar University, Department of Nuclear Technology and Radiation Protection, Istanbul 34672, Turkey d Ataturk University, Faculty of Science, Department of Physics, 25240 Erzurum, Turkey e Uskudar University, Vocational School of Health Services, Medical Imaging Department, Istanbul 34672, Turkey f University of Tabuk, Physics Department, Tabuk, Saudi Arabia g Karamanoglu Mehmetbey University, Department of Physics, 70100 Karaman, Turkey b
A R T I C LE I N FO
A B S T R A C T
Keywords: Bioactive glass Silicate glasses Radiation protection MCNPX
Bioactive glasses are silicate glasses with sodium, calcium and phosphorus in its composition used to fulfill or support the functions of living tissues in the human body. The superiority of physical and mechanical properties of the bioactive glasses leads to the opportunity to use for radiation protection. From this point of view, radiation absorption parameters of nine bioactive glasses were reported in the present research. The mass attenuation coefficient (μ/ρ) for the selected bioactive glasses was calculated using MCNPX simulation code in the photon energy range 0.02–20 MeV and the results were compared with XCOM data. The values of μ/ρ calculated in two methods were found to support each other. Other vital parameters like half and tenth value layer (HVL and TVL), mean free path (MFP) and effective atomic number (Zeff) for the selected bioactive glasses were also evaluated by utilizing the μ/ρ. ICSW9 glass with more phosphate and sodium contents possess the lowest MFP, HVL and TVL values while has the highest Zeff values among the bioactive glasses under study. To evaluate the neutron protection performance of investigated bioactive glasses, effective removal cross-section values (ΣR) have been determined. The results showed that ICSW9 has also superior neutron attenuation properties. Additionally, exposure buildup factor (EBF) values were found with G-P fitting approach depending on the energy and penetration depths. The bioactive glasses with further equivalent atomic number possesses the minimum value of EBF.
Introduction A bioactive material is known as a natural or man-made material that prompts a specific biological response from the body e.g., bonding to tissue. As such, they have numerous applications in the reconstruction and repair of damaged and diseased tissue, and tissue and hard tissue (bone) re-engineering [1]. Bioactive glasses are one type of such biomaterials along with polymers, metals, composites, and ceramics. They are closely related to bioceramics, yet they have an important advantage over other types of bioactive ceramics by enabling to control a range of chemical properties and rate of binding to tissue [2]. In order to use the bioactive glasses effectively, they must have compatible mechanical properties depending on where they are used, they should not be toxic or carcinogenic, or they do not cause reactions (bioavailability) and they should be resistant to corrosion in the body fluid [3].
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Bioactive glasses were first found by Hench et al. around 1960s [4] as such compositions and crystallized ceramics in the Na2O, CaO-P2O5SiO2 system, which is the base components of bioactive glasses, provides strong bonds with living tissues. Chemical bonding occurs between tissues and implants as a result of replacement of some silica groups in the bioactive glass structure with calcium and phosphorus [5]. The role of phosphate (P2O5) in the content of the bioactive glass is to ensure that the glass is bioactive. Because it can enhance a specific different biological response, feature, or function to the glass host. The high melting point of silicate makes the glass composition be fully melted and enhance the homogeneity of prepared glasses [6]. Bioactive glasses produced with calcium phosphate-based generally possess high mechanical strength. Bioactive glasses are passed through a series of mechanical tests. As the crystallization of glass increases, i.e, away from the amorphous structure, mechanical strength improves, but the
Corresponding author at: Uskudar University, Vocational School of Health Services, Radiotherapy Department, Istanbul 34672, Turkey. E-mail address: [email protected] (H.O. Tekin).
https://doi.org/10.1016/j.rinp.2019.02.017 Received 18 January 2019; Received in revised form 5 February 2019; Accepted 5 February 2019 Available online 10 February 2019 2211-3797/ © 2019 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/BY-NC-ND/4.0/).
Results in Physics 12 (2019) 1797–1804
H.O. Tekin, et al.
parameter for shielding purposes. The linear attenuation coefficient (LAC) denotes per unit absorbed photons beams that are absorbed by the per unit thickness of the given absorber. As such, the LAC equals to the multiplication of μ/ρ and the density of the sample namely [13]:
biodegradable property of the glass disappears [7]. The mechanical properties of the bioactive glasses used in order not to affect the routine daily activity of patients should be close to the tissue of interest. Because of both their mechanical properties, amorphous structures and being light, the use of bioactive glasses as radiation protection is very attractive. In addition, the results obtained from the radiation attenuation parameters for the bioactive glasses can also make benefits to selection of the correct bioactive glass for the human body [8,9]. In accordance with this purpose, we have investigated both gamma and neutron interaction quantities of nine bioactive glasses (Na2O-CaOP2O5-SiO2) with different percentages [10,9]. Some substantial parameters for gamma radiation protection namely mass attenuation coefficient (MAC), half/tenth value layer (HVL and TVL), mean free path (MFP) and effective atomic number (Zeff) in wide energy range of 0.02–20 MeV were calculated. The MAC values found with XCOM were compared with the results obtained with MCNPX simulation code. Moreover, to evaluate the neutron protection performance of investigated bioactive glasses, effective removal cross-sections values (ΣR) have been determined. Moreover, EBF which is a very important parameter for radiation dose calculations values of the bioactive glasses at various energies between 0.015 and 15 MeV were calculated for different penetration depths between 1 and 15 mfp.
μ LAC = ⎜⎛ ⎟⎞ ρ ⎝ρ⎠
Half value layer (HVL) HVL value of any material means the thickness that minimized 50% of the radiation entering it. For this reason, HVL (in cm) is one of the appropriate parameters that describe the shielding effectiveness of the given bioactive glass samples. The HVL of the investigated bioactive glasses can be evaluated using the following formula [14]:
HVL =
0.693 μ
(3)
Tenth-value layer (TVL) Tenth-value layer (in cm) denotes the average amount of material thickness that reduces the radiation to the tenth of the original intensity (%90 reduction). TVL is related to the linear attenuation coefficient by the following relation [13]:
Materials and methods Material
(4)
Mean free path (MFP) The MFP denotes the mean distance traveled by a moving photon between sequential collisions. MFP is also important parameter for featuring a better quality of protection. The MFP (in cm) is derived from the following formula [15]:
Mass attenuation coefficient (MAC) The MAC is generally denoted by µ/ρ and represents the possibility of the interactions that occur between the matter of the unit mass per unit area and original photons from source. The µ/ρ values (in cm2/g) of the present bioactive glass samples can be obtained using the mixture rule given as below:
∑ wi (μ/ρ)i
2.303 μ
TVL =
Bioactive glasses with high structural strength can be used for radiation protection purposes. Glasses used for radiation shielding purposes should have high interaction cross-section. This paper deals with bioactive glasses consisting of the different percentage of Na2O, CaOP2O5-SiO2 in the composite. Table 1 demonstrates these bioactive components in detail and the sample coding has been done according to Ref. [10].
(μ/ρ) =
(2)
MFP =
1 μ
(5)
Effective atomic number (Zeff)
where wi denotes the fractional weight of the ith constituent in the elements, The µ/ρ value at a certain energy of an element is calculated by using XCOM software [11,12].
Zeff is quantity that indicates the total number of electrons rotating around the nucleus. As such it is a fitting quantity for corresponding gamma-ray interactions. Zeff varies with photon energy for composite materials and therefore the energy level is an important input for the calculation of Zeff. Zeff is derived by the following formula [16,17]:
The linear attenuation coefficient (LAC)
Zeff =
(1)
i
Table 1 Codes and chemical contents of the bioactive glasses. SiO2 (mol %)
Na2O (mol %)
CaO (mol %)
P2O5 (mol %)
Dc (g/ cm3)
ICIE1 ICSW2 ICSW3 ICSW5 ICSW4 ICSW6 ICSW8 ICSW9 ICSW10
49.46 47.84 44.47 40.96 37.28 48.98 43.66 38.14 40.71
26.38 26.67 27.26 27.87 28.52 26.67 28.12 29.62 28.91
23.08 23.33 23.85 24.39 24.95 23.33 24.60 25.91 25.31
1.07 2.16 4.42 6.78 9.25 1.02 3.62 6.33 5.07
2.701 2.700 2.700 2.699 2.698 2.705 2.715 2.725 2.721
(6)
where σa and σe is the total atomic and electronic cross-section, respectively. More details about the previous parameters and the computational works are available in our previous papers [18,19].
The thickness of an absorber of the photon is an important
Bioactive glass
σa σe
XCOM program XCOM is software that generates attenuation coefficients, total and partial cross sections for different photon interaction mechanisms namely photoelectric absorption, incoherent/coherent scattering and pair production for elements, compounds and mixtures in wide energy region of 1 keV–100 GeV. XCOM as a user-friendly software providing NIST X-ray attenuation database is used to compute total attenuation coefficients as well as photon cross sections for photoelectric absorption, scatterings and pair production of any element, compound or mixture (Z ≤ 100) for energies between 1 keV and 100 GeV [11]. 1798
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Fig. 1. (a) The gamma-ray attenuation setup of MCNPX. (b) 3-D view of total simulation setup obtained from MCNPX Visual Editor (version VE X_22S). Table 2 MAC values (cm2/g) of the bioactive glasses calculated with both MCNPX code and XCOM. Energy (MeV)
0.020 0.060 0.080 0.122 0.356 0.511 0.662 1.173 1.250 1.330 5.000 8.000 10.000 15.000 20.000 Energy (MeV)
0.020 0.060 0.080 0.122 0.356 0.511 0.662 1.173 1.250 1.330 5.000 8.000 10.000 15.000 20.000
ICIE1
ICSW2
ICSW3
ICSW4
MCNPX
XCOM
MCNPX
XCOM
MCNPX
XCOM
MCNPX
XCOM
3.982 0.308 0.217 0.159 0.101 0.087 0.078 0.058 0.057 0.055 0.029 0.025 0.024 0.022 0.021
3.963 0.306 0.216 0.159 0.100 0.086 0.077 0.058 0.056 0.055 0.029 0.025 0.023 0.022 0.021
3.985 0.309 0.219 0.159 0.101 0.088 0.077 0.059 0.057 0.055 0.029 0.025 0.023 0.022 0.022
3.981 0.306 0.216 0.159 0.100 0.086 0.077 0.058 0.056 0.055 0.029 0.025 0.023 0.022 0.021
4.057 0.309 0.219 0.159 0.102 0.088 0.079 0.060 0.056 0.055 0.029 0.025 0.024 0.022 0.022
4.019 0.308 0.217 0.159 0.100 0.086 0.077 0.058 0.056 0.055 0.029 0.025 0.023 0.022 0.021
4.113 0.316 0.218 0.159 0.100 0.089 0.077 0.058 0.057 0.055 0.029 0.025 0.024 0.021 0.020
4.100 0.311 0.218 0.159 0.100 0.086 0.077 0.058 0.056 0.055 0.029 0.025 0.023 0.022 0.021
ICSW5
ICSW6
ICSW8
ICSW9
ICSW10
MCNPX
XCOM
MCNPX
XCOM
MCNPX
XCOM
MCNPX
XCOM
MCNPX
XCOM
4.061 0.310 0.219 0.159 0.101 0.086 0.077 0.060 0.057 0.056 0.029 0.025 0.024 0.022 0.022
4.059 0.309 0.217 0.159 0.100 0.086 0.077 0.058 0.056 0.055 0.029 0.025 0.023 0.022 0.021
3.983 0.310 0.220 0.159 0.101 0.087 0.077 0.059 0.057 0.055 0.029 0.025 0.023 0.022 0.021
3.978 0.306 0.216 0.159 0.100 0.086 0.077 0.058 0.056 0.055 0.029 0.025 0.023 0.022 0.021
4.100 0.310 0.219 0.159 0.100 0.086 0.079 0.059 0.057 0.055 0.029 0.025 0.024 0.022 0.022
4.063 0.309 0.217 0.159 0.100 0.086 0.077 0.058 0.056 0.055 0.029 0.025 0.023 0.022 0.021
4.190 0.314 0.219 0.161 0.100 0.086 0.077 0.059 0.057 0.055 0.029 0.025 0.023 0.022 0.022
4.151 0.313 0.219 0.159 0.100 0.086 0.077 0.058 0.056 0.055 0.029 0.025 0.023 0.022 0.021
4.131 0.312 0.219 0.160 0.100 0.086 0.078 0.059 0.057 0.055 0.029 0.025 0.024 0.022 0.022
4.111 0.311 0.218 0.159 0.100 0.086 0.077 0.058 0.056 0.055 0.029 0.025 0.023 0.022 0.021
1799
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MCNPX code It is well-known that applications of certain mathematical methods such as Monte Carlo simulations capable of solving the large-scale physical problems and frequency of application of mathematical methods is also increasing day-by-day. The term of Monte Carlo simulation code simply simulates the experimental environment considering the physical and geometrical features of the used equipment, crosssection values and different databases have taken experimental studies. From the literature review, it can be clearly seen that Monte Carlo simulation method is utilized to investigate the radiation shielding properties of different glasses [20–24]. In this work, Monte Carlo NParticle Transport Code System-extended namely MCNPX (v 2.6.0) code has been carried out to study the μ/ρ values of the bioactive glasses namely ICIE1, ICSW2, ICSW3, ICSW4, ICSW5, ICSW6, ICSW8, ICSW9, ICSW10 samples by considering the Lambert-Beer law [25]:
I = I°exp(−μt )
(7)
where I0 and t represent the original intensity and the thickness, respectively. Gamma-ray attenuation setup of MCNPX with prime simulation equipment like point isotropic radiation source, lead (Pb) collimator for incident radiation beam, attenuator glass samples, F4 tally meshes detection field and Pb blocks to avoid detection field of scattered radiation can be seen in Fig. 1(a). Moreover, 3-D view of total simulation setup obtained from MCNPX Visual Editor (version VE X_22S) can be also seen in Fig. 1(b). The data-base examination of recent investigation has been completed utilizing the D00205ALLCP03 MCNPXDATA package which includes cross-section libraries. The present library typically extends ENDF/B-VI data from 2 × 104 to 15 × 104 keV. The NPS variable is set as 100 mega particles.
Fig. 2. Half-value layer (HVL) of the glasses as a function of photon energy.
Exposure buildup factor In order to calculate the correct quantity for attenuation for a given shielding material, the build-up factors are utilized and therefore it is a commonly used property in shielding design. There are two variants of build-up factors, Energy Absorption Build-up Factors (EABF) and Exposure Build-up factor (EBF). The latter, which is an important factor for the calculation of radiation protection, is the one that has been used in this paper. EBF basically stems from the radiation of gamma rays [26]. EBF for bioactive glass samples is derived by substituting G-P fitting quantities in the following equation below. It is important to note that the values of these quantities for any the Z1 and Z2 atomic numbers must lie at certain energy between Z1 and Z2 that is known as Zeq. That is Z1 < Zeq < Z2 [27].
Fig. 3. Tenth-value layer (TVL) as a function of photon energy.
B(E, x) = 1 +
b−1 x (K − 1) for K ≠ 1 K−1
(8)
B(E, x) = 1 + (b − 1)x for K = 1
(9)
where K(E, x) is the photon dose multiplication factor, b denotes the buildup factor corresponding to 1 mfp [28] which derived from the following relation:
tanhtanh K(E, x) = cx a + d
(
x Xk
)
− 2 − tanh( −2)
1 − tanh(−2)
for x ≤ 40 mfp
(10)
Macroscopic effective removal cross section for fast neutrons (ΣR)
Fig. 4. Variation mean free path (MFP) values of the glasses with photon energy.
The ΣR (cm−1), briefly the removal cross-section can also be called, is described as the possibility of one neutron undergoing a specific reaction per unit path length of passing through the glass medium [29]. To estimate the ΣR value of the present bioactive glasses, the following equation was used: 1800
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∑ R = ∑ Wi ( ∑ R/ρ)i
(11)
where Wi (g/cm ) and ΣR/ρ (cm /g) are the partial density and the mass removal cross-section of the ith element, respectively. The partial density of the ith element (Wi) is obtained from the following equation: 3
2
Wi = ρ . wi
(12)
where ρ represents the density of the sample (g/cm ) and wi denotes the weight fraction of the ith element, respectively. 3
Results and discussion The MAC (μ/ρ) of nine different bioactive glasses labeled as ICIE1, ICSW2, ICSW3, ICSW4, ICSW5, ICSW6, ICSW8, ICSW9 and ICSW10) were obtained by using MCNPX code and XCOM software in 0.02–20 MeV energy range. Table 2 provides the MAC (μ/ρ) values for the aforementioned bioactive glasses. It can be viewed from this table that the MAC values for all the selected glasses decreases suddenly with increasing photon energy up to 0.511 MeV. In low energy range (i.e. between 0.02 and 0.511 MeV), the cross section of the photoelectric absorbing effect (which is the main interaction process at these energies) depends on the atomic number as Z4-5. This indicates that most
Fig. 5. Zeff values for bioactive glasses in the energy range 0.02–20 MeV.
Fig. 6. (a–i) The exposure buildup factors in the energy region 0.015–15 MeV at 1–15 mfp for bioactive glasses. 1801
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Fig. 7. (a–d) The EBF for the glass samples up to 40 mfp at 0.015, 0.15, 1.5, 15 MeV.
almost constant for all the selected samples at these energies (i.e. E > 0.511 MeV). Additionally, the pair production mechanism is the dominant at higher energies and its cross section is associated with Z2, thus it was found a slight increase in the μm values in this region. It can be seen from Table 2 that the MAC has the largest values for ICSW9 and ICSW10. Figs. 2 and 3 indicate the graphical visualization of the variations of HVL and TVL against the photon energy of the selected bioactive glasses. Contrary to the change in MAC with the energy which shown in Table 2, the HVL and TVL values rise as the energy increases. Both HVL and TVL depend inversely on the density of the sample. In this sense, ICSW9 and ICSW10 bioactive glasses which possess the highest densities possess smaller values of HVL and TVL compared to other bioactive glasses as indicated in Figs. 2 and 3. These results are similar to previous findings reported for different glass systems [30,31]. In addition, the MFP (1/µ) values for these nine bioactive glasses are estimated for the energy range of 0.02–20 MeV as given in Fig. 4. MFP values for ICIE1, ICSW2, ICSW3, ICSW4, ICSW5, ICSW6, ICSW8, ICSW9 and ICSW10 are in the range of 0.0934–17.3818 cm, 0.0930–17.3801 cm, 0.0922–17.3638 cm, 0.0904–17.3442 cm, 0.0913–17.3540 cm, 0.0929–17.3480 cm, 0.0907–17.2436 cm, 0.0884–17.1322 cm and 0.0894–17.1815 cm, respectively. As in the HVL and TVL, ICSW9 and ICSW10 samples have the lowest MFP. We also plotted the variation in Zeff values with the energy for the present bioactive glasses in Fig. 5. It is observed that the Zeff values decrease quickly initially due to the photoelectric effect as discussed in
Fig. 8. The effective removal cross-sections of studied bioactive glasses.
of the interaction between the photons and the bioactive glasses occurs in the low energy region. After 0.511 MeV, owing to the linear dependence between the atomic number and cross-section of Compton scattering, MAC values are very small (in range of 0.077–0.021 cm2/g) and 1802
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Table 3 Macroscopic effective removal cross sections of bioactive glasses ∑R (cm−1). Element
O Na Si P Ca
∑R/ρ (cm2/g)
0.0405 0.0341 0.0285 0.0283 0.0243
ICIE1 (density = 2.701 g/cm3) Partial Density (g cm−3)
∑R (cm−1)
Fraction by weight (%)
Partial Density (g cm−3)
∑R (cm−1)
Fraction by weight (%)
Partial Density (g cm−3)
∑R (cm−1)
0.40344 0.19571 0.23119 0.00471 0.16495
1.089691 0.528613 0.624444 0.012722 0.44553
0.044132503 0.018025693 0.017796659 0.000360024 0.010826378
0.40236 0.19785 0.22362 0.00943 0.16674
1.086372 0.534195 0.603774 0.025461 0.450198
0.043998066 0.01821605 0.017207559 0.000720546 0.010939811
0.40016 0.20223 0.20787 0.01929 0.17045
1.080432 0.546021 0.561249 0.052083 0.460215
0.043757496 0.018619316 0.015995597 0.001473949 0.011183225
O Na Si P Ca
0.091141258 ∑R/ρ (cm2/g)
0.0405 0.0341 0.0285 0.0283 0.0243
ICSW4 (density = 2.698 g/cm3)
O Na Si P Ca Total
0.091082032 ICSW5 (density = 2.699 g/cm3)
0.0405 0.0341 0.0285 0.0283 0.0243
ICSW6 (density = 2.705 g/cm3)
Partial Density (g cm−3)
∑R (cm−1)
Fraction by weight (%)
Partial Density (g cm−3)
∑R (cm−1)
Fraction by weight (%)
Partial Density (g cm−3)
∑R (cm−1)
0.39548 0.21158 0.17426 0.04037 0.17831
1.06700504 0.57084284 0.47015348 0.10891826 0.48108038
0.043213704 0.019465741 0.013399374 0.003082387 0.011690253
0.39788 0.20676 0.19146 0.02959 0.17431
1.07387812 0.55804524 0.51675054 0.07986341 0.47046269
0.043492064 0.019029343 0.01472739 0.002260135 0.011432243
0.40201 0.19785 0.22895 0.00445 0.16674
1.0874371 0.5351843 0.6193098 0.0120373 0.4510317
0.0440412 0.0182498 0.0176503 0.0003407 0.0109601
0.090851459 ∑R/ρ (cm2/g)
0.091029582
Fraction by weight (%)
Total Element
ICSW3 (density = 2.700 g/cm3)
Fraction by weight (%)
Total Element
ICSW2 (density = 2.700 g/cm3)
3
0.090941175 3
ICSW8 (density = 2.715 g/cm )
ICSW9 (density = 2.725 g/cm ) −1
Fraction by weight (%)
Partial Density (g cm−3)
∑R (cm
0.3957 0.20861 0.20408 0.0158 0.17581
1.0743255 0.56637615 0.5540772 0.042897 0.47732415
0.043510183 0.019313427 0.0157912 0.001213985 0.011598977
)
ICSW10 (density = 2.721 g/cm ) −1
Fraction by weight (%)
Partial Density (g cm−3)
∑R (cm
0.38918 0.21974 0.17828 0.02763 0.18517
1.0605155 0.5987915 0.485813 0.07529175 0.50458825
0.042950878 0.02041879 0.013845671 0.002130757 0.012261494
0.0914278
0.091242 3
)
0.091607589
Fraction by weight (%)
Partial Density (g cm−3)
∑R (cm−1)
0.39222 0.21447 0.19029 0.02213 0.18089
1.06723062 0.58357287 0.51777909 0.06021573 0.49220169
0.04322284 0.019899835 0.014756704 0.001704105 0.011960501 0.091543985
represents the variation of EBF depending on photon energy of these bioactive glasses for the following penetration depths; 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14 and 15 mfp. From Fig. 6(a–i), it can be easily seen that the calculated values begin increasing with the further increase in the photon energy initially and they reach largest values in intermediate energy region, and then EBF values for all bioactive glasses decrease with the increment of photon energy up to 15 MeV. The results presented in Fig. 6(a–i) are in parallel with the standard explanation that states the variation in EBF with the energy is owing to the dominance of different gamma ray interaction mechanisms at different energies. The maximum incident photons are absorbed or removed paving way for EBF reached the minimum values for all bioactive glasses in the low energy zone where photoelectric absorption is predominant. With an increase in incident photon energy resulting in a series of multiple Compton scattering events, the EBF values start increasing and reached the maximum values. In the high energy region, where pair production starts to dominate, the EBF values enter a diminishing curve. As a general interpretation, the EBF increases as incident photon energy increase up to the intermediate energies. In addition to that, the EBF values are significantly high at the intermediate energy under the Compton scattering effect. While photons are both completely abolished and their energies are reduced in this mechanism, various Compton scattering maximizes EBF in the energy range of 0.15–0.3 MeV. For E > 4 MeV, EBF is not dependent on the nature of the sample because of the pair production processes. As indicated in Fig. 6(a–i), the highest buildup factor values in the chosen samples belong to ICIE1 while the EBF values of ICSW9 and ICSW10 are the lowest among the bioactive glasses under investigation. Also, at the lowest penetration depth (i.e. 1 mfp), the EBF values of the studied bioactive glasses lie between 1.03 and 1.25. The range of the EBF for the selected bioactive glasses changes from 1.05 to 2.09 with the
the MAC parameter (since Zeff is related to MAC for the given sample). At the intermediate energies, where Compton scattering accounts for practically all photon interactions, the lowest value of Zeff was observed for the glasses. Among the investigated bioactive glasses, ICSW9 and ICSW10 have the highest Zeff values ranging between 15.33 and 11.49 and 15.27–11.46 respectively. The high Zeff values for these two samples in comparison with the other bioactive glasses are owing to the relatively high content of Ca in these two samples. Briefly, the variation in Zeff can be classified into three energy regions namely low, intermediate and high and all these regions occur due to different photon interactions. At low energy region, photoelectric absorption is the dominating photon interaction process. Below 0.511 MeV, the photoelectric process is dominant and thus, the variation of Zeff is large. At the intermediate energy, the dominant process is Compton scattering. Between 0.511 MeV to several MeV, the variation in Zeff as seen in Fig. 5 is almost constant. Otherwise, pair production is the dominating mechanism is in the high energy region of 4 up to 20 MeV. Therefore, all variations are determined by the Z dependence of total atomic cross sections and the elements with high Z derives from photoelectric absorption cross-section process. However, the Compton scattering crosssection is associated with Z, giving less weight to the elements with high Z than photoelectric absorption and pair production mechanisms. All in all, in the low-energy range (E < 0.511 MeV) where Z4-5 dependence of the photoelectric absorption cross section gives a heavy weight for the highest atomic number of the glass sample, Zeff reaches its maximum value (in order of 15.5). At high energies, typically above 4 MeV, Zeff is increasing in a slow rate. This is resulting from the dominance of pair production, the cross section of which possesses a weaker Z2 dependence. Additionally, by using G-P fitting method, we calculated the EBF for the selected bioactive glasses at different energies between 0.015 and 15 MeV for several penetration depths up to 15 MFP. Fig. 6(a–i) 1803
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penetration depth of 5 mfp, while for the penetration depth of 10 mfp, these values are in range of 1.07–3.15. Finally, the EBF reaches its highest values up to 103.75 at the 15 mfp. When the maximum dose conveyed inside the medium, the variation of EBF values of the bioactive glasses with penetration depths is very noticeable. Fig. 7(a–d) demonstrates the EBF values at four energies namely 0.015, 0.15, 1.5 and 15 MeV. From Fig. 7(a, b) it can be seen wide EBF variations for all bioactive glasses at 0.015 and 0.15 MeV. This indicates that at these two low energies EBF depends clearly on the chemical composition of the bioactive glass sample. It is also observed that for the bioactive glasses with low equivalent numbers (Zeq) as well as low Zeff (ICIE1, ICSW2, ICSW3, and ICSW6), the values of buildup factors are large while for the bioactive glasses with higher Zeq and Zeff (ICSW4, ICSW5, ICSW8, ICSW9 and ICSW10) the EBF values are comparatively small. From Fig. 7(c, d), pair production process becomes dominant at 5 and 15 MeV therefore we can see that the EBF values become independent of the chemical composition of the bioactive materials. The effective removal cross-sections for fast neutron (ΣR) of the selected bioactive glasses obtained by using Eqs. (11) and (12) and the results are shown in Fig. 8 and listed in Table 3. It can be obviously viewed from Fig. 8 that the ΣR of the selected bioactive glasses are quite near to each other and ranged from 0.0908515 cm−1 for ICSW4 (density = 2.698 g/cm3) to 0.0916076 cm−1 for ICSW9 (density = 2.725 g/ cm3). The relatively high ΣR value of the ICSW9 sample can be explained by its higher density than the other samples (see Table 1). Also, it can be seen that the ICSW4 sample which already has a low density, has the lowest ΣR value. Therefore, the results presented in Fig. 8 indicate that the density of the bioactive glass sample is an important parameter in neutron attenuation. As a result, it can be said that the ICSW9 sample is the most appropriate sample among the selected bioactive glasses to be developed and used for neutron shielding purposes.
org/10.1002/1097-4636(200010)52:1<66::AID-JBM9>3.0.CO;2-2. [6] Islam MT, Felfel RM, Abou Neel EA, Grant DM, Ahmed I, Hossain KMZ. Bioactive calcium phosphate–based glasses and ceramics and their biomedical applications: a review. 204173141771917 J Tissue Eng. 2017;8. https://doi.org/10.1177/ 2041731417719170. [7] Bertolla L, Dlouhý I, Tatarko P, Viani A, Mahajan A, Chlup Z, et al. Pressureless spark plasma–sintered Bioglass®45S5 with enhanced mechanical properties and stress–induced new phase formation. J Eur Ceram Soc 2017. https://doi.org/10. 1016/j.jeurceramsoc.2017.02.003. [8] Almatari M. Energy absorption and exposure buildup factors for some bioactive glasses samples: penetration depth photon energy, and atomic number dependence. J Optoelectronics Biomed Mater 2017;9:95–105. [9] Sayyed MI, Manjunatha HC, Gaikwad DK, Obaid SS, Zaid MHM, Matori KA, et al. Energy-absorption buildup factors and specific absorbed fractions of energy for bioactive glasses. Dig J Nanomater Biostruct 2018;13:701–12. [10] Doweidar H. Density–structure correlations in Na2O–CaO–P2O5–SiO2 bioactive glasses. J Non Cryst Solids 2009. https://doi.org/10.1016/j.jnoncrysol.2009.02. 007. [11] Berger M, Hubbell J, Seltzer S, Chang J, Coursey J, Sukumar R, et al. XCOM: Photon Cross Sections Database, NIST Stand. Ref. Database. 1998. citeulike-articleid:9783715. [12] Agar O, Sayyed MI, Akman F, Tekin HO, Kaçal MR. An extensive investigation on gamma ray shielding features of Pd/Ag-based alloys. Nucl Eng Technol 2019. https://doi.org/10.1016/j.net.2018.12.014. [13] Eke C, Agar O, Segebade C, Boztosun I. Attenuation properties of radiation shielding materials such as granite and marble against γ-ray energies between 80 and 1350 keV. Radiochim Acta 2017. https://doi.org/10.1515/ract-2016-2690. [14] Agar O, Tekin HO, Sayyed MI, Korkmaz ME, Culfa O, Ertugay C. Experimental investigation of photon attenuation behaviors for concretes including natural perlite mineral. Results Phys 2019;12:237–43. https://doi.org/10.1016/j.rinp.2018.11. 053. [15] Sayyed MI, Akman F, Kumar A, Kaçal MR. Evaluation of radioprotection properties of some selected ceramic samples. Results Phys 2018;11:1100–4. https://doi.org/ 10.1016/j.rinp.2018.11.028. [16] Akman F, Kaçal MR, Akman F, Soylu MS. Determination of effective atomic numbers and electron densities from mass attenuation coefficients for some selected complexes containing lanthanides. Can J Phys 2017. https://doi.org/10.1139/cjp2016-0811. [17] Akman F, Sayyed MI, Kaçal MR, Tekin HO. Investigation of photon shielding performances of some selected alloys by experimental data, theoretical and MCNPX code in the energy range of 81 keV–1333 keV. J Alloys Compd 2019;772:516–24. https://doi.org/10.1016/j.jallcom.2018.09.177. [18] Issa SAM, Sayyed MI, Zaid MHM, Matori KA. Photon parameters for gamma-rays sensing properties of some oxide of lanthanides. Results Phys 2018. https://doi.org/ 10.1016/j.rinp.2018.02.039. [19] Tekin HO, Altunsoy EE, Kavaz E, Sayyed MI, Agar O, Kamislioglu M. Photon and neutron shielding performance of boron phosphate glasses for diagnostic radiology facilities. Results Phys 2019;12:1457–64. https://doi.org/10.1016/j.rinp.2019.01. 060. [20] Issa SAM, Saddeek YB, Tekin HO, Sayyed MI, saber Shaaban K. Investigations of radiation shielding using Monte Carlo method and elastic properties of PbO-SiO2B2O3-Na2O glasses. Curr Appl Phys 2018. https://doi.org/10.1016/j.cap.2018.02. 018. [21] Issa SAM, Tekin HO, Elsaman R, Kilicoglu O, Saddeek YB, Sayyed MI. Radiation shielding and mechanical properties of Al2O3–Na2O–B2O3−Bi2O3 glasses using MCNPX Monte Carlo code. Mater Chem Phys 2018;223:209–19. https://doi.org/10. 1016/j.matchemphys.2018.10.064. [22] Tekin HO, Sayyed MI, Issa SAM. Gamma radiation shielding properties of the hematite-serpentine concrete blended with WO3 and Bi2O3 micro and nano particles using MCNPX code. Radiat Phys Chem 2018;150:95–100. [23] Sayyed MI, Issa SAM, Tekin HO, Saddeek YB. Comparative study of gamma-ray shielding and elastic properties of BaO–Bi2O3–B2O3 and ZnO–Bi2O3–B2O3 glass systems. Mater Chem Phys 2018;217. https://doi.org/10.1016/j.matchemphys. 2018.06.034. [24] Agar O, Khattari ZY, Sayyed MI, Tekin HO, Al-Omari S, Maghrabi M, et al. Evaluation of the shielding parameters of alkaline earth based phosphate glasses using MCNPX code. Results Phys 2019;12:101–6. https://doi.org/10.1016/j.rinp. 2018.11.054. [25] Akman F, Durak R, Kacal MR, Bezgin F. Study of absorption parameters around the K edge for selected compounds of Gd. X-ray Spectrom 2016. https://doi.org/10. 1002/xrs.2676. [26] Harima Y. An approximation of gamma buildup factors by modified geometrical progression. Nucl Sci Eng 1983;83:299–309. https://doi.org/10.13182/NSE83A18222. [27] Kavaz E, Yorgun NY. Gamma ray buildup factors of lithium borate glasses doped with minerals. J Alloys Compd 2018. https://doi.org/10.1016/j.jallcom.2018.04. 106. [28] Harima Y. An historical review and current status of buildup factor calculations and applications. Radiat Phys Chem 1993. https://doi.org/10.1016/0969-806X(93) 90317-N. [29] Sayyed MI. Investigations of gamma ray and fast neutron shielding properties of tellurite glasses with different oxide compositions. Can J Phys 2016;94:1133–7. https://doi.org/10.1139/cjp-2016-0330. [30] El-Mallawany R, Sayyed MI, Dong MG. Comparative shielding properties of some tellurite glasses: Part 2. J Non-Cryst Solids 2017;474:16–23. https://doi.org/10. 1016/j.jnoncrysol.2017.08.011. [31] Agar O, Sayyed MI, Tekin HO, Kaky KM, Baki SO, Kityk I. An investigation on shielding properties of BaO, MoO3 and P2O5 based glasses using MCNPX code. Results Phys 2019;12:629–34. https://doi.org/10.1016/j.rinp.2018.12.003.
Conclusions In this study, different bioactive glasses which are widely used materials in tissue engineering and treatments have been evaluated for their gamma ray shielding performances utilizing simulation (MCNPX code) and theoretical (XCOM software). The MAC results of the bioactive glasses obtained by MCNPX code are in good agreement with those of XCOM values. In addition, ICSW9 and ICSW10 glasses have been found to be MFP values of 0.0884–17.1322 cm and 0.0894–17.1815 cm, respectively. On other hand, by using G-P fitting method, it has been calculated the EBF for the selected bioactive glasses in the energy region of 0.015–15 MeV for several penetration depths up to 15 mfp. The EBF values of the selected glasses vary from 1.03 to 1.25 at 1 mfp penetration depth. The obtained results exhibited that ICSW9 sample with more Ca content and relatively high density has lower MFP, HVL, TVL and EBF values than the studied bioactive glasses. Also, it was observed that ICSW9 has the highest effective removal cross section than the rest of bioactive glasses. Consequently, this sample appears as superior material to protect from both gamma and neutron radiations. References [1] Hench Larry L, Andersson Örjan. Bioactive glasses. An introduction to bioceramics 1993. https://doi.org/10.1142/2028. [2] Kaur G, Pandey OP, Singh K, Homa D, Scott B, Pickrell G. A review of bioactive glasses: their structure, properties, fabrication and apatite formation. J Biomed Mater Res Part A 2014. https://doi.org/10.1002/jbm.a.34690. [3] Baino F, Fiorilli S, Vitale-Brovarone C. Bioactive glass-based materials with hierarchical porosity for medical applications: review of recent advances. Acta Biomater 2016. https://doi.org/10.1016/j.actbio.2016.06.033. [4] Hench LL, Splinter RJ, Allen WC, Greenlee TK. Bonding mechanisms at the interface of ceramic prosthetic materials. J Biomed Mater Res 1971. https://doi.org/10. 1002/jbm.820050611. [5] Qiu QQ, Ducheyne P, Ayyaswamy PS. New bioactive, degradable composite microspheres as tissue engineering substrates. J Biomed Mater Res 2000. https://doi.
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The investigation of gamma-ray and neutron shielding parameters of Na2OCaO-P2O5-SiO2 bioactive glasses using MCNPX code
T
⁎
H.O. Tekina,b, , O. Kilicogluc, E. Kavazd, E.E. Altunsoyb,e, M. Almatarif, O. Agarg, M.I. Sayyedf a
Uskudar University, Vocational School of Health Services, Radiotherapy Department, Istanbul 34672, Turkey Uskudar University, Medical Radiation Research Center (USMERA), Istanbul 34672, Turkey c Uskudar University, Department of Nuclear Technology and Radiation Protection, Istanbul 34672, Turkey d Ataturk University, Faculty of Science, Department of Physics, 25240 Erzurum, Turkey e Uskudar University, Vocational School of Health Services, Medical Imaging Department, Istanbul 34672, Turkey f University of Tabuk, Physics Department, Tabuk, Saudi Arabia g Karamanoglu Mehmetbey University, Department of Physics, 70100 Karaman, Turkey b
A R T I C LE I N FO
A B S T R A C T
Keywords: Bioactive glass Silicate glasses Radiation protection MCNPX
Bioactive glasses are silicate glasses with sodium, calcium and phosphorus in its composition used to fulfill or support the functions of living tissues in the human body. The superiority of physical and mechanical properties of the bioactive glasses leads to the opportunity to use for radiation protection. From this point of view, radiation absorption parameters of nine bioactive glasses were reported in the present research. The mass attenuation coefficient (μ/ρ) for the selected bioactive glasses was calculated using MCNPX simulation code in the photon energy range 0.02–20 MeV and the results were compared with XCOM data. The values of μ/ρ calculated in two methods were found to support each other. Other vital parameters like half and tenth value layer (HVL and TVL), mean free path (MFP) and effective atomic number (Zeff) for the selected bioactive glasses were also evaluated by utilizing the μ/ρ. ICSW9 glass with more phosphate and sodium contents possess the lowest MFP, HVL and TVL values while has the highest Zeff values among the bioactive glasses under study. To evaluate the neutron protection performance of investigated bioactive glasses, effective removal cross-section values (ΣR) have been determined. The results showed that ICSW9 has also superior neutron attenuation properties. Additionally, exposure buildup factor (EBF) values were found with G-P fitting approach depending on the energy and penetration depths. The bioactive glasses with further equivalent atomic number possesses the minimum value of EBF.
Introduction A bioactive material is known as a natural or man-made material that prompts a specific biological response from the body e.g., bonding to tissue. As such, they have numerous applications in the reconstruction and repair of damaged and diseased tissue, and tissue and hard tissue (bone) re-engineering [1]. Bioactive glasses are one type of such biomaterials along with polymers, metals, composites, and ceramics. They are closely related to bioceramics, yet they have an important advantage over other types of bioactive ceramics by enabling to control a range of chemical properties and rate of binding to tissue [2]. In order to use the bioactive glasses effectively, they must have compatible mechanical properties depending on where they are used, they should not be toxic or carcinogenic, or they do not cause reactions (bioavailability) and they should be resistant to corrosion in the body fluid [3].
⁎
Bioactive glasses were first found by Hench et al. around 1960s [4] as such compositions and crystallized ceramics in the Na2O, CaO-P2O5SiO2 system, which is the base components of bioactive glasses, provides strong bonds with living tissues. Chemical bonding occurs between tissues and implants as a result of replacement of some silica groups in the bioactive glass structure with calcium and phosphorus [5]. The role of phosphate (P2O5) in the content of the bioactive glass is to ensure that the glass is bioactive. Because it can enhance a specific different biological response, feature, or function to the glass host. The high melting point of silicate makes the glass composition be fully melted and enhance the homogeneity of prepared glasses [6]. Bioactive glasses produced with calcium phosphate-based generally possess high mechanical strength. Bioactive glasses are passed through a series of mechanical tests. As the crystallization of glass increases, i.e, away from the amorphous structure, mechanical strength improves, but the
Corresponding author at: Uskudar University, Vocational School of Health Services, Radiotherapy Department, Istanbul 34672, Turkey. E-mail address: [email protected] (H.O. Tekin).
https://doi.org/10.1016/j.rinp.2019.02.017 Received 18 January 2019; Received in revised form 5 February 2019; Accepted 5 February 2019 Available online 10 February 2019 2211-3797/ © 2019 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/BY-NC-ND/4.0/).
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parameter for shielding purposes. The linear attenuation coefficient (LAC) denotes per unit absorbed photons beams that are absorbed by the per unit thickness of the given absorber. As such, the LAC equals to the multiplication of μ/ρ and the density of the sample namely [13]:
biodegradable property of the glass disappears [7]. The mechanical properties of the bioactive glasses used in order not to affect the routine daily activity of patients should be close to the tissue of interest. Because of both their mechanical properties, amorphous structures and being light, the use of bioactive glasses as radiation protection is very attractive. In addition, the results obtained from the radiation attenuation parameters for the bioactive glasses can also make benefits to selection of the correct bioactive glass for the human body [8,9]. In accordance with this purpose, we have investigated both gamma and neutron interaction quantities of nine bioactive glasses (Na2O-CaOP2O5-SiO2) with different percentages [10,9]. Some substantial parameters for gamma radiation protection namely mass attenuation coefficient (MAC), half/tenth value layer (HVL and TVL), mean free path (MFP) and effective atomic number (Zeff) in wide energy range of 0.02–20 MeV were calculated. The MAC values found with XCOM were compared with the results obtained with MCNPX simulation code. Moreover, to evaluate the neutron protection performance of investigated bioactive glasses, effective removal cross-sections values (ΣR) have been determined. Moreover, EBF which is a very important parameter for radiation dose calculations values of the bioactive glasses at various energies between 0.015 and 15 MeV were calculated for different penetration depths between 1 and 15 mfp.
μ LAC = ⎜⎛ ⎟⎞ ρ ⎝ρ⎠
Half value layer (HVL) HVL value of any material means the thickness that minimized 50% of the radiation entering it. For this reason, HVL (in cm) is one of the appropriate parameters that describe the shielding effectiveness of the given bioactive glass samples. The HVL of the investigated bioactive glasses can be evaluated using the following formula [14]:
HVL =
0.693 μ
(3)
Tenth-value layer (TVL) Tenth-value layer (in cm) denotes the average amount of material thickness that reduces the radiation to the tenth of the original intensity (%90 reduction). TVL is related to the linear attenuation coefficient by the following relation [13]:
Materials and methods Material
(4)
Mean free path (MFP) The MFP denotes the mean distance traveled by a moving photon between sequential collisions. MFP is also important parameter for featuring a better quality of protection. The MFP (in cm) is derived from the following formula [15]:
Mass attenuation coefficient (MAC) The MAC is generally denoted by µ/ρ and represents the possibility of the interactions that occur between the matter of the unit mass per unit area and original photons from source. The µ/ρ values (in cm2/g) of the present bioactive glass samples can be obtained using the mixture rule given as below:
∑ wi (μ/ρ)i
2.303 μ
TVL =
Bioactive glasses with high structural strength can be used for radiation protection purposes. Glasses used for radiation shielding purposes should have high interaction cross-section. This paper deals with bioactive glasses consisting of the different percentage of Na2O, CaOP2O5-SiO2 in the composite. Table 1 demonstrates these bioactive components in detail and the sample coding has been done according to Ref. [10].
(μ/ρ) =
(2)
MFP =
1 μ
(5)
Effective atomic number (Zeff)
where wi denotes the fractional weight of the ith constituent in the elements, The µ/ρ value at a certain energy of an element is calculated by using XCOM software [11,12].
Zeff is quantity that indicates the total number of electrons rotating around the nucleus. As such it is a fitting quantity for corresponding gamma-ray interactions. Zeff varies with photon energy for composite materials and therefore the energy level is an important input for the calculation of Zeff. Zeff is derived by the following formula [16,17]:
The linear attenuation coefficient (LAC)
Zeff =
(1)
i
Table 1 Codes and chemical contents of the bioactive glasses. SiO2 (mol %)
Na2O (mol %)
CaO (mol %)
P2O5 (mol %)
Dc (g/ cm3)
ICIE1 ICSW2 ICSW3 ICSW5 ICSW4 ICSW6 ICSW8 ICSW9 ICSW10
49.46 47.84 44.47 40.96 37.28 48.98 43.66 38.14 40.71
26.38 26.67 27.26 27.87 28.52 26.67 28.12 29.62 28.91
23.08 23.33 23.85 24.39 24.95 23.33 24.60 25.91 25.31
1.07 2.16 4.42 6.78 9.25 1.02 3.62 6.33 5.07
2.701 2.700 2.700 2.699 2.698 2.705 2.715 2.725 2.721
(6)
where σa and σe is the total atomic and electronic cross-section, respectively. More details about the previous parameters and the computational works are available in our previous papers [18,19].
The thickness of an absorber of the photon is an important
Bioactive glass
σa σe
XCOM program XCOM is software that generates attenuation coefficients, total and partial cross sections for different photon interaction mechanisms namely photoelectric absorption, incoherent/coherent scattering and pair production for elements, compounds and mixtures in wide energy region of 1 keV–100 GeV. XCOM as a user-friendly software providing NIST X-ray attenuation database is used to compute total attenuation coefficients as well as photon cross sections for photoelectric absorption, scatterings and pair production of any element, compound or mixture (Z ≤ 100) for energies between 1 keV and 100 GeV [11]. 1798
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Fig. 1. (a) The gamma-ray attenuation setup of MCNPX. (b) 3-D view of total simulation setup obtained from MCNPX Visual Editor (version VE X_22S). Table 2 MAC values (cm2/g) of the bioactive glasses calculated with both MCNPX code and XCOM. Energy (MeV)
0.020 0.060 0.080 0.122 0.356 0.511 0.662 1.173 1.250 1.330 5.000 8.000 10.000 15.000 20.000 Energy (MeV)
0.020 0.060 0.080 0.122 0.356 0.511 0.662 1.173 1.250 1.330 5.000 8.000 10.000 15.000 20.000
ICIE1
ICSW2
ICSW3
ICSW4
MCNPX
XCOM
MCNPX
XCOM
MCNPX
XCOM
MCNPX
XCOM
3.982 0.308 0.217 0.159 0.101 0.087 0.078 0.058 0.057 0.055 0.029 0.025 0.024 0.022 0.021
3.963 0.306 0.216 0.159 0.100 0.086 0.077 0.058 0.056 0.055 0.029 0.025 0.023 0.022 0.021
3.985 0.309 0.219 0.159 0.101 0.088 0.077 0.059 0.057 0.055 0.029 0.025 0.023 0.022 0.022
3.981 0.306 0.216 0.159 0.100 0.086 0.077 0.058 0.056 0.055 0.029 0.025 0.023 0.022 0.021
4.057 0.309 0.219 0.159 0.102 0.088 0.079 0.060 0.056 0.055 0.029 0.025 0.024 0.022 0.022
4.019 0.308 0.217 0.159 0.100 0.086 0.077 0.058 0.056 0.055 0.029 0.025 0.023 0.022 0.021
4.113 0.316 0.218 0.159 0.100 0.089 0.077 0.058 0.057 0.055 0.029 0.025 0.024 0.021 0.020
4.100 0.311 0.218 0.159 0.100 0.086 0.077 0.058 0.056 0.055 0.029 0.025 0.023 0.022 0.021
ICSW5
ICSW6
ICSW8
ICSW9
ICSW10
MCNPX
XCOM
MCNPX
XCOM
MCNPX
XCOM
MCNPX
XCOM
MCNPX
XCOM
4.061 0.310 0.219 0.159 0.101 0.086 0.077 0.060 0.057 0.056 0.029 0.025 0.024 0.022 0.022
4.059 0.309 0.217 0.159 0.100 0.086 0.077 0.058 0.056 0.055 0.029 0.025 0.023 0.022 0.021
3.983 0.310 0.220 0.159 0.101 0.087 0.077 0.059 0.057 0.055 0.029 0.025 0.023 0.022 0.021
3.978 0.306 0.216 0.159 0.100 0.086 0.077 0.058 0.056 0.055 0.029 0.025 0.023 0.022 0.021
4.100 0.310 0.219 0.159 0.100 0.086 0.079 0.059 0.057 0.055 0.029 0.025 0.024 0.022 0.022
4.063 0.309 0.217 0.159 0.100 0.086 0.077 0.058 0.056 0.055 0.029 0.025 0.023 0.022 0.021
4.190 0.314 0.219 0.161 0.100 0.086 0.077 0.059 0.057 0.055 0.029 0.025 0.023 0.022 0.022
4.151 0.313 0.219 0.159 0.100 0.086 0.077 0.058 0.056 0.055 0.029 0.025 0.023 0.022 0.021
4.131 0.312 0.219 0.160 0.100 0.086 0.078 0.059 0.057 0.055 0.029 0.025 0.024 0.022 0.022
4.111 0.311 0.218 0.159 0.100 0.086 0.077 0.058 0.056 0.055 0.029 0.025 0.023 0.022 0.021
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MCNPX code It is well-known that applications of certain mathematical methods such as Monte Carlo simulations capable of solving the large-scale physical problems and frequency of application of mathematical methods is also increasing day-by-day. The term of Monte Carlo simulation code simply simulates the experimental environment considering the physical and geometrical features of the used equipment, crosssection values and different databases have taken experimental studies. From the literature review, it can be clearly seen that Monte Carlo simulation method is utilized to investigate the radiation shielding properties of different glasses [20–24]. In this work, Monte Carlo NParticle Transport Code System-extended namely MCNPX (v 2.6.0) code has been carried out to study the μ/ρ values of the bioactive glasses namely ICIE1, ICSW2, ICSW3, ICSW4, ICSW5, ICSW6, ICSW8, ICSW9, ICSW10 samples by considering the Lambert-Beer law [25]:
I = I°exp(−μt )
(7)
where I0 and t represent the original intensity and the thickness, respectively. Gamma-ray attenuation setup of MCNPX with prime simulation equipment like point isotropic radiation source, lead (Pb) collimator for incident radiation beam, attenuator glass samples, F4 tally meshes detection field and Pb blocks to avoid detection field of scattered radiation can be seen in Fig. 1(a). Moreover, 3-D view of total simulation setup obtained from MCNPX Visual Editor (version VE X_22S) can be also seen in Fig. 1(b). The data-base examination of recent investigation has been completed utilizing the D00205ALLCP03 MCNPXDATA package which includes cross-section libraries. The present library typically extends ENDF/B-VI data from 2 × 104 to 15 × 104 keV. The NPS variable is set as 100 mega particles.
Fig. 2. Half-value layer (HVL) of the glasses as a function of photon energy.
Exposure buildup factor In order to calculate the correct quantity for attenuation for a given shielding material, the build-up factors are utilized and therefore it is a commonly used property in shielding design. There are two variants of build-up factors, Energy Absorption Build-up Factors (EABF) and Exposure Build-up factor (EBF). The latter, which is an important factor for the calculation of radiation protection, is the one that has been used in this paper. EBF basically stems from the radiation of gamma rays [26]. EBF for bioactive glass samples is derived by substituting G-P fitting quantities in the following equation below. It is important to note that the values of these quantities for any the Z1 and Z2 atomic numbers must lie at certain energy between Z1 and Z2 that is known as Zeq. That is Z1 < Zeq < Z2 [27].
Fig. 3. Tenth-value layer (TVL) as a function of photon energy.
B(E, x) = 1 +
b−1 x (K − 1) for K ≠ 1 K−1
(8)
B(E, x) = 1 + (b − 1)x for K = 1
(9)
where K(E, x) is the photon dose multiplication factor, b denotes the buildup factor corresponding to 1 mfp [28] which derived from the following relation:
tanhtanh K(E, x) = cx a + d
(
x Xk
)
− 2 − tanh( −2)
1 − tanh(−2)
for x ≤ 40 mfp
(10)
Macroscopic effective removal cross section for fast neutrons (ΣR)
Fig. 4. Variation mean free path (MFP) values of the glasses with photon energy.
The ΣR (cm−1), briefly the removal cross-section can also be called, is described as the possibility of one neutron undergoing a specific reaction per unit path length of passing through the glass medium [29]. To estimate the ΣR value of the present bioactive glasses, the following equation was used: 1800
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∑ R = ∑ Wi ( ∑ R/ρ)i
(11)
where Wi (g/cm ) and ΣR/ρ (cm /g) are the partial density and the mass removal cross-section of the ith element, respectively. The partial density of the ith element (Wi) is obtained from the following equation: 3
2
Wi = ρ . wi
(12)
where ρ represents the density of the sample (g/cm ) and wi denotes the weight fraction of the ith element, respectively. 3
Results and discussion The MAC (μ/ρ) of nine different bioactive glasses labeled as ICIE1, ICSW2, ICSW3, ICSW4, ICSW5, ICSW6, ICSW8, ICSW9 and ICSW10) were obtained by using MCNPX code and XCOM software in 0.02–20 MeV energy range. Table 2 provides the MAC (μ/ρ) values for the aforementioned bioactive glasses. It can be viewed from this table that the MAC values for all the selected glasses decreases suddenly with increasing photon energy up to 0.511 MeV. In low energy range (i.e. between 0.02 and 0.511 MeV), the cross section of the photoelectric absorbing effect (which is the main interaction process at these energies) depends on the atomic number as Z4-5. This indicates that most
Fig. 5. Zeff values for bioactive glasses in the energy range 0.02–20 MeV.
Fig. 6. (a–i) The exposure buildup factors in the energy region 0.015–15 MeV at 1–15 mfp for bioactive glasses. 1801
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Fig. 7. (a–d) The EBF for the glass samples up to 40 mfp at 0.015, 0.15, 1.5, 15 MeV.
almost constant for all the selected samples at these energies (i.e. E > 0.511 MeV). Additionally, the pair production mechanism is the dominant at higher energies and its cross section is associated with Z2, thus it was found a slight increase in the μm values in this region. It can be seen from Table 2 that the MAC has the largest values for ICSW9 and ICSW10. Figs. 2 and 3 indicate the graphical visualization of the variations of HVL and TVL against the photon energy of the selected bioactive glasses. Contrary to the change in MAC with the energy which shown in Table 2, the HVL and TVL values rise as the energy increases. Both HVL and TVL depend inversely on the density of the sample. In this sense, ICSW9 and ICSW10 bioactive glasses which possess the highest densities possess smaller values of HVL and TVL compared to other bioactive glasses as indicated in Figs. 2 and 3. These results are similar to previous findings reported for different glass systems [30,31]. In addition, the MFP (1/µ) values for these nine bioactive glasses are estimated for the energy range of 0.02–20 MeV as given in Fig. 4. MFP values for ICIE1, ICSW2, ICSW3, ICSW4, ICSW5, ICSW6, ICSW8, ICSW9 and ICSW10 are in the range of 0.0934–17.3818 cm, 0.0930–17.3801 cm, 0.0922–17.3638 cm, 0.0904–17.3442 cm, 0.0913–17.3540 cm, 0.0929–17.3480 cm, 0.0907–17.2436 cm, 0.0884–17.1322 cm and 0.0894–17.1815 cm, respectively. As in the HVL and TVL, ICSW9 and ICSW10 samples have the lowest MFP. We also plotted the variation in Zeff values with the energy for the present bioactive glasses in Fig. 5. It is observed that the Zeff values decrease quickly initially due to the photoelectric effect as discussed in
Fig. 8. The effective removal cross-sections of studied bioactive glasses.
of the interaction between the photons and the bioactive glasses occurs in the low energy region. After 0.511 MeV, owing to the linear dependence between the atomic number and cross-section of Compton scattering, MAC values are very small (in range of 0.077–0.021 cm2/g) and 1802
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Table 3 Macroscopic effective removal cross sections of bioactive glasses ∑R (cm−1). Element
O Na Si P Ca
∑R/ρ (cm2/g)
0.0405 0.0341 0.0285 0.0283 0.0243
ICIE1 (density = 2.701 g/cm3) Partial Density (g cm−3)
∑R (cm−1)
Fraction by weight (%)
Partial Density (g cm−3)
∑R (cm−1)
Fraction by weight (%)
Partial Density (g cm−3)
∑R (cm−1)
0.40344 0.19571 0.23119 0.00471 0.16495
1.089691 0.528613 0.624444 0.012722 0.44553
0.044132503 0.018025693 0.017796659 0.000360024 0.010826378
0.40236 0.19785 0.22362 0.00943 0.16674
1.086372 0.534195 0.603774 0.025461 0.450198
0.043998066 0.01821605 0.017207559 0.000720546 0.010939811
0.40016 0.20223 0.20787 0.01929 0.17045
1.080432 0.546021 0.561249 0.052083 0.460215
0.043757496 0.018619316 0.015995597 0.001473949 0.011183225
O Na Si P Ca
0.091141258 ∑R/ρ (cm2/g)
0.0405 0.0341 0.0285 0.0283 0.0243
ICSW4 (density = 2.698 g/cm3)
O Na Si P Ca Total
0.091082032 ICSW5 (density = 2.699 g/cm3)
0.0405 0.0341 0.0285 0.0283 0.0243
ICSW6 (density = 2.705 g/cm3)
Partial Density (g cm−3)
∑R (cm−1)
Fraction by weight (%)
Partial Density (g cm−3)
∑R (cm−1)
Fraction by weight (%)
Partial Density (g cm−3)
∑R (cm−1)
0.39548 0.21158 0.17426 0.04037 0.17831
1.06700504 0.57084284 0.47015348 0.10891826 0.48108038
0.043213704 0.019465741 0.013399374 0.003082387 0.011690253
0.39788 0.20676 0.19146 0.02959 0.17431
1.07387812 0.55804524 0.51675054 0.07986341 0.47046269
0.043492064 0.019029343 0.01472739 0.002260135 0.011432243
0.40201 0.19785 0.22895 0.00445 0.16674
1.0874371 0.5351843 0.6193098 0.0120373 0.4510317
0.0440412 0.0182498 0.0176503 0.0003407 0.0109601
0.090851459 ∑R/ρ (cm2/g)
0.091029582
Fraction by weight (%)
Total Element
ICSW3 (density = 2.700 g/cm3)
Fraction by weight (%)
Total Element
ICSW2 (density = 2.700 g/cm3)
3
0.090941175 3
ICSW8 (density = 2.715 g/cm )
ICSW9 (density = 2.725 g/cm ) −1
Fraction by weight (%)
Partial Density (g cm−3)
∑R (cm
0.3957 0.20861 0.20408 0.0158 0.17581
1.0743255 0.56637615 0.5540772 0.042897 0.47732415
0.043510183 0.019313427 0.0157912 0.001213985 0.011598977
)
ICSW10 (density = 2.721 g/cm ) −1
Fraction by weight (%)
Partial Density (g cm−3)
∑R (cm
0.38918 0.21974 0.17828 0.02763 0.18517
1.0605155 0.5987915 0.485813 0.07529175 0.50458825
0.042950878 0.02041879 0.013845671 0.002130757 0.012261494
0.0914278
0.091242 3
)
0.091607589
Fraction by weight (%)
Partial Density (g cm−3)
∑R (cm−1)
0.39222 0.21447 0.19029 0.02213 0.18089
1.06723062 0.58357287 0.51777909 0.06021573 0.49220169
0.04322284 0.019899835 0.014756704 0.001704105 0.011960501 0.091543985
represents the variation of EBF depending on photon energy of these bioactive glasses for the following penetration depths; 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14 and 15 mfp. From Fig. 6(a–i), it can be easily seen that the calculated values begin increasing with the further increase in the photon energy initially and they reach largest values in intermediate energy region, and then EBF values for all bioactive glasses decrease with the increment of photon energy up to 15 MeV. The results presented in Fig. 6(a–i) are in parallel with the standard explanation that states the variation in EBF with the energy is owing to the dominance of different gamma ray interaction mechanisms at different energies. The maximum incident photons are absorbed or removed paving way for EBF reached the minimum values for all bioactive glasses in the low energy zone where photoelectric absorption is predominant. With an increase in incident photon energy resulting in a series of multiple Compton scattering events, the EBF values start increasing and reached the maximum values. In the high energy region, where pair production starts to dominate, the EBF values enter a diminishing curve. As a general interpretation, the EBF increases as incident photon energy increase up to the intermediate energies. In addition to that, the EBF values are significantly high at the intermediate energy under the Compton scattering effect. While photons are both completely abolished and their energies are reduced in this mechanism, various Compton scattering maximizes EBF in the energy range of 0.15–0.3 MeV. For E > 4 MeV, EBF is not dependent on the nature of the sample because of the pair production processes. As indicated in Fig. 6(a–i), the highest buildup factor values in the chosen samples belong to ICIE1 while the EBF values of ICSW9 and ICSW10 are the lowest among the bioactive glasses under investigation. Also, at the lowest penetration depth (i.e. 1 mfp), the EBF values of the studied bioactive glasses lie between 1.03 and 1.25. The range of the EBF for the selected bioactive glasses changes from 1.05 to 2.09 with the
the MAC parameter (since Zeff is related to MAC for the given sample). At the intermediate energies, where Compton scattering accounts for practically all photon interactions, the lowest value of Zeff was observed for the glasses. Among the investigated bioactive glasses, ICSW9 and ICSW10 have the highest Zeff values ranging between 15.33 and 11.49 and 15.27–11.46 respectively. The high Zeff values for these two samples in comparison with the other bioactive glasses are owing to the relatively high content of Ca in these two samples. Briefly, the variation in Zeff can be classified into three energy regions namely low, intermediate and high and all these regions occur due to different photon interactions. At low energy region, photoelectric absorption is the dominating photon interaction process. Below 0.511 MeV, the photoelectric process is dominant and thus, the variation of Zeff is large. At the intermediate energy, the dominant process is Compton scattering. Between 0.511 MeV to several MeV, the variation in Zeff as seen in Fig. 5 is almost constant. Otherwise, pair production is the dominating mechanism is in the high energy region of 4 up to 20 MeV. Therefore, all variations are determined by the Z dependence of total atomic cross sections and the elements with high Z derives from photoelectric absorption cross-section process. However, the Compton scattering crosssection is associated with Z, giving less weight to the elements with high Z than photoelectric absorption and pair production mechanisms. All in all, in the low-energy range (E < 0.511 MeV) where Z4-5 dependence of the photoelectric absorption cross section gives a heavy weight for the highest atomic number of the glass sample, Zeff reaches its maximum value (in order of 15.5). At high energies, typically above 4 MeV, Zeff is increasing in a slow rate. This is resulting from the dominance of pair production, the cross section of which possesses a weaker Z2 dependence. Additionally, by using G-P fitting method, we calculated the EBF for the selected bioactive glasses at different energies between 0.015 and 15 MeV for several penetration depths up to 15 MFP. Fig. 6(a–i) 1803
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penetration depth of 5 mfp, while for the penetration depth of 10 mfp, these values are in range of 1.07–3.15. Finally, the EBF reaches its highest values up to 103.75 at the 15 mfp. When the maximum dose conveyed inside the medium, the variation of EBF values of the bioactive glasses with penetration depths is very noticeable. Fig. 7(a–d) demonstrates the EBF values at four energies namely 0.015, 0.15, 1.5 and 15 MeV. From Fig. 7(a, b) it can be seen wide EBF variations for all bioactive glasses at 0.015 and 0.15 MeV. This indicates that at these two low energies EBF depends clearly on the chemical composition of the bioactive glass sample. It is also observed that for the bioactive glasses with low equivalent numbers (Zeq) as well as low Zeff (ICIE1, ICSW2, ICSW3, and ICSW6), the values of buildup factors are large while for the bioactive glasses with higher Zeq and Zeff (ICSW4, ICSW5, ICSW8, ICSW9 and ICSW10) the EBF values are comparatively small. From Fig. 7(c, d), pair production process becomes dominant at 5 and 15 MeV therefore we can see that the EBF values become independent of the chemical composition of the bioactive materials. The effective removal cross-sections for fast neutron (ΣR) of the selected bioactive glasses obtained by using Eqs. (11) and (12) and the results are shown in Fig. 8 and listed in Table 3. It can be obviously viewed from Fig. 8 that the ΣR of the selected bioactive glasses are quite near to each other and ranged from 0.0908515 cm−1 for ICSW4 (density = 2.698 g/cm3) to 0.0916076 cm−1 for ICSW9 (density = 2.725 g/ cm3). The relatively high ΣR value of the ICSW9 sample can be explained by its higher density than the other samples (see Table 1). Also, it can be seen that the ICSW4 sample which already has a low density, has the lowest ΣR value. Therefore, the results presented in Fig. 8 indicate that the density of the bioactive glass sample is an important parameter in neutron attenuation. As a result, it can be said that the ICSW9 sample is the most appropriate sample among the selected bioactive glasses to be developed and used for neutron shielding purposes.
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Results Phys 2019;12:237–43. https://doi.org/10.1016/j.rinp.2018.11. 053. [15] Sayyed MI, Akman F, Kumar A, Kaçal MR. Evaluation of radioprotection properties of some selected ceramic samples. Results Phys 2018;11:1100–4. https://doi.org/ 10.1016/j.rinp.2018.11.028. [16] Akman F, Kaçal MR, Akman F, Soylu MS. Determination of effective atomic numbers and electron densities from mass attenuation coefficients for some selected complexes containing lanthanides. Can J Phys 2017. https://doi.org/10.1139/cjp2016-0811. [17] Akman F, Sayyed MI, Kaçal MR, Tekin HO. Investigation of photon shielding performances of some selected alloys by experimental data, theoretical and MCNPX code in the energy range of 81 keV–1333 keV. J Alloys Compd 2019;772:516–24. https://doi.org/10.1016/j.jallcom.2018.09.177. [18] Issa SAM, Sayyed MI, Zaid MHM, Matori KA. Photon parameters for gamma-rays sensing properties of some oxide of lanthanides. Results Phys 2018. https://doi.org/ 10.1016/j.rinp.2018.02.039. 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Conclusions In this study, different bioactive glasses which are widely used materials in tissue engineering and treatments have been evaluated for their gamma ray shielding performances utilizing simulation (MCNPX code) and theoretical (XCOM software). The MAC results of the bioactive glasses obtained by MCNPX code are in good agreement with those of XCOM values. In addition, ICSW9 and ICSW10 glasses have been found to be MFP values of 0.0884–17.1322 cm and 0.0894–17.1815 cm, respectively. On other hand, by using G-P fitting method, it has been calculated the EBF for the selected bioactive glasses in the energy region of 0.015–15 MeV for several penetration depths up to 15 mfp. The EBF values of the selected glasses vary from 1.03 to 1.25 at 1 mfp penetration depth. The obtained results exhibited that ICSW9 sample with more Ca content and relatively high density has lower MFP, HVL, TVL and EBF values than the studied bioactive glasses. Also, it was observed that ICSW9 has the highest effective removal cross section than the rest of bioactive glasses. Consequently, this sample appears as superior material to protect from both gamma and neutron radiations. References [1] Hench Larry L, Andersson Örjan. Bioactive glasses. An introduction to bioceramics 1993. https://doi.org/10.1142/2028. [2] Kaur G, Pandey OP, Singh K, Homa D, Scott B, Pickrell G. A review of bioactive glasses: their structure, properties, fabrication and apatite formation. J Biomed Mater Res Part A 2014. https://doi.org/10.1002/jbm.a.34690. [3] Baino F, Fiorilli S, Vitale-Brovarone C. Bioactive glass-based materials with hierarchical porosity for medical applications: review of recent advances. Acta Biomater 2016. https://doi.org/10.1016/j.actbio.2016.06.033. [4] Hench LL, Splinter RJ, Allen WC, Greenlee TK. Bonding mechanisms at the interface of ceramic prosthetic materials. J Biomed Mater Res 1971. https://doi.org/10. 1002/jbm.820050611. [5] Qiu QQ, Ducheyne P, Ayyaswamy PS. New bioactive, degradable composite microspheres as tissue engineering substrates. J Biomed Mater Res 2000. https://doi.
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