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Results in Physics
journal homepage:www.elsevier.com/locate/rinp
The investigation of gamma-ray and neutron shielding parameters of Na
2
O-CaO-P
2
O
5
-SiO
2
bioactive glasses using MCNPX code
H.O. Tekin
a,b,⁎, O. Kilicoglu
c, E. Kavaz
d, E.E. Altunsoy
b,e, M. Almatari
f, O. Agar
g, M.I. Sayyed
faUskudar University, Vocational School of Health Services, Radiotherapy Department, Istanbul 34672, Turkey bUskudar University, Medical Radiation Research Center (USMERA), Istanbul 34672, Turkey
cUskudar University, Department of Nuclear Technology and Radiation Protection, Istanbul 34672, Turkey dAtaturk University, Faculty of Science, Department of Physics, 25240 Erzurum, Turkey
eUskudar University, Vocational School of Health Services, Medical Imaging Department, Istanbul 34672, Turkey fUniversity of Tabuk, Physics Department, Tabuk, Saudi Arabia
gKaramanoglu Mehmetbey University, Department of Physics, 70100 Karaman, Turkey
A R T I C L E I N F O Keywords: Bioactive glass Silicate glasses Radiation protection MCNPX A B S T R A C T
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 theμ/ρ. ICSW9 glass with more phosphate and sodium contents possess the lowest MFP, HVL and TVL values while has the highest Zeffvalues 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-Pfitting approach depending on the energy and pe-netration 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 reconstruc-tion 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 (bioavail-ability) and they should be resistant to corrosion in the bodyfluid[3].
Bioactive glasses werefirst found by Hench et al. around 1960s[4]as such compositions and crystallized ceramics in the Na2O, CaO-P2O5
-SiO2system, which is the base components of bioactive glasses,
pro-vides strong bonds with living tissues. Chemical bonding occurs be-tween 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
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
⁎Corresponding author at: Uskudar University, Vocational School of Health Services, Radiotherapy Department, Istanbul 34672, Turkey.
E-mail address:huseyinozan.tekin@uskudar.edu.tr(H.O. Tekin).
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/).
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. Be-cause 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 at-tenuation 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 (Na2
O-CaO-P2O5-SiO2) with different percentages[10,9]. Some substantial
para-meters for gamma radiation protection namely mass attenuation coef-ficient (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 in-vestigated 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.
Materials and methods
Material
Bioactive glasses with high structural strength can be used for ra-diation protection purposes. Glasses used for rara-diation shielding pur-poses should have high interaction cross-section. This paper deals with bioactive glasses consisting of the different percentage of Na2O,
CaO-P2O5-SiO2 in the composite. Table 1 demonstrates these bioactive
components in detail and the sample coding has been done according to Ref.[10].
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:
∑
= (μ/ρ) w (μ/ρ) i i i (1) where wi denotes the fractional weight of the ith constituent in theelements, The µ/ρ value at a certain energy of an element is calculated by using XCOM software[11,12].
The linear attenuation coefficient (LAC)
The thickness of an absorber of the photon is an important
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 ofμ/ρ and the density of the sample namely[13]:
⎜ ⎟ = ⎛ ⎝ ⎞ ⎠ LAC μ ρ ρ (2)
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]:
= TVL 2.303
μ (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]:
=
MFP 1
μ (5)
Effective atomic number (Zeff)
Zeffis quantity that indicates the total number of electrons rotating
around the nucleus. As such it is afitting quantity for corresponding gamma-ray interactions. Zeffvaries with photon energy for composite
materials and therefore the energy level is an important input for the calculation of Zeff. Zeffis derived by the following formula[16,17]:
=
Z σ
σ
eff a
e (6)
whereσa andσe is the total atomic and electronic cross-section,
re-spectively. More details about the previous parameters and the com-putational works are available in our previous papers[18,19].
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 absorp-tion, scatterings and pair production of any element, compound or mixture (Z≤ 100) for energies between 1 keV and 100 GeV[11].
Table 1
Codes and chemical contents of the bioactive glasses.
Bioactive glass SiO2(mol %) Na2O (mol %) CaO (mol %) P2O5(mol %) Dc(g/ cm3) ICIE1 49.46 26.38 23.08 1.07 2.701 ICSW2 47.84 26.67 23.33 2.16 2.700 ICSW3 44.47 27.26 23.85 4.42 2.700 ICSW5 40.96 27.87 24.39 6.78 2.699 ICSW4 37.28 28.52 24.95 9.25 2.698 ICSW6 48.98 26.67 23.33 1.02 2.705 ICSW8 43.66 28.12 24.60 3.62 2.715 ICSW9 38.14 29.62 25.91 6.33 2.725 ICSW10 40.71 28.91 25.31 5.07 2.721
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) ICIE1 ICSW2 ICSW3 ICSW4
MCNPX XCOM MCNPX XCOM MCNPX XCOM MCNPX XCOM
0.020 3.982 3.963 3.985 3.981 4.057 4.019 4.113 4.100 0.060 0.308 0.306 0.309 0.306 0.309 0.308 0.316 0.311 0.080 0.217 0.216 0.219 0.216 0.219 0.217 0.218 0.218 0.122 0.159 0.159 0.159 0.159 0.159 0.159 0.159 0.159 0.356 0.101 0.100 0.101 0.100 0.102 0.100 0.100 0.100 0.511 0.087 0.086 0.088 0.086 0.088 0.086 0.089 0.086 0.662 0.078 0.077 0.077 0.077 0.079 0.077 0.077 0.077 1.173 0.058 0.058 0.059 0.058 0.060 0.058 0.058 0.058 1.250 0.057 0.056 0.057 0.056 0.056 0.056 0.057 0.056 1.330 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055 5.000 0.029 0.029 0.029 0.029 0.029 0.029 0.029 0.029 8.000 0.025 0.025 0.025 0.025 0.025 0.025 0.025 0.025 10.000 0.024 0.023 0.023 0.023 0.024 0.023 0.024 0.023 15.000 0.022 0.022 0.022 0.022 0.022 0.022 0.021 0.022 20.000 0.021 0.021 0.022 0.021 0.022 0.021 0.020 0.021
Energy (MeV) ICSW5 ICSW6 ICSW8 ICSW9 ICSW10
MCNPX XCOM MCNPX XCOM MCNPX XCOM MCNPX XCOM MCNPX XCOM
0.020 4.061 4.059 3.983 3.978 4.100 4.063 4.190 4.151 4.131 4.111 0.060 0.310 0.309 0.310 0.306 0.310 0.309 0.314 0.313 0.312 0.311 0.080 0.219 0.217 0.220 0.216 0.219 0.217 0.219 0.219 0.219 0.218 0.122 0.159 0.159 0.159 0.159 0.159 0.159 0.161 0.159 0.160 0.159 0.356 0.101 0.100 0.101 0.100 0.100 0.100 0.100 0.100 0.100 0.100 0.511 0.086 0.086 0.087 0.086 0.086 0.086 0.086 0.086 0.086 0.086 0.662 0.077 0.077 0.077 0.077 0.079 0.077 0.077 0.077 0.078 0.077 1.173 0.060 0.058 0.059 0.058 0.059 0.058 0.059 0.058 0.059 0.058 1.250 0.057 0.056 0.057 0.056 0.057 0.056 0.057 0.056 0.057 0.056 1.330 0.056 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055 5.000 0.029 0.029 0.029 0.029 0.029 0.029 0.029 0.029 0.029 0.029 8.000 0.025 0.025 0.025 0.025 0.025 0.025 0.025 0.025 0.025 0.025 10.000 0.024 0.023 0.023 0.023 0.024 0.023 0.023 0.023 0.024 0.023 15.000 0.022 0.022 0.022 0.022 0.022 0.022 0.022 0.022 0.022 0.022 20.000 0.022 0.021 0.021 0.021 0.022 0.021 0.022 0.021 0.022 0.021
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 simu-lation code simply simulates the experimental environment considering the physical and geometrical features of the used equipment, cross-section values and different databases have taken experimental studies. From the literature review, it can be clearly seen that Monte Carlo si-mulation method is utilized to investigate the radiation shielding properties of different glasses[20–24]. In this work, Monte Carlo N-Particle 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 I0and t represent the original intensity and the thickness,
re-spectively.
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 de-tectionfield and Pb blocks to avoid detection field of scattered radiation can be seen inFig. 1(a). Moreover, 3-D view of total simulation setup obtained from MCNPX Visual Editor (version VE X_22S) can be also seen inFig. 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 × 104keV. The NPS
variable is set as 100 mega particles.
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 Z1and Z2atomic
numbers must lie at certain energy between Z1and Z2that is known as
Zeq.That is Z1< Zeq< Z2[27]. = + − − − ≠ B(E, x) 1 b 1 K 1(K 1) for K 1 x (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: = + − − − − − ≤
(
)
K(E, x) cx d tanhtanh 2 tanh( 2) 1 tanh( 2) for x 40 mfp a x Xk (10)Macroscopic effective removal cross section for fast neutrons (ΣR) TheΣR(cm−1), briefly the removal cross-section can also be called,
is described as the possibility of one neutron undergoing a specific re-action per unit path length of passing through the glass medium[29]. To estimate theΣRvalue of the present bioactive glasses, the following
equation was used:
Fig. 2. Half-value layer (HVL) of the glasses as a function of photon energy.
Fig. 3. Tenth-value layer (TVL) as a function of photon energy.
Fig. 4. Variation mean free path (MFP) values of the glasses with photon en-ergy.
∑
R=∑
Wi(∑
R ρ/ )i (11) where Wi(g/cm3) and ΣR/ρ (cm2/g) are the partial density and themass removal cross-section of the ithelement, respectively. The partial
density of the ithelement (Wi) is obtained from the following equation:
=
Wi ρ w. i (12)
whereρ represents the density of the sample (g/cm3) and w
idenotes the
weight fraction of the ith element, respectively.
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 2provides 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 en-ergies) depends on the atomic number as Z4-5. This indicates that most
Fig. 5. Zeffvalues for bioactive glasses in the energy range 0.02–20 MeV.
of the interaction between the photons and the bioactive glasses occurs in the low energy region. After 0.511 MeV, owing to the linear depen-dence between the atomic number and cross-section of Compton scat-tering, MAC values are very small (in range of 0.077–0.021 cm2/g) and
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 theμmvalues in this region. It can be seen fromTable 2that the MAC has the largest values for ICSW9 and ICSW10.
Figs. 2 and 3indicate 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 den-sities possess smaller values of HVL and TVL compared to other bioactive glasses as indicated inFigs. 2 and 3. These results are similar to previousfindings 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 inFig. 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 Zeffvalues with the energy for the
present bioactive glasses inFig. 5. It is observed that the Zeffvalues
decrease quickly initially due to the photoelectric effect as discussed in
Fig. 7. (a–d) The EBF for the glass samples up to 40 mfp at 0.015, 0.15, 1.5, 15 MeV.
the MAC parameter (since Zeffis related to MAC for the given sample).
At the intermediate energies, where Compton scattering accounts for practically all photon interactions, the lowest value of Zeffwas observed
for the glasses. Among the investigated bioactive glasses, ICSW9 and ICSW10 have the highest Zeffvalues ranging between 15.33 and 11.49
and 15.27–11.46 respectively. The high Zeffvalues for these two
sam-ples in comparison with the other bioactive glasses are owing to the relatively high content of Ca in these two samples. Briefly, the variation in Zeffcan be classified into three energy regions namely low,
inter-mediate 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 photo-electric process is dominant and thus, the variation of Zeffis large. At
the intermediate energy, the dominant process is Compton scattering. Between 0.511 MeV to several MeV, the variation in Zeffas seen inFig. 5
is almost constant. Otherwise, pair production is the dominating me-chanism 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 ab-sorption section process. However, the Compton scattering cross-section 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
de-pendence of the photoelectric absorption cross section gives a heavy weight for the highest atomic number of the glass sample, Zeffreaches
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 Z2dependence.
Additionally, by using G-Pfitting 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)
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. FromFig. 6(a–i), it can be easily seen that the calculated values begin increasing with the further in-crease 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 inFig. 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 dif-ferent energies. The maximum incident photons are absorbed or re-moved paving way for EBF reached the minimum values for all bioac-tive 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 in-creasing and reached the maximum values. In the high energy region, where pair production starts to dominate, the EBF values enter a di-minishing 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 abol-ished 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
Table 3
Macroscopic effective removal cross sections of bioactive glasses ∑R (cm−1).
Element ∑R/ρ (cm2/g)
ICIE1 (density = 2.701 g/cm3) ICSW2 (density = 2.700 g/cm3) ICSW3 (density = 2.700 g/cm3) Fraction by weight (%) 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) O 0.0405 0.40344 1.089691 0.044132503 0.40236 1.086372 0.043998066 0.40016 1.080432 0.043757496 Na 0.0341 0.19571 0.528613 0.018025693 0.19785 0.534195 0.01821605 0.20223 0.546021 0.018619316 Si 0.0285 0.23119 0.624444 0.017796659 0.22362 0.603774 0.017207559 0.20787 0.561249 0.015995597 P 0.0283 0.00471 0.012722 0.000360024 0.00943 0.025461 0.000720546 0.01929 0.052083 0.001473949 Ca 0.0243 0.16495 0.44553 0.010826378 0.16674 0.450198 0.010939811 0.17045 0.460215 0.011183225 Total 0.091141258 0.091082032 0.091029582 Element ∑R/ρ (cm2/g)
ICSW4 (density = 2.698 g/cm3) ICSW5 (density = 2.699 g/cm3) ICSW6 (density = 2.705 g/cm3) Fraction by weight (%) 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) O 0.0405 0.39548 1.06700504 0.043213704 0.39788 1.07387812 0.043492064 0.40201 1.0874371 0.0440412 Na 0.0341 0.21158 0.57084284 0.019465741 0.20676 0.55804524 0.019029343 0.19785 0.5351843 0.0182498 Si 0.0285 0.17426 0.47015348 0.013399374 0.19146 0.51675054 0.01472739 0.22895 0.6193098 0.0176503 P 0.0283 0.04037 0.10891826 0.003082387 0.02959 0.07986341 0.002260135 0.00445 0.0120373 0.0003407 Ca 0.0243 0.17831 0.48108038 0.011690253 0.17431 0.47046269 0.011432243 0.16674 0.4510317 0.0109601 Total 0.090851459 0.090941175 0.091242 Element ∑R/ρ (cm2/g)
ICSW8 (density = 2.715 g/cm3) ICSW9 (density = 2.725 g/cm3) ICSW10 (density = 2.721 g/cm3) Fraction by weight (%) 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) O 0.0405 0.3957 1.0743255 0.043510183 0.38918 1.0605155 0.042950878 0.39222 1.06723062 0.04322284 Na 0.0341 0.20861 0.56637615 0.019313427 0.21974 0.5987915 0.02041879 0.21447 0.58357287 0.019899835 Si 0.0285 0.20408 0.5540772 0.0157912 0.17828 0.485813 0.013845671 0.19029 0.51777909 0.014756704 P 0.0283 0.0158 0.042897 0.001213985 0.02763 0.07529175 0.002130757 0.02213 0.06021573 0.001704105 Ca 0.0243 0.17581 0.47732415 0.011598977 0.18517 0.50458825 0.012261494 0.18089 0.49220169 0.011960501 Total 0.0914278 0.091607589 0.091543985
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. FromFig. 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 Zeqand Zeff(ICSW4, ICSW5,
ICSW8, ICSW9 and ICSW10) the EBF values are comparatively small. FromFig. 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 inFig. 8and listed inTable 3. It can be obviously viewed fromFig. 8that theΣRof the selected bioactive glasses are quite
near to each other and ranged from 0.0908515 cm−1for ICSW4 (den-sity = 2.698 g/cm3) to 0.0916076 cm−1for ICSW9 (density = 2.725 g/
cm3). The relatively high ΣRvalue of the ICSW9 sample can be
ex-plained by its higher density than the other samples (seeTable 1). Also, it can be seen that the ICSW4 sample which already has a low density, has the lowestΣRvalue. Therefore, the results presented inFig. 8
in-dicate 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 pur-poses.
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.
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