Radiation shielding features using MCNPX code and mechanical properties of the PbONa2OB2O3CaOAl2O3SiO2 glass systems

Accepted Manuscript Radiation shielding features using MCNPX code and mechanical properties of the PbO Na2O B2O3 CaO Al2O3 SiO2 glass systems Shams A.M. Issa, Yasser B. Saddeek, M.I. Sayyed, H.O. Tekin, Ozge Kilicoglu PII:

S1359-8368(18)32010-9

DOI:

https://doi.org/10.1016/j.compositesb.2018.12.029

Reference:

JCOMB 6358

To appear in:

Composites Part B

Received Date: 5 June 2018 Revised Date:

3 December 2018

Accepted Date: 11 December 2018

Please cite this article as: Issa SAM, Saddeek YB, Sayyed MI, Tekin HO, Kilicoglu O, Radiation shielding features using MCNPX code and mechanical properties of the PbO Na2O B2O3 CaO Al2O3 SiO2 glass systems, Composites Part B (2019), doi: https:// doi.org/10.1016/j.compositesb.2018.12.029. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

ACCEPTED MANUSCRIPT

Radiation shielding features using MCNPX code and mechanical properties of the PbONa2O-B2O3-CaO-Al2O3-SiO2 glass systems

a

RI PT

Shams A.M. Issaa,b,*, Yasser B. Saddeekb, M.I. Sayyeda, H.O. Tekinc,d, Ozge Kilicoglue Physics Department, Faculty of Science, University of Tabuk, Saudi Arabia

b

Physics Department, Faculty of Science, Al-Azhar University, Assiut 71452, Egypt

c

d

SC

Department of Radiotherapy, Vocational School of Health Services, Uskudar University, Istanbul 34672, Turkey

Medical Radiation Research Center (USMERA), Uskudar University, Istanbul 34672, Turkey

e

M AN U

Uskudar University, Vocational School of Health Services, Department of Nuclear Technology and Radiation Protection, Istanbul, Turkey

Abstract

The novel glasses with compositions PbO–Na2B4O7– CaO-Al2O3-SiO2 glasses are prepared by the melt quenching technique. The radiation shielding and mechanical properties of the prepared

TE D

glasses are presented and discussed in details. The mass attenuation coefficient (µ/ρ) which is the basic parameter in the evaluation of the radiation interaction with shielding materials was calculated according to MCNPX code, and the results were compared with those obtained by XCOM program. The simulation results match most of the XCOM data very well. Additionally,

EP

the results revealed that both (µ/ρ) and the effective atomic number (Zeff) of the prepared glasses increase with increasing lead monoxide from 0 to 50 mol. %. Also, the difference of HVL values

AC C

of the prepared glass samples and that for the pure lead decrease when the concentration of lead monoxide increases. It is found that the removal cross-sections, ΣR values for the prepared glasses lie within the range 0.1006 –0.1215 cm−1.

Keywords: Radiation Shielding, MCNPX code, Oxide glass, Elastic properties

1

ACCEPTED MANUSCRIPT

Introduction The technological significance of glasses has led to increased potentials to resolve their structures to gain deep insight into the structure-properties relationships that can be exploited for

RI PT

the design of new materials. Low silica calcium aluminate glasses had a unique position due to their remarkable properties that are presented in their high thermal conductivity, high glass transition temperature, good chemical durability, low phonon energy, and can be used in the manufacture of hard nuclear waste materials [1–5]. In this type of glasses, if the concentration of the silicate structural units Q4 is increased and the Si–O–B linkages are formed, the thermal

SC

parameters of borosilicate glasses will be enhanced. Due to the addition of lead monoxide and aluminum oxide to borosilicate glasses, the borate structural units [BO3] are converted into

M AN U

[BO4]. Consequently, the network of borosilicate glasses may be formed of the borate structural units, namely, BO3 and BO4, three and four bridging oxygen with silicon atoms and Si–O–B/Si– O–Al linkages. Thus, the structural units of B2O3 and SiO2 may interact strongly with the structural units of PbO as lead monoxide modifies the network of borosilicate glasses [6–15]. On the other hand, the major constituents of solid waste cement kiln dust (CKD) are CaO, SiO2 and Al2O3. This dust is a waste of the cement industry and can be recycled either in

TE D

returning to the kiln system or by using as a non-conventional raw material in the glass industry as a safe process for treating hazardous wastes and converting them into inactive materials. The characteristics of the chemical composition of CKD resemble the features of the ternary CaO– Al2O3–SiO2 glass system [16–18]. In some nuclear particular technologies, the human beings

EP

have faced the artificial radiation from different sources, such as nuclear power plants, nuclear reactors, accelerators, medical physics, and radiation treatment. The protection materials against

AC C

artificial radiations are very important and required for workers in these places. Thus, some pertinent parameters such as mass attenuation coefficient (µ/ρ), effective atomic number (Zeff), electron density (Nel), half-value layer (HVL), mean free path (MFP), neutron removal crosssections (ΣR) and elastic moduli must be measured in assessing the properties of radiation shielding. The most important and useful parameter is the (µ/ρ) especially when the mixtures, composites, and compounds are used as radiation shielding. Many studies had been done to identify the radiation shielding performance of borate heavy metal oxide based glasses [19–23].

2

ACCEPTED MANUSCRIPT

It is well known that the radiation protection studies require high-precision pre-decision making especially for investigating the materials. Unlike to a physical experiment, a Monte Carlo simulation performs random sampling and conducts a high number of experiments on workstation computers or personal computers. Afterwards, the statistical characteristics of the

RI PT

experiments are observed and conclusions on the model outputs are drawn based on the statistical experiments. Therefore, one can say that, most of the experimental studies require different types of simulation studies or theoretical investigations before the experiment for maximum protection in accordance with the ALARA principle [24]. In other words, Monte Carlo

SC

method has become a method that closely influences the decision making process before the many experimental investigations. So, it is amazing to synthesize glasses, part of it resembles the

M AN U

CKD in its rigidity, part takes the stoichiometric ratio of Na2B4O7 into consideration and the third part is the addition of PbO. This type of glasses can be considered as a promising candidate in the field of radiation shielding. By following the preceding hypothesis, two series of lead alkali borate glasses modified with CaO-Al2O3-SiO2 were synthesized by the melt quenching method. The first glass series CAS25 had the chemical formula yPbO–75Na2B4O7–(25-y)[CaOAl2O3-SiO2], 0 ≤ y ≤ 25 and the second glass series CAS50 had the chemical formula xPbO–

TE D

50Na2B4O7–(50-x)[CaO-Al2O3-SiO2], 25 ≤ x ≤ 50. The elastic moduli of the two glass series were determined experimentally by measuring the ultrasonic wave velocities at 4 MHz and computed according to Makishima-Mackenzie and Rocherulle models. Moreover, the gamma radiation shielding properties of the studied glasses in the photon energies 0.356, 0.511, 0.662,

EP

1.17 and 1.33 MeV were studied by applying the Monte Carlo code (MCNPX version 2.6.0) and the XCOM program.

AC C

2. Materials and Methods 2.1 Glass preparation

The melt quenching technique has been used to prepare the glass series CAS25 that had the chemical formula yPbO–75Na2B4O7–(25-y)[CaO-Al2O3-SiO2], 0 ≤ y ≤ 25 and the glass series CAS50 that had the chemical formula xPbO–50Na2B4O7–(50-x)[CaO-Al2O3-SiO2], 25 ≤ x ≤ 50. To obtain the glasses in question, the pure quantities of lead monoxide (PbO), sodium carbonate Na2CO3, boric acid (H3BO3), calcium carbonate (CaCO3), aluminum oxide (Al2O3) and silicon dioxide (SiO2) have been mixed together using grinding. Under ordinary atmosphere and by 3

ACCEPTED MANUSCRIPT

using pt crucibles, the powder has been melted in an electrically heated furnace at about 1423 K for four hours to homogenize the melt. The glasses have been formed by quench the melt on a preheated mold which immediately was transferred to another furnace to anneal the glasses at 750 K for two hours. The different compositions given in Table 1 refer to the nominal

RI PT

composition (the starting mixtures). The weight losses were found to be less than 0.5%. The two opposite sides of the prepared glasses had 1 cm thickness have been polished to be suitable for the elastic measurements. The ultrasonic velocities [longitudinal VL and shear VS] at room temperature were obtained using the pulse-echo method. In this method, x-cut and y-cut

SC

transducers operated at the fundamental frequency of 4 MHz along with a digital ultrasonic flaw detector were used. The uncertainty in the measurement of the ultrasonic velocity was ±10 m/s.

M AN U

By using the toluene immersion fluid and the application of the Archimedes method, the densities of the glass samples had been determined at room temperature using the following equation: =

−

×

(1)

where a is the weight of the glass sample in air, b is the weight of the glass sample in toluene and

TE D

ρT is the density of toluene (0.867 g/cm3) respectively. Both velocities and the density were utilized to determine the whole elastic moduli. The uncertainty in the elastic moduli was ±0.15 GPa. The debrits of the prepared glasses were crushed and pulverized for the use in the X-ray diffraction patterns. These patterns were recorded to check the amorphous nature of the glass

40 kV and 30 mA.

EP

samples using an X-ray diffractometer with Ni filtered Cu-Kα radiation (λ=1.542 Å) powered at

AC C

2.2 XCOM and MCNPX (version 2.6.0) Nowadays, the use of mathematical methods for assorted applications such as radiation shielding, medical purposes and material characterization is increasing. Monte Carlo has become a frequently used method in mathematical methods. The term of Monte Carlo method is a powerful tool to overcome the physical complexities when the empirical cases are restricted or inconvenient to achieve. On the other hand, validation of utilized simulation code is also a significant process for the solution of the problem.

4

ACCEPTED MANUSCRIPT

The XCOM program provides total cross sections and attenuation coefficients as well as partial cross sections for the following processes: incoherent scattering, coherent scattering, photoelectric absorption, and pair production in the field of the atomic nucleus and in the field of the atomic electrons. For compounds, the tabulated quantities are partial and total mass

RI PT

interaction coefficients, which are equal to the product of the corresponding cross sections times the number of target molecules per unit mass of the material. The reciprocals of these interaction coefficients are the mean free paths between scatterings events, or between photo-electric absorption events, or between pair production events. The sum of the interaction coefficients for

SC

the individual processes is equal to the total attenuation coefficient. The total attenuation coefficients without the contribution from coherent scattering are also given, because they are

M AN U

often used in gamma-ray transport calculations. The interaction coefficients and the total attenuation coefficients for compounds or mixtures are obtained as sums of the corresponding quantities of the atomic constituents. The weighting factors, that is, the fractions by weight of the constituents, are calculated by XCOM from the chemical formula entered by the user. For mixtures, however, the user must supply the fractions by weight of the various components [25]. In the current study, Monte Carlo N-Particle Transport Code System-extended (MCNPX)

TE D

(version 2.6.0) was employed for the mass attenuation coefficient calculations of several glass systems. This code is a functional and general purpose code for simulating the interaction of different types of particles with the matter at broad energy spectrum. MCNPX can utilize extended nuclear cross-section libraries and uses physics models for particle types. The literature

EP

review showed that, general purpose Monte Carlo code (MCNPX) has been utilized for different types of radiation applications, especially for investigation the shielding properties of different

AC C

types of glassy systems or materials [26–31]. Also, the literature review strongly encouraged us to build a novel Monte Carlo simulation setup for the investigations of the radiation attenuation features of different types of glass systems. In the present paper, Fig. 1 indicates the considered MCNPX geometry of the current investigation. Moreover, the energy source had been defined at 0.356, 0.511, 0.66, 1.17, 1.33 MeV photon energies for each computation, respectively. As it is illustrated in Fig.1, the geometric center of the detection cell (F4 Tally Mesh) on the center axis has been considered for the location of point-isotropic radiation source. Another important parameter of the MCNPX input file is the material card (Mn). This part of the input file is responsible for the definition of 5

ACCEPTED MANUSCRIPT

the used materials in the simulation study. In accordance with the required information for the definition of the material card, the material specification of the used glasses had been defined taking their mass number, atomic number, elemental mass fractions, and density into

RI PT

considerations. 3. Results and discussion

The chemical composition and the density (ρ) of the whole glass samples have been listed in Table 1. The density values of glass samples increase from 2.523 to 5.247 (g/cm3) with the

SC

increase of PbO content from 0 to 50 mol %. This behavior may be attributed to the higher atomic weight of PbO (223.2 g/mol) than that of CaO (56.08 g/mol), Al2O3 (101.96 g/mol) and SiO2 (60.08 g/mol). Hence, the glass matrix becomes denser when PbO added into the glass

M AN U

network. The increase in the glass sample density may be also attributed to converts the less density BO3 structural unit into dense BO4 tetrahedra structure unit [32]. Due to the absences of crystallization peaks as shown in Fig. 2, it means that the prepared glasses are amorphous nature. 3.1 Radiation shielding parameters

The (µ/ρ) represents the total probability of all interaction processes between matter and

TE D

radiation. When a narrow beam of photons having initial intensity I0 is passed through a glass sample of thickness x, the transmitted photons intensity (I) can be determined by Lambert-Beer

( ⁄ )=

( ⁄ )

(2)

EP

Law[33]:

Fig.3 shows the calculated mass attenuation coefficient values of the studied glasses, CAS50 and

AC C

CAS25 using XCOM program and MCNPX code at photon energies 0.356, 0.511, 0.662, 1.17 and 1.33 MeV (Table 2). Fig. 3 and Table 2 observed that the values of (µ/ρ) calculated using MCNPX code are in a good agreement with that values obtained using XCOM program where the error ranged from ±0.10 to ±3.98. As in Fig. 3, the (µ/ρ) values using XCOM program and MCNPX code increase with increasing lead monoxide from 0 to 50 mol. %. This behavior may be attributed to replacing the low-density metal oxides CaO (3.35 g/cm3), Al2O3 (3.987 g/cm3) and SiO2 (2.648 g/cm3) with high-density metal oxide PbO (9.53 g/cm3). As the photon energy increase from 0.356 to 1.33 MeV, the calculated values of (µ/ρ) using both XCOM program and 6

ACCEPTED MANUSCRIPT

MCNPX code decrease from 0.099 to 0.0545 (MCNPX) and from 0.098 to 0.0541 (XCOM), respectively as the PbO increases. This procedure may be attributed to the domination of the photoelectric process in the low energy region. The correlation between the (µ/ρ) values using XCOM program and that obtained from MCNPX code for 20PbO-75Na2B4O7-5(CaO-Al2O3promising agreement between XCOM program and MCNPX code.

RI PT

SiO2) glass sample (as an example) are shown in Fig. 4. The correlation observed noticeable and

Using the obtained values of (µ/ρ), we can calculate the values of half value layer (HVL), mean free path (MFP), effective atomic number (Zeff) and electron density (Nel) according to the

(3)

M AN U

(2)

=

SC

following equations [34,35,44,36–43]:

1 = (4) ( ⁄ )

$

∑"

=

1

%

$

&" '" ( / )" (7) ("

(8)

($++

%

" (9)

AC C

=

(6)

"

($++ = $-

"

TE D

=

(5)

EP

=

"

where the µ is the linear attenuation coefficient, σt is the total photon interaction cross section, M is molecular weight, NA is the Avogadro's number, σa effective atomic cross-section, ni is the number of the formula units of a molecule, Ai is the atomic weight of the ith element, fi indicates to the fractional abundance of the element i and Zi the atomic number of constituent element. As shown in Fig. 5 the values of HVL increase with increasing photon energy and decrease with increasing lead monoxide content. The values of HVL of the studied glass samples have been

7

ACCEPTED MANUSCRIPT

compared with HVL values of pure lead as shown in Fig. 6. The difference between the HVL values of the prepared glass samples and that for a pure lead decrease when the concentration of lead monoxide increasing. This behavior has been confirmed in Fig. 7. This figure observed that the difference in HVL between investigated glass samples and pure lead decrease with increasing

RI PT

both photon energy and PbO concentration. Table 3 illustrates a comparison between the mean free path (MFP) for the 50PbO–50Na2B4O7 sample and those obtained for some types of glass samples and concretes according to the literature at 0.356, 0.551, 0.662, 1.17 and 1.33 MeV photon energies [42,45–49]. For the better shielding materials, the low mean free path is

SC

required. Table 3 observed that the MFP values of the 50PbO–50Na2B4O7 glass sample are lower than that for selected concrete and glasses.

M AN U

The effective atomic number Zeff and electron density values of CAS25 and CAS50 glass samples have been calculated using equations 8 and 9, respectively. The Zeff behavior of investigated glass samples with PbO concentration and photon energy is shown in Fig. 8 (see Table 4). As shown in Fig. 8, the values of Zeff increase with the increasing of PbO content and decrease when the photon energy increases from 0.356 to 1.33 MeV. Table 4 observed that the Nel values of prepared glass samples have the same behavior that for Zeff.

TE D

The removal cross-sections, ΣR for the prepared glass samples were calculated using the mass removal cross section, ΣR/ρ values of the elements constituting the glass samples. The following relations were used to obtain the ΣR values [50]:

"

EP

∑/ = % 0" (∑/ / )" (10)

AC C

where Wi and ∑R/ρ (cm2/g) are the partial density (g/cm3) and the mass removal cross-section of the ith constituent respectively. The values for the removal cross-sections (ΣR/ρ) for the elements and some compounds have been tabulated [51]. The ΣR for the glass samples in this work is illustrated in Figs. 9 and 10. It is found that the values of ΣR for the prepared glasses lie within the range 0.1006 to 0.126 cm-1 and from 0.1201 to 0.1215 cm-1 of CAS25 and CAS50 glass samples, respectively. The Figures show that the ΣR increases with an increase in the concentration of PbO which may be due to the higher density of the glass samples with a high amount of PbO. This indicates that the neutron shielding capability of the glass samples increases with the increase of PbO concentration. 8

ACCEPTED MANUSCRIPT

3.2 Analysis of some physical parameters The physical parameters of the proposed glass shield can be accounted in terms of the oxygen molar volume (OMV) and the Oxygen packing density (OPD) according to the proposed formula as indicated before [44]; =

1 6 (11) ∑ 5" "

RI PT

2

34

2 7 = 1000 8 9 (12)

SC

where Vm is the molar volume, xi is the molar fraction of i-th component, M is the molecular weight of glass sample, ni is the number of oxygen atoms in each constituent oxide and ρ is the

M AN U

density of the glass samples. The calculated values of OMV and OPD of glass samples are listed in Table 5. From the first two columns in Table 5, it is observed that the behavior OMV and OPD values are in opposite trend to each other. The OMV values increase and the OPD values decrease with the increase of PbO content in the two series, namely, for CAS25 and CAS50 based glasses. On the other hand, the fractal bond connectivity (d) is a beneficial parameter relating the mechanical properties of glasses to their structures. The fractal bond connectivity

TE D

gives the information about the effective dimensionality and cross-links of the glass network. The d can take the values 1, 2, 3 for the chain, layer structure and three dimensions networks of tetrahedral coordination polyhedral, respectively [52]. The values of d can be correlated to the values of the number of bonds per unit volume (nb) and the average value of the cross-linking

=

;;;: =

3

%( + )" 5" (13)

AC C

<

EP

density (;;;). : The preceding two parameters can be evaluated according to the formula;

∑ 5" ( : )" ( : )" , >ℎ@A@ B ∑ 5" ( : )"

:

=

+

− 2C (14)

where nf is the coordination numbers, Nc is the number of cations per glass formula unit. The values of the fractal bond connectivity (d) as seen in Table 5 suggested that the increase of the PbO content in the two series transformed the 3D structure of the explored glasses into layer structure. This transformation is associated with a decrease in the number of bonds per unit volume (nb) and the average value of the cross-linking density (;;;) : [53]. The behavior of the 9

ACCEPTED MANUSCRIPT

three physical parameters is in a good agreement with the increase of the oxygen molar volume and the decrease of the oxygen packing density. The rigidity of a glass shield can be analyzed in terms of the preceding physical parameters and

RI PT

their determined elastic moduli. The measured density (g/cm3), the ultrasonic velocities VL (m/s) and VS (m/s) have been used to calculate the longitudinal (L) (GPa), shear (G) (GPa), bulk (K) (GPa), Young’s (Y) (GPa) modulus, micro-harness (H) (GPa) and Poisson’s ratio (σ), of the glass samples as follows [31,45,54–58]:

F= H=

E D

E G

SC

=

I

− ( )F

M AN U

J

K = (1 − )2F = =

L

EM

−1

(NOEP)L Q(NRP)

(15) (16) (17) (18) (19) (20)

TE D

Figure 11 shows the experimental values of L, G, K, Y (GPa) for glass samples contain 75 and 50 mol% of Na2B4O7 (Table 6). As shown in Fig.12, the experimental L, G, K, and Y values of glass samples decrease from 84.06 to 79.02 GPa, from 29.88 to 26.32 GPa, from 44.23 to 41.01 GPa and from 73.15 to 67.67 GPa, respectively, with increasing the content of PbO from 0 to 50

EP

mol. %. Figs. (12-13) represented the elastic modulus according to the Makishima-Mackenzie (MMM) and Rocherulle (RM) models [31,45,59–61], respectively. As shown in these figures,

AC C

the theoretical values of the elastic modulus decrease with increasing the content of lead monoxide, which takes the same trend to that of the experimental values. Fig. 13 observed that the calculated elastic moduli of the glass samples CAS50 are higher than that for glass samples have CAS25. Moreover, Poisson’s ratio (σ) can be used to confirm this hypothesis. If the glass system has high cross link density, the values of σ will be ranged from 0.1-0.2 and for low cross link density, the values of Poisson’s ratio (σ) will be ranged from 0.3-0.5. In our glass samples, the Poisson’s ratio (σ) ranged from 0.224 to 0.250 (in general close to 0.3) (Table 6). The

10

ACCEPTED MANUSCRIPT

obtained elastic values using Rocherulle model are in very good agreement with that obtained from Makishima-Mackenzie model and from the experimental results (Fig. 14). The addition of PbO that had a higher density than the density of the other oxides incorporated in

RI PT

the explored glass matrix and with two structural units, namely, [PbO4] and [PbO6], had the following features:

1) The increased density with higher rates can be attributed to the formation of [PbO4] structural units that played a glass former role.

SC

2) Thus, the glass network will be relaxed due to the formation of the non-bridging oxygens especially in the case of the second series, so, the oxygen molar volume increased while the oxygen packing density decreased.

M AN U

3) The dimensionality of the glasses will be changed from the 3D network that characterized the borosilicate glasses, into layer structured that characterized leadbased glasses, so the d values will be ranged from 2.7 -2.2 and the Poisson’s ratio fluctuated around 0.25.

4) The rigidity of the glasses consequently decreased due to the replacement of rigid linkages such as Si–O, and B–O with a weaker one like Pb–O. This decrease is

TE D

confirmed by the decrease of the elastic moduli, the number of bonds and average cross-link density [4-5].

5) The values of the Young’s modulus (Y) of the explored glasses as an example of the elastic moduli and the values of the Young’s modulus of different glass matrices

EP

containing PbO [60] are shown in Fig. 15. The comparison reveals the high values of the Young’s modulus of the matrix of the studied glasses than that of the other

AC C

matrices. This means that the studied matrix had high connections, high cross-link density and high rigidity than the other matrices due to the presence of CaO-Al2O3SiO2 in their network. Moreover, the density played a vital role in determining the

values of Young’s modulus of these different matrices, which is clear from the lower values of Young’s modulus of the Li2O-V2O5-PbO glasses [61–63] than that of the other glass systems.

11

ACCEPTED MANUSCRIPT

Conclusion Two glass series CAS25 that had the chemical formula yPbO–75Na2B4O7–(25-y)[CaO-Al2O3SiO2], 0 ≤ y ≤ 25 and the glass series CAS50 that had the chemical formula xPbO–50Na2B4O7–

RI PT

(50-x)[CaO-Al2O3-SiO2], 25 ≤ x ≤ 50 have been successfully fabricated with conventional melt quench method. The density of the prepared glasses is increased with PbO addition. The whole prepared glass samples show amorphous nature as verified by XRD. Due to the change of the fractal bond connectivity from 2.7 -2.2, the glass dimensionality has been changed from the 3D network into the layer structure; and the Poisson’s ratio fluctuated around 0.25. The elastic

SC

moduli, the numbers of bonds and average cross-link density decrease with increasing PbO from 0 to 50 mol. %. The radiation shielding features of the prepared glasses were evaluated using

M AN U

both the XCOM program and the MCNPX code. The values of (µ/ρ) calculated using MCNPX code are in a good agreement with those obtained using XCOM program. The results revealed that the µ/ρ values increase while the HVL decrease with increasing lead monoxide from 0 to 50 mol. %. On the other hand, the ΣR for the prepared glasses lies within the range 0.1006 to 0.126 cm-1 and from 0.1201 to 0.1215 cm-1 for the two glass series CAS25 and CAS50, respectively. The MFP values of the 50PbO–50Na2B4O7 glass sample was compared with other glass samples

TE D

and concretes that reported in the literature at different energies, and the comparison revealed that the present glasses can be used for radiation shielding applications to reduce the deleterious effects of gamma radiation.

[1]

EP

References

Sampaio JA, Catunda T, Gandra FCG, Gama S, Bento AC, Miranda LCM, et al. Structure

AC C

and properties of water free Nd2O3 doped low silica calcium aluminate glasses. J Non Cryst Solids 1999;247:196–202.

[2]

Sampaio JA, Catunda T, Coelho AA, Gama S, Bento AC, Miranda LCM, et al. Thermomechanical and optical properties of calcium aluminosilicate glasses doped with Er3+ and Yb3+. J Non Cryst Solids 2000;273:239–45.

[3]

Schirmer H, Keding R, Rüssel C. Thermodynamics of the Sn2+/Sn4+-equilibrium in Li2O/Al2O3/SiO2-glass melts studied by square-wave voltammetry and impedance spectroscopy. J Non Cryst Solids 2004;336:37–43.

12

ACCEPTED MANUSCRIPT

[4]

Baesso ML, Bento AC, Andrade AA, Catunda T, Sampaio JA, Gama S. Neodymium concentration dependence of thermo�optical properties in low silica calcium aluminate glasses. J Non Cryst Solids 1997;219:165–9. Hwa L-G, Lee G-W. Influence of water on the physical properties of calcium aluminate oxide glasses. Mater Chem Phys 1999;58:191–4.

[6]

RI PT

[5]

Parkinson BG, Holland D, Smith ME, Howes AP, Scales CR. The effect of Cs2O additions on HLW wasteform glasses. J Non Cryst Solids 2005;351:2425–32.

Stentz D, Blair S, Goater C, Feller S, Affatigato M. Analysis of the structure of lead

SC

[7]

borosilicate glasses using laser ionization time of flight mass spectroscopy. J Non Cryst

[8]

M AN U

Solids 2001;293:416–21.

Stentz D, Blair S, Goater C, Feller S, Affatigato M. Determination of the mesostructure of lead borate glasses using laser photoionization mass spectroscopy. Appl Phys Lett 2000;76:61–3.

[9]

Martens R, Müller-Warmuth W. Structural groups and their mixing in borosilicate glasses

[10]

TE D

of various compositions--an NMR study. J Non Cryst Solids 2000;265:167–75. Saddeek Y, Hassan HS, others. Fabrication and analysis of new bismuth borate glasses containing cement kiln dust. J Non Cryst Solids 2014;403:47–52. [11]

Pan Y, Wen M. The influence of vacancy on the mechanical properties of IrAl coating:

EP

First-principles calculations. Thin Solid Films 2018;664:46–51.

[12]

Pan Y. Role of S-S interlayer spacing on the hydrogen storage mechanism of MoS 2. Int J

[13]

AC C

doi:10.1016/j.tsf.2018.08.028.

Hydrogen Energy 2018;43:3087–91. doi:10.1016/j.ijhydene.2017.12.185.

Pan Y. RuAl 2 : Structure, electronic and elastic properties from first-principles. Mater Res Bull 2017;93:56–62. doi:10.1016/j.materresbull.2017.04.041.

[14]

Pan Y, Jin C. Vacancy-induced mechanical and thermodynamic properties of B2-RuAl. Vacuum 2017;143:165–8. doi:10.1016/j.vacuum.2017.06.013.

[15]

Pan Y, Wang P, Zhang C-M. Structure, mechanical, electronic and thermodynamic properties of Mo 5 Si 3 from first-principles calculations. Ceram Int 2018;44:12357–62. 13

ACCEPTED MANUSCRIPT

doi:10.1016/j.ceramint.2018.04.023. [16]

Saddeek YB, Mohamed GY, Hassan HS, Mostafa AMA, others. Effect of gamma irradiation on the FTIR of cement kiln dust--bismuth borate glasses. J Non Cryst Solids

[17]

RI PT

2015;419:110–7. Saddeek YB, Mohamed GY, Hassan HS, Mostafa AMA, others. FTIR spectroscopic features of $γ$-ray influence on new cement kiln dust based glasses. Phys Scr 2015;90:85702.

Saddeek YB, Mohamed GY, Mostafa AMA, Hassan HS, others. Effect of cement kiln

SC

[18]

dust and gamma irradiation on the ultrasonic parameters of HMO borate glasses. Nucl

[19]

M AN U

Instruments Methods Phys Res Sect B Beam Interact with Mater Atoms 2017;394:44–9. Sharma R, Sharma V, Singh PS, Singh T. Effective atomic numbers for some calciumstrontium-borate glasses. Ann Nucl Energy 2012;45:144–9. doi:10.1016/j.anucene.2012.03.005. [20]

Singh VP, Badiger NM, Chanthima N, Kaewkhao J. Evaluation of gamma-ray exposure

2014;98:14–21. [21]

TE D

buildup factors and neutron shielding for bismuth borosilicate glasses. Radiat Phys Chem

Kaewkhao J, Pokaipisit A, Limsuwan P. Study on borate glass system containing with Bi2O3 and BaO for gamma-rays shielding materials: Comparison with PbO. J Nucl Mater

[22]

EP

2010;399:38–40. doi:10.1016/j.jnucmat.2009.12.020. Lakshminarayana G, Kumar A, Dong MG, Sayyed MI, Long NV, Mahdi MA. Exploration

AC C

of gamma radiation shielding features for titanate bismuth borotellurite glasses using relevant software program and Monte Carlo simulation code. J Non Cryst Solids 2018;481:65–73. doi:10.1016/j.jnoncrysol.2017.10.027.

[23]

Lakshminarayana G, Baki SO, Kaky KM, Sayyed MI, Tekin HO, Lira A, et al. Investigation of structural, thermal properties and shielding parameters for multicomponent borate glasses for gamma and neutron radiation shielding applications. J Non Cryst Solids 2017;471:222–37. doi:10.1016/j.jnoncrysol.2017.06.001.

[24]

Menser B, Manke D, Mentrup D, Neitzel U. A MONTE-CARLO SIMULATION FRAMEWORK FOR JOINT OPTIMISATION OF IMAGE QUALITY AND PATIENT 14

ACCEPTED MANUSCRIPT

DOSE IN DIGITAL PAEDIATRIC RADIOGRAPHY. Radiat Prot Dosimetry 2016;169:371–7. doi:10.1093/rpd/ncv483. [25]

Berger, M.J. and Hubbell JH. XCOM: Photon Cross-Sections Database, Web Version 1.2

[26]

RI PT

n.d. Tekin HO. MCNP-X Monte Carlo Code Application for Mass Attenuation Coefficients of Concrete at Different Energies by Modeling 3 × 3 Inch NaI(Tl) Detector and Comparison with XCOM and Monte Carlo Data. Sci Technol Nucl Install 2016;2016.

[27]

SC

doi:10.1155/2016/6547318.

Tekin HO, Manici T. Simulations of mass attenuation coefficients for shielding materials

[28]

M AN U

using the MCNP-X code. Nucl Sci Tech 2017;28:95.

Tekin HO, Singh VP, Manici T, Altunsoy EE. Validation of MCNPX with Experimental Results of Mass Attenuation Coefficients for Cement, Gypsum and Mixture. J Radiat Prot Res 2017;42:154–7.

[29]

Tekin HO, Sayyed MI, Altunsoy EE, Manici T. Shielding properties and effects of WO3 and PbO on mass attenuation coefficients by using MCNPX code. Dig J Nanomater

[30]

TE D

Biostruct 2017;12:861–7.

Ozan Tekin H, Sayyed MI, Manici T, Altunsoy EE. Photon shielding characterizations of bismuth modified borate –silicate–tellurite glasses using MCNPX Monte Carlo code.

[31]

EP

Mater Chem Phys 2018;211:9–16. doi:10.1016/j.matchemphys.2018.02.009. Issa SAM, Saddeek YB, Tekin HO, Sayyed MI, Shaaban K saber. Investigations of

AC C

radiation shielding using Monte Carlo method and elastic properties of PbO-SiO 2 -B 2 O 3 -Na 2 O glasses. Curr Appl Phys 2018. doi:10.1016/j.cap.2018.02.018.

[32]

Saddeek YB, Gaafar MS, Bashier SA. Structural influence of PbO by means of FTIR and acoustics on calcium alumino-borosilicate glass system. J Non Cryst Solids 2010;356:1089–95. doi:10.1016/j.jnoncrysol.2010.01.010.

[33]

Issa SAM, Mostafa AMA. Effect of Bi2O3in borate-tellurite-silicate glass system for development of gamma-rays shielding materials. J Alloys Compd 2017;695:302–10. doi:10.1016/j.jallcom.2016.10.207.

15

ACCEPTED MANUSCRIPT

[34]

Kurudirek M, Onaran T. Calculation of effective atomic number and electron density of essen-tial biomolecules for electron, proton, alpha particle and multi-en-ergetic photon interactions. Radiat Phys Chem 2015;112:125–38.

[35]

RI PT

doi:10.1016/j.radphyschem.2015.03.034. Kurudirek M. Effective atomic numbers and electron densities of some human tissues and dosimetric materials for mean energies of various radiation sources relevant to radiotherapy and medical applications. Radiat Phys Chem 2014;102:139–46.

[36]

SC

doi:10.1016/j.radphyschem.2014.04.033.

Manohara SR, Hanagodimath SM, Gerward L. Photon interaction and energy absorption in glass: A transparent gamma ray shield. J Nucl Mater 2009;393:465–72.

[37]

M AN U

doi:10.1016/j.jnucmat.2009.07.001.

Lakshminarayana G, Baki SO, Lira A, Sayyed MI, Kityk I V., Halimah MK, et al. X-ray photoelectron spectroscopy (XPS) and radiation shielding parameters investigations for zinc molybdenum borotellurite glasses containing different network modifiers. J Mater Sci 2017;52:7394–414. doi:10.1007/s10853-017-0974-0.

Issa SAM, Sayyed MI, Kurudirek M. Study of gamma radiation shielding properties of

TE D

[38]

ZnO-TeO glasses. Bull Mater Sci 2017;40:841–57. doi:10.1007/s12034-017-1425-x. [39]

Issa SAM, Sayyed MI, Zaid MHM, Matori KA. Photon parameters for gamma-rays sensing properties of some oxide of lanthanides. Results Phys 2018;9:206–10.

[40]

EP

doi:10.1016/j.rinp.2018.02.039. Elbashir BO, Dong MG, Sayyed MI, Issa SAM, Matori KA, Zaid MHM. Comparison of

AC C

Monte Carlo simulation of gamma ray attenuation coefficients of amino acids with XCOM program and experimental data. Results Phys 2018;9:6–11.

doi:10.1016/j.rinp.2018.01.075.

[41]

Sayyed MI, Issa SAM, Auda SH. Assessment of radio-protective properties of some anti-

inflammatory drugs. Prog Nucl Energy 2017;100. doi:10.1016/j.pnucene.2017.07.003. [42]

Issa SAM. Effective atomic number and mass attenuation coefficient of PbO–BaO–B2O3 glass system. Radiat Phys Chem 2016;120:33–7. doi:10.1016/j.radphyschem.2015.11.025.

[43]

Sayyed MI, Elmahroug Y, Elbashir BO, Issa SAM. Gamma-ray shielding properties of 16

ACCEPTED MANUSCRIPT

zinc oxide soda lime silica glasses. J Mater Sci Mater Electron 2017;28. doi:10.1007/s10854-016-6022-z. [44]

Issa SAM, Darwish AAA, El-Nahass MM. The evolution of gamma-rays sensing

RI PT

properties of pure and doped phthalocyanine. Prog Nucl Energy 2017;100:276–82. doi:10.1016/j.pnucene.2017.06.016. [45]

Issa SAM, Kumar A, Sayyed MI, Dong MG, Elmahroug Y. Mechanical and gamma-ray shielding properties of TeO 2 -ZnO-NiO glasses. Mater Chem Phys 2018;212:12–20.

[46]

SC

doi:10.1016/j.matchemphys.2018.01.058.

Singh S, Kumar A, Singh D, Thind KS, Mudahar GS. Barium-borate-flyash glasses: As radiation shielding materials. Nucl Instruments Methods Phys Res Sect B Beam Interact

[47]

M AN U

with Mater Atoms 2008;266:140–6. doi:10.1016/j.nimb.2007.10.018.

Bootjomchai C, Laopaiboon J, Yenchai C, Laopaiboon R. Gamma-ray shielding and structural properties of barium-bismuth-borosilicate glasses. Radiat Phys Chem 2012;81:785–90. doi:10.1016/j.radphyschem.2012.01.049.

[48]

Kaur K, Singh KJ, Anand V. Structural properties of Bi2O3-B2O3-SiO2-Na2O glasses for

TE D

gamma ray shielding applications. Radiat Phys Chem 2016. doi:10.1016/j.radphyschem.2015.12.003. [49]

Kumar A. Gamma ray shielding properties of PbO-Li 2 O-B 2 O 3 glasses. Radiat Phys

EP

Chem 2017;136:50–3. doi:10.1016/j.radphyschem.2017.03.023. Kaplan MF. Concrete Radiation Shielding. New York: John Wiley & Sons, Inc; 1989.

[51]

Profio A. Radiation Shielding and Dosimetry. New York: John Wiley & Sons, Inc.; 1979.

[52]

AC C

[50]

Saunders GA, Brennan T, Acet M, Cankurtaran M, Senin HB, Sidek HAA, et al. Elastic and non-linear acoustic properties and thermal expansion of cerium metaphosphate glasses. J Non Cryst Solids 2001;282:291–305. doi:10.1016/S0022-3093(01)00311-8.

[53]

Alazoumi SH, Sidek HAA, Halimah MK, Matori KA, Zaid MHM, Abdulbaset AA. Synthesis and elastic properties of ternary ZnO-PbO-TeO2 glasses. Chalcogenide Lett 2017;14:303–20.

[54]

Pan Y, Wang S-L, Zhang C-M. Ab-initio investigation of structure and mechanical 17

ACCEPTED MANUSCRIPT

properties of PtAlTM ternary alloy. Vacuum 2018;151:205–8. doi:10.1016/j.vacuum.2018.02.027. [55]

Pan Y, Guan WM. Probing the balance between ductility and strength: transition metal

[56]

RI PT

silicides. Phys Chem Chem Phys 2017;19:19427–33. doi:10.1039/C7CP03182C. Pan Y, Wang S, Zhang X, Jia L. First-principles investigation of new structure,

mechanical and electronic properties of Mo-based silicides. Ceram Int 2018;44:1744–50. doi:10.1016/j.ceramint.2017.10.106.

Pan Y, Guan WM, Li YQ. Insight into the electronic and mechanical properties of novel

SC

[57]

TMCrSi ternary silicides from first-principles calculations. Phys Chem Chem Phys

[58]

M AN U

2018;20:15863–70. doi:10.1039/C8CP01579A.

Pan Y, Zhou B. ZrB 2 : Adjusting the phase structure to improve the brittle fracture and electronic properties. Ceram Int 2017;43:8763–8. doi:10.1016/j.ceramint.2017.04.007.

[59]

Makishima A, Mackenzie JD. Direct calculation of Young’s modulus of glass. J Non Cryst Solids 1973;12:35–45. doi:10.1016/0022-3093(73)90053-7.

[60]

Makishma A, Mackenzie JD. Calculation of bulk modulus, shear modulus and Poisson’s

[61]

TE D

ratio of glass 1975;17:147–57. doi:doi.org/10.1016/0022-3093(75)90047-2. Rocherulle J, Ecolivet C, Poulain M, Verdier P, Laurent Y. Elastic moduli of oxynitride glasses. Extension of Makishima and Mackenzie’s theory. J Non Cryst Solids

[62]

EP

1989;108:187–93. doi:10.1016/0022-3093(89)90582-6. Saddeek YB. Structural and acoustical studies of lead sodium borate glasses. J Alloys

[63]

AC C

Compd 2009;467:14–21.

Saddeek YB, Shaaban ER, Aly KA, Sayed IM. Characterization of some lead vanadate

glasses. J Alloys Compd 2009;478:447–52.

[64]

Saddeek YB. Synthesis and properties of MoO3--V2O5--PbO glasses. Philos Mag

2009;89:2305–20. [65]

Saddeek YB. Network structure of molybdenum lead phosphate glasses: Infrared spectra and constants of elasticity. Phys B Condens Matter 2011;406:562–6.

18

ACCEPTED MANUSCRIPT

Table 1 The chemical compositions and the density (ρ) of the two glass series. B2O3

CaO

Al2O3

SiO2

ρ (g/cm3)

24.75 24.75 24.75 24.75 24.75 24.75

50.25 50.25 50.25 50.25 50.25 50.25

12.25 9.8 7.35 4.9 2.45 0

5.25 4.2 3.15 2.1 1.05 0

7.5 6 4.5 3 1.5 0

2.523 2.820 3.091 3.348 3.623 3.868

16.5 16.5 16.5 16.5 16.5 16.5

33.5 33.5 33.5 33.5 33.5 33.5

12.25 9.8 7.35 4.9 2.45 0

5.25 4.2 3.15 2.1 1.05 0

7.5 6 4.5 3 1.5 0

RI PT

Na2O

AC C

EP

TE D

4.007 4.220 4.440 4.717 4.934 5.247

SC

M AN U

PbO CAS25 0 5 10 15 20 25 CAS50 25 30 35 40 45 50

ACCEPTED MANUSCRIPT

Table 2 Calculated mass attenuation coefficients xPbO–RNa2B4O7–(100-R-x)[CaO-Al2O3-SiO2] glass samples using MCNPX and XCOM.

±

0.511 MeV MCNPX XCOM

0 5 10 15 20 25

0.099 0.108 0.120 0.125 0.134 0.142

0.098 0.107 0.116 0.124 0.133 0.142

0.57 0.83 3.48 0.49 0.76 0.31

0.085 0.089 0.092 0.095 0.098 0.102

0.085 0.088 0.091 0.095 0.098 0.101

0.20 0.50 0.56 0.38 0.23 0.65

0.076 0.078 0.079 0.081 0.082 0.084

0.143 0.153 0.160 0.170 0.179 0.190

0.143 0.151 0.160 0.169 0.177 0.186

0.48 1.15 0.20 0.73 1.19 2.08

0.103 0.110 0.109 0.112 0.118 0.120

0.102 0.105 0.108 0.111 0.115 0.118

1.62 4.57 0.83 0.81 3.34 1.77

0.084 0.089 0.087 0.089 0.090 0.093

EP AC C

25 30 35 40 45 50

±

0.33 0.50 0.26 0.56 0.20 0.33

0.058 0.058 0.059 0.059 0.060 0.059

0.058 0.058 0.058 0.058 0.058 0.058

0.52 0.21 1.44 0.81 2.63 0.72

0.0545 0.0546 0.0548 0.0547 0.0547 0.0549

0.0541 0.0541 0.0542 0.0542 0.0543 0.0543

0.85 0.84 1.08 0.90 0.75 1.06

0.059 0.059 0.060 0.060 0.060 0.060

0.059 0.059 0.059 0.059 0.059 0.060

0.38 0.16 1.29 1.11 0.99 0.95

0.0550 0.0550 0.0550 0.0550 0.0550 0.0550

0.0547 0.0547 0.0548 0.0548 0.0549 0.0549

0.60 0.53 0.44 0.37 0.23 0.19

TE D

CAS50

0.076 0.077 0.079 0.080 0.082 0.083

±

1.33 MeV MCNPX XCOM

M AN U

CAS25

RI PT

0.356 MeV MCNPX XCOM

Mass attenuation coefficient (cm2/g) 0.662 MeV 1.17 MeV MCNPX XCOM MCNPX XCOM ± ±

0.084 0.085 0.087 0.088 0.090 0.092

SC

PbO %

0.17 3.98 0.10 0.58 0.26 1.25

ACCEPTED MANUSCRIPT

Table 3 Mean free path of 50PbO–50Na2B4O7–(100-R-x)[CaO-Al2O3-SiO2] in comparison with different glass samples and concretes Ref.

RI PT

This work [41] [44] [45] [46] [47]

SC

50PbO–50Na2B4O7 5PbO-45BaO-50B2O3 57.6TeO2-38.4ZnO-4NiO 44BaO-16Flyash-40B2O3 10Bi2O3-50BaO-40Reg 70B2O3-15SiO2-15Na2O Ordinary Concrete Hematite-Serpentine Concrete Ilmenite-Limonite Concrete Basalt-Magnetite Concrete Ilmenite Concrete Steel-Scrap Concrete Steel–Magnetite Concrete

Mean free path (MFP) (cm) 0.356 MeV 0.662 MeV 1.17 MeV 1.33 MeV 1.03 2.08 3.20 3.47 1.84 2.98 4.20 4.52 1.54 2.46 3.42 3.66 2.11 3.33 4.76 5.01 3.25 4.79 5.21 5.51 4.30 5.60 7.34 7.83 4.00 5.22 6.86 7.33 3.51 4.60 6.05 6.46 3.30 4.30 5.64 6.02 2.92 3.82 5.03 5.36 2.54 3.35 4.40 4.69 2.00 2.65 3.49 3.71

[48]

M AN U

Sample

Table 4 Effective atomic number (Zeff) and electron density (Nel) (e-/g) of glass samples.

TE D

0.511 MeV 0.662 MeV 1.17 MeV 1.33 MeV 23 23 23 Zeff Zeff Zeff Zeff Nel×10 Nel×10 Nel×10 Nel×1023 8.33 8.82 9.33 9.87 10.44 11.04

2.949 3.032 3.113 3.192 3.270 3.345

8.33 8.70 9.08 9.49 9.92 10.37

2.949 2.989 3.028 3.067 3.105 3.142

8.33 8.58 8.84 9.11 9.40 9.71

2.948 2.948 2.947 2.946 2.945 2.943

8.33 8.57 8.82 9.08 9.36 9.66

2.949 2.945 2.941 2.937 2.933 2.928

12.37 13.13 13.93 14.79 15.71 16.70

3.352 3.422 3.490 3.554 3.615 3.673

11.64 12.23 12.85 13.53 14.26 15.04

3.153 3.187 3.220 3.251 3.281 3.309

10.92 11.33 11.78 12.27 12.80 13.37

2.957 2.955 2.952 2.949 2.945 2.940

10.86 11.27 11.70 12.17 12.68 13.24

2.942 2.937 2.931 2.925 2.918 2.911

AC C

EP

Pb 0.356 MeV % Zeff Nel×1023 CAS25 0 8.34 2.950 5 9.18 3.154 3.352 10 10.05 15 10.96 3.544 20 11.91 3.730 25 12.90 3.909 CAS50 25 14.41 3.902 30 15.60 4.066 35 16.85 4.221 40 18.17 4.367 45 19.56 4.502 50 21.03 4.626

ACCEPTED MANUSCRIPT

Table 5 Oxygen molar volume (OMV), oxygen packing density (OPD), fractal bond connectivity (d), number of bonds per unit volume (nb) (cm-3) and average cross-link density (n ) of glass samples. OPD (mol/L)

d

nb ×1022 cm-3

9.078 9.183 9.368 9.587 9.749 9.987

82.220 80.933 78.993 76.839 75.213 73.073

2.70 2.63 2.60 2.50 2.49 2.20

8.719 8.567 8.347 8.104 7.917 7.676

1.646 1.585 1.523 1.460 1.396 1.331

11.290 11.689 12.061 12.273 12.646 12.778

69.877 67.208 64.857 63.448 61.290 60.367

2.37 2.40 2.36 2.40 2.40 2.40

9.133 8.802 8.512 8.346 8.081 7.978

1.845 1.778 1.709 1.640 1.570 1.498

SC

RI PT

MOV (cm3/mol)

M AN U

PbO % CAS25 0 5 10 15 20 25 CAS50 25 30 35 40 45 50

VS (m/s)

L (Gpa)

G (Gpa)

K (Gpa)

Y (Gpa)

H (GPa)

σ

5772 5436 5042 4681 4351 4151

3441 3217 2976 2732 2537 2337

84.06 81.83 78.58 73.36 68.58 65.15

29.88 29.18 27.38 24.99 23.32 21.12

44.23 43.67 42.08 40.04 37.49 35.74

73.15 71.81 67.49 62.06 57.94 53.57

5.49 5.24 4.88 4.30 4.00 3.27

0.224 0.231 0.233 0.242 0.242 0.268

2652 2602 2532 2467 2412 2292

85.08 83.97 82.71 81.58 80.34 79.02

28.18 27.58 27.22 27.22 26.97 26.32

47.50 46.63 45.75 44.05 42.31 41.01

72.32 71.17 70.62 70.27 69.26 67.67

4.65 4.76 4.68 4.79 4.79 4.59

0.252 0.250 0.253 0.250 0.250 0.250

AC C

CAS25 0 5 10 15 20 25 CAS50 25 30 35 40 45 50

VL (m/s)

EP

PbO %

TE D

Table 6 Experimental longitudinal ultrasonic velocity (VL), shear ultrasonic velocity (VS), longitudinal (L), shear (G), bulk (B), Young’s (Y) modulus, micro-hardness (H) and Poisson’s ratio (σ) of glass samples.

4608 4507 4406 4271 4176 3971

M AN U

SC

RI PT

ACCEPTED MANUSCRIPT

AC C

EP

TE D

Fig.1. Total simulation geometry of the present investigation

ACCEPTED MANUSCRIPT

R=50

X=50

R=50

X=45

I nt ensi t y (A. U.)

R=50

X=40

R=50

RI PT

X=35

R=50

X=30

R=75

X=25

R=75

X=20

R=75

X=15

SC

R=75

X=10

R=75

X=5

10

20

M AN U

R=75 30

40

50

60

X=0

70

80

2θ θ

AC C

EP

TE D

Fig. 2. X-ray diffraction patterns of xPbO–RNa2B4O7–(100-R-x)[CaO-Al2O3-SiO2] glasses, where 0 ≤ x ≤ 50 and 75 ≤ R ≤ 50 mole %.

Fig. 3 Total mass attenuation coefficients of CAS25 and CAS50 glasses.

ACCEPTED MANUSCRIPT

0.14

=

om

RI PT

MC

X NP

Xc

0.10

MeV 0.356 0.511 0.662 1.710 1.330

SC

(µ/ρ µ/ρ) MCNPX (cm 2 /g) µ/ρ

20PbO-75Na2B4O7-5(CaO-Al2O3-SiO2)

0.06

M AN U

0.06

0.10

0.14

(µ/ρ µ/ρ) µ/ρ Xcom (cm /g) 2

AC C

EP

TE D

Fig. 4. Correlation between the calculated values of (µ/ρ) using XCOM program and that obtained from MCNPX code glass samples.

Fig. 5. Half value layer (HVL) versus photon energy and PbO content of the prepared glass samples.

ACCEPTED MANUSCRIPT

6

5

3

SC

HVL (cm)

4

RI PT

PbO % 0 10 20 30 40 50

2

Lead

0 0.2

0.4

M AN U

1

0.6

0.8

1.0

1.2

1.4

Photon energy (MeV)

Fig. 6. Half value layer (HVL) of the prepared glass samples compared to HVL of pure lead.

80

∆(0PbO-Pb)

∆(10PbO-Pb)

∆(20PbO-Pb)

∆(30PbO-Pb)

∆(40PbO-Pb)

∆(50PbO-Pb)

EP

HVL (PbO-Pb) %

90

TE D

100

70

AC C

60

50

40 0.2

0.4

0.6

0.8

1.0

1.2

1.4

Photon energy (MeV)

Fig. 7. Half value layer difference between prepared glass samples and pure lead.

M AN U

SC

RI PT

ACCEPTED MANUSCRIPT

0.125

TE D

Fig. 8. Variation of effective atomic number (Zeff) as a function of photon energy for the prepared glass samples.

EP

CAS25

0.1233

0.126

0.1188

0.1142

0.1083

AC C

ΣR (cm-1)

0.115

0.105

0.1006

0.095

0PbO

5PbO

10PbO

15PbO

20PbO

25PbO

Fig. 9. Variation of removal cross-section for fast neutron versus composition of CAS25 glass samples

ACCEPTED MANUSCRIPT

0.1215

0.1216

CAS50 0.1211

RI PT

Σ R (cm-1)

0.1212 0.1208

0.1208 0.1205 0.1203

0.1204

0.12 30PbO

35PbO

40PbO

45PbO

50PbO

M AN U

25PbO

SC

0.1201

Fig. 10. Variation of removal cross-section for fast neutron versus composition of CAS50 glass samples

90

70 60

CAS25 L G K Y

CAS50 L G K Y

EP

Elastic modulus (GPa)

80

TE D

Experimental

AC C

50 40 30 20

0

10

20

30

40

50

PbO concentration

Fig. 11. Experimental results of longitudinal (L), shear (G), bulk (K), Young’s (E) modulus against PbO content of glass samples.

ACCEPTED MANUSCRIPT

120 Makishima-Mackenzie model

CAS50 Y G

K L

RI PT

K L

80

60

SC

Elastc molulus (GPa)

100

CAS25 Y G

20 0

10

M AN U

40

20

30

40

50

PbO concentraton

Fig. 12. Theoretical results of longitudinal (L), shear (G), bulk (K), Young’s (E) modulus against PbO content of glass samples according the Makishima-Mackenzie model.

TE D

80

CAS25 Y G

K L

CAS50 Y G

K L

60

EP

Elastc molulus (GPa)

100

AC C

40

20

Rocherulle model (RM) 0

10

20

30

40

50

PbO concentraton

Fig. 13. Theoretical results of longitudinal (L), shear (G), bulk (K), Young’s (E) modulus against PbO content of glass samples according the Rocherulle model.

ACCEPTED MANUSCRIPT

120

T

o he

80

p Ex

e.

SC

60

.=

40

20 20

40

M AN U

Theoretical m odulus

100

RM E L K G

RI PT

MMM E L K G

60

80

CAS25

100

120

Experimental modulus

AC C

EP

TE D

Fig. 14. Correlation between experimental and theoretical values of elastic modulus of CAS25 glass samples.

ACCEPTED MANUSCRIPT

80

CAS25 CAS50 [50] [51] [52] [53]

RI PT

60

SC

Y (GPa)

70

40 0

10

20

M AN U

50

30

40

50

60

70

80

PbO concentration

AC C

EP

TE D

Fig. 15 Comparison of experimental Young’s modulus with different glass matrices containing PbO.

ACCEPTED MANUSCRIPT

Highlights

RI PT

SC M AN U TE D EP

•

Gamma-ray properties for glass samples have been studied using Monte Carlo method. Mechanical properties for xPbO–RNa2B4O7–(100-R-x)[CaO-Al2O3-SiO2] have been measured. 50PbO–50Na2B4O7–(100-R-x)[CaO-Al2O3-SiO2] glass sample is the superior gamma-ray shielding.

AC C

• •