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BY 4.0 license Open Access Published by De Gruyter Open Access October 3, 2023

Physical, mechanical, and gamma ray shielding properties of the Bi2O3–BaO–B2O3–ZnO–As2O3–MgO–Na2O glass system

  • Dalal Abdullah Aloraini , Aljawhara H. Almuqrin , Mohammad Ibrahim Abualsayed EMAIL logo and Ashok Kumar EMAIL logo
From the journal Open Chemistry


This study provides insights into the effects of Bi2O3 on the physical, mechanical, and gamma ray shielding properties of Bi2O3–BaO–B2O3–ZnO–As2O3–MgO–Na2O glasses. The higher Bi2O3 concentrations result in increased density and molecular weight of the glasses. The molar volume also increases with higher Bi2O3 percentages, accompanied by a decrease in the average distance between boron atoms and a reduction in polaron radius and inter-nuclear distance. Electronegativity decreases and electronic polarizability increases with increasing Bi2O3 concentration, indicating higher electron-donating capacity and greater susceptibility to external electric field distortion. The elastic moduli exhibit a downward trend with increasing Bi2O3 concentration, indicating a decreased degree of elastic behaviour. The decrease in cross-linking is further supported by the reduction in Poisson’s ratio. The decrease in values of the hardness also indicates a decline in the stiffness and connectivity of the glass network. The linear attenuation coefficients (LACs) of three different glasses were obtained using Phy-X software in 0.015–15 MeV energy range. Also, the effective atomic numbers are calculated for the selected glasses. The LAC has the highest values for Bi21, indicating that the addition of Bi2O3 causes an improvement in the LAC.

1 Introduction

A key component of modern science that has improved the quality and durability of life on earth is the use of radiation with sufficiently high energy [1,2]. Radiation is used in various domains such as healthcare, manufacturing, energy production, nuclear research, material analysis, and food preservation, showcasing its beneficial impact on both humanity and the environment [3,4,5]. Despite the inherent risks associated with exposure to any artificial radiation, these practical boundaries are continually expanding. This is due to the fact that such hazards have been effectively reduced to the absolute smallest amount, and in certain instances eliminated, as a result of the availability of sufficient radiation control techniques [6,7,8,9]. The damage caused by ionizing radiation in the bodies of living organisms is a complex interaction. One of the essential processes driving these damages is the formation of radicals during exposure to gamma radiation and X-ray. The assessment of radiation interaction factors plays a crucial role in selecting suitable materials for research and development in radiation shielding. These factors provide valuable insights into the absorption of radiation and its energy by different materials [10,11]. Consequently, the analysis of interaction factors enables the evaluation of a material’s potential for providing effective radiation shielding in nuclear facilities [12]. Extensive investigations have been conducted on a diverse range of functional materials, including alloys, steel, concrete, ceramics, polymers, and glasses, to explore their radiation interaction characteristics and their potential for radiation shielding [13,14,15,16]. The effectiveness of several of these shielding materials has been demonstrated to be comparable to, and in some cases even superior to, that of more conventional shielding materials. Over the past few years, there has been a growing demand for novel conventional shielding materials due to various factors. These factors include the instability and lack of uniformity in chemical composition, the existence of cracks, limited transparency, high density, and environmental concerns associated with conventional shielding materials [17,18].

Currently, a wide range of oxide glasses with diverse structural, optical, thermal, mechanical, and chemical properties have been extensively studied for their effectiveness in radiation shielding against various types of radiations. This increased interest can be attributed to their relatively superior chemical and mechanical stability when compared to other materials [19,20]. Mandal et al. [21] studied the lead-free multi-component non-toxic Bi2O3–BaO–B2O3–ZnO–As2O3–MgO–Na2O glass system for their thermal behaviour using dilatometric test, structural and microstructural properties using the X-ray diffraction, Raman and scanning electron microscope, and optical and photoluminescence studies in detail. But as far as the physical and mechanical characteristics are considered, only the variation of density with mol% of Bi2O3 is discussed so far. As the selected glasses contain the sufficient amount of Bi2O3 and possess fairly good density values, their gamma ray shielding behaviour needs to be studied for the application of the glasses in the field of radiation shielding. So in this proposed work, the physical, mechanical, and gamma ray shielding behaviour of the selected glasses have been studied.

2 Materials and methods

2.1 Details of the samples

The composition and density of the Bi2O3–BaO–B2O3–ZnO–As2O3–MgO–Na2O glass system have been obtained from the study of Mandal et al. [21]. Mandal et al. [21] measured the density (ρ) of the glasses using the helium gas pycnometer and Archimedes principle. In this study, the density values measured using the Archimedes principle are used. The sample codes depending on the amount of Bi2O3 present in the samples and their density values are as follows:

Bi15: 15Bi2O3–8BaO–41B2O3–10ZnO–4As2O3–12MgO–10Na2O (density = 4.59 g/cm3).

Bi18: 18Bi2O3–8BaO–38B2O3–10ZnO–4As2O3–12MgO–10Na2O (density = 4.77 g/cm3).

Bi21: 21Bi2O3–8BaO–35B2O3–10ZnO–4As2O3–12MgO–10Na2O (density = 5.07 g/cm3).

2.2 Physical properties

The molar volume (V m) was calculated from its molar mass (M) using the following formula [22]:

(1) V m = M ρ cm 3 mole 1 .

The average boron–boron separation ( d B B ) can be used to infer the impact of dopant gas [22,23]:

(2) d B B = V m b N A 1 3 ,

where V m b represents the molar volume of boron.

If x B is the B2O3’s mole fraction [22], then

(3) V m b = V m 2 ( 1 X B ) .

The dopant concentration (N), inter-nuclear distance (r i), polaron radius (r p), and field strength (F) are calculated as [22,23]:

(4) N = Mol percent of dopant × density of glass × Avogadro no . Average molecular weight of glass ions cm 3 ,

(5) r i = 1 N 1 3 ,

(6) r p = 1 2 Π 6 N 1 3 ,

(7) F = Z ( r p ) 2 ,

where “z” represents the oxidation state of the dopant ions.

The formula for determining the oxygen molar volume (V o) of the glasses is as follows [23]:

(8) V o = V m n ,

where n is the number of oxygen atoms in one formula unit.

The equation for calculating oxygen packing density (OPD) is as follows [23]:

(9) OPD = n ρ M × 1 , 000 .

The equation for calculating optical basicity (Ʌth) is as follows [23]:

(10) Λ th = Λ i x i ,

where Ʌ i and x i are the optical basicities and the mole fractions of each oxide (Ʌ1(Bi2O3) = 1.19, Ʌ2(BaO) = 1.15, Ʌ3(ZnO) = 1.03, Ʌ4(B2O3) = 0.43, Ʌ5(As2O3) = 1.02, Ʌ6(MgO) = 0.78, Ʌ7(Na2O) = 1.15).

The equation for calculating average electronegativity (χ av) is as follows [24]:

(11) Λ th = 0.75 χ av 1.35 .

The equation for calculating electronic polarizability ( α o 2 ) is as follows [25,26,27]:

(12) α o 2 = 1.67 1.67 Λ th .

2.3 Mechanical properties

The equation for calculating average cross-link density ( n c ̅ ) is as follows [28]:

(13) n c ̅ = x i ( n c ) i ( N c ) i x i ( N c ) i , where ( n c = n f 2 ) ,

where n f is the coordination number of the cations present in the sample.

The equation for calculating number of bonds per unit volume of the glasses (n b) is as follows [28]:

(14) n b = N A V m ( n f ) i x i .

The mechanical characteristics of glasses, according to Makishima–Mackenzie’s theory [29,30] are as follows:

The equation for calculating atomic packing density (V t) is as follows [29,30]:

(15) V t = 1 V m V i x i .

The equation for calculating interatomic bonding energy (G t) is as follows [29,30]:

(16) G t = G i x i ,

where V i and G i represent the atomic packing densities and interatomic bond energies of the constituent atoms in glasses, respectively [31].

The equation for calculating Young’s modulus (E) is as follows:

(17) E = 8.36 V t G t .

The equation for calculating bulk modulus (B) is as follows:

(18) B = 10 V t 2 G t .

The equation for calculating shear modulus (G) is as follows:

(19) G = 30 V t 2 G t ( 10.2 V t 1 ) .

The equation for calculating longitudinal modulus (L) is as follows:

(20) L = K + 4 3 G .

The equation for calculating Poisson’s ratio is as follows:

(21) σ = 0.5 1 7.2 V t .

The equation for calculating fractal bond connectivity (d) is as follows:

(22) d = 4 G K .

The equation for calculating Hardness (H) is as follows:

(23) H = ( 1 2 σ ) E 6 ( 1 + σ ) .

2.4 Gamma ray shielding properties

The radiation shielding parameters for the selected glasses were determined in the range of 0.015–15 MeV. The linear attenuation coefficient (LAC) is a basic parameter that can be used to understand the glass’s ability to attenuate the incoming radiation. Also, it is a useful parameter since the other parameters are calculated from the LAC such as the half value layer (HVL) and mean free path (MFP). Any material’s HVL value refers to its thickness, which reduces 50% of the radiation that enters it. It is related to the LAC by the following equation:

(24) HVL = 0.693 LAC .

The MFP stands for the average distance that a travelling photon travels between successive encounters. MFP is a crucial component of offering greater protection quality. It is given by:

(25) MFP = 1 LAC .

The tenth-value layer (TVL) is the average quantity of material thickness, measured in cm, which must be present for the radiation to be reduced to one tenth of its initial intensity (a reduction of 90%), which is calculated by:

(26) TVL = 2.3 LAC .

3 Results and discussion

3.1 Physical properties

Table 1 presents the physical properties of the glasses. The higher concentrations of Bi2O3 (15–21 mol%) resulted in increased density and molecular weight of the glasses. The glass network undergoes a substitution of less dense B2O3 with a denser Bi2O3 form. The greater density observed with increased Bi2O3 concentration (as shown in Figure 1a) can be attributed to the higher atomic mass of Bi2O3 in comparison to B2O3. Figure 1a illustrates that the molar volume of the glasses increases from 30.02 to 31.87 cm3 with an increase in the percentage of Bi2O3 in the glasses. It is due to the fact that incorporation of Bi2O3 results in the increase in molar mass of the sample by higher fraction as compared to increase in its density due to larger size of Bi [32,33,34]. The average distance between boron atoms (d BB) decreases from 3.48 to 3.44 Å as the concentration of Bi2O3 increases. This is likely due to the increase in ion concentration from 3.01 × 1021 to 3.97 × 1021 ions/cm3 with the increase in Bi2O3 concentration. Additionally, the polaron radius and inter-nuclear distance exhibit a decrease from 2.79 to 2.54 Å and from 6.93 to 6.32 Å, respectively. These changes suggest that the glass network is becoming denser. The excessive presence of Bi2O3 enhances the bonding between Bi ions and oxygen, leading to a rise in the field strength around the Bi ion from 2.57 × 1015 to 3.09 × 1015 cm2.

Table 1

Physical parameters

Properties Physical parameters
Bi15 Bi18 Bi21
M (g) 137.79 149.68 161.57
V m (cm3) 30.02 31.38 31.87
N (×1021 ions cm‒3) 3.01 3.45 3.97
V m b (cm3) 25.44 25.31 24.51
d B–B〉 (Å) 3.48 3.47 3.44
r p (Å) 2.79 2.67 2.54
r i (Å) 6.93 6.61 6.32
F × 1015 (cm2) 2.57 2.82 3.09
OPD 73.29 70.11 69.03
V o (cm3 mol‒1) 13.65 14.26 14.49
Ʌth 0.80 0.82 0.84
χ av 2.29 2.26 2.24
α o 2 1.92 1.97 2.02
Figure 1 
                  Variation of physical properties. (a) density and molar volume, (b) V
                     o and OPD, (c) σ and (d) average electro-negativity and electronic polarizability with mol% of Bi2O3.
Figure 1

Variation of physical properties. (a) density and molar volume, (b) V o and OPD, (c) σ and (d) average electro-negativity and electronic polarizability with mol% of Bi2O3.

Incorporating Bi2O3 alters the V o and OPD values. The study reveals a positive correlation between the amount of Bi2O3 in the glass network and the V o, which increases from 13.65 to 14.49 cm3/mol. The OPD declines from 73.29 to 69.03. The observed phenomenon indicates an increase in the V o within the glass network, attributed to the greater space occupied by oxygen atoms. Additionally, the observed decrease in OPD is attributed to a less dense packing of oxygen atoms. Figure 1b illustrates the changes in the said parameters as the mol% of Bi2O3 in the glass composition varies. The inverse relationship between these parameters can be attributed to the impact of glass density and molar volume. The study suggests that Bi2O3 impacts the oxygen atom arrangement, leading to alterations in the V o and OPD [32,33,34].

Optical basicity is a property of glass that is determined by the electron accepting or donating ability of its constituent ions. It is closely linked to the glass’s physical and chemical characteristics. The findings indicate that the optical basicity of the glass increased from 0.80 to 0.84 as a consequence of increased Bi2O3 content as shown in Figure 1c. The inclusion of Bi2O3 results in increased negative charges on the oxygen atoms within the glass network. This trend is due to the amphoteric properties of Bi2O3, enabling it to function as both an acid and a base. The optical basicity of glass can be enhanced by substituting acidic oxide (B2O3) within the glass network. This behaviour underscores the superior capacity of oxide ions to convey electrons to adjacent cations.

The relationship between electronegativity and electronic polarizability in glasses as a function of the mol% of Bi2O3 is examined, as illustrated in Figure1d. Lower electronegativity indicates higher electron-donating capacity. The rise in mol% of Bi2O3 in the glasses results in a reduction of electronegativity from 2.29 to 2.24. The results indicate an increase in electron-donating properties of the samples with increasing Bi2O3 concentration. Electronic polarizability measures the susceptibility of an atom or molecule’s electron cloud to distortion by an external electric field. The electronic polarizability of the glasses increases from 1.92 to 2.02 as the mol% of Bi2O3 is increased [32].

3.2 Mechanical properties

The value of n c ̅ increases from 3.675 to 3.825 when the concentration of Bi2O3 is made higher. When there is a rise in value for n c ̅ , there is also an increase in the complexity of the network. The value of n b should be decreased to 9.886 × 1022 cm−3 from its previous value of 10.23 × 1022 cm−3. The value of n b indicates the degree to which a network is cross-linked. The decrease in degree of cross linkage in the network is evident from the increase in values of V m and V o, which indicates the expansion in the network. The larger ionic radius of Bi2O3 compared to B2O3 may have contributed to the formation of excessive free volume, which in turn led to a decline in the values of packing density (V t), which ranged from 0.575 to 0.552 cm3 mol−1 and the dissociation energy (G t) from 15.979 to 12.245 kcal cm−3.

The V t and G t values may be used in conjunction with the Makishima–Mackenzie’s model to derive additional elastic parameters. The elastic parameters that were determined as a consequence are listed in Table 2. The fluctuations of these parameters with the concentration of Bi2O3 are then analysed, which reveals a downward trend in the values of E, B, G, and L. To be more specific, E drops from a value of 76.843 to a value of 70.329, B drops from a value of 52.875 to a value of 46.423, G drops from a value of 32.588 to a value of 30.088, and L drops from a value of 96.327 to a value of 86.541 [33]. Figure 2 illustrates how those values changed in relation to the amount of Bi2O3 in the sample. These lowering values imply that the samples under investigation exhibit a decreased degree of elastic behaviour. As the concentration of Bi2O3 increases, it leads to an expansion of the network. This expansion, in turn, contributes to the decreasing nature of the elastic behaviour observed in these samples. This tendency is supported even further by the drop in the values of the σ variable. The decrease in σ with increasing Bi2O3 concentration, which ranges from 0.259 to 0.248, verifies the decrease in the amount of cross linking in the network. The range of values for d, which is from 2.465 to 2.593, is indicative of a layered structure in 2D. The decline in the stiffness and connectivity of the network is reflected in the values of H, which ranges from 4.914 to 4.727 before showing a downward trend [33].

Table 2

Mechanical properties

Sample Mechanical properties
n b (×1022 cm−3) n c ̅ V t (cm3 mol−1) G t (kcal cm−3) E (GPa) B (GPa) G (GPa) L (GPa) σ d H (GPa)
Bi15 10.23 × 1022 3.675 0.575 15.979 76.843 52.875 32.588 96.327 0.259 2.465 4.914
Bi18 9.904 × 1022 3.750 0.555 15.612 72.481 48.149 30.967 89.438 0.250 2.573 4.834
Bi21 9.866 × 1022 3.825 0.552 12.245 70.329 46.423 30.088 86.541 0.248 2.593 4.727
Figure 2 
                  Mechanical properties of the samples.
Figure 2

Mechanical properties of the samples.

3.3 Gamma ray shielding properties

Using the Phy-X software, the LACs of three distinct glass types were determined within the energy range of 0.015–15 MeV [35]. Figure 3 illustrates the LAC values for the investigated Bi15, Bi18, and Bi21 glasses. Notably, as the photon energy increases up to 0.2 MeV, the LAC values for all the selected glasses exhibit a significant decline. This can be attributed to the influence of the atomic number (Z) in the Z4–5 form, which affects the cross-section of the photoelectric absorption effect, the primary interaction mechanism at lower energies. Hence, a substantial portion of photon interactions with the glasses occurs within the low-energy region of the electromagnetic spectrum. Beyond 0.2 MeV, where Compton scattering predominates and its cross-section is linearly dependent on the atomic number, the LAC values remain relatively small and consistent across all the samples. However, at higher energies, the dominant interaction process is pair production, which is connected to Z 2. Consequently, a slight improvement in the LAC values is observed in the latter energy range. The LAC has the highest values for Bi21, as can be observed in Figure 3, indicating that the addition of Bi2O3 causes an improvement in the LAC.

Figure 3 
                  The LAC of the samples.
Figure 3

The LAC of the samples.

Figures 4 and 5 illustrate the graphical representation of how the HVL and TVL values vary with photon energy for different glass types. In contrast to the LAC trend shown in the previous figure, the HVL and TVL values increase with increasing energy levels. It is worth noting that both parameters exhibit an inverse relationship with the density of the samples. This can be observed in Figures 4 and 5, where the Bi21 glasses, which have the highest densities, exhibit lower HVL and TVL values compared to the other glasses. These findings align with previous research conducted on various glass systems [13].

Figure 4 
                  The HVL of the samples.
Figure 4

The HVL of the samples.

Figure 5 
                  The TVL of the samples.
Figure 5

The TVL of the samples.

Additionally, Figure 6 presents the MFP [36] values for the three selected glasses within the energy range of 0.015–15 MeV. The MFP values for Bi15, Bi18, and Bi21 glasses range from 0.0032 to 5.508 cm, 0.0029 to 5.096 cm, and 0.0026 to 4.642 cm, respectively. Similar to the HVL, the Bi21 glass exhibits the lowest MFP value. In other words, the addition of Bi2O3 causes a reduction in the MFP for these glasses.

Figure 6 
                  The MFP of the samples.
Figure 6

The MFP of the samples.

Additionally, the fluctuations in Z eff values versus energy for the current glasses are presented in Figure 7. Since Z eff and MAC are related for the glass being examined, it is shown that the photoelectric effect causes the Z eff values to first fall rapidly. The smallest value of Z eff was recorded at the range of intermediate energies, a region where Compton scattering influences almost all photon interactions. Bi21 glass was found to have the highest Z eff values of the glasses that were examined, with values ranging from 66.15 to 19.88. Because this sample has an elevated amount of Bi compared to the other glasses, it has comparatively high Z eff values. To put it simply, the variation in Z eff can be categorized into three specific energy ranges, namely low, moderate, and high. Each of these energy intervals arises from a distinct interaction with photons. In regions of low energy, the photoelectric absorption process predominates as the primary mode of photon interaction. Due to this Z eff is high in this energy range. At intermediate energies, Compton scattering predominates, and as a result, it is observed that Z eff variation is essentially constant. Pair production is the dominant process in the high energy (from 3 to 15 MeV) region. In light of this, all changes are defined by the Z dependence of total atomic cross sections.

Figure 7 
                  The effective atomic number of the samples.
Figure 7

The effective atomic number of the samples.

4 Conclusion

The study examined the effects of incorporating Bi2O3 into glass matrices and its influence on various physical, mechanical, and gamma ray shielding properties. The analysis revealed that higher concentrations of Bi2O3 resulted in increased ρ and M of the glasses. V m of the glasses also increased with the percentage of Bi2O3, indicating expansion within the network. The incorporation of Bi2O3 caused a decrease in d B B , suggesting increased ion concentration. Furthermore, the addition of Bi2O3 affected the optical basicity of the glass, leading to an increase in negative charges on oxygen atoms. The study also investigated the relationship between electronegativity and electronic polarizability, showing a decrease in electronegativity and an increase in electron-donating properties with increasing Bi2O3 concentration. Regarding mechanical properties, the increase in Bi2O3 concentration resulted in decrease in the degree of cross-linkage. This expansion of the network contributed to a decrease in elastic behaviour, as indicated by the lower values of elastic parameters such as E, B, G, and L. The decrease in the σ variable further confirmed the reduction in cross-linking. The decrease in values of the H also indicates a decline in the stiffness and connectivity of the glass network. The radiation shielding part showed that the addition of Bi2O3 has a notable impact on the LAC and other parameters, where the LAC and Z eff were improved with the addition of Bi2O3, where the HVL and TVL were reduced. Bi21 glass was found to have the highest LAC and Z eff values of the glasses that were examined, with the Z eff values ranging from 66.15 to 19.88.

  1. Funding information: The authors express their gratitude to the Princess Nourah bint Abdulrahman University Researchers Supporting Project number (PNURSP2023R57), Princess Nourah bint Abdulrahman University, Riyadh, Saudi Arabia.

  2. Author contributions: D.A.A.: funding acquisition, methodology, software, validation, writing – review and editing. A.H.A.: project administration, funding acquisition. M.I.A.: conceptualization, data curation, supervision, original draft preparation. A.K.: investigation, formal analysis, writing – review and editing, original draft preparation. All authors have read and agreed to the published version of the manuscript.

  3. Conflict of interest: The authors declare no conflict of interest.

  4. Data availability statement: The data presented in this study are available on request from the corresponding author.

  5. Ethical approval: The conducted research is not related to either human or animal use.


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Received: 2023-07-27
Revised: 2023-08-16
Accepted: 2023-08-30
Published Online: 2023-10-03

© 2023 the author(s), published by De Gruyter

This work is licensed under the Creative Commons Attribution 4.0 International License.

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