Introduction

In our present technologically advanced world, glasses are exhaustively being used in a wide variety of applications ranging from household appliances, optical, telecommunication and electronic devices, and so on [1,2,3,4]. Over the years, the scope of glass application continues to develop due to many interesting general properties of glass materials. One major factor that has sustained such development is the chemical compositional flexibility enjoyed by glass materials. The implication of this is that the chemical content of a glass can be varied easily to obtain a different glass composition. Since the general (mechanical, physical, structural, optical, etc.) properties of a glass material rest majorly on its chemical content, it is hence possible for new glass material having novel properties to emerge from existing ones [1,2,3,4,5,6]. This has led to the synthesis and characterization of different glass species for different applications. It has also produced new glasses with potential applications in emerging technologies outside the traditional sphere of glass use [6,7,8,9,10,11,12,13].

The earth and its inhabitants have continued to be irradiated from artificial radiation generators due to the enormous use of these sources in modern technology. As nuclear radiation technology continues to grow, so also are radiation control and protection measures, particularly in the areas of radiation shielding [6, 8,9,10,11,12,13]. The use of radiation barriers (shields) for the absorption and hence the reduction of radiation dose to man and his environment is a very crucial aspect of radiation technology. This is due to the deleterious effect of unhindered exposure of living and nonliving systems to ionizing radiation. Although the major factor to consider before a material can be adopted for radiation shield is its ability to effectively attenuate the radiation type, it is meant to shield to acceptable level; however, many other parameters such as availability, mechanical strength, physical properties, and stability are other characteristics to be considered. These secondary parameters dictate in what form (pure or infused with other materials) and the nature of environment suitable for such material to function effectively.

Environmental factors, stability, and economic concerns have placed restrictions on the use of some shielding materials such as Pb and Pb-based materials. Consequently, the synthesis and testing of environmentally friendly, cheap, and durable radiation shielding materials are very attractive to the research community. Some studies have focused on alloys, steel, metallic glasses, rocks/soil, glasses, and other types of materials for their shielding competence against gamma, neutrons, and charged particles [14,15,16,17,18]. Among these new generation of cheap and nontoxic shields, glasses have received more attention and outshine other materials in terms of ease of production, durability, optical transparency, and superior shielding competence [14,15,16,17,18,19,20]. Today, many glass samples have been produced with good potential for advance shielding applications.

The gamma radiation absorption competence of a glass material depends on the incident photon energy, atomic number, and proportion of the chemical elements in the glass matrix and its thickness. Recently, Aygun et al. [21] investigated photon and fast neutron absorption parameters of metal oxides doped glasses. The metal oxides considered in the study were CoO, CdWO4, Bi2O3, Cr2O3, and Bi2O3. The research showed that photon and fast neutron shielding parameters of the doped glasses were affected by the molecular mass, density, and photon absorption capacity of the metal oxides. Similar observation has been reported for Sb2O3, PbF2, and MoO3 in different glass matrices [15, 20, 22]. The present study presents a glass system with the following formula: 56B2O3-25Li2O3-10Na2O-5CaO-2Al2O3-2SrO-0.5TeO2-1X wt%: X = ZrO2, CoO, NiO, and V2O5 and their photon and fast neutron absorption parameters. The photon attenuation parameters were calculated for typical photon energy sources used in medical and research applications of photons. In addition, the mechanical properties of glasses were examined.

Materials and methods

Materials

Four samples of lithium borotellurite glasses with the formula 56B2O3-25Li2O3-10Na2O-5CaO-2Al2O3-2SrO-0.5TeO2-1X wt%: X = ZrO2, CoO, NiO, and V2O5 were selected from Ref. [23]. More details for the preparation steps and glasses’ physical properties were written in [23]. The investigated glasses were named as follows:

G1-Zr: 56B2O3-25Li2O3-10Na2O-5CaO-2Al2O3-2SrO-0.5TeO2-1ZrO2 wt%

G1-Co: 56B2O3-25Li2O3-10Na2O-5CaO-2Al2O3-2SrO-0.5TeO2-1CoO wt%

G1-Ni: 56B2O3-25Li2O3-10Na2O-5CaO-2Al2O3-2SrO-0.5TeO2-1NiO wt%

G1-V: 56B2O3-25Li2O3-10Na2O-5CaO-2Al2O3-2SrO-0.5TeO2-1V2O5 wt%

Samples name, compositions, and density of investigated glasses are tabulated in Table 1.

Table 1 Sample’s name, chemical composition, and density of 56B2O3-25Li2O3-10Na2O-5CaO-2Al2O3-2SrO-0.5TeO2-1X wt%: X = ZrO2, CoO, NiO, and V2O5 glasses
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Photon and neutron shielding parameters

The radiation attenuating and hence protection efficiency of a medium may be described using radiation interaction parameters. These parameters give the level of attenuation with respect to radiation type and energy. For photons, the mass attenuation coefficient \({\mu }_{m}\) describes the measure of photon intensity that transmits through a medium. Usually, \({\mu }_{m}\) depends on the absorber’s chemical definition and energy of photon. For the present glasses (G1-Zr, G2-Co, G3-Ni, and G4-V), \({\mu }_{m}\) values for photon energy sources usually used in medical applications were calculated via the XCOM software [24]. Other gamma radiation interaction parameters that may be used to describe photon protection capacity include the following: the effective atomic number \({Z}_{eff}\), half-value layer/thickness (HVL), and mean free path (MFP), all of which are strongly dependent on the photon energy. Mathematically, these parameters were obtained directly from \({\mu }_{m}\) for the present glasses according to the following equations [25, 26]:

$${Z}_{eff}=\frac{\sum_{i}{f}_{i}{A}_{i}{\left({\upmu }_{m}\right)}_{i}}{{\sum }_{j}{f}_{j}\frac{{A}_{j}}{{Z}_{j}}{\left({\upmu }_{m}\right)}_{j}}; MFP={~}^{1}\!\left/ \!\!{~}_{{{\rho \mu }}_{m}}\right.;HVL={~}^{ln2}\!\left/ \!\!{~}_{{{\rho \mu }}_{m}}\right.$$
(1)

where \({f}_{i}\), \({Z}_{i}\), \({A}_{i}\), and \(\uprho\) are the molar fraction, atomic number, and atomic mass number of the ith elemental component and density of the absorbing glass.

Fast neutron shielding capacity of the glasses was assessed via the fast neutron removal cross section (\(FNRC-{\Sigma }_{R}\)). The \(FNRC\) measures the probability that a fast neutron interacting with a medium will be removed from the fast beam after its first collision. \(FNRC\) of the glasses were theoretically estimated via [27]: \({\Sigma }_{R}=\sum {w}_{i}{(\frac{{\Sigma }_{R}}{\rho })}_{i}\) where \({w}_{i}\), and \({\left(\frac{{\Sigma }_{R}}{\rho }\right)}_{i}\), is the density fraction and fast neutron mass removal cross section of the ith element in the interacting material. Furthermore, \(\frac{{\Sigma }_{R}}{\rho }\) was estimated according to [20, 28]:

$$\frac{{\Sigma }_{R}}{\rho }=0.19{Z}^{-0.743 }\text{ for }2\leq Z\leq 8; \frac{{\Sigma }_{R}}{\rho }=0.125{Z}^{-0.565 }\text{ for }Z>8$$
(2)

Elastic moduli of the investigated glasses

In order to evaluate the mechanical properties (bulk (KB-C), shear (SB-C), longitudinal (LB-C), Young’s (EB-C)), and Poisson’s ratio (σB-C) of the investigated lithium borotellurite glasses, the bond compression (B-C) model was applied [22, 29, 30]. All physical parameters and relations used for this aim were collected in Tables 2 and 3.

Table 2 Coordination number per cation (nf), crosslink density per cation (nc), stretching force constant (F), and ionic radius (r) of the oxides B2O3, Li2O3, Na2O, CaO, Al2O3, SrO, TeO2, ZrO2, CoO, NiO, V2O5
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Table 3 The values of total number of cationic per glass formula unit (η), average crosslink density (\(\overline{n}_{c}\)), average stretching force constant (\(\overline{F}\)), number of network bond per unit volume (nb), average bond length (l), calculated bond compression elastic moduli (bulk (KB-C), shear (SB-C), longitudinal (LB-C), Young’s (EB-C)), and Poisson’s ratio (σB-C) of the investigated glasses
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Results and discussion

Photon interaction parameters

The value of \({\mu }_{m}\) at different source energies is pictorially represented in Fig. 1. The figure shows that \({\mu }_{m}\) decays in value as energy (E) increases. However, the decay was rapid for each of the glasses at the lower end of the energy spectrum compared to the later end. The maximum value of the mass attenuation coefficient of 2.356, 2.049, 2.073, and 1.958 cm2/g for G1-Zr, G2-Co, G3-Ni, and G4-V, respectively, was obtained at the least energy of 22 keV. The smallest value of \({\mu }_{m}\) was obtained at 1.33 MeV with corresponding value of 0.054 cm2/g for the four glasses. The observed changes in the \({\mu }_{m}\) values within the E spectrum considered can be attributed to the changes in the partial photon absorption coefficients with respect to E. Within the investigated energy spectrum considered in this study, photoelectric (PEAC) and Compton scattering (CSAC) absorption coefficients are the major interaction cross sections dictating the behavior of \({\mu }_{m}\). The PEAC and CSAC vary inversely as the 4th and 1st power of photon energy, respectively. The PEAC dominates \({\mu }_{m}\) at E less than 662 keV, while CSAC dominates proceeding for the rest of the energy spectrum. Value of \({\mu }_{m}\) at each energy increases according to the trend: (\({\mu }_{m}\))G1-Zr > (\({\mu }_{m}\))G3-Ni > (\({\mu }_{m}\))G2-Co > (\({\mu }_{m}\))G4-V. Obviously, this trend is influenced by the atomic weight and density of the doping elements (Zr, Co, Ni, and V). Heavier elements are known to be better photon absorbers due to their higher density and atomic number per unit mass. Consequently, the photon absorption capacity of the glass system is improved by doping with heavy atomic species.

Fig. 1
figure 1

Mass attenuation coefficient as a function of photon energy E of the investigated glasses

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The consequence of the chemical composition on the two major interaction modes is made apparent in the photon interaction-induced effective atomic number \({Z}_{eff}\). Variations in the value of \({Z}_{eff}\) with regard to photon energy for the glasses are portrayed in Fig. 2. The \({Z}_{eff}\) spectra of the four glasses look similar: decreasing as E increases for each glass. This change is similar to that of mass attenuation coefficient of the glasses as predicted by PEAC and CSAC dependence on E. The PEAC depends on the 4th power of \({Z}_{eff}\); hence, the glass with higher cross sections for these interaction process possesses the highest effective atomic number. The range of \({Z}_{eff}\) of the glasses was 7.189–17.88, 7.182–16.242, 7.185–16.353, and 7.171–15.869 for G1-Zr, G2-Co, G3-Ni, and G4-V, respectively, for the considered energy spectrum. Similar to \({\mu }_{m}\), the value and range of the effective atomic number are strongly influenced by the atomic number of the dopant atomic number [25]. The similar trend in the value of \({Z}_{eff}\) and \({\mu }_{m}\) implies that either parameters could be used to characterize the relative photon absorption capacity of the glasses.

Fig. 2
figure 2

Variation of Zeff with E for the investigated glasses

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The mean free path (MFP) of photon is the mean distance moved by a photon between interactions. It is a parameter that can also be used to compare photon absorption in different interacting media. Similar to other photon interaction parameters, MFP is energy dependent; its energy dependence for the investigated glass is shown in Fig. 3. The figure also shows the dopant atom dependence on the MFP. The MFP increases with energy; higher energy photons interact less with absorber due to dwindling photon interaction cross sections. At lower energies, MFP is lower for the higher \({Z}_{eff}\) glasses; however, as energy increases, the effect is reversed. The dominance of the CSAC is responsible for this reversed behavior. The CSAC depends on the number of electron per unit mass, a quantity which decreases with \({Z}_{eff}\). The HVL is a useful parameter which is always used to compare the photon shielding capacity of different absorbers. It defines the thickness of the glass material required to reduce photon intensity by 50%. The variation of HVL of the glasses with energy relative to those of ordinary concrete (OC) [31] and a commercial glass shields (RS-360 and RS-253-G18) [32] at 662 keV is depicted in Fig. 4. Based on the HVL value at 662 keV, it is clear that the present glasses are better photon absorbers than OC and RS-253-G18 glass shield.

Fig. 3
figure 3

Effect of dopant atom on the MFP of the glasses at different photon energy

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Fig. 4
figure 4

Comparison of HVL of the glasses with some commercial shielding materials

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Fast neutron macroscopic removal cross section ( \({FNRCS, \Sigma }_{R}\) )

The values of calculated \({\Sigma }_{R}\) of the glasses are depicted pictorially in Fig. 5a. The \({\Sigma }_{R}\) values varied from 0.1006 to 0.105 cm−1 for the glasses. There is a gradual growth in the FNRCS of the glasses which seems to be in consonance with the quantity of the partial \({\Sigma }_{R}\) of Li and B atoms (Fig. 5b). As the dopant atomic species changes, it alters the atomic distribution of the chemical composition of the glasses. These alterations result in the increase in the partial density and \({\Sigma }_{R}\) of the two mentioned atoms; their relatively higher fast neutron mass removal cross sections buttress this point. These two atomic species thermalize fast neutron via elastic interaction with the fast neutrons better than the other atoms in the glasses. Hence, the observed trend in the fast neutron moderating capacity of the glasses is as dictated by the Li and B weight content of the glasses. The value of \({\Sigma }_{R}\) for the glasses revealed that G4-V is a better fast neutron absorber among the investigated glasses. Comparing the \({\Sigma }_{R}\) of the present glasses with those of recently studied glasses (S30 (0.0506 cm−1) and TVM60 (0.1055 cm−1) [22, 33], graphite (FNRC = 0.077 cm−1), and OC (FNRC = 0.094 cm−1) [31], it is obvious that the fast neutron absorbing capacity of the G4-V glass is comparable to that of TVM60 but superior to those of OC, S30, and graphite.

Fig. 5
figure 5

a FNRCS and b total and partial \({\Sigma }_{R}\) of the investigated glasses

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Elastic moduli

The coordination number per cation (nf), crosslink density per cation (nc), stretching force constant (F), and ionic radius (r) of the oxides B2O3, Li2O3, Na2O, CaO, Al2O3, SrO, TeO2, ZrO2, CoO, NiO, and V2O5 are listed in Table 2. The values of total number of cationic per glass formula unit (η), average stretching force constant (\(\overline{F}\)), average crosslink density (\(\overline{n}_{c}\)), average bond length (l), and number of network bond per unit volume (nb) for each glass sample were calculated and tabulated in Table 3. The elastic moduli (bulk (KB-C), shear (SB-C), longitudinal (LB-C), Young’s (EB-C)), and Poisson’s ratio (σB-C) of BTLBB-glasses are evaluated and gathered in Table 3 and plotted as in Fig. 6. Results revealed that the elastic properties of the investigated glasses were slightly changed with changing the doping in the network structure. The calculated values of (KB-C) were varied from 85.939 GPa for G1-Zr glass sample to 89.151 GPa for G3-Ni, (EB-C) were varied from 106.919 GPa for G1-Zr glass sample to 110.915 GPa for G3-Ni sample, (LB-C) were varied from 140.943 GPa G1-Zr glass sample to 145.463 GPa for G3-Ni sample, and (SB-C) were changed from 41.356 GPa G1-Zr glass sample to 42.902 GPa for G3-Ni sample. These observations concluded that the G1-Zr glass sample has minimum elastic moduli values, but G3-Ni sample has the maximum values.

Fig. 6
figure 6

B-C model elastic moduli of the investigated glasses

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Figure 7 depicts the variation of Poisson’s ratio (σB-C) and the average bond length (l) of the investigated glasses. The values of (σB-C) were fixed around 0.292, while the values of (l) were 0.465 (G1-Zr), 0.460 (G2-Co and G3-Ni), and 0.461 (G4-V).

Fig. 7
figure 7

Variation of Poisson’s ratio and average bond length of the investigated glasses

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Conclusion

This study presents a glass system with the following formula: 56B2O3-25Li2O3-10Na2O-5CaO-2Al2O3-2SrO-0.5TeO2-1X wt%: X = ZrO2 (G1-Zr), CoO (G2-Co), NiO (G3-Ni), and V2O5 (G4-V). The photon attenuation parameters were calculated for typical photon energy sources used in medical and research applications of photons. Indeed, the mechanical properties of glasses were examined. Results revealed that the maximum value of the mass attenuation coefficient of 2.356, 2.049, 2.073, and 1.958 cm2/g for G1-Zr, G2-Co, G3-Ni, and G4-V, respectively, was obtained at the least energy of 22 keV. The smallest value of \({\mu }_{m}\) was obtained at 1.33 MeV with corresponding value of 0.054 cm2/g for the four glasses. The range of \({Z}_{eff}\) of the glasses was 7.189–17.88, 7.182–16.242, 7.185–16.353, and 7.171–15.869 for G1-Zr, G2-Co, G3-Ni, and G4-V, respectively, for the considered energy spectrum. Based on the HVL value at 662 keV, it is clear that the present glasses are better photon absorbers than OC and RS-253-G18 glass shield. The value of \({\Sigma }_{R}\) for the glasses revealed that G4-V is a better fast neutron absorber among the investigated glasses. The G1-Zr glass sample has a minimum elastic moduli values, but G3-Ni sample has the maximum values. Generally, the investigated glasses can be used as appropriate materials for gamma-ray shielding applications.