Introduction

It is possible to upgrade the network properties of boro-tellurite glasses by using rare-earth (RE) oxides as dopants. Tellurite glasses are ideal hosts for RE oxides having widespread application in optical amplifiers due to transparency, low phonon energies, third-order nonlinear susceptibility, and high atomic number of tellurium (Barbosa et al. 2021; Elkholy et al. 2019; Elkholy 2002; Klimesz et al. 2017; Vani et al. 2021). Fabrication of glasses containing TeO2 in our previous work resulted in improved transparency, along with increment in density values up to 5.087 gcm−3 (D’Souza et al. 2023). The tellurite glasses are also comprised of remarkable radiation shielding capacity compared to the borosilicate glasses. Density of heavy metal oxide (HMO) tellurite glass network can be further elevated with RE oxide doping, accompanied by efficient emission and absorption properties of electromagnetic radiation in wide range of wavelength (Vani et al. 2021). El-Mallawany and Sayyed (2017) reported excellent gamma shielding parameters for tellurite glasses containing RE oxides such as La2O3, CeO2, Er2O3, and Sm2O3, the values of which were in close resemblance with ordinary, basalt-magnetite and Ilmenite concrete (El-Mallawany and Sayyed 2017). Erbium-doped zinc tellurite glasses were found suitable for radiation blocking performance in medical diagnostic field at low gamma energy 60 keV and were reported to be good replacement for ordinary concrete (Tijani et al. 2018). Among RE, the Eu3+ ions have shown substantial increase in density, elastic modulus, thermal stability and red/blue luminescence emission (Adamu et al. 2022; Danmallam et al. 2021; Klimesz et al. 2017b). However, very few reports on the radiation shielding effect of europium-doped bismuth boro-tellurite glasses for high radiation photons are available. In the existing literature, the radiation shielding glasses with Eu3+ modifiers are limited to low-energy photons up to 3 MeV (Jagannath et al. 2021; Rammah et al. 2021; Saudi et al. 2020; Teresa et al. 2021), and in this energy range, a significant enhancement in linear attenuation coefficient and reduction in half-value layer with the europium content were observed. Hegde et al. 2022 reported improved shielding behavior for 5 mol% Eu3+-doped 40Bi2O3–50B2O3–10ZnO glass (Hegde et al. 2022) for 0.296–1.458 MeV photons. Recently, an article reported the mass attenuation coefficient (MAC) values for 0.015–15 MeV energy spectrum. The MAC at 0.015 MeV existed between 40.627 and 41.325 cm2/g for Eu2O3 increment from 0 to 1 mol% and nearly constant value of 0.033 cm2/g at 15 MeV (Alsaif et al. 2024). The increment in fast neutron removal cross section (FNR) with europium doping was confirmed too (Alsaif et al. 2024). There are no investigations done so far on the photon buildup factors considering the broad beam geometry and non-monochromatic gamma rays being incident on Eu3+-doped glasses.

Eu2O3-doped glasses have been explored for applications in the field of optoelectronic communication and electrochemical devices (Teresa et al. 2021). Eu3+ ion doping to bismuth telluro-borate glasses exhibits remarkable optical features like near UV light and blue light absorption and luminescence in reddish-orange spectral region (Hegde et al. 2022). Glasses with Eu2O3 and Bi2O3 combination have exhibited good performance as reflecting windows, photonic devices, thermal and mechanical sensors (Saudi et al. 2020). There are many reports of increased polarizability, refractive index, optical basicity and reflection loss due to Eu2O3 incorporation in the glass network.

Keeping the enhanced optical features of Eu3+-doped glasses in mind, the current research is intended to explain the possibility of improvement in radiation shielding property as well, due to Eu3+ ion incorporation in the network. Henceforth, this article displays the physical, structural properties, UV–visible–NIR absorption features along with mechanical properties for Eu3+-doped HMO telluro-borate glasses. Further, the radiation shielding effect is also studied in terms of MAC, LAC, HVL, mean free path, effective atomic number—Zeff, and buildup factors in 0.015 to 15 MeV photon energy region using Phy-X/PSD simulation program. The FNR values were computed using the relations from Ref. (Al et al. 2020).

Experiments and methods

Melt quench technique which is a conventional glass synthesis method was employed to prepare the glass matrix 12B2O3–16SiO2–xEu2O3–(40-x) TeO2–12Bi2O3–12ZnO–8BaO with Eu2O3 mol%, x = 0, 1, 2, 3, 4 mol%. This method involves weighing of constituent chemical powders as per the batch calculations, grinding and mixing them thoroughly in agate mortar and pestle to get a homogenous mixture. The mixture was collected in alumina crucible and melted in a muffle furnace maintained at 1100 °C for three hours. The melt was poured on a pre-heated brass slab to get coin shaped glass samples. To remove the stress developed on the sample, they are maintained at 300 °C for two hours. The prepared samples were polished with the help of Bainpol Polishing machine using abrasive sheets of different grain sizes to get glasses of desired shape and size. The molar composition of the prepared glasses can be seen in Table 1. Density measurement for these glasses was done taking distilled water for immersion using electric balance (Contech) based on Archimedes principle (Prabhu et al. 2019). XRD graphs were recorded with X-ray Diffractometer (Rigaku Miniflex 600, 40 kV and 15 mA), having Cu-Kα target with 2θ = 10–90°, θ being the Bragg’s angle. Recording of SEM images with EDAX measurement was done with Carl Zeiss FESEM instrument. Refractive index was determined using Abbe’s refractometer of Labman make. UV–Vis–NIR spectrometer (PerkinElmer Lambda 750S) was used for recording optical absorption spectra in 250–2500 nm region with resolution of 1 nm. Vibrational spectra were recorded with JASCO FTIR Spectrometer (Model: FT/IR 6300) in 400–4000 cm−1 region. Photon shielding and dosimetry (Phy-X/PSD) program provided gamma shielding parameters, namely LAC, MAC, Zeff, HVL, MFP, Zeq and photon buildup factors of the synthesized glasses for photons of 0.015–15 MeV energy using information such as density, glass composition and radio-isotopes given as inputs (Şakar et al. 2020).

Table 1 Molar composition of the synthesized Eu3+-doped glasses
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Results and discussion

Physical and structural properties

Physical parameters

The synthesized BiTeEu glasses are displayed in Fig. 1 and are seen to exhibit good transparency which is one of the best qualities of the tellurite glasses. To explore the physical and structural changes modifications undergone in a tellurium borosilicate glass because of Eu2O3 doping, various quantities like density (\(\rho\)), molar volume (VM), number of RE ions (NEu), inter-ionic distance ri, polaron radius rp, field strength Fs and oxygen packing density (OPD) were determined. With the help of experimentally measured density values, the following relations (Ahlawat et al. 2023) are used to calculate other parameters;

$$N_{{{\text{Eu}}}} = \frac{{x N_{A} \rho }}{M}$$
(1)
$$d_{B - B} = \left( {\frac{{V_{M}^{B} }}{{N_{A} }}} \right)^{1/3}$$
(2)

where \(V_{M}^{B} = \frac{{V_{M} }}{{2\left( {1 - X_{B} } \right)}}\) is volume per mole of boron atoms.

$$r_{p} = \left( \frac{1}{2} \right)\left( {\frac{\pi }{{6N_{{{\text{Eu}}}} }}} \right)^{1/3}$$
(3)
$$r_{i \, } = \left( {\frac{1}{{N_{{{\text{Eu}}}} }}} \right)^{1/3}$$
(4)
$$F_{s} = \frac{Z}{{r_{p}^{2} }}$$
(5)
$${\text{OPD}} = \frac{\rho }{M}{\text{N}}_{{\text{O}}}^{2 - }$$
(6)
Fig. 1
figure 1

Pictures of synthesized BiTeEu glass samples

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Here, NA is the Avogadro number, XB is the molar fraction of B2O3, Z is the atomic number of europium, and \({\text{N}}_{{\text{O}}}^{2 - }\) is the oxide ion number, respectively (Ahlawat et al. 2023; Pavani et al. 2011). The values of the calculated physical parameters are listed in Table 2. From the table, we noted that the density of the concerned glass matrix increased on successive doping of Eu3+ ions. This is mainly because of the replacement of tellurium atoms having low atomic weight by europium atoms having high atomic weight. Moreover, the ionic radius of Eu3+ ions (1.02 Å) is very close to Te4+ and Bi3+ ions (0.99 and 1.03 Å, respectively), which also justifies the density increase in the glass matrix. On the other hand, molar volume increased with the increase in Eu3+ content. Due to high molecular weight, the Eu2O3 molecules are most likely to fill the interstitial sites of the glass network and hence acts as network modifier. This also leads to improved density due to network formation around Eu3+ ions (Wagh et al. 2018). Decreasing values of molar volume indicate that the bond length is decreasing along with inter-atomic distance, which results in increase in compactness of the glass. When Eu3+ ions enter the glass network, the borate and tellurite bonds start breaking, leading to creation of bridging oxygens. Such bridging oxygen generation accompanied by compact structure results in highly rigid glass network (Bulus et al. 2019; Monisha et al. 2021; Wagh et al. 2018). The modifier role of Eu3+ ions can also be confirmed from average boron–boron separation values, where progressively decreasing < dB-B > values with increasing Eu2O3 content suggests compaction of the network, again leading to density increase.

Table 2 Physical parameters calculated for BiTeEu glass samples
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Table 2 shows reduction in polaron radius values for consecutive doping of Eu3+ ions, which can be associated with increasing concentration of europium ions, which also enhances the field strength around the RE ions as evident from the Fs values in Table 2. There is also a possibility that the RE ions are located between the layers, resulting in decreased average oxygen-RE distance. Due to this, the bond strength of Eu–O bonds enhanced, creating Eu3+ ions of greater field strength around them. One more physical quantity called oxygen packing density (OPD) gives a measurement of tightness of oxygen packing in the glass network. From Table 2, we see that OPD decreased on Eu2O3 substitution, implying more lose packing of oxide network. All these changes introduced by doping Eu3+ ions in the glass network were in accordance with the changes found in many Eu3+-doped glasses found in the literature (Hegde et al. 2022)

SEM/EDAX

The surface morphology of Eu3+-doped tellurium borosilicate glass BiTeEu-2 was examined with the help of SEM image displayed in Fig. 2a. The occurrence of smooth, homogenous texture in the SEM micrograph without any cluster of unresolved particles, proved amorphous character of the present glasses. The compositional analysis of BiTeEu-2 glass was performed using EDAX measurement, which provided a spectrum (Fig. 2a) containing properly distributed elements such as B, O, Si, Eu, Te, Bi, Ba and Zn. It also detected aluminum (Al) in the glass composition because of the alumina crucible used during glass melting process. A bar chart representing weight% of all the constituent elements in Fig. 2b exhibited highest weight% for bismuth element as expected. This is because Bi element with highest atomic number has more probability of detection compared to other elements (Titus et al. 2019).

Fig. 2
figure 2

a SEM micrograph, EDAX spectrum and b bar chart representing weight % of elements present in BiTeEu-2 glass

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XRD patterns

XRD profiles of BiTeEu glasses are stacked in Fig. 3a, and it can be noted that there are no sharp peaks present in the spectra confirming the non-crystalline nature of the glasses synthesized. Broad humps observed in all the spectra in 20–65° region were due to structural disorder of the amorphous glass network.

Fig. 3
figure 3

a XRD profiles and b FTIR absorption data of BiTeEu glasses

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FTIR analysis

Structural vibrational units existing in BiTeEu glass network were examined using FTIR measurement in the spectral range 400–4000 cm−1 and are presented in Fig. 3b. The vibrational bands occurring in 400–600 cm−1 indicate the presence of heavy metal oxides or metal oxides (Mariyappan et al. 2018). The absorption peaks observed in 410–470 cm−1 range signify the vibrations of Te–O–Te linkages and Bi–O bond formation in BiO6 units (Kundu et al. 2014; Mariyappan et al. 2018; Naseer et al. 2021; Saudi 2018; Tasheva and Dimitrov 2017). The bands in 600–800 cm−1 region belong to Bi–O or Te–O bonds in TeO3 or BiO3 structural units (Bachvarova-Nedelcheva et al. 2019a, b; Mansour et al. 2021). The structural units of borosilicate network are mainly present in two spectral regions. One is 800–1200 cm−1 region corresponding to stretching vibrations of B–O and Si–O bonds in tetrahedral BO4 units and SiO4. Other one is 1200–1550 cm−1 region corresponding to asymmetric stretch of B–O bonds in BO3 units (Ananthalakshmi et al. 2019; Hordieiev and Zaichuk 2023; Madhu and Srinatha 2020). The band positions along with band assignments are listed in Table 3. A small shift observed in band positions on adding Eu2O3 designated the structural modifications done by Eu3+ ions by changing the bond strength and length (Hegde et al. 2019). The O–H group vibration at non-bridging oxygen (NBO) sites and hydrogen bonding were verified by the presence of bands centered around 2350 cm−1 and 2608 cm−1, respectively. 2350 cm−1 band intensity was found to increase with the addition of Eu3+ ions. The presence of water content in glass structure was signified by the occurrence of 3200–3600 cm−1 bands (Mariyappan et al. 2018). On adding Eu2O3 to the host glass, the intensity of this band decreased showing less water absorption.

Table 3 Band assignments for the bands present in FTIR spectra for BiTeEu glasses
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Modifier oxides added to tellurite glass network have the ability to alter the number of TeO4 and TeO3 units by generating NBOs. Such property of Eu2O3 in the present glass matrix can be examined by deconvoluting the FTIR spectra corresponding to tellurite network in the 600–800 cm−1 region. The bands in 620–670 cm−1 region characterized the TeO4 units and the bands in 700–780 cm−1 region were attributed to stretching modes of TeO3 units containing NBOs (Bachvarova-Nedelcheva et al. 2019a, b). Figure 4 gives a representative example for deconvolution performed on spectra of BiTeEu-1 and BiTeEu-4 glass samples. On adding Eu2O3, the band intensity of TeO4 units decreased accompanied by increasing band intensity of TeO3 units (Bachvarova-Nedelcheva et al. 2019a, b). The ratio of relative area of TeO4 and TeO3 units for each glass was calculated and is presented in Table 4, which discloses the fact that above 2 mol% concentration of Eu2O3, the TeO4/TeO3 ratio suddenly drops indicating that a greater number of TeO4 units converted to TeO3 units and were linked to the creation of NBOs. This confirmed the cleavage of Te–O–Te bridges in TeO4 units, converting them to TeO3 units through intermediate polyhedral TeO3+1 unit under the influence of Eu3+ ions (Bachvarova-Nedelcheva et al. 2019a, b). From Table 4, it was clear that BiTeEu-4 produced the lowest TeO4/TeO3 ratio suggesting the creation of more NBOs.

Fig. 4
figure 4

Deconvoluted FTIR spectra for BiTeEu-1 and BiTeEu-4 glasses in spectral region containing TeO3 and TeO4 units

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Table 4 TeO4/TeO3 ratio for BiTeEu glasses
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Incorporation of Eu2O3 in the glass matrix can modify the borosilicate glass network by altering the number of BO4 and BO3 units which in turn influence the quantity of NBO created in the network. The knowledge of such modification in BO is also necessary to understand the mechanical properties of Eu3+-doped glasses. One of the necessary tools to get this information is deconvolution of the FTIR absorption spectra corresponding to borosilicate network (800–1600 cm−1). Figure 5 shows deconvoluted spectra for BiTeEu-0 and BiTeEu-3 glasses taken as example. With the help of relative areas of resolved bands, the fraction of BO3 (N3) and BO4 (N4) units can be estimated (Gautam et al. 2012). Table 5 gives a clear picture of variation of N3 with Eu2O3 concentration. The increase in N3 value with initial addition of Eu2O3 reflected the role of Eu3+ ions in the formation of BO3 units, resulting in the increasing NBOs by breaking the BO4 units (Hegde et al. 2017). Also, we note that BiTeEu-3 glass had the highest N3 value and hence can be considered to have more defect centers.

Fig. 5
figure 5

Deconvoluted FTIR curves in spectral region corresponding to borosilicate network

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Table 5 N3 and N4 ratio for Eu3+ doped glasses
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Both Tables 4 and 5 show that for initial addition of Eu2O3, there was increase in number of NBO in the glass network due to breakage of borate and tellurite bonds. But for next higher concentration of Eu2O3, the NBO number decreased and the bridging oxygen (BO) number exceeded. This increase and decrease in NBO further continued for higher Eu3+ concentration too. Such irregularity was due to the difference in ionic radii of Eu3+ (1.3 Å) which is larger than Te4+ ion (0.97 Å). Higher concentration of Eu2O3 caused decrement in NBO corresponding to rising BO number. In this situation, the modifier Eu3+ ions broke the local tellurite bond symmetry and filled the interstitial spaces producing strong Eu–O covalent bonds (Nazrin et al. 2018).

Optical properties

Optical parameters

Different parameters governing the optical parameters of Eu3+-added bismuth tellurium borosilicate glasses such as refractive index (n), dielectric constant (ε), molar refractivity (Rm), reflectance loss R in % (Salem et al. 2012), molar electron polarizability αm and optical basicity \(\Lambda\) were determined by the following set of relations (Divina et al. 2020; Rammah et al. 2021):

$$\varepsilon = n^{2}$$
(7)

Lorentz–Lorenz equation (Dimitrov and Sakka 1996),

$$R_{m} = \left( {\frac{{n^{2} - 1}}{{n^{2} + 2}}} \right)V_{m}$$
(8)
$$R = \left( {\frac{{n^{2} - 1}}{{n^{2} + 2}}} \right) \%$$
(9)
$$\alpha_{m} = \frac{3}{{4\pi N_{A} }}\,\,\,R_{m} = \frac{{R_{m} }}{2.52}$$
(10)

Duffy–Ingram relation (Mansour et al. 2021),

$$\Lambda = 1.67\left( {1 - \frac{1}{{\alpha_{{{\text{O}}^{2 - } }} }}} \right)$$
(11)

The optical parameter values calculated are shown in Table 6. The increasing refractive index values with the increased doping of Eu3+ ions were accompanied by increasing dielectric constant, molar refraction and molar electron polarizability. Therefore, it is worth mentioning that refractive index depends not only on the density but also on polarizability of the glass. Another quantity called optical basicity in a glass is associated with the electron donating ability of oxygen atom. Oxides of high electron density are more basic in nature with weak chemical hardness. Basicity values calculated as per Duffy’s relation show increasing trend with the successive Eu2O3 addition.

Table 6 Different optical parameters along with optical band gap, Urbach energy and cutoff wavelength of BiTeEu glasses
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UV–visible–NIR absorption

The absorption spectra of BiTeEu glass samples were recorded in UV–visible–NIR region (200–2500 nm) and are shown in Fig. 6. Only few absorption bands are found in visible to near-infrared region because of strong absorption of UV light by the host glass. The observed absorption peaks are associated with 4f-4f electronic transitions occurring from 7F0 ground state and 7F1 first excited state to next excited states 5L6, 5D2 and 7F6. Five prominent peaks observed in the absorption spectra can be interpreted as follows:

  • The peak at λ \(\sim\) 393 nm corresponds to 7F0 \(\to\) 5L6 transition and arises only in Eu3+-doped glasses. This absorption band is forbidden by L and S selection rule, but allowed by selection rule for J (Kawano et al. 2022).

  • The peak at λ \(\sim\) 460 nm due to hypersensitive transition 7F0 \(\to\) 5D2 is an electric dipole-allowed transition, whereas a broad and less intense peak at λ \(\sim\) 500 nm can be assigned to 3P1 \(\to\) 1S0 transition of Bi3+ ion (Peng et al. 2009).

  • Two more bands appear at λ \(\sim\) 2083 nm and λ \(\sim\) 2200 nm in NIR region due to 7F0 \(\to\) 7F6 and 7F1 \(\to\) 7F6 transitions, respectively (Teresa et al. 2021).

Fig. 6
figure 6

Optical absorption spectra of BiTeEu glasses in a UV–visible and b NIR region

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The intensity of absorption increases with the increase in Eu3+ concentration in both the regions of the spectra as shown in Fig. 6. The shift in absorption edges is represented by cutoff wavelength (λc) in Table 6. It was also observed that as the Eu3+ concentration increased, a blueshift was seen in the absorption edges, which is also clear from cutoff wavelength values listed in Table 7. With the help of David–Mott relation (Mariselvam et al. 2019), the optical band gap values Eg were calculated,

$$\alpha \left( \upsilon \right) = \frac{{B\left( {h\upsilon - E_{g} } \right)^{n} }}{h\upsilon }$$
(12)

where \(\alpha \left( \upsilon \right)\) is the coefficient of absorption, also given by \(\alpha \left( \upsilon \right)\) = 2.303A/t, A is the absorbance, t is the thickness of the sample material, B is the band tailing parameter, and the exponent n depends on the kind of electronic transition mechanism. By taking n = 2, we consider that the transitions are indirect in nature because we are dealing with amorphous material. Hence, the linear part of \(\left( {\alpha h\upsilon } \right)\) 1/2 versus \(h\upsilon\) plots (also called Tauc’s plots) was extrapolated (Fig. 7a) to zero absorption to calculate the indirect band gap (Eg) as mentioned in Table 6. The parameter measuring the extend of band tailing is called Urbach energy \(\Delta E\) which gives the measure of disorder in the concerned material. The slope of linear part of ln(α) vs \(h\upsilon\) plots (Fig. 7b) was determined, and the reciprocal of slope is equal to \(\Delta E\) and is tabulated in Table 6.

Table 7 Characteristic temperatures from DTA curves and parameters governing thermal stability of the BiTeEu glasses
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Fig. 7
figure 7

Tauc’s plots of BiTeEu samples to determine the optical band gap and ln(α) vs hʋ graph of BiTeEu-1 to determine Urbach energy

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The shift in the edge of the absorption spectra due to the modifier ions is affected by the nature of oxygen bonding in the network. Table 6 depicts the irregular changes in cutoff wavelength which is due to the fluctuation of bridging and NBOs as discussed in FTIR analysis (Section “FTIR analysis”) (Nazrin et al. 2018). The defects created in the glass network due to non-bonded and exposed bonds will give unpredictable results when light interacts with matter. There exist larger optical band gap for regular glass network and narrower band gap for irregular network (Kilic et al. 2022). We observed absurd variation in Eg values also as shown in Table 6 because of the structural phenomenon of Eu3+ ions creating NBO initially and BO in latter stage. The glasses under investigation exhibit maximum band gap (3.243 eV) for BiTeEu-2 glass, while minimum gap for undoped BiTeEu-0 glass. As per this result, the BiTeEu-2 sample contains most regular glass network. Overall, the higher band gap values confirm the insulating character of synthesized glasses. The Urbach energy for the present glasses (Table 6) was estimated to be in 0.2–0.4 eV range, which is coherent with the values found in other reports (Pavani et al. 2011). Small \(\Delta E\) correspond to greater structural stability of the glass network.

Thermal studies

Differential thermal analysis (DTA) was done for BiTeEu-0, 2 and 4 glasses by heating the samples from room temperature to 900 °C and is depicted in Fig. 8. The endotherms present in 550–600 °C were taken as glass transition temperature Tg which is a characteristic nature of glasses. The Tx, Tc and Tm for the selected glasses were marked on the DTA plots (Fig. 8) in accordance with the endothermic and exothermic peak positions. These characteristic temperatures are mentioned in Table 7.

Fig. 8
figure 8

DTA curves of BiTeHost, BiTeEu-2 and 4 glass samples in the temperature range of 350–800 °C

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The thermal stability and ability of glass formation of a glass is usually assessed by calculating the parameter \(\Delta T = T_{x} - T_{g}\) which should be above 100 °C for a material to have good thermal stability. Here, all the three glasses produced \(\Delta T >\) 100 °C and hence are thermally stable glasses. The synthesized glasses also satisfy Kauzmann’s rule with \(\frac{{T_{g} }}{{T_{m} }}\) value lying around 0.67 (Table 6) indicating proper glass forming ability. Other parameters used to check the thermal stability of the glasses are as follows (Wagh et al. 2015):

$${\text{Weinberg parameter}},W = \frac{{\left( {T_{x} - T_{g} } \right)}}{{T_{m} }}$$
(13)
$${\text{Lu and Liu parameter}},\,\,L = \frac{{T_{x} }}{{\left( {T_{g} + T_{m} } \right)}}$$
(14)
$${\text{Saad and Poulain}}^{\prime } {\text{s}}\,{\text{glass stability}},\,S = \frac{{\left( {T_{x} - T_{g} } \right)\left( {T_{c} - T_{x} } \right)}}{{T_{g} }}$$
(15)

The calculated values are listed in Table 7, and they all confirm the fabrication of thermally stable glasses in this work.

Mechanical properties

Understanding the elastic and mechanical nature of Eu2O3-doped HMO tellurite glasses is essential because glasses with poor mechanical strength are of no use in certain applications. Makishima and Mackenzie (MM) model (Prabhu et al. 2019) is based on composition, dissociation energy per unit volume Gt, and packing density Vt is usually recommended for computation of theoretical elastic moduli for glasses. The details of calculation can be referred from reference article (Prabhu et al. 2019). Young’s (Y), bulk (K) and shear modulus (S) along with Poisson ratio (\(\vartheta\)) calculated for current glasses using Eqs. (16) to (19) are noted in Table 8. The relations in following equations are referred from Ref. (Makishima and Mackenzie 1975).

$$Y = 2G_{t} \,V_{t}$$
(16)
$$K = 1.2\,V_{t} \,Y$$
(17)
$$S = \frac{3YK}{{9K - Y}}$$
(18)
$$\vartheta = { }\frac{Y}{2S} - 1$$
(19)
Table 8 Elastic constants of BiTeEu glass series
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The results show that Y, K, S and \(\vartheta\) values lie between 25.049 and 26.142 GPa, 18.252 and 15.740 GPa, 9.852 and 10.685 GPa and 0.271 and 0.2232, respectively. Danmallam et al. (2021) suggested that Poisson’s ratio between 0.1 and 0.2 indicates strong cross-linking in glass network. Therefore, the current Eu3+-doped glasses are said to possess strong cross-link density in turn having enhanced chemical durability. The elastic moduli increased continuously with successive Eu3+ doping, and this can be associated with increasing Gt and density values, resulting in compact glass structure accompanied by enhanced network rigidity (Sayyed et al. 2018).

Microhardness (H) of the prepared Eu3+-doped glasses which signifies their penetration resistance was determined by Vickers micro-indentation measurement using different loads ranging from 50 to 1000 gF (0.49 to 9.8 N). The obtained H values plotted against applied force are represented in Fig. 9, and the indentation images for 1000 gF are shown in Fig. 10. From the graph in Fig. 9, we see that as the load increased, the microhardness of the selected glasses increased drastically till 500 gF, also called reverse indentation size effect, and remains constant for further load application of 1000 gF. As the applied load increased, the indenter penetrated deeper into the glass surface and the reinforced surface atomic layer moved back, implying that the structure is able to withstand the rising internal strain without any disruptions for load up to 500 gF and later develops crack for 1000 gF of load. Indentation images in Fig. 10, showing slight concave nature at the indentation corners, are a proof for compaction of glass structure accompanied by storage of internal strain and elastic restoration at the indentation corners (Grabco et al. 2012). The variation of microhardness with Eu2O3 concentration was also studied, and it was found that with the addition of europium to the tellurite glass network, there was a hike in H values for each load. This can be explained by higher bond strength of Eu–O bond (557 kJ/mol) (Saudi et al. 2020) compared to that of Te–O bond (284 kJ/mol) (Dimitrov and Komatsu 2008). For further addition of Eu2O3, the H values fluctuate between 3.4 and 3.6 GPa with no proper trend followed.

Fig. 9
figure 9

Vickers microhardness for BiTeEu glasses at different applied loads

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Fig. 10
figure 10

Micro-indentation images in FESEM micrographs of BiTeEu-0,1,2,3 and 4 glass surfaces at 9.8 N load

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The fracture toughness Kc of the 1000 gF indented glasses was measured using indentation fracture method with the help of equation introduced by Anstis (1981):

$$K_{c} = \left( \frac{Y}{H} \right)^{1/2} \frac{F}{{L^{3/2} }}$$
(20)

where L is the half-crack length and F is the load applied in N. At least 10 indentations were taken for each polished sample surface for error minimization. L values were obtained from the FESEM images in Fig. 10, and they decreased with Eu2O3 concentration. As a result, the fracture toughness increased with Eu3+ doping owing to higher bond strength of Eu–O. Microhardness, half-crack length and the calculated fracture toughness values of the BiTeEu glass samples for 9.8 N load are shown in Table 9. Brittleness is an important factor to judge the strength of the fabricated glasses for practical application. Brittleness (B) of the selected glasses is calculated with the relation given by Lawn and Marshall (1979),

$$B = \frac{H}{{K_{c} }}$$
(21)
Table 9 Microhardness (H), half-crack length (L), fracture toughness (F) and brittleness (B) of the selected BiTe glass samples for 9.8 N load
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From Table 9, it can be seen that the glasses become less brittle as Eu2O3 is added and BiTeEu-4 produced lowest brittleness of 6.333 μm−1/2. This confirmed the suitability of BiTeEu-4 glass for commercial utilization.

Radiation shielding studies

MAC values for the BiTeEu glasses were determined in 0.015–15 MeV region with the help of PSD software (Şakar et al. 2020). A graph representing the effect of energy and Eu3+ doping on the MAC values is plotted and shown in Fig. 11a. All the glasses behaved in identical manner with maximum MAC at initial energy, and then, a rapid drop of values is till around 0.2 MeV, followed by slower drop of value till 10 MeV. There is a small rise in MAC for energy greater than 10 MeV. Rapid fall of MAC in lower energy region is contributed by absorption of photons by photoelectric effect (PE). Slow drop in MAC in intermediate energy region is ascribed to Compton scattering (CS) process. Occurrence of pair production (PP) process at high photon energy is the reason for small increase in MAC at the end of the spectrum. The discontinuities appearing around 0.035 and 0.1 MeV corresponded to K-shell edges of tellurium and bismuth elements (Saudi et al. 2020). Compositional dependency of MAC values observed in Fig. 11a implied that MAC increased with the increase in Eu2O3 concentration, visible clearly in the inset of Fig. 11a. Thus, BiTeEu-4 glass with highest attenuation capacity acts as a better glass shield. This is in correspondence with increase in density with Eu2O3 mol% because of the replacement of lighter TeO2 molecules by heavier Eu2O3 molecules as shown in Table 2. When compared with Eu3+-doped glasses reported in the literature, at 0.662 MeV the MAC of BiTeEu-4 is 0.0875 cm2/g and MAC of 40B2O3–10CaO–10SiO2–20Bi2O3–15Eu2O3 glass reported by Saudi et al. (2020) was just 0.0545 cm2/g. Therefore, highest MAC for 4 mol% Eu2O3 compared to 15 mol% Eu2O3 is a validation for getting improved shielding ability with limited rare-earth oxide content.

Fig. 11
figure 11

a Influence of photon energy on MAC, b Zeff values, c HVL in 0.015–15 MeV range for Eu3+-doped telluro-borosilicate glasses, and d MFP values of synthesized glasses at 0.662 MeV

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For a composite shielding material containing multiple elements in different proportions, a term called effective atomic number has been defined (Murty 1965). Zeff values generated by PSD for Eu3+-doped glasses are plotted in Fig. 11b. No pattern changes in Zeff values were observed for compositional variation, i.e., at lower energy range below 1 MeV, the Zeff of all the glasses decreased drastically. This is associated with dependence of photoelectric absorption with energy as E−3.5. Following this Compton scattering in 1–6 MeV region causes the constancy region. Increasing trend at the end of the spectrum is because of pair production process (Kaewjaeng et al. 2021). The K-absorption edges of Te and Eu elements at 0.035 and 0.1 MeV were present. Glasses with highest Eu2O3 content produced greatest Zeff values at each energy (Fig. 11c). Therefore, BiTeEu-4 glass with maximum Zeff in 36–60 range is the best radiation blocker among the Eu3+-added glasses under study.

The Phy-X/PSD (Kaur et al. 2016) estimated HVL and MFP using following relations:

$${\text{HVL}} = \frac{0.693}{\mu }$$
(22)
$$\user2{ }{\text{MFP}} = \frac{ 1}{\mu }$$
(23)

The effect of photon energy on HVL was analyzed using the plots in Fig. 11c. Lower HVL and MFP are favorable for radiation shielding because thinner shields would be sufficient to block high-energy radiation photons. In Fig. 11c, at low energy < 0.1 MeV, HVL exhibited a flat line with no compositional variation. Above 0.1 MeV, HVL continuously grew with increasing energy. For BiTeEu-4 glass, corresponding to energy increase from 0.662 to 1.33 MeV, the HVL amplified from 1.458 to 2.236 cm. This indicated high-energy photons require thicker materials for shielding purpose. Additionally, in terms of Eu2O3 content, HVL at 15 MeV decreased from 3.189 to 3.136 to 3.064 cm for BiTeEu-0, BiTeEu-2 and BiTeEu-4, respectively. The calculated HVL for the current glasses was lesser than reported values for europium glasses in studies (Jagannath et al. 2021; Saudi et al. 2020; Teresa et al. 2021). Hence, the BiTeEu-4 glass with minimum range of HVL possessed better attenuation property among the fabricated glasses.

The MFP followed same pattern as HVL. Figure 11d emphasizes the MFP values for different glass composition at 0.662 MeV. We observed clear drop in MFP values with the increasing Eu2O3 content, pointing out the importance of Eu2O3 compound in glasses. At 0.662 MeV, because of least MFP values, the present glasses attenuate low-energy photons better than photons of high energy. Because the glass with 5.4377 gcm−3 density yielded minimum MFP values for all energies, it can infer that BiTeEu-4 glass can perform well in stopping gamma rays of wide energy range. Similar dependency of MFP with Eu2O3 has been reported in the literature (Jagannath et al. 2021; Saudi et al. 2020; Teresa et al. 2021), where glasses with greatest Eu2O3 mol% generated least MFP.

Furthermore, the bar charts in Fig. 12 show a comparison of MAC, HVL and Zeff values of the optimized BiTeEu-4 glass belonging to the present BiTeEu glass system with the optimized ZBiB-12 and BiTe-40 glasses of previously investigated ZBiB and BiTe glass systems (D’Souza et al. 2022) at energies 0.662, 1.17, 1.33 and 15 MeV. It is observed in Fig. 12a that though MAC values saw a downfall after TeO2 addition, the doping of Eu2O3 raised the values again, reaching the level of ZBiB-12 glass, whereas BiTeEu-4 glass had the lowest HVL and highest Zeff at all the energies (Fig. 12b & c) compared to both ZBiB-12 and BiTe-40 glasses. Clearly, this indicates that the incorporation of TeO2 in BiTe and Eu2O3 in BiTeEu glass systems has added up to the increasing shielding effect in the glass matrix.

Fig. 12
figure 12

Bar charts representing comparison of a MAC b HVL and c Zeff values of ZBiB-12, BiTe-40 and BiTeEu-4 glass samples

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Beer–Lambert’s law is applicable for monochromatic rays, narrow beam geometry and thin shields (Elkholy et al. 2019). When one of these conditions (for example, broad beam geometry) is violated, the law takes a modified form “I = BI0 e−μx.” Here, B is the correction term called build up factor of photons (Yonphan et al. 2021). There are two kinds of buildup factors—exposure and energy absorption buildup factor (EBF and EABF). The steps to determine them are discussed in the literature (Harima et al. 2017). The Zeq for the investigated Eu3+-doped glasses determined from Phy-x/PSD software is represented in Fig. 13, where we can see that Zeq had maximum set of values for BiTeEu-4 glass and minimum for BiTeEu-0 glass. The intermediate energy region which is associated with CS process generated maximum Zeq where highest photon buildup was encountered.

Fig. 13
figure 13

Zeq values of BiTeEu glasses varying with the energy in the photon energy range of 0.015–15 MeV

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The graphs showing variation of EBF and EABF with photon energy are plotted (shown in Fig. 14). The three radiation interaction processes: PE, CS and PP occurring at low-, intermediate- and high-energy spectrum region, were responsible for the path followed by BF along photon energy spectrum. Photoelectric absorption of low-energy photons led to the removal of photons from incident beam, reducing the photon count which is the reason behind low photon buildup in the lower end of energy spectrum (Yonphan et al. 2021). The abrupt peaks existing in this region correspond to K-shell edges of Te and Bi elements. The mid-energy region which recorded maximum EBF and EABF for all the glasses is a contribution of CS process which lowers the energy of photons by multiple scattering, populating the medium with more low-energy photons (or photon buildup). Meanwhile, the electron–positron pair production in high-energy region takes out the photons from incident beam, decreasing the photon buildup in that region (Yonphan et al. 2021). However, when the interaction depth is high enough (> 5mfp), the electron–positron pairs without being able to escape undergo reaction to form photons, again leading to more photon buildup.

Fig. 14
figure 14

EBF and EABF values of selected BiTeEu glasses varying with photon energy in 0.015–15 MeV range

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At fixed energies of 0.015, 0.15, 1.5 and 15 MeV, the changes in EBF with penetration depth are shown in Fig. 15. The BFs were low for low interaction depths and increased quickly to reach maximum at 40 mfp. Only at 0.015 MeV, the maximum BF occurred at lower depth. Deeper inside the medium, the photons undergo more collisions resulting in a greater number of low-energy photons or high photon buildup. We do not consider lower penetration depths (< 5mfp) for BF investigation because of insignificant variability of BF in those distances. For depths above 5 mfp, the BF values show inverse proportionality with the Zeq, i.e., EBF of BiTeHost > BiTeEu-1 > BiTeEu-2 > BiTeEu-3 > BiTeEu-4 for incident energies 0.15 and 1.5 MeV. The photon buildup decreases with increasing Zeq, and BiTeEu-4 glass has the minimum photon buildup because almost all the photons are lost by the occurrence of CS in this energy. At 15 MeV, because of the predominance of PP process whose cross section varies as Zeq2, there was more photon buildup with the increase in Eu3+ concentration.

Fig. 15
figure 15

Variation of EBF values with penetration depths at 0.015, 0.15, 1.5 and 15 MeV photon energies

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It is possible to slow down the fast neutrons to thermal neutrons through inelastic and elastic scattering processes with the help of suitable attenuators. FNR (ΣR) is the term used to calculate such ability. For energies in 2–12 MeV region, the cross section of effective removal of neutron is almost same (Tellili et al. 2014). The FNR values (in cm−1) determined for BiTeEu glass compositions are plotted in Fig. 16, which also gives a comparison between previously investigated glasses as well as other shielding glasses found in the literature. It was found that Eu2O3 improved the neutron attenuation capacity because of the increasing FNR values with Eu2O3 substitution. Therefore, BiTeEu-4 glass had the highest FNR value of 0.10362 cm−1. Another observation says that BiTeEu glasses have ΣR values greater than BiTe-40 glass but lesser than ZBiB-12 glass. However, BiTeEu glasses exhibited higher FNRCS values than conventional concrete materials (Kurudirek 2017) and another Eu2O3-doped borate glass system studied by Almisned et al. (2021). Other glass systems such as lead borate (Kurudirek 2017) and 2.5 mol% doped Eu3+-doped bismuth borate glasses (Saudi et al. 2020) produced slightly higher FNR values but comparable with that of the present BiTeEu glass system.

Fig. 16
figure 16

FNR of BiTeEu glasses and other shielding materials found in the literature

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Conclusions

The Eu3+-doped HMO boro-tellurite glasses were successfully manufactured with traditional melt-quench method. The investigated physical, structural, and mechanical properties confirmed the positive role played by Eu2O3 by generating the greatest density value of 5.4377 gcm−3, maximum refractive index of 1.99, Vickers microhardness of 3.667 GPa (at 1000 gF load), improved fracture toughness of 0.579 MPa m1/2 and least brittle nature with B = 6.33 μm−1/2 for 4 mol% Eu2O3-added glass sample. BiTeEu-4 glass showed superiority in blocking both high- and low-energy gamma photons with MAC value of 63.878 cm2/g at 0.015 MeV and 0.0416 cm2/g at 15 MeV. Apart from this, the HVL thickness for attenuating the 15 MeV photons is mere 3.0647 cm. BiTeEu-4 glass had minimum photon buildup in Compton scattering region because of loss of photons by scattering. These results directed toward the conclusion that BiTeEu-4 glass is the best possible matrix for radiation shielding application. FNR value of 0.10362 cm−1 for BiTeEu-4 glass surpassed the other glasses under study.