1 Introduction

Kodama noticed that the stoichiometric ratio of a wide range of binary sodium borate glasses Na2B4O7 is established BO3 is transformed into BO4 [1,2,3,4]. At this ratio, Na2O surrounds the network, preventing the surrounding soft B2O3 from deforming [5,6,7,8,9,10,11,12]. SiO2 incorporated into alkali borate glasses improved their radiation and UV transmittance. As a result, alkali borosilicate glasses show promise for incorporating a variety of modifying oxides [13,14,15,16,17]. In technology, borosilicate glasses are extremely important. High-mechanical-stability household and laboratory glasses, as well as high-performance optical glasses, are some of their applications [15, 18,19,20].

Oxide glasses doped with transition metal ions (TMI) have recently attracted a lot of attention due to their appealing combination of physical and chemical characteristics. In recent years, TMI-doped borate, phosphate, silicate, and borosilicate glasses have been investigated physically, optically, and radiationally [21,22,23,24,25,26,27,28,29,30]. Glasses with semiconducting properties, such as Cr2O3, CdO, CuO, and others, are known as (TMO) glasses. There has been a lot of focus in recent years on borosilicate glasses containing various TMO, such as CoO, NiO, V2O5, and Cr2O3 [4, 31].

TMO-based glasses, such as Cr2O3, also have appealing optical properties, making them ideal for use as non-linear optical (NLO) materials. According to previous research, TMO-containing borosilicate glasses have a variety of intriguing physical, structural, radiation, and spectroscopic characteristics [16, 17, 32]. As a result of the above existing literature, we have expanded our investigations into TM in calcium borosilicate glasses. As a result, we’ve developed calcium borosilicate glasses in a variety of compositions with Cr2O3 substituted. The synthesized glasses are characterized using XRD, FT-IR, and UV–Vis–NIR spectroscopy. The optical of these glasses with the composition 65Na2B4O7–25SiO2–(10 − x) CaO–x Cr2O3, x = (0 ≤ x ≤ 5 mol.%) are investigated in this study. In addition to the aforementioned studies, photons, neutrons, characteristics of Cr3+ doped calcium borosilicate glasses will be investigated using theoretical code in this work.

2 Materials and methodology

Glasses with the following composition were formed using the traditional melt-quench procedure: 65Na2B4O7–25SiO2–10CaO, 65Na2B4O7–25SiO2–9CaO–1Cr2O3, 65Na2B4O7–25SiO2–8CaO–2Cr2O3, 65Na2B4O7–25SiO2–6CaO–4Cr2O3, 65Na2B4O7–25SiO2–5CaO–5Cr2O3. Starting materials for the fabrication of glasses included high purity (Aldrich) CaO (99.5%), Cr2O3 (99.9%), SiO2 (99.5%), and Na2B4O7 (99.5%). The mixtures were then homogenized using a magnetic stirrer for 10 min. Glass was melted at 1100 °C in a platinum crucible. A random error in the melting temperature is ±10 °C. The glasses were annealed at 375 °C for 2 h. To calculate densities in toluene, the Archimedes model was used. On a Perkin Elmer Frontier FT-IR measurements in the 400–1800 cm−1 range were obtained using the KBr procedure. A random error in the center of FT-IR bands was found as ± 2 cm−1. To establish a baseline and correct for noise, spectrum software was used. The optical description of these glasses was obtained in the wavelength range of 250–2500 nm by (JASCO V-670, Japan). The absorption coefficient (α), optical bandgap (\(E_{{{\text{opt}}{.}}}^{{{\text{indir}}}}\)), and refractive index (\(n_{{\text{D}}}\)) were all calculated using absorption spectra. As physical parameters related to optical energy, the following physical parameters were calculated: molar refractivity \(R_{{\text{m}}}\), molar polarizability \(\propto_{{\text{m}}}\), reflection loss \(R_{{\text{L}}}\), metallization \(M\), electronegativity \(\chi\), electron polarizability \(\propto^\circ\), optical basicity \(\wedge\), Bulk module (K) and glass transition temperature \(\left( {T_{{g\left( {thero.} \right)}} } \right){ }\):\(R_{{\text{m}}} = Vm\left( {1 - \sqrt {Eopt./20} } \right), \propto_{{\text{m}}} = \left( {\frac{3}{4\pi N}} \right)R_{{\text{m}}}\). \(R_{{\text{L}}} = \left( {\frac{{R_{{\text{m}}} }}{Vm}} \right)\) \(M = 1 - \frac{{R_{{\text{m}}} }}{Vm}\), \(\chi = 0.2688E_{{{\text{opt}}{.}}} \propto^\circ = - 0.9 \chi + 3.5\) and \(\wedge = - 0.5\chi + 1.7, K_{{{\text{th}}}} = - 478.93 + 200.13 E_{{{\text{opt}}{.}}}\), \(T_{{{\text{g}}\left( {{\text{thero}}{.}} \right)}} = - 701.87 + 403.33 E_{{{\text{opt}}{.}}}\) As physical parameters related to the refractive index \(n_{{\text{D}}}\), \(R_{m}\), \(\propto_{m}\), \(\propto_{0}^{2 - }\), and \(\Lambda\) were calculated: \(R_{m}\), \(\propto_{m}\), \(\propto_{0}^{2 - }\), and \(\Lambda .\) \(R_{{\text{m}}} = \left\langle {n^{2} - 1} \right.|n^{2} + \left. 2 \right\rangle Vm\), \(\propto_{{\text{m}}} \left( {3|4\pi N} \right)R_{{\text{m}}} , \propto_{0}^{2 - } = \frac{{[\frac{Vm}{{2.52}}\left( {\frac{{n^{2 } - 1}}{{n^{2} + 2}}} \right) - \sum \propto_{{{\text{cat}}}} ]}}{{N_{o}^{2 - } }}\), and \(\Lambda = 1.67\left( {1 - \frac{1}{{ \propto_{0}^{2 - } }}} \right)\).

Using the online version of the Phy-X/PSD software, the study’s goal was met by calculating all effective parameters that judge the prepared glasses shielding effectiveness [33]. Zeq predictable with \(eq = \frac{{{\text{Z}}1\left( {{\text{logR}}2 - {\text{logR}}} \right) + {\text{Z}}2\left( {{\text{logR}} - {\text{logR}}1} \right)}}{{{\text{logR}}2 - {\text{logR}}1}}\), The following parameters were calculated for G–P fitting: \(P = \frac{{{\text{P}}1\left( {{\text{logZ}}2 - {\text{logZeq}}} \right) + {\text{Z}}2\left( {{\text{logZeq}} - {\text{logZ}}1} \right)}}{{{\text{logZ}}2 - {\text{logZ}}1}},\) EABF and EBF were calculated using G–P fitting. \(B\left( {E,X} \right) = 1 + \frac{b - 1}{{K - 1}}\)\((K^{x} - 1)\) for \(K \ne 1\), \(B\left( {E,X} \right) = 1 + \left( {b - 1} \right)x\) \(K = 1\) where \(K\left( {E,X} \right) = cx^{a} + d\frac{{\tanh \left( {\frac{x}{Xk} - 2} \right) - \tanh \left( { - 2} \right)}}{{1 - \tanh \left( { - 2} \right)}}\) for x ≤ 40.[30] and [40]

3 Results and discussion

3.1 Physical examinations

Figure 1 depicts the XRD of the samples under investigation. XRD shows no sharp peaks in these samples have a significant level of glassiness [29, 34,35,36].

Fig. 1
figure 1

XRD of synthetic glasses

The density (\(\rho\)) and molar volume (\(V_{{\text{m}}}\)), are exemplified in Fig. 2. (\(\rho\)) of samples increased while (\(V_{{\text{m}}}\)), declined when Cr2O3 was added to them. The exchange of smaller CaO molecules (M = 56.077 g/mol, = 3.34 g/cm3) with thicker and heavier Cr2O3 (M = 151.99 g/mol, = 5.2 g/cm3) is the predominant cause of the increase in density. BO3 have been transformed into BO4 elements by the addition of modifier oxides like Cr2O3. The fact that BO4 units are denser than BO3 units demonstrates an increase in sample density [34, 37, 38].

Fig. 2
figure 2

ρ and \(V_{{\text{m}}}\) of synthetic samples

3.2 FT-IR investigations

FT-IR spectrum of fabricating samples is exhibited in Fig. 3. In Fig. 3, the broad bands are the result of several distinct bands overlapping. Therefore, a deconvoluted process is used to obtain exact band positions. The difference between experimental and simulated Fig. is small than 0.02%. As a result, FT-IR of glasses was deconvoluted with (Peak Fit v4.12) using Gaussian distribution to determine the exact band positions and structural unit concentration. Figure 4 depicts a typical glass deconvoluted FT-IR spectrum including band center (C), and relative area (A) as Table 1[8, 39,40,41,42]. (BO3) is converted to (BO4) in borosilicate glasses with low modifier oxide inclusions. For the borosilicate glasses, Si–O–B bonds must be established. The band at 442 cm−1 is combined with the deformation modes of the network structure. This band could be attributed to the cationic vibration of Ca-O in (CaO6). The (NaO6), (CrO6), SiO4, and Si–O–B vibrations are linked to bands in the 507–534 cm−1 range, which overlap with the O–Si–O. B–O–B bending vibrations of (BO3) may be responsible for the bands observed at ~ 703 cm−1. In borosilicate glasses with a large amount of alkaline earth oxides, SiO4 tetrahedra with two NBOs can be found. Absorptions due to stretching vibrations of B–O–Si linkages between 952 and 1118 cm−1 must be noted, indicating a possible linkage between silicate and borate structural units [45]. The bands of 1000–1080 cm−1 due to the vibrations of the asymmetric stretching vibrations of Si–O–Si, O–Si–O [5]. The broadband between 836 and 1118 cm−1 is designated to B–O bond stretching vibrations of BO4. The band at 1226–1262 cm−1 is recognized to asymmetric stretching vibrations of B–O bonds in (BO3) units (NBO). The peaks at 1302–1357 cm−1 explained by asymmetric stretching modes of borate triangles with NBOs. B–O stretching vibrations in (BO3) related to1440 cm−1. The O–H and H2O bending vibrations in the sample may be responsible for 1534 and 1686 cm−1. The assignments of glass samples are listed in Table 2.

Fig. 3
figure 3

FT-IR of synthesized glasses

Fig. 4
figure 4

De-convolution for synthesized glasses

Table 1 Gaussian fit of synthesized glasses, the band center is (C), and the relative area is (A)
Table 2 Assignments of FT-IR

\(N_{4}\) fraction is defined as \(N_{4} = \frac{{concentration of \left( {BO4} \right)}}{{concentration of\left( {BO4} \right) + concentration of\left( {BO3} \right)}}\) Table 1 shows the \(N_{4}\) values for each of the glasses examined [46, 47]. The concentration of (BOs) increases with increasing Cr2O3 content, according to the Perusal of calculated values for \(N_{4}\). After Cr2O3 is incorporated, BO3 transforms into BO4 tetrahedra. The glass network’s coherence improves, and the structure stiffens as a result.

3.3 Optical investigations

In the wavelength range 250–2500 nm, the UV–Vis absorption spectra of Cr2O3 doped calcium borosilicate glasses are shown in Fig. 5. In comparison to the G1 glass, the absorption edge of all doped glasses has shifted to a lower wavelength. Figure 6 depicts the absorption coefficient (α) of these glasses. (α) calculated as \(\propto = \left( {2.303|d} \right) \times A\). Their intensities have also differed slightly. With Cr2O3 doping, the band’s absorption intensity has increased. The (Cr3+) is correlated to the identified absorption peaks ranging from 550 to 700 nm.

Fig. 5
figure 5

UV–Vis spectra

Fig. 6
figure 6

(α), of fabricated samples

The determination of the energy \(E_{{{\text{opt}}{.}}}\) of the glasses is used Tauc's relation: \(\alpha h\nu = C(h\nu - E_{{{\text{opt}}{.}}} )^{{\text{s}}} .\) The relationship between (\(\alpha h\nu\))1/2 and (\(h\nu\)) is depicted in Fig. 7. Table 3 demonstrates that the \(E_{{{\text{opt}}{.}}}\) values are in the range of 2.57–3.31 eV [9, 43,44,45,46,47,48,49,50]. According to Babu and Cole, structural changes, and the formation of BOs cause differences in \(E_{{{\text{opt}}{.}}}\) values. Increases in the \(E_{{{\text{opt}}{.}}}\) can be linked to density and N4 variation. Cr-ions occupy interstitial site positions, resulting in increased network compactness and \(E_{{{\text{opt}}{.}}}\).

Fig. 7
figure 7

(\(\alpha h\nu\))1/2 against (\(h\nu\)) to calculate \(E_{{{\text{opt}}}}\)

Table 3 Optical explanations for glasses

Calculating (\(R_{{\text{m}}}\)), (\(\propto_{{\text{m}}}\)), (\(R_{{\text{L}}}\)), (χ),\(M, K_{{{\text{th}}}}\) and \(T_{{{\text{g}}\left( {{\text{thero}}{.}} \right)}}\) using values from the (\(E_{{{\text{opt}}{.}}}\)). The values of (\(R_{{\text{m}}}\)), (\(\propto_{{\text{m}}}\)), and (\(R_{{\text{L}}}\)) decrease, although (χ),\(M\) increment. Because \(V_{{\text{m}}}\) has decreased, these observations have been reduced. Because the values of (\(\propto^\circ\) and \(\wedge\)) are different, they both decline. The increment in \(K_{{{\text{th}}}}\) and \(T_{{{\text{g}}\left( {{\text{thero}}{.}} \right)}}\) as Cr2O3 is thought to be caused by an increase in the bandgap. Table 3 displays the data values obtained.

(\(n_{{\text{D}}}\)) was determined as \(nD = \frac{{\left( {1 - R} \right)^{2} + k^{2} }}{{\left( {1 + R} \right)^{2} + k^{2} }}\). The investigated sample’s \(n_{{\text{D}}}\) increases, as shown in Fig. 8. The relationship between \(n_{{\text{D}}}\) and \(\rho\) is similar. As a result, \(n_{{\text{D}}}\) increases as Cr2O3, which is thought to be due to a density increase. Calculating \(R_{{\text{m}}}\), \(\propto_{0}^{2 - }\), and \(\Lambda\) using values from the (\(n_{{\text{D}}}\)). The values of \(R_{{\text{m}}}\), \(\propto_{0}^{2 - }\), and \(\Lambda\) are shown in Figs. 9, 10, 11. \(R_{{\text{m}}}\), \(\propto_{0}^{2 - }\), and \(\Lambda\) have the same value as the refractive index.

Fig. 8
figure 8

(\(n_{{\text{D}}}\)), of manufactured samples

Fig. 9
figure 9

(\(R_{{\text{m}}}\)), of manufactured samples

Fig. 10
figure 10

(\(\propto_{0}^{2 - }\)), of manufactured samples

Fig. 11
figure 11

(\(\Lambda\)), of manufactured samples

3.4 Radiation attenuation capacities

Figure 12 shows the (Zeq) value of glass samples. (Zeq) increased then decreased as the incident photon energy was increased and CaO was replaced with Cr2O3. This result is due to the Compton scattering interaction. At energies greater than 1 MeV, the (Zeq) value decreases due to the pair creation interaction [22, 48, 51,52,53,54].

Fig. 12
figure 12

(Zeq) for glasses

The variation of EAB and EBAF are presented in Fig. 13. EAF and EABF decrease as the density and Cr2O3 in the glasses increase. This also confirms that the photon energy and chemical structure of a material determines its EAF and EABF.

Fig. 13
figure 13

EAF and EABF for G 1 and G 5 samples

Finally, we use effective removal cross-sections \(\sum R\) to investigate the neutron attenuation behaviors of glasses. Figure 14 exemplifies the \(\sum R\) of synthesized glasses. As shown in Fig. 15, \(\sum R\) is a density-dependent parameter. \(\sum R\) enhances as the Cr2O3 content of the glasses increases. G 5 is a better fast neutron absorber when the FNRC of glass samples is compared. For neutron attenuation applications, the glass sample G 5 is the best option [22, 48, 51,52,53,54].

Fig. 14
figure 14

\(\sum R\) for fabricated glasses

Fig. 15
figure 15

FNRC with samples

4 Conclusions

Melt quenching was used to successfully fabricate chromium-modified calcium borosilicate glasses. The optical, structural, and γ shielding characteristics of these glasses are investigated. With CrO6 octahedral structural units, Cr2O3 acts as network modifiers. With the addition of Cr2O3, the glass density increased while molar volume reduces. All glass compositions contain B2O3 in the form of BO3 and BO4 units, as well as SiO2 in the SiO4. The concentration of (BOs) increases with increasing Cr2O3 content, according to the Perusal of calculated values for N4. After Cr2O3 is incorporated, BO3 transforms into BO4 tetrahedra. The glass network's coherence improves, and the structure stiffens as a result. \(E_{{{\text{opt}}}}\) values are in the range of 2.42–3.18 eV. Increases in the \(E_{{{\text{opt}}}}\) can be linked to density and N4 variation. (Zeq) increased then decreased as the incident photon energy was increased and CaO was replaced with Cr2O3. \(\sum R\) enhances as the Cr2O3 content of the glasses increases. G 5 is a better fast neutron absorber when the FNRC of glass samples is compared. For neutron attenuation applications, the glass sample G 5 is the best option. Incorporating Cr2O3 into the investigated glass compositions has a significant impact on their optical, structural, and γ shielding characteristics, according to the findings of this study. This research could be used in the future to improve optical efficiency and reduce radiation's harmful effects on organisms.s