1 Introduction

For a long time, halide glasses like NaF have been known to us [1]. Such glasses are formed by simply quenching the method by moltening their halides. These glasses are inherently hygroscopic and have low values of glass transition temperature, by reducing their applicability. Therefore, these glasses are doped with transition metal ions (TMi) and rare earth ions (REi) to increase the resistance of hygroscopic. The halide glasses doped with (TMi) and (REi) have been more resistant to attack of hygroscopic [2]. To vary the properties of the glass like the dielectric, mechanical, thermal, and optical dopants with halides or sulphates are presented into the host glass [3]. Halides such as NaF and LiF are introduced to the glass matrix to generate mobile ion species Li+, Na+, etc. Several studies have shown that dopant halides do not enter the glass's macromolecular chain. Thus, halide glasses are great metal ion solvents. Due to its unique physical properties, glasses incorporating halide ions have long been studied. The development of numerous devices and technologies, including solid-state batteries and radiation protection, has led to investigations of such glasses [1,2,3,4,5,6,7]. Increasing attention has been devoted to fluoride-based glasses due to their potential use for making infrared optical components and fibres. Interesting and remarkable properties were demonstrated by the modified dimension of fluoroborate glasses synthesized by replacing some oxygen ions with fluoride ions [8,9,10,11].

Borate glasses can be regarded as an adaptable type of glass that is used in various applications because they have high thermal stability and optical properties. Besides, it is considered good for TMi, REi, and halides as host glasses. Due to their attractive structural, optical properties and infrared radiation shielding, there has been considerable interest in the study of borate-based glasses over the last few years [12,13,14,15,16,17,18,19]. Many efforts have been made to doping with lanthanide ions the lead fluoroborate glass, the result showing that this material is a good candidate for laser applications [20].

B2O3–NaF–PbO–BaO glasses have also great attention and La2O3 to investigate their optical properties. FT-IR measurements of these glasses showed that tetrahedral fluoroborate (BO3F) groups have the same characteristics as tetrahedral borate (BO4) groups [21]. Because of their properties, these glasses are of benefit to optoelectronic devices: a high refractive index of about 2.2 and good physical and chemical stability. Studies of B2O3–NaF–PbO–BaO doped with La2O3 are presented. In addition to Phy-X/PSD [22] software calculations, results from FT-IR, mechanical, and radiation are presented.

2 Experimental approaches

53B2O3–2NaF–27PbO–\((20-x)\) BaO–\(x\) La2O3 \((0\le x \ge 15)\) glasses in Table 1 have been prepared according to the chemical equation:

Table 1 Chemical composition of the prepared glasses (in mol%)
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\({\text{NaF}} + {\text{PbO}} + {\text{BaO}} + {\text{La}}_{2} {\text{O}}_{3} + 2{\text{H}}_{3} {\text{BO}}_{4} \xrightarrow{{650\;^{^\circ } {\text{C}}\,\;( - 3{\text{H}}2{\text{O}})}}\;({\text{NaF}} + {\text{PbO}} + {\text{BaO}} + {\text{La}}_{2} {\text{O}}_{3} + {\text{B}}_{2} {\text{O}}_{3} )\xrightarrow{{1200\;^{^\circ } {\text{C}}\;(2{\text{h}})}}\;{\text{glasses}}\;{\text{Table}}\,1\xrightarrow{{{\text{annleadat}}\;400\;^{^\circ } {\text{C}}}}\) glass samples. Glasses are prepared using the technique of melting/annealing.

A Rigaku Miniflex 600 X-ray diffractometer was used to test the glass states. Changes in the structure of these glasses will be explored by Bruker’s VERTEX 70 FT-IR Spectrometers. Physical features of these glasses are projected as ion concentration of La3+ has been considered as

$${\text{Ti}} = \left( {\frac{{6.023 \times 10^{{23}} x\;{\text{mol}}\;{\text{fraction}}\;{\text{of}}\;{\text{cation}} \times {\text{valency}}\;{\text{of}}\;{\text{cation}}}}{{V_{m} }}} \right)$$
(1)

Inter-ionic distance (\({R}_{i}\)) between La and La has been calculated as

$${R}_{i}= {\left(\frac{1}{\mathrm{concentration\, of\, Ti}}\right)}^\frac{1}{3}$$
(2)

La–La separation was projected as

$$(\mathrm{dLa}-\mathrm{La}) = {\left(\frac{{V}_{m}^{B}}{N }\right)}^\frac{1}{3}$$
(3)

and \({V}_{m}^{B}\text{ } = \frac{Vm}{2\left(1- 2\mathrm{Xn}\right)}\). The polaron radius rp, and inter-nuclear distance ri have been calculated as

$$r_{p} = \frac{1}{2}\left( {\frac{\pi }{6N}} \right)^{\frac{1}{3}}$$
(4)
$$r_{i} = \left( \frac{1}{N} \right)^{\frac{1}{3}} .$$
(5)

Pulse-echo technique was applied to calculate ultrasonic velocities at room temperature. In this technique, 4 MHz transducers are x-cut and y-cut. The glass ultrasonic velocities had a measuring uncertainty of ± 15 m/s. The density (ρ) of the combined glass samples was measured using the Archimedes method at room temperature. The elastic moduli have been projected as [23,24,25,26]. Longitudinal modulus,

$$L=\rho {v}_{l}^{2},$$
(6)

Shear modulus,

$$G=\rho {v}_{s}^{2},$$
(7)

Young’s modulus,

$$Y=\left(1+\sigma \right)2G,$$
(7)

Bulk modulus,

$$K=L-\left(\frac{4}{3}\right)G$$
(8)

The theoretical calculation of the dissociation energy and packing density of the elastic module is: [27, 28]

$$V_{i} = \left( {\frac{3\pi }{4}} \right)NA \{ m{\text{R}}{}_{{\text{m}}}^{3} + n {\text{R}}{}_{{\text{i }}}^{3} \} \left( {\frac{{{\text{m}}^{3} }}{{{\text{mol}}}}} \right),$$
(9)

where Rm and Ri are Pauling radii of metal and oxygen. The elastic moduli,

$$L=K+\left(\frac{4}{3}\right)G,$$
(10)
$$G={({V}_{i}}^{2}{G}_{i})/\left({V}_{i}\right){}_{ }{}^{-1},$$
(11)

Poisson's ratio,

$$\sigma {\text{ = }}\frac{1}{2} - \left( {\frac{1}{{{\text{7}}{\text{.2* }}Vi}}} \right),$$
(12)

Microhardness,

$$H=\frac{\left(1-2\sigma \right)Y}{6\left(1+\sigma \right)},$$
(13)

Debye temperature,

$${\theta }_{D}= \frac{h}{k}{\left(\frac{9N}{4\pi {V}_{m}}\right)}^\frac{1}{3}{M}_{s}.$$
(14)

Average of ultrasonic velocities,

$${M}_{s}= \frac{1}{3}{\left(\frac{\frac{2}{{v}_{T}^{3}}}{\frac{1}{{v}_{l}^{3}}}\right)}^\frac{1}{3},$$
(15)

Thermal expansion,

$${\alpha }_{P =23.2 \left({v}_{L}-0.57457\right)},$$
(16)

Oxygen molar volume,

$${V}_{o}=\left(\frac{M}{\rho }\right) \left(\frac{1}{\sum xini}\right)$$
(16)

Oxygen packing density,

$$OPD=\left(\frac{1000 C}{Vm}\right)\left(\frac{Mol}{L}\right).$$
(18)

Phy-X/PSD can calculate numerous shielding variables at any level of energy [22]. The law of Beer-Lambert is written as

$$\mu = - \frac{{\ln \frac{I}{{I_{0} }}}}{x},$$
(19)

where the linear coefficient of attenuation is μ (cm−1) I0 and I , respectively. The mass attenuation coefficient MAC (μ/ρ) has been estimated as

$$\left( {\frac{\mu }{{\uprho }}} \right) = \sum\nolimits_{i} {w_{i} } \left( {\frac{\mu }{{\uprho }}} \right)_{i} ,$$
(20)

where ρ is the density of the material and the coefficient of attenuation of mass is (μ/ρ). The mean free path (MFP) was calculated as

$$\mathrm{MEP}=\left(\frac{1}{\mu }\right),$$
(21)

It is possible to calculate the tenth (TVL) and half-value layer (HVL) as

$$\mathrm{TVL}= \left(\frac{\mathrm{ln}10}{\upmu }\right) ,$$
(22)
$$\mathrm{HVL}=\left(\frac{\mathrm{ln}2}{\upmu }\right).$$
(23)

Zeff can be estimated as

$${Z}_{eff}=\left(\frac{{\sigma }_{a}}{{\sigma }_{e}}\right)$$
(24)

where σa is the atomic cross-sections

$$\sigma_{a} {\upsigma }_{a} = \sigma_{m} \frac{1}{{\mathop \sum \nolimits_{i} n_{i} }} = {{\left( {\frac{\mu }{\rho }} \right)_{{{\text{target}}}} } \mathord{\left/ {\vphantom {{\left( {\frac{\mu }{\rho }} \right)_{{{\text{target}}}} } {N_{A} \mathop \sum \nolimits_{i} \frac{{w_{i} }}{{A_{i} }}}}} \right. \kern-\nulldelimiterspace} {N_{A} \mathop \sum \nolimits_{i} \frac{{w_{i} }}{{A_{i} }}}}$$
(25)

and σe is the electronic cross-sections

$${\sigma }_{e} =\frac{1}{N} \sum_{i}{\left(\frac{\mu }{\rho }\right)}_{i}\frac{{f}_{i}{wA}_{i}}{{z}_{i}},$$
(25)

G-P fitting parameters were estimated as \(P= \frac{P1(\mathrm{log}Z2-\mathrm{log}Z\mathrm{eq})+Z2(\mathrm{log}Z\mathrm{eq}-\mathrm{log}Z1)}{\mathrm{logZ}2-\mathrm{logZ}1}\). G-P fitting parameters have been estimated as \(P= \frac{P1(\mathrm{log}Z2-\mathrm{log}Z\mathrm{eq})+Z2(\mathrm{log}Z\mathrm{eq}-\mathrm{log}Z1)}{\mathrm{log}Z2-\mathrm{log}Z1}\) where P1 and P2 are the G-P fitting parameters corresponding to the atomic numbers Z1 and Z2, respectively. EABF and EBF have been estimated by using G-P fitting \(B(E,X)=1+\frac{b -1}{K-1}\)(\({K}^{x}-1)\) for K \(\ne 1\), \(B(E,X)=1+(b-1)x\) K \(= 1\) where \(K(E,X)=c{x}^{a}+d\frac{\mathrm{tan}h(\frac{x}{Xk} -2)-\mathrm{tan}h(-2)}{1-\mathrm{tan}h (-2)}\) for x \(\le 40\). where E is the photon energy, x is the penetration depth in mfp, and K (E, X) is the dose-multiplicative factor.

3 Results and discussions

3.1 Physical properties of glasses

Figure 1 shows the X-ray results of the studied glasses. These diffractograms show no discrete lines and no sharp peaks and indicate that the glass samples have a high degree of glassy state. The slight shift in the peak at (20–30) 2θ values with respect to La2O3 concentration can be related to the decrease in the bond length and to the higher coordination number with oxygen's.

Fig. 1
figure 1

XRD of the studied glasses

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Glass density is typically directly compared to molecular weights and densities [29,30,31,32,33]. In our paper, at the expense of BaO, La2O3 increased. The molecular weights of La2O3 and BaO [325.809 & 153.326] and densities [6.5 & 5.72 g/cm3] correspondingly. It has been observed that the density of our samples has increased. The increase in density is correlated to changes in the density and molecular weights of La2O3 and BaO. Due to the difference in atomic radii and bond length for Ba2+ and La3+ (0.4347 nm, 0.215 nm) and (0.3739 nm, 0.195 nm), respectively, the decrease in the molar volume of studied glasses. In Fig. 2, the density and molar volume are presented.

Fig. 2
figure 2

Density and molar volume of the prepared samples with La2O3 by mol%

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Because of the reduction in molar volume, the concentration of La3+ has been raised. With the increase in La3+ concentration, the inter-ionic distance decreased, associated with decrease in molar volume. Because of the decrease in molar volume, values of (dLa–La) decreased with La2O3, as well as polaron radius, and inter-nuclear distance are decreasing. These values are shown in Table 2.

Table 2 Various physical parameters of the studied glasses
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3.2 FT-IR analysis

The FT-IR spectrum of synthesised samples consisting of 6 perceptible vibrational absorption bands in the range of 400–4000 cm−1 is illustrated in Fig. 3. The technique of deconvolution is used for resolving wide bands [34,35,36,37,38,39]. Table 3 and Fig. 4 list the outcomes of the deconvolution process. It is therefore possible to the interpretation of the current FT-IR result obtained for B2O3–NaF–PbO–BaO–La2O3 glasses as follows: the first bands at ~ 3434 cm−1, the second bands at ~ 1630 cm−1, the third bands at ~ 1380 cm−1, the fourth bands at ~ 995 cm−1, the fifth bands at ~ 710 cm−1, and the sixth bands at ~ 480 cm−1. The band at ~ 3434 cm−1 is accredited to vibrational modes of H2O, OH, or BOH. The band at ~ 1630–1440 cm−1 is accredited to the stretches of B–O in BO3 (or BO2O−) groups. The band at ~ 1088–830 cm−1 is accredited to vibrations of tetrahedral BO4 groups and B2O3 can be partially improved by NaF and the structural units of (BO3/2 F)− tetrahedra are formed. The band at ~ 709–655 cm−1 is due to bending vibrations of B-O linkages in the borate units. The band at ~ 579–463 cm−1 is accredited to Na+, Ba2+, Pb2+, and La3+.

Fig. 3
figure 3

Infrared spectra of the investigated glasses

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Table 3 The deconvolution parameter of the infrared spectra of studied glasses (C) is the component band centre, and (A) is the relative area (%) of the component band, the area under both (BO4, BO3) and N4 fraction
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Fig. 4
figure 4

Curve-fitting of IR spectra of the investigated glasses

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In the fraction (N4), the area under the bands was considered, \({\mathrm{N}}_{4}=\frac{{\mathrm{BO}}_{4}}{({\mathrm{BO}}_{4}+{\mathrm{BO}}_{3})}\). As a result, the value of the N4 fraction increases with the development of structural units [BO4]. In Table 4, peak assignments for the glass samples are provided. The addition of La2O3 increases the changes of BO3 to BO4 and increases the degree of glass connectivity.

Table 4 Peak assignments for the prepared glasses
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3.3 Mechanical properties

Figure 5 and Table 5 represented sound velocities (VL) and (VT) of glasses. Both velocities have been observed to increase with the increase of La2O3 concentration. This observation because of increased density, cross-link density, and glass matrix connectivity. VL increases from 5155 ms−1 at 0% La2O3 to 5315 ms−1 at 15% La2O3, and VT increases from 2940 ms−1 at 0% La2O3 to 3015 ms−1 at 15% La2O3. Based on the previous analysis of FT-IR, this conduct is associated with the increase in the N4 and La–La separation. As well as the increase in (BO) and, consequently increased glass network connectivity, where the La breaks the bonds of BO4 tetrahedral units with the structural units of (BO3/2 F)− tetrahedra are formed.

Fig. 5
figure 5

Dependence of the longitudinal and shear ultrasonic velocities vL and vT of the investigated glasses with La2O3 by mol%

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Table 5 The values of sound velocities and elastic moduli (experimental and theoretical) of the studied glasses
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Numerous types (experimental and theoretical) of elastic modules have been evaluated for the glass samples displayed in Figs. 6 and 7, and Table 6. Both elastic modules have been observed to increase with the increase of La2O3 concentration. There is a clear link among elastic modules and ultrasonic velocity. This observation because of Ba–O bond strength is (33 kcal/mol) is lesser than La–O (58 kcal/mol) [40]. The increase of La2O3 causes a shift to higher wavenumbers which connected to the formation of BO4 with the structural units of (BO3/2 F)− tetrahedra are formed causes increase the connectivity of glass samples.

Fig. 6
figure 6

Elastic moduli calculated of the studied glasses with La2O3 by mol%

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Fig. 7
figure 7

Elastic moduli theoretically of the studied glasses with La2O3 by mol%, according to Makishima–Mackenzie Model

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Table 6 Values of, packing density (Vi), dissociation energy (Gi), thermal expansion coefficient (αP), acoustic impedance (Z), and Debye temperature (θD), oxygen packing density, oxygen molar volume (Vo), softening temperature (Ts), and microhardness (H) of glass systems
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Other mechanical parameters such as (Vi), (Gi), (H), (αP), (Z), (OPD), (Vo), and (σ) are listed in Table 6. These parameters are affected by the glass network. All these parameters have been observed to increase with the increase of La2O3 concentration except (Vo) as it is decreased because of the decrease in molar volume. This observation is in agreement with the analysis of FT-IR.

3.4 Radiation shielding properties

The degree of shielding in this paper was investigated from the increase of La2O3 at the expense of BaO with a nominal composition of 53B2O3–2NaF–27PbO–\((20-x)\) BaO-\(x\) La2O3 \((0\le x \ge 15)\). First, the mass attenuation coefficients (MAC) is attained by Phy-X/PSD software calculations for the energy range of 0.015–15 meV to gather information about the resistance of the glass samples to ionizing radiation [30, 41,42,43,44,45,46,47,48,49,50]. The behaviour of the glass samples' MAC values is exemplified in Fig. 8 based on the energy of photons and La2O3 content. It has been noted that the MAC values of glass samples are decreased to 1 meV, apart from a small increase at 0.1 meV. This increase can be related to absorption edge of the atomic composition of the glasses. At low energy, this significant decline and small peak are directly linked to the current photoelectric effect. The sample with the highest La2O3 content is owned the MAC 's greatest values. This reduction is related to the molecular masses of BaO (153.326) with La2O3 (325.809) and density of samples. Therefore, the addition of La2O3 leads to an increase of gamma-radiation protection. Figure 9 exemplified of LAC values based on the energy of photons and La2O3 content. It has been noted that the LAC values as MAC. Table 7 characterizes MAC (cm2/g) 53B2O3–2NaF–27PbO–5BaO–15La2O3 in comparison with other glasses.

Fig. 8
figure 8

The mass attenuation coefficient (μ/ρ) of the investigated glasses versus the photon energy for the glasses

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Fig. 9
figure 9

Variation of linear attenuation coefficient (μ) values versus the photon energy for the glasses

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Table 7 Mass attenuation coefficients (in cm2/g) of 53B2O3–2NaF–27PbO–5BaO–15La2O3 in comparison with different glass samples
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The variations of the HVL and TVL values of the glasses based on the energy of photons are exemplified in Figs. 10 and 11. It has been noted that the (HVL) and (TVL) increase with the increase in the photon energy rendering to the achieved results. At low energy, the HVL of all samples is close together due to the increase of secondary scattering photons. These data reveal that the energy increase makes the photon capable of deliberately transmitting the prepared sample. In the energy range of 12–15 meV, HVL values are reduced because of absorption and loss of energy during the PP process. The sample 53B2O3–2NaF–27PbO–5BaO–15La2O3 has the lowest HVL and TVL values. Figure 12 exemplifies that HVL of examined glasses is compared with barite, magnetite, ferrite, chromite, RS-253-G18, and RS-520. HVL values of examined glasses are in the same range of predictable materials. The behaviour of TVL based on the energy of photons and La2O3 content is like HVL.

Fig. 10
figure 10

The half-value layer for the prepared glasses as a function of photon energy

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Fig. 11
figure 11

The tenth value layer for the prepared glasses as a function of photon energy

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Fig. 12
figure 12

The comparison of half-value layer for the prepared glasses as a function of photon energy with standard materials

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The variation of Zeff based on the energy of photons and La2O3 content is exemplified in Fig. 13. It has been noted that the Zeff has the largest values at lower energy and at lowering concentration of La2O3 content. The Zeff values for samples decreased rapidly in the range of 0.05–0.1 meV and from G 1 to G3 because of photoelectric effect. There is a sudden growth in the energy range of 3–15 meV and from G3 to G 6 for all the glasses because of interaction of Compton scattering. The sample 53B2O3–2NaF–27PbO–5BaO–15La2O3 has the highest values of Zeff.

Fig. 13
figure 13

Variation of effective atomic (Zeff) number values as a function of photon energy for the glasses

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Both build-up factors EABF and EBF of glass samples based on the energy of photons are exemplified in Figs. 14 and 15. Tables 8 and 9 provide the G-P fitting parameters of the investigated glasses [30, 41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56]. It has been noted that at low energy levels, the EABFs and EBFs originally possess very high values, as the photoelectric effect dominates and replaces the BaO with La2O3. At 0.01–0.05 meV, it has been noted that there are very sharp bands for EABF and EAB. Clearly, by replacing BaO with La2O3, the intensity of those increments is reduced because of the K absorption edges of La and Ba. At 0.2 meV, it has been noted that the values of EABF and EBF began to rise gradually because of the formation of secondary scatterings. The interaction of photons with matter atoms is more than that of air due to the greater atomic number of La and Ba in the glass composition. Therefore, for all samples, the EABF values are higher than the EBF as shown Figs. 14 and 15. In addition, the EABF and EBF values of 53B2O3–2NaF–27PbO–5BaO–15La2O3 are lower than the other samples.

Fig. 14
figure 14

Variations of the energy absorption build-up factors (EBF) with photon energy for glass samples

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Fig. 15
figure 15

Variations of the energy absorption build-up factors (EABF) with photon energy for glass samples

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Table 8 G-P fitting parameters for EBF and G-P fitting parameters for EABF of glass name G 1
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Table 9 G-P fitting parameters for EBF and G-P fitting parameters for EABF of glass name G 6
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4 Conclusion

The melt-quenching method has been used to fabricate 53B2O3–2NaF–27PbO–\((20-x)\) BaO–\(x\) La2O3 \((0\le x \ge 15)\) glass system. The current glass sample's mechanical and thermal characteristics depend on the glass structure. It is observed that ultrasonic velocities and elastic modulus (experimental and theoretical) for these glasses are increased. FT-IR analysis shows that with the increase of La2O3 increases the changes of BO3 to BO4 and increases the degree of glass connectivity, and the structural units of (BO3/2 F)− tetrahedra are formed. It has been noted that the MAC values of glass samples are decreased to 1 meV, apart from a small increase at 0.1 meV. At low energy, this significant decline and small peak are directly linked to the current photoelectric effect. It has been noted that the (HVL) and (TVL) increase with the increase in the photon energy and La2O3 content rendering to the achieved results. It has been noted that at low energy levels, the EABFs and EBFs originally possess very high values, as the photoelectric effect dominates and replaces the BaO with La2O3.