Optical, thermal and radiation shielding properties of B2O3–NaF–PbO–BaO–La2O3 glasses

The techniques of melt-quenching have been used to generate 53B2O3—2NaF—27PbO – (20-x)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(20-x)$$\end{document} BaO—x\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$x$$\end{document} La2O3(0≤x≥15)glasssystem\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(0\le x \ge 15) glass system$$\end{document}. XRD patterns have been established the amorphous character of glass samples. There is a clear evidence of the role of the La2O3 modifier in the glass network. The thermal characteristics have been identified to increase with an increase in La2O3 content. Increasing La2O3 increases the linear and non-linear optical bandgap energy and the Urbach energy. By adding La2O3 to the glass samples, the refractive index, molar polarizability, polarizability, and optical basicity increased. The bulk modulus and the glass transition temperature increased because of the increase in bond strength. The number of bonds per unit increased with the increase in La2O3 content because of the modifier character of La2O3 in the glass samples. Many optical parameters (ε∞\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\boldsymbol{\infty }$$\end{document}), (εo), χ(1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\chi }^{(1)}$$\end{document}, χ(3)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\left({\chi }^{(3)}\right)$$\end{document} and (n2)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${(n}_{2})$$\end{document} as a function of linear and non-linear Eopt\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${E}_{opt}$$\end{document} have been obtained. The extent of shielding in this article has been examined with the increment in La2O3 at the expense of BaO. The results correspond with similar studies conducted before.


Introduction
Thermal, optical, and gamma-ray shielding properties play important roles in the application of materials. It is well-known that glasses reinforced by lanthanide content improve the optical, thermal, and radiation shielding attributes of a given glass specimen. Such unique features give these glasses a large scale of applications in various optical devices and several nuclear facilities. Consequently, there is an increasing interest to synthesize and characterize different types of glasses for achieve an ideal and multifunctional glass [1][2][3][4].
Issa et al. reported the PbO-SiO 2 -B 2 O 3 -Na 2 O glasses in terms of their basic shielding attributes against gamma rays as well as neutrons beams [1]. The results of this study show that the glass specimen containing 15 mol% of PbO possesses the highest shielding ability against gamma fields. Olarinoye et al. studied zinc borate glasses not only by means of their shielding attributes but also by means of their mechanical attributes under the effect of La 2 O 3 addition [2]. Rammah et al. studied the fluoro-tellurite lithium niobate glasses: TeO 2 -LiNbO 3 -BaO-BaF 2 -La 2 O 3 in terms of their physical properties (density and molar volume), optical transmission factors, and shielding ability [4]. 53B 2 O 3 -2NaF-27PbO -ð20 À xÞ BaO-x La 2 O 3 ð0 x ! 15Þ, glasses as well gain significant interest, and La 2 O 3 to investigate their optical properties. These glasses are of financial advantage to semiconductor applications because of their properties: a greater refractive index, good unique physical and chemical characteristics. The creativity of this research paper reflected in the optical and radiation shielding characteristics of B 2-O 3 -NaF-PbO-BaO-La 2 O 3 glass samples. Results from thermal, optical, and radiation described in this article.
In the present work, we generate 53B 2 O 3 -2NaF-27PbO-ð20 À xÞ BaO-x La 2 O 3 ð0 x ! 15Þ glass system by using the techniques of melt-quenching. XRD patterns have established the amorphous character of glass samples. The thermal characteristics have been studied with an increase in La 2 O 3 content. Many optical parameters (e 1), (e o ), v ð1Þ , v ð3Þ À Á and ðn 2 Þ as a function of linear and non-linear E opt have been obtained. The extent of shielding in this article has been examined with the increment in La 2 O 3 at the expense of BaO.

Methodology
The glasses in Table 1 1 and Table 2).
To verify the status of these glasses the Philips Xray diffractometer (model PW/1710) used. Optical parameters were predictable by using spectrophotometer type JASCO, V-670 (Japan). DTA-50 For the thermal investigation, (Shimadzu-Japan) used. The program developed by Sakar et al. [27], Phy-X/PSD, has been employed to study and determine all of the  ; : Electron density (N eff ) has estimated as: Effective cross-section of removal(R R ) predicted as: 3 Results and discussions

Optical characteristics
There were no sharp peaks in the XRD in graph 1, indicating the high glass status of these samples.

Direct and indirect energy gap E opt
About toTauc's theory [40], bandgap energies for direct transition and indirect one can be determined via ahm ¼ Aðhm À E opt: Þ k , this approach was previously  Wavelength (nm) The absorption coefficient (cm Fig. 4 The absorption coefficient of the prepared glasses described in details elsewhere [21,[28][29][30][31][32][33][34][35][36][37][38][39]. Figure 5 depicts the relation of ln(ahm) k and (hm) in the case of direct (r = 1/2) and indirect (r = 2) transitions. The obtained values of direct E dir opt: and indirect allowed E indir opt: optical energy for the investigated glasses estimated by the help of the straight lines in Fig. 5a, b, thereafter all the results are summarized in Table 3. The values of E dir opt: & E indir opt: increase with increasing La 2 O 3 content, as shown in Table 3, because of the formation of oxygen bridges (BO). Urbach energy E u of samples has projected as / 0 exp ht E u , Fig. 6 and recorded in Table 3, demonstrating that an opposing relation noticed between their values of E opt . Figure 7 presented the values of E opt and E u .

Refractive index (n)
The refractive index of manufacturing glass (n) was already computed as: n ¼ ð1ÀRÞ 2 þk 2 ð1þRÞ 2 þk 2 , here k = ak/4p. (n) of manufacturing glasses obtainable in Fig. 8, it detected that (n) of the investigated glasses are increasing as density increases. It has mentioned that there is a direct equation for both the density and refractive index, i.e., the denser the glass study, the greater the refractive index. So, the refractive index is exactly applicable to reflection and density, and opposite with the molar volume is comparable.

Dispersion parameters
Molar polarization is given by R m ¼ hn 2 À 1jn 2 þ 2iVm; while the polarizability can be described as The optical fundamentality of investigated glasses has a relation with polarization; K ¼ 1: The molar polarizability and all the other important factors of the glass under study are described in Figs. 9, 10, 11. The same refractive index trend with concentrations of La 2 O 3 has been observed. According to Lorentz-Lorenz principles, molar polarizability depends on refractive index and molar volume, as well as polarizability, depend on molar polarizability. So, with the alteration of molar volume and a refractive index indicating that the samples are more polarized because of the increase of La 2 O 3 , so, the molar polarizability of glasses increases.
The molar refractivity as E opt: The values of (R m ) (/ m ) and (R L ) are direct proportional to the molar volume. Thus, these parameters decrease due to a reduction in the molar volume. These parameters are recorded in Table 3. Table 2 shows the values of electronegativity (v), optical basicity, and criterion for metallization. A full description for the previous parameters is discussed extensively in [41,42]. a b Fig. 5 a Plot of (a hm) 1/2 against photon energy (hm) to calculate the direct optical band gap from the intercept of the curves. b Plot of (a hm) 2 against photon energy (hm) to calculate indirect optical band gap from the intercept of the curves  The bulk module (K) and the temperature of the glass transition related to E opt and projected as K th ¼À478:93þ200:13E g , T gðthero:Þ ¼À701:87þ403:33E g . Values K th andT gðthero:Þ in Table 3. It stated that, because of the increase in bond strength, these values increase with La 2 O 3 .
For BO or NBO connection confirmation, a significant parameter is the coordinated average number and defined as m ¼ P n ci X i where cation coordination isn ci . As the value in Table 2, it originated that m increased with the rise in La 2 O 3 content.
The number of bonds per unit calculated as n b ¼ N A =V m P n ci X i . As the value in Table 2, it initiated that n b increased with the rise in La 2 O 3 content. This supports our results that based on the modifier character of La 2 O 3 in the demonstrates the modifier character of La 2 O 3 in the glass samples.
The factor of two-photon absorption TPA (b) cm / GW, expressed as b ¼ 36:67 À 8:1E opt where E opt bandgap energy. For solid-state physics, one of the most significant parameters is TPA. As the value in Table 3, it originated that (b) decreased with the increase in La 2 O 3 content because of E opt increase.
The ionic and covalent features of these specimens can be established in terms of electronegativity difference As the values in Table 3, it was noted that (I b ) slow down as the

Thermal analysis
The thermal behaviours of prepared glasses characterized by DTA in the atmosphere at a heating rate (10°C/min). Figure 14 is the DTA curves of prepared glasses. From DTA curves Fig. 14, it noticed that the glass transition temperature T g increased with increasing La 2 O 3 , it increases from 421°C at 0% to 457°C at 15% as shown in Table 5 and Fig. 5, the onset of crystallization temperature Tc increased with increasing La 2 O 3 , it increases from 455°C at 0% to 488°C at 15% as shown in Table 6 and Fig. 14, the end-set of crystallization temperature T p increased with increasing La 2 O 3 , it increases from 494°C at 0% to 542°C at 15% as shown in Table 6 and Fig. 14. This increases due to a clear raise in the average force constant, connectivity, and an increase in packing density Fig. 15.
Thermal stability projected byDT ¼ T c À T g ,

Radiation shielding properties
This research examined the degree of shielding [50][51][52][53][54][55][56][57][58]  ; andshowninFig:15: It noticed that as the photon energy and the La 2 O 3 content increase the values of MFP increase. This motivation discloses that the rise in energy let to more collisions between photon and the glass sample. This Fig. 15 shows that the lower value of MFP is sample contains a higher content of La 2 O 3 thus it is better sampled for attenuation of c radiation. Figure 16 presented MFP of glasses comparison with standard materials. The behaviour of MFP in the current 53B 2 O 3 -2NaF-27PbO -ð20 À xÞ BaO-x La 2 O 3 ð0 x ! 15Þ glasses is similar to that of several glassy materials [59][60][61][62][63][64]. Figure 17 represented the N eff values of samples against energy. It indicated that N eff decreases with the increase of the energy and then increases. Such decrease is owing to Compton scattering, while the increase in N eff related to the pair production at higher energy where the content of La 2 O 3 is also  Figures 18, 19 represented the ASC and, ESC of glass specimens against photon energy. It suggested that, with the increase in energy, the ASC and ESC values decreased. This decrease is owing to Compton scattering. Figure 20 represented the C eff of the prepared samples against the gamma energy. It is proposed that with the rise of the photon energy, the C eff will decrease, then increasing. This decreases because of the presence of Compton scattering. The increase of C eff correlated to the higher-energy pair-creation effect and increased in La 2 O 3 content.
Cross-through effective removal (RR) designated that the neutron particle crosses the material does not any interaction. RR of investigated glasses with energy characterized in Fig. 21. It confirmed that at lower energy, the almost RR increased. Small deviations of glass samples with a decrease in the value of RR noted at higher energy. Such deviations linked to the increase of La 2 O 3 . It is well known that elements that have a light atomic number have a strong ability to protect neutrons. The increase in the content of La 2 O 3 enhances the shielding of neutrons. FNRCS is referred to the fast neutron removal cross section. This parameter was computed and the results were plotted in Fig. 22. It noted that FNRCS increased with La 2 O 3 . Therefore, the addition of La 2 O 3 play a main role in the glass samples to enhance the FNRCS.    Fig. 16 The comparison of MFP for the prepared glasses as a function of photon energy with standard materials value of (MFP) is higher content La 2 O 3 thus it is a better sample for attenuation of c radiation. N eff decreases with the increase of the energy owing to the Compton scattering interaction and then increases due to the pair production at higher energy where the content of La 2 O 3 is also high. ASC, ESC, C eff, and (RR) obtained. FNRCS increased with La 2 O 3 . The cray and fast neutron radiation-shielding abilities of present samples. The glass system with the composition 53B 2 O 3 -2NaF-27PbO -5BaO-15La 2 O 3 is the best candidate for photon shielding applications. Obtaining the physical, and optical values of these glasses can help develop various equipment and innovations, including batteries with solid-state and gamma-ray protection. The current glassy samples showed promising features for optical, thermal, and shielding uses. The results correspond with similar studies conducted before.