Investigation of Structural, Physical, and Attenuation Parameters of Glass: TeO2-Bi2O3-B2O3-TiO2-RE2O3 (RE: La, Ce, Sm, Er, and Yb), and Applications Thereof

A novel series of glass, consisting of B2O3, Bi2O3, TeO2, and TiO2 (BBTT) containing rare earth oxide RE2O3, where RE is La, Ce, Sm, Er, and Yb, was prepared. We investigated the structural, optical, and gamma attenuation properties of the resultant glass. The optical energy bands, the linear refractive indices, the molar refractions, the metallization criteria, and the optical basicity were all determined for the prepared glass. Furthermore, physical parameters such as the density, the molar volume, the oxygen molar volume, and the oxygen packing density of the prepared glass, were computed. Both the values of density and optical energy of the prepared glass increased in the order of La2O3, Ce2O3, Sm2O3, Er2O3, and then Yb2O3. In addition, the glass doped with Yb2O3 had the lowest refractive index, electronic polarizability, and optical basicity values compared with the other prepared glass. The structures of the prepared glass were investigated by the deconvolution of infrared spectroscopy, which determined that TeO4, TeO3, BO4, BO3, BiO6, and TiO4 units had formed. Furthermore, the structural changes in glass are related to the ratio of the intensity of TeO4/TeO3, depending on the type of rare earth. It is also clarified that the resultant glass samples are good attenuators against low-energy radiation, especially those that modified by Yb2O3, which exhibited superior shielding efficiency at energies of 622, 1170, and 1330 keV. The optical and gamma ray spectroscopy results of the prepared glass show that it is a good candidate for nonlinear optical fibers, laser solid material, and optical shielding protection.


Introduction
Rare earth (RE) elements, such as La, Ce, Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, and Yb have many multilateral applications in advanced technology [1,2]. Recently, glass doped with rare earth (RE) ions has attracted interest due to its utility in various applications in

Experimental Section
The prepared glass (BBTTER) with a composition of 25B 2 O 3 -20Bi 2 O 3 -45TeO 2 -7TiO 2 (BBTT), modified by 3RE 2 O 3 in mol%, where RE is La; Ce; Sm; Er; or Yb, was manufactured using the melt-quenching method. Chemical powders of TeO 2 , B 2 O 3 , Bi 2 O 3 , TiO 2 , and RE 2 O 3 (La 2 O 3 , Ce 2 O 3 , Sm 2 O 3 , Er 2 O 3 , and Yb 2 O 3 ) were homogenized and melted at 930 • C for 30 min in an electric furnace. We used a platinum crucible while melting to obtain a homogeneous mixture, stirring the mixture several times. Then, each melt was put into a polished stainless-steel container and annealed at 300 • C. The prepared glass samples are coded as: BBTTLa, BBTTCe, BBTTSm, BBTTEr, and BBTTYb, as shown in Table 1. Al 2 O 3 powder of 600 grade was used to polish the glass samples. The value density of the samples was determined according to Archimedes' method. The powder X-ray diffraction pattern (XRD) was determined using a Philips PW (1140) diffractometer, and a copper target (Kα = 1.54 Å) was used to study the amorphous properties of prepared glass. A double-beam UV-Visible spectrophotometer (JASCO Corp, v-570, Rel-00, Tokyo, Japan) was used to determine the optical absorption spectrum of the glass. The refractive index was determined with a prism coupler (Metricon Model 2010, Pennington, NJ, USA).
Structural characterization of the glass was carried out using FTIR absorbance spectra (Perkin-Elmer spectrometer). For the prepared glass, the half-value layer, both the linear and mass attenuation coefficients, as well as the mean free pass were measured using a NaI detector system (SPECTECH-NaI 1.5 PX 1.5/2.0 IV, S/N 010723-6), with various gamma sources (Am 241 -5µCI-59.5 keV, Cs 137 -5µCI-662 keV, Co 60 -5µCI-1170, and 1330 keV), which was connected to a computer and based on the multichannel analyzer. Figure 1 shows a collimated beam which was produced at the detector level using a variety of gamma sources (Am 241 -5µCI-59.5 keV, Cs 137 -5µCI-662 keV, Co 60 -5µCI-1170, and 1330 keV), according to the technique described in [4]. pattern (XRD) was determined using a Philips PW (1140) diffractometer, and a copper target (Kα = 1.54 Å) was used to study the amorphous properties of prepared glass. A double-beam UV-Visible spectrophotometer (JASCO Corp, v-570, Rel-00, Tokyo, Japan) was used to determine the optical absorption spectrum of the glass. The refractive index was determined with a prism coupler (Metricon Model 2010, Pennington, NJ, USA). Structural characterization of the glass was carried out using FTIR absorbance spectra (Perkin-Elmer spectrometer). For the prepared glass, the half-value layer, both the linear and mass attenuation coefficients, as well as the mean free pass were measured using a NaI detector system (SPECTECH-NaI 1.5 PX 1.5/2.0 IV, S/N 010723-6), with various gamma sources (Am 241 -5µCI-59.5 keV, Cs 137 -5µCI-662 keV, Co 60 -5µCI-1170, and 1330 keV), which was connected to a computer and based on the multichannel analyzer. Figure 1 shows a collimated beam which was produced at the detector level using a variety of gamma sources (Am 241 -5µCI-59.5 keV, Cs 137 -5µCI-662 keV, Co 60 -5µCI-1170, and 1330 keV), according to the technique described in [4]. pattern (XRD) was determined using a Philips PW (1140) diffractometer, and a copper target (Kα = 1.54 Å) was used to study the amorphous properties of prepared glass. A double-beam UV-Visible spectrophotometer (JASCO Corp, v-570, Rel-00, Tokyo, Japan) was used to determine the optical absorption spectrum of the glass. The refractive index was determined with a prism coupler (Metricon Model 2010, Pennington, NJ, USA). Structural characterization of the glass was carried out using FTIR absorbance spectra (Perkin-Elmer spectrometer). For the prepared glass, the half-value layer, both the linear and mass attenuation coefficients, as well as the mean free pass were measured using a NaI detector system (SPECTECH-NaI 1.5 PX 1.5/2.0 IV, S/N 010723-6), with various gamma sources (Am 241 -5µCI-59.5 keV, Cs 137 -5µCI-662 keV, Co 60 -5µCI-1170, and 1330 keV), which was connected to a computer and based on the multichannel analyzer. Figure 1 shows a collimated beam which was produced at the detector level using a variety of gamma sources (Am 241 -5µCI-59.5 keV, Cs 137 -5µCI-662 keV, Co 60 -5µCI-1170, and 1330 keV), according to the technique described in [4].  BBTTYb  45  25  20  7  ----3   BBTTSm  45  25  20  7  --3 --pattern (XRD) was determined using a Philips PW (1140) diffractometer, and a copper target (Kα = 1.54 Å) was used to study the amorphous properties of prepared glass. A double-beam UV-Visible spectrophotometer (JASCO Corp, v-570, Rel-00, Tokyo, Japan) was used to determine the optical absorption spectrum of the glass. The refractive index was determined with a prism coupler (Metricon Model 2010, Pennington, NJ, USA). Structural characterization of the glass was carried out using FTIR absorbance spectra (Perkin-Elmer spectrometer). For the prepared glass, the half-value layer, both the linear and mass attenuation coefficients, as well as the mean free pass were measured using a NaI detector system (SPECTECH-NaI 1.5 PX 1.5/2.0 IV, S/N 010723-6), with various gamma sources (Am 241 -5µCI-59.5 keV, Cs 137 -5µCI-662 keV, Co 60 -5µCI-1170, and 1330 keV), which was connected to a computer and based on the multichannel analyzer. Figure 1 shows a collimated beam which was produced at the detector level using a variety of gamma sources (Am 241 -5µCI-59.5 keV, Cs 137 -5µCI-662 keV, Co 60 -5µCI-1170, and 1330 keV), according to the technique described in [4]. pattern (XRD) was determined using a Philips PW (1140) diffractometer, and a copper target (Kα = 1.54 Å) was used to study the amorphous properties of prepared glass. A double-beam UV-Visible spectrophotometer (JASCO Corp, v-570, Rel-00, Tokyo, Japan) was used to determine the optical absorption spectrum of the glass. The refractive index was determined with a prism coupler (Metricon Model 2010, Pennington, NJ, USA). Structural characterization of the glass was carried out using FTIR absorbance spectra (Perkin-Elmer spectrometer). For the prepared glass, the half-value layer, both the linear and mass attenuation coefficients, as well as the mean free pass were measured using a NaI detector system (SPECTECH-NaI 1.5 PX 1.5/2.0 IV, S/N 010723-6), with various gamma sources (Am 241 -5µCI-59.5 keV, Cs 137 -5µCI-662 keV, Co 60 -5µCI-1170, and 1330 keV), which was connected to a computer and based on the multichannel analyzer. Figure 1 shows a collimated beam which was produced at the detector level using a variety of gamma sources (Am 241 -5µCI-59.5 keV, Cs 137 -5µCI-662 keV, Co 60 -5µCI-1170, and 1330 keV), according to the technique described in [4]. pattern (XRD) was determined using a Philips PW (1140) diffractometer, and a copper target (Kα = 1.54 Å) was used to study the amorphous properties of prepared glass. A double-beam UV-Visible spectrophotometer (JASCO Corp, v-570, Rel-00, Tokyo, Japan) was used to determine the optical absorption spectrum of the glass. The refractive index was determined with a prism coupler (Metricon Model 2010, Pennington, NJ, USA). Structural characterization of the glass was carried out using FTIR absorbance spectra (Perkin-Elmer spectrometer). For the prepared glass, the half-value layer, both the linear and mass attenuation coefficients, as well as the mean free pass were measured using a NaI detector system (SPECTECH-NaI 1.5 PX 1.5/2.0 IV, S/N 010723-6), with various gamma sources (Am 241 -5µCI-59.5 keV, Cs 137 -5µCI-662 keV, Co 60 -5µCI-1170, and 1330 keV), which was connected to a computer and based on the multichannel analyzer. Figure 1 shows a collimated beam which was produced at the detector level using a variety of gamma sources (Am 241 -5µCI-59.5 keV, Cs 137 -5µCI-662 keV, Co 60 -5µCI-1170, and 1330 keV), according to the technique described in [4].

XRD, Physical Parameters, and UV-VIS-NIR Spectra
The X-ray diffraction (XRD) patterns of the glass samples were measured to investigate the nature of the glass samples, as shown in Figure 2. The absence of any discrete or sharp diffraction peaks in these profiles and the existence of broad bands proves that all the prepared glass samples had an amorphous nature. The density value (ρ) was calculated using Equation (1) [23].
The weight of the glass sample in air is "Wa", whereas the weight of the glass immersed in reference liquid toluene is "Wt", where ρ = 0.864 g cm . The calculated density value of the prepared glass increased from 5.67 g·cm −3 to 6.32 g·cm −3 , which corresponded to BBTTLa and BBTTYb glass, respectively. The results are shown in Table 1.

XRD, Physical Parameters, and UV-VIS-NIR Spectra
The X-ray diffraction (XRD) patterns of the glass samples were measured to investigate the nature of the glass samples, as shown in Figure 2. The absence of any discrete or sharp diffraction peaks in these profiles and the existence of broad bands proves that all the prepared glass samples had an amorphous nature. The density value (ρ) was calculated using Equation (1)

XRD, Physical Parameters, and UV-VIS-NIR Spectra
The X-ray diffraction (XRD) patterns of the glass samples were measured to investigate the nature of the glass samples, as shown in Figure 2. The absence of any discrete or sharp diffraction peaks in these profiles and the existence of broad bands proves that all the prepared glass samples had an amorphous nature. The density value (ρ) was calculated using Equation (1) [23].
The weight of the glass sample in air is "Wa", whereas the weight of the glass immersed in reference liquid toluene is "Wt", where ρ = 0.864 g cm . The calculated density value of the prepared glass increased from 5.67 g·cm −3 to 6.32 g·cm −3 , which corresponded to BBTTLa and BBTTYb glass, respectively. The results are shown in Table 1.  The weight of the glass sample in air is "W a ", whereas the weight of the glass immersed in reference liquid toluene is "W t ", where ρ t = 0.864 g·cm −3 . The calculated density value of the prepared glass increased from 5.67 g·cm −3 to 6.32 g·cm −3 , which corresponded to BBTTLa and BBTTYb glass, respectively. The results are shown in Table 1.
The molecular weights, M wt , of rare earth compounds are ordered as follows: La 2 O 3 < Ce 2 O 3 < Sm 2 O 3 < Er 2 O < Yb 2 O 3 , corresponding to 325.5, 328.24, 348.72, 382.52, and 394.08 g·mol −1 , respectively. Thus, the density increased in the same trend, which means that the highest value of density occurred with Yb 2 O 3 incorporated into the glass matrix; here, the network of the glass is more compact. It is possible to determine the glass sample's molecular volume (V m ) and its oxygen molar volume (V o ) using Equations (2) and (3), respectively. These strongly depend on the value of the densities of the glass samples, tabulated in Table 2.
where "M wti " is the molecular weight and "x i " is the fraction ratio of each oxide. The oxygen molar volume, V O , can be estimated by the relationship as follow: where "n i " is the number of oxygen atoms in each oxide [24]. The number of bonds per unit volume, n b , of the prepared glass and the average force constant (F), calculated from Equations (4) and (5), respectively [25,26].
where n f is the cation coordination number and N a is the Avogadro's number.   The stretching force, f i , of the oxide, i, can be measured using the following formula: The molar volume, V m , decreased from 34.9 cm 3 /mol to 31.6 cm 3 /mol, which corresponded to BBTTLa and BBTTYb, respectively, and the glass structures became more compact due to a reduction in interatomic space or bond length between atoms (r i ). The value of V 0 decreased from 14.1 to 12.7 cm 3 ·mol −1 by increasing both values of n b from 6.5 to 7.14 × 10 22 m −3 and F from 301.21 to 303.04 Nm −1 , when replacing the modified rare earth oxide La 2 O 3 by Yb 2 O 3 . Furthermore, the decrease in V o may indicate a decrement in the formation of NBO atoms reported here. The values of V m , V 0 , n b , and F of the prepared glass are shown in Table 2. Equation (7) was used to compute the oxygen packing density, OPD, [23]: where "C" is the number of oxygen atoms per formula unit. The increase in the value of OPD from 71.06258 mol/liter to 78.40199 mol/liter of BBTTLa and BBTTYb, respectively, was associated with increases in the n b , F, and M wt values of rare earth oxides. The optical absorption spectra of BBTTRE glass are shown in Figure 3. The results on the absorption edge provide important information on the transitions of the band structure of amorphous materials [27]. The absorption bands of BBTTEr glass were detected at 1512, 973, 800, 650, 550, 520, and 490 nm, which corresponded to the transitions from 4 I 15/2 to 4 I 13/2 , 4 I 11/2 , 4 I 9/2 , 4 F 9/2 , 4 S 3/2 , 2 H 11/2 , and 4 F 7/2 , respectively. where "C" is the number of oxygen atoms per formula unit. The increase in the value of OPD from 71.06258 mol/liter to 78.40199 mol/liter of BBTTLa and BBTTYb, respectively, was associated with increases in the nb, F , and Mwt values of rare earth oxides. The optical absorption spectra of BBTTRE glass are shown in Figure 3. The results on the absorption edge provide important information on the transitions of the band structure of amorphous materials [27]. The absorption bands of BBTTEr glass were detected at 1512, 973, 800, 650, 550, 520, and 490 nm, which corresponded to the transitions from 4 I15/2 to 4 I13/2, 4 I11/2, 4 I9/2, 4 F9/2, 4 S3/2, 2 H11/2, and 4 F7/2, respectively. The absorbance spectra of BBTTSm glass exhibited bands at 1620, 1551, 1485, 1379, 1230, 1085, 950, 476, 404, and 368 nm, attributed to the absorption ground state 6 H5/2 to the excited states, 6 H15/2, 6 F1/2, 6 F3/2, 6 F5/2, 6 F7/2, 6 F9/2, 6 F11/2, 4 I13/2 + 4 M15/2, 4 P5/2, and 4 P7/2, respectively. In addition, there was a strong absorption band transition of the level 2 F7/2 to 2 F5/2 of the Yb 3+ -ion-modified BBTTYb glass. The absorption coefficient, α(ν), of the fabricated glass was calculated using the absorbance spectra and the relationship shown below [28]: where A represents the absorbance and d is the glass sample's thickness in cm.
In amorphous material, optical transitions that occur at the absorption edge can be divided into two mechanisms: firstly, direct transitions are where the momentum of the electron from the valance to conduction band is preserved; secondly, there are indirect transitions where it is necessary to cooperate with the absorb/release phonon [29]. Mott and Davis [29] suggested a relationship between photon energy (hν) and absorption coefficient (α) to determine the indirect optical band gap, Eopt, as shown in Equation (9).
where B is a constant known as the band tailing parameter, r, which depends on the type of mechanism transition (r = 2) associated with the allowed indirect transitions [30]. A graph was plotted for (αhν) / versus (hν) to determine the indirect optical band gap, Eopt, as shown in Figure 4. The calculated values of the indirect optical band gap, E , can be obtained by the extrapolation of the linear range of the curve with a linear axis at (Y- The absorbance spectra of BBTTSm glass exhibited bands at 1620, 1551, 1485, 1379, 1230, 1085, 950, 476, 404, and 368 nm, attributed to the absorption ground state 6 H 5/2 to the excited states, 6 H 15/2 , 6 F 1/2 , 6 F 3/2 , 6 F 5/2 , 6 F 7/2 , 6 F 9/2 , 6 F 11/2 , 4 I 13/2 + 4 M 15/2 , 4 P 5/2 , and 4 P 7/2 , respectively. In addition, there was a strong absorption band transition of the level 2 F 7/2 to 2 F 5/2 of the Yb 3+ -ion-modified BBTTYb glass. The absorption coefficient, α(ν), of the fabricated glass was calculated using the absorbance spectra and the relationship shown below [28]: where A represents the absorbance and d is the glass sample's thickness in cm.
In amorphous material, optical transitions that occur at the absorption edge can be divided into two mechanisms: firstly, direct transitions are where the momentum of the electron from the valance to conduction band is preserved; secondly, there are indirect transitions where it is necessary to cooperate with the absorb/release phonon [29]. Mott and Davis [29] suggested a relationship between photon energy (hν) and absorption coefficient (α) to determine the indirect optical band gap, E opt , as shown in Equation (9).
where B is a constant known as the band tailing parameter, r, which depends on the type of mechanism transition (r = 2) associated with the allowed indirect transitions [30]. A graph was plotted for (αhν) 1/2 versus (hν) to determine the indirect optical band gap, E opt , as shown in Figure 4. The calculated values of the indirect optical band gap, E opt , can be obtained by the extrapolation of the linear range of the curve with a linear axis at (Y-axis = 0), which represents the photon energy (hν) [31] and the value of E opt for the prepared glass, as evaluated in Table 3. In the BBTTRE glass system, the formation of TeO 4 caused oxygen anions to be tightly bound to the host materials; thus, the E opt increased with a decrease in the number of NBO [31]. The value of E opt depends on the structure of the prepared glass TBBT modified by 3RE 2 O 3 in mol%, where RE is La, Ce, Sm, Er, or Yb. From the results presented in Table 3, the values of E opt increase from 2.1 to 2.81 eV. The E opt value increased as a result of more bridging oxygen being present (BO) and the decrease in the number of NBO, as confirmed in the FTIR results of the prepared glass discussed here. The value of the refractive index, n, molar polarizability, α m , molar refraction, R m , oxide ion polarizability, (α −2 o ), and the value of optical basicity, (Λ), are important parameters for the fabrication of optical devices, especially fiber optic and laser material. Therefore, we determine these parameters of the studied glass by using the subsequent equations [32]: where N A is Avogadro's number, p is the cation number, and q denotes the number of ions of oxygen. The values of n, R m , α m , and Λ depend on the polarizability of ions; the type of RE was La, Ce, Sm, Er, or Yb, and the prepared BBTT glass was modified with 3RE 2 O 3 in mol%. The values of n, R m , α m , and Λ decreased when the host glass network BBTT was modified with regard to the free ion polarizability due to internal contact and the polarizability of oxide rare earth ions decreased. High oxide ion polarizability and optical basicity are also closely related to the superior optical characteristics of tellurite glass. Herein, rare earth oxides had an order of polarizability of cation, α i , of (La 2 O 3 = 1.32   The metallization criterion, M, for BBTTRE glass was estimated as follow: The change in rare earth La2O3 → Ce2O3 → Sm2O3 → Er2O3 → Yb2O3 → La2O3 modified host matrix TBBT, causing a decrease in the width of the valance band and an increase in M, and consequently, an increase in the optical energy band gap. As shown in Table 3, the BBTTLa glass had the largest value of M and the smallest value of Eopt. In contrast, the BBTTYb glass had the smallest value of M and the highest value of Eopt.

Structural Categorization of Glass Using FTIR Spectra
The FTIR spectra of the investigated glass were measured; consequently, these were deconvoluted using Gaussian fitting into several Gaussian peaks marked as (a − x) bands, as shown Figure   The metallization criterion, M, for BBTTRE glass was estimated as follow: The change in rare earth La 2 O 3 → Ce 2 O 3 → Sm 2 O 3 → Er 2 O 3 → Yb 2 O 3 → La 2 O 3 modified host matrix TBBT, causing a decrease in the width of the valance band and an increase in M, and consequently, an increase in the optical energy band gap. As shown in Table 3, the BBTTLa glass had the largest value of M and the smallest value of E opt . In contrast, the BBTTYb glass had the smallest value of M and the highest value of E opt .

Structural Categorization of Glass Using FTIR Spectra
The FTIR spectra of the investigated glass were measured; consequently, these were deconvoluted using Gaussian fitting into several Gaussian peaks marked as (a − x) bands, as shown Figure [39][40][41]. The different IR peaks observed in the range of 500-800 cm −1 in the investigated glass may be related to the anti-symmetrical and symmetrical vibrations of TeO 2 [41]. The peaks located in the range of 552-563 cm −1 were attributable to Bi-O − bending vibration in BiO 6 octahedral units [42]. The vibration of a continuous TeO 4 trigonal bipyramid network was associated with bands detected in the 576-600 cm −1 range (tbp). These indicated the glass network's more compacted connections [43]. The bands between 616 and 623 cm −1 were related to Ti-O bending vibrations [44]. The occurrence of Te-O ax vibrations in the TeO 4 tetrahedral units was linked to the development of the very strong band which occurred in the region of 648 to 654 cm −1 . The vibrations of BO in TeO 3 /TeO 3+1 units were responsible for the peaks between 671 and 674 cm −1 that were seen in all glass samples. The B-O-B connections in the borate network's mode of vibration were responsible for the bands positioned in the range of 692-695 cm −1 [42]. The bands between 712 and 721 cm −1 were attributable to the NBO stretching modes present in TeO 3 units [43]. The TeO 3 trigonal pyramid (tp) and (TeO 3+1 ) polyhedral units (Te eq -O) as and (Te eq -O) S vibrational modes were responsible for the bands in the 759-772 cm −1 range [42,43]. The bending vibrations of BO 4 at 600 to 800 cm −1 and the B-O bond stretching vibrations of BO 4 tetrahedral units are responsible for the bands that developed between 800 and 1200 cm −1 .
[ [39][40][41]. The different IR peaks observed in the range of 500-800 cm −1 in the investigated glass may be related to the anti-symmetrical and symmetrical vibrations of TeO2 [41]. The peaks located in the range of 552-563 cm −1 were attributable to Bi-Obending vibration in BiO6 octahedral units [42]. The vibration of a continuous TeO4 trigonal bipyramid network was associated with bands detected in the 576-600 cm −1 range (tbp). These indicated the glass network's more compacted connections [43]. The bands between 616 and 623 cm −1 were related to Ti-O bending vibrations [44]. The occurrence of Te-Oax vibrations in the TeO4 tetrahedral units was linked to the development of the very strong band which occurred in the region of 648 to 654 cm −1 . The vibrations of BO in TeO3/TeO3+1 units were responsible for the peaks between 671 and 674 cm −1 that were seen in all glass samples. The B-O-B connections in the borate network's mode of vibration were responsible for the bands positioned in the range of 692-695 cm −1 [42]. The bands between 712 and 721 cm −1 were attributable to the NBO stretching modes present in TeO3 units [43]. The TeO3 trigonal pyramid (tp) and (TeO3+1) polyhedral units (Teeq-O)as and (Teeq-O)S vibrational modes were responsible for the bands in the 759-772 cm -1 range [42,43]. The bending vibrations of BO4 at 600 to 800 cm −1 and the B-O bond stretching vibrations of BO4 tetrahedral units are responsible for the bands that developed between 800 and 1200 cm −1 .  The IR in the regions between 1200 and 1600 cm −1 were attributable to vibrations of B-O bonds from BO3 trigonal units [39]. Absorption from 912 to 925 cm −1 could be related to the stretching vibrations of B-O bond in BO4 units from diborate groups [44,45]. The peaks observed in the region of 990 to 1001 cm −1 may be attributable to the stretching vibrations of B-O-Bi linkages [37,38]. The IR peaks observed in the ranges of 1062-1067 cm −1 may be due to the stretching vibrations of B-O bonds in BO4 units from tri-, tetra-, and penta-borate groups [46]. The two IR peaks in the region of 1118 to 1120 cm −1 and 1162 to 1168 cm −1 in our investigated samples were attributable to TiO4 tetrahedral units [47]. Other IR peaks in the spectral ranges of 1241-1248 cm −1 were associated with the presence of asymmetrical stretching vibrations of B-O bonds in BO3 triangular units from pyroborate groups [47]. The peaks which appeared in the range of 1280-1285 cm −1 were related to the B-O asymmetrical stretching vibration of (BO3) −3 units in meta-and ortho-borate The IR in the regions between 1200 and 1600 cm −1 were attributable to vibrations of B-O bonds from BO 3 trigonal units [39]. Absorption from 912 to 925 cm −1 could be related to the stretching vibrations of B-O bond in BO 4 units from diborate groups [44,45]. The peaks observed in the region of 990 to 1001 cm −1 may be attributable to the stretching vibrations of B-O-Bi linkages [37,38]. The IR peaks observed in the ranges of 1062-1067 cm −1 may be due to the stretching vibrations of B-O bonds in BO 4 units from tri-, tetra-, and penta-borate groups [46]. The two IR peaks in the region of 1118 to 1120 cm −1 and 1162 to 1168 cm −1 in our investigated samples were attributable to TiO 4 tetrahedral units [47]. Other IR peaks in the spectral ranges of 1241-1248 cm −1 were associated with the presence of asymmetrical stretching vibrations of B-O bonds in BO 3 triangular units from pyroborate groups [47]. The peaks which appeared in the range of 1280-1285 cm −1 were related to the B-O asymmetrical stretching vibration of (BO 3 ) −3 units in meta-and ortho-borate groups [45]. The next absorption bands in the spectral ranges of 1348-1349 cm −1 were attributable to symmetrical stretching vibrations of B-O bonds in triangular BO 3 units from meta-, pyro-, and ortho-borate groups [47,48]. The IR peak at 1375 cm −1 in all glass samples may have been due to the asymmetrical stretching vibrations of B-O bonds in triangular BO 3 units [40]. The IR peaks in the ranges of 1401-1404 cm −1 can be attributed to the asymmetrical stretching vibrations of B-O triangles with BO 3 , B 2 O − , and stretching vibrations of borate triangles with NBO in various borate groups. The stretching vibrations of the B-O bonds in BO 3 units obtained from different forms of borate groups were responsible for the bands seen between 1428 and 1430 cm −1 [40]. The peak at 1461 cm −1 may have been the result of three NBO oxygens in B-O-B links stretching in an anti-symmetrical manner [46]. All the IR bands in Table 4 were attributed to deconvolution FTIR spectra, as shown in Figure 5. Additionally, the ratio of TeO 4 (tbp) to TeO 3 (tp) conversion was determined using the FTIR spectra. The ratio values of TeO 4 /TeO 3 were 0.473, 0.504, 0.51, 0.52, and 0.53, corresponding to BBTTLa, BBTTCe, BBTTSm, BBTTEr, and BBTTYb, respectively. The ratio of transferring BO 4 into BO 3 was also determined from the deconvoluted FTIR spectra.
Values of the ratio BO 4 /BO 3 were 0.415, 0.5, 0.51, 0.52, and 0.53, which corresponded to BBTTLa, BBTTCe, BBTTSm, BBTTEr, and BBTTYb, respectively. The increases in the ratios of TeO 4 /TeO 3 and BO 4 /BO 3 show that the glass became more resistant as a result of the formation of additional bridging oxygens (BOs). Thus, the formation of BO sites with increased atomic numbers of rare earth elements resulted in a strictly dense glass structure that confirmed the increment in the ρ and decrement of V m values for BBTTRE in the order similar to that La 2 O 3 → Ce 2 O 3 → Sm 2 O 3 → Er 2 O 3 → Yb 2 O 3 → La 2 O 3 glass samples, which was consistent with the parameter changes.

Attenuation Parameters
The total mass attenuation coefficient, µ m = ln Io I ρd , and the linear attenuation coefficient, µ = ln Io I d , are calculated using the ratio between the intensities of the measured incident, I 0 , and the transmission radiation, I; d is the thickness of the shielding material. HVL = 0.693 µ , and the MFP parameter was calculated as MFP = 1 µ . Figure 6 shows the calculated linear attenuation coefficient (LAC) of the prepared glass for different energies (59.5, 622, 1170, and 1330 keV) compared with commercially available glass shielding materials, namely, RS360 and RS 520. For instance, the LAC value for BBTTYb glass exhibited the best shielding properties at the energies of 622, 1170, and 1330 keV at 59.5 keV, as compared with RS 360 and RS520 glass. Furthermore, the prepared glass (BBTTER) with a composition of 25B 2 O 3 -20Bi 2 O 3 -45TeO 2 -7TiO 2 (BBTT) modified by 3RE 2 O 3 in mol%, where RE was La, Ce, Sm, Er, or Yb, was better than that reported in other glass systems modified with rare earth elements, such as 39B 2 O 3 -30PbO-20MO-10Bi 2 O 3 -1Eu 2 O 3 (where M is K, Na, Ca, Sr, or Ba) [49], B 2 O 3 -CaO-TeO 2 -ZnO-ZnF 2 -Sm 2 O 3 [50], and B 2 O 3 -SrCO 3 -Nb 2 O 3 -BaCO 3 -Dy 2 O 3 [51]. Tables 5 and 6 present the measured mass attenuation coefficients (MACs) of the prepared samples in comparison with the calculated theoretical values using the MIKE and WinXcom software. The HVL parameter signifies the material thickness that reduces the intensity of radiation by half. Herein, the values for HVL and MFP of the prepared glass were lower than that reported for commercial materials, such as window glass, serpentine, concrete, SCHOOT glass RS253, hematite serpentine, Ilmenite, and SCHOOT glass RS323 [52][53][54]. Figure 7 shows the measured values of MAC, LAC, HVL, and MFP for the BBTTEr glass at 59.5, 622, 1170, and 1330 keV, compared with the theoretical values calculated using MIKE software. The results showed good agreement between the measured mass attenuation coefficients and calculated values using MIKE software. Hence, the experimental attenuation results for the investigated prepared glass showed superior radiation shielding performance. Finally, we can estimate that the shielding parameters increased with the increasing ratios of TeO 4 /TeO 3 and BO 4 /BO 3 with bridging oxygens (BOs) of oxide glass, representing a candidate for the fabrication of superior shielding material.

Conclusions
Incorporating the rare earth ions La +3 , Ce +3 , Sm +3 , Er +3 , and Yb +3 as glass matrix modifiers, resulting in 25B2O3-20Bi2O3-45TeO2-7TiO2, it was found that the density of the studied glass increased from 5.67 to 6.31 gm.cm −3 , nb increased from 6.5 to 7.14 × 10 22 m −3 , and the OPD increased from 71.1 to 78.4 mol/L −1 with an increased atomic number of incorporated rare earth ions. This is due to the increased amount of bridging oxygen (BO) and decreased number of NBOs in the prepared glass, which also led to the increased Eopt, from 1.71 to 2.8 eV, when La2O3 was replaced by Yb2O3. In addition, the molar polarizability, αm, decreased from 9.35 to 7.84 (Ӑ 3 ), Λ decreased from 1.15 to 1.03, and the refractive index decreased from 2.69 to 2.45: this was due to the good agreement with the replacement of modifiers of La2O3 = 1.32Ӑ 3 , Ce2O3 = 1.28Ӑ 3 , Sm2O3 = 1.16 Ӑ 3 , Er2O3 = 0.89 Ӑ 3 , Yb2O3 = 0.86 Ӑ 3 , ΛTeO4 0 = 0.99, ΛTeO4 − = 1.23, and ΛTeO3 − = 0.82, in the order of La +3 → Ce +3 → Sm +3 → Er +3 → Yb +3 . The high refractive index, electronic polarizability, and optical basicity of the prepared glass containing La2O3 led to the achievement of significant third-order optical susceptibility. This glass may be used to produce high-quality optical nonlinear devices. The FTIR spectra confirmed the existence of TeO4, TeO3, BO4, BO3, BiO6, and TiO4 in the glass matrix. The glass containing Yb 3+ ions had a high value of the TeO4 phase with BO. When compared with prepared glass, Yb 3+ -ion-containing glass exhibited higher MAC values

Conclusions
Incorporating the rare earth ions La +3 , Ce +3 , Sm +3 , Er +3 , and Yb +3 as glass matrix modifiers, resulting in 25B 2 O 3 -20Bi 2 O 3 -45TeO 2 -7TiO 2 , it was found that the density of the studied glass increased from 5.67 to 6.31 gm.cm −3 , n b increased from 6.5 to 7.14 × 10 22 m −3 , and the OPD increased from 71.1 to 78.4 mol/L −1 with an increased atomic number of incorporated rare earth ions. This is due to the increased amount of bridging oxygen (BO) and decreased number of NBOs in the prepared glass, which also led to the increased E opt , from 1.71 to 2.8 eV, when La 2 O 3 was replaced by Yb 2 O 3 . In addition, the molar polarizability, α m , decreased from 9.35 to 7.84 (Ă 3 ), Λ decreased from 1.15 to 1.03, and the refractive index decreased from 2.69 to 2.45: this was due to the good agreement with the replacement of modifiers of La 2 O 3 = 1.32 Ă 3 , Ce 2 O 3 = 1.28 Ă 3 , Sm 2 O 3 = 1.16 Ă 3 , Er 2 O 3 = 0.89 Ă 3 , Yb 2 O 3 = 0.86 Ă 3 , Λ TeO4 0 = 0.99, Λ TeO4 − = 1.23, and Λ TeO3 − = 0.82, in the order of La +3 → Ce +3 → Sm +3 → Er +3 → Yb +3 . The high refractive index, electronic polarizability, and optical basicity of the prepared glass containing La 2 O 3 led to the achievement of significant third-order optical susceptibility. This glass may be used to produce high-quality optical nonlinear devices. The FTIR spectra confirmed the existence of TeO 4 , TeO 3 , BO 4 , BO 3 , BiO 6 , and TiO 4 in the glass matrix. The glass containing Yb 3+ ions had a high value of the TeO 4 phase with BO. When compared with prepared glass, Yb 3+ -ion-containing glass exhibited higher MAC values and lower HVL values, which was directly related to its high shielding characteristics. This glass is an excellent choice for use in low-energy diagnostic applications as a transparent shielding material.

Informed Consent Statement:
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Data Availability Statement: Not applicable.