Journal of Non-Crystalline Solids xxx (xxxx) xxx–xxx Contents lists available at ScienceDirect Journal of Non-Crystalline Solids journal homepage: www.elsevier.com/locate/jnoncrysol Structural and optical properties of TeO2-Li2O-ZnO-Nb2O5-Er2O3 glass system ⁎ N. Elkhoshkhanya, , Samir Y. Marzoukb, Nourhan Moataza, Sherif H. Kandila a b Department of Material Science, Institute of Graduate Studies and Researches, Alexandria University, 163 Horreya Avenue, Shatby 21526, Egypt Department of Basic and applied science, Faculty of Engineering and Technology, Arab Academy of Science and Technology, Egypt A R T I C LE I N FO A B S T R A C T Keywords: Tellurite glasses Optical properties Er3+ ions Judd-Ofelt Quinary tellurite glass system in the percentages of 75TeO2–5Li2O–10ZnO–(10–x) Nb2O5–xEr2O3 where (x = 0.0, 0.5, 1.0, 1.5, 2.0, and 2.8 mol%) have been prepared and characterized. Both Fourier-transform-infrared (FTIR) and Raman spectroscopies were performed to study the structural changes correlated with the glass network. The thermal characteristics of the system were speciﬁed which showed a higher thermal stability (> 100 °C) due to the formation of more bridging oxygen's (BO's) revealed by (FTIR) and Raman spectroscopies. The optical absorption spectra within near UV–visible regions were performed, and exhibited nine absorption bands centered around 1536, 977, 798, 653, 545, 524, 490, 450, and 443 nm corresponding to the 4I15/2 ground state to the various excited states 4I13/2, 4I11/2, 4I9/2, 4F9/2, 4S3/2, 2H11/2, 4F7/2,4F5/2, and 4F3/2 respectively. The same measurement also showed increasing values of the optical band gap (Eg) form 2.70 to 2.90 (eV) and decreasing the refractive index (n) from 2.48 to 2.42. Both the extinction coeﬃcient data and the complex dielectric functions of the glasses were estimated. The diﬀerent optical parameters were distinctly aﬀected by increasing the Er2O3 (mol %) and the structural changes. The radiative properties of the glass were calculated using J-O parameters. The Branching ratio (β) of 4I13/2 → 4I15/2 transition peaked at 1520.48 nm for Er3+ ions has the highest value (1.000) also, the radiative lifetime (τ) of the same transition changed from 1.4510 to 1.8483. The gain cross-section of the laser transition level from 4G11/2 → 4I15/2 changed from 1.44 × 10−20 to 1.92 × 10−20 cm−1 in the existing glass system. The acquired results exhibited that the existent glass can be a good candidate in the ﬁber drawing and laser, non-linear optical applications. 1. Introduction TeO2-based glasses have been recently the subject of many types of research according to their promising mechanical, electrical, physical, optical, and magnetic properties as well their chemical durability; lower manufacturing temperatures, large refractive indices, high dielectric characteristics, and good optical transmission [1, 2]. All of these unique properties made the TeO2-glass a suitable material for optical applications like laser materials and nonlinear applications . The TeO2-glasses are distinguished by their ability to have two structural units, one is TeO4 with the Te element positioned in trigonal bipyramids (tbps) and the other is TeO3 with the Te element positioned in trigonal pyramids (tps) with a lone pair in both . The TeO2 cannot be vitriﬁed on its own but it can with the aid of a network modiﬁer such as alkaline earth metal, transition metal or rare earth oxides to easily form a glass. It was reported that the insertion of Nb2O5 in tellurite glass stabilizes the glass matrix and it may have a dual modiﬁcation ⁎ role, one as a network former and the other as a network modiﬁer  thereby enhances the thermal stabilization (as proved previously ). The inclusion of Er3+ (as a rare earth metal) increases the chemical durability of the glass due to its lower oxidizing in the air as well its stability. Its addition makes the glass possess speciﬁc applications in the optoelectronics, glass ﬁbers and also the medical ﬁeld [7, 8]. The addition of ZnO increases both the tendency of glass formation, refractive index while decreases the optical energy band gap . Insertion of alkali oxides M2O (where M = Li, Na or K) to TeO2 based glasses create more non-bridging oxygen's (NBO's) which result in decreasing the coordination number of the glass forming units and hence decreasing the glass strength . The present system was chosen due to these oxides and doped with Er3+ due to its advanced applications especially in photonics and laser [11, 12]. This research aims to report our results on the structural, optical properties of the prepared erbium-doped tellurite glass. All the results will be discussed with respect to increasing Er2O3. Corresponding author. E-mail address: Elkhoshkhany@alexu.edu.eg (N. Elkhoshkhany). https://doi.org/10.1016/j.jnoncrysol.2018.08.011 Received 27 May 2018; Received in revised form 8 August 2018; Accepted 9 August 2018 0022-3093/ © 2018 Elsevier B.V. All rights reserved. Please cite this article as: Elkhoshkhany, N., Journal of Non-Crystalline Solids (2018), https://doi.org/10.1016/j.jnoncrysol.2018.08.011 Journal of Non-Crystalline Solids xxx (xxxx) xxx–xxx N. Elkhoshkhany et al. Fig. 1. Shape of the prepared TLZNE glass samples. Fig. 3. The FTIR absorption spectra of TLZNE glasses (the inset ﬁgure is the transmittance spectra for the glass). Fig. 2. XRD charts of TLZNE glasses. Table 2 Band position (cm−1) and its corresponding peak assignments of the FTIR spectra of the TLZNE glasses according to Fig. 4 2. Experimental work Band position A glass system 75TeO2–5Li2O–10ZnO–(10 − x)Nb2O5–(x)Er2O3; (x = 0.0, 0.5, 1.0, 1.5, 2.0, 2.8 mol%) was prepared using meltquenching method by initially mixing appropriate amounts of Tellurium dioxide (TeO2), Lithium oxide (Li2O), Zinc oxide (ZnO), Niobium pentoxide (Nb2O5), and Erbium oxide (Er2O3) which all of them were +99.99% purity, Sigma-Aldrich. The powder admixtures were then placed in a platinum crucible and heated in a muﬄe furnace at 950 °C for 10 min. The mixtures were then whiskered to get homogeneous melts. The melts were poured on a stainless-steel mold in the room temperature which was previously preheated at 340 °C. The glassy nature of the samples was checked using the X-ray diﬀraction (XRD) recording with a Schimadzu 7000 diﬀractometer, (Japan) system with Cu as a radiation source (λ = 1.54060 A), 30 kV accelerating potential and 30.0 mA tube current. The scanning was made from 4 to 90° at a step width of 0.02°. The characteristics temperatures like glass transition (Tg) and crystallization (Tc) temperatures were estimated by DSC (TA Instruments, SDT Q600) by heating 15 mg of the samples in an −1 906 cm 760–788 cm−1 646–660 cm−1 470–450 cm−1 421 cm−1 Assignments Stretching vibration of NbeO in NbO6 (TeeO) symmetrical and (TeeO) asymmetrical vibrational modes of TeO3/TeO3+1units Axial symmetrical stretching vibrational of (TeeO) of tetrahedral (TeO4) unit Symmetrical stretching or bending vibration of (Te-O-Te) linkages ZnO4 tetrahedra group open platinum pan heated with a rate of 10 °C/min from the room temperature up to about 800 °C in a nitrogen atmosphere with a ﬂow rate of 15 Psi. The infra-red (IR) spectra were performed at the room temperature with the help of an FTIR system, type spectrum BX (PerkinElmer) using the KBr pellet technique within the region of 350–4400 cm−1. Raman analysis was used also to characterize the glass which carried out using a Senterra Raman microscope (Bruker Optik, Table 1 Glass code, composition, density (ρ), molar volume (Vm) and oxygen packing density (O.P.D) of the TLZNE glasses. Glass sample code TLZNE1 TLZNE2 TLZNE3 TLZNE4 TLZNE5 TLZNE6 Composition (mol %) TeO2 Li2O ZnO Nb2O5 Er2O3 75 75 75 75 75 75 5 5 5 5 5 5 10 10 10 10 10 10 10 9.5 9.0 8.5 8.0 7.2 0.0 0.5 1.0 1.5 2.0 2.8 2 ρ ± 0.02 (gm/cm3) Vm ± 0.2 (cm3/mol) O.P.D ± 0.3 (mol/l) 4.12 4.21 4.24 4.53 4.71 4.83 37.84 37.11 36.98 34.77 33.57 32.96 43.02 57.66 57.59 60.98 62.85 63.53 Journal of Non-Crystalline Solids xxx (xxxx) xxx–xxx N. Elkhoshkhany et al. polishing the samples to produce two parallel faces through which the beam can be easily passed. The thickness-which is a signiﬁcant parameter in calculating the attenuation and the absorption coeﬃcient - was measured accurately by a micrometer. The small parts and the residues were then ground to be powder form to agree with the needs of (XRD), (FTIR), (Raman), and (DSC). 3. Results and discussion All the synthesized glasses were bubble free, transparent and light pink color as in Fig. 1. The XRD patterns for all the prepared TLZNE glasses were observed to have no sharp peaks which conﬁrm the glassy nature of the samples as in Fig. 2. 3.1. Density, molar volume, and oxygen packing density The density (ρ), the molar volume (Vm), and the oxygen packing density (O.P.D) were obtained according to the relations in Ref  and their values are in Table 1. The density and molar volume values vary from 4.12 to 4.83 ± 0.02 (g/cm3) and from 37.84 to 32.96 ± 0.2 (cm3/mol) respectively. The density values increase with increasing Er2O3 because of the heavy molecular mass of Erbium (III) oxide (382.52 g/mol) rather than the Niobium (V) pentoxide (265.81 g/mol); this makes the glass becomes denser when more Er3+ ions are added . Decreasing the molar volume presented by the glass was due to the variance of the ionic radii between the two oxides (i.e Nb2O5 and Er2O3). The (O.P.D) increases from 43.02 to 63.53 ± 0.3 mol/L as in Table 1 due to the excess of the oxygen atoms number per unit composition . 3.2. FTIR and Raman spectroscopy Fig. 4. De-convolution of Raman spectra of (a) TLZNE1 and (b) TLZNE6 glasses. The FTIR spectra of the present TLZNE glasses are represented in Fig. 3 inside the region 400–1000 cm−1. There are ﬁve major IR absorption bands that were observed at 421, 470–450, 646–660, 760–788 and 906 cm−1. The FTIR bands positions of the current glasses and their assignments are in Table 2. The tellurium oxide may be found in two forms of structural conﬁguration units namely trigonal bipyramids (tbps) (TeO4) and trigonal pyramid (tps) (TeO3) . The bands appear in the region 450–470 cm−1 are assigned to the symmetrical stretching or the bending vibrations of TeeOeTe linkages  which were formed by corner-sharing of TeO4, TeO3+1 polyhedra and TeO3 units . These bands were shifted from higher to lower wave number with increasing Er2O3 (mol %) which indicate the cleavage of TeeOeTe linkages. This can be understood as; the insertion of Er2O3 to TeO2 glass network may forms EreTeeO, EreOeTe and/or EreOeEr bonds instead of TeeOeTe linkages. The bands which appear inside the regions 646–660 and 760–788 cm−1 are ascribed to the axial symmetrical stretching vibrational modes of (TeaxeO)s of TeO4 tetrahedra and the (TeeO)s, (TeeO) as vibrational modes of TeO3+1 polyhedra or TeO3 trigonal bipyramid units . These bands were shifted from higher to lower wavenumber due to the structural changes that took place in the glass network. It was suggested that the addition of Er2O3 could break the axial TeeO bonds of TeO4 units then transform it into TeO3 (tps) via TeO3+1 but still the ratio of TeO4 units is larger [18, 19]. This means that more (BO's) are present within the network which causes the density of the glass to increase and the molar volume to decrease. The bands appear around 906 cm−1 are speciﬁed to NbeO bonds stretching vibrations in NbO6 octahedra. These bands were shifted toward higher wavenumber due to the deformation of the NbO6 octahedra because of the addition of Er2O3 . The bands which appear around 421 cm−1 are assigned to ZnO4 tetrahedra groups . The experimental and de-convoluted Raman spectra of TLZNE1 and TLZNE6 glasses by using Gaussian function are indicated in Fig. 4 and the peaks centers and their assignments are in Table 3. The Raman spectrum consists of three spectral regions, the ﬁrst one is the low Table 3 De-convolution result of Raman spectra of TLZNE1 and TLZNE6 glasses according to Fig. 5. Peak symbol Peak position in cm−1 TLZNE1 TLZNE6 A ___ 367 B 423 434 C 474 510 D ___ 569 E 658 690 F 736 805 G 884 835 Assignments TeO3 tps units with two or three nonbridging oxygen Vibrations of lithium cations and ZnO4 tetrahedra group Symmetrical stretching or bending vibration (TeeOeTe) (OeTeeO) linkages are replaced by (OeTeeEr) Axial Symmetric stretching vibrations of (TeeO) of tetrahydral (TeO4) units Stretching vibration of (TeeO) from TeO3 tp units or TeO3+1 polyhedra Stretching vibration of NbeO in NbO6 Ettlingen, Germany) with a laser excitation line of 785 nm and a power at the surface of the sample 50 mW. The data were collected across three spectral windows that together spanned (40–4450 cm−1) at a spectral resolution of (3–5 cm−1). The optical spectra within the visible and near ultraviolet (UV) regions were recorded at the room temperature. Computer-aided two-beam spectrophotometer (JASCO Corp, v570, Rel-00 Japan) in 200–2500 (nm) region has been used to record the absorption. A resolution of 0.2 nm and a distance of 2 nm were performed for 1155 measuring points. Sample preparation was made to remove the surface irregularities and other impediments to the transmission which may cause scattering to the incident light beam - via 3 Journal of Non-Crystalline Solids xxx (xxxx) xxx–xxx N. Elkhoshkhany et al. Fig. 5. DSC curves of TLZNE glasses (the inset ﬁgure represents the DSC curve of the sample TLZNE1). 884–850 cm−1 is regarded to the stretching of Nb and its neighboring non-bridging oxygen's in NbO6 octahedra . This band shifts to lower wave number likely due to the deformation of NbO6 octahedra with growing Er2O3. Table 4 Glass transition temperature (Tg), onset of the crystallization temperature (Tx), temperature of the crystallization (TC), and thermal stability (ΔT) of the TLZNE glasses. Sample Tg (°C) Tx (°C) TC (°C) ΔT = Tx − Tg(°C) TLZNE1 TLZNE2 TLZNE3 TLZNE4 TLZNE5 TLZNE6 348.45 347.81 352.20 355.03 356.07 360.00 525.47 541.00 522.70 510.00 519.30 516.29 559.03 598.70 581.70 542.00 541.00 533.70 177.02 193.19 170.50 154.97 163.23 156.29 3.3. DSC measurements The Thermal behavior of TLZNE glasses is represented by the DSC curves in Fig. 5. The temperature of the glass transition (Tg), the onset of the crystallization temperature (Tx), the temperature of the crystallization (Tc), and the thermal stability ΔT = (Tx–Tg) of the present glasses are mentioned in Table 4. The large glass thermal stability is a signiﬁcant factor in the ﬁber manufacturing operation  also, large ΔT provides a strong inhibition of the nucleation and hence crystallization. From the results, the temperature Tg changes from 347.81 to 360.00 °C with increasing the concentration of Er3+ ions in the glass as well the higher ΔT values (> 100 °C) (which are higher than other Er3+doped-tellurite glasses ) which indicate increasing the bond strength and hence the rigidity of the glass matrix. This result was also conﬁrmed by the formation of more (BO's) as indicated form IR spectra. frequency part (> 300 cm−1) which is speciﬁed to the combined modes of local structures and heavy metals vibrational modes, the second intermediate region (300–665 cm−1) which is ascribed to deformation of the vibrational modes of the glass network with bridged oxygen's (BO's) while the third is the high-frequency region (< 665 cm−1) which is ascribed to the stretching vibrational modes of the glass network former . The Raman spectra intensity increase with increasing Er2O3 from 0.5 to 2.8 (mol%). The structures of these glasses were investigated as; the band labeled as (A) around 367 cm−1 is assigned to the TeO3 trigonal pyramids units with two or three non-bridging oxygen's . The band that labeled as (B) around 423–434 cm−1 is assigned to the vibrations of lithium cations  and/or ZnO4 tetrahedra groups . The band (C) around 474–510 cm−1 is assigned to the symmetrical or bending vibrations of (TeeOeTe) linkages at corner sharing sites . The band labeled as (D) which resonated at 569 cm−1 is regarded to the asymmetrical stretching of the continuous network composed TeO4 (tbps) and (OeTeeO) linkages replaced by (OeTeeEr) . The band labeled as (E) around 658–690 cm−1 is ascribed to the asymmetrical stretching of the continuous network composed of TeO4 (tbps) . The band that labeled as (F) around 736–805 cm−1 is regarded to the stretching vibrations of (TeeO) bonds containing (NBO's) in TeO3 (tps) and TeO3+1 polyhedra [13, 27]. The band labeled (G) around 3.4. Optical absorption spectra The optical spectra of the rare earth doped glasses are the result of two absorptions; the ﬁrst one is the intrinsic absorption which occurs at the short and long wavelengths, while the second is the extrinsic absorption which is correlated to the internal electronic transitions especially within the 4f-shell of the rare earth ions . The spectra of the synthesized TLZNE glasses are presented in Fig. 6. Energy levels higher than 4F3/2 were not noticed because of the intrinsic absorption band gaps. The absorption bands correlated to the 4f–4f transitions of the Er3+ ions coincided with the 4I15/2 ground state to diﬀerent excited states. The spectra consist of nine absorption bands centered around 1536, 977, 798, 653, 545, 524, 490, 450, and 443 nm coincide to the 4 Journal of Non-Crystalline Solids xxx (xxxx) xxx–xxx N. Elkhoshkhany et al. Fig. 6. Absorption spectra of TLZNE glasses. increase of the electronic absorption edge . The absorption coeﬃcient (α) can be determined via using Relation (1) I˳ α (λ ) = Ln ⎛ ⎞/ d (cm − 1) ⎝I⎠ (1) where, Io and I are the intensities of the incident and the transmitted radiations respectively, and (d) is the thickness of the sample . Practically, the optical band gap (Eg) evaluation is based on the optical absorption coeﬃcient measurement near the absorption edge. It was reported that, glasses with high refractive indices and low energy gaps are favorable for the strong optical ﬁeld . For the amorphous materials, Tauc , Davis and Mott  presented the computation of the optical energy gap. For the absorption by indirect transition, the absorption coeﬃcient α (ν) can be calculated through Relation (2) (αhν )1/2 = A(hν − Eg (eV)) (2) where, A is a constant, and hν is the incident radiation photon energy. The optical band gap can be acquired through extrapolation from the linear parts in the ﬁgures that represent (αhν)1/2 versus hν as in Fig. 7. From Table 5 one can observe that, Eg values increase from 2.7 to 2.9 eV. Increasing the Er2O3 (mol %) led to this increase of Eg which is usually coincide to the excess of bridging oxygen's (BO's) in the network of the glass as deduced from IR results. Actually, pure TeO2 consist mainly of TeO4 trigonal bipyramid polyhedral (tbp) units which may transform to TeO3 through TeO3+1 with the addition of the modiﬁer to TeO2 . Urbach energy (ΔE) is a measure of the disorder in amorphous solids (i.e. the larger is the ΔE, the more disorder there is) . ΔE can be estimated from the slopes of the linear parts of representing Ln(α) against hν corresponding to Relation (3) and as represented in Fig. 8 Fig. 7. Representation of (αhν)1/2 Vs (hν) of TLZNE glasses. 4 I15/2 ground state to the various excited states 4I13/2, 4I11/2, 4I9/2, 4F9/2, S3/2, 2H11/2, 4F7/2,4F5/2, and 4F3/2 respectively [31–33]. The absorption bands < 300 nm could not be measured because of the rapid 4 5 Journal of Non-Crystalline Solids xxx (xxxx) xxx–xxx N. Elkhoshkhany et al. Table 5 Values of optical band gap (Eg), Urbach energy (ΔE), refractive index (n), molar refraction (RM), molar polarizability (∝m), metallization (M), electronic polarizability of the oxide ion (∝°2 − ), the optical basicity (Λ) and Cauchy coeﬃcients (A, B) of TLZNE glasses. Sample Eg (eV) ΔE (eV) n RM (cm3/mol) ∝m×10−24 (cm3/mol) M ∝°2 − (Å3) Ʌ A B × 10−14 (m2) TLZNE1 TLZNE2 TLZNE3 TLZNE4 TLZNE5 TLZNE6 2.70 2.75 2.76 2.76 2.80 2.90 0.208 0.231 0.249 0.279 0.287 0.302 2.48 2.47 2.46 2.46 2.45 2.42 23.94 23.34 23.23 21.83 21.01 20.40 9.49 9.25 9.21 8.65 8.33 8.09 0.367 0.371 0.372 0.372 0.374 0.381 3.82 3.72 3.71 3.46 3.30 3.20 1.23 1.22 1.22 1.19 1.16 1.15 2.26 2.07 2.05 2.03 2.04 2.04 2.28 2.21 1.40 1.20 2.70 0.50 Fig. 8. Representation of Ln(α) Vs (hν) of TLZNE glasses. Fig. 10. Dependence of the refractive index (n) on the wavelength of TLZNE glasses. hν ⎞ Ln (α ) = ⎛ −C ⎝ ΔE ⎠ (3) where C is a constant . The Urbach energies are found to increase from 0.208 to 0.302 eV with increasing Er2O3 as in Table 5. Increasing ΔE values means increasing the level of the disorder with increasing of Er2O3 (mol %) which is compatible with XRD results. The refractive index (n) values can be gained using Relation (4) . 2 ⎛n − 1⎞ = 1 − 2 + 2 n ⎠ ⎝ ⎜ ⎟ Eg 20 (4) Table 5 shows the decreasing of (n) from 2.48 to 2.42 with increasing Er2O3 (mol %) from 0 to 2.8 mol%. The higher values of (n) are expected due to the higher polarization of the TeO2 network . The molar refraction (RM) can be calculated using Relation (5) . n2 − 1 ⎞ Vm (cm3/mol) RM = ⎛ 2 n ⎝ + 2⎠ ⎜ ⎟ (5) where Vm represents the molar volume. The RM of TLZNE glasses decrease from 23.94 to 20.40 (cm3/mol) with increasing of Er2O3 as in Table 5. The RM is correlated to the molar electronic polarizability of a material (∝m) as indicated by Relation (6) . Fig. 9. Dependence of the extinction coeﬃcient (k) on the wavelength of TLZNE glasses. 3 ⎞ RM (cm3/mol) ∝m = ⎛ ⎝ 4π N ⎠ 6 (6) Journal of Non-Crystalline Solids xxx (xxxx) xxx–xxx N. Elkhoshkhany et al. Fig. 12. Representation of the refractive index factor (n2−1) TLZNE glasses. −1 Vs (E2) of where, ∝i is the cation polarizability, P and q denote the numbers of cations and oxide ions respectively. The calculated oxide ions polarizability values (∝°2 −) are mentioned in Table 5 which decrease from 3.82 to 3.20 Å3 across increasing Er2O3 from 0 to 2.8 mol%. This decrease of (∝°2 −) is due to the diﬀerence in the cation polarizability between Te4+ cation (1.595 Å3) and Er3+ cation (0.89 Å3), and this also proves the opposite relationship between (∝°2 −) and the energy gap (Eg). The optical basicity (Λ) depending on the polarizability of oxide ion can be computed using Relation (9) . 1 Λ = 1.67 ⎛1 − 2 − ⎞ ∝° ⎠ ⎝ Fig. 11. (a) The real (ε') and (b) the imaginary (ε″) optical dielectric constant Vs the wavelength of TLZNE glasses. Values of Λ are in Table 5 which decrease from 1.23 to 1.15 with growing Er2O3 mol%. These values of Λ conﬁrm the direct correlation between the optical basicity and the polarizability of the oxide ion where both decrease with increasing Er2O3 . where N is the number of the polarizable ions per mole which assumed to be equal to the Avogadro's number. The resultant values of (∝m) decrease from 9.49 to 8.09 × 10−24 (cm3/mol) with increasing Er2O3 as tabulated in Table 5. Accordingly, decreasing the RM is in direct relation with reducing the glass polarizability . The metallization criterion (M) can be gained by Relation (7) . M=1− Rm Vm 3.5. Determination of the optical constants The real refractive index part (n) of the complex refractive index as a function of the reﬂectance (R) and coeﬃcient of the extinction (k) can be given by Relation (10) which is regarding Fresnel's theory where, the appropriate root of the equation is considered as the refractive index . (7) Values of (M) of TLZNE glasses are mentioned in Table 5 and fell in the range of 0.367–0.381. The existence of (M) in this region conﬁrms the applicability of the existing glass to the non-linear optical applications . The oxygen ion electronic polarizability (∝°2 − ) based on the energy gap can be given from the optical absorption data by using Relation (8) . ⎡ V ∝°2 − = ⎢ m ⎛⎜1 − 2.52 ⎝ ⎣ Eg ⎞ ⎟ − 20 ⎠ ⎤ ∑ P ∝i ⎥ q−1 i ⎦ (9) R= (n − 1)2 + k 2 (n + 1)2 + k 2 (10) The coeﬃcient of extinction (k) can be given by Eq. (11)  which represents a relation between the absorption coeﬃcient (α) and the extinction coeﬃcient. k= (8) αλ 4π (11) Fig. 9 represents the variance of (k) with the wavelength (λ) of the 7 Journal of Non-Crystalline Solids xxx (xxxx) xxx–xxx N. Elkhoshkhany et al. Table 6 Values of Wemple–DiDomenico dispersion parameters (Eo) and (Ed), the average cation coordination number(Nc), linear refractive index n(0), lattice oscillator strength (El), wavelength at zero material dispersion (λc), Abbe dispersion number (νd), second-order index of refraction (n2), third-order nonlinear optical susceptibility (χ3) of TLZNE glasses. Samples Eo Ed Nc n(0) El (eV) λc ± 0.03 (μm) νd n2 ± 0.04 × 1013 χ3×10−13 TLZNE1 TLZNE2 TLZNE3 TLZNE4 TLZNE5 TLZNE6 10.10 10.20 11.64 12.29 9.56 16.97 45.20 38.02 39.77 40.66 36.33 54.05 7.63 6.42 6.71 8.86 6.13 9.13 2.33 2.17 2.10 2.07 2.19 2.05 0.016 0.015 0.014 0.011 0.010 0.009 5.89 5.79 5.50 5.97 7.36 5.57 33 28 26.8 26 24 23.5 6.52 6.79 6.86 7.19 8.00 8.02 0.40 0.38 0.38 0.40 0.44 0.44 where E is the energy of the incident photon in (eV), Eo is the singleoscillator energy (related to the optical band gap) and Ed is the dispersion energy. According to this form, drawing a relation between (n2–1)−1 against photon energy squared (E2) ought to be a direct line with a slope equal to (EoEd)−1 and an intercept on the y-axis of (Eo/Ed) as represented in Fig. 12. It is observed that, values of Eo and Ed change from 9.56 to 16.97 and from 36.33 to 54.05 respectively with increasing Er2O3 mol% in the studied glasses as in Table 6. The dispersion energy (Ed) relates to other physical parameters of the material can be given by the empirical Relation (17) . prepared glasses. It is well known that (k) determines the absorption of the light wave at any wavelength and aids in the computation of the dielectric constant components (real and imaginary). The attenuation coeﬃcient η(λ) can be calculated by Relation (12) based on the thickness (d) of the sample η (λ ) = e α (λ) d (12) The variation of refractive index (n) as a function of wavelength (λ) is represented in Fig. 10. It can be observed that the refractive index of studied glass decreases with increasing both wavelength and Er2O3 (mol %) which conﬁrm increasing the number of (BO's) as indicated by IR spectra. Portions of the dispersion curve in-between the anomalousdispersion branches are known to represent a normal dispersion which obeys the Cauchy dispersion Relation (13) [46, 47]. n=A+ B C + 4 λ2 λ Ed = βNc Ne Za where, β is a constant with two-values either an ionic or a covalent value (βi = 0.26 ± 0.03 eV) or/and (βc = 0.37 ± 0.04 eV), Nc is the eﬀective coordination number of the cation nearest neighbor to the anion, Ne is the number of valence electrons per anion and Za is the solemn chemical valency of the anion. The calculated values of Nc of the present glasses are in Table 6 which change from 6.13 to 9.13 with growing Er2O3 mol%. Value of the linear refractive index (n(0)) related to Eo and Ed at longer wavelength can be estimated through Relation (18) with the value of the incident photon energy E approach zero . (13) where, A, B, and C are known as Cauchy coeﬃcients which are characteristic to the material. The coeﬃcient C can be canceled as a consequence of its small value in the material transparency region. Values of the Cauchy's coeﬃcients were estimated by ﬁtting the curve of n(λ) as in Table 5. The optical complex dielectric function describes the interaction of electromagnetic waves with the matter which reﬂects by that the underlying molecular mechanisms. The complex dielectric constant components (ε) of the material are ε (λ) = ε' (λ) + j ε″ (λ) which are correlated to the wavelength (λ). The real (ε') and the imaginary (ε″) parts in terms of the constants (n) and (k) are presented by the Relations (14 and 15). ε′ = n2 − k 2 (14) ε″ = 2nk (15) E n (0) = ⎛ d + 1⎞ ⎝ E0 ⎠ ⎜ Eo Ed Eo2 − E 2 0.5 ⎟ (18) Table 6 conﬁrms the reverse relation between both (Eo and Ed) and n (0) by looking to their corresponding values within the table. The lattice contribution for wavelengths much shorter than the phonon resonances is presented by Relation (19)  n2 − 1 = Both the real (ε') and the imaginary parts (ε″) of the dielectric constant versus the wavelength for the present glasses are represented in Fig. 11 (a, b). The imaginary part (ε″) could be employed in the determination of the optical relaxation time of glasses . The dielectric constants for all samples have an exponential ﬁxed decrease with the wavelength and a decrease with increasing the Er2O3; this suggests that for all glasses the free carrier concentration changes in the same way with the change of Er2O3 mol% . S. H. Wemple and M. DiDomenico  established the WempleDoDomenico dispersion model (WDD) by analyzing the refractive index dispersion data below the inter-band absorption edge in the ionic and covalent materials and have shown that a single - oscillator ﬁt of the Relation (16) n2 − 1 = (17) E˳Ed E2 − l2 2 2 E˳ − E E (19) 2 where, El represents the lattice oscillator strength. At E < < Eo2 where the long wavelength, drawing (n2–1) against 1/E2 should approach a straight line. Applying this relation to Eq. (19) yields Eq. (20). n2 − 1 = Ed E2 − l2 E0 E (20) Ed E0 El 2 ). where the intercept is the ratio and the slope is (− Values of El are in Table 6. The material dispersion eﬀect parameter M(λ) can be given by using the parameters Eo, Ed and El as given by Eq. (21) . M(λ) = 1.54 × 10 4 Ed λ − 2.17 × 103El 2 n 2λ2E03 (21) The wavelength λc at zero material dispersion (M = 0) can be computed from Relation (22) . (16) 8 Journal of Non-Crystalline Solids xxx (xxxx) xxx–xxx 4.3578 0.8248 0.3896 2.0525 5.0098 1.8448 10.961 2.0232 2.1009 2.1272 2.1562 2.2032 2.2234 2.3752 8.6897 1.7341 2.6499 1.4482 ⎜ 4 ⎟ (22) The wavelength λc values of TLZNE glasses are ﬂuctuating with increasing Er2O3 as in Table 6 from 5.50 to 7.36 (μm). The Abbe number (νd) measures the material's dispersion (changing of refractive index vs. the wavelength) which can be given by Relation (23) . νd = 4.173 1.1854 0.4496 2.0719 3.4218 1.9394 4.3965 fexp n 4.1666 1.2929 1.0528 2.1522 7.152 1.915 9.203 1 E λ c = 1.63 ⎛ 3d 2 ⎞ ⎝ E0 El ⎠ nd − 1 n f − nc (23) 1.9879 2.0660 2.0919 2.1199 2.1644 2.1832 2.3209 3.5758 1.5041 2.7428 1.7510 4.9031 1.4825 1.0116 2.4671 6.982 2.255 8.9821 5.1596 0.994 0.3776 2.3763 7.7108 2.0353 8.5077 1.9672 2.0471 2.0733 2.1015 2.1458 2.1645 2.3009 8.2980 1.8848 3.1573 0.6163 n where K is an empirical constant. Based on this semi-empirical relation, the third-order non-linear optical susceptibility (χ3) of the glass is fundamentally concerning (n2) index and the linear index (n) as given by Eq. (25) . fexp n2 (10−13esu) = K fcal 4.3335 0.8252 0.3977 2.0345 6.1759 1.8189 2.2739 where, nd, nf and nc are the refractive indices at the wavelengths of the yellow He d-line and F-and C-lines of hydrogen (587.56 nm, 486.13 nm and 656.27 nm respectively) in VIS region. The higher dispersion glasses have νd < 55 whereas the lower ones have larger Abbe numbers. From Table 6, the Abbe dispersion number decreases from 33 to 23.5 with increasing Er2O3 mol % which shows that the existing glasses provide a high dispersion. Boling et al.  derived a relation for the second-order refraction index (n2) concerning the glass from the linear refractive index (n) which is given from Relation (24) χ3 = n TLZNE4 TLZNE5 fexp fcal TLZNE6 fcal N. Elkhoshkhany et al. n−1 ν5/4 (24) nn2 12π (25) Values of χ change by increasing Er2O3 (mol %) from 0.38 to 0.44 across the existing glasses as in Table 6. 5.6984 1.631 0.6176 2.649 4.5461 2.6135 5.8424 fcal 3 5.8421 1.0953 0.3983 2.5158 9.1445 2.7056 2.3161 1.9714 2.0511 2.0771 2.1051 2.1492 2.1678 2.3030 4.9110 1.6919 3.7748 2.9139 5.3186 1.646 1.3284 2.7695 9.0539 2.4497 11.65 5.0642 0.9531 0.3778 2.3096 9.169 3.7938 11.710 1.9697 2.0510 2.0770 2.1045 2.1472 2.1651 2.2951 10.9614 2.2569 3.3807 0.9332 n fcal fexp n Numerical integration of the identical absorption bands was utilized to realize the experimental oscillator strengths of the transitions from the ground 4I15/2 level to the diﬀerent excited states. Judd-Ofelt theory was performed to ﬁgure out the transition prospects of Er2O3 excited levels. Determining the experimental oscillator strengths fexp associated with the transitions can be accomplished by integration the absorption bands for each spectrum [55, 56] according to Formula (26) fexp = 2.303 mc 2 LNπe 2 ∫ ODdλ(λ2) dλ 6536 10,225 12,500 15,267 19,120 20,449 26,597 8π 2mc (n2 + 2)2 × × 3hλ (2J + 1) 9n U λ ‖ 〈 (S´. L´) J ´〉 ‖2 λ ∑ Ωλ 〈 (S. L) J 〉 λ = 2.4.6 (27) I13/2 I11/2 I9/2 4 F9/2 2 H11/2 4 F7/2 4 G11/2 Ω 2 ×10−20 cm2 Ω 4 ×10−20 cm2 Ω 6 ×10−20 cm2 RMS 1530 978 800 655 523 489 376 where, m, h, c, λ, n and U are; the mass of electron, Planck's constant, the velocity of light, mean wavelength of the transition, refractive index of the glass forming unit, and doubly reduced matrix elements of the unit tensor that have been taken from Weber  respectively. Table 7 includes all values of both experimental and calculated oscillator strengths of the studied glasses. It was obvious that the values of fcal are the highest for 4I15/2 → 4G11/2 transition in all glasses. From the experimental UV intensities and by using the least squares ﬁt approach, values of Ω2, Ω4, and Ω6 can be predicted as in Table 7. The Judd-Ofelt intensities and strength parameters are remarkable for checking of local structure and bonding in the neighborhood of rare-earth ions where the 4 4 (26) where, e, L, N, and OD(λ) are the electron charge, sample thickness, the number of the active ions, and optical density respectively. The calculated oscillator strength fcal can be gained by the isolation of both electric-dipole and magnetic-dipole contribution from fexp [55, 56] according to Relation (27) fcal [(S. L)J; (S´ . L´)J´] = 4 TLZNE2 Energy (cm−1) Wavelength nm Transition 4I15/2→ Table 7 The experimental (fexp) and calculated (fcal) oscillator strengths for Er3+ of TLZNE glasses. TLZNE3 fexp 3.6. Oscillator strengths and Judd–Ofelt parameters 9 Journal of Non-Crystalline Solids xxx (xxxx) xxx–xxx N. Elkhoshkhany et al. Table 8 Calculated branching ratio (β) and lifetime (τ) of TLZNE glasses. Transition 4I15/2→ 4 I13/2 I11/2 4 I9/2 4 F9/2 2 H11/2 4 F7/2 4 G11/2 4 TLZNE2 TLZNE3 TLZNE4 τ (ms) β τ (ms) β τ (ms) β τ (ms) β τ (ms) 1.0000 0.9362 0.6792 0.9188 0.9561 0.8521 0.9004 1.5472 1.0425 1.3059 0.1371 0.0239 0.0428 0.0052 1.0000 0.9328 0.5965 0.9210 0.9394 0.8791 0.8713 1.4510 1.0479 1.4728 0.1436 0.0466 0.0412 0.0100 1.0000 0.9334 0.6559 0.919 0.9531 0.8606 0.8961 1.6690 1.1619 1.5060 0.1548 0.0310 0.0470 0.0067 1.0000 0.9268 0.6368 0.9223 0.9355 0.8671 0.8700 1.8483 1.3943 1.7586 0.1790 0.0601 0.0533 0.0128 1.0000 0.9298 0.6717 0.9169 0.9557 0.8542 0.9038 1.7378 1.2046 1.5344 0.1607 0.0274 0.0496 0.0058 3.7. Emission spectra, absorption and emission cross-sections Depending on the emission and absorption properties and the threelevel nature on their spectral shape and population inversion, the potential performance of the erbium-glass laser can be obtained. The absorption cross-section σabs(λ) has been established by Eq. (32) σabs (λ ) = 2.0303 (28) U λ ‖ 〈 (S´. L´) J ´〉 ‖2 ∑ σemis (λ ) = σabs (λ ) Ωλ 〈 (S. L) J 〉 λ = 2.4.6 (29) (33) (34) G (λ ) = σems (λ ) NP − σabs (λ ) N (1 − P ) (30) where, P is population inversion rate for G11/2 → I15/2 laser transition, N is the concentration of Er3+ ions. Values of G(λ) are in Fig. 14 where the values of P are: 0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9 and 1.0 respectively. The emission proﬁle of TLZNE samples (Fig. 14) shows that, the peaks of the gain coeﬃcient are shifted toward the shorter wavelength. In the end, G(λ) at 1531 nm transition 4G11/2 → 4I15/2 changes from 1.44 × 10−20 to 1.92 × 10−20 cm−1 in the existing glass system. 4 For whole likely transitions, the radiative lifetimes can be located from the upper J manifolds 4I13/2, 4I11/2, 4I9/2, 4F9/2, 4F7/2, and 2H11/2 to all lower lying states of the Er3+ ions in the existing glasses. The radiative lifetimes of the 4G11/2 state of the glass samples are in Table 8 which are higher other than Er3+doped zinc boro-tellurite glasses synthesized by Z.A. Said Mahraz et al. . The current glasses are in good harmony and tuning inside the region of latest laser host glasses doped with Er3+ . The ﬂuorescence branching ratio β(J. J´) can be presented by Relation (31) A (J . J ´) β (J . J ´) = ∑J ´ A (J . J ´) EZ − hcλ−1 ⎤ Zl exp ⎡ l ⎢ ⎥ Zu KB T ⎣ ⎦ where Zl and Zu are the partition function for lower and upper levels concerned in the measured optical transition, T is the room temperature and Ezl is the zero-line energy which is the energy segregation among the lowest components of the upper and lower states. Fig. 13 explains the predicted absorption and emission cross sections of the synthesized glasses. Values of the stimulated emission cross sections σemis(λ) are about 1.65 × 10−20, 1.95 × 10−20, 1.7 × 10−20, 1.45 × 10−20 and 1.5 × 10−20 cm−2 for TLZNE2 to TLZNE6 glasses respectively. From both the absorption and emission cross sections for the transitions between two laser operating states, the optical gain coeﬃcient G(λ) - that drive to an estimation of the probable operating laser wavelength - can be gained by Eq. (34) . The lifetime of the radiative excited levels is given by the reverse of the sum of A(J, J') values calculated over all the terminal levels . 1 A (J . J ´) (32) ions in each glass where N is the concentration of the respective Er sample. The stimulated emission cross-section σemis(λ) of Er3+ for 4G11/ 4 2 → I15/2 transition was calculated by McCumber method  which can be detected from their matching ground state absorption crosssection σabs(λ) through Eq. (33) . where P is the number of the signiﬁcant transitions in the absorption spectra. The parameters Ω2, Ω4 and Ω6 can be applied in the Eq. (29) to obtain the radiative transition probabilities for the electric dipole transitions between the excited states and the lower-lying level of Er3+ . 64π 2e 2 n (n2 + 2)2 × × 3hλ3 (2J + 1) 9n OD (λ ) Nl 3+ 1 (f − fmeas )2 ⎤2 ⎡ r . m . s = ⎢∑ cal ⎥ P−3 ⎣ P ⎦ τrad = TLZNE6 β value of Ω2 is related to the coincidence of the glass hosts. Ω6 is related the covalence nature of the EreO bonds in inverse relation and inﬂuenced by the overlap integrals of 4f orbitals rather than Ω2 and Ω4 . Both Ω4 and Ω6 are parameters related to characteristics such as rigidity. From Table 7, decreasing both Ω2 from 10.9614 × 10−20 to 8.6897 × 10−20 and Ω6 from 3.3807 × 10−20 to 2.6499 × 10−20 with increasing Er2O3 (mol %) conﬁrms increasing the covalency of bonds and also increasing the thermal stability and the energy gaps as indicated from IR results. To obtain the quality of ﬁtting of the calculated oscillator strengths to the experimental one Relation (28) the rootmean-square (r. m. s) can be used A (J . J ´) = TLZNE5 4 4. Conclusion The glass system 75TeO2–5Li2O–10ZnO–(10–x)Nb2O5–xEr2O3 with (x = 0.0, 0.5, 1.0, 1.5, 2.0, and 2.8 mol%) was synthesized and characterized by XRD, FTIR, Raman, DSC, and optical absorption studies. Increasing the density from 4.12 to 4.83 ± 0.02 (g/cm3) and decreasing the molar volume from 37.84 to 32.96 ± 0.2 (cm3/mol) was due to the increase in the packing of the glass, which in turn caused an increase of the transformation temperature and the thermal stability of the glass. Both FTIR and Raman spectroscopes showed a presence of a mix of (BO's) and (NBO's) but the dominated eﬀect was attributed to (BO's). The optical measurements showed an increase of the band gap energy from 2.7 to 2.9 eV by the action of the (BO's) with increasing (31) The ratio of branching can be used to characterize the transition in the emission spectra. The value of β is larger than 0.5, which implies that the emission radiation is stronger relative to transition and shows the possible application of this transition for laser creation . The highest β is founded in the 4I13/2 → 4I15/2 transition peaked at 1520.48 nm for Er3+ ions in all glasses as in Table 8 which is greater than other Er3+ doped tellurite glasses . 10 Journal of Non-Crystalline Solids xxx (xxxx) xxx–xxx N. Elkhoshkhany et al. Fig. 13. Absorption cross-sections σabs(λ) and stimulated emission Cross section σemis(λ) of TLZNE glasses. exponential ﬁxed decrease with the wavelength and a decrease with increasing the Er2O3. The Judd-Ofelt parameter (Ω2, Ω4, Ω6) were calculated. Both Ω2 and Ω6 decreased with increasing Er2O3 (mol %) which conﬁrmed increasing the covalency of bonds and also increasing the thermal stability and the energy gaps as indicated from IR results. The present system opposed higher branching ratio (1.000) and radiative lifetime (1.8483 ms) compared to other tellurite glasses. Er2O3 mol %. Decreasing the molar refraction from 23.94 to 20.40 (cm3/mol) was related to decreasing of the glass polarizability. Both the oxide polarizability and the optical basicity of the present glass were in direct relation where both decreased with increasing Er2O3. The glass became optically more dispersive with a higher refractive index with increasing Er2O3 mol% due to the higher polarization of the TeO2 network. The complex dielectric constants for all samples have an 11 Journal of Non-Crystalline Solids xxx (xxxx) xxx–xxx N. Elkhoshkhany et al. Fig. 14. Gain coeﬃcient for 4G11/2 → 4I15/2 transitions of TLZNE glasses. References  M. Niyaz Ahamad, K.B.R. Varma, Crystallisation, dielectric and optical characteristics of TeO2–K2O–Li2O–Nb2O5 glasses, Phys. Chem. Glasses Eur. J. Glass Sci. Technol. B 47 (2006) 659–664.  Hooi Ming Oo, Halimah Mohamed-Kamari, Wan Mohd Daud Wan-Yusoﬀ, Optical properties of bismuth tellurite based glass, Int. J. Mol. Sci. 13 (2012) 4623–4631.  W. Stambouli, H. Elhouichet, M. Ferid, Study of thermal, structural and optical properties of tellurite glass with diﬀerent TiO2 composition, J. Mol. Struct. 1028 (2012) 39–43. 12 Journal of Non-Crystalline Solids xxx (xxxx) xxx–xxx N. Elkhoshkhany et al.  Tomokatsu Hayakawa, Masahiko Hayakawa, Masayuki Nogami, Philippe Thomas, Nonlinear optical properties and glass structure for MO–Nb2O5–TeO2 (M = Zn, Mg, Ca, Sr, Ba) glasses, Opt. Mater. 32 (2010) 448–455.  M.M. Umair, A.K. Yahya, Eﬀect of Nb2O5 network stabilizer on elastic and optical properties of xNb2O5-(20-x) BaO-80TeO2 tellurite glass system, Chalcogenide Lett. 12 (2015) 287–300.  N. Elkhoshkhany, Eslam Syala, Kinetics characterization of erbium-doped tellurite glass, Ceram. Int. 44 (2018) 6829–6835.  N. Baizura, A.K. Yahya, Eﬀects of Nb2O5 Replacement by Er2O3 on elastic and structural properties of 75TeO2–(10−x) Nb2O5–15ZnO–(x)Er2O3 glass, J. NonCryst. Solids 357 (2011) 2810–2815.  Hai Lin, Shibin Jiang, Jianfeng Wu, Feng Song, Nasser Peyghambarian, E Y B Pun, Er3+ doped Na2O–Nb2O5–TeO2 glasses for optical waveguide laser and ampliﬁer, J. Phys. D 36 (2003) 812–817.  Azlan Muhammad Noorazlan, Halimah Mohamed Kamari, Siti Shaﬁnas Zulkeﬂy, Daud W. Mohamad, Eﬀect of erbium nanoparticles on optical properties of zinc borotellurite glass system, J. Nanomater. (2013) 1–8.  Patange Satya Gopal Rao, Rajesh Siripuram, Sripada Suresh, Structural evaluation onTeO2–SeO2–R2O ternary glass system using Raman and IR, Emerg. Mater. Res. 5 (2015) 95–99.  Shixun Dai, Jialu Wu, Junjie Zhang, Guonian Wang, Zhonghong Jiang, The spectroscopic properties of Er 3+-doped TeO2–Nb2O5 glasses with high mechanical strength performance, Spectrochim. Acta A 62 (2005) 431–437.  Longjun Lu, Qiuhua Nie, Tiefeng Xu, Shixun Dai, Xiang Shen, Xianghua Zhang, Upconversion luminescence of Er3+/Yb3+/Nd3+-codoped tellurite glasses, J. Lumin. 126 (2007) 677–681.  N. Elkhoshkhany, R. El-Mallawany, Eslam Syala, Mechanical and thermal properties of TeO2–Bi2O3–V2O5–Na2O–TiO2 glass system, Ceram. Int. 42 (2016) 19218–19224.  M. Anand Pandarinath, G. Upender, K. Narasimha Rao, D. Suresh Babu, Thermal, optical and spectroscopic studies of boro-tellurite glass system containing ZnO, J. Non-Cryst. Solids 433 (2016) 60–67.  Y.B. Saddeek, E.R. Shaaban, F.M. Abdel-Rahim, K.H. Mahmoud, Thermal analysis and infrared study of Nb2O5–TeO2 glasses, Philos. Mag. 88 (2008) 3059–3073.  I. Jlassi, H. Elhouichet, S. Hraiech, M. Ferid, Eﬀect of heat treatment on the structural and optical properties of tellurite glasses doped erbium, J. Lumin. 132 (2012) 832–840.  El Sayed Yousef, A.E. AL-Salami, Mario Hotzel, Optical and thermal characteristics of glasses based on TeO2, Bull. Mater. Sci. 35 (2012) 961–967.  N. Elkhoshkhany, M.A. Khatab, Marwa A. Kabary, Thermal, FTIR and UV spectral studies on tellurite glasses doped with cerium oxide, Ceram. Int. 44 (3) (2018) 2789–2796.  M.R. Sahar, K. Sulhadi, M.S. Rohani, Spectroscopic studies of TeO2–ZnO–Er2O3 glass system, J. Mater. Sci. 42 (2007) 824–827.  M.A. Villegas, J.M. Frenández Navarro, Physical and structural properties of glasses in the TeO2–TiO2–Nb2O5 system, J. Eur. Ceram. Soc. 27 (2007) 2715–2723.  H. Doweidar, B. Yasser, Saddeek, FTIR and ultrasonic investigations on modiﬁed bismuth borate glasses, J. Non-Cryst. Solids 355 (2009) 348–354.  Hong-tao Sun, Lei Wen, Zhong-chao Duan, Li-li Hu, Jun-jie Zhang, Zhonghong Jiang, Intense frequency upconversion ﬂuorescence emission of Er3+/Yb3+codoped oxychloride germanate glass, J. Alloys Compd. 414 (2006) 142–145.  K. Annapoorani, N. Suriya Murthy, T.R. Ravindran, K. Marimuthu, Inﬂuence of Er3+ ion concentration on spectroscopic properties and luminescence behavior in Er3+ doped Strontium telluroborate glasses, J. Lumin. 171 (2016) 19–26.  Hatem A. El-Batal, Zeinab S. El-Mandouh, Hamdia A. Zayed, Samir Y. Marzouk, Gihan M. El-Komy, Ahmed Hosny, Optical and infrared properties of lithium diborate glasses doped with copper oxide: Eﬀect of gamma irradiation, Indian J. Pure Appl. Phys. 50 (2012) 398–404.  G. Senthil Murugan, Yasutake Ohishi, Raman spectroscopic studies of TeO2-BaOSrO-Nb2O5 glasses: Structure-property correlations, J. Appl. Phys. 96 (2004) 2437–2442.  El S. Yousef, H.H. Hegazy, M.M. Elokr, Y.M. Aboudeif, Raman spectroscopy and Raman gain coeﬃcient of telluroniobium- zinc-lead oxyglasses doped with rare earth, Chalcogenide Lett. 12 (2015) 653–663.  N. Jaba, A. Mermet, E. Duval, B. Champagnon, Raman spectroscopy studies of Er3+ doped zinc tellurite glasses, J. Non-Cryst. Solids 351 (2005) 833–837.  V. Kamalaker, G. Upender, Ch. Ramesh, V. Chandra Mouli, Raman spectroscopy, thermal and optical properties of TeO2–ZnO–Nb2O5–Nd2O3glasses, Spectrochim, Acta, Part A 89 (2012) 149–154.  H. Chen, Y.H. Liu, Y.F. Zhou, Q.Y. Zhang, Z.H. Jiang, Spectroscopic properties of Er3+ doped TeO2–BaO (Li2O,Na2O)–La2O3 glasses for 1.5-μm optical ampliﬁers, J. Non-Cryst. Solids 351 (2005) 3060–3064.  M. Maaoui, Z. Haouari, I. Zaaboub, F. Fraj, H. Saidi, Ben Ouada, Concentration eﬀects on the optical spectroscopic properties of Er3+- doped TeO2-Nb2O5-ZnO vitreous system, J. Alloys Compd. 663 (2016) 395–406.  K. Maheshvaran, S. Arunkumar, V. Sudarsan, V. Natarajan, K. Marimuthu, Structural and luminescence studies on Er3+/Yb3+ co-doped boro-tellurite glasses, J. Alloys Compd. 561 (2013) 142–150.  D. Ramachari, L. Rama Moorthy, C.K. Jayasankar, Gain properties and concentration quenching of Er3+-doped niobium oxyﬂuorosilicate glasses for photonic applications, Opt. Mater. 36 (2014) 823–828.  P. Suthanthirakumar, P. Karthikeyan, P.K. Manimozhi, K. Marimuthu, Structural                                 13 and spectroscopic behavior of Er3+/Yb3+ co-doped boro-tellurite glasses, J. NonCryst. Solids 410 (2015) 26–34. El-Diasty Fouad, F.A. Moustafa, F.A. Abdel-Wahab, M. Abdel-Baki, A.M., Fayad, Role of 4p-3d orbital hybridization on band gap engineering of heavy metal glass for optoelectronic applications, J. Alloys Compd. 605 (2014) 157–163. J. Tauc, F. Abeles (Ed.), J Optical Properties of Solids, 22 1970, p. 903 North Holland, Amsterdam. E.A. Davis, N.F. Mott, Conduction in non-crystalline systems V. Conductivity, optical absorption and photoconductivity in amorphous semiconductors, Philos. Mag. 22 (1970) 903–922. S. Lakshimi Srinivasa Rao, G. Ramadevudu, Md. Shareefuddin, Abdul Hameed, M. Narasimha Chary, M. Lakshmipathi Rao, Optical properties of alkaline earth borate glasses, Int. J. Eng. Sci. Technol. 4 (2012) 25–35. Yanfei Chen, Qiuhua Nie, Tiefeng Xu, Shixun Dai, Xunshi Wang, Xiang Shen, A study of nonlinear optical properties in Bi2O3–WO3–TeO2 glasses, J. Non-Cryst. Solids 354 (2008) 3468–3472. N. Elkhoshkhany, Raﬁk Abbas, R. El-Mallawany, A.J. Fraih, Optical Properties of quaternary TeO2–ZnO–Nb2O5–Gd2O3 glasses, Ceram. Int. 40 (2014) 14477–14481. Yousef El Sayed, M.M. Elokr, Y.M. Abou Deif, Optical, elastic properties and DTA of TNZP host tellurite glasses doped with Er3+ ions, J. Mol. Struct. 1108 (2016) 257–262. Fouad El-Diasty, Fathy A. Abdel Wahab, Manal Abdel-Baki, Optical band gap studies on lithium aluminum silicate glasses doped with Cr3+ ions, J. Appl. Phys. 100 (2006) 093511. S.A. Umar, M.K. Halimah, K.T. Chan, A.A. Latif, Physical, structural and optical properties of erbium doped rice husk silicate borotellurite (Er-doped RHSBT) glasses, J. Non-Cryst. Solids 472 (2017) 31–38. Vesselin Dimitrov, Sumio Sakka, Electronic oxide polarizability and optical basicity of simple oxides I, J. Appl. Phys. 79 (1996) 1736–1740. Xinyu Zhao, Xiaoli Wang, Hai Lin, Zhiqiang Wang, Electronic polarizability and optical basicity of lanthanide oxides, Physica B 392 (2007) 132–136. Samir Y. Marzouk, Roshdi Seoudi, Doaa A. Said, Mai S. Mabrouk, Linear and nonlinear optics and FTIR characteristics of borosilicate glasses doped with gadolinium ions, Opt. Mater. 35 (2013) 2077–2084. M. Emam-Ismail, E.R. Shaaban, M. El-Hagary, I. Shaltout, Optical investigation of electron-beam-deposited tungsten-tellurite (TeO2)100-x (WO3)x amorphous ﬁlms, Philos. Mag. 90 (2010) 3499–3509. I. Jlassi, H. Elhouichet, M. Ferid, Thermal and optical properties of tellurite glasses doped erbium, J. Mater. Sci. 46 (2011) 806–812. S.H. Wemple Jr., M. DiDomenico, Behavior of the electronic dielectric constant in covalent and ionic materials, Phys. Rev. B 3 (1971) 1338–1351. S.H. Wemple, Optical oscillator strengths and excitation energies in solids, liquids, and molecules, J. Chem. Phys. 67 (1977) 2151–2168. K. Petkov, P.J.S. Ewen, Photoinduced changes in the linear and non-linear optical properties of chalcogenide glasses, J. Non-Cryst. Solids 249 (1999) 150–159. S.H. Wemple, Material dispersion in optical ﬁbers, Appl. Opt. 18 (1979) 31–35. N. Sultanova, S. Kasarova, I. Nikolov, Dispersion properties of optical polymers, Acta Phys. Pol. A 116 (2009) 585–587. N. Boling, A. Glass, A. Owyoung, Empirical relationships for predicting nonlinear refractive index changes in optical solids, IEEE J. Quant. Elec. 14 (1978) 601–608. Zhao Zhenyu, Shi Jiatian, Sun Zhenrong, Jian Lin, Huang Wenhai, Zugeng Wang, Nonlinear optical properties of Eu2O3 doped 5ZnO- 20Nb2O5-75TeO2 glasses, Chin. Sci. Bull. 49 (2004) 2446–2448. B.R. Judd, Optical absorption intensities of rare-earth ions, Phys. Rev. (1962) 750–761. Shiqing Xu, Zhongmin Yang, Guonian Wang, Shixun Dai, Junjie Zhang, Lili Hu, Zhonghong Jiang, Optical transitions and upconversion mechanisms in Er3+−doped heavy metal oxyﬂuoride germanate glass, J. Alloys Compd. 377 (2004) 253–258. M.J. Weber, Spontaneous emission probabilities and quantum eﬃciencies for excited states of Pr3+ in LaF3, J. Chem. Phys. 48 (1968) 4774–4780. M.S. Gaafar, S.Y. Marzouk, Judd–Ofelt analysis of spectroscopic properties of Er3+ doped TeO2-BaO-ZnO glasses, J. Alloys Compd. 723 (2017) 1070–1078. Zahra Ashur Said Mahraz, M.R. Sahar, S.K. Ghoshal, M. Reza Dousti, Concentration dependent luminescence quenching of Er3+-doped zinc boro-telluriteglass, J. Lumin. 144 (2013) 139–145. W.T. Carnall, P.R. Fields, K. Rajnak, Electronic energy levels in the trivalent lanthanide aquo ions. I. Pr3+, Nd3+, Pm3+, Sm3+, Dy3+, Ho3+, Er3+, and Tm3+, J. Chem. Phys. 49 (1968) 4424–4442. M.J.F. Digonnet, Rare-earth-doped Fiber Lasers and Ampliﬁers, Second ed, Marcel Dekker, New York, 2001. Raja J. Amjad, M.R. Dousti, M.R. Sahar, Spectroscopic investigation and Judd–Ofelt analysis of silver nanoparticles embedded Er3+-doped tellurite glass, Curr. Appl. Phys. 15 (2015) 1–7. D.E. Mccumner, Theory of phonon-terminated optical masers, Phys. Rev. 134 (1964) A299–A306. Xuelu Zou, Hisayoshi Toratani, Evaluation of spectroscopic properties of Yb3+doped glasses, Phys. Rev. B 52 (1995) 15889–15897. J.F. Philipps, T. Töpfer, H. Ebendorﬀ-Heidepriem, D. Ehrt, R. Sauerbrey, Spectroscopic and lasing properties of Er3+: Yb3+-doped ﬂuoride phosphate glasses, Appl. Phys. B Lasers Opt. 72 (2001) 399–405.