Unvelling the elastic properties of samarium oxide zinc tellurite-based glasses: Judd-Ofelt intensity parameters through structural, experimental, and theoretical studies

Abstract

The melt quenching technique was used to prepare zinc tellurite glasses with composition of [(TeO₂)_0.7 (ZnO)_0.3]_1-x [Sm₂O₃]_x, where x is the molar fraction. The glasses were synthesized at various x values of 0.01, 0.02, 0.03, 0.04, and 0.05. Xray diffraction patterns depict the absence of distinct absorption peaks, indicating its amorphous nature. The shear and longitudinal velocities of the samples were measured using 5 MHz of frequency at room temperature. Physical properties such as density ($\rho )$, and molar volume (${V}_{m})$ increases from 5.142 to 5.324 g/cm³ and 27.412 to 27.590 cm³/mol. Variations in ultrasonic velocity, elastic moduli, Debye temperature (${\uptheta }_{{\text{D}}}$), Softening temperature (${{\text{T}}}_{{\text{S}}}$) and Poisson’s ratio (σ) were discussed and correlated with the composition of the glass samples. Additionally, elastic moduli and Poisson’s ratio were compared with the theoretically measured data using the four theoretical elastic models of Makishima and Mackenzie, Rocherulle, Bond compression and Ring Deformation models. The Judd-Offelt parameters (${\Omega }_{2}$, ${\Omega }_{4}$ and ${\Omega }_{6}$) are obtained using Judd-Ofelt theory. To determine the possible applications of the synthesized glasses, the spectroscopic parameters were calculated for each band: radiative transition probabilities [${A}_{MD}$/${A}_{ED}$], branching ratio ${\beta }_{R}$, spectroscopic quality factor (${\Omega }_{4}$/${\Omega }_{6}$), gain bandwidth (Δλeff × σp) and the optical gain (σp × τ). The obtained higher values of gain bandwidth, optical gain, branching ratio, spectroscopic quality factor (1.550) and the radiative transition probabilities show that the glasses prepared are appropriate for laser applications.

1 Introduction

Highly potential applications of rare-earth-doped glass systems in the field of photonics have attracted significant interest in recent years (Desirena 2011). Tellurite glasses exhibit promising potential applications in various industries, including electric, optical, and electronic fields. Their advantageous semiconducting properties, large electrical potential, highly dense network, excellent capability of infrared transmission, large dielectric constant, high refractive index, stability, and low melting points collectively contribute to their exceptional characteristics (Sidek et al. 2007). Currently, there is a growing scientific and technological interest in tellurium oxide (TeO₂)-based glasses due to their unique characteristics of commendable stability in their mechanical and chemical strengths, along with a minimum melting temperature. (Tio et al. 2006). Furthermore, they exhibit significant linear as well as nonlinear refractive indices and demonstrate excellent optical transmission at both visible and infrared wavelengths. (Mohamed et al. 2010). The aforementioned properties position tellurite glasses as promising candidates for the advancement of optical devices (Tafida et al. 2022). Under normal conditions, TeO₂ lacks the capability to form glass independently and requires the presence of modifiers such as alkali or alkaline earth, rare earth or transition metal oxides (Tafida et al. 2020). In this investigation, the choice of Sm³⁺ (4f⁵) among the RE³⁺ ion series is motivated by its remarkable fluorescence in visible region. Furthermore, it possesses favorable traits that make it particularly well-suited for spectral hole burning studies (Lim et al. 2013). Moreover, the Sm³⁺ ion is highly suitable for the analysis of energy transfer processes, thanks to its relatively high quantum efficiency in the lowest emitting ⁴G_5/2 level and the presence of distinct quenching emission channels. Glasses containing Sm³⁺ ions are also captivating owing to their promising applications in highly-dense optical storage, underwater communications, and color displays, as evidenced by previous research (Lim et al. 2013). In our study, Tafida et al. (2022) discovered that addition of ZnO can effectively cover all interstices within glass system, resulting in structural modifications. ZnO can serve as a glass former, modifier, or both, enabling it to occupy spaces within the glass system.

EL-Mallawany et al. reported, elastic constants provide detailed structural information of solids due to their direct relation with interatomic forces and potentials (El-Mallawany 1998). Ultrasonic longitudinal and shear velocity measurements play a vital role in the investigation of elastic properties in glasses. The ultrasonic velocity can be closely linked to elastic moduli, and changes in these moduli which can provide insights into the structural stability, formation of the glass network, and rigidity. This relationship has been confirmed by previous studies (El-Mallawany 1998). Numerous authors have extensively investigated RE-doped ZnTeO₂ glass systems, and their studies have provided insights into the optical and elastic characteristics of glass systems. The literature contains a significant body of work reporting on these aspects (Usman et al. 2018; Hasnimulyati et al. 2017; Maheshvaran et al. 2011). To our knowledge, there is currently no comprehensive report available on the experimental and theoretical elastic properties of Sm³⁺ doped zinc tellurite glasses analyzed using Judd-Offelt intensity parameters. Hence, this study represents the synthesis of zinc tellurite glass network incorporated with Sm³⁺ ions, focusing on characterization of their structural properties as well as experimental and various theoretical elastic properties.

The main objectives of the current study are as follows: (i) To synthesize zinc tellurite glasses with Sm³⁺ ions doping. (ii) To investigate the structural properties of glass system. (iii) To examine the influence of samarium oxide concentration on the experimental and theoretical elastic properties of the glasses. (iv) To study the gain bandwidth and optical gain along with branching ratio, and the radiative transitions detected in ⁴G_5/2 → ⁶H_7/2 transition. Thus, suggesting the potential use of fabricated glasses as visible lasers emitting intense orange (604 nm) light in visible region.

2 Experimental procedure

2.1 Sample preparation

Different compositions of Sm₂O₃ were used to dope the zinc tellurite glass system. Glass samples were fabricated by employing the melt quench technique and subjected for characterization. In the present study, the glass samples were synthesized following the specified chemical arrangements. The Sm₂O₃ doped zinc tellurite with chemical composition of [(TeO₂)_0.7 (ZnO)_0.3]_1-x [Sm₂O₃]_x were fabricated, where x = 0.01, 0.02, 0.03, 0.04, and 0.05. The necessary ingredients, namely tellurium oxide (TeO₂), zinc oxide (ZnO), and samarium oxide (Sm₂O₃) with a purity of 99.99% from Alfa Aeser, were accurately weighed using weighing balance with a precision of 0.0001 g. The chemical powders were then stirred for approximately 30 min. The preheating and melting processes were made at temperatures of 400 °C and 900 °C, respectively. The molten liquid was rapidly poured into a preheated mold and immediately transferred to the annealing process in the furnace at kept 400 °C for duration of 90 min. The resulting glass samples were carefully sliced to a thickness of 5 mm and underwent meticulous polishing to achieve parallel and transparent surfaces.

2.2 Sample characterization

The density of the samples was measured using an electronic densimeter (MD-300S) based on the principle of Archimedes, with distilled water as the submerging liquid at room temperature. To determine the density of glass system, the following relation was used (Hamza et al. 2019a);

$$ \rho_{s} = \frac{{M_{a} }}{V} $$

(1)

where, $M_{a }$ denotes the mass of the sample in air, $\rho_{s}$ represents the density of the glass sample measured in g/cm³, and $V$ represents its corresponding volume measured in grams or cubic centimeters (cm³). The values of molar volume $V_{m}$ were computed using relation given in Eq. (2) (Umar et al. 2017);

$$ V_{m} = \sum \frac{{X_{i} M_{i} }}{\rho } $$

(2)

where $X_{i}$ is the molar fraction, $M_{i}$ represents the molecular weight for ith component, and $\rho$ represents density of the sample. The X'Pert PRO Panalytical Philips instrument was employed to analyze the spectra and validate the amorphous nature of the synthesized glasses. The values of OPD and ${\text{V}}_{{\text{o}}}$ were computed by employing Eq. (3) (Usman et al. 2018).

$$ OPD = n \times \frac{\rho }{M} \times 1000 $$

(3)

where $n$ is the number of oxygen’s present in sample, $\rho$ is density whereas $M$ is the molecular weight of glass samples.

$$ V_{o} = \frac{{V_{m} }}{{\sum X_{i} n_{i} }} $$

(4)

where $n_{i}$ is the number of oxygens in ith component of sample. The values of Sm³⁺ ion concentration ($N$) and interionic distance ($R_{i}$) in glass samples are determined using Eqs. (5) and (6) (Rao et al. 2014).

$$ N = \frac{{N_{A} \rho x}}{{M_{w} }} $$

(5)

$$ R_{i} = \left( \frac{1}{N} \right)^{{{\raise0.7ex\hbox{$1$} \!\mathord{\left/ {\vphantom {1 3}}\right.\kern-0pt} \!\lower0.7ex\hbox{$3$}}}} $$

(6)

where $N_{A}$, $\rho$, $x$, $M_{w}$ represents the Avogadro’s number, glass samples’ density, mole fraction of samarium ion and average molecular weight of samples respectively. The measuring unit used for calculating $N$ is (ions/cm³). It is an important parameter used in determining and investigating the interionic forces of samples. The Ritec Ram-5000 Snap Ultrasonic System was employed to estimate the elastic parameters and passage time of the ultrasonic wave in the sample. The determination of ultrasonic velocities data was based on time-interval data (Sidkey and Gaafar 2004).

$$ v = \frac{2x}{{\Delta t}} $$

(7)

The measurements of ultrasonic velocities were performed at room temperature using a 5 MHz frequency. In this context, $x$ represents the thickness of the sample, $v$ denotes the ultrasonic velocity, and $\Delta t$ represents the time difference of flight. Further to ensure accuracy, each measurement was repeated multiple times. The experimentally determined values of longitudinal and shear ultrasonic velocities are denoted as $v_{l}$ and $v_{s}$ respectively. The experimental elastic moduli of synthesized samples are determined by employing following relations (Alazoumi et al. 2017);

$$ L = v_{l}^{2} \rho $$

(8)

$$ G = v_{s}^{2} \rho $$

(9)

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

(10)

$$ E = \left( {1 + \sigma } \right)2G $$

(11)

$$ \sigma = \frac{{\left( {L - 2G} \right)}}{{2\left( {L - G} \right)}} $$

(12)

where $G$ represents shear modulus, $v_{s}$ is shear velocity, $K$ the bulk modulus and $E$ is Young's modulus whereas $\sigma$ denotes the Poisson's ratio. $L$ represents the longitudinal modulus, $v_{l}$ is longitudinal velocity. The theoretical models utilized to describe elastic behavior encompass various models, including bulk compression, the Makishima-Mackenzie model, and the Rocherulle model. The measurements of elastic moduli are done by using following equations (Sidkey and Gaafar 2004).

$$ K_{bc} = \frac{{N_{A} \rho }}{9M}\mathop \sum \limits_{i} x_{i} \left( {n_{f} } \right)_{i} r_{i}^{2} f_{i} $$

(13)

$$ \sigma_{bc} = 0.28\left( {\overline{n}_{c} } \right)^{ - 1/4} $$

(14)

$$ G_{bc} = \left( \frac{3}{2} \right)K_{bc} \left( {\frac{{1 - 2\sigma_{bc} }}{{1 + \sigma_{bc} }}} \right) $$

(15)

$$ L_{bc} = K_{bc} + \left( \frac{4}{3} \right)G_{bc} $$

(16)

$$ E_{bc} = 2G_{bc} \left( {1 + \sigma_{bc} } \right) $$

(17)

where $x_{i}$ is molar fraction of $ith$ oxide, $n_{f}$ is number of network bonds per unit glass, $r$ is bond length, $f$ is first order stretching force constant, $\left( {\overline{n}_{c} } \right)$ is per unit cross-link density and $n$ is coordination number. Additionally, $\left( {n_{b} } \right)$ is number of bonds per unit volume and to estimate the first order stretching force constant F following equations are being employed (Bootjomchai 2015);

$$ n_{b} = \frac{{N_{A} \rho }}{M}\mathop \sum \limits_{i} x_{i} \left( {n_{f} } \right)_{i} $$

(18)

$$ \left( {\overline{n}_{c} } \right) = \frac{1}{\eta }\mathop \sum \limits_{i} x_{i} \left( {n_{c} } \right)_{i} \left( {N_{c} } \right)_{i} $$

(19)

$$ f = \frac{1.7}{{r^{3} }} $$

(20)

where $n_{c}$ is density of cross-link per unit cation and is equals to (no. of bands-2), $N_{c}$ is no. of cations per unit glass and $\eta$ is the total cations present per unit glass. In order to calculate the elastic behaviour of gases, the theoretical models such as the Makishima and Mackenzie can be employed by using energy dissociation value of oxides per unit volume ($G_{i}$) and their packing density ($V_{i}$) (Tafida et al. 2023). The equations given below are used to estimate elastic moduli and Poisson’s ratio (Hasnimulyati et al. 2017).

$$ K_{mm} = 1.2V_{t} E_{mm} $$

(21)

$$ E_{mm} = 83.6V_{t} \mathop \sum \limits_{i} G_{i} X_{i} $$

(22)

where $G_{t}$ and $V_{t}$ factor is the summation component expressed as follows;

$$ G_{t} = \mathop \sum \limits_{i} G_{i} X_{i} $$

(23)

$$ V_{t} = \left( {\frac{\rho }{{M_{w} }}} \right)\mathop \sum \limits_{i} V_{i} X_{i} $$

(24)

$$ G_{mm} = \frac{{3E_{mm} K_{mm} }}{{9K_{mm} - E_{mm} }} $$

(25)

$$ \sigma_{mm} = \frac{{E_{mm} }}{{2G_{mm} }} - 1 $$

(26)

where symbols used such as Gi and Vi, have meanings that have been previously discussed. In the Rocherulle model, the elastic moduli of a glass sample are known to be affected by both the dissociation energy and their configuration. Experimental investigations have revealed that elastic moduli are not dependent on overall density of the glass sample, but rather on the densities of each oxide present in the glass network. To incorporate these considerations, specific adjustments were made to determine the packing factor of each individual oxide, denoted as C_i, as expressed in the following equation (Zaid et al. 2011).

$$ C_{i} = N_{A} .\frac{\rho }{M}.\frac{4\pi }{3}. \left( {mR_{A}^{3} + nR_{O}^{3} } \right) $$

(27)

where $m$ is no. of cations, $R_{A}$ the ionic radii of cations, $n$ is anions and $R_{O}$ is ionic radii of the anion in glass network. The remaining equations utilized for calculating the elastic moduli bear resemblance to those found in the Makishima and Mackenzie model. However, there is a notable difference in the determination of the total packing density, $C_{t}$, which is assessed independently of the sample density.

$$ C_{t} = \mathop \sum \limits_{i} C_{i} X_{i} $$

(28)

The following equations can be used to obtain elastic moduli suggested by Rocherulle model;

$$ E_{rm} = 2C_{t} \mathop \sum \limits_{i} G_{i} X_{i} $$

(29)

$$ K_{rm} = 1.2C_{t} E_{rm} $$

(30)

$$ G_{rm} = \frac{{3E_{rm} K_{rm} }}{{9K_{rm} - E_{rm} }} $$

(31)

$$ \sigma_{rm} = \frac{{E_{rm} }}{{2G_{rm} }} - 1 $$

(32)

3 Results and discussion

3.1 Investigation of X-ray diffraction (XRD)

X-ray diffraction (XRD) is a technique for identifying the crystalline phase of a sample material. It is used to analyse the structure of amorphous materials such as glass, as well as to confirm the absence of any crystalline phases (Azlan et al. 2017a). Figure 1 shows the XRD pattern for Sm₂O₃ doped zinc tellurite glass system at different concentrations. A broad diffuse pattern is observed ranging from 20° to 40° at 2θ scale due to the absence of long-range periodic order arrangement in glass structure. Thus, the absence of such sharp diffraction peaks confirm amorphous nature of glass system (Maheshvaran et al. 2012).

Fig. 1

XRD spectra for [(TeO₂)_0.7 (ZnO)_0.3]_1-x [Sm₂O₃]_x glass system

3.2 Analysis of density and molar volume

Density is an important physical parameter that reflects the change in glass composition (Hajer et al. 2014). The recorded values of density and molar volume can be found in Table 1, while Fig. 2 illustrates the comparative behavior of these two quantities. It is observed that the density increases as the Sm₂O₃ content increases. The increase in density can be ascribed to the substitution of tellurium oxide, a glass former with a smaller atomic mass (Te = 127.6 g/mol), by the dopant samarium, which possesses a larger atomic mass (Sm = 150.36 g/mol) within the glass system (Linda et al. 2013). Additionally, the upward trend in density can be attributed to the introduction of a modifier oxide, disrupting the Te–O–Te bonds and consequently expanding the available space within the glass network (Hajer et al. 2016). Moreover, the rise in densities can be ascribed to alterations in coordination and geometrical configuration, as well as structural softening/compactness and changes in the dimensions of interstitial spaces within the glass system (Hajer et al. 2016). The expansion in molar volume within the range of 27.412 cm³/mol to 27.590 cm³/mol can be attributed to the increase of free volume within the glass system (Tafida et al. 2020). The increase can also be attributed to the substitution of smaller atomic/ionic radius atoms (Te and Zn) with larger atomic/ionic radius Sm³⁺ atoms within the glass system.

Table 1 Density, molar volume, Oxygen packing density (OPD) and oxygen molar volume (Vo), samarium ionic concentration (N) and inter ionic distance (R_i) for [(TeO₂)_0.7 (ZnO)_0.3]_1-x [Sm₂O₃]_x glass system

Fig. 2

Density and molar volume for [(TeO₂)_0.7 (ZnO)_0.3]_1-x [Sm₂O₃]_x glass system

3.3 Oxygen packing density (OPD) and oxygen molar volume (V_o)

The oxygen packing density and oxygen molar volume serve as indicators of compactness in oxide network (Bhatia et al. 2015). Figure 3 depicts OPD and V_o and their corresponding values are listed in Table 1. The packing density of Sm₂O₃ glasses exhibits a gradual increase as the dopant concentration increases, with values ranging from 62.463 g/litre to 63.741 g/litre. This rise in packing density can be attributed to the increase in glass rigidity and density of the fabricated samples. The presence of Sm³⁺ ions occupying the interstices in the glass network structure leads to a closely packed structure, thereby increasing the glass packing density (Bootjomchai 2015). Furthermore, the increase in packing density can be attributed to the variations in glass network structure around the dopant cations, which result in an increase in their cation field strength. This change in the network configuration contributes to the higher packing density observed in the samples (Abd Elfadeel et al. 2017). Besides that, the observed rise in OPD implies the absence of non-bridging oxygens (NBOs) in the structure of the glass network (Usman et al. 2018). Nevertheless, the declining values of OPD can be attributed to the presence of NBOs within the glass network. (Ashur et al. 2014). As the dopant content increases, the oxygen molar volume of Sm₂O₃ exhibits a consistent decline. This decrease in oxygen molar volume further contributes to a reduction in the overall molar volume of glass network. It signifies a decrease in the formation of non-bridging oxygen (NBO), consequently leading to a decrease in the available free or excess volume within the glass network. The observed trend favors the formation of a more densely packed structure within the glass network (Gaafar et al. 2014).

Fig. 3

Oxygen packing density and oxygen molar volume for [(TeO₂)_0.7 (ZnO)_0.3]_1-x [Sm₂O₃]_x glass system

3.4 Samarium ionic concentration $({\varvec{N}})$ and inter ionic distance ${({\varvec{R}}}_{{\varvec{i}}})$

These two factors are crucial in explaining the structural characteristics of tellurite doped glasses. Literature suggests (Hamza et al. 2019a) that as the ionic concentration in the glass system increase, the distance between ions decreases, resulting in a higher level of connectivity within the glass network. The ionic concentration (N) demonstrates an upward trend with the increase of dopant concentration. Conversely, the interionic distance ${(R}_{i})$ decreases with an increase in dopant content, as depicted in Fig. 4, and their respective values are provided in Table 1.

Fig. 4

Ionic concentration and inter ionic distance for [(TeO₂)_0.7 (ZnO)_0.3]_1-x [Sm₂O₃]_x glass system

4 Experimental elastic properties

The elastic properties play a crucial role in providing detailed descriptions of the structure of solids. Moreover, they enable the study of material strength under applied forces (Elkhoshkhany et al. 2015). Elastic properties are additionally vital parameters utilized to assess the suitability of glasses for various applications (Halimah et al. 2021).

4.1 Longitudinal velocity ${({\varvec{V}}}_{{\varvec{l}}}$) and shear velocity $({{\varvec{V}}}_{{\varvec{s}}})$

The variation of longitudinal and shear velocity with different dopant concentration is presented in Fig. 5 and their corresponding values are listed in Table 2. Both the longitudinal and shear ultrasonic velocities exhibit similar pattern of behaviour. It is observed that ultrasonic velocities decrease from (3392 to 3379) ms⁻¹ and (1946 to 1920) ms⁻¹ respectively on increasing the dopant content. Nevertheless, when the molar fraction reaches x = 0.02, both longitudinal and shear ultrasonic velocities begin to rise until x = 0.03. However, from x = 0.03 to x = 0.05, the velocities start to decline with the increase in dopant. This decrease in longitudinal and shear velocities can be attributed to the formation of NBOs in the glass network (Zaitizila et al. 2018).

Fig. 5

longitudinal and shear velocities for [(TeO₂)_0.7 (ZnO)_0.3]_1-x [Sm₂O₃]_x glass system

Table 2 Longitudinal velocity $\left({V}_{l}\right)$, Shear velocity $\left({V}_{s}\right)$ and elastic moduli for [(TeO₂)_0.7 (ZnO)_0.3]_1-x [Sm₂O₃]_x glass system

On the contrary, the observed increase in value with addition of more dopant can be attributed to the enhanced rigidity of glass system (Nazrin et al. 2018). The increase in rigidity can be linked to the escalation in the quantity of trigonal bipyramid TeO₄ units within the glass network, corresponding to the rise in dopant content (Bahari et al. 2013). Additionally, as given in the literature, an increase in both ultrasonic velocities results in an increase of packing density. This phenomenon arises from the alteration in coordination within the synthesized glasses, leading to the formation of more bridging oxygen (BOs). Consequently, the increase in ultrasonic velocities is directly correlated with this increase in BOs (Saddeek et al. 2005).

4.2 Elastic moduli

The elastic moduli are directly influenced by the interatomic forces and packing density of the constituents oxide (Nazrin et al. 2018). The elastic moduli of the studied glasses were calculated using the measured ultrasonic velocities and density. Table 2 presents the values of the elastic moduli, while Fig. 6 illustrates the variation of the elastic moduli at different dopant concentrations. It is observed that the elastic moduli L, G, K, and E increase with increasing dopant concentrations. This increase is attributed to the enhanced glass rigidity resulting from the addition of more dopants into the glass network (Sidek et al. 2007). Moreover, as the elastic modulus increases with the addition of dopants, it indicates an improvement in the strength of the materials (Alazoumi et al. 2017). With an increase in connectivity, the samples demonstrate a higher level of atom bonding within the glass network, resulting in improved resistance to strain.

Fig. 6

Elastic moduli for [(TeO₂)_0.7 (ZnO)_0.3]_1-x [Sm₂O₃]_x glass system

4.3 Poisson’s ratio (σ) and Fugacity (${{\varvec{f}}}_{{\varvec{g}}}$)

According to the literature, Poisson's ratio present the degree of cross-link density within the glass network (Gupta et al. 2014). This suggests that Poisson's ratio is influenced by the density of cross-links and can be analyzed using cross-link density data. Poisson's ratio is also linked to the internal changes occurring within the glass materials (Abd Elfadeel et al. 2017). The data for Poisson's ratio is listed in Table 3 and presented in Fig. 7. The values of Poisson's ratio increase up to a dopant concentration of 0.03 molar fractions and then decrease until 0.05 molar fractions with the addition of dopant. The increase in Poisson's ratio suggests a higher level of transverse contracting strain among the atoms, resulting in a more tightly packed glass system (Kannappan et al. 2009). Furthermore, the observed decrease in Poisson's ratio at certain concentrations can be attributed to the gradual increase in the average cross-link density. This increase in cross-link density contributes to the deformation and distortion of the glass network, resulting in the decrease in Poisson's ratio (Sidek et al. 2007).

Table 3 Poisson’s ratio (σ), Fugacity (${f}_{g}$), Debye temperature (${\theta }_{D})$ and Softening temperature (${T}_{s})$ for [{(TeO₂)_0.7 (ZnO)0.3}_1-x] [Sm₂O₃]_x glass system

Fig. 7

Poisson’s ratio and fugacity for [(TeO₂)_0.7 (ZnO)_0.3]_1-x [Sm₂O₃]_x glass system

Another crucial parameter investigated in this study is fugacity, which represents the fluctuation free volume in the glass system. Fugacity is influenced by the changes in Poisson's ratio and serves as a measure of the rigidity of the glass network (Saddeek et al. 2005). Figure 7 illustrates the variation of fugacity, as presented in Table 3. The fugacity values decrease in the molar fraction range of 0.01 to 0.03 and increase from 0.03 to 0.05 with the addition of more dopants. The decrease in fugacity signifies a reduction in glass rigidity and connectivity, resulting from the formation of NBOs in the glass structure (Saddeek et al. 2005). The observed increase in fugacity is attributed to the formation of more bridging oxygen (BO) in the glass system, as stated in Sidkey and Gaafar (2004). This increase enhances the glass rigidity and connectivity.

4.4 Debye temperature (${{\varvec{\uptheta}}}_{\mathbf{D}}$) and Softening temperature (${\mathbf{T}}_{\mathbf{S}}$)

Debye temperature is an important parameter that characterizes the lattice vibrations in a solid. It signifies the temperature at which almost all vibration modes in a solid are excited (Bahari et al. 2013). Debye temperature is a significant parameter for analyzing solid materials like glass. A decrease in its values suggests a decrease in the rigidity of the glass system. Figure 8 illustrates the behavior of Debye temperature, as recorded in Table 3, at various dopant concentrations. The values of Debye temperature generally increase with increasing dopants, with a slight decrease observed at 0.04 molar fractions. The increase in Debye temperature indicates an enhancement in the rigidity of these glasses, which can be attributed to the increase in the number of atoms in the glass system's chemical formula and the rise in the mean ultrasonic velocity (Halimah et al. 2005). The observed decrease in Debye temperature in this study can be primarily attributed to two factors: the change in the number of atoms per unit volume and the presence of non-bridging oxygen in the glass system. These factors influence the vibrational modes and overall dynamics of the lattice, leading to a decrease in the Debye temperature (Saddeek 2004). Furthermore, the reduction of bond strength is recognized as one of the significant factors contributing to the decrease in Debye temperature, as reported by Hasnimulyati et al. (2017). When the bond strength decreases, it affects the overall vibrational behavior and leads to a lower Debye temperature in the material. Softening temperature is a critical parameter that signifies the transition from viscous flow to plastic flow in a material. It serves as an indicator of the temperature stability of the glass system, marking the temperature at which the material undergoes a change in its flow behavior (Halimah et al. 2005). Higher values of softening temperature play a significant role in determining the stability of glass materials, as indicated in El-Mallawany and Abd El-Moneim (1998). The softening temperature data for the glass system are presented in Table 3 and Fig. 8. It is observed that the values of softening temperature increase with the addition of more dopants. This increase can be attributed to the greater number of atoms in the chemical formula and higher ultrasonic velocities of the glass system, indicating a strengthening effect due to the formation of bridging oxygen (Eevon et al. 2016). However, there is a slight decrease in softening temperature at 0.04 molar fractions. This decrease indicates that the glass becomes less rigid at that concentration, which can be attributed to the creation of NBOs (Halimah et al. 2010).

Fig. 8

Softening temperature and Debye temperature for [(TeO₂)_0.7 (ZnO)_0.3]_1-x [Sm₂O₃]_x glass system

5 Theoretical elastic properties

The elastic properties are also analyzed using the theoretical models. Four different theoretical elastic models were employed to assess the structure and compare the elastic moduli with the corresponding experimental values.

5.1 Makishima and mackenzie model

The Makishima-Mackenzie theoretical elastic model was used to analyze the elastic modulus of oxide glasses. This model takes into account the chemical composition of the glasses, as well as two key parameters: the packing density (V_i) and dissociation energy (G_i) of the constituent oxides per unit volume. The values of packing density and dissociation energy for all the chemical oxides are presented in Table 4.

Table 4 Packing density (${{\text{V}}}_{{\text{i}}}$) and dissociation energy (${{\text{G}}}_{{\text{i}}}$) for [{(TeO₂)_0.7 (ZnO)0.3}_1-x] [Sm₂O₃]_x glass system

Table 5 provides the values of total packing density, total dissociation energy, Poisson's ratio, and elastic moduli. Figure 9 displays the graph illustrating the relationship between total packing density and total dissociation energy with varying dopant concentrations.

Table 5 Total packing density (V_t), total dissociation energy (G_t), young modulus (E_mm), bulk modulus (K_mm), shear modulus (G_mm) and Poisson’s ratio (σ_mm) for [{(TeO₂)_0.7 (ZnO)0.3}_1-x] [Sm₂O₃]_x glass system

Fig. 9

Packing density and dissociation energy for [(TeO₂)_0.7 (ZnO)_0.3]_1-x [Sm₂O₃]_x glass system

The packing density of Sm₂O₃ glasses exhibits a gradual increase as the dopant concentration increases. This rise in packing density can be attributed to the increase in glass rigidity and density of the fabricated samples. The presence of Sm³⁺ ions occupying the interstices in the glass network structure leads to a closely packed structure, thereby increasing the glass packing density (Bootjomchai 2015). Furthermore, the increase in packing density can be attributed to the variations in glass network structure around the dopant cations, which result in an increase in their cation field strength. This change in the network configuration contributes to the higher packing density observed in the samples (Abd Elfadeel et al. 2017).

The strong polarization of the cations in the glass network leads to increased ion–dipole interactions, thereby enhancing the packing density. On the other hand, the dissociation energy per unit volume (${G}_{t}$) decreases with an increase in dopant concentration, as indicated in Table 5. This decrease in dissociation energy is associated with a reduction in the rigidity of the glass structure. The Makishima and Mackenzie model also calculates the elastic moduli and Poisson's ratio based on the packing density and dissociation energy per unit volume. The values of these parameters are provided in Table 5, and their corresponding graphs are depicted in Figs. 10 and 11, showcasing the variations at different dopant concentrations.

Fig. 10

Makishima and Mackenzie elastic moduli for [(TeO₂)_0.7 (ZnO)_0.3]_1-x [Sm₂O₃]_x glass system

Fig. 11

Makishima and Mackenzie Poisson’s ratio for [(TeO₂)_0.7 (ZnO)_0.3]_1-x [Sm₂O₃]_x glass system

The elastic moduli, including Young's modulus, bulk modulus, and shear modulus, generally decrease with increasing dopant concentration, with a slight increase observed at 0.04 molar fractions. This decreasing trend in elastic moduli is attributed to the decrease in glass rigidity and the dissociation energy per unit volume of the glass system. However, the observed increase in elastic moduli can be attributed to the increase in glass packing density (Hasnimulyati et al. 2017). Moreover, the glass network's elevated field strength can additionally induce an increase in the stiffness of the glass structure, consequently leading to enhanced bond strength and increased elastic moduli (El-Mallawany and Abd El-Moneim 1998). According to Table 5, there is a noticeable upward trend in the Poisson's ratio as the concentration of dopants increases. The observed increase in the Poisson's ratio aligns with the corresponding packing density of the glass system, indicating a similar behavior. This rise can also be attributed to the tightly packed structure of the synthesized glasses (Makishima and Mackenzie 1975).

5.2 Rocherulle model

The Rocherulle model made certain modifications to the packing density calculation initially proposed by Makishima and Mackenzie. In this model, we opted to consider the density of each individual oxide constituent rather than the density of the synthesized glass. Table 6 presents the packing density, Young's modulus, and Poisson's ratio calculated using this model. Figure 12 illustrates the relationship between packing density and dopant concentration as predicted by this model.

Table 6 Packing density (C_t), Young modulus (E_rm), bulk modulus (K_rm), shear modulus (G_rm) and Poisson’s ratio (σ_rm) for [{(TeO₂)_0.7 (ZnO)0.3}_1-x] [Sm₂O₃]_x glass system

Fig. 12

Rocherulle packing density for [{(TeO₂)_0.7 (ZnO)_0.3}_1-x] [Sm₂O₃]_x glass system

With the increase in the dopant amount, the modified packing density demonstrates a continuous decrease. This decline in packing density can be attributed to the lower density value (Ct = 2.7484) of Sm₂O₃ in comparison to that of the glass system, resulting in a reduction in Young's modulus (Saddeek 2004). The packing density obtained from the Rocherulle model is comparatively higher than the overall packing density derived from the Makishima and Mackenzie models. Figure 13 presents a plot depicting the elastic moduli for this model at various dopant concentrations.

Fig. 13

Rocherulle elastic moduli for [{(TeO₂)_0.7 (ZnO)_0.3}_1-x] [Sm₂O₃]_x glass system

The Young's modulus and Poisson's ratio values, as presented in Table 6, exhibit a decreasing trend as the dopant concentration increases. This decrease can be attributed to the corresponding decrease in the packing density of the fabricated glasses, resulting in a decrease in the overall stiffness of the glass (Hasnimulyati et al. 2017). Figure 14 illustrates the graph depicting the relationship between the Poisson's ratio and various dopant concentrations.

Fig. 14

Rocherulle Poisson’s ratio for [{(TeO₂)_0.7 (ZnO)_0.3}_1-x] [Sm₂O₃]_x glass system

5.3 Bond compression model

In Bond compression model, the data for various oxides, including coordination number, bond length, number of cations per glass formulation, and oxide unit for each component, were collected and reported. The elastic modulus of the composite glass is then calculated utilizing the data provided in Table 7.

Table 7 First order stretching force constant $\left(f\right)$, number of cross link density per cation (${n}_{c}$), number of cations per glass formula unit $\left({N}_{c}\right)$, coordination number $\left({n}_{f}\right)$ and bond length $\left(r\right)$

The elastic moduli obtained through the Bond compression model incorporate several factors, including the total number of cations per glass formula unit $\left(\eta \right)$, the number of network bonds per unit volume (${n}_{b})$, and the average cross-link density per unit formula (${\overline{n} }_{c})$ of the synthesized glasses, as presented in Table 8.

Table 8 Total number of cations per glass formula unit $\left(\eta \right)$, number of network bond per unit volume $\left({n}_{b}\right)$ (m⁻³) and average cross link density per unit formula $({\overline{n} }_{c}$) for [{(TeO₂)_0.7 (ZnO)0.3}_1-x] [Sm₂O₃]_x glass system

Table 8 reveals that the average density of cross-links per unit formula exhibits a consistent increase with an escalating dopant concentration. This behavior can be attributed to the incorporation of Sm₂O₃, which possesses a high coordination number, thereby enhancing the dimensionality of the network structure and resulting in a higher average density of cross-links per unit formula. Additionally, as indicated in Table 8, the reported number of bonds per unit volume $\left({n}_{b}\right)$ also increases with dopant concentration. This rising trend can be attributed to the creation of BO, which contributes to greater compactness and rigidity within the synthesized glass network. The computed elastic moduli of the Bond compression model are presented in Table 9. Furthermore, Fig. 15 depicts the corresponding graphs.

Table 9 Elastic moduli, Poisson’s ratio and ratio K_bc/K_e for [{(TeO₂)_0.7 (ZnO)0.3}_1-x] [Sm₂O₃]_x glass system

Fig. 15

Bond compression elastic moduli for [{(TeO₂)_0.7 (ZnO)_0.3}_1-x] [Sm₂O₃]_x glass system

With the addition of more dopants, the elastic moduli exhibited a decrease within the 0.01 to 0.03 molar fraction range, followed by an increase at 0.04 and 0.05 molar fractions. It is worth noting that the elastic moduli obtained through the bond compression model are generally larger in comparison to their corresponding experimental values. This behavior is expected and has been reported in numerous literature sources, stating that the moduli obtained using this model can be higher by a factor of 3 to 10 compared to the experimental moduli (El-Mallawany and Abd El-Moneim 1998). In cases where the elastic moduli values increase, there is a concurrent decrease in molar volume, leading to the production of closely packed and rigid structures in the synthesized glasses. Consequently, there is an increase in the number of network bonds per unit volume. Conversely, the decrease in elastic moduli at certain concentrations can be attributed to an increase in molar volume resulting from an increasing dopant concentration. Among all the estimated moduli, the bulk modulus (K_bc) is found to be the most significant for the geometrical study of the glass structure, earning the model the occasional designation of the bulk compression model. As indicated by Sidkey and Gaafar (2004), the observed increase can be explained by the K_bc parameter, which depends on the number of network bonds per unit volume and the first-order stretching force constant. In Table 9, the values of K_bc/K_e exhibit a decrease from 3.126 at 0.01 to 2.910 at 0.05 molar fractions, except for the 0.04 molar fraction where the value increases. The obtained values fall within the ranges reported for tellurium oxide-based glasses, as revealed by El-Mallawany (1998). According to the literature, the ratio of K_bc/K_e falls within the range of 1–3 for an ideal isotropic compression mechanism and 3–10 for ring deformation mechanisms. Based on this information, it can be inferred that the current glass systems undergo isotropic ring compression, as illustrated in Fig. 16.

Fig. 16

Ratio of K_bc/K_e and atomic ring size l for [{(TeO₂)_0.7 (ZnO)_0.3}_1-x] [Sm₂O₃]_x glass system

The Poisson's ratio exhibits a gradual decrease from 0.219 at 0.01 to 0.217 at 0.05 molar fractions, corresponding to the increase in dopants, as indicated in Table 9 and depicted in Fig. 17. The relationship utilized in calculating the Poisson's ratio within the bond compression model highlights its dependency on the average cross-link density, which justifies the observed behavior. Consequently, the decrease in Poisson's ratio can be attributed to the increase in the average cross-link density within the glass system. This outcome aligns with expectations, as an increase in average cross-link density implies the presence of more bonds in the lateral direction, enhancing resistance to lateral strain and thereby reducing the Poisson's ratio of the glass (Sidkey and Gaafar 2004).

Fig. 17

Bond compression Poisson’s ratio for [{(TeO₂)_0.7 (ZnO)_0.3}_1-x] [Sm₂O₃]_x glass system

5.4 Ring deformation model

The ring deformation model is an adapted version of the bulk compression model, relying on the K_bc/K_e value ratio. It has been observed that higher values of K_bc/K_e lead to the formation of a layer or chain network, suggesting that the network bond bending process becomes prominent under bulk compression conditions (Azlan et al. 2017b). In this model, the atomic ring size (l) is directly proportional to K_bc/K_e, which is calculated using the average stretching force constant and the measured bulk modulus. An increase in the atomic ring size signifies the potential for bond bending within the glass system. Table 10 presents the values of atomic ring size and average stretching force constant for the synthesized glasses.

Table 10 Average stretching force constant, atomic ring size for [{(TeO₂)_0.7 (ZnO)0.3}_1-x] [Sm₂O₃]_x glass system

Figure 16 illustrates the correlation between atomic ring size and dopant concentration. As the concentration of dopants increases, the values of atomic ring size decrease. This trend in atomic ring size aligns with the trend observed in K_bc/K_e ratio values, providing further evidence of the direct relationship between these two parameters. A larger atomic ring size indicates a more compact glass structure. Table 11 presents the elastic moduli and Poisson's ratio for this model, while Figs. 18 and 19 display their respective graphs against dopant concentration. With an increase in dopants, the elastic moduli show an upward trend. In this model, the increasing trend of the elastic moduli can be attributed to the behavior of their molar volume. Higher molar volume values lead to the formation of closely packed and rigid structures within the glass system (Gaafar et al. 2011). As dopants increase, the Poisson's ratio decreases, indicating a relationship with the cross-link density of the glass system.

Table 11 Ring deformation elastic moduli, Poisson’s ratio for [{(TeO₂)_0.7 (ZnO)0.3}_1-x] [Sm₂O₃]_x glass system

Fig. 18

Ring deformation elastic moduli for [{(TeO₂)_0.7 (ZnO)_0.3}_1-x] [Sm₂O₃]_x glass system

Fig. 19

Ring deformation Poisson’s ratio for [{(TeO₂)_0.7 (ZnO)_0.3}_1-x] [Sm₂O₃]_x glass system

The theoretical and experimental data of elastic moduli were compared, and their analysis is presented and depicted in Figs. 20, 21, 22. Upon comparing the theoretical and experimental elastic moduli, it is evident that all calculated elastic moduli from the theoretical models align closely with the experimental elastic moduli, with the exception of the Bond compression elastic moduli. However, it is worth noting that the Bond compression elastic moduli are still considered valid, as long as their values are higher than the experimental values by a factor of 3–10, as mentioned by El-Mallawany (1998). This comparison highlights the level of agreement between the experimental and calculated elastic moduli. It can be concluded that the experimental results demonstrate a very good agreement with the theoretical models.

Fig. 20

Correlation of the experimental young modulus with theoretical young moduli for [{(TeO₂)_0.7 (ZnO)_0.3}_1-x] [Sm₂O₃]_x glass system

Fig. 21

Correlation of the experimental Bulk modulus with theoretical Bulk moduli for [{(TeO₂)_0.7 (ZnO)_0.3}_1-x] [Sm₂O₃]_x glass system

Fig. 22

Correlation of the experimental Shear modulus with theoretical Shear moduli for [{(TeO₂)_0.7 (ZnO)_0.3}_1-x] [Sm₂O₃]_x glass system

6 Judd-Ofelt intensity parameters

The incorporation of RE-ions into the host materials can be quantitatively assessed through the application of Judd-Ofelt theory. By utilizing experimental data to establish the initial absorption state, which determines the electrical dipole intensity under specific conditions, it becomes possible to measure three parameters (${\Omega }_{2}$, ${\Omega }_{4}$ and ${\Omega }_{6}$) (Li et al. 2019). In this investigation, the J-O parameters are employed to gather data regarding chemical and physical characteristics of Sm³⁺ ions embedded into the glass network. The Ω₂ parameter provides insights into the covalency of Sm³⁺ bond within the glass matrix and the asymmetries surrounding Sm³⁺ ions. Consequently, there exists an inverse relationship between the Ω₆ parameter and covalency of Sm³⁺ bond. The J-O parameters Ω₄ and Ω₆ have a significant impact on glass properties such as dielectric constant and glass viscosity, as they are influenced by the vibrionic transition of Sm³⁺ ions coupled to the ligand atoms. Moreover, the stiffness of the host material housing the Sm³⁺ ions is interconnected with Ω₄ and Ω₆ (Mawlud et al. 2017).

The J-O (${\Omega }_{2}$, ${\Omega }_{4}$ and ${\Omega }_{6}$) parameters are then used to calculate other radiative parameters such as branching ratio (${\beta }_{R}$), magnetic dipole radiative transition probability (${A}_{MD}$), electric dipole radiative transition probability (${A}_{ED}$), gain bandwidth (Δλeff × σp) and optical gain (σp × τ). As stated in Mawlud et al. (2017), these properties are utilized to ascertain the likely laser transitions of rare-earth ions within the host material. Table 12 shows the computed values of J-O parameters (${\Omega }_{2}$, ${\Omega }_{4}$ and ${\Omega }_{6}$) as well as the spectroscopic quality factor Ω₄/Ω₆ of the synthesized glass samples.

Table 12 The JuddOfelt intensity parameters and spectroscopic quality factor for [{(TeO₂)_0.7 (ZnO)0.3}_1-x] [Sm₂O₃]_x glass system

The J-O parameters are found to be exhibiting an order i.e. ${\Omega }_{2}$ > ${\Omega }_{4}$  > ${\Omega }_{6}$ with an increase in the dopant concentration, ${\Omega }_{2}$ demonstrates an upward trend. This rise in ${\Omega }_{2}$ values can be attributed to the presence of strong covalent bonding within the glass system. The higher ${\Omega }_{2}$ values also suggest a decrease in ionicity and an increase in the asymmetry of rare-earth (RE) ions in relation to their surrounding ligands (Li et al. 2019). With an increase in dopant concentration, both ${\Omega }_{4}$ and ${\Omega }_{6}$ display an ascending trend, although there are certain concentrations where the values decrease. The upward trend in ${\Omega }_{4}$ and ${\Omega }_{6}$ suggests enhanced rigidity and viscosity within the glass matrix.

According to Tanko et al. 2016a, the decreasing values of ${\Omega }_{4}$ and ${\Omega }_{6}$ indicate that vibrionic transitions between the ligand atoms and rare-earth ions have an impact on viscosity. Materials with a better spectroscopic quality factor (${\Omega }_{4}$/${\Omega }_{6}$) are advantageous for investigating the active laser medium (Li et al. 2019). In Table 12, the values of (${\Omega }_{4}$/${\Omega }_{6}$) are presented, and each value is observed to be greater than 1, with the highest value recorded as 1.550. The obtained higher value of (${\Omega }_{4}$/${\Omega }_{6}$) indicates that the examined glass samples serve as superior optical media for active laser applications (Tanko et al. 2016b). Table 13 provides a comparison between the experimental and measured line strengths, demonstrating the validity of the fitting process. Additionally, the small root-mean-square deviation values (${\updelta }_{rms}$) of the experimental and calculated oscillator strengths indicate a strong correspondence between the two values, confirming the accuracy of the Judd-Ofelt intensity parameters and the overall validity of the analysis.

Table 13 Comparison between the experimental and measured line strength, root mean square deviation (δ_rms) for [{(TeO₂)_0.7 (ZnO)0.3}_1-x] [Sm₂O₃]_x glass system

To assess the validity of the fitting, the experimental and computed line strengths were compared with existing literature (Azlan et al. 2017a). The calculations were performed following the methodology employed in the majority of previously reported studies on Sm₂O₃ doped glasses found in the literature (Ahmadi et al. 2017). The minimal difference observed between the calculated and experimental spectral intensities, as indicated by the (${\updelta }_{rms}$) values, highlights the exceptional agreement between the calculated and experimental line strengths (Ahmadi et al. 2017). The small values of (${\updelta }_{rms}$) further indicate a robust fit between the experimental and estimated spectral intensities, affirming the validity of the Judd-Ofelt intensity parameters (Mawlud et al. 2017).

As per the reference (Seshadri et al. 2015), the spectral intensities exhibit variations at different concentrations, indicating varying degrees of crystal field asymmetry. To explore the potential applications of the prepared glasses, additional calculations were performed to determine the magnetic dipole radiative transition probability $({A}_{MD}$), electric dipole radiative transition probability (${A}_{ED}$), branching ratio (${\beta }_{R}$), gain bandwidth (Δλeff × σp), and optical gain (σp × τ). These calculations were based on the methodologies commonly employed in relevant literature. The outcomes of these calculations are presented in Table 14.

Table 14 Calculated transition probabilities [${A}_{MD}$, ${A}_{ED}$], branching ratio $({\beta }_{R})$, gain band width (Δλeff × σp), and optical gain (σp × τ) in ⁴ ${G}_{5/2}$ transition level of Sm³⁺ ions for [{(TeO₂)_0.7 (ZnO)0.3}_1-x] [Sm₂O₃]_x glass system

In the present glass system, the transition ⁶H_7/2 has recorded the highest radiative transition rate when compared with other transitions and thus, making it ideal for laser emission (Li et al. 2019). Transitions with the highest values of radiative transition probabilities are associated with large branching ratios. The luminescence branching ratio serves as a characterization of the lasing power of a transition (Mawlud et al. 2017). The ⁴G_5/2 $\to$ ⁶H_7/2 transitions demonstrate higher values of branching ratio $({\beta }_{R})$ compared to other transitions investigated in this study, and these values are consistent with those reported in literature (Hua et al. 2022). The symmetry of the surroundings for trivalent rare-earth (RE) ions is determined by the ratio of electric dipole to magnetic dipole transition intensities (Sun et al. 2023). The evaluated asymmetry ratios for the transitions ⁴G_5/2 → ⁶H_9/2 and ⁴G_5/2 → ⁶H_5/2 decrease from 4.820 to 0.651 with increasing Sm³⁺ concentration. From the results, the dominance of the electric dipole (ED) transition over the magnetic dipole (MD) transition suggests that low asymmetry present in the sites occupied by Sm³⁺ ions within the glass. However, the 0.05 dopant level show significant asymmetry in nature. Furthermore, the relaxation from a higher state to all of its lower levels is influenced by the values of electric dipole transition probability ${A}_{ED}$ and magnetic dipole transition probability ${A}_{MD}$. Consequently, transitions that possess generally higher values of ${A}_{ED}$, ${A}_{MD}$, ${\beta }_{R}$ and an energy gap greater than a few photons may exhibit laser activity among all possible relaxations to lower levels (Mawlud et al. 2017).

The radiative transition probabilities indicate that ⁴G_5/2 → ⁶H_7/2 transition possesses the highest values, with ${A}_{ED}$ measured at 863.712 S⁻¹ and A_MD at 864.945 S⁻¹. These moderately higher values highlight the suitability of the ⁴G_5/2 → ⁶H_7/2 transition for laser emission compared to other transitions (Hamza et al. 2019b). Transitions with the highest radiative transition probabilities are associated with high branching ratios. As shown in Table 13, the ⁶H_7/2 transition exhibits higher ${\beta }_{R}$ values. The luminescence branching ratio holds significant importance for laser designers as it indicates the potential for achieving stimulated emission from a specific transition (Yu et al. 2023). To prevent distortion of the medium in which the rare-earth (RE) ions are arranged, the examination of gain bandwidth (σp × λeff) and optical gain (σp × τ) is crucial. According to Li et al. (2019), a stronger optical amplifier would display larger values of (σp × λeff) and (σp × τ). Notably, the values of (σp × λeff) and (σp × τ) are higher in the ⁴G_5/2 → ⁶H_11/2 and ⁶H_7/2 transitions, suggesting that the glasses are well-suited for high-gain laser applications (Li et al. 2019).

7 Conclusion

Zinc tellurite glasses doped with Sm³⁺ ions were produced using the chemical formula of [{(TeO₂)_0.7 (ZnO)_0.3}_1-x] [Sm₂O₃]_x with molar fractions of x = 0.01, 0.02, 0.03, 0.04, and 0.05 obtained through the melt quenching method. XRD data confirmed the amorphous nature of the materials. Increasing the Sm₂O₃ content led to higher density and molar volume, attributed to modifications in coordination, structural softening/compactness, and interstitial space of the glass system. Elastic properties investigated revealed unstable patterns in longitudinal and shear velocities, likely due to the formation of non-bridging oxygen’s (NBOs) and disruption of the glass network. The ultrasonic velocities decrease from 3392 to 3379 ms⁻¹ and 1946 to 1920 ms⁻¹, for V_L and Vs, respectively. Theoretical elastic models have good agreement with the experimental elastic measurements, validating their application. Judd-Ofelt (J-O) intensity parameters indicated higher asymmetry and spectroscopic properties in the synthesized glasses. The glasses exhibited visible emission bands, with the ⁴G_5/2 → ⁶H_7/2 transition showing the most intense emission. The evaluated asymmetry ratios for the transitions ⁴G_5/2 → ⁶H_9/2 and ⁴G_5/2 → ⁶H_5/2 decrease from 4.820 to 0.651 with the electric dipole (ED) transition dominates the magnetic dipole (MD) transition. This suggests low asymmetry present in the sites occupied by Sm³⁺ ions within the glass. The glasses with 0.01 molar percentage of Sm³⁺ showed potential as laser-active media at 604 nm wavelength. These glasses demonstrated higher gain bandwidths, optical gains, branching ratios, and radiative transition probabilities, making them suitable for visible lasers in the strong orange (604 nm) region.