Polarizability, optical basicity and optical properties of SiO₂B₂O₃Bi₂O₃TeO₂ glass system

Abstract

Glasses having a composition xSiO₂xB₂O₃ (95−2x) Bi₂O₃5TeO₂ where x = (5, 10, 15, 20, 25) prepared by the melt-quenching technique. Thermal stability, density, optical transmittance, and the refractive index of these glasses investigated. Glass samples were transparent in the visible to near-infrared (NIR) region and had a high refractive index. A number of glass samples have high glass-forming ability. This indicates that the quarterly glasses are suitable for optical applications in the visible to the NIR region. Bi₂O₃ substituted by B₂O₃ and SiO₂ on optical properties discussed. It suggested that the substitution of Bi₂O₃ increased the density, molar volume, the molar polarizability, optical basicity and refractive index in addition to, the oxygen packing density, the optical energy gap, and metallization decrease. These results are helpful for designing new optical glasses controlled to have a higher refractive index. All studied glass presented high nonlinearities, and the addition of network modifiers made a little contribution. Results clarified the bandgap energy reduction, which associated with the growth within the non-bridging oxygen content with the addition of the network modifier. An increase in the refractive index nonlinearity explained by the optical basicity and the high electronic polarizability of the modifier ions.

1 Introduction

According to a technological and scientific application of Bismuth borate glasses [1,2,3], these glasses become interesting materials for structural, optical and electrical investigations [4,5,6,7]. Tasheva and Dimitrov [8] studied the nonlinear optical properties of TeO₂ Bi₂O₃ B₂O₃ oxide glasses. It established that the glasses posses’ high third-order nonlinear susceptibility in the (0.64–2.31 × 10⁻¹³ esu) range. Lin et al. [9] studied the ultra nonlinear properties of Bi₂O₃ B₂O₃ oxide glass, they found that the nonlinear response time is lesser than 90 femtosecond and the nonlinear refractive index estimated to 1.6 × 10⁻¹⁴ cm²/W.

Adding composition compounds containing lone pairs ions or ions unoccupied d-orbital to the glass samples increased the nonlinear optical properties of oxide glass. Metal and semiconductor nano-particles (Si, Cu, Ge, and Bi)-doped glasses prepared by the melt-quenching method display large third-order optical nonlinearity [10, 11]. Third-order nonlinearity of some promising oxide glasses were investigated and developed [12]. Optical properties [13] of silicate, borosilicate, telerate and heavy metal oxide glasses were studied. Several studies found that the nonlinear optical properties are created in the all-glass system. A number of researchers investigated the nonlinear optical properties of borate glass. Borate glasses have photonic properties which contain a transparent, low glass transition temperature (T_g), high density, high thermal expansion coefficient and high vitrifying ability besides the ability to dissolve large quantities of other glass formers, modifiers, intermediate, rare-earths and metal nano-particles without reduction of the glass-forming ability. Optical non-linearity of Bi₂O₃-based glasses are increasing by the addition of either a second lone pair holder (such as Te⁴⁺, Pb²⁺) or cations with empty d-orbital (such as W⁶⁺, Ti⁴⁺, Nb⁵⁺) [14]. Silicon tetrahedra SiO₄ has similar behavior observed with transition metals having either a d⁰ or d¹⁰ electronic.

No systematic study has been done for SiO₂B₂O₃Bi₂O₃TeO₂ glasses, so far, so in the present article we report the optical properties of xSiO₂ xB₂O₃ (95−2x) Bi₂O₃ 5TeO₂ where x = (5, 10, 15, 20, 25).

2 Experimental

Glasses having a composition xSiO₂ xB₂O₃ (95−2x) Bi₂O₃ 5TeO₂ where x = (5, 10, 15, 20, 25) prepared by the conventional melt-quench technique. Raw materials have employed: SiO₂ (Sherwood Medical USA, 99.99%), Bi₂O₃ (STREM Chemical, USA 99.9%), H₃BO₃ (Merck Germany, 99.8%), TeO2 (STREM Chemical, USA 99%). SiO₂, B₂O₃, Bi₂O₃, and TeO₂ weighted (10 g) in molar ratio and mixed in an agate mortar to obtain a homogeneous fine powder.

The mixture was melted in a porcelain crucible using an electric furnace at 1100 °C for half hour. Then, the melt-quenched is pouring on a copper plate and subsequently pressing it with another at room temperature. Differential thermal analysis (DTA) (Shimadzu 50) used to obtain the glass-transition temperature T_g, crystallization temperature T_c, and melting temperature T_m with a heating rate 25 °C min⁻¹ in the temperature range of 20–1000 °C, using Al₂O₃ as a reference.

Optical transmission spectra for all the studied glass samples recorded using a computerized recording spectrophotometer (type JASCO, V-570). Glass sample density determined to use the Archimedes method. Glass sample was weighed in the air and in toluene three times at room temperature (25 °C). The density determined by the equation is:

$$\rho ={\text{ }}0.8635{\text{ }}\left[ {{{{W_{\text{a}}}} \mathord{\left/ {\vphantom {{{W_{\text{a}}}} {\left( {{W_{\text{a}}} - {W_{\text{b}}}} \right)}}} \right. \kern-0pt} {\left( {{W_{\text{a}}} - {W_{\text{b}}}} \right)}}} \right]$$

where ρ is the density of the glass sample, W_a is the weight of the glass sample in air, W_b is the weight of the glass sample in toluene and 0.8635 is the density of toluene.

3 Results and discussions

3.1 Density and DTA studies

As-prepared glass samples were transparent and dark yellow color. Figure 1 shows the photographs of glass samples as prepared.

Fig. 1

Photograph of as-prepared glass samples

Figure 2 shows the scanning electron microscope (SEM) images of xSiO₂xB₂O₃ (95−2x) Bi₂O₃5TeO₂ where x = (5 and 25) glass samples and the percentages of the elements present in the studied glass samples obtained using the energy-dispersive X-ray spectra (EDS). The morphologies of these glass samples confirming the amorphous nature of the glass sample.

Fig. 2

The scanning electron microscope (SEM) images of xSiO₂xB₂O₃ (95−2x) Bi₂O₃5TeO₂ where x = (5 and 25) glass samples the percentages of the elements present in the studied glass samples obtained using the energy-dispersive X-ray spectra (EDS)

Figure 3 shows the relation between the (theoretical and experimental) density and bismuth oxide content.

Fig. 3

The relation between the theoretical and experimental density as a function of bismuth oxide content

Figure 3 demonstrates that the density increases as the increase of Bi₂O₃ content due to the Bi₂O₃ molecular weight (465.96 g/mol) greater than the B₂O₃ molecular weight (69.6182 g/mol) and SiO₂ molecular weight (60.08). In addition, the molar volume increases as the Bi₂O₃ content increase as appeared in Fig. 4.

Fig. 4

Variation of the theoretical and experimental molar volume (Vm) with Bi₂O₃ content for xB₂O₃–(95−2x) Bi₂O₃–xSiO₂–5TeO₂ glass system

This increase attributed to the atomic radii and bond length of Bi₂O₃ larger than those of B₂O₃ and SiO₂ thus caused the expansion of free volume [15]. For instance, Bi³⁺ ions act as the modifier in the network structure in the Bi₂O₃–B₂O₃ glass when Bi₂O₃ content is over 45 mol% [16] and the emerging (BiO₆) structure of a high Bi₂O₃ content play the same role in the glass. Another possible reason for the confusion is the closeness or coincides of the Si–O in the glass network with that of the Bi–O and B–O units [17, 18].

Oxygen packing density (OPD) determines the arrangement of the oxygen atoms in glass network. OPD is calculated using the relation [19,20,21].

$${\text{OPD }}={\text{ }}1000 \times {\text{O}}/{\text{Vm}}$$

where ‘O’ represents the sum of oxygen in the oxide glass component. OPD determines and is represented in Fig. 5. From Fig. 5, it observed that the oxygen packing density decrease with the Bi₂O₃ concentration increase.

Fig. 5

The relation between the OPD as a function of bismuth oxide content

But the molar volume has the opposite behavior. The OPD value decrease indicates the conversion of BO₄ to BO₃ that initiate the increase in the bridging oxygen that makes the glass more open structured.

The thermal curves obtained (DTA) for all the studied samples are displayed in Fig. 6.

Fig. 6

DTA curves for different xB₂O₃–(95−2x) Bi₂O₃–xSiO₂–5TeO₂ glass compositions

The thermal spectrum of DTA contains distinct transitions such as glass-transition temperature (T_g) which indicates a transition from a rigid to flexible structure. The second transition is crystallization temperature (T_c) observed as an exothermic peak. The third transition is melting temperature (T_m), which of course is an endothermic peak. Table 1 represents the values of T_g, T_c, and T_m for all the studied samples. It is clear that the transition temperature values [T_g, T_c, T_m] decrease with increasing the Bi₂O₃ content. Which results in the splitting of the glass network former bonds and for this reason the bridging oxygen changed into non-bridging oxygen and the glass structure becomes a weakness [22].

Table 1 Transition temperature T_g, T_c, T_m, values of glass-forming ability Kgl and the values of the average single bond strength B–O for all the studied glasses

The values of glass-transition temperature decrease caused by the increase of the Bi–O bond which is weaker than that of other glass former bond strength (Si–O and B–O) [22, 23]. Now, it is essential to calculate the average single-bond strength for all the studied glasses. The average single-bond strength B_M−O determined as follows: [24, 25],

$$B_{{{\text{M}} - {\text{O}}}} = x_{{\text{SiO}}_{\text{2}}} B_{{{\text{Si}} - {\text{O}}}} + x_{{\text{B}}_{\text{2}}} {{\text{O}}_{\text{3}}} B_{{{\text{Bi}} - {\text{O}}}} + x_{{{\text{TeO}}_{{\text{2}}} }} B_{{{\text{Te}} - {\text{O}}}}$$

where $x_{{\text{SiO}}_{\text{2}}}$is the molar fraction of SiO₂, $x_{{\text{B2O}}_{\text{3}}}$ is the molar fraction of B₂O₃, $x_{{\text{Bi}}_{\text{2O}_{\text{3}}}}$ is the molar fraction of Bi₂O₃ and $x_{{\text{TEO}}_{\text{2}}}$ is the molar fraction of TeO₂. The single-bond strength of Si–O, B–O, Bi–O and Te–O are 443, 373, 102.5 and 391 KJ/mol, respectively.

Table 1 shows the average single-bond strength for the glass samples. It is clear that the values of average single bond decrease by increasing the Bi₂O₃ content.

Hruby’s parameter [26], K_gL = (T_c − T_g)/(T_m − T_c), evaluated for studying samples. Hruby’s parameter gives information concerning the stability of glass sample against nucleation and crystal growth. At K_gL > 0.1, it suggests that the glass samples are good glass formers [26]. Table 1 clears that the glass-forming ability, K_gL, for the studied samples decrease by increasing Bi₂O₃ content and greater than 0.1.

3.2 Optical properties

Figure 7 shows the optical transmission spectrum for xB₂O₃–xSiO₂–(95−2x) Bi₂O₃ 5TeO₂ where x = (5, 10, 15, 20 and 25) glass samples. The absorption coefficient α of each sample determined to use the relation [27].

Fig. 7

The optical transmission spectra of the studied glass samples

$$\alpha =(\ln {I_o}/{I_t})/d$$

where I_o and I_t are the intensities of the incident and transmitted radiation and d is the sample thickness. Mott and Davis [28] proposed the relation between the absorption coefficient α(ω) and the photon energy ћω of the incident radiation, this relation is written as follows:

$$\alpha h\omega =~\beta {(h\omega - ~{E_{{\text{opt}}}})^n}$$

where ω is the angular frequency of radiation, β is constant (band parameter), E_opt is the optical energy gap (Tauc’s method) and n equal 2, 3, 1/2, 3/2 transition process, n = 1/2, 2 for a direct, indirect allowed transition, n = 3/2, 3 for a direct, indirect forbidden transition. Plots of αћω, (αћω)^1/2, (αћω)^3/2, (αћω)² (αћω)^1/3, against the photon energy obtained.

The optical energy gap (E_opt) value for samples containing 45 and 85 mol% Bi₂O₃ as an example definite from the meeting point between (αћω)^1/n and ћω as exposed in Fig. 8. In addition, the optical band gap ${E_{{\text{opt}}}}\left( {{\lambda _{\text{g}}}} \right)~$ (photon energy’s method) determined using the expression from the cutoff wavelength $~{\lambda _{\text{g}}}$ [29, 30].

Fig. 8

dependence of (αhv)1/n on the photon energy (hv) of the glass samples containing 45 and 85 mol% Bi₂O₃

$${E_{{\text{opt}}}}({\lambda _{\text{g}}})=~\frac{{1239.38}}{{{\lambda _{\text{g}}}}}$$

The optical band gap values ${E_{{\text{opt}}}}({\lambda _{\text{g}}})$ of present glass samples calculated using the values of the cutoff wavelength ${\lambda _{\text{g}}}$. From observing the optical band gap E_opt far from the ${E_{{\text{opt}}}}({\lambda _{\text{g}}})$ It indicates that the E_opt method does not correct for all compounds. $~{E_{{\text{opt}}}}(M)$ is determined from the absorption coefficient α or n or k, and found that the optical band gap$~{E_{{\text{opt}}}}(M)$ is closed to ${E_{{\text{opt}}}}({\lambda _{\text{g}}})$ and is more accurate.

And from the equation, $~\ln {\text{ }}(ahv)\,=\,\ln B\,+\,n\ln {\text{ }}\{ hv\, - {E_{{\text{opt}}}}(M)\}$ determined the weather of transition [31].

Table 2 is clear that the decreasing of optical band gap energy value by increasing Bi₂O₃ content. Optical band gap energy decreasing due to the bond strength of bismuth oxide is lower than silicon oxide and boron oxide bond strength besides the increasing number of non-bridging oxygen indicates the increasing number of free electrons [32]. The Urbach energy gives the width of the tails of the localized states within the optical energy gap. The dependence of the absorption coefficient in the region of lower photon energy of the absorption edge is described by the following formula [33]:

Table 2 Optical energy gap E_opt, Urbach energy U(eV), and refractive index n for all the studied glass samples

$$\alpha h\omega =\beta ~\exp (h\omega / \cup )$$

where $\cup$ is the Urbach energy. The value of the Urbach energy $\cup$ is calculated from the reciprocal of the slope of the linear portion of drawn the relation between ln α and such plots. The Urbach energy values for all the studied samples are calculated and tabulated in Table 2. The Urbach energy values for the studied glasses are found in the range from 0.2 to 0.38 eV. Mott and Davis [34] reported that, for the semiconductor amorphous materials, U values should be lying in the range from 0.045 to 0.67 eV. The refractive index, n, calculated from the value of E_opt using the formula proposed by Dimitro and Sakka [35] is as follows:

$${{\left( {{n^2} - 1} \right)} \mathord{\left/ {\vphantom {{\left( {{n^2} - 1} \right)} {\left( {{n^2}+1} \right)}}} \right. \kern-0pt} {\left( {{n^2}+1} \right)}}=1 - {\left( {{E_{{\text{opt}}}}/20} \right)^{1/2}}$$

The values of the refractive index for all the studied glass samples are calculated and tabulated in Table 2. It clears that by increasing Bi₂O₃ content, the refractive index increases slightly. This attributed to large atomic weight, coordination number of Bi₂O₃ and high polarizability of the Bi₃ + ions [36] in the glass system as well as the more ionic refraction of Bi ions present in the glass.

To understand better the effect of composition on the refractive index, the empirical relation is derived by Lorentz [37] and Lorenz [38] used to estimate the molar refraction (R_m).

$${R_{\text{m}}}=~\frac{{({n^2} - 1)}}{{({n^2}+2)}}\left( {\frac{W}{\rho }} \right)$$

where W is the average molecular weight and ρ is the density of the glass.

The theoretical optical energy gap is calculated using the relation [25]

$${E_{{\text{opt}}}}=20{\left( {1 - \left( {{R_{\text{m}}}/{V_{\text{m}}}} \right)} \right)^2}$$

Table 2 clears that the E_opt theoretical values larger than the experimental values, this is due to the amorphous nature of glass samples studied.

The metallization criterion (metallic and nonmetallic of glass nature) depend on the refractive index and band gap energy is calculated and explained [24] on predating the nature of solids. The nature of solids metallic or nonmetallic based on the condition of the ratio (molar refraction /molar volume) < 1 (insulator) and > 1 (metal), by using the following equation [25],

$$\begin{aligned} M & =1 - ({\text{molar}}\,{\text{refraction}}/{\text{molar}}\,{\text{volume}}) \\ M & ={R_{\text{m}}}/{M_{\text{v}}} \\ M & =1 - ({n^2} - 1)/({n^2}+2) \\ M & ={({E_{{\text{opt}}}}/20)^{(0.5)}} \\ \end{aligned}$$

The metallization parameter $M$ is calculated and listed in Table 3. It is clear that the metallization parameter values of the present glasses are found lesser than one and thus all the studied samples exhibit insulating behavior [25].

Table 3 Molar polarizability, molar refraction, χ³ third-order non-linear susceptibility, Ath optical basicity, α₀₂₋ ion polarizability, M_optical, M_from n metallization from optical energy gap and from refractive index, linear and nonlinear refractive index for all the studied samples

Molar refraction (${R_{\text{m}}}$) linked with the glass structure and proportional to the electronic polarizability [39] of the glass $~{\alpha _{{\text{m~}}}}$, as:

$${\alpha _{{\text{m~}}}}=~\frac{3}{{4\pi N}}~{R_{\text{m}}}$$

where N is the Avogadro number (N = 6.023 × 10²³) that relates to the number of polarizable ions per mole. The ease of deformation of electronic clouds in the structure upon application of an electromagnetic field gives a measure of the ion electronic polarizability. Multiple properties of a material are defined by the electronic polarizability, such as refraction, conductivity, optical basicity along with optical nonlinearity, electro-optical effect, and ferroelectricity.

In this system, the lone pair of electrons present in the outermost shell of Bi³⁺ induces polarization on the application of an electric field or interaction with light. This type of interaction can govern a nonlinear response in these types of glass systems. In conventional optics, a linear relationship observed between the induced polarization (P) and the applied electric field (E), as,

$$P=~{\varepsilon _o}~{x^{(1)}}~E$$

where ${x^{(1)}}$ is the linear susceptibility and ${\varepsilon _o}$ is the free-space permittivity. And in nonlinear optics describes as:

$$P=~{\varepsilon _o}[{x^{(1)}}E+~{x^{(2)}}E+{x^{(3)}}E+ \cdots ]$$

where ${x^{(2)}}$ and ${x^{(3)}}$ are known as the second- and third-order nonlinear optical susceptibilities, respectively. Since glass is an isotropic material, with inversion symmetry ${x^{(2)}}$ becomes zero. On the other hand, third-order nonlinear optical interactions (described by the ${x^{(3)}}$ susceptibility) are observed in both centrosymmetric and non-centrosymmetric mediums. Third-order susceptibility ${x^{(3)}}$ is estimated according to the equation derived by Vogel et al. [40] as:

$${x^{\left( 3 \right)}}=\frac{n}{{12\pi }}.~{n_2}=\frac{{17}}{{3\pi }}.\frac{{\left[ {\left( {n - 1} \right){{\left( {{n^2}+2} \right)}^2}} \right]}}{{v{{\left[ {1.52+\frac{{\left( {{n^2}+2} \right)\left( {n+1} \right)v}}{{6n}}} \right]}^{0.5}}}}$$

where n is glass refractive index at 587.6 nm and n2 is a nonlinear refractive index that are approximated from the empirical relation derived by Vogel et al. According to the semi-empirical equation derived by Boling’s [41], both the nonlinear refractive index (n2) and the linear refractive index (n) gives a measure of the ${x^{\left( 3 \right)}}~$ material value. The third-order nonlinear susceptibility ${x^{\left( 3 \right)}}$ estimated by this equation [42]

$${x^{\left( 3 \right)}}={\left[ {{x^{\left( 1 \right)}}} \right]^4} \times {10^{ - 10}}$$

where χ⁽¹⁾ is the linear optical susceptibility calculated in accordance with

$${x^{(1)}}=~({n^2} - 1)/4\pi$$

The values of ${x^{\left( 3 \right)}}$ for the studied glass samples are calculated and given in Table 3. From Table 3 it is clear that the high values of third-order nonlinear optical susceptibility are located in the range [(0.38–0.53) × 10⁻¹² esu], this means that all the studied samples are good applicants for nonlinear optical applications [42].

The third-order nonlinear optical susceptibility $x^{(3)}$ of materials is dependent on both the nonlinear refractive index (n2) and linear refractive index (n). The theoretical optical basicity (A_th), addresses the ability of oxide glass in contributing the negative charges in the glass matrix. In other words, it defines the electron-donating power of the oxygen in the oxide glass. The theoretical optical basicity (A) is calculated according to the approach proposed by Duffy and Ingram [43].

$${A_{{\text{th}}}}=x\left( {{\text{Si}}{{\text{O}}_2}} \right)A\left( {{\text{Si}}{{\text{O}}_2}} \right)+x\left( {{{\text{B}}_2}{{\text{O}}_3}} \right)A\left( {{{\text{B}}_2}{{\text{O}}_3}} \right)+x\left( {{\text{B}}{{\text{i}}_2}{{\text{O}}_3}} \right)A\left( {{\text{B}}{{\text{i}}_2}{{\text{O}}_3}} \right)+x\left( {{\text{Te}}{{\text{O}}_2}} \right)A\left( {{\text{Te}}{{\text{O}}_2}} \right)$$

where X(SiO₂), X(B₂O₃), X(Bi₂O₃) and X(TeO₂) are the equivalent fraction of the different oxides, i.e., the proportion of the oxide atom that contributes to the glass system; A(SiO₂), A(B₂O₃), A(Bi₂O₃) and A(TeO₂) are the optical basicity values of the constituent oxides. Here, the values of A(SiO₂) is 0.50, A(B₂O₃) is 0.425, A(Bi₂O₃) is 1.19 and A(TeO₂) is 0.93 taken from the literature [25].

Table 3 collected the theoretical optical basicity values of glass samples. It clears that with the increasing Bi₂O₃ content, the theoretical optical basicity values increase. This increase due to Bi⁺³ ions possesses a lone pair in the valence shell, and therefore, the non-bridging oxygen increase with the increase the Bi⁺³ ion concentration. The increased optical basicity of the glasses with large Bi₂O₃ content indicates that the acid–base properties of Bi₂O₃ have a significant effect. The high optical basicity means high electron donor ability of the oxide ions to the cations [22].

The relationship between electronic polarizability of oxide ions ${a_{02 - }}$ and optical basicity of oxide Ath given by this equation [25]

$${a_{02 - }}=~\frac{{1.67}}{{1.67 - {A_{{\text{th}}}}}}$$

The oxide ion electronic polarizability is determined and listed in Table 3. Table 3 clears that the oxide ion electronic polarizability increases by increasing Bi₂O₃.This means that the increasing Bi₂O₃ content caused the non-bridging oxygen increases, which makes the glasses become more polarized.

4 Conclusions

The bismuth oxide substituted by silicon and boron oxides decreases the glass-transition temperature values. The Hruby’s parameter K_gL, for all the studied samples decreases by increasing Bi₂O₃ content and is greater than 0.1. The optical band gap decreases with the increasing of Bi₂O₃ content.. The optical band gap ${E_{{\text{opt}}}}$ (Tauc’s method) far from the ${E_{{\text{opt}}}}\left( {{\lambda _g}} \right),$ (Photon energy’s method) indicates that the Tauc’s method is not correct for all compounds. The optical band gap $~~{E_{{\text{opt}}}}\left( M \right)\left[ {{\text{my}}\,{\text{method}}} \right]$ from the absorption coefficient α or n or k is closed to the optical band gap (photon energy’s method) $({\lambda _{\text{g}}})$ and is more accurate. Studied samples have higher values of third-order nonlinear optical susceptibility (3.82–5.33) × 10⁻¹³ esu which indicates that the all studied samples are good candidates for nonlinear optical applications. And the nonlinear refractive index change from (7.08 to 9.58) × 10⁻¹² for studied samples.

The increasing Bi₂O₃ content, the present glasses becomes more basic. The metallization parameter values of the present glasses are found lesser than one and thus all the studied samples exhibit insulating behavior.