# Study on the Optical Properties of High Refractive Index TeO2-PbO-ZnO-BaF2 Glass System

Authors: Shiyu Yin; Hao Wang; Aifeng Li; Haoyu Huang; Jing Zhang; Lin Liu; Yuanzhi Zhu
Journal: Advances in Materials Science and Engineering
 (2021)

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## Abstract

The tellurite 60TeO2-20PbO-(20-x)ZnO-xBaF2 (x = 1, 3, 5, 6, 7, 9, and 11) series glass samples were prepared. The samples’ SEM, XRD, DSC, density, refractive index, and absorption spectra were tested. A self-made optical platform was used to measure and calibrate the refractive index. The relationship between glass composition and crystallinity was discussed. The effects of density, molar refractive index, and metal standard value on the refractive index of glass samples were studied. The results showed that TPZBF glass has a high refractive index, and the refractive index increases with the increase in BaF2 content.


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## Body

## 1. Introduction

With the rapid development of precision optical instruments, optical information communication, optoelectronic products, and other fields, the demand for optical glass with excellent performance has increased, and the requirements are getting higher and higher. In optical design and communication, high-quality optical glass with a refractive index between 1.9 and 2.2 is significant to simplify the optical system and improve the imaging quality. It plays a vital role in the miniaturization of mobile phones, digital cameras, infrared applications, and the development of optical communication technology [1–3].Tellurite glass uses TeO2 as a leading glass-forming body. It has a higher refractive index (n > 1.8), a lower melting temperature (800–950°C), low phonon energy (600–850 cm−1), good chemical stability, and other characteristics. It is an excellent material for preparing highly refractive index optical glass [4–6].The TeO2-PbO glass system has been extensively studied. This system has a large glass-forming area, good chemical stability, and thermal properties and is suitable for further research based on this system [7, 8]. Adding the transition metal zinc oxide to the glass system can extend the transparent area of the glass in the ultraviolet region. It can improve the moisture resistance, chemical durability, and thermal stability of the glass to a certain extent and comprehensively enhance the strength of the glass so that the glass can be a stable application under complicated working conditions [9–11]. Barium is the alkaline earth metal element with the most significant atomic number, largest ionic radius, and strongest basicity. Therefore, adding barium to the tellurite glass matrix adjusts the glass’s structure and improves the glass’s refractive index, density, gloss, and chemical stability. At the same time, a small amount of BaO will also accelerate the glass’s melting and promote the glass’s clarification [12, 13]. At present, studies have shown that TeO2-PbO-ZnO system glass has excellent thermal stability, high mechanical strength, high absorption and emission cross section, broad effective fluorescence linewidth, long fluorescence lifetime, and low threshold. It is an ideal gain medium for realizing the high-energy ultrashort tunable laser [14, 15]. In addition, there are studies on adding the TeO2 to the B2O3-PbO-ZnO glass system to obtain boron tellurite glasses with high rare-earth ion doping concentrations. These glasses can be used in optical devices such as visible light lasers and fibre amplifiers. However, the composition of these glasses contains more B2O3, resulting in a lower refractive index of these glasses [9, 16]. Therefore, it is of great significance to study the factors affecting the refractive index of the TeO2-PBO-ZnO-BaF2 glass system for finding new optical materials.The purpose of this research was to study the TeO2-PbO-ZnO-BaF2 glass system by measuring its scanning electron microscopy (SEM), X-ray diffraction (XRD), differential scanning calorimetry (DSC), density, refractive index, absorption spectrum, and so on. The relationship between refractive index and glass composition is discussed.


## 2. Materials and Methods

### 2.1. Fabrication of Glass

The conventional melt quenching technique was adopted to synthesise 60TeO2-20PbO-(20-x)ZnO-xBaF2 (wherex = 1, 3, 5, 6, 7, 9, and 11 mol %) glasses, named TPZBF−1,−3, −5, −6, −7, −9, and −11, respectively. We used reagent-grade chemicals as raw materials and mixed them evenly after weighing. Each batch was melted in a pure Al2O3 ceramic crucible in the range of 850°C for 1.5 h and then cast onto the 200–250°C preheated brass mould. The obtained bulk glass was annealed and cooled to room temperature from 250°C to 300°C at a cooling rate of 1°C/min. The cooled glass was cut into glass pieces of about 20 × 10 × 1 mm, and the surfaces of 20 × 10 mm and 20 × 1 mm were optically polished.


### 2.2. Refractive Index Test of Glass

The refractive index was measured using a self-made optical platform. The structure diagram of the platform is shown in Figure1. The light source was provided by a He-Ne laser (LSR650NL-100) with a wavelength of 650 nm. The beam emitted from the laser was linearly polarised light with a diameter of about 3 mm. The beam was thicker and had low intensity; therefore, two convex optical lenses were used to focus the beam. As shown in Figure 1, the second convex lens located was twice the focal length of the first convex lens. A high-intensity parallel beam with a diameter of about 0.8 mm was obtained through the convex lens’s focusing effect. The end of the optical platform had a unique inclination angle, where it could install adjustment blocks of different angles (30°, 45°, and 60°). We used screws to fix the angle adjustment block and platform together and then inserted baffles into the groove of the platform. On the one hand, the baffle could firmly lock the angle adjustment block and the convex lens on the platform, and on the other hand, it could help locate the angle and reduce the error in the measurement.Figure 1
Schematic and actual setup for the refractive index test platform. 1: He-Ne laser, 2: baffles, 3: optical convex lens, 4: angle adjustment block, 5: height-adjustable stage, and 6: glass sample.The position of the light beam passing through the glass was recorded on a unique piece of paper. We marked the paper with the tangent, normal, and positioning lines on the stage. The paper sheet is shown in Figure2(a). The positioning lines on the paper sheet coincided with the edge of the stage. In addition, the height of the stage could be adjusted. Then, the glass was placed on the stage, the edge of the 20 × 1 mm surface of the glass was bonded to the tangent line, and the glass and the stage were glued together. After that the stage was pressed onto the angle adjustment block’s oblique side to find a convenient position for observation and recording, as shown in Figure 2(b). We beamed the light across the glass at the intersection of the tangent line and normal line on the paper sheet, fixed the stage firmly on the base, adjusted it to the appropriate height, and started the test.Figure 2
(a) Paper with positioning lines. (b) Schematic diagram of measurement. (c) Physical image of measurement. (d) Use computer aided design software to measure refraction angle.
(a)(b)(c)(d)It should be noted that after starting the test, except for the replacement of the paper sheet and angle adjustment block, other parts of the platform were not disassembled to avoid other errors.After starting the test, we could observe the light passing through the glass and refracting, as shown in Figure2(c). We marked the position where the light exited from the glass with a needle and pierced a spot as small as possible on the paper. After the test, we scanned the paper with a printer and uploaded it to the computer to accurately measure the refraction angle. We used computer aided design software to open the scanned picture, connected the incident point and the exit point, and measured the angle between the normal line and this line. This angle is the angle of refraction, as shown in Figure 2(d). We measured six data at each grade (30°, 45°, and 60°), found the average value, and put it into the following formula:(1)n=sin∝sinβ,where n is the refractive index, α is the angle of incidence, and β is the angle of refraction.In the case of incident angles of 30°, 45°, and 60°, test the samples to find the average refraction angle at each incident angle and put the average refraction angle into equation (1) to find the corresponding refraction rate. Then, take the average of the three refractive indexes measured at the incident angle of 30°, 45°, and 60°, and the average value obtained is the measured refractive index ntest obtained by the optical platform.To eliminate error, the following formula was used to correct the measured refractive indexntest:(2)ntheory=a×ntest+b,where ntheory is the theoretical refractive index and a and b are two correction coefficients. To obtain a and b, the standard optical quartz glass and an ellipsometer were used for calibration.The refractive index of the standard optical quartz glass under the irradiation of visible light with a wavelength of 650 nm was 1.4565. The self-made optical platform was used to test the standard optical quartz glass under the same conditions, taking its test and theoretical values as conditions for findinga and b. Then, the refractive index of TPBZF-1 glass was measured with an ellipsometer (J. A. Woollam Co., Inc. M2000XF), and the theoretical and measured values of TPBZF-1 glass were used as the other conditions for finding a and b. Bringing these two conditions into equation (2), getting the values of a and b, and then bringing the measured values of other glasses into equation (2) got the corresponding modified glass refractive index n.


### 2.3. Other Characterisations of the Glass

The prepared glasses were subjected to different characterisations: SEM was performed using a high-resolution environmental scanning electron microscope (FEI Quanta 650). SEM images were obtained in a high vacuum mode and with an acceleration of 500 kV. To eliminate the charging effect, the sample surface was sprayed with gold; X-ray diffraction (Ultima IV) patterns were determined at room temperature with a diffraction angle of 2θ = 10°–100° and at a rate of 0.02°/min; glass transition temperature and crystallisation temperature were determined by DSC (NETZSCH STA 449F3). A 10 mg sample was heated in Al2O3 crucible at a heating rate of 30°C/min in N2 gas atmosphere; the density was measured according to the Archimedes principle using pure water (ρ = 0.99980 g/cm3, 16°C) as immersion liquid at room temperature; the absorption spectra were measured in the wavelength range of 190 nm to 900 nm using a UV-VIS spectrophotometer (PerkinElmer Lambda 650) with optically polished samples of approximately 5 mm thickness.


## 2.1. Fabrication of Glass

The conventional melt quenching technique was adopted to synthesise 60TeO2-20PbO-(20-x)ZnO-xBaF2 (wherex = 1, 3, 5, 6, 7, 9, and 11 mol %) glasses, named TPZBF−1,−3, −5, −6, −7, −9, and −11, respectively. We used reagent-grade chemicals as raw materials and mixed them evenly after weighing. Each batch was melted in a pure Al2O3 ceramic crucible in the range of 850°C for 1.5 h and then cast onto the 200–250°C preheated brass mould. The obtained bulk glass was annealed and cooled to room temperature from 250°C to 300°C at a cooling rate of 1°C/min. The cooled glass was cut into glass pieces of about 20 × 10 × 1 mm, and the surfaces of 20 × 10 mm and 20 × 1 mm were optically polished.


## 2.2. Refractive Index Test of Glass

The refractive index was measured using a self-made optical platform. The structure diagram of the platform is shown in Figure1. The light source was provided by a He-Ne laser (LSR650NL-100) with a wavelength of 650 nm. The beam emitted from the laser was linearly polarised light with a diameter of about 3 mm. The beam was thicker and had low intensity; therefore, two convex optical lenses were used to focus the beam. As shown in Figure 1, the second convex lens located was twice the focal length of the first convex lens. A high-intensity parallel beam with a diameter of about 0.8 mm was obtained through the convex lens’s focusing effect. The end of the optical platform had a unique inclination angle, where it could install adjustment blocks of different angles (30°, 45°, and 60°). We used screws to fix the angle adjustment block and platform together and then inserted baffles into the groove of the platform. On the one hand, the baffle could firmly lock the angle adjustment block and the convex lens on the platform, and on the other hand, it could help locate the angle and reduce the error in the measurement.Figure 1
Schematic and actual setup for the refractive index test platform. 1: He-Ne laser, 2: baffles, 3: optical convex lens, 4: angle adjustment block, 5: height-adjustable stage, and 6: glass sample.The position of the light beam passing through the glass was recorded on a unique piece of paper. We marked the paper with the tangent, normal, and positioning lines on the stage. The paper sheet is shown in Figure2(a). The positioning lines on the paper sheet coincided with the edge of the stage. In addition, the height of the stage could be adjusted. Then, the glass was placed on the stage, the edge of the 20 × 1 mm surface of the glass was bonded to the tangent line, and the glass and the stage were glued together. After that the stage was pressed onto the angle adjustment block’s oblique side to find a convenient position for observation and recording, as shown in Figure 2(b). We beamed the light across the glass at the intersection of the tangent line and normal line on the paper sheet, fixed the stage firmly on the base, adjusted it to the appropriate height, and started the test.Figure 2
(a) Paper with positioning lines. (b) Schematic diagram of measurement. (c) Physical image of measurement. (d) Use computer aided design software to measure refraction angle.
(a)(b)(c)(d)It should be noted that after starting the test, except for the replacement of the paper sheet and angle adjustment block, other parts of the platform were not disassembled to avoid other errors.After starting the test, we could observe the light passing through the glass and refracting, as shown in Figure2(c). We marked the position where the light exited from the glass with a needle and pierced a spot as small as possible on the paper. After the test, we scanned the paper with a printer and uploaded it to the computer to accurately measure the refraction angle. We used computer aided design software to open the scanned picture, connected the incident point and the exit point, and measured the angle between the normal line and this line. This angle is the angle of refraction, as shown in Figure 2(d). We measured six data at each grade (30°, 45°, and 60°), found the average value, and put it into the following formula:(1)n=sin∝sinβ,where n is the refractive index, α is the angle of incidence, and β is the angle of refraction.In the case of incident angles of 30°, 45°, and 60°, test the samples to find the average refraction angle at each incident angle and put the average refraction angle into equation (1) to find the corresponding refraction rate. Then, take the average of the three refractive indexes measured at the incident angle of 30°, 45°, and 60°, and the average value obtained is the measured refractive index ntest obtained by the optical platform.To eliminate error, the following formula was used to correct the measured refractive indexntest:(2)ntheory=a×ntest+b,where ntheory is the theoretical refractive index and a and b are two correction coefficients. To obtain a and b, the standard optical quartz glass and an ellipsometer were used for calibration.The refractive index of the standard optical quartz glass under the irradiation of visible light with a wavelength of 650 nm was 1.4565. The self-made optical platform was used to test the standard optical quartz glass under the same conditions, taking its test and theoretical values as conditions for findinga and b. Then, the refractive index of TPBZF-1 glass was measured with an ellipsometer (J. A. Woollam Co., Inc. M2000XF), and the theoretical and measured values of TPBZF-1 glass were used as the other conditions for finding a and b. Bringing these two conditions into equation (2), getting the values of a and b, and then bringing the measured values of other glasses into equation (2) got the corresponding modified glass refractive index n.


## 2.3. Other Characterisations of the Glass

The prepared glasses were subjected to different characterisations: SEM was performed using a high-resolution environmental scanning electron microscope (FEI Quanta 650). SEM images were obtained in a high vacuum mode and with an acceleration of 500 kV. To eliminate the charging effect, the sample surface was sprayed with gold; X-ray diffraction (Ultima IV) patterns were determined at room temperature with a diffraction angle of 2θ = 10°–100° and at a rate of 0.02°/min; glass transition temperature and crystallisation temperature were determined by DSC (NETZSCH STA 449F3). A 10 mg sample was heated in Al2O3 crucible at a heating rate of 30°C/min in N2 gas atmosphere; the density was measured according to the Archimedes principle using pure water (ρ = 0.99980 g/cm3, 16°C) as immersion liquid at room temperature; the absorption spectra were measured in the wavelength range of 190 nm to 900 nm using a UV-VIS spectrophotometer (PerkinElmer Lambda 650) with optically polished samples of approximately 5 mm thickness.


## 3. Results and Discussion

### 3.1. Scanning Electron Microscope (SEM)

The fabricated TPZBF1-7 glass was clear, bright, and light green glass. TPZBF-9 glass was also relatively clear but had obvious crystallisation points. TPZBF-11 glass was completely crystallised and could not transmit light.SEM images for the TPZBF-7 glasses are presented in Figure3(a). These images show a glassy surface with no crystal precipitate since only the common constituents were present. TPZBF1-7 sample profiles were found to be similar. The TPZBF-9 sample had obvious crystallisation points on the surface; the SEM image of the crystallisation point position is shown in Figure 3(b).Figure 3
SEM micrographs of TPZBF7 (a) and TPZBF9 (b).
(a)(b)


### 3.2. X-Ray Diffraction (XRD)

The XRD diffraction pattern of TPZBF glass is shown in Figure4. It can be seen from Figure 4 that when x = 0 and 7, the X-ray pattern of the glass powder is basically the same. They have a wide diffraction peak near 2θ = 30° and 2θ = 50°, respectively, in the diffraction pattern. There is no very sharp diffraction peak, which is a very typical diffraction pattern of an amorphous substance. These show that when the mole percentage of BaF2 is between 1% and 7% (corresponding to the mole percentage of ZnO between 19% and 13%), the product obtained after the smelting of the TPZBF glass system is a stable glass structure without precipitation of crystalline phases [17].Figure 4
X-ray diffraction pattern of samples TPZBF-1, TPZBF-7, and TPZBF-9.In the glass melting process, a part of BaF2 combines with O2 in the environment and is transformed into BaO that enters the glass network as a modifier and F2 that escapes to the atmosphere; the other part of BaF2 breaks the MO bond (M = Te, Pb, Zn) and enters the glass network to form an oxyfluoride glass structure. Hence, the crystallisation tendency of the glass increases sharply and crystalline phases begin to appear. When the mole percentage of BaF2 reaches 11%, the glass is completely crystallised. The crystalline phases observed in the TPZBF-9 sample were identified as PbF2 and Ba2ZnF6. We found that a chemical reaction occurs in the melt that forms the glass, the content of which is as follows:(3)PbO+ZnO+BaF2⟶PbF2+Ba2ZnF6+O2↑.The addition of excess F element replaces the O element in the glass network structure, leading to these PbF2 and Ba2ZnF6 crystalline phases. In Figure 4, the phase peaks of the PbF2 crystal are located at 2θ = 28.9°, 42.7°, 47.0°, and 48.2°, respectively, while the phase peaks of the Ba2ZnF6 crystal are located at 2θ = 39.2°.


### 3.3. Differential Scanning Calorimetry (DSC)

Figure5 is the DSC spectrum of TPZBF-7 glass. From the figure, the glass transition temperature Tg, the onset of crystallisation temperature Tc, and the difference ΔT of the glass can be estimated. The values of Tg, Tc, and ΔT are 266, 325, and 59°C, respectively.Figure 5
Differential scanning calorimetry of sample TPZBF-7.The ΔT value can be used to evaluate the thermal stability of the glass. The larger the ΔT, the wider the operable range without devitrification during glass melting and the better the thermal stability. The ΔT value of the TPZBF-7 sample is 59°C, which is a small value in tellurite glass. It can also be seen from Figure 5 that the first crystallisation peak of the glass is next to the glass transition temperature peak, so the series of glasses are relatively easy to crystallize [18–20].


### 3.4. Density

The composition and density of the glass are shown in Table1. As the TPZBF-11 component glass was devitrified, the properties of TPZBF-11 are not studied below. It can be seen from Table 1 that as BaF2 gradually replaced ZnO, the density of the glass gradually increased from 6.243 g/cm3 to 6.327 g/cm3.Table 1
Compositions and density of glass sample.
SampleMole fraction (%)Densityd (g·cm−3)TeO2PbOZnOBaF2TPZBF160201916.243TPZBF360201736.267TPZBF560201556.295TPZBF660201466.306TPZBF760201376.313TPZBF960201196.327The density of the glass depends not only on the mass of the atoms constituting the glass but also on the tightness of the atomic packing and the coordination number. The following two aspects mainly determine the gradual increase in density of TPZBF series glass. On the one hand, the relative atomic mass of Ba is 137.32, while the relative atomic mass of Zn is 65.38, which is much lower than Ba. On the other hand, according to the classification of oxides in the glass network, BaO and ZnO belong to modified bodies and intermediates, respectively. As a modified body, BaO can enter the structural gaps of the glass network, making the structure of the glass more compact, thereby increasing the density. Since the polarisability of Zn2+ ions is lower than that of Ba2+ and Pb2+ ions, ZnO tends to play the role of network structure in the glass network (for example, in the TeO2-ZnF2-ZnO glass system, Zn2+ participates in the formation of the glass network in the form of zinc oxide tetrahedrons [21]). The decrease in ZnO weakens the construction of the glass network, which reduces the molecular volume and increases the glass density. Therefore, under the combined effect of the above two reasons, when BaF2 replaces ZnO, the density of the glass increases significantly.In addition, although the density of the glass increases, the increase is not apparent. This is because the glass composition contains 20% PbO (molar ratio). PbO is also a glass network modification body, and the molecular weight of Pb is greater than that of Ba, so the addition of BaF2 can only slightly increase the density of the glass.


### 3.5. Refractive Index and Factors Affecting the Refractive Index

The refractive indexntheory of TPZBF-1 glass and standard optical quartz glass was measured with an ellipsometer. The test refractive index ntest of TPZBF1-9 glass was measured with a self-made optical platform. The ntheory and ntest of the two were brought into equation (2) and calculated as a and b:(4)a=ntheory⋅Quartz−ntheory⋅TPZBF−1ntest⋅Quartz−ntest⋅TPZBF−1,b=ntheory⋅TPZBF−1−a×ntest⋅TPZBF−1.The value ofa is 0.9821, and the value of b is 0.0246. The ntest of TPZBF1-9 glass was then brought into equation (2) to obtain the correct refractive index n of each component glass. The results are shown in Table 2.(5)nTPZBF−i=a×ntest⋅TPZBF−1+b.Table 2
ntheory, ntest, and n of each component glass, at 650 nm.
ntheoryntestNError (%)Quartz glass1.45651.45531.45650.0824TPZBF12.01061.99952.01060.5521TPZBF32.04372.0320TPZBF52.06442.0523TPZBF62.08142.0690TPZBF72.08912.0766TPZBF92.11022.0973TPZBF11CrystallizationThe self-made optical platform had a refractive index error of 0.0824% for the standard optical quartz glass and 0.5521% for glass with a composition of TPZBF-1. The values of these two errors were below 1%. Therefore, the measurement result is relatively accurate.The refractive index and other physical properties of the glass are shown in Table3.Table 3
Physical parameters of TPZBF glasses.
SampleMolar massM (g·mol−1)Molar volumeVm (cm3·mol−1)Molar refractionRm (cm3·mol−1)Rm/VmRefractive indexnTPZBF1157.615025.246715.23310.60332.0106TPZBF3159.494225.459915.52610.61002.0320TPZBF5161.373425.635115.79840.61622.0523TPZBF6162.313025.739515.99140.62122.0690TPZBF7163.252625.859816.12390.62352.0766TPZBF9165.131826.099516.43090.62952.0973It can be seen from Table3 that as BaF2 replaced ZnO, the refractive index of the glass increased. The refractive index of glass depends on the density of the glass and the polarisability of internal ions.H. N. Ritland’s research shows that the refractive index of glass is a single-valued function of the density [22]. Generally, the greater the density of the glass, the denser the glass network and the more compact the structure and the slower the propagation of light in the glass, so the refractive index increases accordingly. Conversely, the lower the density, the smaller the refractive index. The density and refractive index of TPZBF series glass also conform to this rule.According to Maxwell’s electromagnetic field theory, the propagation speed of light in a medium should be(6)v=1εμ=1ε0μ0×1εrμr=cεrμr=cn.The expression ofn is inferred from the following:(7)n=εrμr,where c is the speed of light in a vacuum, μ is the magnetic permeability of the medium, ε is the dielectric constant of the medium, μ0 is the magnetic permeability in a vacuum, ε0 is the dielectric constant in a vacuum, μr is the relative permeability of the medium, and εr is the relative dielectric of the medium electric constant. In dielectrics such as inorganic materials, μr ≈ 1, so n ≈ εr1/2.This shows that the refractive index of the medium increases with the increase in its dielectric constant. The dielectric constant is related to the polarisation of the medium. The higher the polarisation of the medium, the greater the refractive index.When light passes through the glass, it causes the polarisation of the ions inside the glass. The polarisation of the ions, in turn, affects the propagation speed of the light wave in the glass. The greater the polarisability, the greater the energy absorbed after the light wave passes, the more significant the reduction in propagation speed, and the greater the refractive index.The polarisation process is divided into passive polarisation and active polarisation [23]. Passive polarisation means that an ion is polarised under an external electric field generated by other ions. The polarisation rate α expresses its magnitude. Active polarisation means that an ion uses its electric field to act on surrounding ions to polarise other ions. Generally, the anion (O2-, F−) has a large radius and is easy to deform and polarise but the active polarisation ability is low. The cation radius (Te4+, Pb2+, Ba2+, and Zn2+) is relatively small, and when the electricity price is high, its active polarisation effect is large but the polarisation degree is low. The radius and polarisability of the ions contained in the TPZBF series glass are shown in Table 4.Table 4
Ion radius and polarisability [23].
IonTe4+Pb2+Ba2+Zn2+O2-F-Ion radius/nm0.0560.1200.1350.0740.1400.136Polarizability/×10−3 nm30.7502.0001.5500.2883.8801.040The polarisability of Ba2+ ions is much higher than that of Zn2+ ions, so as BaF2 replaces ZnO, the refractive index of the glass increases.It can be seen from Table4 that the ionic radius of Ba2+ ions was also larger than that of Zn2+ ions. When the radius of cations with the same atomic valence increased (Ba2+⟶Zn2+), the molar volume and molar refraction of the glass increased at the same time, and the increase in the molar volume reduced the refraction of the glass. The increase in the molar refraction increased the refractive index of the glass, so there was no linear relationship between the refractive index of the glass and the ionic radius. However, it can be demonstrated from other angles that the large ion radius of Ba2+ ions can provide glass with a higher refractive index.The molar volumeRm of the glass can be calculated using the following formula [24]:(8)Rm=n2−1n2+1Md,where M is the molar mass of the glass, d is the density, and n is the refractive index of the glass.The refractive index of glass can be regarded as the sum of its linear and nonlinear refractive indexes, as shown in the following formula [25]:(9)n=n0+n0E2,where n0 is the linear refractive index, n2 is the nonlinear refractive index, and E is the field strength of the beam. This means that the higher the nonlinear refractive index n2, the higher the refractive index n of the glass.According to the research conclusion of Nasu [26], the nonlinear refractive index n2 of glass is directly proportional to the ratio of molar refractive index to molar volume (Rm/Vm). The molar volume Vm, molar refractive index Rm, and their ratio of the glass are shown in Table 3. As the content of BaF2 increased, the value of Rm/Vm of the glass increased from 0.6033 to 0.6295. Therefore, the replacement of ZnO by BaF2 increased the refractive index of the glass.


### 3.6. Absorption Spectrum

Figure6 shows the absorption spectra of the TPZBF glasses. It can be seen from the figure that as BaF2 gradually replaced ZnO, the absorption boundary of the glass in the ultraviolet region gradually shifted to the long-wavelength direction. This phenomenon is mainly because the polarisability of Ba2+ ions is higher than that of Zn2+, which leads to stronger absorption of ultraviolet light by the glass, which shifts the absorption boundary to the long-wavelength direction.Figure 6
Optical absorbance spectra of TPZNF glasses in the 300–900 nm range (a) and in the 500–700 nm range (b).
(a)(b)The TPZBF-9 sample underwent a certain degree of crystallisation, so its transmittance was also affected accordingly and was significantly lower than that of other glasses in the system.The small picture on the upper righthand corner of Figure6 is a partial picture of the 500–700 nm segment. It can be seen from the picture that as BaF2 gradually replaced ZnO, the absorption strength of the glass decreased. This is because the following formula exists in the transparent area of the glass [27]:(10)OD=lgn2+12n,where OD is the optical density and n is the refractive index of glass. If OD is regarded as a function of n, when n > 1, OD monotonically decreases, that is to say, the higher the refractive index, the lower the absorption intensity. The absorption intensity of TPZBF series glass in this area decreases with the increase of BaF2 content. This phenomenon is consistent with the change rule of refractive index.


## 3.1. Scanning Electron Microscope (SEM)

The fabricated TPZBF1-7 glass was clear, bright, and light green glass. TPZBF-9 glass was also relatively clear but had obvious crystallisation points. TPZBF-11 glass was completely crystallised and could not transmit light.SEM images for the TPZBF-7 glasses are presented in Figure3(a). These images show a glassy surface with no crystal precipitate since only the common constituents were present. TPZBF1-7 sample profiles were found to be similar. The TPZBF-9 sample had obvious crystallisation points on the surface; the SEM image of the crystallisation point position is shown in Figure 3(b).Figure 3
SEM micrographs of TPZBF7 (a) and TPZBF9 (b).
(a)(b)


## 3.2. X-Ray Diffraction (XRD)

The XRD diffraction pattern of TPZBF glass is shown in Figure4. It can be seen from Figure 4 that when x = 0 and 7, the X-ray pattern of the glass powder is basically the same. They have a wide diffraction peak near 2θ = 30° and 2θ = 50°, respectively, in the diffraction pattern. There is no very sharp diffraction peak, which is a very typical diffraction pattern of an amorphous substance. These show that when the mole percentage of BaF2 is between 1% and 7% (corresponding to the mole percentage of ZnO between 19% and 13%), the product obtained after the smelting of the TPZBF glass system is a stable glass structure without precipitation of crystalline phases [17].Figure 4
X-ray diffraction pattern of samples TPZBF-1, TPZBF-7, and TPZBF-9.In the glass melting process, a part of BaF2 combines with O2 in the environment and is transformed into BaO that enters the glass network as a modifier and F2 that escapes to the atmosphere; the other part of BaF2 breaks the MO bond (M = Te, Pb, Zn) and enters the glass network to form an oxyfluoride glass structure. Hence, the crystallisation tendency of the glass increases sharply and crystalline phases begin to appear. When the mole percentage of BaF2 reaches 11%, the glass is completely crystallised. The crystalline phases observed in the TPZBF-9 sample were identified as PbF2 and Ba2ZnF6. We found that a chemical reaction occurs in the melt that forms the glass, the content of which is as follows:(3)PbO+ZnO+BaF2⟶PbF2+Ba2ZnF6+O2↑.The addition of excess F element replaces the O element in the glass network structure, leading to these PbF2 and Ba2ZnF6 crystalline phases. In Figure 4, the phase peaks of the PbF2 crystal are located at 2θ = 28.9°, 42.7°, 47.0°, and 48.2°, respectively, while the phase peaks of the Ba2ZnF6 crystal are located at 2θ = 39.2°.


## 3.3. Differential Scanning Calorimetry (DSC)

Figure5 is the DSC spectrum of TPZBF-7 glass. From the figure, the glass transition temperature Tg, the onset of crystallisation temperature Tc, and the difference ΔT of the glass can be estimated. The values of Tg, Tc, and ΔT are 266, 325, and 59°C, respectively.Figure 5
Differential scanning calorimetry of sample TPZBF-7.The ΔT value can be used to evaluate the thermal stability of the glass. The larger the ΔT, the wider the operable range without devitrification during glass melting and the better the thermal stability. The ΔT value of the TPZBF-7 sample is 59°C, which is a small value in tellurite glass. It can also be seen from Figure 5 that the first crystallisation peak of the glass is next to the glass transition temperature peak, so the series of glasses are relatively easy to crystallize [18–20].


## 3.4. Density

The composition and density of the glass are shown in Table1. As the TPZBF-11 component glass was devitrified, the properties of TPZBF-11 are not studied below. It can be seen from Table 1 that as BaF2 gradually replaced ZnO, the density of the glass gradually increased from 6.243 g/cm3 to 6.327 g/cm3.Table 1
Compositions and density of glass sample.
SampleMole fraction (%)Densityd (g·cm−3)TeO2PbOZnOBaF2TPZBF160201916.243TPZBF360201736.267TPZBF560201556.295TPZBF660201466.306TPZBF760201376.313TPZBF960201196.327The density of the glass depends not only on the mass of the atoms constituting the glass but also on the tightness of the atomic packing and the coordination number. The following two aspects mainly determine the gradual increase in density of TPZBF series glass. On the one hand, the relative atomic mass of Ba is 137.32, while the relative atomic mass of Zn is 65.38, which is much lower than Ba. On the other hand, according to the classification of oxides in the glass network, BaO and ZnO belong to modified bodies and intermediates, respectively. As a modified body, BaO can enter the structural gaps of the glass network, making the structure of the glass more compact, thereby increasing the density. Since the polarisability of Zn2+ ions is lower than that of Ba2+ and Pb2+ ions, ZnO tends to play the role of network structure in the glass network (for example, in the TeO2-ZnF2-ZnO glass system, Zn2+ participates in the formation of the glass network in the form of zinc oxide tetrahedrons [21]). The decrease in ZnO weakens the construction of the glass network, which reduces the molecular volume and increases the glass density. Therefore, under the combined effect of the above two reasons, when BaF2 replaces ZnO, the density of the glass increases significantly.In addition, although the density of the glass increases, the increase is not apparent. This is because the glass composition contains 20% PbO (molar ratio). PbO is also a glass network modification body, and the molecular weight of Pb is greater than that of Ba, so the addition of BaF2 can only slightly increase the density of the glass.


## 3.5. Refractive Index and Factors Affecting the Refractive Index

The refractive indexntheory of TPZBF-1 glass and standard optical quartz glass was measured with an ellipsometer. The test refractive index ntest of TPZBF1-9 glass was measured with a self-made optical platform. The ntheory and ntest of the two were brought into equation (2) and calculated as a and b:(4)a=ntheory⋅Quartz−ntheory⋅TPZBF−1ntest⋅Quartz−ntest⋅TPZBF−1,b=ntheory⋅TPZBF−1−a×ntest⋅TPZBF−1.The value ofa is 0.9821, and the value of b is 0.0246. The ntest of TPZBF1-9 glass was then brought into equation (2) to obtain the correct refractive index n of each component glass. The results are shown in Table 2.(5)nTPZBF−i=a×ntest⋅TPZBF−1+b.Table 2
ntheory, ntest, and n of each component glass, at 650 nm.
ntheoryntestNError (%)Quartz glass1.45651.45531.45650.0824TPZBF12.01061.99952.01060.5521TPZBF32.04372.0320TPZBF52.06442.0523TPZBF62.08142.0690TPZBF72.08912.0766TPZBF92.11022.0973TPZBF11CrystallizationThe self-made optical platform had a refractive index error of 0.0824% for the standard optical quartz glass and 0.5521% for glass with a composition of TPZBF-1. The values of these two errors were below 1%. Therefore, the measurement result is relatively accurate.The refractive index and other physical properties of the glass are shown in Table3.Table 3
Physical parameters of TPZBF glasses.
SampleMolar massM (g·mol−1)Molar volumeVm (cm3·mol−1)Molar refractionRm (cm3·mol−1)Rm/VmRefractive indexnTPZBF1157.615025.246715.23310.60332.0106TPZBF3159.494225.459915.52610.61002.0320TPZBF5161.373425.635115.79840.61622.0523TPZBF6162.313025.739515.99140.62122.0690TPZBF7163.252625.859816.12390.62352.0766TPZBF9165.131826.099516.43090.62952.0973It can be seen from Table3 that as BaF2 replaced ZnO, the refractive index of the glass increased. The refractive index of glass depends on the density of the glass and the polarisability of internal ions.H. N. Ritland’s research shows that the refractive index of glass is a single-valued function of the density [22]. Generally, the greater the density of the glass, the denser the glass network and the more compact the structure and the slower the propagation of light in the glass, so the refractive index increases accordingly. Conversely, the lower the density, the smaller the refractive index. The density and refractive index of TPZBF series glass also conform to this rule.According to Maxwell’s electromagnetic field theory, the propagation speed of light in a medium should be(6)v=1εμ=1ε0μ0×1εrμr=cεrμr=cn.The expression ofn is inferred from the following:(7)n=εrμr,where c is the speed of light in a vacuum, μ is the magnetic permeability of the medium, ε is the dielectric constant of the medium, μ0 is the magnetic permeability in a vacuum, ε0 is the dielectric constant in a vacuum, μr is the relative permeability of the medium, and εr is the relative dielectric of the medium electric constant. In dielectrics such as inorganic materials, μr ≈ 1, so n ≈ εr1/2.This shows that the refractive index of the medium increases with the increase in its dielectric constant. The dielectric constant is related to the polarisation of the medium. The higher the polarisation of the medium, the greater the refractive index.When light passes through the glass, it causes the polarisation of the ions inside the glass. The polarisation of the ions, in turn, affects the propagation speed of the light wave in the glass. The greater the polarisability, the greater the energy absorbed after the light wave passes, the more significant the reduction in propagation speed, and the greater the refractive index.The polarisation process is divided into passive polarisation and active polarisation [23]. Passive polarisation means that an ion is polarised under an external electric field generated by other ions. The polarisation rate α expresses its magnitude. Active polarisation means that an ion uses its electric field to act on surrounding ions to polarise other ions. Generally, the anion (O2-, F−) has a large radius and is easy to deform and polarise but the active polarisation ability is low. The cation radius (Te4+, Pb2+, Ba2+, and Zn2+) is relatively small, and when the electricity price is high, its active polarisation effect is large but the polarisation degree is low. The radius and polarisability of the ions contained in the TPZBF series glass are shown in Table 4.Table 4
Ion radius and polarisability [23].
IonTe4+Pb2+Ba2+Zn2+O2-F-Ion radius/nm0.0560.1200.1350.0740.1400.136Polarizability/×10−3 nm30.7502.0001.5500.2883.8801.040The polarisability of Ba2+ ions is much higher than that of Zn2+ ions, so as BaF2 replaces ZnO, the refractive index of the glass increases.It can be seen from Table4 that the ionic radius of Ba2+ ions was also larger than that of Zn2+ ions. When the radius of cations with the same atomic valence increased (Ba2+⟶Zn2+), the molar volume and molar refraction of the glass increased at the same time, and the increase in the molar volume reduced the refraction of the glass. The increase in the molar refraction increased the refractive index of the glass, so there was no linear relationship between the refractive index of the glass and the ionic radius. However, it can be demonstrated from other angles that the large ion radius of Ba2+ ions can provide glass with a higher refractive index.The molar volumeRm of the glass can be calculated using the following formula [24]:(8)Rm=n2−1n2+1Md,where M is the molar mass of the glass, d is the density, and n is the refractive index of the glass.The refractive index of glass can be regarded as the sum of its linear and nonlinear refractive indexes, as shown in the following formula [25]:(9)n=n0+n0E2,where n0 is the linear refractive index, n2 is the nonlinear refractive index, and E is the field strength of the beam. This means that the higher the nonlinear refractive index n2, the higher the refractive index n of the glass.According to the research conclusion of Nasu [26], the nonlinear refractive index n2 of glass is directly proportional to the ratio of molar refractive index to molar volume (Rm/Vm). The molar volume Vm, molar refractive index Rm, and their ratio of the glass are shown in Table 3. As the content of BaF2 increased, the value of Rm/Vm of the glass increased from 0.6033 to 0.6295. Therefore, the replacement of ZnO by BaF2 increased the refractive index of the glass.


## 3.6. Absorption Spectrum

Figure6 shows the absorption spectra of the TPZBF glasses. It can be seen from the figure that as BaF2 gradually replaced ZnO, the absorption boundary of the glass in the ultraviolet region gradually shifted to the long-wavelength direction. This phenomenon is mainly because the polarisability of Ba2+ ions is higher than that of Zn2+, which leads to stronger absorption of ultraviolet light by the glass, which shifts the absorption boundary to the long-wavelength direction.Figure 6
Optical absorbance spectra of TPZNF glasses in the 300–900 nm range (a) and in the 500–700 nm range (b).
(a)(b)The TPZBF-9 sample underwent a certain degree of crystallisation, so its transmittance was also affected accordingly and was significantly lower than that of other glasses in the system.The small picture on the upper righthand corner of Figure6 is a partial picture of the 500–700 nm segment. It can be seen from the picture that as BaF2 gradually replaced ZnO, the absorption strength of the glass decreased. This is because the following formula exists in the transparent area of the glass [27]:(10)OD=lgn2+12n,where OD is the optical density and n is the refractive index of glass. If OD is regarded as a function of n, when n > 1, OD monotonically decreases, that is to say, the higher the refractive index, the lower the absorption intensity. The absorption intensity of TPZBF series glass in this area decreases with the increase of BaF2 content. This phenomenon is consistent with the change rule of refractive index.


## 4. Conclusions

60TeO2-20PbO-(20-x)ZnO-xBaF2 tellurite series glass was prepared, and SEM, XRD, DSC, density, refractive index, and absorption spectrum tests were carried out. A refractive index test platform for bulk solids was established, and the error was found to be within 1% after testing with standard optical quartz glass and TPZBF series glass.Through the test and calculation of the prepared TPZBF series glass, the following regular was found. As the BaF2 in the glass composition replaces ZnO, the density and refractive index of the glass gradually increase. The absorption edge in the absorption spectrum shifts to the long-wavelength direction, and the ultraviolet absorption increases. When the molar ratio of the BaF2 component exceeds 9%, the glass begins to show a more obvious tendency to crystallize and the transmittance is significantly reduced.



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*Source: 6466344-2021-09-21.xml*